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Michigan State
University

This is to certify that the
dissertation entitled

A THEORETICAL, EXPERIMENTAL AND CFD
ANALYSIS OF REGENERATIVE FLOW
COMPRESSORS AND PUMPS FOR MICROTURBINE
AND AUTOMOTIVE FUEL APPLICATIONS

presented by

Muhammad Mukarram Raheel

has been accepted towards fulfillment
of the requirements for the

Ph.D. Mechanical Engineering

 

 

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6/01 cJCIRC/DateDuepGS—p. 15

 

A THEORETICAL, EXPERIMENTAL AND CFD ANALYSIS OF
REGENERATIVE FLOW COMPRESSORS AND PUMPS FOR
MICROTURBINE AND AUTOMOTIVE FUEL APPLICATIONS

By

Muhammad Mukarram Raheel

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Mechanical Engineering

2003

ABSTRACT

A THEORETICAL, EXPERIMENTAL AND CFD ANALYSIS OF REGENERATIVE
FLOW COMPRESSORS AND PUMPS FOR MICROTURBINE AND AUTOMOTIVE
FUEL APPLICATIONS
By
Muhammad Mukarram Raheel
Regenerative ﬂow compressors and pumps, hereafter known as RFC/RFP are
rotodynarnic machines capable of producing high heads at very low ﬂow rates. They can
produce heads equivalent to that of several centrifugal stages from a single rotor with
comparable tip speed. The compression process is usually not regarded as efﬁcient.
Typically regenerative compressors produce less than 50 % efﬁciency but still they have
found many applications, because they allow the use of ﬂuid dynamic compressors in
place of positive displacement compressors for duties requiring high heads at low flow
rates. Recently Capstone Turbine Corporation has made use of RFC in low pressure (0.2-
15 psig) natural gas compression required by its Model C30 microturbine system.
Moreover, due to compact size and self priming characteristics of the regenerative pumps,

Delphi Automotives has utilized RFP for automotive fuel pumping application.

A detailed discussion of fundamentals, hypothesis of operation, applications, limitations,
challenges and future trends in regenerative turbomachines is presented. Experimental
data on Capstone single and multistage RFC with radial blades is analyzed in the form of
various non-dimensional parameters. A mathematical model to describe the complex
three dimensional corkscrew ﬂow pattern in radial and non-radial blade RFC/RFP is

presented. Governing equations for blade and channel region are developed and various

losses are correlated with geometric and aerodynamic parameters. A performance

prediction code for RFC based on these governing equations and loss models is
developed and performance results are compared with test data on Capstone multistage
RFC. An extensive sensitivity analysis from the code is performed, based on which some
design changes are suggested for performance improvement. Moreover, a generalized
design procedure for radial and non-radial blade RFC is proposed in this work.

Application of regenerative turbomachines in automotive fuel pumping is discussed in
detail. Delphi Automotives replaced radial blades by non-radial blades to improve
performance. Performance of Delphi fuel pump is predicted from the code and compared
with test data and some design improvements are suggested after performing a sensitivity
analysis on various geometric parameters. Details of CFD analysis on a 3D model of the
fuel pump using commercial software “STAR CD” are presented. The regenerative pump
with non-radial blades produces hydraulic efﬁciencies around 40% surpassing all the
existing regenerative fuel pump designs in the automotive industry. However, there is
still a lot of room for improvement in hydraulic efficiency by employing aerodynamically
designed aerofoil blades. Therefore, need was felt to investigate RFC/RFP with aerofoil
blades. A compressible flow theory for aerofoil blade RFC is presented in this work.
Theoretical performance results are compared with published test data on aerofoil blade
RFC. Extensive sensitivity analysis from the code is performed and design changes are
suggested for performance improvement. Theoretical analysis shows that aerofoil blading
introduced in these turbomachines can enhance isothermal efﬁciency above 60%. Based
on suggested design changes, a new RFC model with aerofoil blades is developed and a
CFD analysis is performed. Currently work is in progress to optimize the inlet manifold

of aerofoil blade RFC.

To my parents’ innumerable sacrifices and untiring support throughout my life

iv

ACKNOWLEDGEMENT

The author is extremely grateful to his thesis advisor, Professor Abraham Engeda for his
valuable guidance, support, continuous encouragement and willing attitude throughout
this research work. Special thanks go to Professor Torn Shih, Professor Harold Schock
and Professor Charles MacCluer for their advice, discussion and interest in this work.
The author would like to thank Douglas Hamn'n, Greg Rouse, Greg Priddie and Murali
Chinta at Capstone Turbine Corporation, CA for initiating this work and providing useful
discussions. Special interest taken by Mohammed Aslarn and Partab Jeswani at Delphi
Energy and Engine Management System, MI in this work is highly appreciated. The
author is grateful to Dr. David Nye and Dr. Yunbae Kim at Dresser-Rand Turbo products
division, NY for their encouragement and keen interest in this work. Moreover, the
author is thankful to Dr. Herbert Sixsmith and Walter Swift at Creare Inc, for their useful
suggestions towards completion of this work. The author also appreciates technical
assistance, productive discussions and great friendship with Jae Wook Song, who was
extremely helpful in completion of this work. Author would like to express special thanks
to all the members of Turbomachinery lab including Dr. Norbert Mueller, Jae Wook
Song, Faisal Mahroogi, Zeyad Alsuhaibani, Donghui Zhang, Yinghui Dai, Pezhman
Akbari, Amir Kharazi, Toshiyuki Sato, Devon Washington, Umar Farooq and Saqib Riaz.
Moreover, it is my duty to mention the contribution of all my instructors in the National
University of Sciences and Technology (NUST), Pakistan who taught and encouraged me
to reach this point. Last but not the least, the author is grateful to members of his family:
his father, Ch. Mohammad Altaf, his mother Mrs. Parveen Altaf, elder brother Khurram

Adeel and endless love and continuous support of his wife Saddaf Raheel.

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

 

LIST OF TABLES - IX
LIST OF FIGURES X
NOMENCLATURE XIX
CHAPTER 1 1
INTRODUCTION - l
1.1 TURBOMACHINERY .............................................................................................. 1
1.2 CLASSIFICATION OF COMPRESSORS ..................................................................... 2
1.3 TURBOCOMPRESSORS ........................................................................................... 5
1.4 OBJECTIVE OF RESEARCH ..................................................................................... 6
1.5 OUTLINE OF THESIS .............................................................................................. 9
CHAPTER 2 - 11
THE REGENERATIVE TURBOMACHINES - 11
2.1 ELEMENTS OF A REGENERATIVE TURBOMACHINE ............................................. 13
2.1.1 Impeller ......................................................................................................... 13
2.1.1.1 Classiﬁcation of Impeller blades .......................................................... 14

2.1.2 Inlet and Discharge Ports ............................................................................. 14
2.1.3 Stripper ......................................................................................................... I4

2. 1.4 F low channel ................................................................................................. 15

2.2 WORKING PRINCIPLE .......................................................................................... 15
2.3 COMPARISON OF REGENERATIVE AND CENTRIFUGAL COMPRESSORS ................. 17
2.4 APPLICATIONS ................................................................................................... 20
2.5 LIMITATIONS AND CHALLENGES ........................................................................ 23
2.6 CONCLUSIONS .................................................................................................... 24
CHAPTER 3 34
LITERATURE SURVEY - 34
3.1 INTRODUCTION .................................................................................................. 34
3.2 THEORETICAL MODELS ...................................................................................... 35
3.3 EXPERIMENTAL WORK ...................................................................................... 46
3.4 IMPELLER BLADE PROFILE ................................................................................. 55
3.5 Loss CATEGORIZATION ...................................................................................... 56
3.6 CFD WORK ....................................................................................................... 59
3.7 CONCLUSIONS .................................................................................................... 60
CHAPTER 4- - - -- -- 70
APPLICATION OF RFC IN MICROTURBINE SYSTEMS - -- 70
4.1 THE NEED FOR Low COST AND EFFICIENT GAS BOOSTER COMPRESSOR .............. 71
4.2 RFC IN MICROTURBINE SYSTEMS ....................................................................... 73
4.3 NON-DIMENSIONAL PARAMETERS ...................................................................... 75

vi

4.4 SINGLE STAGE RFC ........................................................................................... 76

 

 

 

 

 

4.4.1 Design point .................................................................................................. 76

4.5 MULTISTAGE RFC ............................................................................................. 81
4.6 CORRELATIONS AMONG NON-DIMENSIONAL PARAMETERS ................................ 84
4.7 CONCLUSIONS .................................................................................................... 86
CHAPTER 5 108
THEORETICAL INVESTIGATION OF RADIAL BLADE RFC/RFP ................. 108
5.1 MATHEMATICAL MODEL ................................................................................. 109
5.1.1 Assumptions ................................................................................................ 109

5. 1.2 Governing Equations .................................................................................. 1 10

5.2 SLIP LOSS ........................................................................................................ 1 13
5.3 SHOCK Loss ..................................................................................................... 115
5.4 CIRCULATORY HEAD LOSSES ............................................................................ 116
5.4.1 Channel turning losses (k, ) ....................................................................... I 16
5.4.2 Channel and Blade Mixing Losses .............................................................. 117
5.4.3 Blade turning loss ( kb ) ............................................................................... 119
5.4.4 Sudden expansion ( kse ) .............................................................................. 1 19

5.5 TANGENTIAL HEAD LOSSES ............................................................................. 120
5.6 LEAKAGE LOSSES ............................................................................................ 120
5.7 LOSSES IN PORTS ............................................................................................. 121
5.8 PERFORMANCE PREDICTION AND COMPARISON WITH TEST DATA ..................... 121
5.9 CONCLUSIONS .................................................................................................. 122
CHAPTER 6 129
DESIGN SENSITIVTY ANALYSIS - -- - 129
6.1 ANALYSIS OF CHANNEL GEOMETRY ................................................................. 130
6.1.1 Radial clearance "c, " .................................................................................. 130
6.1.2 Channel inlet area " A.,A " ........................................................................... 133
6.1.3 Channel height "e" ..................................................................................... 136
6.1.4 Area ratio Am /Ar‘3 ................................................................................... 136

6.2 DESIGN CHANGES IN CHANNEL GEOMETRY ...................................................... 137
6.3 ANALYSIS OF BLADE GEOMETRY ...................................................................... 141
6.4 PERFORMANCE IMPROVEMENT BY ROTOR BLADE CHEVRONING ....................... 143
6.5 RFC DESIGN GUIDELINES ................................................................................ 144
6.6 CONCLUSIONS .................................................................................................. 145
CHAPTER 7 - -_ - - 159
REGENERATIVE AUTOMOTIVE FUEL PUMP - - 159
7.1 ADVANTAGES OF A REGENERATIVE AUTOMOTIVE FUEL PUMP ......................... 160
7.2 DELPHI AUTOMOTIVE FUEL PUMP ................................................................... 162
7.3 CFD ANALYSIS ON REGENERATIVE AUTOMOTIVE FUEL PUMP ......................... 165
7.4 CONCLUSIONS .................................................................................................. 167

vii

CHAPTER 8 - -- - -
COMPRESSIBLE FLOW THEORY FOR AEROF OIL BLADE RFC .................

8.1 AEROFOIL BLADE RFC ....................................................................................
8.2 COMPRESSIBLE FLOW THEORY .........................................................................
8.2.] Assumptions ................................................................................................
8.2.2 Derivation of the governing equations .......................................................
Continuity ...........................................................................................................
Momentum ..........................................................................................................
Energy .................................................................................................................

8.3 PRESSURE LOSS MODELS .................................................................................
8.3.1 Tangential pressure loss .............................................................................
8.3.2 Circulatory pressure loss ............................................................................
8.4 INLET PORT AND DECOMPRESSION DUCT ..........................................................
8.5 EFFICIENCY ......................................................................................................

8.6 REGENERATIVE NUMBER (N) ........................................................................

8.7 PERFORMANCE PREDICTION .............................................................................
8.8 SENSITIVITY ANALYSIS ....................................................................................
8.9 CONCLUSIONS ..................................................................................................

CHAPTER 9
CFD ANALYSIS ON AEROFOIL BLADE RFC

9.1 CFD ANALYSIS ...............................................................................................
9.2 LACK OF CIRCULATORY FLOW .........................................................................
9.4 MODIFIED INLET DESIGN .................................................................................
9.5 CONCLUSIONS ..................................................................................................

CHAPTER 10 - - -
CONCLUSIONS AND RECOMNIENDATIONS
BIBLIOGRAPHY
APPENDIX A
APPENDIX B - - - -
APPENDIX C

 

 

 

 

 

 

 

 

 

viii

177
177

178
179
180
I80
181
182
184
188
I88
189
189
191

192

193
197
199

209
209

211
212
213
215

225
225
230
238

241

LIST OF TABLES

TABLE 3.1 PERFORMANCE COMPARISON AT 4000 RPM AND PRESSURE RATIO OF 1.17

(AFTER SIXSMITH AND ALTMANN [60]) ..................................................................... 64
TABLE 4.1 GEOMETRY OF VARIOUS SINGLE STAGE RFC CONFIGURATIONS ....................... 89
TABLE 4.2 GEOMETRY OF INDIVIDUAL STAGES OF FOUR STAGE RFC ................................ 99

TABLE 6.1 VARIOUS CONFIGURATIONS TESTED BY WILSON FOR EXPERIMENTAL
SENSITIVITY ANALYSIS ............................................................................................. 153
TABLE 7.1 GEOMETRIC DATA FOR Two RFP DESIGNS (LENGTH (MM) AND AREA (MMZ )) 17 3

TABLE 8.1 GEOMETRIC DATA AND SOME PARAMETERS USED IN CALCULATION ............... 204

ix

LIST OF FIGURES

(Images in this dissertation are presented in color)

FIGURE 1.1 CLASSIFICATION OF COMPRESSORS ................................................................... 3
FIGURE 2.1 A REGENERATIVE TURBOMACHINE (AFTER MUGELE [42]) ............................. 26
FIGURE 2.2 A REGENERATIVE TURBOMACHINE (AFTER MOFFAT [41]) .............................. 26
FIGURE 2.3 EFFICIENCY VS. SPECIFIC SPEED FOR VARIOUS COMPRESSORS ......................... 27
FIGURE 2.4 SCHEMATIC OF A REGENERATIVE TURBOMACHINE .......................................... 27
FIGURE 2.5 SECTION A-A ENLARGED (RADIAL BLADE) .................................................... 27

FIGURE 2.6 LAYOUT OF A TWO-STAGE REGENERATIVE COMPRESSOR (AFTER SIXSMTTH [60])

................................................................................................................................... 28
FIGURE 2.7 REGENERATIVE TURBOMACHINES WITH RADIAL AND NON-RADIAL BLADES

(AFTER ABDALLAH [1]) .............................................................................................. 29
FIGURE 2.8 REGENERATIVE TURBOMACHINES WITH SEMI-CIRCULAR BLADES (AFTER

ABDALLAH [1]) .......................................................................................................... 30

FIGURE 2.9 REGENERATIVE COMPRESSORS WITH AEROFOIL BLADES (AFTER ABDALLAH [1])

................................................................................................................................... 31
FIGURE 2.10 TANGENTIAL PRESSURE VARIATION IN A REGENERATIVE TURBOMACHINE 31
FIGURE 2.11 PERFORMANCE CHARACTERISTICS OF REGENERATIVE TURBOMACHINES ....... 32
FIGURE 2.12 BLOWERS TYPICAL OPERATING RANGE (AFTER ROPPENECKER [51]) ............. 32
FIGURE 2.13 PRESSURE FLOW CURVES OF REGENERATIVE BLOWERS (AFTER ROPPENECKER

[51]) ........................................................................................................................... 33
FIGURE 3.1 SIMPLIFIED REGENERATIVE COMPRESSOR FOR FORCE ANALYSIS (AFTER

IVERSON [34]) ............................................................................................................ 62

FIGURE 3.2 PERFORMANCE CHARACTERISTICS OF REGENERATIVE COMPRESSOR (AFTER
IVERSON [34]) ............................................................................................................ 62
FIGURE 3.3 TYPICAL FLOW CYCLE ALONG A STREAMLINE (AFTER, EL HAG [22]) .............. 63
FIGURE 3.4 VELOCITY DIAGRAMS FOR COMPRESSOR BLADES (AFTER SIXSMITH AND
ALTMANN [60]) ......................................................................................................... 63
FIGURE 3.5 HEAD COEFFICIENTS OF ORGDP-l REGENERATIVE COMPRESSOR (AFTER
CATES [15]) ............................................................................................................... 64
FIGURE 3.6 HEAD COEFFICIENTS DEPENDENCE ON IMPELLER TIP MACH NUMBER (AFTER
CATES [15]) ............................................................................................................... 65
FIGURE 3.7 INFLUENCE OF CLEARANCES ON PRESSURE RATIO (AFTER CATES [16]) ........... 65
FIGURE 3 .8 COMPARISON OF SEVERAL REGENERATIVE COMPRESSORS (AFTER CATES [16])
................................................................................................................................... 66
FIGURE 3.9 PERFORMANCE OF MKl COMPRESSOR (AFTER SIXSMITH AND ALTMANN [60])
................................................................................................................................... 67
FIGURE 3.10 PERFORMANCE OF MK2 COMPRESSOR WITH UNSYMMETRIC BLADING (AFIER
SIXSMITH AND ALTMANN [60]) ................................................................................. 67
FIGURE 3.11 PERFORMANCE OF MK2 COMPRESSOR WTTH SYMMETRIC BLADING (AFTER
SIXSMITH AND ALTMANN [60]) ................................................................................. 68
FIGURE 3.12 PRESSURE RISE VS. FLOW CURVE FOR UHTREX GAS CLEANUP SYSTEM
REGENERATIVE COMPRESSOR (AFTER CROWE [18]) .................................................. 68
FIGURE 3.13 OVERALL EFFICIENCY CURVE FOR UHTREX GAS CLEANUP SYSTEM

REGENERATIVE COMPRESSOR (AFTER CROWE [18]) ................................................... 69

xi

FIGURE 3.14 LOSS ANALYSIS BASED ON MK2 REGENERATIVE COMPRESSOR WITH

SYMMETRIC BLADES AT 4500 RPM (AFTER SIXSMITH AND ALTMANN [60]) ............... 69
FIGURE 4.1 THE CAPSTONE MODEL 330 MICROTURBINE GENERATOR ............................... 88
FIGURE 4.2 SCHEMATIC OF CAPSTONE MODEL 330 MICROTURBINE SYSTEM ..................... 88

FIGURE 4.3 SCHEMATIC OF BLADE AND CHANNEL GEOMETRY FOR SINGLE STAGE RFC
CONFIGURATION ........................................................................................................ 89
FIGURE 4.4 PRESSURE RATIO VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP MACH
NUMBERS FOR CONFIGURATION SI ............................................................................ 90
FIGURE 4.5 ISOTHERMAL EFFICIENCY VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP MACH
NUMBERS FOR CONFIGURATION Sl ............................................................................ 90
FIGURE 4.6 PRESSURE RATIO vs. SPECIFIC MASS FLOW RATE AT VARIOUS TIP MACH
NUMBERS FOR CONFIGURATION S2 ............................................................................ 91
FIGURE 4.7 ISOTHERMAL EFFICIENCY VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP MACH
NUMBERS FOR CONFIGURATION 82 ............................................................................ 91
FIGURE 4.8 PRESSURE RATIO VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP MACH
NUMBERS FOR CONFIGURATION S3 ............................................................................ 92
FIGURE 4.9 ISOTHERMAL EFFICIENCY VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP MACH
NUMBERS FOR CONFIGURATION S3 ............................................................................ 92
FIGURE 4.10 PRESSURE RATIO VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP MACH
NUMBERS FOR CONFIGURATION S4 ............................................................................ 93
FIGURE 4.11 ISOTHERMAL EFFICIENCY VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP

MACH NUMBERS FOR CONFIGURATION S4 ................................................................. 93

xii

—

   

FIGURE 4.12 PRESSURE RATIO vs. SPECIFIC MASS FLOW RATE AT VARIOUS TIP MACH

NUMBERS FOR CONFIGURATION S5 ............................................................................ 94

FIGURE 4.13 ISOTHERMAL EFFICIENCY VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP

MACH NUMBERS FOR CONFIGURATION S5 ................................................................. 94

FIGURE 4.14 PRESSURE RATIO VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP MACH

NUMBERS FOR CONFIGURATION S6 ............................................................................ 95

FIGURE 4.15 ISOTHERMAL EFFICIENCY VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP

MACH NUMBERS FOR CONFIGURATION S6 ................................................................. 95

FIGURE 4.16 PRESSURE RATIO VS. SPECIFIC MASS FLOW RATE AT VARIOUS TIP MACH

NUMBERS FOR CONFIGURATION S7 ............................................................................ 96

FIGURE 4.17 ISOTHERMAL EFFICIENCY VS. SPECIFIC MASS FLOW AT VARIOUS TIP MACH

NUMBERS RATE FOR CONFIGURATION S7 ................................................................... 96
FIGURE 4.18 FOUR STAGE RFC FULL ASSEMBLY ............................................................... 97
FIGURE 4.19 SKETCH OF FOUR STAGE RFC ........................................................................ 97
FIGURE 4.20 1ST STAGE IMPELLER OF FOUR STAGE RFC ........................................................ 98
FIGURE 4.21 15'r STAGE CHANNEL OF FOUR STAGE RFC ..................................................... 98
FIGURE 4.22 SCHEMATIC OF BLADE AND CHANNEL GEOMETRY ......................................... 99

FIGURE 4.23 PRESSURE RATIO AND ISOTHERMAL EFFICIENCY vs. IMPELLER TIP MACH
NUMBER FOR VARIOUS INLET PRESSURES ................................................................. 100

FIGURE 4.24 PRESSURE RATIO AND ISOTHERMAL EFFICIENCY VS. IMPELLER TIP MACH
NUMBER FOR VARIOUS INLET PRESSURES ................................................................. 101

FIGURE 4.25 PRESSURE RATIO AND ISOTHERMAL EFFICIENCY vs. IMPELLER TIP MACH

NUMBER FOR VARIOUS INLET PRESSURES ................................................................. 102

xiii

FIGURE 4.26 PRESSURE RATIO VS. IMPELLER TIP MACH NUMBER (AFTER CATES, 1964) . 103
FIGURE 4.27 PERFORMANCE MAP OF THE ORGDP-l REGENERATIVE COMPRESSOR (AFTER
CATES, 1964) ........................................................................................................... 104
FIGURE 4.28 EFFICIENCY OF THE ORGDP-l REGENERATIVE COMPRESSOR (AFIER CATES,
1964) ....................................................................................................................... 105
FIGURE 4.29 PRESSURE RATIO VS. IMPELLER TIP MACH NUMBER AND FLOW COEFFICIENT
FOR FOUR STAGE RFC .............................................................................................. 105
FIGURE 4.30 ISOTHERMAL EFFICIENCY VS. IMPELLER TIP MACH NUMBER AND FLOW
COEFFICIENT FOR FOUR STAGE RFC ......................................................................... 106
FIGURE 4.31 PRESSURE RATIO vs. IMPELLER TIP MACH NUMBER AND SPECIFIC MASS FLOW
RATE FOR FOUR STAGE RFC ..................................................................................... 106
FIGURE 4.32 ISOTHERMAL EFFICIENCY VS. IMPELLER TIP MACH NUMBER AND SPECIFIC
MASS FLOW RATE FOR FOUR STAGE RFC .................................................................. 107

FIGURE 5.1 CONTROL VOLUMES REPRESENTING SECTION d 6 OF OPEN CHANNEL AND

IMPELLER ................................................................................................................. 123
FIGURE 5.2 SCHEMATIC OF BLADE AND CHANNEL GEOMETRY ......................................... 123
FIGURE 5.3 GEOMETRY FOR SHOCK Loss MODEL ............................................................. 124

FIGURE 5.4 GEOMETRIC PARAMETERS GOVERNING CHANNEL TURNING Loss COEFFICIENT
................................................................................................................................. 124
FIGURE 5.5 MDGNG PROCESS OF FLOW ENTERING CHANNEL THROUGH BLADES .............. 125
FIGURE 5.6 GEOMETRIC PARAMETERS GOVERNING BLADE TURNING LOSS COEFFICIENT . 125
FIGURE 5.7 FLOW CHART OF PERFORMANCE PREDICTION CODE ....................................... 126

FIGURE 5.8 THEORETICAL AND TEST DATA OVERLAPPED FOR FLOW RATE 195 slpm ........ 127

xiv

FIGURE 5.9 THEORETICAL AND TEST DATA OVERLAPPED FOR FLOW RATE 250 slpm ........ 128

FIGURE 6.1 VARIOUS LOSS PARAMETERS vs. RATIO "c, /r2 " ............................................ 146
FIGURE 6.2 RADIAL CLEARANCE VS. PRESSURE RATIO FOR FIRST STAGE ......................... 147
FIGURE 6.3 RATIO " d A / r2 " vs. SHOCK LOSS PARAMETER "a" ........................................ 147

FIGURE 6.4 INFLUENCE OF CHANNEL GEOMETRY ON PRESSURE RATION (AFTER CATES [15])
................................................................................................................................. 148

FIGURE 6.5 INFLUENCE OF CHANNEL GEOMETRY ON ADIABATIC EFFICIENCY (B=CHANNEL
DEPTH, H=RADIAL CLEARANCE, AFTER CATES [15]) ................................................ 148

FIGURE 6.6 EFFECT OF CHANNEL GEOMETRY ON HEAD COEFFICIENT (AFTER WILSON [69])

................................................................................................................................. 149
FIGURE 6.7 RATIO "d, / r2 " VS. CHANNEL TURNING LOSS COEFFICIENT ........................... 150
FIGURE 6.8 d A / e VS. CHANNEL TURNING COEFFICIENT ..................................................... 150
FIGURE 6.9 RATIO "d, /r2 " VS. SKIN FRICTION LOSS ........................................................ 151

FIGURE 6.10 EFFECT OF CHANNEL DIMENSIONS ON PERFORMANCE, (AFTER BURTON [11])

................................................................................................................................. 152
FIGURE 6.11 PRESSURE RATIO vs. CHANNEL AREA RATIO ............................................... 153
FIGURE 6.12 SLIP AND SHOCK LOSS PARAMETER VS. IMPELLER RADIUS RATIO ................ 154
FIGURE 6.13 PRESSURE RATIO VS. IMPELLER RADIUS RATIO ............................................ 154
FIGURE 6.14 SLIP FACTOR VS. NUMBER OF BLADES ......................................................... 155
FIGURE 6.15 PRESSURE RATIO VS. NUMBER OF BLADES ................................................... 155
FIGURE 6.16 BLADE CHEVRONING ................................................................................... 156
FIGURE 6.17 SLIP FACTOR VS. CHEVRON ANGLE ............................................................. 156
FIGURE 6.18 PRESSURE RATIO VS. CHEVRON ANGLE ....................................................... 157

XV

FIGURE 6.19 VARIATION OF SHOCK LOSS WITH CHEVRON ANGLE (AFTER DEWITT [21]).. 157
FIGURE 6.20 EFFECT OF BLADE CHEVRONING ON HEAD COEFFICIENT (AFTER DEWITT [21])
................................................................................................................................. 158
FIGURE 7.1 A TYPICAL AUTOMOTIVE FUEL SYSTEM (COURTESY OF DELPHI AUTOMOTIVES,
MI) .......................................................................................................................... 168
FIGURE 7.2 A REGENERATIVE AUTOMOTIVE FUEL PUMP (AFTER HUBEL [3 2]) ................. 168

FIGURE 7.3 SCHEMATIC VIEW AND GEOMETRIC SYMBOLS OF A TWO STAGE PERIPHERY PUMP

(AFTER BADAMI [7]) ................................................................................................ 169
FIGURE 7.4 PUMP AND MOTOR ASSEMBLY OF DELPHI AUTOMOTIVE FUEL PUMP .............. 169
FIGURE 7.5 COMPONENTS OF THE PUMP-MOTOR ASSEMBLY ............................................ 170
FIGURE 7.6 IMPELLER WITH BOTH SIDE CHANNELS .......................................................... 170
FIGURE 7.7 BLADE AND CHANNEL SHAPE OF DELPHI AUTOMOTIVE FUEL PUMP ............... 171

FIGURE 7 .8 NON-DIMENSIONAL EXPERIMENTAL DATA OF HEAD VS. FLOW RATE FOR DELPHI

RFP ......................................................................................................................... 171
FIGURE 7.9 EFFICIENCY vs. FLOW RATE FOR DELPHI RFP ............................................... 172
FIGURE 7.10 FLOW, CURRENT DRAWN AND EFFICIENCY vs. PRESSURE FOR DELPHI RFP 172

FIGURE 7.11 THEORETICAL AND EXPERIMENTAL NON-DIMENSIONAL HEAD VS. FLOW 17 3

FIGURE 7.12 THEORETICAL AND EXPERIMENTAL EFFICIENCY VS. FLOW .......................... 174
FIGURE 7.13 UNIGRAPHICS MODEL OF REGENERATIVE AUTOMOTIVE FUEL PUMP ....... 174
FIGURE 7.14 N ON-RADIAL BLADES IN IMPELLER OF RFP ................................................. 17 5
FIGURE 7.15 WEB BETWEEN TWO BLADES OF RFP .......................................................... 175

FIGURE 7.16 HEAD DISTRIBUTION ACROSS PERIPHERY OF REGENERATIVE AUTOMOTIVE

FUEL PUMP ............................................................................................................... 176

xvi

FIGURE 7.17 CIRCULATORY VELOCITY IN THE TWIN CHANNELS ...................................... 176

FIGURE 8.1 REGENERATIVE COMPRESSOR WITH AEROFOIL BLADES (AFTER ANDREW [2])201

FIGURE 8.2 COORDINATE AND MERIDIONAL GEOMETRY .................................................. 201
FIGURE 8.3 ARBITRARY SMALL CONTROL VOLUME ......................................................... 202
FIGURE 8.4 VELOCITY TRIANGLES AT R1 AND R2 ............................................................ 202
FIGURE 8.5 SCHEMATIC DIAGRAM FOR INLET REGION AND DECOMPRESSION DUCT ......... 203
FIGURE 8.6 TANGENTIAL VELOCITY AND ANGLE DISTRIBUTION PER CYCLE ..................... 203
FIGURE 8.7 COMPARISON OF PRESSURE RATIO OF MKl COMPRESSOR ............................. 204
FIGURE 8.8 COMPARISON OF PRESSURE RATIO OF MK2 COMPRESSOR ............................. 205
FIGURE 8.9 COMPARISON OF EFFICIENCY OF MKI COMPRESSOR ..................................... 205
FIGURE 8.10 COMPARISON OF EFFICIENCY OF MK2 COMPRESSOR ................................... 206
FIGURE 8.11 THEORETICAL HEAT TRANSFER RATIO IN MKI AND MK2 .......................... 206
FIGURE 8.12 THE RATIO OF DECOMPRESSION POWER To HYDRAULIC POWER ................. 207
FIGURE 8.13 THE VARIATION OF REGENERATIVE NUMBER VS. FLOW RATE ..................... 207
FIGURE 8.14 HEAD COEFFICIENT VS. FLOW COEFFICIENT ................................................. 208
FIGURE 8.15 EFFICIENCY VS. FLOW COEFFICIENT ............................................................ 208
FIGURE 9.1 BLADE DIMENSIONS ...................................................................................... 216
FIGURE 9.2 BLADE DESIGN .............................................................................................. 216
FIGURE 9.3 BLADE AND CHANNEL GEOMETRY ................................................................. 217

FIGURE 9.4 FULL ASSEMBLY OF REGENERATIVE COMPRESSOR WITH AEROFOIL BLADES . 218

FIGURE 9.5 MESHING FOR CFD ANALYSIS ...................................................................... 218
FIGURE 9.6 INLET MANIFOLD ........................................................................................... 219
FIGURE 9.7 CROSS SECTIONAL VIEW OF TWIN BLADE AND CHANNEL ................................ 219

xvii

FIGURE 9.8 MESHING AROUND TWIN BLADE AND CHANNEL ............................................ 220

FIGURE 9.9 ABSOLUTE VELOCITY VECTORS REPRESENTING THE FLOW DIRECTION .......... 220

FIGURE 9.10 ABSOLUTE VELOCITY VECTORS REPRESENTING FLOW AROUND THE CORE IN

THE CHANNEL .......................................................................................................... 221

FIGURE 9.11 ABSOLUTE VELOCITY VECTORS REPRESENTING FLOW IN THE INLET MANIFOLD

................................................................................................................................. 221
FIGURE 9.12 MODIFIED INLET DESIGN (3D VIEW) ........................................................... 222
FIGURE 9.13 MODIFIED INLET DESIGN (3D VIEW) ........................................................... 222

FIGURE 9.14 VELOCITY VECTORS DESCRIBING CIRCULATORY FLOW PATTERN THROUGH THE
INLET MANIFOLD ...................................................................................................... 223
FIGURE 9.15 VELOCITY VECTORS SHOWING CIRCULATORY FLOW PATTERN NEAR INLET

PORT ........................................................................................................................ 223

FIGURE 9.16 VELOCITY VECTORS SHOWING CIRCULATORY FLOW AT 19 2 180° FROM INLET

PORT ........................................................................................................................ 224

FIGURE 9.17 PROPOSED “OWL” SHAPED INLET DESIGN ................................................. 224

xviii

fR’fc

S

NOMENCLATURE

Shear area of casing

Shear area of impeller

Area of blade

Channel area

Area at any radial location Rp

Blade depth
Blade blockage factor

Axial clearance

Radial clearance

Shear stress coefﬁcient of easing
Orifice discharge coefﬁcient
Shear stress coefﬁcient of impeller
Speciﬁc heat at constant pressure
Channel depth at station A and B
Peripheral distance

Hydraulic diameter

Impeller blade height

Rotor and Casing friction factor

Fraction of periphery occupied by impeller seal

xix

pin’ pout

Pdecomp.

Acceleration due to gravity
Head

Aerofoil blade height

Total enthalpy of ﬂuid at inlet and exit of impeller blade
Blade turning loss coefﬁcient

Inlet and discharge port loss coefﬁcients

Blade mixing loss

Sudden expansion loss

Channel turning loss coefficient

Head loss coefﬁcient

Aerofoil blade chord length or Flow path length

Length of blading at inlet and outlet edges

Mass ﬂow rate

Impeller tip Mach number

Mass flow rate through annular channel

Mass ﬂow rate through blading

Number of passages of ﬂuid between inlet and outlet ports
Speciﬁc speed

Pressure

Inlet and discharge pressure

Decompression power

XX

P disk

Phyd

PC

Qleak

Q.

72,];

Re

Disk friction loss power
Hydraulic power

Power

Pitch to cord ratio

Non-dimensional heat transfer rate (Q/p00 (2301132)

Volume ﬂow rate
Circulatory ﬂow rate
Leakage ﬂow rate

Flow rate based on solid body rotation

Heat transfer rate
Centroidal radius

Impeller tip and hub radius

Gas constant

Reynolds number

Transverse component of path length

Blade thickness

Torque, Temperature

Absolute temperature of ﬂuid at inlet and exit port
Tangential velocity Of impeller at hub and tip

Circulatory velocity

Tangential velocity

xxi

Vm Mean tangential ﬂuid velocity

V9,,V02 Tangential velocity of ﬂuid at inlet and exit of impeller
W1 ,W2 Relative velocities of ﬂuid with respect to blading
Z Number of impeller blades

Z, Number of blades in stripper
Symbols

a Shock loss coefﬁcient

,6 Blade angle

[91,,62 Fluid angles at inlet and outlet edges of blading
7 Ratio of speciﬁc heats

Y Power coefﬁcient

77 Efﬁciency

,01 , ,02 Density at inlet and outlet edges of blading

[2,, Mean density of ﬂuid in annular channel

0) RPM

6 Tangential angle

are, Pumping and stripper angle respectively

0' Slip factor

‘P Head coefﬁcient

4 Flow coefﬁcient

U Pressure ratio
‘13 Speciﬁc mass ﬂow rate

xxii

CHAPTER 1

INTRODUCTION

1.1 Turbomachinery

Turbomachinery iS the science of using working ﬂuids to boost output, either increase or
decrease pressure by using machinery. The original meaning of turbo is “spins or whirls
around”. The term turbomachinery applies to rotating (as opposed to reciprocating)
machinery that either extracts or adds energy to ﬂuids by the dynamic action of one or
more moving blade rows. The rotor changes the stagnation enthalpy, kinetic energy and
stagnation pressure of the ﬂuid. This broad deﬁnition covers everything from a classic
Dutch windmill to the space shuttle main engine turbopumps. Turbomachinery is a major
component in aerospace and marine vehicle applications, land propulsion systems, energy
applications, hydraulic, gas and steam turbines, industrial pipeline and processing
equipment such as gas, petroleum and water pumping plants. Moreover, turbomachinery
has a wide variety of other applications (e.g. heart-assist pumps, industrial compressors
and refrigeration plants).

Turbomachines can be of different types depending on application. Turbines are
turbomachines which produce power by expanding a continuously ﬂowing ﬂuid to a

lower pressure or head. Pumps are turbomachines which increase the pressure or head of

a flowing liquid. Fans is term used for turbomachines imparting only a small pressure rise

 

 

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;
T

31173. 'Ilﬁitiiiiiﬁh’lfrﬁé

‘ -33.'I.I;~'.?:,r.z..~

 

to a continuously ﬂowing gas, usually with a density ratio across the machine of less than
1.05 such that the gas may be considered to be incompressible. Compressors are
turbomachines imparting a large pressure rise to a continuously ﬂowing gas with a
density ratio in excess of 1.05. The fundamentals and operating principle of pumps and
compressors is very similar. Pumps are used primarily for pumping the liquid media and
compressors are employed for gas compression. Due to close resemblance in pumps and

compressors, this dissertation discusses regenerative ﬂow pumps and compressors in

tandem.

