.1

lei...

V...‘ :9 q
r,

b: 3.12 .
aria-6...;
3...)! a."

’1 .9“. M. 3a:-
n :. i»...
I‘ I... 1. 4 ii}... r61...
ivy 1D:c...§..flr 12.3.42: 1.... 59‘...
in. l;t‘>“o.l—.v\. . 1...“. x
. 35.... ‘ 31:1.

1.1;:
.i. .i , .x:
33.35.. 3

97.95.3424 :.

3:: “3...... 9.»
a 1 gels.
in

Q
~ 3 x~:§...:y.....§
.' 1:33:
.. .21.

.4
c,-
F.
A. I
(0

 

300!
LIBRARY

Michigan Sia‘ie

University

"‘3'

 

 

l

——v~v

This is to certify that the

dissertation entitled

THE INFLUENCE OF INLET FLOW DISTORTION ON THE PERFORMANCE
OF A CENTRIFUGAL COMPRESSOR AND THE DEVELOPMENT OF AN
IMPROVED INLET USING NUMERICAL SIMULATIONS

presented by

Yunbae Kim

has been accepted towards fulfillment
of the requirements for

PhD. . Mechanical Engineering
degree in

 

 

Wprofessor

0mm

MS U is an Aflirman’w Action/Equal Opportunity Institution 0-12771

 

 

 

PLACE IN RETURN Box to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 cJCIFiC/Dateouasz-pjs

 

THE INFLUENCE OF INLET FLOW DISTORTION ON THE PERFORMANCE
OF A CENTRIFUGAL COMPRESSOR AND THE DEVELOPMENT OF

AN IMPROVED INLET USING NUMERICAL SIMULATIONS

By

Yunbae Kim

AN ABSTRACT OF A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Mechanical Engineering
2001

PrOfessor Abraham Engeda

ABSTRACT

THE INFLUENCE OF INLET FLOW DISTORTION ON THE PERFORMANCE
OF A CENT RIFU GAL COMPRESSOR AND THE DEVELOPMENT OF

AN IMPROVED INLET USING NUMERICAL SIMULATIONS

By

Yunbae Kim

The performance of centrifugal compressors can be seriously affected by inlet
flow distortions due to the unsatisfactory nature of the inlet configuration and the
resulting inlet flow structure.

Experimental tests have been carried out for the comparison of a centrifugal
compressor stage performance with two different inlet configurations: one of which is
straight pipe with constant cross-sectional area and the other is a 90-degree curved pipe
with nozzle shape. The comparative test results indicated significant compressor stage
performance difference between the two different inlet configurations, and the details are
discussed to understand the performance behavior of the compressor exposed to the
distorted flow from the bend inlet configuration.

The experimental investigation motivated the need of a new inlet design as well
as a clear picture of the detailed flow field in the existing inlet design using numerical
simulations. Two design approaches are reported in this research work: one of which is
the location of vanes and the other is the length of curvature radius. For more effective

way of design, a generalized formula is developed for the optimum position and the

 

number of vanes in such a way that each divided flow passage with vanes shares the same
pressure gradient in radial direction. Numerical simulation results are presented and
discussed in terms of mass averaged parameters and flow structures, based on the
comparison of flow properties at the pipe exit cross-sectional area of each design. Finally,
new designs of different inlet systems are proposed to reduce the secondary flow and
provide enhanced flow for a compressor.

Steady-state compressor stage simulation including an impeller and a diffuser
with three different inlets attached for each case has been carried out to investigate the
influence of three different inlet systems including the proposed inlet model on the
compressor performance. Since the flow from the bend inlet is not axisymmetric for the
circumferential and radial distortion, the diffuser and the impeller are modeled with fully
360 degree passages, which makes it possible to detect the distortion influence on all of
the impeller and the diffuser passages as well as the interaction between the impeller and
the diffuser causing circumferentially non-uniform properties among the passages. The
stage performance and the diffuser performance are compared quantitatively for each
inlet system.

Additional experimental tests has been carried out for the comparison of three
different diffusers with the combination of the straight and the bend inlet systems. The
influences of the inlet distortion on the compressor stage performance for each diffuser
are presented in terms of the stage efficiency, the head coefficient, the work coefficient,
the static and the total pressure ratio. The contributions of the different difiusers to the

stage performance for each inlet system are discussed in detail.

number of vanes in such a way that each divided flow passage with vanes shares the same
pressure gradient in radial direction. Numerical simulation results are presented and
discussed in terms of mass averaged parameters and flow structures, based on the
comparison of flow properties at the pipe exit cross-sectional area of each design. Finally,
new designs of different inlet systems are proposed to reduce the secondary flow and
provide enhanced flow for a compressor.

Steady-state compressor stage simulation including an impeller and a diffuser
with three different inlets attached for each case has been carried out to investigate the
influence of three different inlet systems including the proposed inlet model on the
compressor performance. Since the flow from the bend inlet is not axisymmetric for the
circumferential and radial distortion, the diffuser and the impeller are modeled with fully
360 degree passages, which makes it possible to detect the distortion influence on all of
the impeller and the diffuser passages as well as the interaction between the impeller and
the diffuser causing circumferentially non-uniform properties among the passages. The
stage performance and the diffuser performance are compared quantitatively for each
inlet system.

Additional experimental tests has been carried out for the comparison of three
different diffusers with the combination of the straight and the bend inlet systems. The
influences of the inlet distortion on the compressor stage performance for each diffuser
are presented in terms of the stage efficiency, the head coefficient, the work coefficient,
the static and the total pressure ratio. The contributions of the different difiusers to the

stage performance for each inlet system are discussed in detail.

With blessings to my daughter, Hannah.

ACKNOWLEDGMENTS

The author is very grateful to his advisor, Professor Abraham Engeda for his
guidance, support and encouragement throughout the course of the research work.
Sincere thanks go to Professors John R. Lloyd, Craig W. Somerton, Charles R. MacCluer
for their advice, discussions, and interest in this work. Particular thanks go to Mr. Ron
Aungier and Dr. Wonjoong Kim, Dr. Naresh Amineni, and Mr. Greg Direnzi at Elliott
Company for initiating this work and for fruitful discussions. Special thanks go to
Professor Tom Shih and Dr. Bin Zhu at Michigan State University for their machine
support on CFD simulation and helpful discussions.

The author is also very thankful to Dr. Jeffrey Moore at Dresser-Rand company
for his encouragement. Mr. Craig Gunn at Michigan State University is specially
acknowledged for his help in preparing this dissertation. The author also appreciates
criticism, assistance and great friendship from Dr. Fahua Gu and all other students in
turbomachinery lab during his Ph.D. program at Michigan State University: Hooman
Rezaei, Faisal Mahroogi, Hou Kit Sam, Guy Phuong, Yinghui Dai and Donghui Zhang.

Last but not least, the author would like to thank his wife, Daesil Kwak for her

endless love and support and his daughters, lenny Kim and Hannah Kim for their love.

vi

TABLE OF CONTENTS

 

 

 

LIST OF TABLES x
LIST OF FIGURES xi
NOMENCLATURE xv
CHAPTER 1 : INTRODUCTION

1.1 CLASSIFICATION OF TURBOMACHINERY .................................................................. l
1.2 DEMANDS ON CENTRIFUGAL COMPRESSOR .............................................................. 2
1.3 DEMANDS ON INLET STUDY ...................................................................................... 3
1.4 OBJECTIVE AND STRUCTURE OF THE PRESENT STUDY .............................................. 3

CHAPTER 2 : FUNDAMENTALS OF CENT RIFU GAL COMPRESSOR

2.1 CONFIGURATION OF A CENTRIFU GAL COMPRESSOR .................................................. 6
2.2 INLET ....................................................................................................................... 8
2.3 IMPELLER ............................................................................................................... 10
2.3.1 Euler equation ............................................................................................... l 1
2.3.2 Head rise ....................................................................................................... 14
2.3.3 Slip factor ...................................................................................................... 15
2.3.4 Efliciency ....................................................................................................... 18
2.3.5 Compressor operating range ........................................................................ 19
2.3.6 Non-dimensional parameters ........................................................................ 21
2.4 DIFFUSER ............................................................................................................... 22
2.4.1 Difiusion process ........................................................................................... 22
2.4.2 Vaneless difi‘user ........................................................................................... 25
2.4.3 Vaned difi‘user ............................................................................................... 26
2.5 NOZZLE .................................................................................................................. 28

CHAPTER 3 : LITERATURE REVIEW

3.1 VARIOUS TYPES OF COMPRESSOR INLETS IN PRACTICAL APPLICATIONS .................. 30
3.2 PIPEFLOWASINAXIALINLET ................................................................................. 31
3.2.1 Classification of pipe flow ............................................................................. 31
3.2.2 Friction loss in pipe flow ............................................................................... 32

3.3 FLOW STRUCTURE IN CURVED PIPES ....................................................................... 35

. 3.4 INLET DISTORTION INFLUENCE ON IMPELLER PERFORMANCE ................................. 43
3.5 Two DIMENSIONAL SIMPLE DIFFUSER ..................................................................... 47
3.6 VANELESS DIFFUSER .............................................................................................. 48
3.7 VANED DIFFUSER ................................................................................................... 50

vii

CHAPTER 4 : EXPERIMENTAL TESTING WITH DIFFERENT INLETS

4.1 EXPERIMENTAL SETUP ............................................................................................ 62
4.1.1 Test rig setup ................................................................................................. 62
4.1.2 Geometric specifications of the compressor ................................................. 63
4.1.3 Geometry of the tested inlet models .............................................................. 65

4.2 EXPERIMENTAL PROCEDURE AND METHODOLOGY ................................................. 66

4.3 EXPERIMENTAL RESULTS AND DISCUSSION ............................................................. 72

CHAPTER 5 : NUMERICAL SIMULATIONS FOR VARIOUS INLETS

5.1 NEW INLET DESIGN CONSIDERATION ...................................................................... 79
5.1.1 Effect of the curvature radius in bend section ............................................... 79
5.1.2 New inlet design with vane spacing method .................................................. 91

5.2 COMPUTATIONAL MODELS AND SPECIFICATIONS .................................................... 94
5.2.1 Computational models ................................................................................... 94
5.2.2 Three dimensional viscous solver ................................................................. 95