1.2 Classification of Compressors

A compressor converts shaft power to a rise in enthalpy of a ﬂuid. The ﬂuid, often a gas,
enters the compressor at a low pressure (low enthalpy) and exits at a high pressure (high
enthalpy). The rotating shaft is attached to a blade assembly. The rotating blades push on
the gas and increase the pressure, thereby increasing the enthalpy. The earliest
compressors were bellows, used by blacksmiths to intensify the heat in their furnaces.

The ﬁrst industrial compressors were Simple reciprocating piston-driven machines

powered by a water Wheel.

There are various types of compressors being used in industry because of the almost
inﬁnite range of service requirements. Before a compressor type can be selected for a
particular application, certain basic information relating to its performance requirements
should be at hand. This includes: pressure ratio, flow rate, efﬁciencies desired and could
include other special characteristics. One can then consider the type of machine desired

from a range of types of compressors available, as shown in Figure 1.1. Broadly

speaking there are two basic compressor types: positive displacement compressors and

continuous ﬂow compressors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Compressors
Positive Displacement ] [ Continuous Flow ]
Reciprocating Rotary Ejector [ Dynamic
[ Liquid (Straight Lobe ][ Sliding Helical

 

 

 

 

 

 

 

 

 

 

 

 

 

Centrifugal Axial Regenerative Mixed

 

 

 

 

 

 

Turbocompressors

 

 

 

Figure 1.1 Classification of compressors

In the positive displacement type, a given quantity of air or gas is trapped in a
compression chamber and the volume which it occupies is mechanically reduced, causing
a corresponding rise in pressure prior to discharge. At constant speed, the air ﬂow

remains essentially constant with variations in discharge pressure. These compressors are

available in two types: reciprocating and rotary. Reciprocating compressors work like
bicycle pumps. A piston, driven through a crankshaft and connecting rod by an electric
motor reduces the volume in the cylinder occupied by the air or gas, compressing it to a
higher pressure. Single-acting compressors have a compression stroke in only one
direction, while double-acting units provide a compression stroke as the piston moves in
each direction. Large industrial reciprocating air compressors are double-acting and
water-cooled. Multistage double-acting compressors are the most efﬁcient compressors
available, and are typically larger, noisier and more costly than comparable rotary units.
Reciprocating compressors are available in sizes from less than 1 hp to more than 600 hp.
Rotary compressors have gained popularity and are now the "workhorse" of American
industry. They are most commonly used in sizes from about 30-200 hp. The most
common type of rotary compressor is the helical twin screw-type (also known as rotary
screw or helical lobe). Male and female screw-rotors mesh, trapping air and reducing the
volume Of the air along the rotors to the air discharge point. Rotary screw compressors
have low initial cost, compact size, low weight and are easy to maintain. Rotary screw
compressors are available in sizes from 3-600 hp and may be air or water-cooled. Less
common rotary compressors include sliding vane, liquid piston and straight lobe. Both

Reciprocating and rotary compressors will not be considered further in this dissertation.

Continuous ﬂow compressors work by the principle of accelerating the ﬂuid to a high
velocity and then converting this kinetic energy into potential energy, manifested by an
increase in pressure by decelerating the gas in diverging channels. The continuous flow
compressors are categorized into ejector and dynamic type compressors. The dynamic

compressors are subdivided into axial, centrifugal, mixed type and regenerative

compressors. These four categories are also called Turbocompressors. They can be
further classiﬁed into three broad categories based on the path of ﬂow through the

machine as discussed below.

1.3 Turbocompressors

Turbcompressors can be classiﬁed based on the nature of ﬂow path through the passages
of the rotor. When the meridional ﬂow path is axial, the compressors are called axial
compressors. They are composed of several rows of airfoil cascades. Some of the rows,
called rotors, are connected to the central shaft and rotate at high speed. Other rows,
called stators, are ﬁxed and do not rotate. The job of the stators is to increase pressure
and keep the ﬂow from spiraling around the axis by bringing the ﬂow back parallel to the
axis. The second category is radial or centrifugal compressors, which have predominantly
radial ﬂow path. In axial compressors the deceleration takes place in the stator blade
passages and in centrifugal compressors it takes place in the diffuser. One obvious
difference between these two types of compressors is that, in axial compressors, the ﬂow
leaves the compressor in the axial direction, Whereas, in centrifugal compressors, the
ﬂows leaves the compressor in a direction perpendicular to the axis of the rotating shaft.
The third category is called the mixed ﬂow compressors in which the ﬂow path is
partially axial and partially radial. Mixed ﬂow compressors have impellers and rotors
which combine the characteristics of both axial and centrifugal compressors.

The regenerative ﬂow compressors and pumps, hereafter known as RFC/RFP are
rotodynamic turbomachines capable of developing high pressure ratios in a single stage.
They permit a head equivalent to that of several centrifugal stages Obtained from a single

rotor with comparable tip speeds. The ﬂuid in a regenerative ﬂow compressor moves

helically in the casing and reenters the impeller many times in its peripheral path from
inlet to discharge. This repetitive action of the impeller blading on ﬂuid is, in effect,
“multistaging” and accounts for the high head per stage characteristic of this type of
turbomachines. The regenerative ﬂow pumps are also known as Peripheral pump, Side
channel pump. Turbine pump, Drag Pump, Traction pump, Tangential pump and Vortex
pump in literature. The main characteristics of regenerative turbomachines are their
ability to generate high heads at low ﬂow rates. They have a very low speciﬁc speed and
Share some of the characteristics of positive displacement machines such as a roots
blower, but without problems of lubrication and wear. In addition to self priming
characteristics, the main advantage offered by a RFP/RFC is the ability to develop much
higher heads than any other type of turbomachine with the same tip speed. When a
regenerative ﬂow turbomachine is applied as a gas compressor, there is further advantage

of no surge or Stall instability.

1.4 Objective of research

The Objective of present study is to improve existing designs of regenerative
turbomachines and improve the efﬁciency. During last twenty years, there has not been
much research done on RFC/RFP to improve the efﬁciency. With the development of
commercial softwares and advanced manufacturing techniques over last few years, the
industry has shown interest to modify the conventional designs of regenerative
turbomachines with aerodynamically improved designs. There are no reliable theoretical
models to forecast performance of regenerative turbomachines using geometric
parameters as input. Most of the available theoretical models need extensive experimental

support to predict the performance. Therefore, it is not easy to make design changes and

improve the performance. Most of the researchers carried out experimental analysis to
study the effect of various geometric and aerodynamic parameters on performance.
Experimentation is always very expensive and time consuming. Therefore, the objective
of current research is to develop theoretical means to predict the performance of existing
regenerative turbomachines. After predicting the performance, extensive sensitivity
analysis is performed to study which design changes are effective for performance
improvement. Design guidelines for improved performance are proposed from the
sensitivity analysis. Some design criteria are developed in this work, which can be very
useful for designers and engineers working in regenerative turbomachinery. Proposed
design changes need validation by CFD before prototype models can be built. There is
not much evidence available in the literature about CFD analysis on regenerative
turbomachines using commercially available CFD softwares. Therefore, it is one of the
objectives of this dissertation to introduce and motivate industry to use CFD analysis to
get a better insight in the complicated ﬂow mechanism in regenerative turbomachines.

This research is carried out in association with two organizations. Capstone Turbine
Corporation, CA has made use of a multistage RFC for low pressure (0.2-15 psig) natural
gas compression for its C30 microturbine system. The compressor design builds required
pressure ratio but with very low isothermal efﬁciency in the range of 15—20% at the
design point. These efﬁciency levels are very low and there is signiﬁcant room for
improvement. Thus, experimental data on Capstone single and multistage RFC is
analyzed to study the performance characteristics of the compressor. Correlations among
various non-dimensional parameters are developed from experimental data to make this

discussion attractive for designers and engineers working in regenerative turbomachinery.

A theory to describe the complex helical ﬂuid ﬂow in radial and non-radial blade
RFC/RFP is presented. Governing equations are derived and loss models are proposed,
based on which a performance prediction code is developed. This code takes compressor
geometry information and inlet conditions as input and predicts the performance. The
theoretical results are matched with the test data to verify the proposed model. After
overlapping theoretical results and test data, a design sensitivity analysis is performed on
various geometric parameters to study which design changes affect compressor
performance. A new and improved design for Capstone multistage RFC is proposed
based on sensitivity analysis results.

Delphi Automotives, MI utilizes regenerative fuel pumps for raising head of gasoline
contained in the fuel tank and delivering it to fuel injectors at sufﬁcient ﬂow rate and
pressure. The present design of Delphi fuel pump comprises of non-radial blades
producing hydraulic efﬁciency around 40%, making it best available RFP design in
automotive industry at the moment. However, there seems a lot of room for improvement
by replacing the non-radial impeller blades by aerodynamically designed aerofoil blades.
The performance prediction code for RFC/RFP is used to predict the performance of non-
radial blade automotive fuel pump. After predicting the performance with the code and
performing a sensitivity analysis on various geometrical elements of the pump, few
design suggestions are proposed. However, it is observed that there is not much increase
in hydraulic efﬁciency expected by keeping the traditional non-radial blades. This
motivated the researcher to investigate the possibility of employing aerofoil blades to the
regenerative turbomachines and proposing an entirely new design. There is not much

evidence available in literature on aerofoil blade RFP. However, it is found from

literature that aerofoil blade RFC can produce isothermal efficiencies in excess of 55%.
Some experimental data and geometry information on two aerofoil blade RFC designs is
available in literature.

A compressible ﬂow theory is proposed which enables to predict the performance of
aerofoil blade RFC/RFP. The compressible ﬂow theory is used to develop another
performance prediction code, speciﬁcally to predict performance of aerofoil blade
RFC/RFP. Excellent agreement between theoretical prediction and experimental data on
available RFC designs is observed. This led the researcher to perform a sensitivity
analysis for various geometric parameters of aerofoil blade design to improve the
performance. The idea of decompression ducts is used to reduce the power consumption
which results in signiﬁcant performance improvement. Based on ﬁndings from the theory,
a new RFC model with aerofoil blades is developed in “UNIGRAPHICS”. A CFD
analysis is performed in “STAR CD” to validate the theoretical prediction of efﬁciencies
in excess of 55%. Currently work is in progress to optimize the inlet manifold of aerofoil

blade RFC for better performance.

1.5 Outline of thesis

This dissertation consists of ten chapters starting with a detail discussion of fundamentals,
hypothesis of Operation, applications, limitations and challenges faced by regenerative
turbomachines in chapter 2. Chapter 3 deals with previous research work done on
RFC/RFP. The literature survey presented in chapter 3 consists of previously presented
theoretical models, experimental investigations, blade designs, loss analysis and CFD
work performed on regenerative turbomachines. Chapter 4 discusses application of RFC

in microturbine systems. Non-dimensional geometry and experimental data of Capstone

single and multistage RFC is presented and analyzed. Chapter 5 discusses a theoretical
analysis of complex helical ﬂow in regenerative turbomachines. Governing equations and
loss models are developed in chapter 5. Chapter 6 presents results of design sensitivity
analysis from the performance prediction code along with suggestions for improved
design of multistage RFC for Capstone C30 microturbine system.

Chapter 7 opens up a new subject and discusses application of regenerative
turbomachines in automotive fuel pumping. Performance prediction of Delphi
regenerative fuel pump is compared with experimental data along with some suggestions
for design improvement. Moreover details of CFD analysis on Delphi fuel pump are also
presented in this chapter. Chapter 8 targets on development of aerofoil blade regenerative
compressors with the idea of decompression ducts to reduce the power requirement. A
compressible ﬂow theory for aerofoil blade RFC is presented. Theoretical and available
test data are compared and suggestions for design improvement are provided. Chapter 9
discusses CFD analysis on aerofoil blade RFC design. In chapter 10, attempts are made to
draw conclusions focusing mainly on performance improvement of regenerative
turbomachines. Suggestions for future research in this area are provided at the end of

dissertation.

10

CHAPTER 2

THE REGENERAT IVE TURBOMACHINES

The unique design and Operational features of regenerative turbomachines have excited
many researchers to investigate their characteristics. They are identiﬁed by the
application of combined radial and toroidal ﬂow. They are partly axial and partly radial
in design and function. A typical regenerative turbomachine is shown in Figures (2.1 and
2.2). In contrast to other popular types of continuous ﬂow compressors and pumps in
which the ﬂuid passes through the impeller once, regenerative turbomachines have the
ﬂuid exposed to the impeller many times. The ﬂow through a RFC/RFP resembles a
corkscrew ﬂow pattern as illustrated in Figure 2.1 by the help of a streamline passing
through the impeller. To Visualize the path which the ﬂuid follows, imagine a spring that
has been stretched too far, so that the coils no longer touch. Take that stretched Spring,
form it into a circle, and lay it on the impeller blade. This situation is depicted in Figure
2.1. AS the coiled Spring is followed, the progression of movement from one blade to the
trailing blade is seen. Depending on how far the spring has been stretched (the distance
between coils could be large relative to the coil diameter) the pitch of one loop may Span
more than the distance between adjacent blades. As the discharge pressure increases, the
pitch of the loops in the helix gets smaller in a manner analogous to compression of the
spring. It has been Visually conﬁrmed that as the discharge pressure increases, the helical

pitch of the ﬂuid becomes shorter. There is additional energy imparted to the ﬂuid each

11

time it passes through the blades of the impeller, allowing substantially more motive
force to be added which enables much higher pressures to be achieved in a more compact
design. Each passage through the vanes may be regarded as a conventional stage of
compression. It is due to the repeated ﬂow through impeller blades that has made a
regenerative compressor capable of replacing a 7 or 8 stage centrifugal compressor,
producing the same head. Thus the equivalent of several stages of compression may be
obtained from a single impeller in a relatively smaller compressor. This is because the
head coefﬁcient obtainable from this machine is of an order of magnitude higher than
obtainable from a centrifugal machine. This compression process, however, cannot be
regarded as efﬁcient. Typically the regenerative compressors have less than 50%
efﬁciency, but still they have found many applications because they allow the use of ﬂuid
dynamic compressors in place of positive displacement compressors for duties requiring
high head and low ﬂow rates. The efﬁciency limitation of regenerative turbomachinery is
shown in Figure 2.3, which shows the comparative efficiency of low speciﬁc speed
compressors of centrifugal type and various regenerative designs as a function of speciﬁc
speed. It can be seen that the regenerative machine has tended to peak at about 50%
efﬁciency in the low speciﬁc speed range, while centrifugal picks up from this point.
Also, it can be noted that in very low specific speed ranges, the regenerative is more
efﬁcient than the centrifugal compressors. Although, regenerative turbomachines are
widely used in the industry but there is still a need to study and make design changes in

their geometry to improve the performance.

12

2.1 Elements of a Regenerative Turbomachine

The essential elements of a regenerative turbomachine are shown in Figure 2.4. Typically,
they have an impeller, inlet port, discharge port, stripper, ﬂow passage and a casing.

These components are discussed below:
2.1.1 Impeller

Regenerative turbomachines utilize a free rotating impeller just like other types of
continuous ﬂow compressors and pumps. The impeller has vanes machined into each side
at its periphery, which produce a series of helical ﬂows, returning the ﬂuid repeatedly
through the vanes for additional energy as it passes through an open annular channel.
Thus the rotation of the impeller causes a helical corkscrew ﬂow pattern of the ﬂuid. The
ﬂuid does not discharge freely from the tips of the blades but circulates back to blades
many times before leaving the impeller. This motion is composed of a peripheral motion
induced in the peripheral stator channel by the rotation of the wheel, superimposed by a
circulatory motion in the rotor pockets and stator caused by the centrifugal pressure
gradient. The effect of these motions is a gradual increase of air pressure in peripheral
direction. It is from this internal “multistaging” or “regeneration” that these
turbomachines derive their name. The action of impeller blades operating in series
instead of parallel to each other makes them different from centrifugal turbomachines.
The impeller is ﬁtted with blades to promote the toroidal ﬂow pattern, consisting of a
combined impeller-to-Side channel circulation and an annular ﬂow from inlet to outlet.
This complex ﬂow regime is not readily amendable to detailed theoretical ﬂow analysis.
The ﬂuid is in contact with the ﬂuted portion of the impeller. The impeller, through

centrifugal forces, propels the ﬂuid radially outward. The enclosing chambers conduct

l3

the ﬂuid into twin vortices around the impeller blade as shown in Figure 2.5. A very
small pressure rise occurs in the vicinity of each impeller blade. Regenerative
turbomachines are also designed in multistage conﬁgurations to meet certain design

requirements. A two stage regenerative compressor is shown in Figure 2.6.

2.1.1.1 Classification of Impeller blades

The impeller of RFC/RFP can have blades of different shapes. Some of the widely used
types are radial blades, non-radial blades, semi-circular blades and aerofoil blades. Some
examples of these blade shapes are given in Figures 2.7, 2.8 and 2.9. Usually regenerative
compressors with the aerofoil blades are ﬁtted with a core. The core serves to guide the
circulation through the blading and to minimize the loss due to formation of vortices at
the tips of blades. The core can be ﬁxed to the blades and rotate with them or be ﬁxed to
machine casing. The blades or vanes are usually cast into the face of the impeller or
machined at the periphery. The blades can be constructed as a single row, or as two rows

side by side to provide parallel contrarotatin g paths.
2.1.2 Inlet and Discharge Ports

Inlet and discharge ports connect the external system piping to the ﬂow channel. The
ﬂuid enters the ﬂow channel via the inlet port, which is shaped to set up Spiral ﬂow
around the annular channel. The ﬂuid at high pressure is discharged to the piping from

the discharge port. The inlet and outlet ports are shown in Figure 2.4.
2.1.3 Stripper

Between discharge and inlet, the casing clearance is reduced to block the high pressure
discharge from the low pressure inlet. In this region, which is also known as stripper or

septum, the open channel closes to within a few thousandths of an inch of the sides and

14

tip of the rotor and allows only the ﬂuid within the impeller to pass through the suction.
Clearances between the impeller disk and the casing are kept to a minimum to prevent
leakage from the high pressure side back to the low pressure side. The stripper forces the
ﬂuid to go out through the discharge port. The stripper also helps to cause the

establishment and maintenance of the regenerative ﬂow pattern.
2.1.4 Flow channel

Around greater portion of the periphery, the vanes project into an annular channel in
which the cross sectional area is greater than that of the impeller vanes. The casing
contains a ﬂow channel or raceway. It is this annular ﬂow channel through which the
ﬂuid circulates repeatedly through the impeller vanes. The ﬂuid between the vanes is
thrown out and across the annular channel. A violent mixing occurs and the angular
momentum acquired by the ﬂuid in its passage between the vanes is transferred to the
ﬂuid in this annular channel. The rrrixing process is accompanied by production of a great

deal of turbulence, and this implies an undesirable waste of power.

2.2 Working principle

In conventional ﬂuid dynamic compressors and pumps, the predominant direction of ﬂow
through the machine is at right angles to the velocity of the blades, whereas in RFC/RFP
the predominant direction of ﬂow through the machine is parallel to the velocity of the
blades. Superimposed on the parallel ﬂow is a circulation through the blades and around
the core of the annular channel. Every time the ﬂuid passes through the rotor, work is
done on it and its stagnation pressure and tangential velocity are increased. The tangential

velocity is removed, not by a row of stator blades as in a conventional turbomachine, but

15

by the action of tangential pressure gradient around the periphery of the machine between
the exit conditions and the inlet conditions. Thus by the time the ﬂuid re-enters the blade
row, the magnitude of its tangential velocity will be reduced and its direction will be
reversed. Hence during each loop of the spiral, the ﬂuid is accelerated in the tangential
direction as it passes through the blades and is decelerated by the tangential pressure
gradient as it passes round the unbladed part of the channel. Because the ﬂow passes
through the same blade row several times between the entry and the exit, the work done
on it and hence the pressure rise is considerably greater than that which can be obtained
from a conventional turbomachine with the same tip speed. The speciﬁc speed is
therefore low and the machines operate in the usual range of positive displacement
machines. Pressure variation of the ﬂuid as it circulates through the pump for several
ﬂow rates is shown in Figure 2.10. These curves suggest ﬁve regions in the pump

operation, which are also marked in Figure 2.4.

o Inlet region (A): The ﬂow experiences some pressure loss through the inlet region.

0 Acceleration region (A-B): The ﬂow enters the working section of pump with a
velocity and pressure dependent largely on the inlet region.

0 Linear region (B-C): The pressure gradient is constant as indicated in the diagram.
This region is referred to as the working section of the pump where the ﬂow
pattern is fully developed.

0 Deceleration region (C-D): In this region, a deceleration occurs and the kinetic
energy of the circulatory velocity is changed as a pressure rise. Therefore, there is

a little pressure rise as shown in Figure 2.10.

16

0 Outlet region (D): A loss similar to that at the inlet region occurs at the outlet

region.

The head, power, and efﬁciency relationships as a function of ﬂow rate for a typical
regenerative turbomachine are Shown in Figure 2.11. It indicates that comparatively high
heads can be obtained at low ﬂow rates. This is due to the fact that circulatory velocity is
higher at lower ﬂow rate resulting in higher pressure rise. However, the power
requirement is also higher at low ﬂow rates. The maximum efﬁciencies in regenerative

turbomachines occur at comparatively large ﬂow rates as shown in Figure 2.11.

2.3 Comparison of regenerative and centrifugal
Compressors

The regenerative compressors are frequently in competition with centrifugal compressors
for meeting application requirements. Therefore, it is interesting to mention the relative
merits of the two operationally different compressors being widely used in the industry.
Some of the characteristics of both compressors are discussed below.

1. Centrifugal compressors take in the ﬂuid at center of the impeller and push it
radially outward with no axial component of velocity, however regenerative
compressors impart both radial and an axial component to ﬂuid ﬂow.

2. In centrifugal compressors, ﬂuid passes through the impeller only once while in
regenerative compressors, ﬂuid is exposed to impeller many times, thus adding
more energy to the ﬂuid.

3. One of the most signiﬁcant structural advantages of the regenerative type

compressors is that no complex ﬂow passages or vaning is required. They are

17

simple and easy to machine and there is no need of diffusers and scrolls.
Regenerative compressors tend to have more internal components than the
centrifugal compressors, and we can cast the centrifugal compressor impeller with
the outside diameter machined, however regenerative compressor impeller is
completely machined.

Centrifugal compressors have large axial length per stage and large overall
diameter because of diffusers and scrolls. On the other hand, in the regenerative
compressors, the suction and discharge nozzles are at periphery, thus the axial and
radial dimensions are small compared to centrifugal compressor. Regenerative
compressors provide much more pressure rise in a more compact compressor
design.

Performance wise, while it is true that centrifugal compressors are inherently
more efﬁcient than regenerative compressor types, this may not be true under
many conditions. The regenerative compressor is considered a low speciﬁc speed
machine, and in its normal range of speciﬁc speeds, its efﬁciency compares
favorably with that of centrifugal compressors.

The power requirement of a regenerative compressor decreases with increasing
ﬂow rate, whereas the power requirement increases with increasing ﬂow rate in
case of a centrifugal compressor. Moreover, the head and ﬂow rate characteristics
of the two machines are also significantly different.

The centrifugal compressor surges at low ﬂow rate, sometimes at ﬂow rate as
great as 50% of maximum ﬂow rate. In a regenerative compressor, the ﬂow can

be Shut Off without surging; however, there will be a temperature rise. The

18

regenerative compressors have advantages of stability, since they have a stable
operation throughout the ﬂow range (a regenerative compressor will not surge
under any condition).

Since the regenerative compressor does not surge even at zero ﬂow, stage
matching is less critical and off-design Operation less restricted than with the
centrifugal.

Higher rotative speeds and/or a large number of stages are usually required with
centrifugal compressors. Regenerative compressors produce heads several times
greater for a given impeller tip speed. Head coefficients greater than 5 have been
measured on the regenerative types, compared to about 0.7 to 0.8 for the
centrifugal. (The maximum theoretical head coefﬁcient for a radial bladed

centrifugal compressor with zero prerotation is 1.0).

10. The head vs. ﬂow rate graph for a centrifugal compressor is ﬂatter than for a

11.

regenerative compressor. This means that a regenerative compressor can have
more ability to deliver ﬂuid at a variable (desired) ﬂow rate, which is something a
centrifugal compressor lacks. The volume of ﬂuid in a centrifugal compressor is
generally much higher than in a comparable regenerative compressor.

Another difference between a regenerative compressor and a centrifugal
compressor is that in the centrifugal compressor, gain in pressure is proportional
to the square of the peripheral velocity of the impeller, whereas in a regenerative
compressor it is the relative velocity to the blades that depends on the pressure

gradient.

19

12.

l3.

14.

15.

2.4

The clearances for regenerative compressors are held to closer tolerances than for
the centrifugal compressors.

The radial positioning is important in some centrifugal compressor designs; axial
positioning should be within about 0.05 inch. In a regenerative compressor,
however the axial positioning is within 0.01 to 0.03 inch; radial clearance of 0.01
to 0.020 inch (depends on machine size).

The centrifugal compressors have no radial shaft loading except gravitational, but
with usual design there can be high axial loading. However, in a regenerative
compressor there are no axial shaft loadings with usual design, but there is a
radial loading due to pressure difference around periphery.

The regenerative compressors have an advantage on centrifugal compressors in

quietness and problems due to wear are minimal.

Applications

Although the efﬁciency of RFC/RFP is not very high, being usually less than 50%, still

they have found many applications in industry because they allow the use of rotodynamic

action

in place of positive displacement actions. They are being used in increasing

number of applications that require high delivery head at low ﬂow rates. The relative

simplicity Of construction and stable operating characteristics of the regenerative ﬂow

compressors are making them more and more attractive to users in several areas,

including chemical, petroleum, and nuclear industries. The regenerative gas compressors

and liquid pumps have important applications as gas circulators and liquid pumps in

accessory systems to the above mentioned activities. RFCs have been proposed for use in

hydrogen gas pipelines and as helium compressors for cryogenic applications in space

20

 

vehicles. If hydrogen comes into widespread use as a synthetic fuel, large scale pipeline
transmission of gaseous hydrogen becomes necessary. Compressor stations along these
pipelines will be required to boost the pressure, as is now the practice in natural gas
industry. Utilization of regenerative compressor as a hydrogen pipeline compressor offers
several advantages as discussed by Hollenberg [30]. RFCs can also be used as natural gas
pipeline compressors; in fact, they can be designed to handle both natural gas or
hydrogen or any mixture of the two. Further, it may be possible to accomplish this in a
single design, which can be adjusted to handle a varying mixture by speed control or
other means. Crowe and Schwarz [18] developed a helium regenerative compressor
operating on hydrodynamic gas bearings. It was designed for use in Ultra High
Temperature Reactor Experiment (UHTREX) because of the highly radioactive system
contamination resulting from the investigation of unclad fuel elements. Moreover, RFCs
are advantageous for incorporation in small closed cycle helium refrigerators. Gessner
[25] reported the development of a four stage regenerative compressor, which was
employed in the development of a highly reliable, long life cryogenic refrigerator for
space vehicle application. One of the recent applications is in accessory loops and
auxiliary systems for nuclear pile operation. They have been considered for pneumatic
control drive mechanisms for reactor control systems. Grindell [26] developed a
regenerative compressor for gas cooled in-pile loops. Another application of RFCs is in
plants, which can be used to separate isotopes of gases whose speeds of sound are in the
300-600 ft/sec range. This takes the compressor operation in the compressible ﬂow range.
Because of the reliability, compact size and low maintenance, recently there is an

increasing use of regenerative compressors in low pressure (0.2 - 15 psig) natural gas

21

compression required by rrricroturbine systems. Other applications of RFC include
boosting and recycling of hydrogen mixtures and hydrocarbon gases, gas phase reactor
recycling, molecular sieve regeneration in gas drying processes, vent/purge gas recovery,

fuel gas boosting for GT feed and gas compression in many other industrial processes.

Regenerative blowers are also getting popular in industry. There have been various
publications describing different applications of regenerative blowers in industry. Figure
2.12 gives the typical operating range of certain type of blowers. One advantage of
regenerative blowers is that relatively simple design changes can produce signiﬁcant
changes in shape of the pressure-ﬂow curves as shown in the Figure 2.13. Pressure is
proportional to the square of impeller diameter, and ﬂow is proportional to the cross
sectional area swept by the impeller. Therefore, special blowers matched to a particular
application may be only a little more costly than standard blowers. Manufacturers can
tailor the characteristics of a particular model by varying impeller diameter, impeller
cross sectional area, and clearance between impeller and easing.

Cundari and Nuti [19] described the use of regenerative blowers in scavenging of small
S.I power plants. The regenerative blower was found to be the most suitable option since
it was able to match the engine air breath demand all over its utilization range.
Regenerative blowers have found many industrial applications in solids conveying
systems. Historically, the pressure and ﬂow rates demanded by many solids conveying
systems made roots or vaned-type blowers the almost automatic choice despite their
limitations. Some conveying systems operate during severely restricted hours because of
the noise of roots type blowers normally used. Many packaging and paper handling jobs

were historically beyond the regenerative blowers capability, but now with increasing

22

emphasis on working environment, the low noise regenerative blowers are welcomed in
these areas. Regenerative blowers also find use in sewage treatment and anti-icing
services, both of which require considerable volume to be blown against a head of water.
There is increasing interest in customers for use of regenerative blowers to provide air for
ﬂuidizing powder products in bag ﬁlling machines; in pressure and vacuum conveying
machinery and for use in the textile industry to provide vacuum for removing stray fibers
and lint from knitting machines. Regenerative blowers are also used for powder coating
recovery applications, plating, cleaning and rinse tank agitation. Since regenerative
blowers provide high airﬂow capacities at low pressure differentials, they become
excellent for air moving applications, such as agitation of bath or aeration of a pond.

RFPs ﬁnd applications in automotive and aerospace fuel pumping, booster systems, water
supply, agriculture industry, shipping and mining, chemical and foodstuff industries and
regulation of lubrication and filtering. One of the advantages of regenerative pump is that
operation under cavitation does not generally lead to mechanical failure. More

advantages of RFP are discussed in chapter 7.

2.5 Limitations and Challenges

Main limitations of regenerative turbomachines are:
1) Low efﬁciency levels in regenerative turbomachines compared to those levels
enjoyed by centrifugal compressors and pumps.
2) Low range of speciﬁc speed.

Some of the vital challenges faced by regenerative turbomachines are discussed below:

23

 

l) The biggest challenge faced by regenerative turbomachines is to raise the
efﬁciency beyond the levels reached already. This can be achieved by means of
improving ﬂow guidance in the compressor.

2) The speciﬁc speed range can be extended by designing for higher ﬂow rate
through improvement in the inlet and outlet ports, creating a better match of the
blading geometries. As a side beneﬁt, this may also contribute to the raising of
efﬁciency if the inlets and outlets can also be designed to provide some turning
for the ﬂow.

3) Most of the performance data available in literature dealt with relatively low
Mach numbers. Performance data are much needed where compressibility effects
must be considered.

4) Research on multistaging presents a big challenge in regenerative turbomachinery.

5) Investigation of ﬂow passage geometry (shape and channel area distribution along
the periphery) is a critical factor for performance.

6) Improvement in geometry of the impeller vanes (bending radius, height,
penetration and angle) is another challenging area.

7) Improvement in location, orientation and area of inlet/outlet ports can create huge
difference in efﬁciency.

8) Investigation of axial and radial clearances can improve performance.

2.6 Conclusions

The detail insight in regenerative compressors and pumps gives an idea of the hidden
potential in these turbomachines for duties requiring high head and low ﬂow rates. The

compact size, high reliability and low noise of regenerative turbomachines make them

24

attractive in certain applications. Better efﬁciency at low speciﬁc speeds makes them a
tough competitor of centrifugal turbomachines in low speciﬁc speed applications. Thus,
there is a need to do research and make design changes in RFC/RFP to improve their

performance and make them more attractive to industry.

25

 

/ ’

/'

“4Q;
- “J

:«7 ’
N.»

\
\
=: \\ ‘
\
\

’ ' o
. 'i'l.’ .0
\u o
’ 9'. .0
.\/l' ' ..
o
C
.
.9
.‘

 

 

Figure 2.2 A regenerative turbomachine (after Moffat [41])

 

Efficiency vs. Specific speed for various oormressors ‘
l
l

 

d

 

l — Initial Regenerative designs |

—FIegenerative designs by
most manufactures

l
|
—-—Advanced Regenerative ‘
1 designs l

l

Efﬂclency
.° .O .O .0
N -b 0) OD

 

———Centrifugal compressors

O

05101520253035404550!

Specific speed
L_____L_mr LL ___ L

 

 

 

 

Specific Speed = N, = J53“
H:
where, Q (ft’lsec), (I) (rpm), H (ft)

Figure 2.3 Efﬁciency vs. speciﬁc speed for various compressors

 

Ll,‘ 67" l/ ’/A”// ’1' 4 I 1 //

, /
Stripper
\\
3:1}:E :::\ ‘

A
r l l I ,’ A
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t'/ / {/1 L f l’vi/v'il
Acceleration { T/ \J/ [Cox “ -.V/"
W1

 

 

 

 

 

 

 

 

 

Deceleration > \SN ,\ l .
. z 2' . . , /
Reston , .. \ - \ Region V . , ”99/”‘2. [4,.
I I, /'«l/ 1/ . \ ":4
// // {//L; [,1]. / V/ '// / I .//‘ V X I, 7:4’x (,4
STATION B //// / / STATION A r. I/L .//,/ , 71/, ,/ r44" ,7. 71,‘
I I 1 ﬂ vi, ,4 I, V : ;' ll I ll’tr / ,
_. / ////’/./ I: /// [ff/l, {<0 (”T/x17;
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// ///: r/r'i/ 4.4 ”/04“ 01/. r"'///,"'///"/
"' , , /:-, Flow Path ,... // / ’/,»,/.{//i/,.» ..//4. 1;» /,.
// ’ -~’,' 47/. '/.i
’0 Casing :17; ,2;.v-,//';::>--1
‘ r',0‘,ﬁ,/x’/ //
,, [In/,I/A.
(f////lil"l_,/', ,‘/’//’/1
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Linear Region Cam me r, ,7, ,. ./
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Figure 2.4 Schematic of a regenerative Figure 2.5 Section A-A Enlarged (Radial
turbomachine Blade)

27

 

\\\

 

 

 

 

 

 

 

VA\\\\\ \

 

 

 

 

 

1'7""

 

 

 

Blades

/\

\\\\V

 

 

 

 

 

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P 8/

Figure 2.6 Layout of a two-stage regenerative compressor (after Sixsmith [60])

 

 

 

28

//A£// ’ ////////l

 

 

 

 

 

 

 

\\\XAAA§AQ\\.
\X\X\\\\\\
\AELX\NQRX§\
\\\\\\x\\\\

 

 

 

73S [5’9

 

 

 

 

 

we“
%
é

 

 

 

 

 

 

 

 

 

 

 

C!
TN
1\

Figure 2.7 Regenerative turbomachines with radial and non-radial blades (after Abdallah
[1D

29

 

 

 

 

K\\ /

 

 

RR:

Figure 2.8 Regenerative turbomachines with semi-circular blades (after Abdallah [1])

30

 

 

Figure 2.9 Regenerative compressors with aerofoil blades (after Abdallah [1])

 

 

 

 

 

 

 

 

 

 

 

A
lower
flow rat
poutlet
A
prise
design
VLilow rate
SS. pinlgt y
\
I. - - 24.] higher
' flow rate
ApinletlossT \ . k
. A . TlL Q .QF'
Inlet Accelera on Linear eceleration &
_outlet
gpumping QStripper

Figure 2.10 Tangential pressure variation in a regenerative turbomachine

31

 

r.____ﬁ__ﬁ___wv___ ___. ___—___.___-_____L._4_

 

Efficiency, Head and Power vs. flow

 

 

 

 

 

 

 

 

Efficlency, Head and Power

 

 

 

 

 

 

 

 

140. ~ ~ — r— ~
120— ————~~———~——————————i———~——-
100
80 \\ —Efliciency. 7
\ —ldealEflicrency l
60 —Power ll
.. x .________.|
20 WW“ \ \ -—. ’
o “- 1

Flow

Figure 2.11 Performance characteristics of regenerative turbomachines

 

 

 

 

“7* ROTARY LOBE PosITIVE
’ DISPLACEMENT BLOWERS #400
.6]-
, -I
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II ‘9
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orsm. CEMENT . .
‘ GLOVE ' S
o ItIIIr-JrI-Idau(31:1!ch_I-zibxr'H-J- .
10 20 so 100 200 500 1000 2000

F LOW (m’lh)

Figure 2.12 Blowers typical Operating range (after Roppenecker [51])

32

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8 \ I4.0
6 \ \ 10.5
<
'5’ ‘\ i
a
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e N \ ‘5‘:
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oi . o
5 10 20 50 100 200 500 1,000 2,000
Flow (scfm)

Figure 2.13 Pressure ﬂow curves of Regenerative Blowers (after Roppenecker [51])

33

CHAPTER 3

LITERATURE SURVEY

3.1 Introduction

Regenerative turbomachines have appeared to originate in either Germany or Holland
after the First World War. Although they have found many applications in industry, still
they are the most neglected in the family of dynamic turbomachines. The number of
publications existing in literature is very small compared to the large number of papers
about the centrifugal and axial turbomachines. After there origin, they became the subject
of a number of doctoral theses at German technical universities during the period
between the wars. Regenerative turbomachines have been studied as pumps, turbines,
blowers and compressors. Most of the existing literature can be broken down into ﬁve
broad areas of regenerative turbomachine research:

1) Theoretical Models

2) Experimental work

3) Impeller blade Proﬁle

4) Loss categorization

5) CFD Analysis
The literature survey presented in this chapter is based on work done in regenerative

turbomachines in the above mentioned ﬁve areas. The idea behind discussing both RFC

34

 

and RFP together is due to the very close resemblance in the operating principle of the

two machines.