5.3 SIMULATION RESULTS AND DISCUSSIONS ............................................................... 97
5.3.1 Flow structure aflected by bend curvature ................................................... 97
5.3.2 Mass flow rate weighted averaging of exit flow parameters ........................ 98
5.3.3 Total pressure loss contribution to the stage efi‘iciency .............................. 107

CHAPTER 6 : STEADY STATE COMPRESSOR STAGE SIMULATION

6.1 NECESSITY OF 360 MODEL WITH WHOLE PASSAGE ............................................... 109
6.2 COMPUTATIONAL MODEL AND SPECIFICATION ..................................................... 1 10
6.2.1 CF D model discription ................................................................................ 110
6.2.2 Grid generation and boundary condition .................................................... 112
6.3 IMPELLER-DIFFUSER INTERACTION ....................................................................... 117
6.4 SIMULATION RESULTS AND DISCUSSIONS ............................................................. 119

CHAPTER 7 : EXPERIMENTAL TESTING WITH VARIOUS DIFFUSERS

7.1 SPECIFICATIONS OF THE TESTED DIFFUSERS ......................................................... 126
7.2 DESIGN PROCEDURE OF A CONVENTIONAL DIFFUSER ............................................ 128
7.3 DESIGN PROCEDURE OF A LOW SOLIDITY VANED DIFFUSER .................................. 131
7. 3. I Singularity method ...................................................................................... 13 1
7.3.2 Conformal mapping ..................................................................................... 132
7.3.3 Geometric relations ..................................................................................... 134
7.4 THROAT AREA VARIATION IN A Y A N?!) DIFFUSER ................................................. 137
7.5 EXPERIMENTAL RESULTS AND DISCUSSIONS ......................................................... 139
7.5.1 Comparison ofchoke limit ................ 139
7.5.2 Comparison of surge limit ........................................................................... 140
7.5.3 Comparison of stage performance .............................................................. 141

viii

CHAPTER 4 : EXPERIMENTAL TESTING WITH DIFFERENT INLETS

4.1 EXPERIMENTAL SETUP ............................................................................................ 62
4.1.1 Test rig setup ................................................................................................. 62
4.1.2 Geometric specifications of the compressor ................................................. 63
4.1.3 Geometry of the tested inlet models .............................................................. 65

4.2 EXPERIMENTAL PROCEDURE AND METHODOLOGY ................................................. 66

4.3 EXPERIMENTAL RESULTS AND DISCUSSION ............................................................. 72

CHAPTER 5 : NUMERICAL SIMULATIONS FOR VARIOUS INLETS

5.1 NEW INLET DESIGN CONSIDERATION ...................................................................... 79
5.1.1 Effect of the curvature radius in bend section ............................................... 79
5.1.2 New inlet design with vane spacing method .................................................. 91

5.2 COMPUTATIONAL MODELS AND SPECIFICATIONS .................................................... 94
5.2.1 Computational models ................................................................................... 94
5.2.2 Three dimensional viscous solver ................................................................. 95

5.3 SIMULATION RESULTS AND DISCUSSIONS ............................................................... 97
5. 3.1 Flow structure affected by bend curvature ................................................... 97
5.3.2 Mass flow rate weighted averaging of exit flow parameters ........................ 98
5.3.3 Total pressure loss contribution to the stage efiiciency .............................. 107

CHAPTER 6 : STEADY STATE COMPRESSOR STAGE SIMULATION

6.1 NECESSITY OF 360 MODEL WITH WHOLE PASSAGE ............................................... 109
6.2 COMPUTATIONAL MODEL AND SPECIFICATION ..................................................... l 10
6.2.1 CFD model discription ................................................................................ 110
6.2.2 Grid generation and boundary condition .................................................... 112
6.3 IMPELLER-DIFFUSER INTERACTION ....................................................................... 1 17
6.4 SIMULATION RESULTS AND DISCUSSIONS ............................................................. 1 19

CHAPTER 7 : EXPERIMENTAL TESTING WITH VARIOUS DIFFUSERS

7 .1 SPECIFICATIONS OF THE TESTED DIFFUSERS ......................................................... 126
7.2 DESIGN PROCEDURE OF A CONVENTIONAL DIFFUSER ............................................ 128
7.3 DESIGN PROCEDURE OF A LOW SOLIDITY VANED DIFFUSER .................................. 131
7.3.1 Singularity method ...................................................................................... 13 1
7.3.2 Conformal mapping ..................................................................................... 132
7. 3.3 Geometric relations ..................................................................................... 134
7 .4 THROAT AREA VARIATION IN A YA NI-‘D DIFFUSER ................................................. 137
7 .5 EXPERIMENTAL RESULTS AND DISCUSSIONS ......................................................... 139
7.5.1 Comparison of choke limit .......................................................................... 139
7.5.2 Comparison of surge limit ........................................................................... 140
7. 5.3 Comparison of stage performance .............................................................. 141

viii

CHAPTER 8 : CONCLUSION .................................................................................... 155

BIBLIOGRAPHY ......................................................................................................... 158

APPENDIX .................................................................................................................... 164

 

ix

 

LIST OF TABLES

TABLE 4.1 DIMENSION OF IMPELLER AND DIFFUSER ........................................................... 64
TABLE 5.1 INLET DESIGNS AND DESCRIPTIONS ................................................................... 94
TABLE 5.2 CONTRIBUTION OF INLET MODEL TOTAL PRESSURE LOSS TO STAGE EFFICIENCY
................................................................................................................................. 108
TABLE 6.1 GRID SIZE OF EACH COMPONENT AND ENTIRE STAGE FOR NUMERICAL
CAICULATION .......................................................................................................... 1 16
TABLE 7 .1 SPECIFICATIONS OF THREE DIFFERENT DIFFUSERS (ANGLE BASED ON
TANGENTIAL) ........................................................................................................... 126

 

 

 

 

 

Fit
FIC

FIG
F10‘

F10.
F161
FIGL'
HGT

LIST OF FIGURES

FIGURE 2.1 EXAMPLE OF CONFIGURATION FOR A SINGLE STAGE CENTRIFUGAL COMPRESSOR

..................................................................................................................................... 6
FIGURE 2.2 EXAMPLE OF H-S DIAGRAM FOR A CENTRIFUGAL COMPRESSOR STAGE .............. 7
FIGURE 2.3 ACTUAL AND IDEAL HEAD CHARACTERISTIC OF A COMPRESSOR ........................ 8
FIGURE 2.4 INCIDENCE VARIATIONS UPON MASS FLOW CHANGE AND BOUNDARY LAYER

SEPARATION ............................................................................................................... 10
FIGURE 2.5 INLET AND EXIT VELOCITY TRIANGLES OF IMPELLER ....................................... 11
FIGURE 2.6 EFFECT OF EXIT BLADE ANGLE ON THE HEAD RISE AND THE FLOW RANGE ....... 13
FIGURE 2.7 VELOCITY TRIANGLES FOR THE DIFFERENT BLADE SHAPES .............................. 13
FIGURE 2.8 SLIP EFFECT ON VELOCITY TRIANGLE AT IMPELLER EXIT FOR BACKWARD—SWEPT

BLADE ........................................................................................................................ 16
FIGURE 2.9 INFLUENCE OF THE BLADE NUMBER AND THE EXIT BLADE ANGLE ON THE SLIP

FACTOR ...................................................................................................................... 17
FIGURE 2.10 REPRESENTATION OF A COMPRESSION PROCESS IN A T-S DIAGRAM ................ 19
FIGURE 2.1 1 A TYPICAL PERFORMANCE CURVE OF A CENTRIFUGAL COMPRESSOR ............. 20
FIGURE 2.12 T-s DIAGRAM OF DIFFUSION PROCESS ............................................................ 24
FIGURE 2.13 VELOCITY TRIANGLE IN A VANELESS DIFFUSER ............................................. 25
FIGURE 2.14 H-s DIAGRAM OF NOZZLE PROCESS ................................................................ 29
FIGURE 3.1 SECONDARY FLOW STRUCTURE IN A CURVED PIPE ........................................... 36
FIGURE 3.2 SECONDARY FLOW PATTERNS IN A CURVED PIPE .............................................. 37
FIGURE 3.3 RECOVERY OF THE DISTORTED FLOW STRUCTURES .......................................... 38
FIGURE 3.4 EFFECT OF CURVATURE RATIO RID ON FULLY DEVELOPED AXIAL VELOCITY .. 40
FIGURE 3.5 AXIAL PRESSURE DROPS FOR RECTANGULAR CURVED DUCTS .......................... 41
FIGURE 3.6 FLOW STRUCTURES AFFECTED BY BEND CURVATURE ...................................... 42
FIGURE 3.7 CONFIGURATIONS OF ARTIFICIAL INLET DISTORTION ....................................... 43
FIGURE 3.8 VELOCITY PROFILE AT INDUCER FOR VARIOUS TYPE OF DISTORTIONS ............. 44
FIGURE 3.9 INCIDENCE ANGLE DISTRIBUTION AT IMPELLER INLET FOR NolRADIAL

DISTORTION ................................................................................................................ 44
FIGURE 3.10 INCEDENCE ANGLE DISTRIBUTION AT IMPELLER INLET FOR CIRCUMFERENIIAL

DISTORTION ................................................................................................................ 45
FIGURE 3.1 1 TOTAL PRESSURE RATIO AND SURGE MARGIN FOR VARIOUS TYPE OF

DISTORTIONS .............................................................................................................. 45
FIGURE 3.12 IMPELLER EFFICIENCY COMPARISON FOR VARIOUS TYPES OF DISTORTIONS 46
FIGURE 3.13 FLOW REGIME IN STRAIGHT WALL TWO DIMENSIONAL DIFFUSERS ................. 47
FIGURE 3.14 REPRESENTATIVE LOCATIONS OF DIFFUSER PERFORMANCE AT CONSTANT

LENGTH To WIDTH RATIO (IJW1) ............................................................................... 48
FIGURE 3.15 FLOW PATH IN A VANELESS DIFFUSER ............................................................ 48
FIGURE 3.16 EFFECT OF THROAT BLOCKAGE AND ASPECT RATIO ON PRESSURE RECOVERY

COEFFICIENT ............................................................................................................... 50
FIGURE 3.17 CHANNEL DIFFUSER PERFORMANCE MAP ....................................................... 51
FIGURE 3.18 PASSAGE HEIGHT EFFECT ON COMPRESSOR MAPS .......................................... 52
FIGURE 3.19 PRESSURE RISE THROUGH THE VANED DIFFUSER PASSAGE ............................. 53
FIGURE 3.20 AREA RATIO EFFECT ON THE PRESSURE RECOVERY OF DIFFUSERS ................. 55

xi

 

 

 

 

 

 

 

 

 

 

 

 

  

LI .I-’ .L’ ,l,’ .',’ ,'.' ._L’ .I.’ .'.'

p—4

#—

._s” .5,

FT:

FIG

 

FIG
F101

F101

F161”

FIGI;

 

FIGURE 3.21 CIRCURFERENIIAL STATIC PRESSURE DISTRIBUTION FOR DIFFERENT RADIUS

RATIOS ....................................................................................................................... 56
FIGURE 3.22 EFFECT OF DIFFUSER VANE NUMBER ON THE STAGE PERFORMANCE .............. 57
FIGURE 3.23 VANE NUMBER EFFECT FOR r,-,, /r2 = 1.106 .................................................. 58
FIGURE 3.24 EFFECT OF DIFFUSER LEADING EDGE MACH NUMBER AND INCIDENCE ON

RANGE ........................................................................................................................ 59
FIGURE 3.25 FLOW RANGE VERSUS INCIDENCE ANGLE ....................................................... 60
FIGURE 4.1. SCHEMATIC OF EXPERIMENTAL TEST RIG ........................................................ 62
FIGURE 4.2 THE TESTED IMPELLER AND DIFFUSER FOR THE COMPRESSOR .......................... 63
FIGURE 4.3 GEOMETRIC SPECIFICATIONS ON THE COMPRESSOR CROSS-SECTION ................ 64
FIGURE 4.4 GEOMETRY OF STRAIGHT INLET (’SP’) .............................................................. 65
FIGURE 4.5 GEOMETRY OF THE ORIGINAL BEND INLET (BPO_NO_VANE) ........................... 66
FIGURE 4.6 CONFIGURATION OF PROBES AND MASS FLOW RATE MEASUREMENT ............... 67
FIGURE 4.7 INCIDENCE AND BOUNDARY LAYER SEPARATION ............................................. 73
FIGURE 4.8 COMPRESSOR STAGE EFFICIENCY COMPARISON FOR STRAIGHT AND BEND INLET

................................................................................................................................... 76
FIGURE 4.9 HEAD COEFFICIENT COMPARISON FOR STRAIGHT AND BEND INLET .................. 76
FIGURE 4.10 WORK INPUT COMPARISON FOR STRAIGHT AND BEND INLET .......................... 77
FIGURE 4.1 1 TOTAL PRESSURE RATIO COMPARISON FOR STRAIGHT AND BEND INLET ........ 77
FIGURE 4.12 STATIC PRESSURE RATIO COMPARISON FOR STRAIGHT AND BEND INLET ........ 78
FIGURE 4.13 TOTAL TEMPERATURE RATIO COMPARISON FOR STRAIGHT AND BEND INLET .78
FIGURE 5.1 GEOMETRY OF SP_EQUI_BP ............................................................................. 79
FIGURE 5.2 GEOMETRY OF BP7 WITH SHORTER RADIUS OF CURVATURE ............................ 81
FIGURE 5.3 PRESSURE GRADIENT VARIATIONS ALONG BEND SECTION OF BPO AND BP7 ...... 81
FIGURE 5.4 STREAK LINES WITH PRESSURE VARIATION FOR BPO_NO_VANE

(IMAGES ARE PRESENTED IN COLOR) .............................................................. 83
FIGURE 5.5 TOTAL PRESSURE DISTRIBUTION ON THE CENTER PLANE FOR BPO_NO_VANE

(IMAGES ARE PRESENTED IN COLOR) ............................................................. 84
FIGURE 5.6 SURFACE VECTOR PLOT AT THE EXIT OF BPO_NO_VANE

(IMAGES ARE PRESENTED IN COLOR) ............................................................. 85
FIGURE 5.7 SURFACE VECTOR PLOT AT THE EXIT OF BP7_NO_VANE

(IMAGES ARE PRESENTED IN COLOR) ............................................................. 86
FIGURE 5.8 FLOW ANGLE DISTRIBUTION AT THE EXIT OF BPO_NO_VANE

(IMAGES ARE PRESENTED IN COLOR) ............................................................. 87
FIGURE 5.9 FLOW ANGLE DISTRIBUTION AT THE EXIT OF BP7_NO_VANE

(IMAGES ARE PRESENTED IN COLOR) ............................................................. 88
FIGURE 5.10 VELOCITY VECTOR PLOT ON THE CENTER PLANE OF BPO_NO_VANE

(IMAGES ARE PRESENTED IN COLOR) ............................................................. 89
FIGURE 5.1 1 VELOCITY VECTOR PLOT ON THE CENTER PLANE OF BP7_NO_VANE

(IMAGES ARE PRESENTED IN COLOR) ............................................................. 90
FIGURE 5.12 VANE SPACING WITH EQUAL AP IN EACH DTVIDED FLOW PASSAGE ................. 91
FIGURE 5.13 GRID TOPOLOGY OF VANELESS INLET MODELS FOR SIMULATION ................... 94
FIGURE 5.14 GRID TOPOLOGY OF VANE INSERTED INLET MODELS FOR SIMULATION .......... 95
FIGURE 5.15 FLOW STRUCTURE OF THE ORIGINAL INLET WITH 40D PIPE LENGTH EXTENSION

................................................................................................................................... 98

xii

 

FIGURE 5.16 MASS FLOW AVERAGED FLOW PROPERTIES AT INLET MODEL EXIT FOR NEAR

SURGE POINT .............................................................................................................. 99
FIGURE 5.17 MASS FLOW AVERAGED FLOW PROPERTIES AT INLET MODEL EXIT FOR DESIGN
POINT ........................................................................................................................ 100
FIGURE 5.18 MASS FLOW AVERAGED FLOW PROPERTIES AT INLET MODEL EXIT FOR NEAR
CHOKE POINT ............................................................................................................ 101
FIGURE 5.19 SURFACE VECTOR PLOTS FOR ALL OF INLET MODELS ................................... 103
FIGURE 5.20 NORMAL VELOCITY CONTOUR PLOTS FOR ALL OF INLET MODELS ................ 104
FIGURE 5.21 FLOW ANGLE CONTOUR PLOTS FOR ALL OF INLET MODELS .......................... 105
FIGURE 5.22 NORMAL VORTICIIY CONTOUR PLOTS FOR ALL OF INLET MODELS ............... 106
FIGURE 6.1 SECONDARY FLOW STRUCTURE IN A BEND INLET ........................................... 109
FIGURE 6.2 VANE SPACING FOR THE LOCATION OF EACH VANE To BE INSERTED IN BP2
MODEL ...................................................................................................................... 1 13
FIGURE 6.3 GRID OF INLET MODELS USED FOR COMPRESSOR STAGE SIMULATION ............ 114
FIGURE 6.4 CONVENTION OF THE STATION ON COMPRESSOR CROSS-SECTION .................. l 15
FIGURE 6.5 GRID OF 360 DEGREE IMPELLER AND DIFFUSER ............................................. 1 16
FIGURE 6.6 HEAD COEFFICIENT COMPARISON .................................................................. 121
FIGURE 6.7 STAGE EFFICIENCY COMPARISON ................................................................... 121
FIGURE 6.8 TOTAL PRESSURE LOSS COEFFICIENT COMPARISON ........................................ 123
FIGURE 6.9 DIFFUSER PRESSURE RECOVERY COEFFICIENT COMPARISON .......................... 124
FIGURE 6.10 FLOW ANGLE COMPARISON .......................................................................... 124
FIGURE 6.1 1 MACH NUMBER COMPARISON ...................................................................... 125
FIGURE 7.1 VANE SHAPE OFCVND#1 ............................................................................. 127
FIGURE 7.2 VANE SHAPE OF CVND#2 ............................................................................. 127
FIGURE 7.3 VANE SHAPE OF LSVD .................................................................................. 128
FIGURE 7.4 GEOMETRY OF CONVENTIONAL VANED DIFFUSER DESIGN ............................. 129
FIGURE 7.5 STNGULARITY METHOD .................................................................................. 132
FIGURE 7.6 CONFORMAL MAPPING OF A RADIAL CASCADE INTO AN AXIAL CASCADE ....... 133
FIGURE 7.7 GEOMETRY OF A LSVD DESIGN WITH MAXIMUM SOLIDITY ........................... 135
FIGURE 7.8 EXACT VANE GEOMETRY OF FLAT PLATE LSVD VANE .................................. 136
FIGURE 7.9 THROAT AREA VARIATION UPON INLFT FLOW ANGLE CHANGE IN A VANED
DIFFUSER .................................................................................................................. 138
FIGURE 7.10 STAGE EFFICIENCY FOR STRAIGHT AND BEND INLET WITH CVND#l ........... 143
FIGURE 7 .1 1 HEAD COEFFICIENT FOR STRAIGHT AND BEND INLET WITH CVND#I .......... 143
FIGURE 7.12 WORK COEFFICIENT FOR STRAIGHT AND BEND INLET WITH CVND#I ......... 144

FIGURE 7.13 TOTAL PRESSURE RATIO FOR STRAIGHT AND BEND INLET WITH CVND#1144
FIGURE 7.14 STATIC PRESSURE RATIO FOR STRAIGHT AND BEND INLET WITH CVND#I .. 145
FIGURE 7.15 TOTAL TEMPERATURE RATIO FOR STRAIGHT AND BEND INLET WITH CVND#l

................................................................................................................................. 145
FIGURE 7.16 STAGE EFFICIENCY FOR STRAIGHT AND BEND INLET WITH CVND#2 ........... 146
FIGURE 7.17 HEAD COEFFICIENT FOR STRAIGHT AND BEND INLET WITH CVND#2 .......... 146
FIGURE 7.18 WORK COEFFICIENT FOR STRAIGHT AND BEND INLET WITH CVND#2 ......... 147