3.2 Theoretical Models

Some investigators after the Second World War attempted to develop rational theories for
the type of ﬂow developed within a regenerative turbomachine. Various theoretical
models have been used in attempts to describe the ﬂow in regenerative turbomachinery.
One school Of thought, the leading exponents of which were Crewdson [17] and Iverson
[34] postulated the essential ﬂow mechanism as being one of drag induced by the
impeller on the stationary ﬂuid in the Side channel. Iverson put forward a viscous model
for the performance. He analyzed the performance of regenerative pump in terms of shear
stresses imparted to the ﬂuid by the impeller. The performance equations were derived by
considering a linear system with a linear motion of rough surface as shown in Figure 3.1.
A force balance on the ﬂuid in the horizontal ﬂow channel was applied to derive
performance equations. The resulting expressions included two shear coefﬁcients and an
average impeller velocity, which were determined experimentally. The output head,

power and efﬁciency of the pump were given as

 

 

 

 

2 2 2
H _C._-U_[(,_E) -2119.) j (3,.)
2A UA c,a,. UA
3 2
P: Quiz/9U (17sz (3.2)
Q 2
,7: PQSH =_Q__ 1_Crac /UA (3.3)
P UA Cid, 1_QUA

The shapes of the head, power, and efﬁciency curves as a function of ﬂow were predicted
as Shown in Figure 3.2. The shear coefﬁcients and pump performance were shown to be
functions of impeller roughness and ﬂow area. This gave a characteristic of increasing
pressure with decreasing ﬂow rate with a concave form. Thus, the predicted maximum
ﬂow rate was some 23% higher than was practically found, probably due to losses. The
predicted shapes of performance curves were found to be in reasonable agreement with
the test curves as reported in Iverson [34]. Certain explanations of observed performance
were obtained by means of this hypothesis which however proved to be limited in
explaining complete features of performance. The procedure outlined by Iverson is not
directly applicable to the prediction of performance of any selected pump geometry due
to the unknown magnitudes of the Shear coefﬁcients and effective vane velocity, but at
least it provides a simple representation of the performance of regenerative pumps.

Balje [8] examined the regenerative turbomachines using a simpliﬁed approach
analogous to Iverson. He concluded that the optimum efﬁciency Of a regenerative turbine,
based on experiment is 35%, which is less for regenerative pumps. Theory presented by
Balje enabled fair prediction of regenerative turbomachine performance for compressible
as well as incompressible media, accounting for the inﬂuence of design geometries on
performance range and peak efﬁciency.

Wright disagreed with theories presented by Iverson and Balje indicating that they did
not take any account of the blade shape, which is of great importance [34]. Wright
suggested an alternative theory in his discussion of Iverson’s work based upon a
momentum transfer between the blade row and the ﬂuid in the channel. The major

ﬁnding of Wright’s theory was his suggestion that it is possible to increase the pump rpm

36

without increasing the shutoff pressure rise, if the blades were given a suitable backward
curvature. Thus he found that by increasing the speed of such a device and by curving the
blades backwards, the same pressure rise was possible, demonstrating the inadequacy of a
purely viscous Iverson and Balje model.

Wilson, Santalo and Oelrich [69] presented a hypothesis of regenerative pump operation
by considering a helical ﬂow and made various allowances for losses and provided
experimental corroborations of their results. Theory presented by Wilson was based on
the idea that the ﬂuid gains angular momentum in the impeller and then imparts it to the
slower moving ﬂuid in the casing channel. The ﬂuid re-enters the impeller with a lower
angular momentum. The rate of change of angular momentum is the torque exerted by
the impeller upon the ﬂuid. An analysis based on the hypothesis led to a series of
expressions for pump performance over the entire operating range in terms of only three
empirical constants. The basic model developed by Wilson [69] was to represent the
phenomenon in the linear region as Shown in Figure 2.10. He made several assumptions
and applied ﬂuid dynamic equations to arbitrary control volumes of the pump. The entire

pump ﬂow was characterized by the tangential velocities V, and circulatory velocity V,

along a mean streamline. The overall head rise, net power input and efﬁciency of the

pump were given as

 

2
gH=ép£=-Q—C-(0U§—aUlz)—K,[ Q ] (3.4)

2
P=st[gH+K,[ Q2]] (3.5)

 

37

_Q.

 

pQgH Q3
27: = , (3.6)
P ,,_K_.Q_4
gH (2r2)

The dimensionless performance characteristics of STA-RITE TH 7 regenerative pump
were tested and reported by Wilson [69]. The experimental plots of ﬂow versus head
were obtained at seven different speeds with air as working ﬂuid. The calculated and
experimental performance curves were compared and excellent agreement was observed.
Qualitatively, the relations presented by Wilson satisfied the major details of the
observed ﬂow phenomena, but it was only limited to predict the head—ﬂow characteristics
in the linear region of the pump. His model assumed incompressible ﬂow, thus unable to
predict performance of compressors producing high pressure ratio. Moreover, Wilson’s
model lacked in correlation of losses with geometric and aerodynamic parameters. The
most remarkable aspect of the design was that it only required three performance
parameters to describe performance of the regenerative pump throughout its operating

range.

The circulatory ﬂow mechanism on which Wilson’s theory was based was recorded by
Burton [13] using an experimental machine with Perspex walls. Small energized beads
were introduced into the stream and their path was recorded photographically. Burton
presented a theoretical and experimental analysis of regenerative pumps and regenerative
turbines. His analysis led to expressions for turbomachine performance over entire
operating range in terms of empirical constants. The coefﬁcients of the theoretical
equations were chosen to give the best overall match to their experimental results.

The characteristics obtained by Wilson [69] were not dissimilar to those found by

Whitehead [68], although both authors used machines considerably different

38

geometrically. Therefore direct comparison was not possible between their works.
Whitehead experimentally investigated the performance of a Reavell RCSO regenerative
compressor. He found a maximum aerodynamic efﬁciency of 44% occurring at a speciﬁc
speed of 0.05. The mechanical losses were signiﬁcant and reduced the efﬁciency to 30%
at maximum speed. A theoretical model of the internal ﬂuid mechanics was presented in
his paper which assumed that the blades are unstalled and circulation is zero at inlet to the
machine. The assumptions in the model were poor, since the blades were stalled most of
the time. The predictions were not in good agreement with the experimental results.
Another ﬁnding by Whitehead was that the performance is affected to some extent by
Mach number effects, however Reynolds number effects were found to be negligible.
Many authors have reported simpliﬁed theoretical models for regenerative pump with
different blade designs. Grabow [23] developed a theoretical model for both radial and
semicircular blades. Abdallah [1] extended Grabow model to develop a theoretical model
for the regenerative compressor with aerofoil blades. This model included inlet effect
which was neglected in most theories. The correlation between theoretical and
experimental pump performance showed close agreement.

Wilson et a1. [69], Burton [13] and Abdallah [1] developed theoretical models to correlate
the performance of the machines on the basis of the recirculating ﬂow pattern. However,
all these methods suffer from two basic defects which severely limit their use as a design
tool. The ﬁrst of these is that they contain empirically derived loss coefﬁcients which are
not directly related to geometric and aerodynamic parameters. Therefore, they give no
indication of how the design might be modiﬁed to reduce the losses and cannot be used to

evaluate designs which differ Significantly from those on which the models are based.

39

The second defect is that they are mainly useful for incompressible pump ﬂow, thus
making them inaccurate for compressible ﬂow in RFC. Thus these models are unable to
provide any design guidelines.

El Hag [22] developed a theoretical analysis of regenerative pumps. He derived ﬂow
equations for regenerative turbomachines revealing that the familiar Euler equation for
the head across rotordynamic machines has to be supplemented by an extra term
accounting for the tangential pressure gradient so that it can be applied to regenerative
turbomachines. Thus, in order to compute head rise, the tangential displacements of ﬂow
in the rotor have to be computed. In his analysis, a section of pump circumference was
deﬁned and it was assumed that tangential pressure gradient is essentially constant. In
this section, ﬂow was modeled such that when the principles of ﬂuid mechanics were
applied to it, the resulting ﬂow equations were solvable by numerical methods with the
aid of a digital computer. The ﬂow equations derived in his work enabled detailed
calculations of the ﬂow in the linear section of these machines. He gave the net increase

in the ﬂuid head between any two points 1 and 2 at the same streamline in the impeller by,
1 3p
A(gH)=(U2V92-—U,Vm)+——At9—gHL (3.7)
p 86
The ﬁrst term on the RHS of equation 3.7 is the familiar Euler’s head. The second term is
the energy added to the ﬂuid because of its angular displacement (t92 —6,)in a ﬁeld in
which there is a tangential energy gradient 3H / 86. E1 Hag [22] showed the variation of

ﬂuid energy along a ﬂow cycle on energy gH -angular displacement ((9) plane as shown

in Figure 3.3. He considered ﬂow along a streamline, which starts just inside the impeller,

passes through the impeller exit, goes through the channel and reaches just inside of the

40

 

 

 

 

impeller for next circulation. The losses experienced by this streamline were compared
with the ideal ﬂow cycle as shown in Figure 3.3. In Figure 3.3, actual ﬂow cycle is
indicated by 123.3 and the ideal cycle is represented by path 145. The increase in the
ﬂuid speciﬁc energy is given by

A(gH)a =(gH3—ng) (3.8)
Analysis by El Hag did not involve empirical factors which are needed to be determined
experimentally from tests on the pumps like in the case of Wilson [69]. However, well
established loss empirical parameters, such as the friction loss factors of ﬂows in conduits
were used to estimate losses where appropriate in the analysis. The proposed method
predicts the performance of a given pump, provided shape and dimensions of impeller,
the dimensions Of the channel, the number of blades, the stripper angle and clearances are
known. However, the model presented by El-Hag is also limited to regenerative pumps.
Hollenberg [29] did an experimental and theoretical analysis on regenerative pumps and
blowers and reported the parameters controlling their efﬁciency. He presented a
correlation between torque, pressure and ﬂow rate which was dependent only on one
experimental parameter. This correlation was used to examine the variation in efﬁciency-
Speciﬁc speed characteristics of regenerative turbomachines over the range of their
probable designs. The maximum efﬁciency was shown to be a function of radius ratio
parameter and a friction head coefﬁcient ratio.
Kupryashin [30] discussed theoretical approaches to design of regenerative pumps. Both
approaches adopted by Wilson and Iverson were discussed and proved unsuitable for
practical calculations because of the analytically indeterminate coefﬁcients contained in

the performance curve equations. He recommended the circular radial section as most

41

favorable due to its promotion of the secondary circulation. Experimental results were
presented showing pump efﬁciencies close to 50 %.

A more theoretical approach was taken by Jakubowski et a1 [35]. They analyzed
rotational ﬂow of an incompressible, non-viscous ﬂuid in a toroidal enclosure. However,
the cumbersome nature of the mathematics involved and the simpliﬁcations necessary to
obtain a solution limited the usage Of the model.

Schively [53] theoretically solved the ﬂow within a regenerative pump assuming a one-
dimensional ﬂow model. In his model, all signiﬁcant variables were given as function of
only the radius. He divided the ﬂow in the vortex chamber into three regions and
analyzed the ﬂow by applying the Navier Stoke’s equations and momentum balance for
each region. The performance of a simple regenerative pump was also investigated
theoretically and experimentally by Bullough [10], however the model was not able to
predict performance of any given pump design.

Senoo [55] reviewed both viscous and momentum exchange theories and found them
compatible with the differences occurring only in their assumptions. The theories
discussed in his paper were developed for incompressible ﬂow. The experimental data
which had been examined till that time showed that none of these theories was broad
enough to cover all the inﬂuences that the geometry had on the performance. This
remains true to this day even though we are now interested in extending the theories and
design into compressible ﬂow range.

Theories for the ﬂow of compressible ﬂuid in regenerative turbomachines are rarely
found in literature. Burton [11] made an effort in this direction and reported a Simplified

theory, which took account Of area change and compressibility effects in regenerative

42

turbomachines. He assumed that energy exchange is obtained through shear stress
between the impeller and the ﬂuid in casing. Any radial components of ﬂow were
ignored. The continuity, momentum and energy equations were applied to a linear control
volume and differential equations were obtained. Following differential equations were
derived in Burton [11]:

Continuity:

dp__ d(AVm)
,o _ AVm+ARUp (3'9)

Momentum:
R 2 -2 +2b+t AU V
FIE: PM ’° )fR[(Up—vm)2—iv,;]da+—LL”L£’£—ﬁn—dvm (3.10)

p 248 Ag p s
where,

’1: fr 2bl +2b2"!
fR 2h+t

Energy:

 

11”.: Cp [1+ AV” )dnA—VMV—mdvm +-—1—(U; —V,3)i-’i
p

 

p ARUP ARUP g 2g (3“)
R 2 —2 +2b+t
_ P( r22 ’1 )fR(Up-Vm)2d6
gAR

The equation of state can also be used for gases showing behavior close to perfect gas.

p = pRT (3.12)
The equations presented by Burton comprise a set of equations for determining the
performance Of a compressor if the speed, gas, and compressor geometry is Speciﬁed.
Burton’s model was also based on shear stress theory which was experimentally proven

as unable to explain the ﬂuid motion inside regenerative turbomachines.

43

Given dearth of design information in regenerative turbomachinery, it is hardly surprising
to know that most designs of regenerative turbomachines retained a fairly basic
geometrical conﬁguration with simple vanes either machined or cast into the impeller.
However, the addition of a core in the ﬂow channel to direct the circulating ﬂow together
with the provision of aerofoil blades was Shown by Sixsmith and Altmann [60] and it
resulted in signiﬁcant improvements in the performance. They replaced the radial vanes
by blades with an aerofoil section as shown in Figure 3.4. The blades were designed to

transfer momentum to the ﬂuid with a minimum of turbulence and friction. They were

designed to turn the ﬂuid through a deﬁnite angle, which preferably should be about 90°.
The annular channel had the core to assist in guiding the ﬂuid such that it circulates
through the blading with a minimum of loss. The core also acted as a shroud to reduce
losses due to formation of vortices at the tips of the blades.
The enthalpy transfer by the action of blades on impeller in one blade passage was given
as

AHo =a)(r2W2 sin ,62 +r3W1sin/3l) (3.13)

The mass ﬂow rate through the blading was estimated by
M3 =27r(1—F_,.)r°LlpIchosﬂ (3.14)

The forward mass ﬂow rate through the ﬂow channel was estimated by

MA zﬂME’i‘w. +U2+Wzsinﬂz—Wlsin,61) (3.15)

The number Of times ﬂuid passes through the blades N was Obtained by dividing the

mass ﬂow rate through the blading by the mass ﬂow rate through the annular channel, i.e.

47t(1— F, )r,L.p,W1 cos/31

:pMAr(U]+U2+Wzsinﬂ2-Wlsinﬂ.) (3'16)

 

44

The pressure ratio was related to the enthalpy of a Stream Of gas being compressed from
H, to H2 in the form of the following equation

MCPT. p, [77']
=——— H

M(H2_Hl) 77 p]

-1 (3.17)

Relationship between the inlet velocity with respect to the blades, the pressure gradient in

the annular channel and the geometry of the annular channel was given as

 

 

1 2 (Pz-Pl)S
—pW = (3.18)
2 l L[l+ All )[Ahsmﬂzooszﬂﬁinﬂoosﬂj

p212 pzlawsﬂz

whereS is the circulation distance from trailing edges to the leading edges of blades
perpendicular to blade motion.

An interesting conclusion drawn by the authors was that the pressure gradient is
dependent on velocity of the ﬂuid relative to the blades and not on the velocity of blades
themselves. Conversely, and more correctly, it is velocity relative to the blades that
depends on the pressure gradient. This is one signiﬁcant difference between a
regenerative compressor and a centrifugal compressor. In a centrifugal compressor, the
gain in pressure is proportional to the square of the peripheral velocity of the impeller.
Regenerative compressor tends to behave like positive-displacement machines such as a
roots blower. The torque is almost directly proportional to the pressure difference across
the ports. Sixsmith and Altmann [60] constructed two regenerative compressors with
aerodynamic blading to validate the theoretical results. The efﬁciency was considerably
improved compared to the efﬁciency of regenerative compressor tested by Wilson [69]

who employed the radial blades. These authors reported a performance comparison to

45

illustrate the advantages of aerofoil blade RFC over purely radial blade RFC design as

Shown in Table 3.1.

3.3 Experimental Work

The earliest investigators on regenerative turbomachines were concerned with exploring
over a wide range, the effects of varying geometry on the design of regenerative
turbomachines. The experimental work involved varying the proportions of blading to
coverage of the side channel over the blading, shape of the side channel and blade
proﬁles. As a result of these investigations, a great deal of information was derived but
still not allowing one to reach the optimum proportions for conventional regenerative
turbomachinery design.

Bartles tried to experimentally investigate exact ﬂow mechanism in regenerative
turbomachines. He tested three rotors in same pump casing. The ﬁrst rotor was a smooth
disc having no grooves or vanes, the second was grooved out to leave the radial vanes of
conventional design, and the third had conventional radial vanes plus additional vanes
normal to them. He proposed that if the ﬁrst rotor pumped, it would have to be due to the
viscous drag of a smooth metal disc. If the second rotor pumped, it might be due either to
the shearing stresses of viscous and turbulent drag or to the mechanism in which the ﬂuid
circulates into and out of the impeller along helical paths under the centrifugal forces. If
the third rotor produced pumping it would prove that the shearing stresses are the primary
force causing the pumping because any possible radial ﬂow was largely prevented by the
cross blades. If it did not pump or was largely rendered ineffective, it implies that the
pumping was caused mainly due to the centrifugal action because the shearing capacity

of the radial blades could hardly be affected by the cross blades. He found that the pump

46

would only work when the impeller design permitted circulatory motion and centrifugal
pumping, thus supporting Wilson’s regenerative theory of pumping mechanism in these
turbomachines.

Crewdson also examined the role of the circulatory ﬂow or the centrifugal pumping in the
process of enthalpy transfer in a regenerative pump. He soldered a thin brass Strip along
the middle of the side channel so that the side channel was divided into two parts. Thus
any circulatory ﬂow which is mainly radially inwards in the channel would be greatly
affected and it might have been splitted into two: one in the lower part of the channel and
one in the upper part. The effect of this arrangement on the ﬂuid motion inside the
impeller could not be easily judged. However, the suggestion was that although greatly
hindered, the circulatory ﬂow was not eliminated completely because there were still the
centrifugal forces present although the channel was split into two. From the performance
curves, it was concluded that the reduction in the circulatory ﬂow greatly reduced the
pumping effectiveness.

Pﬂeiderer summarized early German and Japanese (prior to 1949) experimental work in
which the variation of impeller and side channel geometry was examined for its effect on
the performance curves of the machine. He also presented a one-dimensional momentum
analysis for the head developed and gave a Simplified design approach based on this and
available experimental data at that time.

Mason [39] carried out an experimental investigation of a regenerative pump with two
channel diameters (2 inch and 1.25 inch), each with 40 and 20 blades in the pump
impeller. He compared experimental performance characteristics with a theoretical

analysis of the ﬂuid dynamic mechanism of regenerative pumps. He aimed to correlate

47

empirical parameters with pump geometry, however no obvious relation could be found.
Bicard [9] designed a new inlet for a regenerative pump based on a proposed model of
the ﬂuid dynamic mechanism in the inlet region. He achieved some improvement in inlet
design by getting an increase in linear region of the channel and therefore increasing the
head across the channel.

Senoo [57] experimentally investigated the inﬂuences of the suction port location on the
characteristics of a regenerative pump. He established that when the inlet port is very
close to the barrier, the ﬂuid enters the pumping passage too far upstream where the
impeller effect is not fully realized. A pressure difference is thus needed between the inlet
port and the entry region to maintain the incoming ﬂow. Such a pressure drop constitutes
a considerable energy loss when the discharge ﬂow rate is high because the necessary
acceleration is high. He reported that the pump performance could be improved
considerably if the inlet port is appropriately located downstream from the barrier such

that ﬂuid entered the pump passage in a region where the impeller effect was reasonably

established. He gave the ﬁgure of 65° for the angle between the barrier and the inlet port
as the optimum angle for the design he considered. However, such a parameter was not
correlated with other design parameters.

Shimosaka and Yamazaki [58] investigated the effects of varying the dimensions of the
channel, impeller and the clearances. Fixing some of the dimensions, they established the
effects of varying the other on performance of the pump. They found that, due to the
numerous variables involved, it was not possible to establish a comprehensive scheme for
the performance prediction. They concluded that the dimensions of a high efﬁciency

pump can be obtained by systematic experimentation.

48

There is very limited data available on gases as the working ﬂuids in regenerative
turbomachines, resulting in a scarcity of design information. Organizations which have
done some experimentation with gases include the United Kingdom Atomic Energy
Authority, Mechanical Technology Incorporated, Massachusetts Institute of Technology,
the Los Alamos Scientiﬁc Laboratory, Compair Ltd., of Ipswich and the Oak Ridge
National Laboratory (ORNL); however, most of their work dealt with relatively low
Mach numbers. Performance data with compressibility effects considered are needed in
many areas that affect performance, including ﬂow passage geometry, impeller blade
geometry, nozzle design, radial and axial clearances and multistaging. The research at
ORNL was aimed at utilizing the regenerative machine as a light gas compressor and
circulator in the gas-cooled reactor designs, which were being developed at ORNL. Oak
Ridge gaseous diffusion plant studied performance characteristics of the regenerative
compressor on gases covering a wide range in molecular weights from 4 to 400 and
speeds from 5000 to 14000 rpm. Cates [15] published a paper and reported the test data
of the regenerative compressor with a variety of gases having molecular weights of 4 to
400. He presented general characteristics in Mach numbers extending well into the
compressible realm of operation. The regenerative compressor operated satisfactorily
without surging or unstable operation with the variety of gases. Compressibility effects
had an important inﬂuence on performance because lower pressure ratios were measured
at impeller tip Mach numbers approaching 1.0. Isentropic efﬁciencies over 50% were
measured at low Mach numbers. Generally, the efﬁciency was lower at higher Mach
number and went down as low as 10% at Mach numbers exceeding 1.1. Performance map

of ORGDP-l regenerative compressor was reported in Cates [15]. The total pressure ratio

49

was plotted against speciﬁc mass ﬂow with tip Mach number as the speed parameter. It
was noted that pressure ratio with various gases increased fairly consistently with Mach
number up to 0.769, after that there was a detrimental effect to pressure ratio with further
increase in Mach number. It is thought that compressibility effects start to appear at such
a high Mach number. Cates calculated the compressor efﬁciencies based on an isentropic

process between suction and discharge pressure as ideal. This isentropic efﬁciency 775 was

deﬁned by

 

(3.19)

where HOD , HOS were average total enthalpies at discharge and suction respectively

and HOD was total enthalpy at discharge total pressure along the isentropic path. He

treated the test gases as perfect gases with CP and y evaluated at an average of the

suction and discharge temperatures. The isentropic efﬁciency can be rewritten as

 

11:1
{—1
Clam-T.) ”in
775 =————><100= x100 (3.20)
CP(T1 -Tl) (Ti-71)

Efficiency was plotted with specific mass ﬂow rate for several test gases. It was observed
that values of :75 greater than 50% were obtained under certain conditions. The efficiency
generally decreased with increasing Mach number. Moreover, pressure level or Reynolds
number appeared to effect efﬁciency described by data measured on air at 2, 6 and 10

psia which exhibited a decrease in efﬁciency with an increase in pressure level.

Generally speaking, where different gases were tested at the same Mach number, the

heavier ones showed lower efﬁciencies. Also, very low efficiencies were measured when

50

the tip Mach number exceeded 1.0. The performance of compressor on the various gases
in terms of ‘P—l curves is Shown in Figure 3.5 with approximate efﬁciency contours

included. The head coefﬁcient ‘1’ and ﬂow coefﬁcient A were deﬁned as:

gH
‘I’ = — 3.21
U,2 ( )
Q
= -—‘ (3.22)
UZAC

where H is developed adiabatic head, Q, is suction volume ﬂow rate and A, is cross

sectional area of open channel.

It must be noted from Figure 3.5 that at small ﬂows, the efficiency was lower and the
delivery head was also found to be reduced. The logarithmic plot of the head coefﬁcient
as a function of tip Mach number is given in Figure 3.6 for three values of ﬂow
coefﬁcient. At low Mach numbers, ‘I’ was nearly constant for a given ﬂow, however,
when compressibility effects began their inﬂuence, ‘I’dropped off rapidly. Cates also
reported the effects of changes in ﬂow channel geometry on compressor performance.
The effects of the geometry changes were quite different at different Mach number levels.
Moreover, Cates presented the effect of impeller-to-casing clearances on pressure ratio as
shown in Figure 3.7. The regenerative compressors have been described in the literature
as machines which require small clearances between the rotating impeller and the
stationary casing at the stripper section and sides in order to minimize cross leakage. The
conclusion that was reached by the tests performed by Cates indicated that increasing
impeller-to-casing clearances had little effect on performance; probably because of the

high carry over ﬂow characteristic of this impeller. He also presented a brief comparison

51

of six regenerative compressors tested by independent organizations as shown in Figure
3.8.

Hollenberg [29] investigated regenerative turbomachines using both air and water as
working ﬂuids. He investigated three machines, representing two geometries and
developed a non-dimensional correlation, relating pressure and ﬂow to driving torque.
This was conﬁrmed by experiments using data from widely separated investigations. He
used this information to prepare a study of maximum efﬁciency as a function of speciﬁc
speed. A single loss coefﬁcient was found to be the governing parameter. He found that
the optimum head and maximum efﬁciency were adversely affected by increasing the
clearance between the impeller and stripper. Moreover, he concluded that improved
efﬁciency might be obtained at higher speciﬁc speeds.

Many other authors have investigated the effect of impeller clearance in the regenerative
pump using different impeller blade designs. Senoo [56] reported on the theoretical and
experimental effects of clearance in the case of radial blades while Hollenberg [29]
reported on the experimental effects in the case of semi-circular blades. Senoo [56]
developed a theoretical model to study the effect of clearance on the pump performance.
He carried out a series of experimental tests using a pump with radial blades. He changed
the pump clearance eight to ten times from 0.04 mm to 0.36 mm and clariﬁed the
inﬂuence of the clearance experimentally and compared it with his theoretical results. He
found that the pump head depends considerably on the value of pump clearance. In his
experiment the shut-off head at large clearance was only one fourth of that at the small
clearance. Hollenberg [29] carried out a series of experimental tests using regenerative

blower of semi-circular blades. He changed the clearance from 0.25mm to 0.5 and 0.7.

52

He found that the shut-Off head at large clearance was only 0.4 of that at the small
clearance value. The maximum efficiency at 4500 rpm at large clearance was 0.28
compared to 0.43 at small clearance value. He examined the effect of speciﬁc speed on
the maximum efficiency of regenerative turbomachines. Moreover, in another publication
he determined the effect of Reynolds number on a typical regenerative pump.

The effect of stripper is studied by Sixsmith [60] and he suggested that the regenerative
pump performance might be improved if the solid stripper were modified to form a row
of stationary blades to allow ﬂow between the blades to continue in a toroidal rather than
a peripheral path only. This suggestion was taken by Abdallah [1] in his thesis in which
he explored aerofoil blade RFC.

Sixsmith and Altmann [60] tested two regenerative compressors with aerofoil blading by
blowing air through them. MKl regenerative compressor was designed to run up to
10,000 rpm and deliver 250 liter/sec at a pressure of 2 atm. It had an impeller of 300 mm
diameter with a Single row of blades. The performance of MKl compressor is given in
Figure 3.9. The characteristics resembled to those of a positive displacement compressor
and the efﬁciency was maintained over a wide range of operating conditions. The torque
was almost directly proportional to the back pressure and the compressor could be
operated from maximum to zero ﬂow without surging or stalling. The authors also tested
a second MK2 regenerative compressor with the same basic layout but with two blade
rows. The performance curves for MK2 RFC are shown in Figure 3.10. The main
features of its performance compared to that of the first compressor were the increased
peak efﬁciency to 52% , the lower pressure ratio at which this efﬁciency occurred, the

gentler slope Of pressure-volume curves, the lower efﬁciency at high pressure ratio, and

53

the large volume ﬂow at low pressure, i.e., approximately 2.5 times greater than before.
The authors retested the MK2 regenerative compressor by making the blading symmetric
and the improved performance characteristics are shown in Figure 3.11. When compared
to Figure 3.10, the gain in efﬁciency was particularly marked at high pressure ratios. For
example at 4000 rpm, the efficiency increased by 10 percent at a pressure ratio of 1.5.

Sixsmith and Watson [62] constructed an experimental helium regenerative compressor
having four stages yielding an overall pressure ratio of 10.521. Tests were carried out

with 0.5 mm clearance between stripper seal and rotor. A pressure ratio of 1.3 for single

Stage was achieved with volumetric ﬂow rate of 0.14 m3/s yielding a maximum

isothermal efﬁciency of 31%. Further testing carried out on reduced clearance of 0.25

mm yielded a pressure ratio of 1.3 at volumetric ﬂow rate of 0.31 m3/s with a maximum
isothermal efﬁciency of 42%.

Swift et al [66] developed a regenerative compressor with aerodynamically shaped blades
primarily for use in cryogenic helium systems. Test data demonstrated a pressure ratio of
1.5 at a ﬂow rate of 12 g/s with measured isothermal efﬁciencies in excess of 30%.
Authors developed a performance prediction model of the compressor to support the
design of prototype machine. The model incorporated important performance and loss
mechanisms that related pressure rise, ﬂow rate and speed to geometry of the machine.
The model was used to predict performance and to assess the relative importance of basic
geometric features, such as blade angles, inlet and exit port Sizes, internal clearances etc.
Important loss mechanisms were incorporated in the model.

Crowe [18] reported the overall performance curve Of a UHTREX gas bearing

regenerative blower developed by Mechanical Technology Incorporated for Los Alamos

54

Scientiﬁc Laboratory. This blower design was selected for use in the Ultra High
Temperature Reactor Experiment (UHTREX) because of highly radioactive system
contamination resulting from the investigation of unclad fuel elements. Figure 3.12
shows the pressure rise versus ﬂow rate curve and Figure 3.13 gives overall efficiency
versus ﬂow coefﬁcient curve for the regenerative blower. It must be noted that this
blower was capable of producing a pressure rise of 30 psi at design ﬂow rate and
temperature, but the overall efﬁciency was just about 10% at the design conditions.

A four stage regenerative compressor was adopted by Gessner [25] for the compression
of helium gas in the development of a highly reliable, long life cryogenic refrigerator for
space vehicle application. The advantage of RFC is due to its ability to produce high
pressure ratio at low ﬂow rate with a small overall size of machine. Further advantages
are oil-free operation and freedom from stall or surge instability. These characteristics are
advantageous in compressors intended for incorporation in small closed cycle helium

refrigerators.

3.4 Impeller blade Proﬁle

Many authors have studied regenerative turbomachines with radial blades, e.g., Senoo
[54, 55, 56, 57], Iverson [34], Wilson [69], Shimosaka [59], Burton [13], Gessner [25]
and Grabow [23]. Iverson [34] reported the experimental effect of blade number on
regenerative pump performance. He tested impellers with 31, 36 and 39 blades and found
that the pump head and efﬁciency were increased with an increase in the number of
blades within the tested range. The optimum number of blades for the greatest head at a
given ﬂow rate was not reached. Burton [13] reported that the pump performance could

be improved by using a non-radial blade. The shut-off head coefﬁcient obtained by using

55

a 47° blade angle was nearly twice of that obtained by using the straight blade. Yamazaki
[72, 73, 74] studied non-radial blades and Grabow [23] and Hollenberg [29) studied the
semi-circular blade Shapes. Sixsmith and Altmann [60], Sixsmith [61] and Abdallah [1]
studied the regenerative compressor with aerofoil blades. Grabow [23] reported
theoretical and experimental effects of the blade angle for both radial and semi-circular
blades. He tested the pump in both cases with different blade angles in the range of i‘60°
with a step size of 20°. He found from the theoretical research that the optimum shut off
head was reached for the blade angle in the range of 40° —55° , whereas experimental
study resulted in Optimal blade angle in the range Of40° —45°. Abdallah found from the
theoretical study of the blade angle effect on the shut-Off head that optimum range of

aerofoil blade angle is 55-61 degree.

3.5 Loss categorization

It is thought that more than 40% of the input power in a regenerative turbomachine is
consumed in overcoming losses. The regenerative pump Operation is affected by different

types of losses including

0 Losses due to Slip

0 Hydraulic losses in the circulation process between impeller and free channel
0 Shock losses at the blade inlet

0 Peripheral friction loss in the ﬂow channel

0 Inlet and outlet losses

56

o Leakage losses between the impeller face and the pump casing and between the

inlet and outlet ports through the stripper

Sixsmith and Altmann [60] concluded that the major source of loss of efficiency is due to
slip. The slip loss represents the ﬂow rate down the pressure gradient that is needed to
maintain the circulation through the annular channel in the presence of losses due to
turbulence, ﬂuid friction and the blade drag. All these losses, for a range of pressure
ratios, are Shown in Figure 3.14. True corresponding ﬂow rates for various blade designs
are also plotted. The slip loss is by far the greatest and efforts to raise the efﬁciency
should be directed towards its reduction. In addition to the slip, these authors pointed out
various types of leakage losses and carryover loss of compressed gas between the blades
as they pass through the stripper. The ﬂow rate delivered by the compressor was reduced
by leakage through the clearances from the high pressure region to the low pressure
region of the annular channel. Estimates of these leakage losses were made for a
compressor speed of 4500 rpm and a pressure ratio of 2.0 as shown in Figure 3.14. A
clearance between the faces of the rotor and the casing of 0.25 mm was reported to allow
a leakage rate of about 4% . A clearance of 0.305 mm between the proﬁled edge of the
impeller and the stripper allowed a leakage rate of about 3%. The leakage rate past the
edges and tips of the blades in the stripper was about 3%. A small but signiﬁcant fraction
of the compressed gas was found to be carried through the stripper from the high pressure
region and expanded down to the inlet pressure as the blade pockets between the blades
open into the annular channel at the inlet end. This is usually referred to as carry over loss

and it represents a loss of efﬁciency. When a regenerative compressor Operates with an

57

incompressible ﬂuid, the stripper seal plays an entirely passive role except for a certain
amount of leakage. However, under compressible ﬂow conditions, the small seal will
become a major factor in machine performance. Large quantities of compressible ﬂuid
near the exit port are taken through the seal to mix in a highly irreversible process with
the ﬂuid entering the machine. This mixing process places a limit on pressure ratio as the
Mach number increases. The seal plays a decisive role in reducing the overall efﬁciency
of the machine.

Sixsmith and Altmann replaced the usual straight radial vanes on the rotor by the
aerodynamic blading and also redesigned the annular channel in order to reduce the
losses due to slip. They proposed a circular cross section annular channel to promote
vortex circulation and a minimum of turbulence. They suggested that the blade angles
should be designed to match ﬂuid angles to ensure smooth entry to the blades. The angles
depend on the rate of variation of the circulation component of velocity with respect to
the radius of a streamline. When the effects of ﬂuid friction are allowed, the actual vortex
should lie somewhere between a free vortex and a constant linear velocity vortex. This
led to blading in which the deﬂection increases with radius, the tangent of the inlet and
outlet angles being proportional to the square of radius. The adoption of this type of
blading improved the performance and extended the range of applicability of regenerative
turbomachinery.

Burton [12] pointed out that the carryover loss might be reduced by extracting some of
the compressed gas passing through the stripper and feeding it back at an intermediate
pressure to the annular channel. Thus instead of being deposited inefﬁciently near the

suction, the stripper carry over gas would be made to expand some of its energy inducing

58

the incoming supply. This idea is further explored in this dissertation by employing
decompression ducts to feed high pressure ﬂow entrapped in the stripper blades to

various locations in the ﬂow channel.

3.6 CFD Work

Computational Fluid Mechanics (CFD) has been widely used for the ﬂow analysis of
various turbomachines in last few years. The computational methods seem very attractive
to be applied to RFC/RFP because they provide a possibility of calculating the ﬂow in
order to predict the likely effects of design modiﬁcations and in the hope of gaining a
clearer insight into some of the losses. An attempt to calculate the ﬂow in regenerative
turbomachines was undertaken by Abdallah [1], who applied an incompressible version
of time marching scheme to the ﬂow outside the blade row of a regenerative compressor
with aerofoil blades. However, he took no account of losses and because the solution did
not include the blade row, it suffered from an uncertainty in the correct speciﬁcation of
the boundary conditions. Andrew [2], by contrast proposed a method based on an
adaptation of the streamline curvature technique commonly used for axisymetric
throughﬂow calculations in conventional axial and radial ﬂow turbomachines. Although
this method did not calculate the details of the blade-tO-blade ﬂow, his work seems very
attractive. There is a potential of extending the calculation through a blade row in which
the mean ﬂow angles can be Speciﬁed, and it is also relatively easy to incorporate loss

models into the basic scheme presented by Andrew.

59

3.7 Conclusions

In this chapter, a summary of previous research on regenerative turbomachines is
presented. After reviewing the literature, need was felt to do a theoretical, experimental
and CFD analysis on these turbomachines to improve the performance. Although, there
are few mathematical models available in literature, but none of them is general enough
to predict performance without experimental support. Wilson’s incompressible ﬂow
theory seems very attractive, however it lacks in correlation of losses with geometric and
aerodynamic parameters. Therefore, in this work, Wilson’s incompressible ﬂow theory is
extended to incorporate compressibility effects. Loss correlations are introduced to
predict the performance. Looking at previous experimental work, there are evidences of
some good experimental data available in literature. However, most of the data was on
single stage pumps. No evidence of test data on multistage turbomachines is available.
Moreover, the test data are not used to develop any correlations which can prove useful
for designers and engineers. Therefore, need is felt to investigate single and multistage
test data on regenerative compressors and develop correlations to quickly estimate the
performance characteristics.

Sixsmith’s theory [60] seems to be the best effort so far towards designing aerofoil blade
RFC. However, there is a further need to theoretically investigate aerofoil blade RFC and
perform a sensitivity analysis on various geometric parameters for performance
improvement. Therefore, in this work a compressible ﬂow theory for aerofoil blade RFC
is put forward. Extensive design sensitivity analysis is performed to find out which
geometric parameters have maximum effect on performance. There is little effort done in

the past to apply CFD techniques to solve ﬂow details inside regenerative turbomachines.

60

One reason for this is because most of the research work on these turbomachines was
done prior to 19808 during which not many commercial CFD softwares were available.
Therefore, it seems very attractive to solve the ﬂow details inside regenerative
turbomachines to improve the geometry for better performance. In the present work, CFD
analysis on a regenerative automotive fuel pump and an aerofoil blade RFC is performed
using commercial software “STAR CD”. Details of CFD analysis can be found in

chapters 7 and 9.

61

DISCHARGE A INLET

 

 

 

SECTION A - A

89211111555

1

X29... 1 C22

330i

 

 

PA :: J o "— «AP:
p/77777777H7777'77/771/l/7//
(I) (2)

Figure 3.1 Simpliﬁed regenerative compressor for force analysis (after Iverson [34])

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LG
0.9 ago—“c o
\ C50.
>— 0.8‘
g \ PQHEB [gr 911 a
l_t_r 0.7 70
2
u. 0.6
iii EFFICIENCY
0.5
w /W a: O_|
04 3 ’9.2\
If ' \
E 0.3 \\
‘ 0.2 HEAD S.
{a 3:0 \Q \
B'OJ X
I 0" 0:0.2
0

 

 

 

 

o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.3 0.9 1.0
o/UA

Figure 3.2 Performance characteristics of regenerative compressor (after Iverson [34])

62

Pump: STA-RITE 'I'H-7
Stream function: A'=0.00818

123'3 - Computed cycle at converging
conditions

 
   
   
   

 

 

 

 

 

 

 

 

 

 

145 - Ideal cycle to Show losses mg
Rm=0.7
100‘
Loss in
30‘ (5)
g Loss in Impeller (4) Shock loss at
:50 60‘ T -- ------------------ 00
z (3 U)
a Euler Head-Loss
'- 40 in Blade Conditions at
g (3) constant T , z
a" Start of
:2 Cycle
m ' as
(7)
(1) 012 0'4 016 , 0:8 1:0
6 6

C C

Tangential Displacement 0 - (rad)

Figure 3.3 Typical ﬂow cycle along a streamline (after, El Hag [22])

 

 

 

 

Figure 3.4 Velocity diagrams for compressor blades (after Sixsmith and Altmann [60])

63

Table 3.1 Performance Comparison at 4000 rpm and pressure ratio of 1.17 (after

 

 

 

 

 

 

 

 

Sixsrrrith and Altmann [60])
Performance Formula Wilson Sixsmith and Ratio
Altmann
' RTl PZ
Efﬁciency m n}; 45% 58% 1.29
Shaft Power
Speciﬁc 12 Q )6
Speed 7 0.244 0.220 0.90
(8H ) 4
Head gH
Coefﬁcient U7 1.5 4.2 2.8
Flow Q
Coefﬁcient DZU 0.014 0.044 3.14

 

 

 

 

 

HEAD COEFFICIENT, LI}

‘¥=g.H/U.°
1‘: Qs/Ac Ur

 

CAPACITY COEFFICIENT, 2.

64

Figure 3.5 Head Coefﬁcients of ORGDP-l Regenerative Compressor (after Cates [15])

 

HEAD COEFFICIENT, ‘P

 

IMPELLER TIP MACH NUMBER, MOT

Figure 3.6 Head Coefficients dependence on impeller tip Mach number (after Cates [15])

SPEED 11000 RPM
IMPELLER-
was
AXIAL RADIAL
ORGDP-3 0.012 0.005
-o— exam-3.1 0.030 0.005
a masons—2 0.028 0.015

0
0

TOTAL PRESSURE RATIO, Pap/Pas

 

SPECIFIC MASS FLOW, (D

Figure 3.7 Inﬂuence of clearances on pressure ratio (after Cates [16])

65

5.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

COMPRESSOR TEST GAS SUCTION
P (psla) T °r
5,0 ORNL CRDT IIELIUM 315 150
\ ORNL FPD IIELIUM 115 175
X\ ORNL HECT-Z HELIUM 400 ‘00
\ LASLUHTREX HELIUM 492 100
4'5 a ORGDP-l HELIUM 10 9g
\ oﬁf'EXTA-RITE TH-‘7 AIR 125 :00
4 0 \OPGDE 1 ORGDP-l AIR
\\ Q) S}A—RITE 111.7
\
9*“ 3.5 \
m ‘ ‘ \ 2=Q./U.
8 3.0\\\ §\\ ORNLX \\ A"
E \\ I (CDR': \
8 2.5 ~ . \ ’LASL \
0 \ \( mlm‘ l\
\ \
.‘I‘.

ORNL FPD‘ll/\\\\ \\N
1 5 ORNL HECT-E.\\\& \\

x
1.0 \\\
\

 

 

 

 

.\
\ \
\\\\ _ﬁ
.5 \

\
.. x} \

0 0.1 0.2 0.3 0.4 0.5 0

 

 

.\
\

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CAPACITY COEFFICIENT. A

Figure 3.8 Comparison of several regenerative compressors (after Cates [16])

66

Regenerative Compressor MKl

 

 

 

 

 

2'50? . ' . 7000
3000 4000 5000 6000 38% . speedmRPM
Isothermal Emclency
225.
2.00-
.9.
a
2 2000
2 l 7 ‘
3
3
0
I-
9.. 1.5:
1.25
‘ 1000 . , _
1.009; 0 ' 100 150 2‘00 250 Mo 0
. ft3/ minute . l ‘ L
0 20 40 60 80 100 120 I40 160

Inlet Volume Flow (litres/second)

Figure 3.9 Performance of MKl Compressor (after Sixsmith and Altmann [60])

REGENERATIVE COMPRESSOR MK 2
Unsmmetrica! Blades

3000 30%
1.5r' 2000 - . . 4000 5000 5°°°SpeedinRPM
35'. 40% 45% . Isothermal Efﬁciency
1'4.
50%

.2 103} -
C.)
a
h 0 O .
0
g .
0
I- .
OI. .

 

 

 

' . l I __J
1'00 100 200 300 3 400 500 600 700 800
ft I minute
I 1 1 *1 l 1 l 3 0
0 50 100 150 200 250 300 g

Inlet Volume Flow liters/second

Figure 3.10 Performance of MK2 compressor with unsymmetric blading (after Sixsmith
and Altmann [60])

67

REGENERATIVE COMPRESSOR m
Symmetrical Blades

 

    

 

 

2.0 0002 ' 9" 4000 30% 5000 Speed in RPM
° 25 . 35% Isothermal Efﬁciency
12000 40%
1.8 . -
. 45%
- 6000
O
3 1. - - ' '
h .
0
I-
: - , . .
a -
2 1.4
On ‘ . .
.2. ’
1 0 . '” ' - I I ' 1 . I !_J
'0 10 200 300 3 400 500 600 700 800
ft I minute
I #L I I 1 I 1 l
0 50 100 150 200 250 300 350

Inlet Volume Flow liters/second

Figure 3.11 Performance of MK2 compressor with symmetric blading (after Sixsmith and

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Altmann [60])
J Gas. HELIUM, R=386
_ INLET TEMPERATURE, 100°F
\ If INLET PRESSURE, 483 psia
20 #f E.
l\;\l DESIGN POINT
,- ' 14,000 E FLOW = 120 lb/hr
1 AP = 15 pdg
a 1‘ \wI-ggggi” \ RPA = 12,250
a , \
=- .'_ \ 12 500 \ MOTORINPUTFREQ=209 cps
a! 12 , \’ MOTOR SIJP VARIES FROM 1
8 \ 7 \ to 2.5% DEPENDING ON LOAD
E \l \ —J \\ I
g 8 ,-’ 1 10,000 ‘ p \\ I __
O \ , R
I: '\ \\ i ‘\ \\\ \ I _—
I
<1 ‘ I \w \ \J \L
I
'1' \ \ \ \
’l \\ \\ \\ \ I __
0 ’ i " \\ \\ N
0 100 200 300 400 500 600 7 ’0 l 8 00 —

 

 

 

 

 

 

 

 

HELIUM FLOW, lb/hr

Figure 3.12 Pressure rise vs. ﬂow curve for UHTREX Gas Cleanup System Regenerative
Compressor (after Crowe [18])

68

40

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

77c=ESTIMATED (MIN)
35 =COMPRESSORS EFFICIENCY
\/ \l\
3.. / \\
25 / /"\\ K
S y r/f \
I / /
5 2” / \ \
g 15 / / \(177W
0 / \6
E I
m 10
i // DESIGN l
Pomu‘
5//
0
0 02 04 06 08
¢=£L
UA

770v = OVERALL EFFICIENCY

Figure 3.13 Overall efﬁciency curve for UHTREX gas cleanup system regenerative
compressor (after Crowe [18])

  
  

 

 

 

 

 

 

Measured Flow Rates Estimated Losses
2.0r .
MKl Unsymmetrlcal Blades\ . 1.129“),- face Leakage
MK2 Symmetrical Blades ‘ 1 -—Stripper clearance loss
1, (filmed Outlet) \ l --Blade labyrinth
MK2 SMOII‘ICII Blades —Carfyover loss
.3 MK2 Symmetrical Blades 3 b Slip loss
3 1-6 ’ (Chwd stripper Chum”) - Ideal Performance
.3 MK2 Unsymmetrlcal Blades
‘5
a: .1
On
1.21
1.0L - J . . 0""
0 100 200 300 3 400 500 600 I I 800
L J . 1ft / minute J 1 .
0 50 100 150 200 250 300 350

Inlet Volume Flow liters/second

Figure 3.14 Loss analysis based on MK2 regenerative compressor with symmetric blades
at 4500 rpm (after Sixsmith and Altmann [60])

69

CHAPTER 4

APPLICATION OF RFC IN MICROTURBINE
SYSTEMS

For small scale power generation, there is currently great interest in microturbines.
Microturbines offer a number of potential advantages compared to other technologies for
small scale power generation. These advantages include a small number of moving parts,
compact size, light weight, greater efficiency, lower emissions, lower electricity costs and
opportunities to utilize waste fuels. Waste heat recovery can be used with these systems
to achieve efﬁciencies greater than 80%.

Microturbines can burn various types of fuel, but the most popular microturbine fuel is
natural gas. Therefore microturbines require a gaseous fuel compressor to raise a low
pressure natural gas supply to that required for injection into the combustion system.
Presently, most microturbine manufacturers use high cost and inefﬁcient small
compressors for this purpose. This has become one of the weak points of the
microturbines despite their other numerous advantages. In microturbine research there is
an immediate need for the development of a natural gas pressure booster compressor

which is low cost and efficient.

70

4.1 The need for low cost and efﬁcient gas booster
compressor

Microturbines are small combustion turbines with output less than approximately 200
KW and can be located on sites with space limitations for power production.
Microturbines are composed of a compressor, combustor, turbine, alternator, recuperator,
generator and fuel gas pressure booster compressor. Microturbine application area has

recently expanded to include:

Distributed power generation
0 Combined heat and power (co- generati on)

- Offshore Rigs

0 Hospitals
0 Backup Generators
0 Vehicle applications: (1) Hybrid vehicle (microturbine connected to high speed

alternator) (2) Hybrid vehicle (microturbine and fuel cell together)

The U.S. Department of Energy's Advanced Microturbine Program is working with
utilities, energy service companies, industrial manufacturers and equipment suppliers to
identify technologies that will improve the energy, environmental, and ﬁnancial
performance of power systems for manufacturing, processing, and commercial
applications. The Advanced Microturbine Program is a six-year program for FY 2000-

2006 with a Government investment of over $60 million. End use applications for the

71

program are open and include stationary power applications in industrial, commercial,
and institutional sectors.
Planned activities for this program focus on the following performance targets for the

next generation of "ultra-clean, high efﬁciency" microturbine product designs:

0 High Efﬁciency — Fuel-to-electricity conversion efﬁciency of at least 40%

0 Environment —- NOx < 7 ppm (natural gas)

0 Durability — 11,000 hours of reliable operations between major overhauls
and a service life of at least 45,000 hours

0 Cost of Power — System costs '< $500/kW, costs of electricity that are
competitive with the alternatives (including grid) for market applications

0 Fuel Flexibility — Options for using multiple fuels including diesel, ethanol,

landﬁll gas, and bio-fuels

With the development of uprated and higher thermal efﬁciency microturbines, engine
design point pressure ratio has been rising. At the same time, the current trend towards
more dispersed generation increases the number of occasions when an engine needs to be
sited on a lower pressure branch of the natural gas network. This potentially presents a
problem in that the gas flow has to overcome engine combustor pressure plus a
substantial control/manifold system pressure drop.

Most microturbine manufacturers produce a new range of industrial gas turbine engines,
having pressure ratios as high as ten. Experience indicates that, at engine pressure ratios

above about 5:1, the chance of having inadequate gas line pressure rises sharply. In such

72

cases, the gas pressure is boosted by a high cost compressor, comprising of a drive motor,
cooler, moisture separator, accumulator and an intercooler (for two-stage units). For
example a microturbine may cost about $100, 000 and a typical natural gas pressure
booster compressor adds $10,000 — $15,000 to the installation. Therefore it is an urgent
need to develop a fuel gas pressure booster compressor which is low cost and efficient.

Because of their compact size, relatively low capital costs, low operations and
maintenance costs and automatic electronic control, microturbines are expected to
capture a signiﬁcant share of the distributed generation market if improvements both in

cost and efﬁciency of fuel gas pressure booster compressor are achieved.

4.2 RFC in microturbine systems

The power section of a typical microturbine generator includes a compressor, turbine,
combustor and permanent magnet generator as shown in Figure 4.1. A schematic
diagram of a typical microturbine system is shown in Figure 4.2. Compressor and turbine
sections of the system can rotate at speeds as high as 100,000 rpm. Air is compressed in a
centrifugal compressor to several atmospheres before it goes to the combustor. Fuel is
burnt in the combustor which heats the air which then expands through the turbine wheels.
Turbine wheels drive the compressors and through the reduction gear box, the generator.

If natural gas is used as fuel in the combustor, it provides the advantage of less cost, no

storage problems, cleaner burning, less NOx emissions and above all it provides higher

efﬁciency and more power output than with any other gaseous fuel. A major problem
with the use of natural gas is that it must be compressed enough to enter the combustor

and known gas compressors are very expensive and require signiﬁcant energy to run.

73

Most of the compressors available are screw type or reciprocating compressors. These are
generally equipped with gas coolers, oil separators and accumulators. Due to high costs,
it is desirable to provide a cheap method and apparatus for compressing the gas in a
manner which eliminates typical problems associated with screw type or reciprocating
compressors and also maintains the required concentration of natural gas in the mixture
which is injected into the combustor.

Natural gas coming from pipelines in a residential or commercial area is kept at very low

pressure z 0.2 psig for ﬁre safety reasons. Natural gas is required to be supplied to the
combustor nozzle manifold at pressure as low as lpsig. Typical gaseous fuel-air

requirements are (20:1). Centrifugal compressors meet requirements of oil free operation
and no rubbing shafts and seals and no sliding surfaces, however centrifugal compressors
operate best (with high efﬁciencies) when they have a high through flow rate and a low
pressure rise relative to their tip speed. These operating conditions are characterized as
high Speciﬁc speed conditions. Highest efﬁciency is generally achieved at moderate
speciﬁc speeds. Under these conditions, a centrifugal compressor can operate with
efﬁciency on the order of 78%. However, for the operating conditions needed for
microturbine operation, a centrifugal compressor can only provide an efﬁciency of 20%.
Under these low flow and high head conditions, a centrifugal compressor would need as
many as 10 stages to produce the same pressure rise for a given tip speed as could single
stage RFC can do. RFC provides Simple, reliable design with only one rotating assembly.
Operation is stable and surge free over a wide range. They have a long life which is
mainly dependent on bearing life. They require fewer stages when compared to

centrifugal compressors. Moreover they have higher efﬁciencies when compared to very

74

low speciﬁc speed centrifugal compressors. Regenerative ﬂow compressor operating at
low specific Speed and at its best operating flow range can have efﬁciencies of about 55%
with aerofoil blades and efﬁciencies of about 38% with straight radial blades.
Requirements of the microturbine systems are low fuel flow and high discharge head.
RFCs overcome all the shortcomings of typical compressors which can be used for
microturbine operation. This makes RFC a good match for the fuel compression
requirements in a microturbine system.

Capstone Turbine Corporation, CA has tested single and multistage RFC with air and
natural gas as working ﬂuids. Non-dimensionalized geometry data and non-
dimensionalized performance curves for both single and multistage RFCs are presented
in this chapter. Such information can be useful for predicting performance of

geometrically similar machines.

4.3 Non-dimensional parameters

Six non-dimensional parameters are very critical in analysis of RFC, the impeller tip
Mach number, pressure ratio, flow coefﬁcient, speciﬁc mass ﬂow rate, power coefﬁcient

and isothermal efﬁciency as deﬁned below.

 

 

Impeller tip Mach number M or = _r2_a)__ (4.1)
7”.
Pressure ratio T1 = P0“, /Pm (4.2)
Flow coefﬁcient/1 = Q 3 (4.3)
8a»,
Specific mass flow rate (I) = :1 RT‘" (4.4)
4r. .. r

75

Power Draw

 

Power coefficient Y‘ = 3 S (4.5)
32pma) r2
thTm In 113—”-
Isothermal efficiency ’7... = "' (4.6)

 

Power Draw

4.4 Single Stage RFC

Several geometric configurations of single stage RFCs were tested at Capstone. These
tests were carried out using air as the working fluid. The impeller of all the single stage
conﬁgurations consists of straight and radial blades with rectangular flow channel.
Channel depth and hence the channel area from inlet to outlet decreases linearly. Stations
A and B refer to peripheral locations near inlet and outlet respectively. A schematic
diagram of impeller and channel shape is shown in Figure 4.3. Non-dimensionalized
geometry data of these conﬁgurations is presented in Table 4.1. It must be noted that
channel depth at both station A and B is speciﬁed in the table for clarity. The single stage
conﬁgurations were investigated to study the effect of various geometric parameters
related to blade and channel on performance. Below is a comparison and discussion of

performance characteristics of various conﬁgurations.
4.4.1 Design point

Design point refers to the point where RFC is desired to operate for microturbine

operation. The design point which is selected yields an impeller tip Mach number of

0.369 and speciﬁc mass flow rate of air equal to 1.04x10‘3. An attempt is made to

compare various conﬁgurations and optimize the geometry at the given design point.

76

Configurations SI, 82, S3 and S4 have different channel inlet and exit areas. We
categorize these four conﬁgurations in terms of non dimensional channel inlet areas and

channel area ratios. Thus, we can say

o 81 (Lower non-dimensional channel inlet area, Normal channel area Ratio)
. 82 (Higher non-dimensional channel inlet area, Normal channel area Ratio)
. S3 (Normal non-dimensional channel inlet area, Higher channel area Ratio)
0 S4 (Normal non-dimensional channel inlet area, Lower channel area Ratio)
Where

Higher non-dimensional channel inlet area = 0.0577

Normal non-dimensional channel inlet area = 0.0386

Lower non-dimensional channel inlet area = 0.0283

Higher channel area ratio = 1.309

Normal channel area ratio = 1.179

Lower channel area ratio = 1.0

Test data obtained for these four configurations is plotted in terms of impeller tip Mach
number and speciﬁc mass flow rate. Figures 4.4 and 4.5 show pressure ratio and
isothermal efﬁciency plotted against Specific mass flow rate for conﬁguration 81. It can
be seen from Figure 4.4 that higher pressure ratios can be achieved at higher Mach

numbers and lower speciﬁc mass flow rate. Figure 4.5 shows that a peak efﬁciency of

12% can be achieved at a Mach number of 0.433 and specific mass flow rate of 1.0x10‘3 .
However, at this operating point, a pressure ratio of 1.36 can be achieved with

conﬁguration 81. The data is correlated to obtain an approximate efficiency and pressure

77

ratio at the design point under consideration. From the correlation, a peak efﬁciency of
8.6% and a pressure ratio of 1.15 is predicted at the design point.
Performance characteristics of conﬁguration S2 can be seen in Figure 4.6 and Figure 4.7.

Figure 4.7 suggest that a peak isothermal efﬁciency of 6% can be obtained at Mach

number 0.325 and speciﬁc mass ﬂow rate of 9.77 x10“. The corresponding pressure ratio
at this operating point is found to be 1.19. Performance at design point is calculated by
correlating the test data and it is found that an efﬁciency of 5.77% and pressure ratio of

1.24 can be achieved using conﬁguration S2.

The channel inlet and exit area are larger for 52 than 81, thus making the ratio 11,."er2

and A0“, Ir,2 larger. This causes a small effect on pressure ratio but huge detrimental

effect on isothermal efﬁciency. Exactly similar trend was observed by Cates [15] in his
experimental data, however no explanation was provided. The reason for this trend is
ﬂow separation at the channel walls. If the channel area is too large, the ﬂuid does not
attach to the channel walls and hence fails to circulate properly. This ﬂow separation at
channel walls results in extreme turbulence. Moreover, the ﬂuid which fails to circulate
mixes with incoming stream of ﬂuid coming from compressor inlet and creates a
blockage effect, resulting in huge loss of efficiency. In contrast, if there is small channel
area, the ﬂuid attaches to the walls and gets proper guidance and circulation. The more
the circulations through the impeller, the more energy transferred to the ﬂuid and more is
the pressure ratio. Thus, a smaller channel area helps to create better pressure ratio as
well. In the case of S2, pressure ratio dropped slightly because not many circulations
were lost by increasing channel area, however if channel area is increased further, more

pressure drop is expected.

78

Isothermal efficiency and pressure ratio for configuration S3 can be seen in Figure 4.8

and 4.9. A peak efﬁciency of 10.57% can be achieved at Mach number of 0.325 and

speciﬁc mass ﬂow rate of 1.2x10'3. A pressure ratio of 1.18 is achieved at this operating
point. For the design point under consideration, test data is correlated and it is found that
isothermal efﬁciency of 9.82% and pressure ratio of 1.33 can be obtained using
conﬁguration S3.

Performance characteristics of configuration S4 can be seen in Figure 4.10 and Figure

4.11. Figure 4.10 suggests that a peak isothermal efﬁciency of 8.1% can be obtained at

Mach number 0.325 and specific ﬂow rate of 9.73x10“. The corresponding pressure ratio
at this operating point is 1.19 . Performance at design point is calculated by correlating the
test data and it is found that an efﬁciency of 8.13% and pressure ratio of 1.30 can be
achieved using conﬁguration S4.

Best performance at the design point is obtained using S3 conﬁguration yielding an
efﬁciency of 9.82% and pressure ratio of 1.33.Thus it can be concluded that for the
design point under consideration, S3 is the best geometric conﬁguration for RFC. This
means that at least for the design point, we can say that a normal non-dimensional inlet
channel area around 0.0386 and a higher channel area ratio around 1.309 is optimal for
best performance.

To investigate further, configuration S3 is chosen and pitch to cord ratio is varied. Pitch
to cord ratio depends on number of impeller blades and impeller tip and hub radius.
Conﬁguration S5 is designed with higher pitch to cord ratio than pitch to cord ratio of S3
by reducing number of impeller blades "Z ". Configuration S3 has a pitch to cord ratio of

0.287 , while conﬁguration S5 is designed with pitch to cord ratio of 0.418. Performance

79

 

map of
efﬁcient
09.le
isothen
citric:
there 1
hard 1
31111 e
Som
can

S6

C01
(165
We
ma:

All!

1110

map of conﬁguration S5 can be seen in Figure 4.12 and 4.13. A peak isothermal

efﬁciency of 11.08% is obtained at Mach number of 0.433 and speciﬁc mass ﬂow rate

of 9.25x 10“. However, these ﬁgures suggest that as speciﬁc mass ﬂow rate increases, the
isothermal efﬁciency decreases significantly. Therefore, at design point, the isothermal
efﬁciency will be much lower than the efﬁciency obtained using S3 conﬁguration. Thus
there is no advantage of reducing the number of impeller blades. However, still it is very
hard to conclude that a pitch to cord ratio of 0.287 is optimal for RFC design, because
still effect of radius ratio on performance needs to be investigated.

Some single stage test data is available where effect of radius ratio on RFC performance
can be studied. Two such conﬁgurations are discussed below.

S6 conﬁguration has a smaller radius ratio ( 1; /r2 = 0.6 ) than conﬁguration 83
(r. /r2 = 0.757) which is considered optimal so far. A peak isothermal efﬁciency of 10.19%

is achieved at Mach number of 0.324 and speciﬁc mass ﬂow rate of 2.6x10‘3 .The
pressure ratio corresponding to this operating point is 1.21.

It can be seen from Figure 4.14 that a very high pressure ratio can be obtained from S6
conﬁguration, however Figure 4.15 shows that the isothermal efﬁciency is very low at
design point. Such a conﬁguration is good for high speciﬁc mass ﬂow rate applications.
We can achieve a good pressure ratio and higher isothermal efﬁciency at higher speciﬁc
mass ﬂow rates using geometry of conﬁguration S6.

Another interesting conﬁguration tested is S7 with a higher radius ratio of (r. /r2 = 0.840)

than conﬁguration S3 with radius ratio of ( 1; /r2 = 0.757 ). S7 operates best at Mach number

0.433 and specific mass ﬂow rate of 4.82x10" producing isothermal efficiency of

12.62% and pressure ratio of 1.43. However, it can be seen from Figure 4.16 and Figure

80

 

llirhas
more suit
mmitn.
lawn
dEpIndc
aloutr
111081
Him
lea d
Optim;

RFC.

H001

C

Capw

4.17 that such a configuration does not give a good performance at our design point. It is
more suited with applications of very low speciﬁc mass ﬂow rate and high Mach
numbers.

It is very hard to draw any precise conclusions from presented experimental data about
dependence of RFC performance on radius ratio. However, the above analysis shows that
a lower radius ratio is beneficial at high values of speciﬁc mass ﬂow rate and higher
radius ratio is beneficial at low values of speciﬁc mass ﬂow rate. Therefore, authors
believe that conﬁguration S3 is better among all single stage conﬁgurations investigated.
Test data is not enough to establish any design criteria about what sort of radius ratio is
optimal. However, the authors have developed a [D performance prediction code for
RFC. This code has a capability to predict the performance and then do a sensitivity
analysis on various design parameters to study what design changes are beneﬁcial for
performance improvement. Findings from the performance prediction code are
collaborated with single and multistage test data presented in this chapter and with Single
stage test results published by other authors to establish some design criteria. A detailed
discussion of such analysis is presented in next chapter.

Single stage conﬁgurations do not produce pressure ratios desirable for microturbine
operation. Capstone has developed a multistage RFC to meet fuel compression
requirements of Capstone Model C30 microturbine system. Non-dimensional geometry

and performance curves for this multistage RFC are discussed below.

4.5 Multistage RFC

Figure 4.18 shows full assembly of four stage RFC used in natural gas compression for

Capstone Model C30 microturbine system producing 30 KW power. Lower side in

81

 

Figure 4.18 is called the motor Side while top side is called the pump side. Impeller
mounted on the motor side represents the ﬁrst stage, while fourth stage impeller is on the
pump side. Layout of the four stages can be seen in Figure 4.19. It can be seen that the
cross sectional area of channel for the ﬁrst stage is largest and that of the fourth stage is
smallest. The ﬂow enters from the pump side and travels all the way down and enters the
impeller of the ﬁrst stage. The inlet hole has a constant cross sectional area and it takes
the ﬂuid entering from the pump side to the ﬁrst stage inlet. The discharge nozzle is
tapered to match the channel areas at discharge of each stage. Figure 4.20 represents the
impeller of ﬁrst stage of RFC containing straight radial blades machined across the

periphery. The inlet and discharge ports are separated by stripper which constitutes about

30° of the periphery. Blades of the four stage RFC are straight and radial like those in
single stage RFC conﬁgurations, however the channel is semi-circular in cross section as
shown in Figure 4.21. This figure shows serrri-circular ﬂow channel of ﬁrst stage built in
the casing. Channel area from inlet to discharge port decreases linearly.

A schematic diagram of impeller and channel shape is shown in Figure 4.22. At design

point, the impeller tip Mach number is 0.369 and speciﬁc mass ﬂow rate of natural gas
isl.04x10". Although multistage RFC builds required pressure ratio, however very low
isothermal efﬁciency levels (IS-20%) are achieved. When comparing efﬁciency to
historical test results it appears that signiﬁcant improvements in efﬁciency could be

achieved. Non-dimensionalized geometry of all four stages of RFC can be found in Table

4.2.
Figure 4.23 shows pressure ratio and isothermal efficiency plotted against the impeller tip

Mach number using natural gas as the working ﬂuid. Test data is plotted for four inlet

82

pressures of Opsig, Spsig, 10 psig and15 psig at ﬂow rate of 195 slpm keeping inlet

temperature at 70° F . It can be observed that if the inlet pressure is low, the compressor
needs to run at higher rpm (higher Mach number) to produce same pressure ratio. A
maximum pressure ratio of 4.4 is obtained at a very low efﬁciency of 14.14% . Maximum
efﬁciency of 38.85% is achieved, however this corresponds to a very low pressure ratio
of 1.5. Higher Mach numbers produce lower isothermal efﬁciencies, but higher pressure
ratio and vice versa. The pressure ratio increases with the Mach number consistently.

Figure 4.24 is a plot of pressure ratio and isothermal efﬁciency using natural gas as

working ﬂuid at inlet pressures of 0 psig,5 psig,10 psig and15 psig at ﬂow rate of 250 slpm

keeping inlet temperature at 70°F . It can be observed that higher ﬂow rates produce
relatively low head, however they result in better isothermal efﬁciency. Moreover, at
higher ﬂow rates, the peak efﬁciencies and maximum pressure ratios are obtained at
relatively higher Mach numbers. Maximum efﬁciency of 40% is obtained and maximum
pressure ratio of 3.72 is obtained with an isothermal efﬁciency of 18.43% . Figure 4.25 is

performance map of four stage RFC with air as working ﬂuid. The inlet temperature was
again kept at 70°F and through ﬂow rate was 250 slpm. Non-dimensional test data for

pressure and isothermal efﬁciency is presented for four inlet pressures of
0 psig, 5 psig, 10 psig and15 psig. The trends look similar to previous results for natural
gas shown in Figure 4.23 and Figure 4.24. Higher pressure ratios and lower isothermal
efﬁciencies are obtained at high Mach numbers. Lower inlet pressures produce higher
pressure ratios. The maximum obtainable efﬁciency increases to almost 45% and

maximum pressure ratio of 4.4 is obtained with an isothermal efﬁciency of 19.25% .

83

These trends have been validated by many researchers in the past through testing. A good
example is testing done by Cates [15], who conducted extensive tests on various gases
with molecular weight varying from 4 -— 400. Figure 4.26 reproduced from Cates [15]
suggests that pressure ratio increases fairly consistently with Mach number

until M 0, 20.75 . From that point onward, an increase in Mach number results in

decrease in performance indicating a maximum obtainable pressure ratio. The curves

depart from a straight line at about M 0, :04 to 0.6 , where we believe that

compressibility effects start to inﬂuence. Figure 4.27 shows the pressure ratio plotted
against speciﬁc mass ﬂow rate for various gases at various tip Mach numbers. Figure
4.28 shows the variation of adiabatic efﬁciency with speciﬁc mass ﬂow rate for various
gases at various impeller tip Mach numbers. Exactly same trends are observed for
Capstone RFC as were obtained by Cates through testing. There is an interesting
difference between regenerative compressors and centrifugal compressors in power
coefﬁcient. Centrifugal compressors draw more power at higher ﬂow rates, however
regenerative compressors draw more power at low ﬂow rates. The primary reason for that
is increased number of circulations through the impeller blades at low ﬂow rate
producing very high heads at low ﬂow rates for RFC. However, these large number of
circulations through the blades require high amount of power draw. This is the reason

why in RFCs we see a high pressure ratio at low ﬂow rates, but very low efﬁciency.

4.6 Correlations among non-dimensional parameters

The above analysis discussed performance characteristics of Capstone multistage RFC.

Extensive test data is presented in the form of various non-dimensional parameters.

84

However, to make this discussion useful for designers and engineers, a three dimensional
representation of performance characteristics of multistage RFC is provided. Various
correlations are developed by best ﬁt curve from three dimensional plots to quickly
estimate the performance of geometrically similar machines. These correlations are
provided in Appendix A.

Figure 4.29 is a three dimensional plot of impeller tip Mach number, ﬂow coefﬁcient and
pressure ratio for the four stage RFC. The scattered points were taken at various inlet
pressures, various speeds and ﬂow rates using air and natural gas as working ﬂuids. Test
data are non-dimensionalized and a best ﬁt curve is drawn to see the overall trend among
various non-dimensional variables. A higher pressure ratio is obtained at low ﬂow
coefﬁcient and higher Mach number. This is a characteristic of RFC to produce high
heads at low ﬂow rates. Isothermal efﬁciency is plotted against impeller tip Mach number
and ﬂow coefﬁcient in Figure 4.30. The test data collected at various operating
conditions is non-dimensionalized and plotted in this ﬁgure. To see the overall trend, a
best ﬁt curve is plotted as shown in the ﬁgure. Efﬁciency initially increases with
increasing ﬂow coefﬁcient, but after a certain limit it starts to go down. Similar trends
were found by Cates [15] and Wilson [69]. Moreover, it is obvious from Figure 4.30 that
isothermal efficiency decreases with increasing Mach numbers at a given ﬂow coefﬁcient.
Speciﬁc mass ﬂow rate is another non-dimensional parameter plotted against impeller tip
Mach number and pressure ratio as shown in Figure 4.31. Scattered test data points are
plotted on this curve along with the best ﬁt curve. Higher pressure ratios are obtained at
higher Mach number and lower values of specific mass ﬂow rate. Similar trends were

observed by Cates [15]. Figure 4.32 represents isothermal efﬁciency plotted against

85

impeller tip Mach number and Specific mass ﬂow rate. Once again, it is obvious that
lower Mach numbers produce higher efﬁciency. Moreover, the efﬁciency starts to go up
with increasing speciﬁc mass ﬂow rate, however after reaching a certain point, it starts to
go down. The correlations provided in Appendix A are very useful to study performance
characteristics of RFC. Generally, there is a compromise between efﬁciency and pressure
ratio. If a designer strives for higher efﬁciency, he needs to sacriﬁce some pressure ratio
and vice versa. Thus, these correlations provide the designer with information that what
performance characteristics can be obtained at given operating point using geometry

similar to the multistage RFC.

4.7 Conclusions

Experimental data on single and multistage RFCs is presented in the form of various non-
dimensional parameters. Moreover, a systematic experimental sensitivity analysis on
Single stage RFC is discussed to get an understanding how various geometric parameters
(impeller radius ratio, channel area ratio, channel dimensions and pitch to cord ratio etc)

effect RFC performance. The following conclusions can be drawn from this analysis.

. RFCs are capable of producing high pressure ratios at low speciﬁc mass ﬂow
rates.
. Higher efficiencies are obtained as specific mass ﬂow rate increases, however

after a certain point where peak efﬁciency is achieved, the efﬁciency starts to go
down.
. Higher pressure ratios and lower isothermal efficiencies are obtained at higher tip

Mach numbers and vice versa.

86

Higher pressure ratios and lower isothermal efficiencies are obtained at lower
inlet pressure for a given tip Mach number. As the inlet pressure is increased,
pressure ratio goes down but higher efﬁciency levels can be achieved.
Correlations for various non-dimensional parameters are provided through
experimental analysis. These correlations can be very useful for designers and
engineers to estimate performance of geometrically similar regenerative
compressors.

It is difﬁcult to optimize RFC geometry for its full operating range. However, it is
possible to use the above test data to optimize the geometry at a given design
point.

A complete analysis of various geometric parameters on performance is very
much needed, so that the effect of RFC geometry on performance can be studied.
Design criteria need to be established and used to optimize the geometry for best

performance. Such a theoretical analysis is presented in next two chapters.