FIGURE 7.19 TOTAL PRESSURE RATIO FOR STRAIGHT AND BEND INLET WITH CVND#2... 147

FIGURE 7.20 STATIC PRESSURE RATIO FOR STRAIGHT AND BEND INLET WITH CVND#2 .. 148

FIGURE 7.21 TOTAL TEMPERATURE RATIO FOR STRAIGHT AND BEND INLET WITH CVND#2
................................................................................................................................. 148

xiii

FIGURE 7.22 STAGE EFFICIENCY FOR STRAIGHT AND BEND INLET WITH LSVD ................ 149
FIGURE 7.23 HEAD COEFFICIENT FOR STRAIGHT AND BEND INLET WITH LSVD ............... 149
FIGURE 7.24 WORK COEFFICIENT FOR STRAIGHT AND BEND INLET WITH LSVD .............. 150
FIGURE 7.25 TOTAL PRESSURE RATIO FOR STRAIGHT AND BEND INLET WITH LSVD ........ 150
FIGURE 7.26 STATIC PRESSURE RATIO FOR STRAIGHT AND BEND INLET WITH LSVD ....... 151
FIGURE 7.27 TOTAL TEMPERATURE RATIO FOR STRAIGHT AND BEND INLET WITH LSVD 151

FIGURE 7.28 STAGE EFFICIENCY WITH THREE DIFFUSERS AT DESIGN SPEED ..................... 152
FIGURE 7.29 HEAD COEFFICIENT WITH THREE DIFFUSERS AT DESIGN SPEED .................... 152
FIGURE 7.30 WORK COEFFICIENT WITH THREE DIFFUSERS AT DESIGN SPEED ................... 153
FIGURE 7.31 TOTAL PRESSURE RATIO WITH THREE DIFFUSERS AT DESIGN SPEED ............. 153
FIGURE 7.32 STATIC PRESSURE RATIO WITH THREE DIFFUSERS AT DESIGN SPEED ............ 154

FIGURE 7.33 TOTAL TEMPERATURE RATIO WITH THREE DIFFUSERS AT DESIGN SPEED ...... 154

xiv

NOMENCLATURE

O

O O
'0

D.

#0

.2“

23‘"

Speed of sound

Area

Area ratio

Aspect ratio

Passage width from hub to shroud
Blockage

Constant or speed of sound or chord length
Absolute velocity

Specific heat at constant pressure or Pressure recovery coefficient
Diameter

Diameter or Dean number

Friction factor for bend pipe or frequency
Friction factor for straight pipe

enthalpy

Head

Incidence angle

Equivalent roughness

Flow passage length or blade loading
Mach number

Impeller tip Mach number

Mass flow rate

Impeller rotating speed [rpm]

XV

SS

St

N~<g§<

N

GREEK

Pressure

Pressure

Pressure side

Volume flow rate
Radius of cross-section

Reynolds number (= umd / v)

Radial location or radius of curvature of curved section
Space or pitch

Suction side

Strouhal number

Temperature

Throat

Average velocity of flow regime

Blade peripheral speed at impeller inlet

Blade peripheral speed at impeller tip

Speed (=xiu2 +v2 + wz)
Normal velocity to cross-section
Relative velocity or Width

Total pressure loss coefficient
Axial coordinate

Vane number

Flow angle with reference to radial or axial direction

xvi

 

‘1

7L

 

Sou

SL’I

Ow

 

 

 

Cu

Ctotal

SUBSCRIPT

0

Relative flow angle with reference to radial direction
Flow coefficient

Flow coefficient

Specific heat ratio

Efficiency

Work coefficient or dynamic viscosity

Kinematic viscosity

Static pressure ratio

Total pressure ratio

Angle

Density

Slip factor or standard deviation( SD.)

Total temperature ratio

Specific work input for a compressor or impeller rotating speed [rad/s]
Head coefficient

Normal vorticity to cross-sectional area

Total vorticity consisting of three components

Station at pipe inlet
Station at pipe exit or impeller inlet
Station at impeller exit

Station at diffuser leading edge

xvii

Ill

 

 

 

3V6

DP

orf

ref

Station at diffuser trailing edge
Station at volute inlet

Station at compressor discharge
Actual

Averaged quantity

Design point.

Friction

ideal

Isentropic

Meridional direction

Number of vanes or normal direction
Nozzle

Orifice

Radial component

Reference

Static or isentropic

Total

Station 2 (impeller tip)
Total-to—total

Total-to-static

Tangential component

Axial component

Tangential component

xviii

 

 

 

 

 

 

CHAPTER 1

INTRODUCTION

1.1 Classification of turbomachinery

Lakshminarayana (1995) made a brief classification on turbomachinery.
Turbomachines are devices in which energy is transferred either to or from a
continuously flowing fluid by the dynamic action of one or more moving blade rows. The
word turbo is of Latin origin, meaning that Which spins. The rotor changes the stagnation
enthalpy, kinetic energy, and stagnation pressure of the fluid. In a compressor or pump,
the energy is imparted to the fluid by a rotor. In a turbine, the energy is extracted from the
fluid. If the turbomachinery is Without a shroud or annulus wall near the tip, the machine
is termed “extended”. Examples of this are aircraft and ship propellers, wind turbines,
and so on. On the other hand, “enclosed” machines are accommodated in a casing so that
a finite quantity of fluid passes through the machine per unit of time. Examples of this are
jet engine compressors, turbines, and pumps. Turbomachines are classified according to
the type of flow path as well as the fluid as a medium of energy transfer. In axial flow
turbomachinery, the meridional flow path is axial. In radial or centrifugal
turbomachinery, the flow path is predominantly radial. If the flow path is partially axial
and partially radial, the device is called mixed-flow turbomachinery. Among those
Turbomachines, pumps use liquid for a working fluid While compressors use gas. For a
compressor, it is further classified as a fan, a blower and a compressor depending on the
pressure ratio achieved less than unity, equal to unity, and more than unity respectively.

Turbomachines are used as major components in many applications such as

aircraft, marine, space, and land propulsion systems; hydraulic, gas, and steam turbines;

industrial pipeline and processing equipment such as gas petroleum, and water pumping

plants; and a wide variety of other applications.

1.2 Demands on centrifugal compressor

Because of the advantages of higher single-stage pressure ratio and the wider
stable operating range, the compactness over axial compressors the centrifugal
compressor has been widely used. Centrifugal compressors are found in the applications
of pipeline boosters, small gas turbine engines, turbochargers, refrigeration systems, and
petrochemical and in the process industry.

The Wide range of demands on centrifugal compressors brings many design
considerations mainly based on three major fields: stress, rotordynamics, and
aerodynamics. Stress problems, especially on impeller blades and diffuser vanes, are
caused by the material strength limitations due to the conflict with the aerodynamic
performance requirement and the manufacturing cost. Rotordynamics is another
important field considering the purely mechanical vibratory behavior of the machine
caused by the impeller rotating motion as well as the flow induced vibratory effect, which
give restrictions on the design of compressor components to prevent the entire machine
from resonance.

The goal of aerodynamics on the design of a compressor based on the agreement
of the other two areas is to efficiently accomplish high efficiency and pressure ratio under
the circumstances with large air deflections and diffusion at high flow velocity, with the
added difficulty of the small flow passage requirement. Even though the individual

components of the compressor are capable of achieving high efficiency, it is more

important to obtain the best possible efficiency of the whole stage, which can be

accomplished by appropriate component matching as an essential aspect of the design.

1.3 Demands on inlet study

A multi-stage centrifugal compressor is commonly used to produce a higher
pressure ratio than What a single stage one can produce and in the multi-stage
compressor, it is generally inevitable for the stages to be interconnected with curved
pipes as inlet systems that include a cross-over and return channel to guide the flow to the
next stage Within the Spatial limitation. By using the curved pipes, the secondary flow
structure is present due to the pressure gradient held between the inner and outer walls in
the bend section of the pipe. This results in a distorted velocity profile as well as non-
uniform concentrated flow angle causing high incidence and inducer stall in the impeller.
The unstable asymmetric flow propagates to other components in the compressor stage
and finally degrades the compressor stage aerodynamic performance.

Therefore, the importance of the nature of the flow at the impeller inlet has drawn
the special attention to the inlet study with the main purpose of designing and validating
new inlet systems to provide the inlet flow as unifOrm as possible and thus the recovery

from the degraded compressor aerodynamic performance.

1.4 Objective and structure of the present study.
The objective of the present study is to obtain the compressor Stage performance

with the existing inlet system and to design a new inlet for the improvement of the

C0

(115

Of;

aerodynamic performance. The research work has been accomplished systematically to

achieve the goals with the following steps.

1. Experimental testing of the compressor for the comparative stage performance
with two different circular pipes as inlet systems, one of which is Straight with constant
area representing an ideal inlet system and the other is 90 degree curved pipe with a
nozzle shape as the actual model.

2. Numerical simulations of the inlet models to investigate the details of the flow
structure at three different operating points including near-surge, design, and near-choke
point obtained from the previous experimental study.

3. Design of new inlet systems based on the analysis of the previous numerical
study and numerical simulations of the new inlet systems for the comparison of the
designated flow properties at the exit of all of the models

4. Further numerical Simulations for the compressor stage including inlet models,
the impeller, and the diffuser to investigate the flow characteristic in the compressor
responding to each inlet model at the three different operating points.

5. Additional experimental study with three different diffusers, combined with
two different inlet systems to compare the compressor stage performance based on the

contribution and influence of different diffuser and inlet systems

Based on the results from numerous experimental and numerical study, this
dissertation consists of eight chapters starting with the general and theoretical discussion

of a centrifugal compressor in Chapter 2. Chapter 3 deals with the previous research-work

 

related with the current study. Chapter 4 presents the experimental work and the
discussion of the results comparing the compressor stage performance between two
different inlet systems. Chapter 5 is targeted for the design of new inlet systems and the
numerical simulations of all of the models followed by the aerodynamic parameter
comparison from the simulation results among those models. Chapter 6 is devoted to the
compressor stage simulation including an impeller and a diffuser as 360 degree models
attached to the different inlet models, followed by the detailed flow characteristic and
performance analysis of the compressor. Chapter 7 presents additional experimental work
to compare the compressor stage performance among three different diffusers (two
conventional type of diffuser and a low solidity diffuser) with the combination of two
different inlet systems. In Chapter 8, attempts are made to draw conclusions focusing
mainly on the improvement of the compressor stage performance and flow characteristics
with the new inlet system as well as the contribution and influence of each diffuser on the

aerodynamic performance of compressor.