87

Generator
Cooling Fins Exhaust
Outlet

   
 
 
 
  
 
    

 

 

 

 

Air Recuperator
Intake
Combustion
Chamber
Generator
Compressor
Air Bearings
Turbine Fuel
Injector
Figure 4.1 The Capstone Model 330 microturbine generator
Fuel SIM Mr Exhaust
A
V V i
M Spun. Hkrowahc Digital Power Controller > 5"“
I Output
A A
Communication- Usu- Inn-bu

Figure 4.2 Schematic of Capstone Model 330 microturbine system

88

‘—-W"—‘

ca

 

 

 

 

 

 

 

 

 

/////

I'o

 

 

Figure 4.3 Schematic of blade and channel geometry for single stage RFC conﬁguration

Table 4.1 Geometry of various single stage RFC conﬁgurations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Non-Dim N on-Dim Non-dim N on-dim Non-dim
RFC Radius Blade Blade Radial impeller Axial
Conﬁ g. Ratio Depth Height clearance width clearance
1;,lr2 b/r2 e/r2 c,/r2 (2b+t)/r2 ca/r2
81 0.757 0.0606 0.298 0.0566 0.1392 0.00302
S2 0.757 0.0606 0.298 0.0566 0.1392 0.00302
S3 0.757 0.0606 0.298 0.0566 0.1392 0.00302
S4 0.757 0.0606 0.298 0.0566 0.1392 0.00302
S5 0.757 0.0606 0.298 0.0566 0.1392 0.00302
S6 0.6 0.1 0.492 0.0935 0.23 0.005
S7 0.840 0.04 0.196 0.0374 0.092 0.002
Contd
Non-dim Channel Pitch to Non-dim Non-dim Channel
RFC channel depth at cord channel channel area
Conﬁ g. depth at inlet exit ratio inlet area exit area ratio
dA/r2 dBIr2 PC Arr/r22 ADM/r22 An/AM
S1 0.0484 0.0314 0.287 0.0283 0.0240 1.179
82 0.1696 0.135 0.287 0.0577 0.0489 1.179
S3 0.0908 0.0532 0.287 0.0386 0.0295 1.309
S4 0.0908 0.0908 0.287 0.03 86 0.03 86 1.0
SS 0.0908 0.0532 0.418 0.0386 0.0295 1.309
S6 0.15 0.055 0.461 0.105 0.0892 1 . 179
S7 0.06 0.022 0.4 0.0168 0.0142 1.179

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

rNNNN
GON4503

 

 

 

Pressure Ratio
L '0:

 

 

 

 

HI/aif

_s
C
'1

 

.0
on

 

 

 

 

 

 

 

 

 

 

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00
+ Mach Number=0,103 Swmcmme (xro‘)

+ Mach number = 0.21

+ Mach number = 0.325
+ Mach number = 0.433
—O— Mach number = 0.542

 

.0
a:

 

 

 

 

Figure 4.4 Pressure ratio vs. speciﬁc mass ﬂow rate at various tip Mach numbers for
conﬁguration S1

 

_L
h

 

Q
/

 

\

4"
/§ \

 

 

m

 

 

b

Isothermal efficiency
03
\

 

 

N

 

O
1

 

 

 

 

 

 

 

 

 

 

 

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00

+ Mach Number = 0.108 sP°¢m° "'8" ﬂow 0 010“)
+ Mach number = 0.21

+ Mach number = 0.325
+ Mach number = 0.433
+ Mach number = 0.542

 

 

 

 

Figure 4.5 Isothermal efficiency vs. specific mass ﬂow rate at various tip Mach numbers
for configuration 81

90

2.6
2.4
2.2
2.0
1 .8
1 .6
1 .4

Pressure Ratio

1.2
1.0
0.8

 

0.6
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 20.00

+ Mach Number = 0,103 SM” "I” ﬂow 0 (x104)

+ Mach number = 0.21

+ Mach number = 0.325
+ Mach number = 0.433
+ Mach number = 0.542

 

 

 

 

Figure 4.6 Pressure ratio vs. speciﬁc mass ﬂow rate at various tip Mach numbers for
conﬁguration 82

 

14

 

—L
N

 

_A
O

 

 

 

 

 

Y
1 .
i
1
l

 

 

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2 «4% ‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.00 2.00 4.00 6.00 8.00 10.0012.0014.0016.0018.0020.00

+ Mach Number = 0.108 Specific mass flow 4» (x104)
+ Mach number = 0.21

+ Mach number = 0.325
—I— Mach number = 0.433
+ Mach number = 0.542

 

 

 

 

Figure 4.7 Isothermal efﬁciency vs. speciﬁc mass ﬂow rate at various tip Mach numbers
for conﬁguration 82

91

 

0.00 2.00 4.00 6.00 8.00 10.0012.0014.0016.0018.0020.00
Specific mass ﬂow 0 (x10‘)

 

—v— Mach Number = 0.108
-+— Mach number = 0.21

+ Mach number = 0.325
+ Mach number = 0.433
—O— Mach number = 0.542

 

 

 

Figure 4.8 Pressure ratio vs. Speciﬁc mass ﬂow rate at various tip Mach numbers for
conﬁguration S3

 

 

 

 

14
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0.00 2.00 4.00 6.00 8.0010001 2.001 4.001 6.001 8.0(2000
Specific mass ﬂow 0 (x10‘)

 

 

A

Isothermal eiﬂciency
a:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

—v— Mach Number = 0.108
+ Mach number = 0.21

+ Mach number = 0.325
—I— Mach number = 0.433
+ Mach number = 0.542

 

 

 

Figure 4.9 Isothermal efficiency vs. speciﬁc mass ﬂow rate at various tip Mach numbers
for conﬁguration S3

92

:‘NNNN
030th

Pressure Ratio
: a:

1.2
1.0
0.8

 

0.6
0.00 2.00 4.00 6.00 8.00 10001200140016.0018002000

Specific mass flow 0 0:10“)

 

+ Mach Number = 0.108
-+— Mach number = 0.21

+ Mach number = 0.325
+ Mach number = 0.433
—0— Mach number = 0.542

 

 

 

Figure 4.10 Pressure ratio vs. speciﬁc mass ﬂow rate at various tip Mach numbers for
conﬁguration S4

 

 

 

 

 

 

 

 

 

 

14
12
S10
i a
0 /
g 6 714; \ﬁ
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o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00 2000
Specific mass flow o (xto‘)

 

—v— Mach Number = 0.108
+ Mach number = 0.21

+ Mach number = 0.325
+ Mach number = 0.433
+ Mach number = 0.542

 

 

 

Figure 4.11 Isothermal efﬁciency vs. speciﬁc mass ﬂow rate at various tip Mach numbers
for conﬁguration S4

93

 

2.6

 

2.4

 

2.2
2.0

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\

 

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0.6

 

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.001600

+ Mach Number = 0.108 smm‘: mm "m” ° (”‘04)
-O— Mach number = 0.216
+ Mach number = 0.325
+ Mach number = 0.433
+ Mach number = 0.542

 

 

 

 

Figure 4.12 Pressure ratio vs. speciﬁc mass ﬂow rate at various tip Mach numbers for
conﬁguration SS

 

12

K14

2.9/W \
. / \ \ N
/ \.

 

_A
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isothermal efficiency
on
2;.
\

 

 

 

 

 

 

 

 

 

 

 

0 .
0.00 2.00 4.00 6.00 8.00 10.00 12.0014001600

Specific mass flow 11> (X1094)

 

+ Mach Number = 0.108
-+— Mach number = 0.216
—e— Mach number = 0.325
+ Mach number = 0.433
+ Mach number = 0.542

 

 

 

Figure 4.13 Isothermal efﬁciency vs. speciﬁc mass ﬂow rate at various tip Mach numbers
for conﬁguration S5

94

 

 

 

 

NNNN
CN¢O§

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.2
‘6 1.8
K
g 16
3 14 ‘ﬂ‘ .
1'2 H‘N ‘\
w ‘9
1.0
0.8
0.6
0.00 1.00 2.00 3.00 4.00
Specific mass flow 0 (x103)

 

+ Mach Number = 0.108
+ Mach number = 0.216
+ Mach number = 0.325

 

 

 

Figure 4.14 Pressure ratio vs. speciﬁc mass ﬂow rate at various tip Mach numbers for
conﬁguration S6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14
12
>'10
§ \
'25 a - \
g \ \
E \o
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E
3 4
2
0
0.00 1.00 2.00 3.00 4.00
+ Mach Number = 0.108 Specific mass ﬂow O (x103)

+ Mach number = 0.216
+ Mach number = 0.325

 

 

 

Figure 4.15 Isothermal efﬁciency vs. speciﬁc mass ﬂow rate at various tip Mach numbers
for conﬁguration S6

95

 

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—v— Mach Number = 0.108
+ Mach number = 0.21

+ Mach number = 0.325
+ Mach number = 0.433
+ Mach number = 0.542

 

 

 

6.00

Specificmessflowdi

 

8.00

(x10“‘)

Figure 4.16 Pressure ratio vs. speciﬁc mass ﬂow rate at various tip Mach numbers for
conﬁguration S7

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

14
12 AC/A
5’ ‘0 1
5 \
1% 8 /
2 j \ V
5" ’ x
3 4
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o
0.00 2.00 4.00 6.00 8.00
_,_ Mach Number = 0103 Specific mass flow as (x104)
+ Mach number = 0.21
—¢-— Mach number = 0.325
+ Mach number = 0.433
—O— Mach number = 0.542

 

 

 

Figure 4.17 Isothermal efﬁciency vs. speciﬁc mass ﬂow at various tip Mach numbers rate

for conﬁguration S7

96

 

Figure 4.18 Four stage RFC full assembly

First itage Secind Stage Third Stage Porn Stage
7
C71) <r> <71) <70

 

 

C!) (E) <10 CE)

 

 

 

 

 

 

 

 

Figure 4.19 Sketch of four stage RFC

97

 

Figure 4.21 1St Stage channel of four stage RFC

98

athba

 

 

 

 

 

 

 

 

 

 

Figure 4.22 Schematic of blade and channel geometry

Table 4.2 Geometry of individual stages of four stage RFC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Radius Non-dim N on-dim Non-dim Non-dim Non-dim
RFC Ratio Blade Blade Radial Blade Axial
Stage 1; / r2 Depth Height Clearance thickness Clearance
b/r2 e/r2 c,/r2 t/r2 ca/r2
1St 0.828 0.0477 0.200 0.0286 0.0151 0.00310
2‘“I 0.849 0.0429 0.174 0.0238 0.0145 0.00310
3rd 0.866 0.0381 0.155 0.0226 0.0145 0.00286
4th 0.888 0.031 0.131 0.0193 0.0151 0.00286
Contd
Channel Channel impeller Channel Channel Channel Pitch
depth at depth at width inlet exit area area to
RFC inlet exit (2b + t)/ r2 area AM / r22 ratio cord
Stage d A / r2 d B / r2 Am / r22 A." / AM ratio
PC
15' 0.107 0.0878 0.1104 0.0172 0.0134 1.281 0.406
20d 0.0932 0.0763 0.1004 0.0130 0.0101 1.286 0.463
3rd 0.0818 0.0672 0.0909 0.0100 0.00789 1.279 0.525
4m 0.0689 0.0563 0.0770 0.00723 0.00562 1.286 0.619

 

 

 

 

 

 

 

 

 

99

 

Natural Gas, 0 = 195 slpm, Tin = 70°F

 

 

 

 

 

 

 

 

 

 

 

5 45

A f h 40
4 >
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9 A .9
a 3011:
II \ / UJ
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5 3 X m
a / ’25 E
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2 // y i _

‘.//‘/ \ ' 15

1 10

0.15 0.20 0.25 0.30 0.35 0.40

Impeller tip Mach number

 

Impeller tip Mach number vs. pressure ratio for Pin = 0 psig
impeller tip Mach number vs. pressure ratio for P1. = 5 psig
impeller tip Mach number vs. pressure ratio for Pin = 10 psig
impeller tip Mach number vs. pressure ratio for Pin = 15 psig
impeller tip Mach number vs. isothermal efficiency for Pin = 0 psig
impeller tip Mach number vs. isothermal efficiency for Pm = 5 psig
Impeller tip Mach number vs. isothermal efficiency for P," = 10 psig
Impeller tip Mach number vs. isothermal efficiency for P,n = 15 psig

 

 

 

Figure 4.23 Pressure ratio and isothermal efﬁciency vs. impeller tip Mach number for
various inlet pressures

100

NaturaIGas,Q=-.2503lpm,Tin=70°F

r _.

 

 

0)

/r$

% a.

‘/ ~20

 

 

M

 

Pressure Ratio
V ‘b
8
Isothermal Efﬂcrency

 

 

 

 

 

 

1 1 15
0.15 0.20 0.25 0.3) 0.35 0.40 0.45

Irrpeiler tip Mach nunber

 

 

Impeller tip Mach number vs. pressure ratio for PIn = 0 psig
Impeller tip Mach number vs. pressure ratio for Pin = 5 psig
impeller tip Mach number vs. pressure ratio for P,n = 10 psig
Impeller tip Mach number vs. pressure ratio for Pin = 15 psig
impeller tip Mach number vs. isothermal efficiency for P," = 0 psig
Impeller tip Mach number vs. isothermal efficiency for Pin = 5 psig
impeller tip Mach number vs. isothermal efficiency for Pin = 10 psig
Impeller tip Mach number vs. isothermal efficiency for Pin = 15 psig

 

 

 

Figure 4.24 Pressure ratio and isothermal efﬁciency vs. impeller tip Mach number for
various inlet pressures

101

Air,o=250s1pm,1',n=7o°1=

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5 50

r“ i "5
4 1405‘
«1 .2
.2”) 351
J cog
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2 I ~25§
f ./ —'

ﬂ/ 5"» ~20

M
1 15

 

0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
Irrpelier tip Mach nurrber

 

impeller tip Mach number vs. pressure ratio for Pin = 0 psig
impeller tip Mach number vs. pressure ratio for P," = 5 psig
Impeller tip Mach number vs. pressure ratio for Pin = 10 psig
Impeller tip Mach number vs. pressure ratio for P," = 15 psig
impeller tip Mach number vs. isothermal efficiency for Pin = 0 psig
impeller tip Mach number vs. isothermal efficiency for Pm = 5 psig
impeller tip Mach number vs. isothermal efficiency for Pm = 10 psig
impeller tip Mach number vs. isothermal efficiency for Pin = 15 psig

 

 

 

Figure 4.25 Pressure ratio and isothermal efﬁciency vs. impeller tip Mach number for
various inlet pressures

102

(POD/POS)—l

LEGEND= MOLECULAR
SYMBOL GAS WEIGHT
He 4
Air 29
32%N2 ,68% CHCLF2 6‘7

CHCLF2 86
SF 147

6
C8F16 400
202—1:43.145"
as

foe—raw?

(3

 

. 0.1 0.2 0.3 0.4 0.6 0.8 1.0 2.0

IMPELLER TIP MACH NUMBER, MOT

Figure 4.26 Pressure ratio vs. impeller tip Mach number (after Cates, 1964)

103

3.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.6 R
MOLECULAR
\‘ CURVE GAS WEIGHT
\ \ _.--_... He 4
2 4 \v \ Air 29
' \\\\ w.‘ ...... CHCLF2 s6
55‘ ‘P\\\’ \\ ‘ —_.— SF6 147
E N “‘s \\l~\ “\\
a. \_ \ \g g.
d v ‘V‘ v\"\ ““
:1 \\ \\ b\\ \\‘\
g 2.0 5 f“ \‘\~ “\
\\ x x v MOT =0 509
x \A \ 4» ___.
\ \ T f
. ‘ 0623
E \ \\v \N\ x // 0.769
53 1-8 \ \ . A ‘ s/ /
0 383 \ c . /0.847
E - . x ‘ x z 1037
V \ '
S i ‘\ \x \\ ‘ /1133
E. 1.6 0.322 \ ‘f\1K./\\
O 0.314 . 2f 1“ \_
E" '- 1, \\ \\
‘ \ \\ M
14 \ _ \ \ \ ‘_
' 0.260 \ \ X ‘
‘ \ \\ ‘ \\
\L “s \ \‘ ‘3.\‘\#\
~ ‘\ \x ‘V
1.2 .
t \ \ \
\ 0.174\ s. ‘
\‘ >\</ ' \ * \
0.127 “\1 if
L00 1 2 3 4 6x10‘3
SPECIFIC MASS FLOW, (I)o

Figure 4.27 Performance map of the ORGDP-l regenerative compressor (after Cates,
1964)

104

CURVE
___.Ai

l'

—— -—SF6
—'—C8F16

ISENTROPIC EFFICIENCY, Us %

 

3 4
SPECIFIC MASS FLOW, 0°

Figure 4.28 Efﬁciency of the ORGDP-l regenerative compressor (after Cates, 1964)

 

Figure 4.29 Pressure ratio vs. impeller tip Mach number and ﬂow coefﬁcient for four
stage RFC

105

>
o
c
.2
9
3:
UJ
E
E
L
a)
.C
._.
o
2

 

Figure 4.30 Isothermal efﬁciency vs. impeller tip Mach number and flow coefﬁcient for
four stage RFC

Pressure Ratio

 

Figure 4.31 Pressure ratio vs. impeller tip Mach number and speciﬁc mass flow rate for
four stage RFC

106

 

Figure 4.32 Isothermal efﬁciency vs. impeller tip Mach number and speciﬁc mass flow
rate for four stage RFC

107

CHAPTER 5

THEORETICAL INVESTIGATION OF
RADIAL BLADE RF C/RF P

There are very few mathematical models in literature which explain the behavior of
regenerative turbomachines and predict the performance. Most of these models need
extensive experimental support for performance prediction. Hence, it is very interesting
from an industrial stand point of view to ﬁnd efﬁcient theoretical means which are able to
forecast the regenerative turbomachine performances using easy to ﬁnd geometric and
ﬂuid dynamic parameters.

Wilson et al [69] presented a theoretical analysis of the three-dimensional ﬂuid motion
inside a regenerative pump. Basic model developed by Wilson was to represent the
phenomenon in the linear region as shown in Figure 2.10. He made several assumptions
and applied fluid dynamic equations to arbitrary control volumes of the pump. The entire

pump flow was characterized by tangential velocity V, and circulatory velocity Vt along a

mean streamline. Dimensionless performance characteristics for STA-RITE TH 7
regenerative pump were tested and reported in Wilson et a1 [69]. Experimental plots of
flow versus head were obtained at seven different speeds with air as working fluid.
Calculated and experimental performance curves were compared and excellent agreement
was observed. Qualitatively, the relations presented by Wilson satisﬁed the major details

of the observed ﬂow phenomena, but they needed extensive experimental support to

108

predict performance. Moreover, his model assumed incompressible flow, thus unable to
predict performance of compressors producing high pressure ratio. Moreover, Wilson
model lacked in correlation of losses with geometric and aerodynamic parameters.
Wilson's work is extended here to incorporate compressible flow to predict the
performance characteristics of Capstone multistage RFC. Moreover, l-D loss modeling is
done to correlate various losses with geometric and aerodynamic parameters, thus

eliminating need of experimental support.

5.1 Mathematical Model

Mathematical formulation is based on an arbitrary element of depth dXG = erH in the

peripheral direction of compressor as shown in Figure 5.1. Equations of motion can be
derived by considering these arbitrary small elements of one side blade and channel.
Dimensions of the impeller and flow channel are given symbolically in Figure 5.2 where
points 1 and 2 denote the locations at which assumed streamline enters and leaves the
impeller respectively. For simplicity in the presentation of the analysis, wall friction and

other irreversibility are introduced as head losses.
5.1.1 Assumptions

Following assumptions are made to develop the mathematical model.

. Fluid is assumed incompressible locally within a control volume. In the case of a
pump, the ﬂuid is assumed incompressible throughout the pump operation and
there is no variation in density from one control volume to the other. However, in
the case of a compressor, density changes from one control volume to the other.

Thus density is incremented from one control volume to the next using a

109

correlation which is developed from experimental data. This correlation is generic
because it is expressed in terms of non-dimensional parameters. It can be used for
the analysis of geometrically similar RFC. Details of this correlation can be found
in Appendix B.

o Fluid shear is assumed negligible in the model, however it is considered later in
the calculation by assuming a model for tangential head loss.

0 Steady flow without any leakages is assumed. Leakages are considered in a
separate model to avoid complexity in mathematics. Thus leakages are assumed
zero in the basic model.

0 Characteristic flow is one-dimensional in which major direction is radial,
tangential, and axial. The actual path traversed by a streamline is shown in Figure
5.2.

0 There are no end effects of suction, discharge and stripper carryover. The inlet
and exit losses are considered in a separate model.

0 Tangential pressure gradient is independent of radius. Literature and experimental
studies have conﬁrmed that this assumption is quite valid.

0 Although, tangential pressure gradient around the periphery is not perfectly linear,
however for simplicity, assumption of linear pressure rise across the periphery is

reasonable.
5.1.2 Governing Equations
The tangential components of velocity at points 1 and 2 can be given as

V =aU

01

(5.1)

V

a, = 0'U (5.2)

2

110

where 0' is the slip factor and a is a shock loss parameter introduced at blade entrance
to quantify shock losses. More details on calculation of slip factor and shock loss
parameter are provided later in this chapter.

Circulatory velocity at point 1 and 2 is assumed to be equal. Thus,

Vrl : Vr2 : Vr (5'3)
Circulatory ﬂow rate can be approximated by
er = crvchG (5.4)

Applying angular momentum equation to the impeller control volume of Figure 5.1, we

get
dp
dT = de. (r200, — nay, ) + rGA, d—gda (5.5)

Last term on the right hand side in the above equation represents the work done in raising
the pressure of the fluid between the impeller blades. This pressure rise is utilized across
the stripper to perform a turbine work. Therefore this term is ignored. Power input to the
differential control volume can be given as

dP = wdT (5.6)
Thus we can write,

(IF = dec (0U,2 - aUlz) (5.7)

Applying Bemoulli’s equation to the impeller control volume of Figure 5.1, we get

2 2 v2 2 2 V2
dpzder $+£+.p_2_.q_ul__4__p_l. (58)
2 2 p 2 2 p

Equations (5.7) and (5.8) yield,
2 2 2 2

2 2 -

V. Vn
El—+—‘i+£ﬂ-+0’U§=&+#+g—U-2—+aUlz+gHrb (5,9)

,0 2 2 ,0 2

111

where Sth is the head loss of circulatory velocity through the impeller region.
Applying continuity equation to the channel control volume of Figure (5.1).
,0(V9m + avg," /2)(Ar +dA‘. /2) + ﬂag: = ,0(V9m -—dV9m /2)(A, —trAr /2) +919? (5.10)
or
d(V9mAc)=O (5.11)

where V0," is mean tangential velocity which can be obtained as

Angular momentum equation in the tangential direction yields

pRGWo... +th... I2><A. +dA./2)dvt.. = RG<P—dP/2)(A. —dA./2) 5 13
-de€(R1Vgl — szm) — RC (P + dP/ 2)(Ac + (01c / 2) + RGPdAt — wall friction term ( ° )

By using continuity equation, the above equation can be reduced to the following

equation.
dgH = (IQ, /Qs(U,v,_,_ -U1V01)+ ﬁnd/1,121, —dgHL (5.14)
where Q. = (URGAc is ﬂow rate based on solid body rotation.

In the right side of the above equation, the ﬁrst term refers to head rise caused by
momentum exchange of blade, the second term gives head rise caused by the deceleration
of the mean tangential velocity and the last term gives head loss caused by the friction
and the contraction or expansion of the tangential velocity.
Applying Momentum equation in the circulatory direction, we get

m — W + ,onv( = pZHBdez — leBlXm - wall friction term (5.15)

VdV -
Q r c =p2 pl _gH”.
d0. 9

 

(5.16)

112

where 3H“. is the head loss of circulatory velocity through the impeller region.

Energy equation applied to channel control volume of Figure 5.1 after some

simpliﬁcations yields

2 2 2
—‘-+—+-—-—-‘-=—+—-+--——l-+gH“ +
p 2 p 2 2

 

Q (dgH + dgHL — Kind/1r IAC + Vch() (5.17)

If equation 5.9, equation 5.14 and equation 5.16 are used in equation 5.17, the ﬁrst order

nonlinear ordinary differential equation can be obtained for the circulatory ﬂow as follow.

VdV o
_Q_.‘_L = (1——Q-)(0'V6’2 -aV921)— SHt (5.18)

(1Q. Q.»
where ch = chb + gH“ is the sum of head losses related to the circulatory velocity, also

called circulatory head losses.

5.2 Slip Loss

Tangential pressure gradient in regenerative turbomachines enhances the slip factor
considerably. Pressure difference between any two adjacent blades of an impeller causes
a tendency for a secondary circulation about each blade such that the ﬂuid leaving the
impeller deviates from the path prescribed by the blade surface, backwards with respect
to the positive direction of impeller rotation. The result is that the ﬂuid tangential velocity
at exit is less than that which would be expected from the velocity triangle based on the
outlet blade angle. In order to allow for the reduction in the ideal tangential velocity, a
slip factor is usually introduced which is deﬁned as ratio between actual tangential
velocity and that obtained with the assumption that. the ﬂow angle and blade angle are

identical.

113

Slip factor is one of the vital items of design information because of its direct effect on
energy transfer. A number of methods have been developed by various investigators for
the assessment of the effect of slip. Noteworthy are the contributions from Stodola,
Busemann, Fergusons and Stantiz. However, these and other authors published methods
for the cases where there is essentially no tangential energy gradient. Hence, formulations
suggested by these authors are not applicable to regenerative turbomachines in which the
sole purpose is to develop tangential pressure gradient.

El-Hag [22] developed a method of analysis of the ﬂow in regenerative turbomachines.
He suggested that slip factor for regenerative turbomachines should be viewed as a
function of the circumferential gradient of pressure as well as ﬂow variables, impeller
speed and dimensions, the angle and number of impeller blades.

i.e.

a=f(r2,w,ﬂ2,Z,W2,§a%j (5.19)

El-Hag extended the expression proposed by Stodola and proposed a slip factor
correlation given below for computing a ﬁrst order estimate of the slip factor in

regenerative turbomachines.

0:1.0—M ”491?: (5.20)
02 W

2 p

This relation however needs velocities to be determined experimentally. In this work,
authors have proposed an alternative slip factor correlation for regenerative compressors

given below.

114

0': (5.21)

 

 

where SP is a factor to incorporate the effect of tangential pressure gradient on slip factor.
The term SP is correlated with impeller tip Mach number and speciﬁc mass ﬂow rate.

This correlation is valid for all stages of Capstone multistage RFC.

In M
SP = 1.38 —0.00317—L—0t2-)+8.l63x10"°ln—£(:—))-

0T

(5.22)

5.3 Shock loss

Shock or incidence losses are caused by difference between blade angle and ﬂow angle
when ﬂuid enters the blades. Wilson [69] introduced a shock loss parameter a to
quantify such losses. He related shock loss with various geometric and aerodynamic
parameters. Although Wilson’s model was based on rectangular channel geometry,
however still it can be used for Capstone multistage RFC channel geometry. The channel
shape and dimensions used by Wilson for his shock loss model can be seen in Figure 5.3.
Wilson related the through ﬂow rate with shock loss parameter and known geometry.

Following relation was proposed in Wilson [69].

Q = 1[1]Q. [190%- Kza] (5.23)
2 r0 r2

where, Q = rGA‘w denotes the ﬂow associated with solid body rotation and K1,K2 and
K3 are dimensionless coefficients depending only on the geometry of the open channel.

These coefﬁcients are given as:

115

 

 

 

 

 

(A3+A.)2_(A.+A2)Z+CA.A2
K =’_2 A: A3 GA?
3
r. 1
‘ —— A3+A4-bd£
L W n .
+
2:16.201 A.)_cA._ 01.
c 5A6 2r2Ar
2 +A 2
K,=—K,+ “(A3 ‘)— A“; 5—2-3
«A. 3AM! 6
where
bC b+d
A.=--’-, Ai=(——)C~ A.=(r3-rt)d
2 2
bd

A =—2- and A=A1+A,+A3+A4

4

5.4 Circulatory head losses

Circulatory head losses have two contributions.
0 Head loss of circulatory velocity through the impeller region is referred as 8’th-
0 Head loss of circulatory velocity through the channel region is referred as chr.
The sum of these two head losses is the total circulatory head loss given as:
g”r = 8”“, + 8H”.
Circulatory head losses arise from many sources. Following sources of circulatory head
loss are quantiﬁed.
5.4.1 Channel turning losses (k,)
These losses are due to 180° turn of the ﬂuid through the channel. Flow pattern is similar

to ﬂow patterns in 180° turn without guide vanes. Channel turning losses can be

simulated using the following equation.

116

AP =§p1gvf (5.24)

where k, is channel turning loss coefﬁcient and If. is the circulatory velocity. The channel

turning loss coefficient is correlated with channel geometry to study effect of channel

geometry on channel turning losses while doing design sensitivity analysis. k' is a

function of channel geometry. It is correlated with two geometric parameters of channel,

which are "d " and "e" as shown in Figure 5.4. Correlation of k, with the ratio x = d leis

given below.
k, : a +th2 + C):4 +dx6 +ex8 + fxlo + g):12 + hx" +ix16 + jx18 +k.1r20
where x=d/e, a=—4.58, b: 335.31, c=—9.87x103

d =l.63x105,e=-1.68x106,f =1.14x107,g =-5.20x107
h: 1.56x103,i= -2.97x108. j: 3.25x108,k=-1.55x108

5.4.2 Channel and Blade Mixing Losses

Fluid after passing through blade makes a 90°tum and enters the channel. Circulating
ﬂuid mixes with incoming stream of ﬂow and thus it encounters channel mixing loss.
Moreover, there is also a loss encountered in the blade passage due to this mixing and we
call it blade mixing loss. These losses are simulated by procedure followed in literature to
simulate losses in merging streams of ﬂows. It can be assumed that this mixing process
takes place at 45° with the incoming stream as shown in Figure 5.5.

Two non-dimensional geometric and aerodynamic parameters are introduced to quantify
the mixing losses encountered in the side branch (ﬂow going out from the blade towards
channel).

Q. A.

Q Arirr‘ulmion

where,

117

Qr is the circulatory ﬂow through one blade passage
Q is the through ﬂow through the channel

A is the area through which ﬂow circulates from blade towards channel

('rrr'ulamm

Ar is the channel through ﬂow area

The mixing losses which occur at the exit of blade region when ﬂow takes 90° turn and
mixes with the incoming stream of through ﬂow can be simulated by introducing a loss

coefﬁcient k, given by,

(”my-2(1-c.)’-1-4IC.C5)

 

(QC. )2
Blade mixing losses can be determined from,

1
AP. =-2-pk.vf (5.25)

Mixing losses in the peripheral branch (through ﬂow in the channel) result in pressure
drop in the peripheral direction and they can be simulated by introducing a loss

coefﬁcient k“ given by,

 

1-(1—C,)’ 141ch
"' (l-C.)’

Channel mixing losses can be determined from,

l.

1
APh = 2 pkrhVQf" (5.26)

Thus the mixing losses are correlated to aerodynamic parameter Cl and geometric

parameter C2 .

118

5.4.3 Blade turning loss ( kb)

Blade turning losses can be simulated using the following equation.
1 2
AP = -2- pka, (5.27)

where kb is blade turning loss coefficient. It is a function of channel geometry. It is been

correlated with two geometric parameters of channel, which are radial clearance “c, ” and

blade width “b ” as shown in Figure 5.6. The correlation helps to study the variation of
radial clearance and blade width on blade turning loss while doing the sensitivity analysis.

Ratio x = c, lb and peripheral distance dXG which ﬂuid takes to complete turn through
the blades are the inputs for the correlation. Peripheral distance dXG is estimated by
dXG = rGQ. (5.28)

k, rs grven as

C
k = 0.322 - 0.053(4) - 0.00863 dXG
b

in

5.4.4 Sudden expansion (k3,)

This loss is caused by the increase in ﬂow area when ﬂuid ﬂows from blades to channel.

Sudden expansion loss coefﬁcient is related to blade blockage factor given as
2
l —- BF
Sudden expansion loss can be quantified by
l 7
EphJ/J (5.29)

Consequently, model for the circulatory head loss can be arranged as follows.

119

1 . 1 7 1 7 1 . 1 .
Ht. =—k,V‘.~ +—ks.V‘.“ +—k V; +—k(,,V‘m +—k.eV(.‘ 5.30
g 2 2 ‘ 2 ” 2 ’ 9 2 ‘ ( )

5.5 Tangential Head Losses

Head losses caused by channel friction are referred as tangential head losses denoted by

dgHL. They involve the channel curvature effect and can be determined by applying the

classic pipe-loss formula.

 

,1 V2 dX
d H zﬂT—G- 5.31
8 L 20h ( )
where
D 0.5)
A :2 1+0.075R 0'25 —"—
f i 8 (2,) J (5.32)
’10 is defined for straight channel as,
20 = 0316126“)-25 (5.33)
where Re is given based on hydraulic diameter as,
Re = We“ (5.34)

V

5.6 Leakage Losses

Total leakage ﬂow rate can be estimated by the following equation suggested by El-Hag

[22].

 

 

(Ur C r
= 2 b+—"—i 5.35
Qt.“ 2 (C, 2 J ( )

5

120

5.7 Losses in Ports

Losses in inlet and discharge ports are estimated by

l

Inlet port AB” = 3 kmme2 (5.36)
1

Outlet port APO", = EkoquVOi, (5.37)

The two loss coefﬁcients Km and KM need to be correlated with the nozzle geometries

and ﬂow rates to study the effect of inlet and discharge ports on performance. Discharge
nozzle of Capstone multistage RFC is contoured and has very complicated geometry,
while the inlet manifold is a straight through hole. Effect of inlet and discharge manifold
is not primary aim of this work, so port loss coefﬁcients are not correlated with
aerodynamic parameters. Instead, reasonable values of these coefﬁcients are assumed and

held constant.

5.8 Performance prediction and comparison with test data

Based on proposed mathematical model and loss correlations, a performance prediction
code is developed to predict Capstone multistage RFC performance. Mathematical
formulation is based on some geometrical parameters which are assumed to be known
from multistage RFC drawings. A high level ﬂow chart of the code is provided in Figure
5.7. Performance prediction code predicts pressure ratio for the entire operating range.
Results are compared with test data for Capstone multistage RFC. Excellent comparison
is observed as seen from Figure 5.8 and 5.9. These figures represent theoretical and test

data overlapped for natural gas as working ﬂuid at four different inlet pressures of

Opsig,5 psig,10 psig and 15 psig at inlet temperature of 70°F . To condense the

121

presentation, Figure 5.8 represents results at 195 slpm and Figure 5.9 represents results at
250 slpm ﬂow rate. The close agreement in theoretical and experimental results led the

researcher to carry out extensive sensitivity analysis on various design parameters of RFC
to improve performance. In chapter 6, results from design sensitivity analysis are
presented along with suggestions for improvement. Moreover, a design procedure for
radial and non-radial blade RFC is suggested which can be very useful for designers and

engineers.

5.9 Conclusions

To assist in improving efﬁciency of Capstone multistage RFC, governing equations for
the blade and channel region are developed and loss modeling is done to develop
correlations of losses with geometric and aerodynamic parameters. The presented
mathematical model is useful to predict performance of regenerative pumps and
compressors with radial and non-radial blades. A performance prediction code based on
governing equations and loss models is developed and performance results are compared
with test data on Capstone multistage RFC. Excellent agreement between theoretical and
test data is observed which motivated to carry out an extensive design sensitivity analysis

to improve RFC performance. Findings of sensitivity analysis are discussed in chapter 6.

122

VrZ

 

 

 

 

 

 

 

 

 

u V92
: Ar + dAr / 2
1| HB2 p + dp/ 2~
1‘ HTz P2;
xx"? + dp/ 2 Va... + We. /2
x V HBl Va + dV,1 /2
‘ cl
“___ p _
V t_pl l
0 1
p — dp / 2
l/dxo: Roda dXG = Roda
impeller region channel region

Figure 5.1 Control volumes representing section (10 of open channel and impeller

 

<—-—W f—Ca
—-lti—b .__d_.

 

 

 

 

 

 

23

 

 

---—-——----ﬁ-

————-

1

 

 

 

74
/

Figure 5.2 Schematic of blade and channel geometry

 

 

 

 

 

 

 

 

e—W—ﬂ Ca
—11:r-b —i Pd—t

 

 

r——-+--— Y "_I.-3--'ﬂ'

 

A

 

 

2? E
I‘2

 

L---..- ___-..-

 

/
-—|——-_--___------

 

 

I
| I
: I
1 [I \
L---_:..l’ / i.
: A L , b/2

 

 

N—

 

 

L

 

 

 

 

 

Figure 5.3 Geometry for shock loss model

 

Figure 5.4 Geometric parameters governing channel turning loss coefﬁcient

124

 

\/
\/

 

 

Side Branch
ﬂow enters in charmel ﬁom balde

Acirculation

Figure 5.5 Mixing process of ﬂow entering channel through blades

 

/ cr

 

 

 

 

 

 

 

 

 

 

 

Figure 5.6 Geometric parameters governing blade turning loss coefficient

125

 

Inputs: geometry information
Gas properties

Operating point

 

 

 

 

 

Calculate MOT and (I)

 

 

 

 

 

Estimate number of passes
" N " using correlation of

N with Morand (I).

 

 

 

 

 

Calculate Density distribution
across the periphery

 

 

 

 

 

Calculate slip factor n 0' "

 

 

 

 

 

 

Start calculation for N = 1

 

 

 

 

 

Calculate shock loss
parameter " a "

 

 

 

 

N=N+l

 

 

 

 

 

Calculate circulatory losses,
circulatory velocity and
circulatory ﬂow rate

 

 

 

 

 

Calculate tangential head
losses

 

 

 

 

 

Calculate Pressure rise and
temperature rise.

P =PN+§P

Nol

T =T~+§T

NH

 

 

 

 

 

 

 

Go to second stage and so on for all 4 stages
using same procedure and predict pressure ratio.

 

 

 

Figure 5.7 Flow chart of performance prediction code

126

MG, 195 slpm, Pin = o to 15 psig, Tin=70°F

 

 

 

.h

 

 

 

l

 

 

Pressure ratio

N

/
45%;“

 

 

 

 

 

 

 

 

 

0.20 0.25 0.30 0.35 0.40
Mach number

 

Code Prediction for P," = 15 psig
Experimental Result for Pm = 15 psig
Code Prediction for P," = 10 psig
Experimental Result for P," = 10 psig

Code prediction for P1,, = 5 psig
Experimental Result for P," = 5 psig
Code Prediction for P," = 0 psig
Experimental Result for P," = 0 psig

 

 

 

Figure 5.8 Theoretical and test data overlapped for ﬂow rate 195 slpm

127

Pressure ratio

NG, 250 slpm, Pin = 0 to 15 psig, Tin=70°F

 

 

 

 

 

 

 

2 / /
K

0.20 0.25 0.30 0.35 0.40

Mach number

 

 

 

 

 

 

 

 

Code Prediction for P," = 15 psig
Experimental Result for P," = 15 psig
Code Prediction for Pm = 10 psig
Experimental Result for Pm = 10 psig

Code prediction for P," = 5 psig
Experimental Result for P," = 5 psig
Code Prediction for P," = 0 psig
Experimental Result for P," = 0 psig

 

 

 

Figure 5.9 Theoretical and test data overlapped for ﬂow rate 250 slpm

128

CHAPTER 6

DESIGN SENSITIVTY ANALYSIS

Performance prediction code predicts the pressure ratio, however isothermal efﬁciency is
the parameter which designers usually want to maximize. To predict the isothermal
efﬁciency, power draw needs to be predicted as well, which requires heat transfer
calculations. An alternate method is adopted here to perform design sensitivity analysis.
Pressure ratio and power coefﬁcient are directly proportional to impeller tip Mach
number. Moreover, in order to maximize isothermal efﬁciency of RFC, higher pressure
ratio is desired for a given impeller tip Mach number. Usually, it is difﬁcult to optimize
the design for all operating points. Therefore, it is a standard practice in turbomachinery
to select a design point where designer intends to achieve peak efﬁciency. Design point

selected to perform sensitivity analysis yielded impeller tip Mach number of 0.369 and
speciﬁc mass ﬂow rate of natural gas equal to 1.04x 10". RFC builds the required pressure
ratio for microturbine operation, however very low isothermal efﬁciency levels
(IS—20%) are achieved. When comparing efﬁciency to historical test results, it appears
that significant improvements to efficiency could be achieved. The idea of sensitivity
analysis lies in the fact that if higher pressure ratio is obtained at MOT =0.369 keeping

<1) = 1.04x10" by making design changes in the geometry of RFC, it means the isothermal

efﬁciency is improved. Therefore, the code is run at this design point to do an extensive

129

sensitivity analysis and study various losses and their behavior with different design
changes. The trend in pressure ratio is predicted for each design change. Design changes
are optimized so that head losses are minimized and for a given tip Mach number and
speciﬁc mass ﬂow rate, higher pressure rise and better efficiency is obtained. Sensitivity

analysis is performed on blade and channel geometry as discussed independently.

6.1 Analysis of channel geometry

Extensive sensitivity analysis is carried out using the code by varying some channel
dimensions listed below and trying to maximize head at given tip Mach number and
speciﬁc mass ﬂow rate. These dimensions are listed below and are also shown in Figure

6.1.

1. Radial clearance"c, "
2. Channel inlet area " Am, "

3. Channel height "e "

4. Area ratio AKA/An,3
6.1.1 Radial clearance "c, "

Radial clearance "c, " has effect on three types of losses:
0 Shock Loss
0 Blade turning Loss
0 Channel and blade mixing Losses
Shock loss is minimized by increasing radial clearance"c,". This effect is studied by

varying radial clearance. Shock loss parameter inversely affects the pressure ratio. In

order to get higher pressure ratio and isothermal efﬁciency, shock loss parameter should

130

be as small as possible and actually a negative value is beneﬁcial since it increases the
pressure ratio. Usually, at very low ﬂow rates, negative values of "a" are obtained, which
mean higher pressure ratios.

Blade turning loss is also minimized by increasing radial clearance "c, ". Effect of radial
clearance on blade turning loss coefﬁcient is studied by keeping all other terms constant
in correlation of blade turning loss coefﬁcient with channel geometry. The trend in blade
turning loss coefﬁcient with variation in radial clearance can be seen in Figure 6.2 in
which various loss coefﬁcients are plotted against the ratio"c, /r2 It must be noted that
the tip radius is held constant while performing sensitivity analysis for radial clearance.
This ﬁgure shows that increasing radial clearance helps to minimize losses associated
with ﬂow turning through the blades.

Channel and blade mixing losses are also affected with the change in radial clearance.
The two loss coefﬁcients "km " and "km " are plotted with ratio "c,/ r2 " as shown in Figure
6.2. Blade mixing loss does not show any trend and it is very hard to conclude anything
that either increasing or decreasing radial clearance helps to reduce this loss. However, a
deﬁnite trend is obvious in the channel mixing loss. Channel mixing loss becomes more
and more negative with increasing radial clearance which helps to increase pressure ratio
and efﬁciency. In order to study the cumulative effect of above losses and effect of radial
clearance on pressure ratio, the pressure ratio for ﬁrst stage of Capstone multistage RFC

at design point is plotted against ratio "c, /r2 " as shown in Figure 6.3. It is obvious fromv
Figure 6.3 that pressure ratio is directly proportional to the radial clearance"c, Thus it

can be concluded that for a given impeller tip Mach number, increasing "or "will increase

pressure ratio and isothermal efﬁciency.

131

Another interesting point which is observed in the sensitivity analysis is that it is not
suggested to increase radial clearance indeﬁnitely. After a certain percentage increase in
clearance, the pressure ratio actually starts going down as shown in Figure 6.3. It is found
that after a 40% increase in radial clearance, the pressure ratio starts to go down. This is
detrimental to the efﬁciency as well. This is illustrated in Figure 6.4 and Figure 6.5 taken
from Cates [15], which show a reduction in pressure rise and decrease in efﬁciency with
huge increase in radial clearance. Cates presented the data at two values of tip Mach

numbers; 1) Air with M 0, =0.383 and 2) SF6 at M 0, =1.04. However, results on air

which are at low Mach number should only be considered. Moreover, in air tests, speciﬁc
mass ﬂow rate range close to operating point of Capstone RFC should be observed. It is

reminded again that emphasis is to optimize the geometry at
MOT =0.369 and<I>=1.04X10‘3. Thus SF6 results should be ignored due to the high

Mach number.

Cates varied radial clearance from 0.2 to 0.5, which was a huge increase. This proved
detrimental to the adiabatic efﬁciency as shown in Figure 6.5. It must be noted that in
Figure 6.5 “h” represents the radial clearance and “b” is the channel depth. This ﬁgure
shows that increasing radial clearance is harmful to the efﬁciency, however, still it can be
argued that increasing the radial clearance to a small percentage is beneﬁcial to
performance. It was only because Cates increased the clearance by 150% during his
testing, which made the efﬁciency to go down. Sensitivity analysis presented here
suggests that increasing radial clearance immensely will prove detrimental. However, the
mismatch between trends observed by the code and Cates data need more clariﬁcation.

Thus results presented in Wilson [69] are studied to learn about the exact behavior of

132

radial clearance. The same effects were observed by Wilson [69] as shown in Figure 6.6
where it can be seen that a small increase in radial clearance was beneﬁcial for head rise,
however a huge increase in radial clearance proved detrimental. It is interesting to
compare conﬁguration 1, 2 and 4 in this diagram, where it can be seen that as one moves
from 2 to 4, which means a small increase in radial clearance, there is an increase in head
coefﬁcient. However, when the radial clearance was increased too much as shown in
conﬁguration 1, the head coefficient decreased. It is true that conﬁguration 4 has channel
area reduction as well in addition to radial clearance change, but still it can be observed
from the three conﬁgurations that increasing the clearance indeﬁnitely is detrimental as
depicted by conﬁguration 1. However, it will be more useful to study the effect of the

ratio "q/d, " and try to optimize that parameter. This will be presented later in this

chapter. Thus as a guideline, it is recommended that for RFC under consideration, radial
clearance should not be increased more than 25-30%. However, generally speaking an

increase in radial clearance is beneﬁcial to its performance.

6.1.2 Channel inlet area "Am"

Channel area at inlet is a function of channel depth "d A " and channel height e as
shown in Figure 5.2. Channel depth effects following losses.

0 Shock Loss

0 Channel turning Loss

0 Skin friction loss
Shock loss model is based on rectangular cross sectional area channel, which is also
similar to the cross section of Capstone single stage RFC discussed in chapter 4. Figure

6.7 describes the variation of shock loss parameter "a" with ratio of channel depth at

133

station A and tip radius "d, / r2 It must be noted that tip radius is held constant while
doing sensitivity analysis for channel inlet area. It is obvious from Figure 6.7 that a
higher value of "d, "minimizes the shock loss. Thus shock loss model suggests that a
higher value of "d," is beneﬁcial for improved performance. Channel turning loss

coefﬁcient k, is plotted against ratio "d, / r2 " in Figure 6.8 to see the effect of channel

depth on channel turning loss. This figure suggests that when "d, " becomes greater,
turning loss in the channel also increases. Thus this suggests that a smaller "d, "is suited

to minimize the channel turning loss.

Figure 6.8 is plotted keeping channel dimension "e" as constant and varying "d, "only.
However, it was suggested above that radial clearance has to be increased slightly for
better performance. This means, dimension "e" has to be increased as well to match the
radial clearance. Therefore, it is essential to study the effect of ratio x=dA/e on the
channel turning loss coefﬁcient. Thus, the ratio xsz/e is plotted against channel
turning loss coefficient as shown in Figure 6.9. It is interesting that a lower value of this
ratio is beneﬁcial for more head rise and efﬁciency. This also suggests that "d A " must be
reduced for better performance.

Another loss which is affected by varying "d, "is channel skin friction loss. Skin friction
head loss is plotted with ratio "d, /r2 "in Figure 6.10 to see the effect. It is obvious that as

we make the channel depth smaller, skin friction effect increases. This is intuitive as well,
because a smaller channel depth would mean more interaction of ﬂuid with channel, thus

increasing frictional losses. This suggests that a larger channel depth "d A " is beneﬁcial

for performance.

134

Above analysis on shock loss, channel turning loss and skin friction loss suggested
different behavior with varying channel depth. This random behavior led to confusion in
determining which loss is more inﬂuential to pressure ratio and efﬁciency in the RFC.

Should channel depth "d, "be decreased or increased? To help this out, Capstone single

stage test data presented in chapter 4 and test data in literature on varying channel depth
and its effect on performance is consulted. Figures 6.4, 6.5, 6.6 and 6.10 suggest that at

low speciﬁc mass ﬂow rate values, a smaller value of "d A " increases the head and

efﬁciency. Figure 6.4 and 6.5 suggest that the effects of geometry are quite different at
different Mach number and speciﬁc mass ﬂow rate values. With each successive increase
in channel dimensions, the air data exhibits a decrease in pressure ratio at shutoff but a
considerable increase at high ﬂow rates. The effects of geometry changes on isentropic
efﬁciency are shown in Figure 6.5. Increase in channel depth causes a sharp drop in
efﬁciency. Figure 6.6 adopted from Wilson [69] also suggests that decreasing channel
depth helps to improve the performance. Figure 6.10 obtained from Burton [11] also
suggests that at low ﬂow rates, it is beneﬁcial to decrease the channel depth. It is obvious
from Figure 6.10 that the trend of channel depth depends on ﬂow rate through the RFC. If
this ﬁgure is carefully analyzed in terms of head and adiabatic efﬁciency, it shows that
for low ﬂow rate applications, decreasing channel depth is beneﬁcial. This analysis from
literature hints that the test data cited is based on a rectangular channel cross sectional
area. Rectangular channel area does not guide the ﬂow properly and there can be huge
mismatch between the blade angle and ﬂuid angle. This means that rectangular cross

sectional shape is responsible for more shock loss. It is true for a rectangular cross

sectional area channel that increasing "d, "will enhance performance, because it reduces

135

the shock loss. However, it is obvious that increasing channel area will increase channel
turning loss signiﬁcantly. Thus, increasing the channel depth does not seem to provide
the solution of the problem. It is thought that the circular cross section channel area of
multistage RFC helps to minimize the shock loss. Thus, there is no need to increase the

channel depth and rather a decrease in the channel depth "d A " will prove beneﬁcial to

enhance isothermal efﬁciency. A reduction in channel depth will reduce channel turning
loss and moreover provide higher through ﬂow velocity, which might lead to more
circulations at low ﬂow rates. The more the number of circulations through the impeller
means more head at a given impeller tip Mach number. Thus it can be concluded that a

smaller channel depth "d, "is beneﬁcial for multistage RFC or in other words, smaller

channel area is beneﬁcial for better performance at least at the design point. A design
criterion for selection of channel depth is not addressed at this point. Based on
experimental data and sensitivity analysis, some design criteria for channel depth are

presented towards end of this chapter.
6.1.3 Channel height "e"
It is obvious from the above discussion that channel height "e" must be increased as a

result of increased radial clearance "or

6.1.4 Area ratio ARA/An,

Another important parameter effecting the pressure ratio and hence isothermal efﬁciency
is channel area ratio. From sensitivity analysis of the code, it is concluded that higher the
area ratio, higher is the pressure ratio and efficiency at a given impeller tip Mach number.
This fact was validated by Capstone single stage experimental test data presented in

chapter 4. It was found through test data that a higher area ratio is beneﬁcial for improved

136

pressureratio and isothermal efﬁciency. Figure 6.11 shows the increase in pressure ratio
obtained by increasing the area ratio. Unfortunately, there is not much information
available in literature on varying cross sectional area RFC to compare and validate our
conclusion about area ratio. However, it is intuitive to have a higher area ratio for better

compression of ﬂuid.

6.2 Design changes in channel geometry

Performance prediction code suggests which design changes in channel geometry are
beneﬁcial for RFC performance. However, it does not provide any precise idea about
what percentage variation in each design variable is optimal for performance. It is
essential to study the existing multistage RFC geometry and analyze it with other
geometrically similar regenerative compressor designs available in literature ,to get
further insight. Thus, an analysis is conducted based on non-dimensional parametric
study using available geometric data in literature, geometry of various conﬁgurations of
Capstone single stage RFC (presented in chapter 4) and geometry of individual stages of
multistage RFC. Based on this study, some design criteria for each variable are
established as discussed below. Design criteria for sizing the radial clearance and
channel depth of RFC is suggested below.

0.2 < c, /d, < 0.65 (6.1)
0.03 < c, /r2 < 0.05 (6.2)

Some authors did experimental sensitivity analysis on channel dimensions in the past.
Their analysis is also presented in this work for discussion purpose. Table 6.1 gives some

of the dimensions of six configurations tested by Wilson [69]. The maximum

137

dimensionless head at low ﬂow coefﬁcients was obtained from conﬁgurations 2. It is
interesting to note that the radial clearance and channel depth for conﬁguration 2 lie in
the established bounds.

An experimental sensitivity analysis was also performed by Cates [16]. It is found from
Cates paper that best performance at design point resulted by keeping ratio
c, /d, = 0.4 and c, /r2 = 0.04 , which lies in the bound established above.

Test data on ORNL CRDT regenerative compressor was also available in Cates [16] and
it was calculated that their design used c, /d, = 0.44 and c, /r2 = 0.044 which also lie in the
established bound. Moreover, data on ORNL FPD design of RFC is also cited and values

of q/d, =0.25 and c,/r, =0.048 were used in their design, which also fall in the

established criteria.

Capstone single stage test data is another source to validate the established design criteria.
As discussed in chapter 4, S3 conﬁguration was found to be the best conﬁguration. Thus
it is interesting to ﬁnd out values for the two design criteria for conﬁguration 83. When it

is explored, it is found that for station A, cr/dA =0.623 and c,/r2 z0.05 gives the best
performance. For station B, cr/dB = 1.06 is found. Fortunately, the value for station A

falls in the established bound, however the value at station B is very high. The reason for
this high value is that the analysis conducted above is based on a constant channel area
throughout the periphery of RFC. However, Capstone multistage RFC and Capstone
single stage RFC have varying cross sectional areas. Based on the above discussion, it
can be concluded that the suggested design criteria in (6.1) and (6.2) are valid and very
useful for designers and engineers to size dimensions at inlet station A for regenerative

compressors desired to operate at low specific mass ﬂow rate.

138

 

The established design criteria motivated the researcher to analyze existing geometry of
multistage RFC in the light of established design criteria. The key geometric parameters
for all four stages of the multistage RFC are reproduced in Appendix C. After analyzing
the four stages and checking for the established criteria, it was concluded that it is

possible to increase radial clearance " c, " of individual stages by a certain percentage, but

it must be noted that it should not be increased too much so that it violates the design
criteria in (6.1) and (6.2). A 25-30% increase might be possible without violating the
criteria. However, increasing the clearance would imply an automatic increase in channel
height "e" as shown in Figure 5.2. Thus channel inlet area and the channel area ratio will

have to be established properly by controlling the channel depth d, and d3. Another

important ﬁnding from this analysis is that it might be beneﬁcial for performance
improvement to increase the inlet cross sectional area by 10-15% and reduce the exit
cross sectional area by 5-10%, so that the channel area ratio can be increased slightly and
inlet cross sectional area is increased as well. The logic behind increasing inlet cross
sectional area is that as the ﬂow enters from the inlet port, a higher inlet cross sectional
area will help the ﬂow to settle and form helical ﬂow pattern. Moreover, the carryover
ﬂuid coming from stripper seal (blocking the outlet port pressurized ﬂuid to mix with
inlet low pressure ﬂuid) will mix with incoming stream of ﬂuid and extreme turbulence
could be reduced by the larger cross sectional area at inlet. Moreover, by this
modiﬁcation, the acceleration region as shown in Figure 2.10 might be reduced and linear
region might be increased, which means more head rise can be obtained. This calls for
slightly enlarged inlet port as well. It is learnt from literature that higher diameter of inlet

and discharge nozzles helps to produce higher heads and better efﬁciency by reducing

139

losses in the ports region. Based on the above discussion, following design changes to

channel geometry are suggested to improve Capstone multistage RFC performance.

0 Increase radial clearance "c, "by 25-30%.

0 Adjust channel height "e" accordingly.

0 Increase inlet channel area at station A " Ac. A " by 10-15%

0 It is been proven by many authors and even sensitivity analysis that a smaller

value of d, is beneﬁcial for isothermal efﬁciency. However, still it is suggested
to size d, based on "e" and value of inlet channel area at station A. d, can be

calculated to produce required inlet cross sectional area at station A.

o Decrease discharge channel area at station B " A“, " by 5-10% or rather little less

so that the channel area ratio must be less than 1.35 or maximum 1.40. However,

to ﬁt the values and make it look realistic, the increase in "An A " can also be

moved around from 10-15% value to a lower value as desired.

H N

0 Based on e and "ACE" it is very easy to calculate dB to produce required

discharge cross sectional area at station B.

0 Keep a linear area distribution from station A to B.

o Inlet nozzle cross sectional area should be increased 10-15% in order to reduce
losses in the inlet port.

0 Discharge nozzle is tapered and it should be modiﬁed to match with the discharge

area at each stage.

140

6.3 Analysis of blade geometry

First set of design changes focused on relatively simple modiﬁcations to channel
dimensions. In this phase of sensitivity analysis, focus is on making some design changes
to impeller radius ratio to study that how this will effect performance. Impeller tip radius
is a very important geometric parameter for performance. It controls overall size of the
machine and also the impeller tip Mach number. Impeller tip radius affects two most
important sources of losses, i.e., slip and shock. It is found from the code that shock and
slip losses are minimized by increasing the tip radius. Moreover, it is found that slip and
shock losses can be reduced by making impeller hub radius smaller. To see the
cumulative effect, a non-dimensional parameter called radius ratio is introduced which is

deﬁned as r2/1; . It dictates that what sort of radius ratio will be beneﬁcial for the

performance of RFC. Slip factor, shock loss parameter and pressure ratio are plotted
against impeller radius ratio in Figures 6.12 and 6.13.

It is very obvious that increasing radius ratio is helpful for better performance. However,
after a certain radius ratio, the pressure ratio starts to go down. In order to establish some
design criteria for radius ratio, literature is cited to see what sort of radius ratios were

used in other RFC designs. The two important non-dimensional parameters to be

investigated are rz/I; and AM /r,2 .

Wilson [69] used values, r2 /1; = 1.48, AM/r,2 = 0.068
Cates [15] used rz/r; = 1.428, AM/r: =0.077
ORNL CRDT used t, /t; = 1.56, A”, /r; = 0.0896
ORNL FPD used r, /t; =1.66, A”, /t,2 = 0.186

141

Capstone single stage RFC conﬁguration S3 used
r,/rl =1.32, rim/t,2 =0.0128

Capstone multistage RFC for all 4 stages

Stage 1. r,/r, = 1.2074, AKA/t; =0.0172
Stage 2. r,/t; = 1.176, AM/r; =0.0130
Stage 3. rz/ro =1.153, AAA/’22 = 0.010
Stage 4. rz/i; = 1.126, Ara/’22 =0.007

When these designs are compared, it is observed that for individual stages of Capstone

multistage RFC, a slight increase in radius ratio is suggested. However, no ﬁrm criteria

could be established for rim/r,2 . It is believed that making other design changes to
geometry automatically establishes the ratio Am, /r,2 . Moreover, establishing a bound for

Am/rz2 might as well make the problem over constrained. Therefore, it is suggested that

a 5-7% increase in impeller tip radius and 5-7% reduction in impeller hub radius for each
stage will be helpful to improve performance of Capstone multistage RFC.

Number of impeller blades is being investigated by many researchers in literature,
noteworthy of which is Iverson [34]. Blade number has an obvious effect on slip factor as
shown in Figure 6.14. Slip losses are increased immensely when blade number is reduced,
which implies very detrimental effect to pressure ratio and efﬁciency. Experimental
sensitivity analysis on Capstone single stage RFC showed that blade number between 75

and 90 seems reasonable for RFC design. Further increase in blade number might prove

detrimental, because it will make angle between blades less than 4°, which might not

allow enough circulations through the impeller. Instead impeller will look like a rough

142

surface to the ﬂuid and there will be reduced number of circulations, which is detrimental
to performance. Moreover frictional losses can increase due to too many blades in the

impeller. Figure 6.15 shows improvement in pressure ratio with increasing blade number.

6.4 Performance improvement by rotor blade chevroning

It has been suggested by many authors that rotor blade shaping or chevroning as shown in
Figure 6.16 beneﬁts RFC performance. A sensitivity analysis is carried out based on the
code to see how blade angle affects the performance. Basically, the slip losses can be

minimized by rotor chevroning. To study the effect of blade chevroning on the slip factor,
the blade angle is varied from purely radial 90° blade to chevroned blade with angle

of 150° . The geometry described in Figure 6.16 results from chevroning the blades of the
impeller in the direction of rotation. It is believed that better guidance and circulation is
provided to the ﬂow by chevroning the blades. This helps to reduce the slip losses as
shown in Figure 6.17. The effect of blade chevroning on pressure ratio is shown in Figure
6.18. There is a clear advantage in chevroning the impeller blades by a certain angle. It
must however be noted that the chevron angle should not be more than150° , because
doing that might bring in extra retardation to the ﬂow. Mathematical formulation
proposed in this thesis does not include the effect of blade chevroning on shock loss.
However, the literature suggests that shock losses are minimized by making the chevron
angle close tolSO° as shown in Figure 6.19. It must be noted that the 60° angle shown in
Figure 6.19 is same as 150° according to our convention. The variation of head
coefﬁcient with rotor blade chevroning is compared with test data published in literature.

It is found consistent as shown in Figure 6.20 by the increasing trend in head coefﬁcient

143

obtained with blade chevroning. Moreover, it is also believed that chevroning the blades
will help to increase the number of circulations of the ﬂow through the impeller blades,
which means more head rise for a given impeller tip Mach number. Such a concept of
rotor blade chevroning is employed to develop a regenerative fuel pump for automotive
fuel pumping by Delphi Automotives, MI. This design is very promising and yields very

good performance as discussed in chapter 7.

6.5 RFC Design Guidelines

So far the discussion is focused on trying to improve the geometry of Capstone
multistage RFC. However, to make this discussion more meaningful, it is essential to
propose a design procedure for radial and non-radial blade RFC design. There is no
evidence available in literature about the existence of any design criteria and guidelines
for radial and non-radial blade RFC design. A design procedure is proposed below, which
can be followed for sizing dimensions of impeller and channel of radial and non-radial
blade RFC.

To avoid the compressibility effects, it is suggested to choose impeller tip Mach number
to be less than 0.8, thus

M0,. < 0.8 (6.3)

Using the design criteria in (6.1) and (6.2), the radial clearance and channel depth at

station A can be established. The channel area at station A can be found by

A, = A (6.4)

 

The impeller hub radius can be calculated using

r;=r2+cr—2dA (6.5)

144

A design criteria for the area ratio at station A and station B is proposed

1.15 < AM/Aw < 1.35 (6.8)

Moreover, it is suggested that the number of impeller blades must be selected using the
following design criteria

75 < Z < 90 (6.9)
For best performance, the blade chevron angle must be selected using the following
design criteria

45° < ,6 < 60° (6.10)

6.6 Conclusions

Extensive design sensitivity analysis is performed on impeller and channel geometry
using the performance prediction code. Sensitivity analysis results from the code are
collaborated with published test data in literature to propose some design guidelines.
Various suggestions pertaining to design improvement of Capstone multistage RFC are
laid down. In order to make this discussion more meaningful, a design procedure for
radial and non-radial blade RFC is suggested. There is a need to reﬁne the proposed
design procedure by incorporating more design criteria. Moreover, CFD analysis must be
performed to validate the established design criteria. The performance prediction code
takes geometric data and operating point as input and predicts the performance. The next
step is to extend the code to work in the design mode, i.e., taking the operating point and

desired performance as input, it should be able to design the compressor geometry.

145

Various Loss parameters
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Shock loss parameter “or" vs. ratio C,/ r2
Blade turning loss coefficient “k,” vs. ratio Cr / r2
Blade mixing loss coefficient “kn," vs. ratio C,/ r2

Channel mixing loss coefficient ”kc,“ vs. ratio C,/ r2

 

 

Figure 6.1 Various loss parameters vs. ratio " c, / r2 "

146

 

Shock Loss parameter "a"

1.65

8

Pressure ratio of 1st stage

1

1

1.55

1.50

1.45

 

 

 

 

 

.40

 

 

 

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0.015 0&0

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Figure 6.2 Radial clearance vs. pressure ratio for ﬁrst stage

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Figure 6.3 Ratio "d, / r2 " vs. shock loss parameter "a"

147

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50

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h=radial clearance, after Cates [15])

148

 

 

 

 

 

 

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I49

Channel turning loss coefficient " ,"

Channel turning loss coefﬁcient " ,”

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0.20

/

 

 

0.18

 

 

 

 

0.46

 

 

0.48 0.50 0.52 0.54 0.56
Ratio "(1, / e"

Figure 6.8 d A / e vs. channel turning coefﬁcient

150

 

0.58

 

0.60

Skin friction Head Loss ” L “

 

55

 

 

45

 

‘\

 

 

 

 

25

 

0.06

 

 

 

 

 

0.07 0.08 0.09 0.10 0.11
Ratlo dA/ r2

Figure 6.9 Ratio " d A / r2 " vs. skin friction loss

 

0.12

 

0.13

 

M
O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8000 rpm
15’ 10,000 rpm 10300
> 1 mm
0 o 20
z a 12,000 rpm
«,1
g 8 ' 10,000
1—1 1
1:.
a e.
a
0
17,000
16,000 37‘- '" . Y=0.215
15,000 . Y=0.3l6
- Y=0.440 ,Y
14,000 . ,
13,000 1
12,000 - , -—- 2 00rp «

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7000 ‘ | \
6000 \ 10,000 rpm

T8000 rpm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 10 20 30 40 50 60 70 ‘80
GAS FLOW AT SUCTION CONDITIONS (Qfm)

Figure 6.10 Effect of channel dimensions on performance, (after Burton [11])

152

Pressure Ratio for the ﬁrst stage

Table 6.1 Various configurations tested by Wilson for experimental sensitivity analysis

 

1.570

 

1.569

 

1 .568

/

 

1 .567

/

 

1 .566

 

 

 

 

 

 

 

 

 

1.565
1.00

1 .05

1.10 1

.15
Am] Aout

1 .20

1 .25

1.30

Figure 6.11 Pressure ratio vs. channel area ratio

1 .35

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Radial Channel depth Ratio Ratio Channel
Conﬁg # clearance " c, " "d, " inch 6, E; Area,
inch d A r, " A" inch2
1 0.875 1.7 0.515 0.092 7.38
2 0.365 1.7 0.215 0.038 6.12
3 1.130 1.41 0.802 0.119 6.80
4 0.620 1.06 0.585 0.065 4.39
5 0.875 0.76 1.15 0.092 3.68
6 0.365 0.76 0.480 0.038 2.89

 

153

 

Pressure ratio for the first stage

Shock loss parameter
0

-- /

0.94

 

0.92

 

 

\wa/

0.90

0.88

 

l

/ A.

0.86

 

0.84

 

/

 

 

 

 

 

 

1 .o 1 .1 1 .2 1.3 1 .4
Impeller radius ratio

 

+ Shock loss parameter 'a' vs impeller radius ratio
+ Slip factor '0' vs. impeller radius ratio

 

 

 

 

0.82
1 .5

Figure 6.12 Slip and shock loss parameter vs. impeller radius ratio

1.7

1.6

1.5

1.4

1.3

1.2

Shock loss parameter

 

/‘\’\

 

/ \.

 

 

 

 

 

 

 

 

 

 

1.0 1.1 1.2 1.3 1.4
Impeller radius ratio r2/ r0

Figure 6.13 Pressure ratio vs. impeller radius ratio

154

1.5

 

0.90

 

0.88

 

0.86

slip factor

 

0.84

 

0.82 /

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.80
40 50 60 7o 80 90 100
Number of Blades "2"
Figure 6.14 Slip factor vs. number of blades

1.58
q) /l
o: 1.56
it!
a) /
17$
,5 1.54
<0
5 /
k
Q 1.52
g
10
D: 1.50
“2
8 /
Q) 1.48
k
n. /

1.46

40 50 60 70 80 90 100

Number of Blades "2"

Figure 6.15 Pressure ratio vs. number of blades

155

Slip factor

(1920

(1915

(1910

(1905

(1900

(1895

(1890

(1885

 

 

 

Figure 6.16 Blade chevroning

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/’
80 90 100 110 120 130 140
Blade Chevron Angle 13°

 

Figure 6.17 Slip factor vs. Chevron angle

156

160

 

1.61

1.59 /
1.58 /
1.57 T/

80 90 100 110 120 130 140 150 160
Blade Chevron Angle 8°

Figure 6.18 Pressure ratio vs. Chevron angle

 

 

 

 

Pressure ratio for the first stage

 

 

 

 

 

 

 

 

 

 

1.56

 

 

 

 

.5

 

 

 

 

 

 

SHOCK LOSS
m

N

 

 

 

 

 

 

 

 

0 0.2 0.4 0.6 0.8 1.0

Figure 6.19 Variation of shock loss with chevron angle (after Dewitt [21])

157

 

0.7 I I l

 

 

0.6

\
d‘I’ 0'5 \\ i
716' 0.4 \\,8?60°
03 \\\é§p = 37.5°

.i. \\

0.1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0

0 0.2 0.8 1.0

0.4 0.6

Figure 6.20 Effect of Blade chevroning on head coefﬁcient (after Dewitt [21])

158

CHAPTER 7

REGENERATIVE AUTOMOTIVE FUEL PUNIP

A typical automotive fuel system consists of a gasoline tank, a fuel pump, fuel filter and
connecting lines. Schematic of an automotive fuel system is shown in Figure 7.1. Fuel
pump is a device which draws the fuel in the fuel tank through the fuel lines to the
carburetor or injectors of the engine. Gasoline is stored in the tank under the rear ﬂoor in
the front-engine automobiles. To function correctly, the fuel pump must move the
gasoline in the fuel system from the tank to the carburetor or fuel injection system in
sufﬁcient volume and pressure. The sufﬁcient pressure of gasoline in the line between the
carburetor and the pump can keep the fuel from boiling and prevent the vapor lock. This
gasoline transfer keeps the carburetor bowl full of clean gasoline, regardless of vehicle
speed or maneuvering. The fuel pump has to lift against a head of 0.6 m from the tank or
more to the carburetor or fuel injection. The fuel metering and atomization system is
located higher in the vehicle than the fuel tank. A mechanical or electrical fuel pump is
employed to draw the fuel from the tank and deliver it to the carburetor or fuel injectors.
It must have sufﬁcient capacity to supply the engine with fuel under all operating
conditions. The fuel pump should also maintain sufficient pressure in the line to the
carburetor to keep the fuel from boiling and causing vapor block due to high engine
temperature under the hood. Fuel pumps for automotive applications have requirements

for very high pressure rise at very low volumetric ﬂow rates. In order to achieve this,

159

regenerative fuel pumps are found to be more useful than any other available pumps.

Regenerative pumps achieve very high pressure rise and typically operate around

hydraulic efﬁciency of 20-30%. Due to their low speciﬁc speed, regenerative pumps

allow high heads at low ﬂow rates and present performance curves with very stable

features. In Figure 7.2, a complete pump-motor group similar to those directly inserted in

the vehicle fuel tank is schematically presented. The fuel enters through the inlet port as

shown in the bottom part of Figure 7.2 and goes through the pump. Impeller of RFP is

visible in this ﬁgure. The attached motor rotates this impeller and ﬂuid circulates through

the blades and discharges out from the outlet at high pressure. There are many reasons for

the competitive advantage enjoyed by regenerative pumps over its competitor pumps as

discussed below.

7.1

Advantages of a regenerative automotive fuel pump

The biggest advantage offered by a regenerative pump is its extremely compact
design. Typical regenerative fuel pumps employed in automotives are less than
40 mm in diameter which makes the pump motor assemble very compact. This
feature is very attractive in automotives because of space limitations.

Self priming capability offered by regenerative automotive fuel pump makes it
very attractive. They have an ability to purge out vapors at start of pump
operation and draw liquid fuel inside the impeller, something which other fuel
pumps lack. Regenerative pumps are known to have excellent priming behavior.
Operation at high fuel temperature is another huge advantage offered by these

pumps. The fuel coming back from the injection system through the return line is

160

very hot and thus requires the pump to operate at higher temperature. This is
something possible only by using a regenerative pump.

0 Simplicity in construction is another huge advantage offered by these pumps.

0 They are very cheap to manufacture. A regenerative pump can be manufactured
and sold to the market as cheap as $ 20 - $ 50.

o Ignition safety is another advantage offered by regenerative pumps.

. Regenerative automotive fuel pumps are very durable. They have been tested to
operate up to 10,000 hours without any problems.

a Low noise level is another highly desired attribute in automotives. RFP are very
quiet and present a huge advantage over other fuel pumps.

. No wearing problems in RFP like those found in positive displacement machines.

Over the past few years, regenerative pumps have been subject to more and more interest
in the automotive ﬁeld as injection pumps in spark ignition engines. Badami [7]
presented a hypothesis for the evaluation of the circulatory ﬂow rate and based his theory
on the consideration of the centrifugal force ﬁeld in the side-channel and in the impeller
vane grooves. He used momentum exchange theory to predict head-ﬂow curves and
presented a comparison between theoretical and experimental data. He constructed two
innovative regenerative pumps and tested them. Badami attempted to ﬁnd some new
technical solutions for the design of periphery pumps with the aim of enhancing their
performance and simplifying their construction. The first pump designed by Badami was
a double stage regenerative pump as shown in Figure 7.3. It presented better performance

characteristics than those obtained using a traditional regenerative pump with same

161

overall dimensions. The second pump designed by Badami offered a particular technical
solution which allowed some interesting features for the construction of the motor-
impeller group. With this solution, the vane grooves were machined directly on to the

external periphery of the electric motor, thus reducing the number of parts.

7 .2 Delphi Automotive Fuel Pump

Delphi Automotives, MI has designed regenerative fuel pumps with non-radial blade and
semicircular channel geometry. Several pump designs have been made for different
applications. The pump and motor assembly is very compact as shown in Figure 7.4. The
assembly is disassembled and various components are shown in Figure 7.5. The impeller
has channels on both sides as shown in Figure 7.6. These channels are built is the casing
and help to promote the circulatory ﬂow around the blades. Blade and channel geometry

of typical Delphi fuel pump can be seen in Figure 7.7. The blades are non-radial with an

angle of 45° in an attempt to provide better guidance to the ﬂow. Channel shape is made
semi-circular for better circulation of ﬂow and minimize circulatory losses.