CHAPTER 2

FUNDAMENTALS OF CENT RIFUGAL COMPRESSOR

2.1 Configuration of a centrifugal compressor

Generally, a centrifugal compressor consists of four basic components: an inlet,
an impeller, a vaneless or vaned diffuser, and a collector or a volute as shown in Figure
2.1. The fluid is drawn in through the inlet into the eye of the impeller parallel to the axis
of rotation. In order to add angular momentum, the impeller whirls the fluid outward and

turns it into a direction perpendicular to the rotation axis.

 

 
 
  

 

 

 

Flow path within
5 vaned diffuser
4 /Diffuser vanes ..............
3 Flow path within
2 _. vaneless diffuser
Shroud
-lmpeller
0 Flow © 1
_ _______ ,fi Q
=:>

 

 

q:

 

 

 

 

 

Figure 2.1 Example of configuration for a single stage centrifugal compressor

As a result, the energy level is increased, resulting in both higher pressure and

velocity. The purpose of the following diffuser is to convert some of the kinetic energy of

ov'a'

5". {A

Few w-

‘Iv-b

o

the fluid into static pressure. Outside the diffuser is a scroll or volute whose function is to
collect the flow from the diffuser and deliver it to the discharge pipe. It is possible to gain
a further deceleration and thereby an additional pressure rises Within a volute.

An example of the contribution of each component of the compressor is shown in
Figure 2.2. The solid line represents the static pressure rise while the dotted line indicates
the total pressure change for the individual component in a single stage of centrifugal

compressor.

 

 

 

 

 

 

 

 

 

, Inlet Diffuser Volute

Impeller

 

- - - -
p—----
b------
p“..--

II

 

 

 

v—v— . v v—

Figure 2.2. Example of h-s diagram for a centrifugal compressor stage

2.2 Inlet

In centrifugal compressors, many different inlets are used. These include a
straight inlet, a curved inlet, and a sidestrearn inlet either as radial or axial. The objective
of an inlet device is to bring the flow as uniform as possible to the eye of the impeller
with or without a prescribed level of inlet swirl. By matching the design parameters
properly between an inlet and an impeller, it is possible to bring the best efficiency and
operating range for a compressor. Therefore, the flow properties after an inlet component
have a strong influence on the performance of the entire compressor stage.

Figure 2.3 compares the actual and ideal head characteristic of a compressor. The
ideal compressor characteristic of head versus flow is modified by the internal losses,
including mainly the friction loss as a function of the square of the flow velocity and the
passage length that the fluid particles follow, and the incidence loss that can be

significant even at the design condition if the inlet flow is highly distorted or swirling.

 

 

 

 

 

'O

m

0

J:

friction
loss
incidence
loss
flow

 

 

 

Figure 2.3 Actual and ideal head characteristic of a compressor

 

 

III-
bet]
due

heat

neg;
Can

Inpc
€311.51
P1685
intre'

COUdl

The incidence loss occurs due to the angle of attack of the flow at the impeller
blade and vaned diffuser leading edge. The incidence at the impeller blade is defined as
the difference between the relative flow angle at impeller inlet and the actual blade angle.

i=fl1 "IBlb (2.1)

If the relative flow angle does not coincide with the blade angle, there is a
tangential component of relative velocity that is wasted and appears as a head loss. If the
incidence is excessive, additional losses due to the boundary layer separation occurs.
Positive incidence corresponds to the incidence that causes the flow to impinge on the
pressure side of the blade which is the side pushing the flow in the direction of rotation
while negative incidence acts on the suction side of the blade as shown in Figure 2.4.

At the design point, the incidence is close to zero and the efficiency is the
maximum provided that the inlet system of the compressor has uniform flow condition
before entering the impeller inducer. However, the distortion of flow is often inevitable
due to the spatial limitation in practical applications, and the distorted flow degrades the
head rise and thus the efficiency due to the incidence.

Figure 2.4 also illustrates the boundary layer separation due to high positive and
negative incidence in case of off-design points or prescribed swirl at impeller inlet, which
can be possible with a device such as inlet guide vane. From the velocity triangle at
impeller inlet, the relative flow angle decreases with the increased mass flow rate, which
causes negative incidence and, at the extreme condition, boundary layer separation on the
pressure side of the impeller blade. On the other hand, the decreased mass flow rate
increases the relative flow angle and, hence, causes positive incidence and, at the extreme

condition, boundary layer separation on the suction side of the impeller. Flow in the

 

Lil

lid 1‘-

 

impeller has less momentum on the suction side than on the pressure side. This is the
reason why small negative incidence is beneficial for the impeller performance since the
flow with the small negative incidence makes up for the momentum deficit on the suction

Side.

 

 

 

 

 

 

 

 

Figure 2.4 Incidence variations upon mass flow change and boundary layer separation

2.3 Impeller
The impeller is the only rotating component of a centrifugal compressor stage,

and the energy is transferred to the fluid by the mechanical work of the driving motor.

10

‘ ‘
em

.I'

,~.'

 

 

J

ch

Figure 2.5 shows the typical velocity triangles at inlet and exit of impeller in case of

prewhirl at the impeller inlet.

 

 

 

 

 

uoneertp
Sutimor

 

 

 

 

 

A
V
o
-—-——-——- —— -_--—-—--——

Figure 2.5 Inlet and exit velocity triangles of impeller

2.3.1 Euler equation

The Euler equation relates the head change in a compressor to the velocities at the
impeller inlet and exit. The Euler equation is derived from the conservation of linear
momentum, which is, the rate of change in linear momentum of a volume moving with
the fluid is equal to the surface forces and body forces acting on the fluid. By the
conservation of momentum principle, the change of angular momentum obtained by the

change in tangential velocities is equal to the summation of all forces acting on the rotor,

11

'13

C011

ch~

 

Figure 2.5 shows the typical velocity triangles at inlet and exit of impeller in case of

prewhirl at the impeller inlet.

 

 

 

 

 

uoiroertp
Butrmor

 

 

 

 

   

Figure 2.5 Inlet and exit velocity triangles of impeller

2.3.1 Euler equation

The Euler equation relates the head change in a compressor to the velocities at the
impeller inlet and exit. The Euler equation is derived from the conservation of linear
momentum, which is, the rate of change in linearmomentum of a volume moving with
the fluid is equal to the surface forces and body forces acting on the fluid. By the
conservation of momentum principle, the change of angular momentum obtained by the

change in tangential velocities is equal to the summation of all forces acting on the rotor,

11

vfl'fi‘r’fil

 

he

 

Inn

31

Fill

“his

i.e. the net torque of the rotor. Mathematically, between inlet and exit, this can be written
as

T = m(r2Cu2 " rlCul) (2.2)
where C,” and Cuz are the tangential velocity at inlet and exit respectively.
The rate of change of energy transfer is the product of the torque and the angular
velocity; and, therefore, the total energy transferred is

E = m = m(r2wCu2 — rleul ) = maze“, — UlCul) (2.3)
where U1 and U; are the peripheral velocity at r. and r2 respectively.
The energy transferred per unit mass flow is equal to the change in total enthalpy ho and
hence

Aho=UzCuz —U1Cul =h02 ‘hm =Cp(T02-TOI) (2-4)
It is useful to relate the enthalpy change to the exit blade angle. Using the velocity
triangle at the impeller exit and assuming no prewhirl, the enthalpy rise is given by

Cu2 = U2 + sz tan fiz (2.5)

With the convention that B2<O for a backward swept impeller, meaning that the blades of

an impeller are inclined backward at outlet.

 

Introducing the theoretical head rise u! = Ah; and the flow coefficient c) = Eilm—z- to make
U 2 2

a non-dimensional representation of the enthalpy rise versus mass flow rate, the

' following relation is obtained.

W=1+¢tanfl2 (2.6)

Which is plotted in Figure 2.6.

12

Figure 2.7 shows the velocity triangles and flow angle change upon the increased

mass flow rate for three different impeller blade shapes.

 

1.8 ~
1.61
1.41
1.2 ‘

B2=+45°

 

0.8 -
0.6 T
0.4 T
0.2 —

 

 

 

Figure 2.6 Effect of exit blade angle on the head rise and the flow range

 

 

 

 

 

 

 

 

 

(a) forward blade (b) radial blade (c) backward blade

Figure 2.7 Velocity triangles for the different blade shapes

13

\l

 

 

C(lf

dif:
“'0:
of :

for .

[\J
(A)

 

 

With related to equation (2.6), if mass flow rate is increased, the actual head is increased
for a forward-leaned blade impeller, is independent for a radially-ending impeller, and is
decreased for a backward-swept impeller as shown in Figure 2.6. The increasing head
with decreasing mass-flow rate for backward-swept impeller gives a more stable
compressor stage characteristics and consequently a greater operating range.

The enthalpy change in the machine can also be expressed in the following way.
1 2 2 2 2 2 2
Aho = -2' [(U2 "" U1 )‘l" (W1 — W2 )+ (C2 — C1 )1 (2.7)

After having introduced the relations inside the inlet and exit velocity triangles
W2 =C2 +02 -2UC,, (2.8)

Hence, it is seen that the enthalpy rise in a centrifugal compressor is due to three different
contributions. The first term in equation (2.7) represents the change of energy of a
particle as it moves from one radius to another. This contribution by the centrifugal
forces represents about one-half of the work input, and is accomplished without loss
(Casey and Marty 1986). The second term represents the rise in enthalpy due to the
diffusion of the relative flow. This term represents approximately one-fifth of the total
work input. Assuming that the velocity at the exit stage is equal to the velocity at the inlet
of the stage, the last term represents the diffusion of the absolute velocity and accounts

for about one-third of the work input.

2.3.2 Head rise
The isentropic head represents the energy transferred through a compressor per
unit mass of fluid. If a compressor produces 1 m of head, it means that one kg-force will

be required to elevate one kg of gas mass to a height of one meter. The head cannot be

14

1..

75
Hit

YES

 

 

measured directly and an exact relation for a compressible flow, considering an ideal gas

is given by

Aha“ = CpATois (2.9)
where C p = JR— and for an isentropic compression process

7-1
3:1
7
ATM = To, 391 —1 (2.10)
For

The head, the enthalpy rise, and the total pressure ratio are quantities used to express the

energy exchange into the impeller. They can all be used interchangeably.