Non-dimensional experimental data of head and hydraulic efﬁciency versus non-
dimensional ﬂow rate is presented in Figure 7.8 and 7.9 using viscor as working ﬂuid.
Viscor has properties very close to gasoline, but it is less combustible and better suited
for testing. Test data is obtained at different speed (rpm) of the impeller. It is interesting
that non-dimensional test data for head and efﬁciency falls on the same curve. The
hydraulic efficiency graph shows that a peak efﬁciency around 40% can be achieved
using regenerative automotive fuel pump. This efficiency does not include the power lost
in motor. When motor efficiency is also considered, the net efﬁciency comes out to be

very low, approximately 18% at design point. Figure 7.10 shows the ﬂow rate, current

162

drawn and overall efﬁciency versus pressure. Most automotive fuel pumps operate
between 12 Volts - 13.5 Volts. The current drawn and voltage can be multiplied to get the
power drawn by the pump. Typically the power drawn by this type of pump is around 50-
60 Watts. It is very important to make this pump efﬁcient because when the engine is
turned on, the pump keeps on operating and draws the power from the battery. If there is
a large amount of power drawn from the battery, it can be harmful to life of the battery.
Due to unique operational features and advantages offered by regenerative pump, it is of
great interest to industry that these pumps operate with better efﬁciency.

To assist in improving regenerative fuel pump efﬁciency, the mathematical formulation
presented in chapter 5 is used to predict the performance of Delphi regenerative fuel
pump. Blade and channel geometry data of two test pump designs can be found in Table

7.1. Hydraulic power (Phyd) transferred from impeller to ﬂuid is consumed by both

power required for head rise (Ph) and circulatory power (PC ). The circulatory power

keeps the ﬂow circulating through the blades. It is this circulatory power which makes
the regenerative pump less efficient than the centrifugal pump.

Hydraulic efﬁciency can be determined by

 

 

pQgH
7711 = (7-1)
yd Piryd
Including the power lost in motor and other mechanical parts, the overall efﬁciency is
given by
H
72...... = ”98 (72>
(Phyd + Pdisk )

163

The performance prediction code is used to predict the performance of the fuel pump and
then carry out a sensitivity analysis on various design variables to see which changes can
increase the efﬁciency. Figure 7.11 shows that the theoretical results of head rise vs. ﬂow
are in good agreement with the experimental results at high ﬂow rates. The comparison is
good at the design point; however, it has some deviations at off design ﬂow rates. Figure
7.12 however does not show good agreement between efﬁciency vs. ﬂow rate. The
predicted efﬁciency—ﬂow rate curve is higher than that of experimental data. The reason
for this trend is that if the predicted head is higher than the experimental head, it makes
the predicted efﬁciency higher than experimental efﬁciency. It is obvious that the ﬂow

rate at which predicted hydraulic efﬁciency (nhyd) is maximum is slightly higher than the

ﬂow rate at which the predicted maximum efﬁciency (17) occurs. The reason for this

trend is that the ratio of the disk friction power to hydraulic power is considerably
increased at higher ﬂow rates. An explanation of this is that disk friction power is
independent of ﬂow rate, however, the hydraulic power of a regenerative pump reduces
as the ﬂow rate increases.

After predicting the performance, an extensive sensitivity analysis is performed in which

it is observed that hydraulic efficiency is largely inﬂuenced by R,,-p , A, and Rhub . The main

conclusions from the sensitivity analysis are that if R, and Ac are increased and RM, is

in
reduced by 10%, efficiency can increase 3—7%. Of course the pressure rise of that point is
different from that at design point. The prediction from the code and design suggestions

mentioned above need to be validated by CFD analysis on a full pump model before

prototype pump with the new design can be made.

164

7 .3 CFD Analysis on regenerative automotive fuel pump

A CFD analysis is performed on a complete pump model to study its internal ﬂow
mechanism and performance characteristics at design point. The CFD analysis takes a
long time to complete the simulation, thus only selected design points are used to perform
CFD. Therefore, it is not easy to get CFD results for the full operating range of the pump.
Figure 7.13 shows the complete pump model with inlet and discharge ports, non radial
blades on both sides and the ﬂow channels. The pump model is generated in
UNIGRAPHICS, while the grid is generated in GAMBIT using hexahedral (Brick)

elements. The element count for the full model comes out to be nearly 200,000. A

transient analysis is performed with a time step At=2.083><10‘5 sec for half degree

impeller revolution. The simulation is run for two complete revolutions of the impeller.

This implies that for 720° impeller rotation, the simulation uses 1440 time steps.

Flow enters the impeller through the inlet port and is divided into two sides of the
impeller. Figure 7.11 describes the shape of non-radial blades on both sides of the
impeller. Figure 7.12 shows the web between any two blades, which serves to promote
the circulatory ﬂow pattern. The ﬂuid coming from the channel circulates through this
web and gets entrapped between the blades, which hit the ﬂow. The blades add energy to
the ﬂuid until it gets out of the blades and circulates through the channel. After passing
through the channel, ﬂow enters the blade row for next circulation. It is this repetitive
action of blades on the ﬂow, which makes it possible to produce high heads at very low

ﬂow rates in regenerative turbomachines.

Pressure boundary conditions at both inlet and discharge ports are applied and rest of

parameters are calculated by the simulation. The reason for applying pressure boundary

165

condition at inlet and outlet is that since there is a pressure regulator downstream of the

pump which maintains a constant pressure of 400 Kpa , it is an automatic choice to apply

the known pressure boundary condition at the discharge. Similarly, the inlet port draws
ﬂuid from the fuel tank which is at ambient pressure (zero gauge pressure), thus again
making it convenient to apply pressure boundary condition at the inlet. With the pressure
at inlet and discharge known, CFD analysis calculates the mass ﬂow rate. The fuel pump
runs at 5000 rpm when 12 V is applied to it. Torque applied to the impeller is also
calculated by CFD, which gives power consumed after multiplying by rpm. The CFD
simulations take a very long time to produce the results, therefore it is usual practice to
choose a design point to perform CFD analysis. The design point for CFD analysis was

chosen to be 5000 rpm and discharge pressure of 400 Kpa .

Figure 7.13 describes the total pressure variation across the periphery of the pump. It can
be seen that the pressure gradually builds up as the ﬂow circulates through the blades.
The pressure at discharge port is the highest as indicated in the legend. Figure 7.14 shows
the circulatory ﬂow pattern in a cross section. The absolute velocity vectors show the
circulation in the blades and channel, which is a characteristic of these turbomachines.
The CFD model works very well and helps to understand the ﬂow mechanism inside the
pump. So far, the suggested design changes from theoretical analysis are not validated by
CFD analysis. Instead, the set up of CFD model and ﬂow analysis is completed till now
to convince ourselves that this complex ﬂuid ﬂow inside RFP can be modeled by CFD.
Currently work is in progress to make suggested design changes in the pump geometry
and verify the results by CFD analysis and see if design changes suggested by the

performance prediction code can increase the efﬁciency by 3-7%.

166

Although current Delphi RFP design performs well and it is currently best design
available in automotive industry. However, after doing research on existing design of
non-radial blade RFP, need was felt to make fundamental changes to this design to create
signiﬁcant improvement. Therefore, aerodynamically designed aerofoil blades are
investigated in next two chapters for RFP/RFC design. Unfortunately, there is almost no
information available in open literature about aerofoil blade RFP. However, Sixsmith and
Altmann [60] did extensive research on aerofoil blade RFC. This motivated us to carry
out a detail investigation on RFC with aerofoil blading in a hope to produce regenerative
turbomachines with better efﬁciency. A compressible ﬂow theory for aerofoil blade RFC

is presented in the next chapter.

7 .4 Conclusions

The application of regenerative pumps for automotive fuel pumping is discussed in detail.
Various advantages of regenerative fuel pumps are explored. Proposed mathematical
model is used to predict the performance of Delphi automotive fuel pump. Excellent
agreement between theoretical and experimental data is observed at the design point. A

sensitivity analysis is performed and it is suggested that if R, and Ar are increased and

ip
Rhub is reduced by 10%, hydraulic efﬁciency can increase 3-7%. A CFD analysis on
Delphi fuel pump is presented. Currently, work is in progress to make proposed design
changes in the Unigraphics model and perform a CFD analysis. Such an analysis will

help to validate the effect of proposed design changes on performance.

167

 

 
 
 
 
 
 

BLEED HOSE

GAGE ASSEMBLY
RETURN
FUEL PRESSURE LINE

    
 
 
 

FUEL PUMP
FEED HOSE

 

 

 

 

r"

Ln; 1‘. -‘ I I
Outlet Port

\
u SE

:1
.0

P
Regenerative Pump

Casing Flow Channel DC Motor

12> -
III,

Inlet
Impeller

Figure 7.2 A Regenerative automotive fuel pump (after Hubel [32])

168

 

Figure 7.3 Schematic view and geometric symbols of a two stage periphery pump (after
Badami [7])

 

Figure 7.4 Pump and motor assembly of Delphi automotive fuel pump

169

 

Figure 7.5 Components of the pump-motor assembly

 

Figure 7.6 Impeller with both side channels

170

blade Ab

channel

H8

H8

'''''' ° ° ' —°-'C.'.-.'.--:.'.—.L.:.:.'. '

   

q------------------

tip

Figure 7.7 Blade and channel shape of Delphi automotive fuel pump

 

 

 

 

 

 

 

 

40.0 C1
1:1 1000 RPM
0, o 3000 RPM
'0 \ o 5000 RPM
3 30-0 ' U: A 7000 RPM
m 9 <1 9000 RPM
._. x ——— BEST FIT
«1 c ..
8 o,
g 20.0 r ‘,
a) 035)
E ’1.
Q 8.5
I \
g 10.0 ~ @>\
v-9
2 AN
0.0 . . . W
0.00 0.20 0.40 0.60 0.80

Non-Dimensional Flow rate

1.00

Figure 7.8 Non-dimensional experimental data of head vs. ﬂow rate for Delphi RFP

171

 

 

 

 

 

 

 

 

 

 

    
 

 

 

 

 

 

 

 

 

 

 

0.50
. ‘ g g . . ERIK
>. 0-40‘ 9 <0 9909 I .121
O u u L] ‘ Q‘w Q
:3 .' ‘2 :1 L' ‘1 o "
0) C ‘. «1A
.8 I 1.] "ﬂ A1
21:: 030» .04 G: “3A
m I 1 L <3
.2
"'5 .6 L a
g 030’ 1:1 3000 RPM ‘. 9
>4 o 5000 RPM -‘ *3
:1: e A 7000 RPM 1:, A
0 10 <1 9000 RPM 1
' * -—- BEST FIT ‘5),
[’9
0.0 . . . . . . . . x .
0.0 0.1 0.2 05 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Non-Dimensional F low
Figure 7.9 Efﬁciency vs. ﬂow rate for Delphi RFP
Performance curves at 13.5, 12.0 & 8.0 VOLT DC
? 50 1 f I V I ‘T 1
°\ I 1 I I I 1 I
45 r . 1 - - .............................................
5 l . Flow f .. I l T q
2 40l ------ .1 ................... J ...... I .....
é . 12.0 v : :
I I 1
m35»-----7-F:'97--; -------------------- 1 ------
i 30» - - . .3- _ - 1 ............................
3; : : :
EZSr—un-i ------ : ------------- : ------ ———-~~-. ----------
g l 8 0v 2 i f l I ‘ .3
______ _I_ o '_-__ _--~‘-1-~_-__‘-~----l__-___1_--_--1--_ 1_-___-
3 20 7. Flow , ,r : f I ' T I
U 1 9 ' “___,“ 77—— '
A15 -------- 12.0v ----- . -/ ---------- ----- 1"
gm lgrggencv/ . , : ; : :
33 Efﬁciency. : g ' : ' """ : ': ''''''
l l a 1 1 r
3 5*»13.5VCurrent‘:-u—f j: --r-- "3 --;------E:t'-:-:----j ------
.2 12.0 V Current I ' l I l i i
u" 0 1 4 1 . I. 4. 1 i +
0 50 100 150 200 250 300 350 400 450
PRESSURE (KPa)

Figure 7.10 Flow, current drawn and efficiency vs. pressure for Delphi RFP

172

Table 7.1 Geometric data for two RFP designs (Length (mm) and Area (mm2 ))

 

 

Test 1 Test 2
Rtip 16.375 18.1
RM) 13.125 14.9
R2 15.608 17.33
R1 13.984 15.73
Ac 3.27 3.20
3,) 2.1 2.1
ﬂ 45° 45°
lb 37 41
C 0.01 0.01
BF 0.08 0.08
6,, 255° 255°

 

 

 

 

 
    
    
 

 

Symbol : Experiment
Line : Prediction

 

 

- Test 1
0 Test 2
— Test 1

---- Test2

 

 

 

 

 

 

4
34 ‘
’22-?
NC) 2_ I
I?
00
1.
0 a .
0.6 0.7

Figure 7.11 Theoretical and experimental non-dimensional head vs. flow

173

09

 

. Symbol : Experiment
0 8 - Line : Prediction

07-
06«
05-

04—

 

03-

 

; I Test 1 “
02 - __ ”’94 \
- - - - ’1 (including \

1 — .
0 |:mechanlcal power loss) ‘

 

 

00

 

. . , . , . , . r .
04 05 06 07 08 09 10
0105

Figure 7.12 Theoretical and experimental efﬁciency vs. ﬂow

 

Figure 7.13 UNIGRAPHICS model of regenerative automotive fuel pump

174

1'11“
11.111“
\ “$0 .

\\
1‘10

. \'
‘8‘. A“

0' 00
0:11 ‘
\

’ ﬂ
ll,
41, “‘5'

I
’7 .1” ’I
,, ’1’4’5’7'05”

/" ’71", ’1’, /
ﬁ’ //‘ ’II”"/”,//H'I/p‘r' ,
/ ’01’4/10’14' 401’".
I o/ffﬂglfﬂba/Im pt...—
”f. //’/ ’f’ ’10‘? On, $1,
yf’IS’II/I/ﬁ ’11,, [pa
”II/7V’0l I”! "
254’

,v

.....“\\\ _

1
‘\ 1‘
....;§.‘.‘\

1
t1 t‘é‘ﬁ
\ ‘1 '

i“ t '\\\
.1111
\‘1

Q , .
“0‘5

 

Figure 7.15 Web between two blades of RFP

175

 

T/ P.
”FESSLF‘E BU‘LD—l P rpm-1a PLMP s ‘

PROSTAR 3.10

PRESSURE
RELATIVE

TIME- UBOOOOQE— 01
LOCAL MX= 0385§E+06
LOCAL MN- ~430

0 3958EsDG

 

   

 

 

 

Figure 7.17 Circulatory velocity in the twin channels

176

CHAPTER 8

COMPRESSIBLE FLOW THEORY FOR
AEROFOIL BLADE RFC

Theories for the flow of compressible ﬂuid in regenerative turbomachines are rarely
found in literature. Burton [11] made an effort in this direction and reported a simpliﬁed
theory, which took account of area change and compressibility effects in RFC. However
it was unable to explain the circulatory flow pattern in RFC because it was based on
Iverson’s shear stress theory [34]. Cates [15] investigated performance of RFC with
radial blades experimentally using various gases covering a wide range of molecular
weight and observed compressibility effects at Mach number greater than 0.8. Burton [12]
investigated these compressibility effects and related them to mass flow rate through the
stripper, which were ignored by other researchers in incompressible ﬂow analysis.
Sixsmith and Altmann [60] introduced a new type of RFC with aerofoil blades and
decompression ducts to increase the efﬁciency. In chapter 5, Wilson’s regenerative
theory was extended to incorporate compressible flow to predict performance of
RFC/RFP with radial and non radial blades and semicircular channel shape. In this
chapter, the aim is to predict performance of RFC/RFP with aerofoil blade design by
incorporating compressible flow in Wilson’s momentum exchange theory. Governing
equations for fully compressible flow are developed and loss models are introduced to

make performance prediction independent of experimental support. Based on new

177

formulation, a performance prediction code is developed to predict performance of
aerofoil blade RFC. Geometries of MK] and MK2 regenerative compressors tested by
Sixsmith and Altmann [60] are used as input to the code and theoretical prediction is
compared with the test data. An extensive sensitivity analysis is performed to determine
which geometric parameters affect the performance. After carrying out the sensitivity

analysis, suggestions for design improvement are laid down.

8.1 Aerofoil Blade RFC

Most designs of regenerative turbomachines in literature retain a fairly basic geometrical
conﬁguration with simple vanes either machined or cast into the impeller. However, the
addition of a core in the ﬂow channel to direct the circulating ﬂow together with the
provision of aerofoil blades was ﬁrst shown by Sixsmith and Altmann [60]. They
replaced the radial vanes by blades with an aerofoil section. Blades were designed to

transfer momentum to the ﬂuid with a minimum of turbulence and friction. They were

designed to turn the ﬂuid through a deﬁnite angle, which preferably should be about 90°.
The annular channel had the core to assist in guiding the ﬂuid such that it circulates
through the blading with a minimum of loss. The core also acted as a shroud to reduce
losses due to formation of vortices at the tips of the blades. A typical RFC/RFP with
aerofoil blades is shown in Figure 8.1.

These authors tested two regenerative compressors with aerofoil blading by blowing air
through them. First design was MKl regenerative compressor designed to run up to
10,000 rpm and deliver 250 liter/sec at a pressure of 2 atm. It had an impeller of 300 mm
diameter with a single row of blades. The performance characteristics resembled those of

a positive displacement compressor and efﬁciency was maintained over a wide range of

178

operating conditions. The torque was almost directly proportional to the back pressure
and the compressor could be operated from maximum to zero ﬂow without surging or
stalling. The authors also tested MK2 regenerative compressor with the same basic layout
but with two blade rows. Main features of MK2 compressor compared to MKl were the
increased peak efﬁciency to 52% , the lower pressure ratio at which this efﬁciency
occurred, the gentler slope of pressure-volume curves, the lower efﬁciency at high
pressure ratio and the large volume ﬂow at low pressure, i.e., approximately 2.5 times
greater than before. The authors retested the MK2 regenerative compressor by making
the blading symmetric and found improved performance characteristics. The gain in
efﬁciency was particularly marked at high pressure ratios. For example, at 4000 rpm the

efﬁciency increased by 10 percent at a pressure ratio of 1.5.

8.2 Compressible ﬂow theory

The analysis presented here is a mean line analysis, which represents the helical ﬂow

pattern inside a regenerative turbomachine by a streamline. Because of helical ﬂow

pattern, this analysis is based on coordinates composed of radial (R), circulatory(¢) and
tangential direction (6) as shown in Figure 8.2. Regenerative compressors found in

literature have different meridional geometries. The meridional geometry chosen in this
analysis is also shown in Figure 8.2, which shows the projected area and length of
circulatory ﬂow path in blade and channel region. The existence of a core, which is ﬁxed
to the channel helps to guide the ﬂuid such that it circulates through the blade with a

minimum loss.

179

8.2.1 Assumptions
Following assumptions are used in the analysis:
1. Steady and compressible ﬂow

2. Fluid is considered as ideal gas (p = pRmT)
3. Helical ﬂow can be described by a mean streamline with tangential velocity (V9)
and circulatory velocity (V') at any position.

4. Circulatory velocity, density, pressure and temperature are considered to vary

only along the tangential direction i.e.

V..p.T.p=f(X./.a>
5. Each decompression process is a quasi-equilibrium process.
6. All pressure losses can be categorized into losses related to circulatory and
tangential velocity.
7. The effects of inlet and exit regions on performance are not considered in the

model, rather they are considered separately.

8.2.2 Derivation of the governing equations

The equations of motion can be derived for an arbitrary small control volume comprising
of blade and channel regions as shown in Figure 8.3.

Velocity triangle relation betweenV ,W , and U at location R2 can be obtained on the

basis of the velocity triangle shown in Figure 8.4.

W02 = V¢2Tan( 132) (8.2)

180

V92 = UVQZb (8.3)

Similar relation can be obtained at locations R1. These relations are useful in developing

the governing equations.

Continuity

Ignoring ﬂow leakages, it can be assumed that total mass ﬂow rate in tangential direction
remains constant. The total mass ﬂow rate can be calculated by adding mass ﬂow rates
through channel and blade cross sectional areas. Moreover, total mass ﬂow rate is also
equal to the summation of mass ﬂow rate entering the compressor through the inlet port

and mass ﬂow rate carried over by the blades through the stripper to the ﬂow channel,

referred as carryover mass ﬂow rate denoted by n'zs. Thus we can write,
1516+ 110,, = ,ov‘gmAr + pUbAb = m + ﬁts (8.4)
Where, the mean tangential velocity (Va...) in the channel region is calculated as the

average of tangential velocities at RI and R2.

Differentiating equation 8.4, the relation between channel mass ﬂow rate and blade mass

ﬂow rate can be expressed as follows

dmc = —d (pub/1,) (8.5)

In addition, it can be assumed that circulatory mass ﬂow rate at inlet and exit of the blade
region stays same. Thus,

am, .—. pV¢Hb (8.7)

181

Assuming constant density at an arbitrary tangential location and constant ﬂow areas for
incoming and outgoing circulatory ﬂow, it can be concluded that the circulatory velocity

also stays same at an arbitrary tangential location. Thus,

Momentum

Applying the angular momentum equation to channel region in tangential direction,

. drizr de . drhc de .
[[mr-P 2 )(ng+ 29 )“(m"- 2 )(Wm‘ 20 )]r0+dmo(’iVm—rzvoz)

_, _gg _dA. _, g cm
”L” ALA” 2) GLP+2)[A‘+2

F )‘i'erMc — I erAT
A,
Simplifying and using equation 8.5, we get

 

 

 

 

 

 

drir¢
UGAc

 

dP = (U 2V02 " U1V61) " .0149de0»: + d [0%(1 bvom - dPL
Dividing by dX and using equation 8.7, we get

d pV H d
_E = 4’ ” (Uzvé,2 - U1V0,)— pvgm —— + iiubvﬂm (8.9)
dX UGAc dX dX dX A,

 

Where, (Uh. = th.) refers to the velocity associated with solid rotation.

In R.H.S. of equation 8.9, first term refers to the pressure rise caused by momentum
exchange of the blade; second term represents pressure gradient caused by the
deceleration of mean tangential velocity; third term gives pressure loss related to
tangential velocity caused by friction or other irreversibilities and the last term represents

the deceleration of tangential velocity caused by the increment in density.

Applying momentum equation in the circulatory direction and simplifying, we get

182

[-+f’:—)tv¢+f’—:—¢1-lm-5’—:’ltv-—l M M

:(pz “p1)dAe-prdA¢
. . _ 102 -p1 _ AP.»
v, (m,dv, +v,dm,) _ p dA,pV, p dA,pV,

where, Apex. is the pressure loss related to circulatory velocity in the channel region.

After some manipulations, we get the governing equation for circulatory velocity which

can be expressed as,

 

 

 

2
av2 VI-I — V
___¢ -_-2 ¢ b [p2 191—pr)1 ¢ ldp'A—QUbVBm (8'10)
dX V,,,,,Ac p 0 Va...

Equation 8.10 represents a highly non-linear differential equation for circulatory velocity.

Angular momentum equation in the blade region can be given as,

day, = war

dPhyd=dmr(U2V92_U1V01)+[p+id£]UbAbU2-[p—Q]UbAbUb2
+[p+-‘—’—) U-—.A. [p -d2”]U.A.

Simplifying we get,
dPhyd : dn'tr (Uzvaz '— U1V01)+ debAbsz + W

Dividing by dX and ignoring the last term in above equation because of negligible

pressure rise in the blade region, we get

dPhyd
dX

 

d
= pV¢Hb (U2V02 41,110, ) +ﬁU§Ab (8.11)

183

If last term is ignored in R.H.S. of the above equation, ﬁrst term refers to power
consumed in momentum exchange of blade and the second term represents increment in

power caused by increment in density.

Energy

The energy equation is applied to channel and blade region at two thermodynamic

conditions where regenerative compressors operate. These conditions are

. Adiabatic condition
. Isothermal condition

Equations for the two thermodynamic conditions are developed separately.

. Adiabatic condition

Under the adiabatic condition, there is no channel heat transfer. Thus, we can say
dQC = 0

The energy equation applied to channel control volume of Figure 8.3 yields

01:111M1M11:61:11 __11...

 

 

Simplifying above equation yields,
(1112,2120, — dn'zmhm = #1th0 + hodn'zc (8.12)
Similarly for the blade region,

de =0

184

Total enthalpy in blade region can be expressed in terms of enthalpy in the channel

regionas,
1 l 2
ho=h+—2'V‘2+-2-V9m
_ l 2 1 2
hm, —h+-2—V¢ +§Ub
Thus,

1 l
th :ho 4’5sz -§V92m

The energy equation applied to blade control volume of Figure 8.3 yields

- . . d l l d
dayd=dm¢2hm—dm¢lhm+ [ll-10+; —Ub2—-2-V9:+ —2’i—-2' [EVW ])[p+—p) UbAb

1 2 1 , _d_h, of.) [ dp)
- +—Ub ——V —V —— U
Simplifying, we get

dmezhoz - dmvihor : dPhyd " pUbAbdhO + pUbAbvodeom

(8.13
—hoU.A.dp—-:-(U:—V.:)U.A.dp )

From equation 8.12 and 8.13, we get
. . . 1
mcdho + hodmc = dB... —pU.Abdho + pubAbvgmdva... — hovbAbdp -§(Ui—V§.)U1Abdp

. - 1
(me +pUbAb)dh0 = dPhyd +I0UbAbV0de0m —§(U§ _Vﬂzm )UbAbdp

dVg l 2 2 dp
m -— U -V U — 8.14
dX 2( 1) 6m) bAbdX] ( )

 

d7“ 1 di’ha
0: [dX-F Ub Abv 6m

P dX (m +mb)

185

Operating under adiabatic condition, equation (8.14) can be used to calculate total

temperature distribution.

0 Isothermal Condition

Another thermodynamic condition in which RFC usually operates is the isothermal

condition. The compressor work can be reduced by maintaining the temperature of the

gas as low as possible during compression. The isothermal condition is given by
T=constant

The energy equation applied to channel control volume under isothermal conditions

yields
—dQ', + d 1..., + (1111,2110, — (1112,11,, — n'zrdho — hodn'zr = 0

er : d’hazhoz " d’hwhor " mrdho " 110er

(1112,2110, —dm,,ho, = dQc + mrdh, + mm, (8.15)
Energy transfer process in the blade region happens rapidly, so it can always be assumed
an adiabatic process. Thus, we can equate equation 8.15 with equation 8.13 to calculate
the heat transfer from the compressor as

-er : mr‘dho + hOdmr — dizzyd + dhOpUbAb _ V6mdv9mpUbAb

1
+hode.A. +3(U: —V.E. )de.A.

er : (ml + ml) )dhO -t:di)hyd + pUbAbVdeVOm _édebAb (sz _Vefn ):| (8'16)

In order to calculate pressure difference between incoming and outgoing ﬂow in a control
volume of blade region, Bernoulli equation along the streamline is applied and static

pressure rise in the blade region is obtained as

186

92¢

“egg—pL=(U2V02‘U1V01)’V0m(V02“V61 - (8.171

where, Ap¢b is the pressure loss due to circulatory velocity through the blade region.

Some researchers assumed that mean streamline enters and exits the blades rows at same

tangential location(6). However, it is referenced in Krishnan et a1 [37] that there is a
slight difference in tangential location (6) between the location where the mean

streamline enters the blade row and the location where mean streamline exits the blade
row 6,. This slight difference in tangential locations is denoted by A9_,. and is also
shown in Figure 8.4. It is believed that the larger the stagger angle of blades, greater
is A19“. It is due to this A624. that the pressure difference in equation 8.17 needs to be
supplemented by a correction term, so that resulting equation can be compared with
equation 8.10.

Under the assumption that the relative tangential velocity within the blade is linearly
distributed, the distances traveled in the circulatory and tangential directions can be

expressed in the relative frame along the streamline as,

 

 

Wad: _ Rd6
V,dt Fd¢
We can say approximately,
WW” = RbAg (8.18)
V, lb
Referring to Figure 8.4, we can say
319
P1 " Pr = ﬁAgz-r'

At an arbitrary tangential position, pressure difference across the blade is given by

187

132-171 =(p2-p1-)-(P1 -n-)

3
p2 - p1 = p2 - 10.- -£A0H (8.19)

Substituting equation 8.19 in equation 8.17, we get

_ AP 6
___—p2 pl : (U2V62 _U1V6])—ng (V92 —V01 _i-“E'AQZ..1' (8'20)
10 p 89

Equating equation 8.10 and 8.20, a ﬁrst order nonlinear ordinary differential equation for

circulatory velocity (V¢) is obtained as

 

de 2V H Ap d
¢ ¢ b ¢ P

= (U V —UV )-Vm(V -V )-—-—AX _~
1X ng l [ 2 612 1 61 6 02 01 dX 2 1

(8.21)

b6m

2
V
V0». deAc

where, (An, = pr + pr ) is sum of pressure loss related to the circulatory velocity.

8.3 Pressure Loss Models

There are two contributions to pressure losses:
0 Tangential pressure loss

0 Circulatory pressure loss

8.3.1 Tangential pressure loss

The skin friction pressure loss in tangential direction causes reduction of tangential
pressure rise and is given by applying the classic pipe loss formula using the concept of

hydraulic diameter ( Dh ).

188

xi
ﬂzil ng (8.22)
dX Dh 2

Where, the friction factor is estimated by correlation used for straight channels given in
[20].
,1) = 0.3 161160-25

8.3.2 Circulatory pressure loss

The pressure loss related to circulatory velocity is categorized into several pressure losses
as follows. Loss models discussed in chapter 5 were used in the formulation.

Consequently, by summing circulatory pressure loss models, we get,

1
harmel JEV; (8-23)

 

é’l = km (Tanﬂl —Tan,81b)2 + kblad‘z +kc
,0 Cos/31b

where kblade and kchwme, represent all circulatory losses in blade and channel region.

8.4 Inlet port and decompression duct

High pressure gas enclosed by each blade pocket is delivered to the inlet region through
the stripper. Stripper carryover ﬂuid is mixed irreversibly with the incoming ﬂow
entering the compressor from inlet port as shown in Figure 8.5. This causes an increase in
inlet temperature. Moreover, there is a blockage effect for the incoming ﬂow because of
the expansion of high pressure gas in the inlet region. This causes lower pressure rise and
proves detrimental to the efﬁciency of RFC. Burton [12] suggested a possible way to
increase the efficiency by extracting some of the compressed ﬂuid entrapped in the
blades and feeding it either to less harmful regions of the ﬂow channel or to an ejection

slot placed around the inlet port. Assuming adiabatic condition and neglecting the

189

leakage ﬂow rate, Burton considered process in the inlet region as expansion and mixing.

The total temperature at the inlet region was calculated by

 

 

. 5

T0,: m T00+ "’3 (y_l-’31—+l]r

 

m-Hizs tir+rhs s
y p y (8.24)
ms 7‘1 2 P1 V0m12
+ M T l-— l— —
n'z+n'rs 2 " COL s( (Ub ))

Therefore, the total temperature can be reduced by either reducing temperature (7;) or
reducing carryover mass ﬂow rate (ms) through the stripper. Sixsmith and Altmann [60]

adopted Burton’s idea and introduced decompression ducts to decrease total temperature
and hence improve RFC efﬁciency. Compressed ﬂuid entrapped in the stripper blades
was fed through decompression ducts to various positions in the channel as shown in

Figure 8.5.

The use of decompression ducts helps to reduce the power input to the compressor by
transferring power entrapped in stripper blades to the channel. In this analysis, the
decompression process is simulated by assuming ﬂow from a high pressure rigid pocket
opened to channel conditions in a quasi-equilibrium manner. Thus, it is expected from
this assumption that power transferred by decompression process becomes maximum.
The governing equation for decompression is given by

ms, Cst’. _ ms“, CstM = (ms, —' ms”, )CpTHl (8'25)

8‘. Ti
(8.26)

1)., p.

m T. _ m

 

MI

190

8.5 Efficiency

Power transferred to impeller of RFC can be obtained by summation of hydraulic power
and power caused by disk friction. Input power is reduced by the power transferred from
decompression ducts to the channel. Power loss caused by the leakage ﬂow through

radial and axial clearances is ignored. Therefore, isothermal efﬁciency can be determined

 

by
'R T 1 p03
m gas 00 n( Poo)
77,-5.0 = . . . (8.27)
Phyd '- Pdecomp + Pdisk
Also, adiabatic efficiency is given by
p03 (Y-l)/}’
' C T —1
m ” 00 L Poo)
77m. = 7 (8.28)

 

Phyd _ Pdecomp + Pdr'sk
After circulatory velocity distribution along the channel is obtained, the pressure rise and

hydraulic power can be calculated by integrating equation (8.9) and equation (8.11).

p = ,1 dp (8.29)
X

PM = 1 day, (8.30)
X

Power transferred through the successive quasi-equilibrium decompression processes is

expressed using equation (8.25) as,

Pdecomp : 2071C T - ’h'HCstM ) : meCvTZ _ mszTs (8'31)

tvs, r

191

Sc

ca

\1

Some of the input power is lost by friction between rotating impeller disk and stationary
casing wall. This disk friction power can be calculated using experimental correlations of
Daily [20].

C?" pUSPRip (8.321

 

P disk :

Where, Cm is suggested in Daily [20] as function of clearance and Rea-p.

8.6 Regenerative Number (N)

Regenerative number refers to the number of circulations of ﬂuid from inlet to discharge
port of RFC. In order to calculate the regenerative number, the magnitude of tangential
angle corresponding to one cycle must be calculated. Figure 8.6 shows the distances
traveled in the circulatory and tangential directions along a streamline. Moreover, it
shows that at the tip of the impeller blade, the ideal possible velocity is V92, . However, it

is reduced due to slip losses to a lower value denoted by V92 which represents the actual

ﬂuid velocity at the impeller tip. Similarly at the entrance of the blade, the maximum gas

velocity is V9,, however, due to the incidence losses, this velocity reduces ton. The
horizontal axis in this diagram describes the angular displacement with A¢c representing

the angle traversed by the ﬂuid in circulatory direction while passing through the channel

region and A¢b represents the angle traversed by the ﬂuid in circulatory direction while

passing through blade. Thus(A¢r +A¢b) represents circulatory angle traversed by the

ﬂuid in one cycle.

192

If absolute tangential velocity is assumed to be linearly distributed within blade and

channel region, it can be expressed,

 

 

 

ngt __ Rd19
V,dt Fd¢
V9” = RGAQ‘ (8.33)
V¢ 1,
Similarly,
y—b- = RbAg” (8.34)
V¢ lb
Therefore, the regenerative number can be given as,
_—___2_”:_&_ (8.35)
AQ+AQ

8.7 Performance prediction

Based on proposed mathematical formulation for compressible ﬂow and loss models, a
performance prediction code is developed and numerical results are compared to
published experimental data. The non—linear ordinary differential equation for circulatory
velocity is solved using predictor-corrector technique for each control volume. The code
takes geometric and inlet ﬂow conditions as input and predicts pressure rise, power input,
efﬁciency and other thermodynamic properties.

Geometric data and inlet ﬂow conditions for MKl and MK2 regenerative compressors
tested by Sixsmith and Altmann [60] is used as input to the code. Table 1 reproduces
fundamental geometric data of MKl and MK2 regenerative compressors as suggested in

[60]. Moreover, Table 8.1 also contains values of some constants used in calculation.

193

Air is the working ﬂuid with ambient inlet conditions. A linear distribution of all
geometric parameters and loss coefﬁcients is assumed across the periphery between inlet
and exit. Blade and channel turning loss coefﬁcient are calculated in a similar way as
described in chapter 5. There is no slip loss model available in literature for aerofoil blade
RFC. The shape and arrangement of blades in RFC is very similar to axial cascades.
Therefore, the deviation correlation of axial cascades for accelerated ﬂow suggested by
Howell [31] is chosen to calculate slip factor for MKl and MK2 compressors. The value
of slip factor for MKl was found to be 0.92, whereas symmetric MK2 design blade

yielded slip factor of 0.9 as shown in Table 8.1.

Performance prediction results from the code are superimposed on experimental data for
the two compressors as shown in Figures 8.7 — 8.10. These ﬁgures include the effect of
water-cooling jacket and decompression ducts on performance. Water-cooling jacket was
used in the experiment to extract heat from the compressor. The magnitude of extracted
heat was not mentioned in Sixsmith and Altmann [60]. Therefore, performance at two
thermodynamic conditions, adiabatic and isothermal is predicted in this work. In order to
investigate the effect of decompression ducts, comparison with or without decompression
ducts is performed. The symbols in each ﬁgure mean the combination of two effects,
adiabatic vs. isothermal and with decompression duct vs. without decompression ducts.

For example, symbol (ISO:3) means isothermal condition with three decompression ducts.