2.3.3 Slip factor

The relative flow leaving an impeller is not perfectly guided by a finite number of
blades, which is called slip, leading to the modified velocity triangle as shown in Figure
2.8. The effect of slip is to reduce the magnitude of the tangential component of velocity,
resulting in the reduction of the pressure ratio as well as compressor power consumption.
Therefore, the slip effect requires a higher impeller rotating speed to obtain the same
pressure ratio as the case of no Slip, and this causes increased stress levels and relative
velocities in the impeller, which finally leads to increased friction losses and reduced

efficiency. A slip factor in general form is defined by

 

 

Cslip = 1" C92” -' C92
U2 U 2

0'=1- (2.11)

From the velocity triangle shown in Figure 2.8, the tangential component of velocity is

reevaluated by

15

C02 = 0112 + sz tan flZb (2.12)

 

 

 

 

 

 

 

 

 

 

U2

Figure 2.8 Slip effect on velocity triangle at impeller exit for backward-swept blade

Many correlations are available in the literature to predict the value of the slip factor.
Stodola (1927) used the concept of a relative eddy to explain and derive slip
velocity and its correlation. Initially, the flow into the impeller has no rotation and at the
impeller exit after passing through the passage, the flow relative to the impeller has an
angular velocity with the equal magnitude and the opposite direction to the impeller
rotating speed, which forms the actual relative velocity as the vector summation of the

eddy and the radial component of velocities.

 

nU cos
Cslip : 2 Z flZb (2.13)
cur—flé—fli (2.14)

16

where [32b is the impeller exit blade angle and Z is the number of blades.

One of the most conunonly used correlations is given by Wiesner (1967).

g=1____\/°°S[32b (2.15)

20.7

This equation is a data fit of the theoretical curves obtained by Buseman (1928) for
inviscid flow in an impeller with logaritlunic-spiral shaped blades. The validity of this
expression was checked by Wiesner with over 60 compressor and pumps with various
blade angles and blade numbers and compared to other correlations. The agreement was
found to be fairly good, but this relation may be off by a few percent for some machines.

The effect of the blade angle and blade number on the slip factor is shown in Figure 2.9.
The slip factor is seen to be smaller for a radial impeller than for a backward-swept

impeller. It increases with an increasing blade number.

 

1.0

0.95
2:30/

P
(O
C)

 

Slip factor a
o
(:1
Ln

.0
on
.9

 

.0
\I
Q‘

 

 

0.70 . . . . . - .
0 -10 -20 -30 -4o -50 -60 -70 -80

Exit blade angle Bab

 

Figure 2.9 Influence of the blade number and the exit blade angle on the slip factor

17

Stanitz (1952) also provided a slip-factor correlation, which is considered to be

satisfactory for blade angles in the range of —45° to 445°.

o=1-—'—— (2.16)

2.3.4 Efficiency

The steady flow equation by the first law of thermodynamics in its complete form
relates the work input and exchanged heat to the change in total enthalpy and elevation as
the following.

Q+W
m

=(h2‘hl)+':‘(C22‘C12)+8(Zz-ZI) (2-17)

 

Neglecting the change in altitude and heat exchange and considering a perfect gas, the
change in energy is directly related to the change in total temperature. It is then natural to
represent the compression process in a T-s diagram. A typical compression process is
shown in Figure 2.10. The isentropic efficiency compares the actual enthalpy change
during the compression process to the one that would have taken place for an isentropic

process. It is defined by

h025 _ hOI
"is = (2.18)
hoz - hor

State 1 generally refers to the total conditions at the inlet. State 2 corresponds to the exit
conditions. If the total conditions are used at state 2, the total-to-total isentropic
efficiency is obtained. If the static conditions are used, it is the total-to-static isentropic
efficiency. The difference between these two efficiencies will be large for stages having a

large exit velocity. Depending on the type of application, one type of efficiency or the

18

other will be used. Generally, if the exit velocity is used, the total-to-total efficiency is
used; and if the exit velocity is not used, the total-to-static efficiency is used. For a

perfect gas with constant specific heat, the expression of the efficiency becomes

7—1

1 02 7
— _ l
Cp (1021's T01 ) POI

 

 

 

 

 

 

 

 

 

171's = = (2.19)
Cp(T02—T01) $22-1
T01

T

P02

23/

TOa 25
T03

P01
T01

1
S

 

 

 

Figure 2.10 Representation of a compression process in a T-S diagram

2.3.5 Compressor operating range
The compressor performance is represented with a plot Showing the efficiency

and pressure ratio versus the mass-flow rate for different rotational speeds, or the head

19

‘J
,' ,1

obn;
(I 1111;}
rm:

1:1er

 

versus the volume-flow rate, or in a dimensionless form, the head coefficient versus the
flow coefficient. A typical performance curve for a centrifugal compressor stage is shown

in Figure 2.11.

ii

i
T

Constantimpeller
/’ speedllnes

I

 

 

Mmflowrate

Figure 2.11 A typical performance curve of a centrifugal compressor

Three different regions may be distinguished. On the right is the choke limit
obtained when sonic conditions are reached in the minimum section of the machine
(impeller throat or diffuser throat, whichever is smaller). The choke limit appears as a
vertical line in the compressor map because the efficiency and the pressure ratio drop
drastically. On the left is the stall region and surge line, which correspond to a region of
instability. Rotating stall is an unstable phenomenon often preceding surge. It-can take
place in the impeller or in the diffuser. Rotating stall is a local instability in which zones

of separated flow, called cells, rotate in one component of the machine. When operating

20

.11.
«1.6

' *‘9o.o'.
‘ - I
I

at high pressure level, the pressure fluctuations corresponding to rotating stall generates
mechanical vibration that can severely damage the machine. Operation in this area should
therefore be avoided. In the case of vaneless diffusers, the onset of phenomenon has been
correlated to the diffuser inlet flow angle (Senoo 1978).

During surge operation, oscillations of the mass flow rate between the compressor
exit and inlet occur that may damage the machine especially for high density gas. Van
den Braembussche (1984) showed that for a negative value of d‘P/dq) (i.e. increasing
pressure for decreasing mass flow) any perturbation will be damped out, resulting in a
stable operating point. As soon as d‘I’ldq) is positive, the flow may become unstable
depending on the characteristic of the global system (i.e. the compressor as well as the
inlet and the discharge pipe). The compressor should not be operated in this region. At
medium flow coefficient, a region of high efficiency is generally close to the design

point, where the compressor Should be operated.

2.3.6 Non-dimensional parameters

Dimensional analysis and similarity considerations can be applied to
turbomachines. They state that for geometrically similar machines, a similar velocity
triangle will be obtained. Non-dimensional parameters include the head coefficient, work
coefficient, the flow coefficient, the efficiency and the impeller tip mach number.
Dimensional analysis can be used to compare data from different machines, to predict the
performance of an actual machine when the testing has been performed on a scaled
model, and to predict the performance at different rotating speed or operating flow point.

The flow coefficient based on inlet volume flow rate is defined by

21

¢ = ___Q__ (2.20)

It 2
—DU
42 2

and the isentropic head coefficient by

 

P
Cme [732.]? -1
01
Ah.
w=1 0” = 1 (2.21)
—U 2 —U 2
2 2 2 2

and the work coefficient or actual head coefficient by

Ah, = C p (T02 -T01) = UZC,2 -U,C,,l

 

 

l1 = l l l (2.22)
-—U 2 —U 2 —U 2
2 2 2 2 2 2
and then the efficiency is given by
n = Z (2.23)

,u
The impeller tip Mach number or machine Mach number is used as an index for
representing the same shape of velocity triangle sealed with mass flow rate at impeller

exit and is defined as

M, = — =———— = —— (2.24)

2.4 Diffuser
2.4.1 Diffusion process
The process of diffusion or decrease of velocity to gain static pressure is an

essential portion of a centrifugal compressor. Because of the possibility of separation, the

22

rate of diffusion must be strictly limited and the process is inevitably accompanied by a
loss of energy that is expressed by using diffuser effectiveness.

Diffuser effectiveness can be defined as the ratio of actual to ideal static pressure
rise. For incompressible flow, the total pressure is constant for ideal flow case and the

initial and the final states can be written with the Bernoulli equation as

1 2 1 2
+— V = +- V
PI 2,0 1 P2 2,0 2
1
P2 — P1 = 5.0(1’12 -V22) (2-25)

A
From continuity, m = le A1 = pV2 A2 , hence V2 = A—‘V, and
2

1 2 A] 2
192 121 2,011 (—A2)]
If the actual final pressure is p20 , then the diffuser effectiveness is

_ Pza ‘PI _ Pza “P1
0.1 - -

l A (2.26)
P2‘P1 _ V21- _12
21311 (A2)]

For compressible flow, the diffuser effectiveness is defined with the ratio of the
isentropic enthalpy change corresponding to the actual rise of pressure to the enthalpy
change corresponding to the isentropic rise of pressure caused by the reduction of
velocity. The actual rise of static pressure is less than that of the isentropic change of

velocity and the process is shown in Figure 2.12 on the T-s diagram.

23

 

 

 

 

 

 

 

T
P2
p20
/3
1 2 2
5011 _V2 ) PI
1
8
Figure 2.12. T-s diagram of diffusion process
The diffuser effectiveness of compressible flow is then defined as
"3 - h]
= 2.27
77d hz _ hr ( )
Since h3 — hl is the isentropic enthalpy change from p1 to p2,,
T 2:1
h3 —h1 = Cp(r3 —T1)= CpT1(?3—l) = cprlu’ga) 7 -1]
l l

and hz — h] = %(V,2 - V22) , which finally leads to

a
CpTIKEF—I 7 —11
PI

 

"d = (2.28)

1 2 2
—V-V
2(1 2)

24

2.4.2 Vaneless diffuser

Vaneless diffusers are frequently used in process compressors, refrigeration
compressors, and turbocharger compressors. With a vaneless diffuser, a reasonable level
of static pressure recovery can be achieved and the manufacturing cost is inexpensive. It
essentially consists of two parallel walls forming an open radial annular passage from the
impeller tip to some outer radius, which frequently followed by a volute for accumulating
and delivering the flow to a stage exit.

A characteristic of the vaneless diffuser is the absence of a throat. Therefore,
choking is not likely to occur in the diffuser, which leads to the possibility of a wide
range of operation. The simple description of vaneless diffuser performance is shown in

Figure 2.13.

 

 

 

 

 

Figure 2.13 Velocity triangle in a vaneless diffuser

25

 

 

rlCm = r2C02 = C (2.29)

 

m = pCm 271Tb (2.30)
tana= C9 = , C/r =cx£bi (2.31)
Cm m/27zrbp m

These equations represent the conservation of mass, angular momentum, and the
flow angle at each Station, which indicates that the flow angle in the vaneless diffuser
depends mainly on density and passage depth. For a constant density fluid, the flow angle
is constant at a given mass flow rate, forming a logarithmic spiral flow path through the
vaneless diffuser. For air, the density varies with pressure and temperature in such a way
that the flow angle increases with radial extent and, thus, the flow turns more than the
simple logarithmic spiral. The flow angle can also be changed by changing the passage
width b, that is, by pinching or enlarging, resulting in more radial and tangential flow
respectively. By comparison with a vaned diffuser of similar performance, the
logarithmic spiral of a vaneless diffuser implies a longer path of the fluid particles than

that of a vaned diffuser, resulting in greater friction losses.

2.4.3 Vaned diffuser

The vaned diffuser consists of diffusing channels between vanes Where more
diffusion is accomplished compared to a vaneless diffuser with the same radial space.
Although the loss is often high in a vaned diffuser, high efficiency still can be achieved
with a vaned diffuser since the more diffusion in a vaned diffuser brings the efficiency
gain for the next component such as a volute. The vaned diffuser throat is the Window

between the leading edge of one vane and the other side of the next vane. The aspect ratio

26

 

 

‘0

if

 

 

 

 

of the vaned diffuser channel is the ratio between the vane height and the diffuser width.
The geometry of each diffusing channel, the number of vanes, and the position of each
leading edge determine the diffuser area ratio, the optimum angle of attack and the effect
on surge or on choke.

The vanes are located at certain distances from the impeller tip to reduce the
noise, vibration and the value of Mach number reaching the vane leading edge. The
higher the diffusing channel area ratio, the higher the ideal static pressure recovery.
However, the increased recovery is accompanied by the losses, which are due to friction
and flow mixing at channel exit. If the diffuser area ratio is conservative, the flow
remains attached to the walls and the losses are due to skin friction only. If the area ratio
is higher, the pressure gradient increases and small streaks of flow start separating from
the walls and mixing with the main flow, dissipating their energy. Those losses are of
higher magnitude than the ones due to friction and start counter-balancing the increase of
ideal static pressure recovery. If the area ratio is too high, the actual static pressure
recovery is reduced. The optimum area ratio for maximum static pressure recovery is a
function of the channel length to inlet width, the inlet throat width to depth ratio, the inlet
boundary layer thickness and the inlet Mach number. The diffusing channel that begins at
the throat is a function of the number of vanes, vane setting angle and vane shape. The
throat area is extremely important due to the incidence losses and the resulting boundary
layer blockage. The vaned diffuser may control the compressor maximum flow (“choke”)
or the minimum flow (“surge”) depending on the throat area of the impeller blade
passage. The matching of the vaned diffuser to the impeller, which is dependent on the

vaned diffuser area and the vane setting angle, is a critical part of the aerodynamic

27

design, affecting the overall efficiency as well as the flow range of the compressor.
Vaned diffusers, due to their higher area ratio in a given diameter ratio, are more efficient
for static pressure rise than vaneless diffusers, especially for low specific speed
compressor stages. However, due to the effect of flow incidence on the vane leading
edges, the range of flow that can be handled by the compressor is much smaller than with
vaneless diffusers. Thus, the vaned diffuser provides more efficiency at the expense of

flow range.

2.5 Nozzle

A nozzle is a device for accelerating a fluid with a drop in pressure and for
incompressible and subsonic flow, a reduction of area is required. Because the pressure
gradient is in the direction of flow, there is no danger of separation and loss is very small
because of the formation of thin boundary layer, for which small portion of nozzle is used
between inlet and impeller inducer typically as a part of inlet casing to improve the
following impeller flow profile, especially at its shroud.

For the design of a nozzle, the rate of area decrease can be very rapid and the only
requirement is that the circular arcs need to be blended into straight lines without
discontinuities. The nozzle efficiency is expressed as the ratio of the available kinetic
energy at nozzle outlet to the isentropic kinetic energy at inlet as given in equation (2.32)

and it is often 90 percent or better. Figure 2.14 shows h-s diagram for a nozzle process.

 

 

 

' _i
V 2 h —h T
”N: 2a = 01—h2 = Olk_1 (2.32)
V25 hOI 2s P T
1.. __Z_

28

 

 

 

 

 

 

 

28

2a

PI

 

 

 

Figure 2.14 h—s diagram of nozzle process

29

 

 

CHAPTER 3

LITERATURE REVIEW

3.1 Various types of compressor inlets in practical applications
Axial inlet

An integral gear type of a multi-stage centrifugal compressor generally includes a
straight-axial inlet to supply atmospheric air to the first Stage and curved-axial inlets

between the next stages due to the spatial limitation on the design of the machine.

Radial inlet

Radial inlets provide the atmospheric air to the first stage of in-line type of
centrifugal compressor that has a common rotating shaft to drive the impellers. Because
of the driving shaft in the core of the impellers, a radial inlet has an annulus type of flow

passage on the cross-section.

Side-stream inlet
Special applications of a centrifugal compressor need side-stream inlets in
addition to other type of main inlet to accommodate the additional flow merged into

certain stages out of a multi—stage compressor.

Crossover and return channel
In-line type of a multi-stage centrifugal compressor utilizes crossovers that is a

180° bent passage connected to return channels to guide the diffuser discharged flow

30

from a radial to an axial direction for the next stage of the impeller. Since the flow
discharged from the diffuser channels has strong swirling feature, return vanes are
constructed inside of a return channel system to reduce the swirling intensity before
entering the impeller of the next Stage. Return channel systems are used after the first

stage and before the last stage of a multi-stage compressor.

3.2 Pipe flow as in axial inlet
3.2.1 Classification of pipe flow

A fluid flowing in a duct is characterized by either laminar or turbulent flow and
the Reynolds number is a measure of the flow behavior. Laminar flow occurs with the
lower range of Reynolds number from zero, and the physical interpretation is that the
viscous forces are dominant over the inertia of the flow. Thus, in laminar flow there is a
considerable shearing force between layers of fluid and a solid surface where the fluid is
in contact, which makes the flow slow down and stagnate considerably right next to the
surface. A particle of laminar flow tends to travel in a line parallel to the main body of
fluid and does not move in a direction with a normal component to that flow. With
turbulent flow, inertia effects are predominant, and, thus, the Reynolds number is
relatively high. The particles of turbulent flow have small fluctuating velocity
components normal to the flow direction and tend to cross parallel streamlines. These
small-scale fluctuations of velocity, amounting to a few percent of the bulk velocity, are
called turbulence. Although the inertia effect is predominant, viscous forces are still
present, and, thus, the effect of a surface is to cause a velocity gradient in the fluid but of

smaller extent than for laminar flow. At near surface even in fully turbulent flow, there

31

”‘21—;

 

 

 

exists a laminar sublayer, although this may be extremely thin. For evaluating Reynolds
number for flow in a duct, the characteristic dimension is taken normal to the flow, for
example, the diameter for a circular duct or the cross-sectional area normal to flow
divided by the wetted perimeter for a rectangular duct. It is found that a transition from
laminar to turbulent flow in a duct occurs at a Reynolds number of about 2100, although
the precise value is dependent on the local conditions. Laminar pipe flow seldom occurs

in Turbomachines except for very viscous liquids such as oil for a seal system.

3.2.2 Friction loss in pipe flow

The pressure drop associated with Darcy-Weisbach equation is given by

pL V2

AP=Pghf =f'd—7 (3‘1)

This relationship is valid for duct flow of any cross section and for laminar and turbulent
flow. Many researchers have developed a friction factor for the range of Reynolds
numbers and the characteristic length of a duct based on the experimental work and the
dimensional analysis.

Colebrook and White (1939) developed the correlated resistance formula for both

smooth and rough surface flow regime inside of a straight pipe.

 

#— = 1.74 — 2.Olog[£Rf— + 18'7 ] (3.2)

1?; Re A

For ks —> 0, equation (3.2) transforms into equation (3.3), which is Prandtl’s universal
law of friction for a smooth surface in pipe (1935), which has been verified by

Nikuradse’s experiments (1932) up to Reynolds number of 3.4x 106.

32

 

1 u d
__.=2,010g ave f -0.8 (3.3)
II; 1 v 171

For Re —-) oo , equation (3.2) transforms into equation (3.4) for the completely rough flow

regime, which is the resultant formula from the comparison between the first formula
derived by Von Karman (1923) from the similarity law and the experimental results by
Nikuradse.

1

 

f 0 = (3-4)

2
[2.0log§+l.74]

S

The preceding equations for the resistance calculation are valid only for straight
pipes. In the case of curved pipes, the presence of the secondary flow affect the resistance
stronger in laminar than in turbulent flow. White (1929) and Adler (1934) carried out
experiments on laminar flow. The turbulent case was investigated experimentally by
Nippert (1929) and Richter (1930). Theoretical calculations for the laminar case were
carried out by Dean (1928) and Adler (1934). The characteristic dimensionless variable,

which determines the influence of curvature in the laminar case, is the Dean number.

2 r V r

According to Adler’s calculations, the friction factor f for laminar flow in a curved pipe is

given by
l
—f—-=0.1064[Re‘/E]2 (3.6)
f 0 r

33

where f0 denotes the friction factor of a straight pipe in equation (3.3). However,
measurements indicated that equation (3.6) has only asymptotic validity, and may be used
for values of the Dean number exceeding about 102's. The results of measurements are
approximated with a higher degree of precision by the following empirical equation, first

given by Prandtl (1952).

i = 03700-36 (3.7)
0

Equation (3.7) gives good agreement with experimental results in the range

1

101-6 < Re[5)2 <103-O
r

Ito (1969) extended the validity of equation (3.6) to lower Dean numbers. According to

his calculations, the friction factor f is given by

l l 3
-f—=0.103K2 l+3.945K 2 +7.782K_1+9.097K 2 in] where K = ZD (3.8)

in )’
If 0.101 replaces the numerical coefficient outside the parentheses, equation (3.8) gives
good agreement with experimental results in the range of K > 30.