Figure 8.7 and 8.8 show pressure ratio of MKl and MK2 compressors at different rpm. It
can be seen that the pressure ratio at isothermal condition is much larger than at adiabatic
condition. This trend is obvious because at same input power and mass ﬂow rate,

pressure rise should be maximum at isothermal conditions and minimum at isentropic

194

conditions. An interesting ﬁnding is that most of the experimental data lies between the
two thermodynamic conditions, indicating that experimental process is polytropic.
Moreover, both compressors show that at low speed (3000 rpm), the results in isothermal
condition are in very good agreement with experimental data excluding the low ﬂow rate
region. At higher speed, there is a large difference between isothermal prediction and
experimental result. Moreover, it is observed that at higher speed there is a smaller
difference between adiabatic prediction and experimental data. There can be two possible
reasons to explain these trends. Firstly, the compressibility effects can be regarded as a
reason for this mismatch and secondly, it can be explained in terms of inadequate
compressor cooling. Cates [15] suggested that compressibility effects start to appear
when the value of Mach number is larger than 0.4. However, the operating machine
Mach number for both MKl and MK2 ranges from 0.14 to 0.23, which is much smaller
than 0.4. Therefore, the mismatch cannot be explained based on compressibility effect.
The other possible explanation could be that the compressor did not operate under
isothermal condition at higher rpm because of the lack of capacity in water-cooling jacket.
Figure 8.11 shows the theoretical magnitude of heat transfer required to be extracted in
order to maintain the isothermal condition. The extracted heat increases with decrease in
ﬂow rate and increase in speed. Especially, because MK2 is composed of two parallel
channels and it needs to extract almost twice amount of heat than MKl. This makes it
more difficult to maintain constant temperature than in case of MKl. Therefore in Figure
8.8, it seems that MK2 running 5000 rpm is operating under the adiabatic condition.
Figures 8.7 and 8.8 also show that the existence of decompression has little inﬂuence on

pressure ratio.

195

Figures 8.9 and 8.10 give comparison of predicted and experimental efﬁciency under
different thermodynamic conditions. Since each decompression process is assumed as a
quasi-equilibrium process, decompression power calculated by equation 8.31 is
maximum possible power to be extracted from decompression. Therefore, the lines ISO:3
in MK] and ISO:4 in MK2 represent the line of maximum obtainable efﬁciency.
Moreover, as expected, lines ADI:0 in MKl and MK2 give minimum efﬁciency lines as
shown in each ﬁgure. The maximum efﬁciency and corresponding ﬂow rate become
smaller when changed from isothermal condition to adiabatic condition. These ﬁgures
show that all experimental data exist between two ultimate thermodynamic conditions.
The maximum obtainable efﬁciency for MK] and MK2 is similar and lies around 60%.
However, a difference of about 7% in the maximum efﬁciency of line ISO:0 is observed,
which represents the effect without decompression ducts. It can be explained by the fact
that the power expelled through the stripper in MKl is greater than that in MK2
compressor because of larger carryover mass ﬂow rate in MK]. Figure 8.10 shows that
the overall results for MK2 compressor are in very good agreement with experimental
data. Prediction at isothermal condition for 3000 rpm and adiabatic condition at 5000 rpm

are good just as in the case of pressure ratio comparison.

Figure 8.12 shows that the ratio of decompression power to hydraulic power, which can
be theoretically obtained from quasi-equilibrium equations, is greater in MKI than in
MK2 compressor in spite of less decompression ducts. The reason is that carryover mass
flow rate and decompression power are larger as known from equation 8.31 in case of
MKl compressor with larger ratio of blade area to channel area. Therefore, it can be seen

from the comparison between line [3023 (or ISO:4) and Line ISO:0 in Figure 8.9 and

196

8.10 that theoretically MK] can achieve 18% increase in efﬁciency and MK2 can achieve
an increase up to 10% using decompression ducts. However, it must be noted that the
complete decompression does not happen in actual compressor when tested
experimentally. In particular, since the space surrounded by blades in MKl is larger than
in MK2, the possibility of quasi-equilibrium process is reduced in MK] than MK2 while
rotating at same speed. Due to this reason, in case of MK2 compressor, there is little
difference between predicted ISO:4 line and experimental data in Figure 8.10, but a big
difference between predicted ISO:3 line and experimental data as shown in Figure 8.9 in
case of MK] compressor. More explanation of this can be given by the fact that although
MK] has three decompression ducts, but physically it can only obtain the effect of one or
two decompression ducts. Figure 8.13 shows the variation of regenerative number in
MK] and MK2 with respect to ﬂow rate under the condition ISO:3 and [80:4 using
equation 8.34. The regenerative number at maximum efﬁciency in MK] is about 7 and
that in MK2 at maximum efﬁciency point is 5. This can help to explain experimental
results showing that pressure ratio at maximum efficiency in MK] is 1.2 times larger than

that in MK2.

8.8 Sensitivity Analysis

There are many design variables which inﬂuence performance of RFC. These variables
depend on each other, thus making the design process difﬁcult. It is important to
investigate all design variables initially and then short list important design variables,
which have maximum effect on performance. The idea is to reduce number of controlled
design variables to make the design process easy. Therefore, while performing sensitivity

analysis, the effect of design variables on head coefﬁcient, efﬁciency, regenerative

197

number etc is investigated. A i20% variation in the base value of each design
variables A, , Rp ,RG , [3,, ,1b , kn. , and 0' is investigated. While performing sensitivity
analysis for one variable, other variables are kept constant. Geometry of MK2
compressor with no decompression duct operating in adiabatic condition with a slip

factor of 0.9 is chosen as starting point for sensitivity analysis.

Figures 8.14 represents sensitivity analysis of head coefﬁcient (Wadi) with respect to

design variables. Steep variations in head coefﬁcient with respect to all design variables
can be observed with the exception of almost no variation in gradient in case of chord

(lb ). It shows a signiﬁcant rise in head coefﬁcient with increasing blade angle. However,

this rise in head coefﬁcient becomes gradual at very high values of blade angle. It can be

observed that decreasing A, and increasing Rp causes an increase in shut-off head ((00 =0).
Conversely, increasing Ac and decreasing RP decreases shut-off head ((00 =0) and makes

the slope of (Ill-w) less steep. This means that if the compressor is operating at higher

ﬂow coefﬁcient, it is better to decrease tip radius and increase channel area. However,

close to lower ﬂow coefﬁcients, it is beneﬁcial to decrease Ar and increase RP. The
reason is that at high ﬂow rate, A. must be increased to reduce the friction loss and

because circulatory velocity increase at the same time, it is not needed to increase RP.

Defining a ratio Ri/Ar , it can be said that the designer should strive to minimize this

ratio at higher ﬂow coefficients and maximize it at lower ﬂow coefﬁcients. Various
authors verified this trend experimentally. Cates [15] did an experimental sensitivity
analysis and he concluded that at low speciﬁc mass ﬂow rate, a decrease in channel area

is beneﬁcial for RFC performance and vice versa. The theoretical and experimental

198

analysis on Capstone single and multistage RFC also suggest that at low specific mass
ﬂow rate values, it is beneﬁcial to decrease channel area and increase tip radius and vice

VCI’SB.

Figure 8.15 shows that maximum efficiency increases with decreasing channel area and
increasing tip radius because the circulatory velocity and hydraulic power decrease. It is
interesting that the ﬂow range, where compressor can operate effectively, is reduced in
spite of the increase in maximum efﬁciency. However, the decrease in centric radius
increases efﬁciency without changing the overall ﬂow range and the ﬂow rate at which
maximum efﬁciency occurs. In addition, it can be seen that the variation in chord length

causes a little effect on efﬁciency.

8.9 Conclusions

A compressible ﬂow theory for analysis of helical ﬂow in regenerative compressors is
put forward for the ﬁrst time. The continuity, momentum and energy equations are
developed for differential control volume containing blade and channel region. The idea
of decompression ducts is utilized and governing equations for quasi-equilibrium
decompression process are developed. Loss models are introduced in the formulation to
predict head rise and efficiency. A performance prediction code is developed based on
mathematical formulation and loss models. Geometries of MK] and MK 2 regenerative
compressors are used as input to the code. The code predicts performance characteristics
of these compressors. Excellent agreement is seen in comparison with experimental data
on these compressors. The idea of decompression ducts proves beneﬁcial to the

efficiency. It is found theoretically that 18% increase in efﬁciency can be achieved using

199

decompression ducts in case of MK] design and 10% efficiency can be increased in case
of MK2. This conclusion still needs to be validated by introducing decompression ducts
in an actual compressor design and test it.

Design sensitivity analysis is performed on important variables effecting RFC
performance. It is concluded that at low ﬂow coefﬁcient, an increase in tip radius and
decrease in channel area is beneﬁcial to performance and vice versa. A signiﬁcant rise in
head coefﬁcient is achieved with increasing blade angle, however this rise in head
coefﬁcient becomes gradual at very high values of blade angle. Observed trends are

compared with other published data in literature and found consistent.

200

Inlet Port Exit Port

 

 

 

 

 

Figure 8.2 Coordinate and meridional geometry

201

   
  

  
    
 
  

_Izz_
”b2 Ac—dAc/Z

 

 

'2 V0," -dV9m / 2 V"2

-dp/2 V,-dV,/2 “a... Ac+dA,./2
p-dp/2 . V," +dV0m/2
Hm T-dT/Z :01 V,+dV,/2

p-dp/ 2 e

p+dpl2 pi- P+dp12

1 T +dT / 2

+d /2

dx = Rbda '0 p
R2 R0
blade region channel region

Figure 8.3 Arbitrary small control volume

 

 

 

 

 

 

 

 

 

 

Figure 8.4 Velocity triangles at R1 and R2

202

    
   

decompression ducts

 

 

 

—’ "'2‘, ”+1 TH]

 

m
i 3m 3M

< D

 

 

 

stripper region

Figure 8.5 Schematic diagram for inlet region and decompression duct

 

 

 

 

 

 

 

 

 

 

 

 

 

T A6 ‘
V921: . f
V...” - slip +1.19,
A19,
V91
V '\
m \\ incidence
P 4
At”r A¢c + A¢b A191. A¢c + 13¢»

Figure 8.6 Tangential velocity and angle distribution per cycle

203

Table 8.1 Geometric data and some parameters used in calculation

 

blade
R1 R7 ”b1 ”b2 Ab lb Zb 1611; 1621) ktb dUCt 0'

h

region

 

MK] 14] 140 18 15 330 20 120 -500 40° 0.35 3 0.92

 

MK2 141 141 18 18 270 15 150 -480 48° 0.36 4 0.9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Contd
Inlet Exit A
channel clnlet
' A A“ 1 R k A A“ 1 R k 4.5,,
1' egron (' Ab r‘ G 11' 6 Ab (' G (C

 

MKl 2553 7.7 155 172 1.0 1501 4.6 95 154 1.0 1.7

 

MK2 2774 10.3 159 175 1.0 2135 7.9 122 166 1.0 1.3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Length (mm) and Area(mm2)

2-4 +3000H=M

+ 4000mm

2-2 i ** r ' ' ’ ’ +5000PPM
—— 150.3 (3000 rm
.9. 2.01 ~-~Is<23(4ooorl=M)
’6 1503 (5000 RPM)
1: 1.811 -——Aota(3ooomw1
8 —— A113 (4000 m0
3 1.6.. —~—Aﬂ:3(5000FFM
a 60:0(3000 PM
a 1.4 . —— 600(4000 WM)
— 150.0 (5000 FFM)
1.2 1 — A110 (3000 m0
—Aoto (4000 m
1.0 , . 1 7 A110 (5000 RM

20 40 60 80 100 120

Volume How Rate ( liter/s)

 

 

 

Figure 8.7 Comparison of pressure ratio of MK] compressor

204

 

 

 

 

 

 

 

 

 

 

+3000RPM
2.6 . +4000RFM
+5000RPM
2-4 ‘ —Iso4 (3000RPM)
_o 2.2 - $1504 (4000RPM)
7i 2 _ lSQ4(5000RPM)
I! —ADl:4(3000RPM)
2 1.8 - ~——ADt4(4000FlHﬂ)
3 16— —#ADt4(5000RPM)
w ' —Iso0(3ooonm)
E 1.4 « —SO:0(4000RPM)
1 2 j ——50.0(5000H=M)
' —ADl:0(3000RFlW
1 < -——ADt0(4000FlPM)
0.8 . —— ADt0(5000FlFM)
20 70 120 170 220 270 320

 

 

Volume Flow Rate( liter/s )

 

Figure 8.8 Comparison of pressure ratio of MK2 compressor

 

 

0.7

 

0.6 1

0.5 -

0.4 -

0.3 4

   

 

 

 

 

l W

 

 

0.2
20

40 60 80 100 120
Volume Flow Rate( liter/s)

+3000FFM
+4000FFM
‘1—9—5000FPM
——rsoa(3ooon=M)
, soamooonm;
303(me
—ADt3(3000FFM)
——Apta(4ooonPM)
—Apta(5ooonm)
——ISO:0(3000F1FM)
——SQO(4000RPM)
—SO:0(5000RPW
—AotO(aooor=m)
—ADl:0(4000FlFM)
.7 ,, AU:0(5000RPM)

 

 

 

 

Figure 8.9 Comparison of efﬁciency of MKl compressor

205

 

 

 

 

 

 

0.7

 

 

+_r—_(

0.6 1

0.5 .

C

0.4 1

 

0.3 -

 

 

 

 

0.2

 

 

 

   

T

20 70 120 1 70 220 270
Volume Flow Rate( liter/s )

320

 

{—4—- 3000F1PM
+4000RFM
+5000F1FM
—-—— 1604 (3000 RPM)
------ 1604 (4000 mm)
160.4 (5000 RPM)
—-— ADM (3000 RFM)
-~-—— A014 (4000 RPM)
——-— ADM (5000 FlFM)
-— 1800 (3000 RPM)
--— 180:0 (4000 FHA)
— 160.0 (5000 RPM)
— ADtO (3000 RPM)
—--AD|:O (4000 FFM)
ADtO (5000 M11)

 

 

 

 

Figure 8.10 Comparison of efﬁciency of MK2 compressor

 

 

3-
2.51

 

'0' 24

 

 

 

 

 

 

 

 

 

—I-— M<1(3000RFM
—o— M<1(4000H=M
—O- MMSOOOHWD
+ MQ(3000RPM)
—-)(-— M<2(4000RFM
——t— MQ(5000F1FM)

 

 

5:1

 

 

Volume Flow Rate(literls)

 

050100150200250300350

 

Figure 8.11 Theoretical heat transfer ratio in MK] and MK2

206

 

 

 

 

 

 
 

 

 

 

'.‘..* ’ * * - +M<1(3000RPM)
—o— M11 (4000RFM)
>1 +1011 (5000mm
‘ _ 7 7 + M<2(3000RFM)
/ +Me(4ooonPM)
—1— M<2(5ooo1=u=M)

in?“

 

 

 

 

 

 

 

 

 

 

0 50 100 150 200 250 300 350
Volume How Rate(llterle)

 

Figure 8.12 The ratio of Decompression power to Hydraulic power

 

 

 

—I- M11 (SOOOFPM)
-o— M<1(4000H=M)
+ M(1(5000H=M)
—o— M<2(3000RFM)
—-)(-— M<2(4000RFM)
—-l— M<2(SOOORFM)

 

 

 

n in :3

 

0 50 100 150 200 250 300 350
Volume How Rate(llterls)

 

Figure 8.13 The variation of regenerative number vs. Flow rate

207

 

 

 

\Vo (Idlebtlc)

 

 

—Base

 

Ac (-20%)
— Ac (+20%)
— R1 020%)

' R) (+20%)
— HQ 020%)
— 99 (+20%)
— beta (-20%)

— beta (+20%)

 

 

 

chord (-20%)

 

chord (+20%)

 

 

 

Figure 8.14 Head coefﬁcient vs. ﬂow coefﬁcient

 

 

0.7

 

 

 

0.6 « , l \
l
0.5 -

 

 

 

— Base
Ac (-20%)
—— Ac (+20%)
— R) (-20%)
l7 a: (+20%)
— Fig (-20%)
— Rg (+20%)
I beta (-20%)
(— beta (+20%)
-—-— chord (-20%)

—— chord (+20%)

 

 

 

i 1
s.-

0.4 4

\
0.3 - \ —\
0-2 I
0.1 0.15 0.2 0.25 0.3
‘00

Figure 8.15 Efﬁciency vs. ﬂow coefﬁcient

208

 

CHAPTER 9

CF D ANALYSIS ON AEROF OIL BLADE RFC

Theoretical performance prediction of two aerofoil blade RFC with the inclusion of
decompression ducts was discussed in chapter 8. Design sensitivity analysis on these
compressor designs suggested a potential improvement in efficiency by making various
design changes. The theoretical investigation motivated to perform a CFD analysis on
aerofoil blade RFC to validate the effects of design changes on performance.
Computational Fluid Mechanics (CFD) has been widely used for the flow analysis in
various turbomachines during the last few years. However, there is not much evidence
available in literature discussing the utilization of a commercial CFD code to solve ﬂow
details in a RFC/RFP. CFD seems to be an attractive tool to analyze and calculate the
complex three dimensional flow in regenerative turbomachines to validate the likely
effects of design modiﬁcations prior to constructing the prototype compressor. Moreover,
CFD helps to optimize the geometry for the best performance. The inlet and discharge
ports can be designed for minimum losses.

For this purpose, a compressor model is generated in UNIGRAPHICS based on blade

geometry of MK2 RFC provided in Table (8.1). The dimensions of aerofoil blades used

in the model are provided in Figures 9.1 and 9.2. Symmetric aerofoil blades with 48°
angle are used in the model. Blade profiles are drawn using two arcs for simplicity.

Channel and blade geometry is shown in Figure 9.3. It can be seen that there is a channel

209

on each side of the impeller. The top portion represents geometry at a section near the
inlet and the bottom portion describes geometry at a section near the outlet. The channel
area decreases linearly from inlet to outlet with an area ratio of 1.3. The cores promote
circulatory ﬂow in the channel as shown by the arrows in Figure 9.3. A full model of the
compressor can be seen in Figure 9.4. Flow goes in the compressor through two inlet
manifolds. The twin blade impeller has channel on each side shown by red and green
colors. Blades are shrouded by a core on each side around which a helical toroidal flow
path is established. Mesh is generated on the Unigraphics model using GAMBIT to
perform CFD analysis as shown in Figure 9.5. Mostly hexahedral (Brick) elements are
used for meshing, however near the outlet port due to complicated geometry, triangular
elements are used. Element count for the full RFC model is 568900 cells. The green and
red portions represent the flow in the channel, whereas blue portion represents the flow in
the blades.

The inlet manifold of RFC is shown in Figure 9.6. Flow is injected in the impeller blades
above the core and then it passes through the blades and goes through the channel for ﬁrst
circulation. It must be noted that that there are two inlet manifolds, one for each channel
and blade side. Some RFC are designed with single inlet manifold with a mechanism to
divert half of the fluid to each blade and channel geometry. However, this causes lot of
turbulence and mixing losses, which led the researcher to design separate inlet manifolds
for both sides. In order to explain the path of fluid through the blades and circulation in
the channel around the core, Figure 9.7 is presented. The ﬂow goes through the two
blades shown on each side in this ﬁgure and then goes in the two corresponding channels.

There are many circulations of the ﬂow from the inlet port to the discharge ports. Figure

210

9.8 is a section of the compressor containing few blades, core and channel showing

meshing in the cut section.

9.1 CFD Analysis

In order to perform CFD analysis, it is general practice to select a design point where the

compressor is likely to operate. Following design point is chosen for analysis.

Working fluid: Air

QM = 0.225 m3/s
RPM = 4000
pm = 1.205 kg/m3

The total volume ﬂow rate of 0.225 m3/s is divided equally to the two sides. Thus,

0.1125 m3/s goes into the compressor from each inlet manifold. Inlet velocity is obtained

by dividing the ﬂow rate by inlet manifold area. The inlet port area is 0.00187 m2 , which
yields an inlet velocity of 60.133 m/s from each inlet manifold. This is selected as the
inlet boundary condition. Moreover, at the discharge, pressure boundary condition is
speciﬁed. The pressure ratio at design point is obtained from experimental data to be1.2.
Assuming ambient inlet pressure of 100000 pa , a pressure of. 100000x1.2 = 120000 pa is
applied at the discharge port.

CFD simulation is run in commercial CFD software STAR CD. A transient analysis is
performed with a time step At = 2.083X10‘5 sec for half degree impeller revolution. The

simulation is run for two complete revolutions of the impeller. This implies that for

720° impeller rotation, the simulation uses 1440 time steps.

211

 

After running the simulation, it was expected that a pressure close to 100000 pa at the

inlet should be obtained to verify that pressure ratio of approximately 1.2 is obtainable
through this design. However, unexpected trends are observed and desired pressure ratio
cannot be achieved. The observed trends are discussed below based on absolute velocity
vector diagrams. Preliminary results of the simulation are shown in Figure 9.9 which
shows absolute velocity vectors representing the flow direction. It can be seen that all the
ﬂow is going in the peripheral direction with almost no circulatory flow. Ideally, some
ﬂow should circulate in the channels as it was in case of regenerative fuel pump shown in
Figure 7.17. These circulations are actually responsible for pressure rise because the
impeller hits the ﬂow and adds energy to it which is recovered as pressure rise. Figure
9.10 represents a cross section of impeller, core and channel and it can be seen that all the
ﬂow is coming out without any circulation. Due to this predominantly straight through
ﬂow direction, the compressor model is unable to generate required pressure ratio. Thus,
the ﬂuid sees the impeller blades as a rough surface and instead of building any pressure,
the ﬂow goes through the flow channel without passing through the blades. This implies
that the model is not acting as a compressor. After observing these unexpected trends,
flow mechanism at the inlet port is investigated to ﬁnd out the reason of no circulation

through the blades.

9.2 Lack of circulatory flow

It is thought by many researchers that the circulatory flow pattern in regenerative
turbomachines is set up by the inlet manifold. Fluid entering the inlet from the piping has
no circulatory velocity component associated with it. Thus, the inlet manifold has to be

designed such that for the very ﬁrst circulation, it forces the ﬂuid to circulate through the

212

 

blades and then for the second circulation, ﬂuid uses its circulatory velocity component
and keeps on circulating through the periphery.

The inlet design shown in Figure 9.6 is not good enough to provide the desired
circulation. Figure 9.11 indicates that after passing through the inlet manifold, the ﬂow
enters the blade from both sides thus eliminating the possibility of any circulation
through the blades. Therefore, the ﬂow is pushed through the compressor in the
peripheral direction, making it impossible to build pressure. Typically, it is desired that
the inlet port directs the ﬂow straight at the inlet edges of the blading so as to get the ﬂow
circulating. The inlet port is arranged so that most of the inlet ﬂow has to go through the
blading. Without this feature, it is very difﬁcult for the compressor to build up any
pressure. This motivated the researcher to modify the inlet port to improve the ﬂow

guidance.

9.4 Modiﬁed Inlet Design

In order to direct the ﬂow at the inlet edges of the blading, the inlet manifold is modified
as shown in Figure 9.12. A 2D view of this inlet design is shown in Figure 9.13. The new
design has a constriction (nozzle effect) at entrance of RFC which accelerates the ﬂow
before it enters the blade row. This design prevents the ﬂow being fed from both sides of
blades, which hindered the circulatory ﬂow pattern in the previous inlet design. A CFD
analysis is performed on aerofoil blade RFC using the modified inlet design. Results from
this CFD analysis show that ﬂow circulates through the blades, however, the new
compressor design is also unable to build desired pressure ratio. There is a marked
improvement in pressure ratio in the modiﬁed design compared to the previous design,

however, still it is less than the pressure ratio obtained from experimental data. The

213

 

circulatory ﬂow pattern can be observed in Figure 9.14, which shows that the ﬂow is
injected from only one side of the blades, thus forcing it to circulate through the blades.
The constriction (nozzle) helps the ﬂow to establish the circulatory motion which is key
for pressure build up in regenerative turbomachines. The ﬂow pattern in the blade and
channel region at two peripheral locations is shown in Figures 9.15 and 9.16. Figure 9.15

represents a section taken close to the inlet describing the circulatory ﬂow pattern close to

inlet. Figure 9.16 represents a section taken at 6 =180° away from the section shown in
Figure 9.15. It is interesting to note that there is much higher circulatory velocity close to
inlet as compared to somewhat lesser circulatory velocity at a larger peripheral angle. The
ﬂow pattern depicted in these ﬁgures resembles to that reported in Sixsmith and Altmann
[60].

The modified inlet has a constriction (nozzle) which accelerates the ﬂow at entrance
producing a huge velocity. The high velocity imparted by the nozzle shape creates
extreme turbulence and does not permit enough circulations through the blades. A higher
velocity implies that the ﬂuid skips many blades before it becomes fully developed. It is

only after settling down that the ﬂuid really starts to circulate through the blades and
creates some pressure rise. Thus the ﬂow becomes developed after 0=90° and initial

turbulence is somehow reduced resulting in good pressure rise from6=90° to 360°.
Currently, work is in progress to further modify the inlet to remove the nozzle effect and
inject the ﬂuid with proper guidance and minimum turbulence. The inlet should be
designed to direct all the ﬂow through the blades. It should be wide enough to carry the
ﬂow and at the same time to accelerate the ﬂow velocity through the blade passages up to

the velocity of circulation. CFD analysis is being performed on a proposed “OWL”

214

 

 

 

shaped inlet as shown in Figure 9.17. Details of this CFD analysis will be reported in a

publication to appear shortly.

9.5 Conclusions

An attempt is made to solve ﬂow details in a regenerative compressor using STAR CD.
Two inlet designs are proposed, however still the required pressure ratio has not been
achieved. The circulatory ﬂow pattern is observed in blade and channel region which is a
characteristic of regenerative turbomachinery. Currently research is under way to
optimize the inlet manifold so that desired pressure ratio and isothermal efﬁciency could
be achieved. It will be very interesting to implement suggested design changes of chapter
8 in this compressor mode] to get further improvement in efﬁciency. Further details on

CFD analysis will be reported in a publication to appear shortly.

215

 

 

 

 

 

PITCH I 5.9!!!!)

 

Figure 9.2 Blade design

216

 

 

 

 

 

TRANSVERSE
PATH LENGTH

 

 

 

 

 

 

 

 

 

 

 

 

 

15mm
Radius-7.5m I .. .— .— .1
\‘
\
s l t
\
tn
2
\ a:
12 {PM gamma-21mm
Radius=75mm E
\\ .-
In
\
\ \
\\\ \\\ O
15 mm 30 rum—~21 W

 

Figure 9.3 Blade and channel geometry

217

 

 

Figure 9.4 Full Assembly of regenerative compressor with aerofoil blades

 

Figure 9.5 Meshing for CFD analysis

218

 

 

 

Figure 9.6 Inlet manifold

u

-~

5
MV ~+-~‘- "

 

Figure 9.7 cross sectional view of twin blade and channel

219

 

 

am

”no"???
If],

,1 u
"5m”
’Jtm

 

 

 

Figure 9.8 Meshing around twin blade and channel

 

Figure 9.9 Absolute velocity vectors representing the ﬂow direction

220

 

Figure 9.10 Absolute velocity vectors representing ﬂow around the core in the channel

 

Figure 9.11 Absolute velocity vectors representing ﬂow in the inlet manifold

221

 

 

Figure 9.13 Modiﬁed Inlet Design (3D view)

222

 

 

Figure 9.14 Velocity vectors describing circulatory ﬂow pattern through the inlet

manifold

 

Figure 9.15 Velocity vectors showing circulatory ﬂow pattern near inlet port

223

‘ .::'ors T-I'I 5:031:21“: giro its» scc‘ic-r

   

Figure 9.16 Velocity vectors showing circulatory ﬂow at 6 =180° from inlet port

 

Figure 9.17 Proposed “Owl” shaped lnlet design

224

 

CHAPTER 10

CONCLUSIONS AND RECOMMENDATIONS

Performance characteristics of regenerative compressors and pumps are investigated in
detail. Regenerative turbomachines have great potential due to their unique design and
operational features. There are numerous applications of these turbomachines, specially
for duties requiring high heads at low ﬂow rates. Low efﬁciency and limited range of
speciﬁc speed are the only drawbacks of these turbomachines. Therefore, this research
was started with an aim to improve the performance of RFC/RFP. Several new
contributions in this neglected area of research have been made in this dissertation. A
thorough explanation of fundamentals and working principle is provided along with
various applications. Research is broken down into two main applications of regenerative
turbomachines, i.e.

. Application as regenerative compressors for low pressure (0.2-15 psig) natural

gas compression for microturbine systems.

. Application as regenerative automotive fuel pump.

Extensive test data on single and multistage RFC with radial blades is presented in terms
of various non-dimensional parameters. Test data on multistage RFC was not available in
open literature before this dissertation, therefore various correlations between non-
dimensional parameters are presented which can prove to be very useful for designers

and engineers. A theoretical model is presented to predict performance of radial and non-

225

radial blade regenerative turbomachines. The model is generic and can be applied to
predict the performance of regenerative turbomachines employing compressible media.
Various losses are investigated and correlated with geometric and aerodynamic
parameters of RFC/RFP. Governing equations and loss models are used to develop a
performance prediction code. Excellent agreement between theoretical and test data on
multistage RFC is obtained. Based on sensrtivity analysis from the code and published
test data in literature, design improvement guidelines for multistage RFC are provided. It
is believed that these design changes can increase the efﬁciency of radial blade
multistage RFC by 5% or more. However it needs to be validated by CFD and
experimentation. To make the discussion more meaningful, a generalized design
procedure for radial and non-radial blade RFC is presented in this dissertation.

Automotive fuel pumping is another attractive application of regenerative pumps. Delphi
Automotives has developed a regenerative automotive fuel pump with non-radial blades.
Proposed theoretical model is used to predict performance of Delphi automotive fuel
pump. Performance prediction results are compared with the test data and reasonable
agreement is observed. Based on sensitivity analysis from the code, few design
recommendations are made. It is believed that such design variations can improve RFP
efﬁciency by 3-7 %. Details of CFD analysis on non-radial blade automotive fuel pump
are presented in this dissertation to motivate industry to apply CFD techniques on these
turbomachines. A hydraulic efﬁciency around 40% is obtained from Delphi fuel pump,
which is more than any other automotive fuel pump in the market. However, there is still
a lot of room for improvement in hydraulic efﬁciency by employing aerodynamically

designed aerofoil blades. Therefore, need was felt to investigate RFC/RFP with aerofoil

226

blades. There is not much evidence available in literature on aerofoil blade RFP.
However, it is found from literature that aerofoil blade RFC can produce isothermal
efﬁciencies in excess of 55%.

In an attempt to further increase the efficiency of regenerative turbomachines, a
theoretical analysis on RFC with aerofoil blade is presented. The idea of decompression
ducts is utilized to take some of the high pressure ﬂuid entrapped in the stripper blades
and feed it to various locations in the channel, thus reducing the power consumed by the
compressor. The proposed theory is validated by comparing the obtained results with
published experimental data on MKl and MK2 regenerative compressors with aerofoil
blades. The idea of decompression ducts proves beneﬁcial to the efﬁciency. It is found
theoretically that 18% increase in efﬁciency can be achieved using decompression ducts
in case of MKl design and 10% efﬁciency can be increased in case of MK2. This
conclusion still needs to be validated by introducing decompression ducts in an actual
compressor design and testing it. It is concluded from the theoretical analysis that
efﬁciency in excess of 60% can be obtained using aerofoil design RFC.

To further explore the aerofoil blade design applied to a regenerative turbomachine, CFD
analysis on a 3D compressor model generated in UNIGRAPHICS is performed. This is a
ﬁrst attempt to perform CFD analysis on aerofoil blade RFC. Preliminary results from the
CFD analysis have indicated that the inlet manifold design is very important to RFC
performance, a fact which was neglected by almost all researchers in the past. The inlet
manifold is responsible for setting up spiral ﬂuid motion in a regenerative turbomachine.

Currently work is in progress to design an effective inlet to direct the ﬂow on to the

227

blades and set up the helical ﬂow pattern with minimum losses. Such an inlet design can
create huge effect on efficiency of regenerative turbomachines.

The future direction of research in regenerative turbomachinery should be focused on
CFD analysis. The compressor model should be generated in a modeling software like
UNIGRAPHICS and CFD analysis should be performed to understand the ﬂow pattern
inside these machines. Once the model is generated, various changes in blade geometry,
channel geometry, channel area ratios, inlet and discharge ports and stripper design
should be performed to optimize the geometry for best performance.

However, such a procedure is very tedious and time consuming, because of complications
in grid generation and lengthy CFD simulations. Therefore, theoretical means can help to
reduce the CFD work by suggesting important geometries and operating points where
CFD analysis needs to be performed.

Once enough work in CFD is performed, there is a need to develop several design criteria
in terms of non-dimensional parameters. Such an analysis would lead to development of a
generic design code which can take the desired operating point and size the compressor
dimensions. The analysis presented in this dissertation was focused on performance
prediction and improvement through sensitivity analysis. Thus, tools are developed which
take in the geometry data and predict the performance. The next step is to extend such
tools to design mode, which mean that the user speciﬁes the desired operating point and
the tools should be able to size the compressor dimensions including impeller and
channel dimensions, inlet and outlet ports and stripper design etc. Such tools are in huge
demand in industry because neither research papers nor text on turbomachinery discusses

these design approaches for regenerative turbomachinery. There is a lot of design

228

 

information on axial and centrifugal turbomachinery available in literature, however not
much work is done in regenerative turbomachinery design. The design tools must be
developed after performing a lot of CFD analysis on regenerative turbomachinery to
establish more design criteria.

Ongoing research is also focused on building a regenerative ﬂow compressor to be
utilized in refrigerators employing water as refrigerant. The compact size and unique

features of RFC makes them very attractive for refrigerators.

229

BIBLIOGRAPHY

[l] Abdalla H.M.M., “A Theoretical and Experimental Investigation of the
Regenerative Pump with Airfoil Blades, PhD thesis, September 1981, Applied Mechanics
Branch, Royal Military College of Science.

[2] Andrew D.N., “The Calculation of Flow in Regenerative Turbomachines by a
Streamline Curvature Method”, Proc. Instn. Mech. Engrs., Part A: J. of Power and
Energy, Vol. 204, 1990. pp 121-129.

[3] Aoki M., “Studies on the Vortex Pump (lSt Report)”, Bulletin of JSME, Vol. 26,
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237

APPENDIX A

. Correlation between impeller tip Mach number(M(,,), ﬂow coefﬁcient (21) and

pressure ratio (fl) produced by multistage RFC is given as,

 

3.28x10‘S
n = 0.82+21.81M3,, +—7— (A.l)
Regression coefficient r2 = 0.766
. Correlation between impeller tip Mach number(MU,) , ﬂow coefﬁcientU.) and
isothermal efficiency (77) produced by multistage RFC is given as,
27 = 20.73 — 34.16M0T — 42.80.0821 + 9.7x 106,12 — 1.87 x109/l3 (A2)
Regression coefficient r2 = 0.724
. Correlation between impeller tip Mach number(M0,) , speciﬁc mass ﬂow rate
((1)) and pressure ratio (H) produced by multistage RFC is given as,
n = —5.6 + 47.13M0, — 13561143,, + 16127143,, + 00019 (A.3)
Regression coefficient r2 = 0.724
. Correlation between impeller tip Mach number(M,,,) , specific mass ﬂow rate

((1)) and isothermal efficiency (77) produced by multistage RFC is given as,

238

26.1_0.064 3.77_1.51x10*‘+ 0.0121

4» "M3. cw («004.0 “‘4’

 

 

n=249+

0T

Regression coefficient r2 = 0.725

239

APPENDIX B

. Density Distribution across the RFC

The density has to be incremented by a small value as we move from one control volume
to next one to make the ﬂuid behave as compressible. Increment in density depends on
many factors such as rotational speed, ﬂuid properties and inlet conditions. An
approximate way to ﬁnd the density distribution across periphery of RFC is to estimate
the density at the exit of RFC and then use a linear density distribution from inlet port to
discharge port. Density at discharge port is estimated by studying Capstone multistage
RFC test data. A correlation for exit density in terms of impeller tip Mach number and

speciﬁc mass ﬂow rate is developed:

p,m = 0.525-5.45(Mm.)21n(M0T)+1.24x103<1>3 (13.1)
where M m is impeller tip Mach number and <1) is speciﬁc mass ﬂow rate deﬁned as.

r260

 

 

M = (8.2)
or (___yRTm

ch: ’7“ R—T‘L (8.3)
4r. R. 7

The density distribution across the linear region of the compressor can then be obtained
using

p,”l = ,0" +[ﬂ’l’é—pijx6n + pm (B.4)

P

6‘ ,9

where n represents number of control volume.

240

APPENDIX C

Appendix C provides non-dimensional geometry for all four stages of the Capstone

multistage RFC. Figure 4.22 provides some geometry of all four stages, however more

detail is provided here which is helpful in design sensitivity analysis performed in chapter

6.

First Stage

Area Ratio = A“ A”, = 1.2814
Impeller tip radius = r2 = 1.65 in
Impeller hub radius = r; = 1.3665 in
Radius ratio = rz/r; = 1.2074
arm/r,2 = 0.0172

c, /r, = 0.0293

c, /d, = 0.274

c, / d B = 0.334

Second Stage

Area Ratio = AM /A.,a = 1.2862
Impeller tip radius = r2 = 1.65 in
Impeller hub radius = r; = 1.403 in
Radius ratio = rZ/I; = 1.176
arm/r,2 = 0.013

c, /r2 = 0.0257

c, /d, = 0.275

c, /d, = 0.337

241

Third Stage

Area Ratio = AM /A..a = 1.279
Impeller tip radius = r2 =1.65 in
Impeller hub radius = r, = 1.431 in
Radius ratio = rz/rg = 1.153
AM/r,2 = 0.010

c, /r2 = 0.0227

c, /d, = 0.277
c, /d, = 0.337
Fourth Stage

Area Ratio = AM/AC'B = 1.287
Impeller tip radius = r2 =1.6S in
Impeller hub radius = I; = 1.4645 in
Radius ratio = rz/r, = 1.126

AM/r: = 0.010

c, /r2 = 0.0193

c, /d, = 0.280

c, /d, = 0.344