For the case of turbulent flow in a curved pipe, which is of interest when related

to the present study, White (1932) has found that the friction factor for turbulent flow in a

curved pipe can be represented by the equation below.

1 1
7f— =1+0.075Re4[—f—)2 (3.9)
0

Equation (3.9) indicates clearly that the Dean number can no longer serve as a suitable

independent variable for turbulent flow case.

34

In more recent times, Cuming (1955) carried out an investigation into the

phenomenon of secondary flow in curved pipes. Ito (1952) has shown theoretically that

the ratio of the friction factor, f / f0, can be expressed in terms of the dimensionless

variable Re(R/r)2 and experimentally proved the sufficient accuracy of the equation

below.

I ~

r r

2 0.05 2
L=|:Re(£] J ; R615] >6 (3-10)
fo r r

Coffield (1999) experimentally determined pressure drops of multiple piping elbows for

r 2 R R
f [1?] = 0.029 + 0.304[Re[—) ] ; 300 > Re[—) > 0.034

various high Reynolds numbers.

3.3 Flow structure in curved pipes

In curved pipes, it is known that the pressure gradient is developed between the
inner and the outer wall in the bend section. The strength of the pressure gradient depends
on the radius of curvature, the radius of the curved flow passage and the angle of the bend
as geometric parameters, which are compatible with aerodynamic parameters such as the
density, the velocity, and the Reynolds number or the mass flow rate in the flow regime

as indicated in equation (3.11).

a V2
25sz (3.11)

It can be noticed that there is no secondary flow driven force in the case of a straight pipe

with uniform flow given at the beginning because of the infinite radius of curvature.

35

On the other hand, in the bend section of a curved pipe, the corresponding
pressure gradient induces secondary flow because the particles near the inner wall of the
curvature have higher velocity and are acted upon by a larger centrifugal force than the
slower and higher pressure particles near the outer wall due to the lack of the centrifugal
force to overcome the pressure gradient over the cross-section in the curved section of the
pipe. As a result, this pressure gradient driven secondary flow has the complicated flow
structure consisting of the outer flow directed inwards along the wall and the inner flow
directed outwards to fill up the deficit of the flow regime due to the continuity as shown

in Figure 3.1 and 3.2.

 

outer wall

 
   
  

outer wall

 

 

 

 

 

inner wall

 

 

 

Figure 3.1 Secondary flow structure in a curved pipe

36

 

 

Turbulence-Driven Cell \
b

(a)laminar flow with parabolic inlet (b)turbulent flow with fully developed inlet

Figure 3.2 Secondary flow patterns in a curved pipe

So (1993) carried out experimental tests to investigate the flow field recovered
from the distortion that is caused by the upstream ISO-degree bend curvature. He
observed that the angular momentum of the flow was found to decrease by approximately
74% in a length of 25 diameters. Mean flow measurements at 49 diameters downstream
of the curved bend exit showed that the radial and tangential velocities are essentially
zero everywhere while the axial velocity was identical to that of a fully developed pipe
flow as show in Figure 3.3. He concluded that the effect of bend curvature is to accelerate

swirl decay in pipe flows and, in the process, to significantly shorten the recovery length.

37

 

 

 

 

1.0

0.6

 

 

 
   

 

 

0.4 ‘ ‘ .
1.0 0.5 0.0 0.5 1.0
Outer % I000!
(TOP) (300%)

0.50 __

 

0.25

 

 

 

 

 

 

-o.so . -
1 .0 0.5 0 0 0.5 1 0
Outer 2r Inner
(Top) '0' (Bottom)

Figure 3.3 Recovery of the distorted flow structures (b) mean tangential velocity

38

 

 

 

 

 

0.250

 

-0.254 >

 

 

 

.050 & - - - 90 I 1
1.0 0.5 0.0 0.5 1.0
001" {‘1 Inner
(TOP) (Bottom)

Figure 3.3 Recovery of the distorted flow structures (c) mean radial velocity

Anwer (1993) conducted experiments on turbulent swirling flow by solid body
rotation before the flow entering a 180—degree curved pipe and compared the results with
a no-swirl case. He observed that the superimposed solid body rotation completely
dominates the flow in the curved pipe. The resultant pattern was a single cell whose
characteristics were very similar to a decaying combined free and forced vortex.

Roberge et a1. (1999), Cain et al. (1999), and Cheng et a1. (1975) among others
have reported the importance of the flow structure and flow mechanism upstream of an

impeller and its influence on the performance of the impeller and the stage as a whole.

39

Ghia (1997) investigated the flow field by numerical simulation for fully
developed, incompressible, laminar flow in a 90 degree curved rectangular channel,
considering the effect of the ratio of curvature to an equivalent hydraulic diameter in the

formulation.

 

r]:
0 2 .4 .6 .8 I 0
——R/O-l00
2.0. —--—R/D-l4 ,

-----R ID -3

  
   
 

 

 

r/a-O.5 \\\
K-IOO

  

 

Figure 3.4 Effect of curvature ratio RID on fully developed axial velocity

40

He showed that the Dean number has the main influence on the laminar flow structure
containing the secondary flow cells over the cross-sectional area in the curved section of
the channel. He showed the insignificant effect of the curvature ratio for the same Dean
number on the radial and tangential velocity in the case of a fully developed axial flow
before the rectangular bend curvature, which implies that Reynolds number is another

determining factor for the flow structure as shown in Figure 3.4.

urn-none?
o 1. ' ‘2 a a s

 

{.3100m. 1.
"No".'“‘
5*- goga,m.1m,
“unto-u

 
   

YOLO

¢ r-
at )y- . . N
3 , - 3
.3} \. .3
O
i / sf

 

 

 

. chasm-no.9
o' A 1 - 1.0. m ., «.0
;' 0v - 2.0. m - 21.0 .
AL ..L 1 n 4 _ L . l. J. o
o I z. a a- s‘ s 7 a 9 I0
cumm .102

Figure 3.5 Axial pressure drops for rectangular curved ducts

(a) Effect of Dean number (b) Effect of aspect ratio

41

He also indicated the comparison of the pressure drops in the rectangular curved duct for
various Dean numbers and concluded that the pressure drops increase more with a higher
Dean number as show in Figure 3.5.

Kajishima (1989) compared a numerically simulated result with an actual flow

field using flow visualization for laminar flow in curved rectangular channel.

 
 
   

 

lllllll||||l|||||lllllllllllllllllll

 

 

 

 

 

111|U|||||||||||||||||l| W

    

(5) +11: (downstream) (6) +2a (downstream) (7) +54 (downstream)

Figure 3.6 Flow structures affected by bend curvature (a : duct width)

He indicated that the pressure loss in the bend section corresponds to that in the same
cross-sectional area of a straight duct with the length of 6 diameters. It is shown that flow
upstream of the duct is also influenced by the bend curvature while the down stream

condition seriously affects the development of secondary flow. From the simulation

42

result, it is observed that the developed vortices persist far downstream after bend
curvature and the most intensive secondary flow occurs in the middle of the curved duct
where the pressure difference between inner and outer wall is the maximum. His result
combined with the spatial limitation faced for the present study rules out the possibility of

the length extension after the bend section of inlet pipe.

3.4 Inlet distortion influence on impeller performance

Ariga (1982) investigated experimentally the influence of inlet distortion on the
performance of a low speed centrifugal compressor with vaneless diffuser, mainly in the
impeller with artificially created radial (hub and tip) and circumferential distortion
generators by locating multiple layers of honey comb at the upstream of impeller and

compared the result with the case of no distortion as shown in Figure 3.7.

@ ......

H00 0151'

lunatic:

  

 

 

 

CIRC OISI’

Figure 3.7 Configurations of artificial inlet distortion

43

puff

 

 

Figure 3.8 though 3.12 show his experimental results on the distorted velocity profile and

performance degradation caused by the various types of inlet distortion.

 

 

 

 

“Pt

 

 

T” '-’ ...
z .
0‘ " I 0|!
2 w .71.;
'
hobo ,, , .
O m [-00 20 400 z) 400 2) ‘0

Wm lm/sl

Mm orsr [11 crnc [.1 HUB firTrrp ]
Figure 3.8 Velocity profile at inducer for various type of distortions

sz rpm
:05 V=0.L

 

 

 

 

 

 

 

Z W
.- w? I‘m/kg“
o as: I

 

 

 

 

 

 

 

Figure 3.9 Incidence angle distribution at impeller inlet for no/radial distortion

No=6000_r_g31 CIRC

07:0?— Fp'EbTIT'l" :03 "'7
m m g

 

 

 

 

’\ 4 N l
_ +——-+ + «
320—362 B'/ \‘%/

0 1208240 360

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.10 Incidence angle distribution at impeller inlet for circumferential distortion

‘_’_."'_‘_'}Sur9-
1'07 l Mild surgo
X Counties
Value
1.06
105 No='6000
i 5000
21.04

 

1.03 .
A HUB
, u TIP
1.02 rpm °
0 0.5 1.0 1.5 ”10.1.
mlTE/Po

Figure 3.11 Total pressure ratio and surge margin for various type of distortions

45

N0 = 6000 rpm

 

 

 

 

 

 

 

 

 

 

 

 

100
90
.3
r
80 ~ 0
*7
E
.2.
70o 0.5

‘P

Figure 3.12 Impeller efficiency comparison for various types of distortions

According to his results, the distorted inlet profile degrades the impeller efficiency
significantly by changing the incidence angle, especially in case of tip distortion. The
highest pressure is obtained in case of no distortion, and it falls gradually in the order of
circumferential, tip, and hub distortion. He observed the tendency that the performance
degenerating effect due to the distortion grows as the rotational speed and the flow rate
increases. He also showed the results in terms of a violent surge limit that is the highest
for no distortion case, and it moves to the lower flow rate in the order of hub, tip, and
circumferential distortion indicating the highest degree of movement.

His experimental results support the cause of the stage efficiency degradation for
the present study that can be described as the combination of locally concentrated
circumferential and tip distortion as well as the non-uniformity of the flow properties

before the impeller inlet.

46

3.5 Two dimensional simple diffuser
Kline et al. (1959) have identified the significant flow regimes in straight-wall
two—dimensional diffusers with thin turbulent inlet boundary layers and completed a

stability map as shown in Figure 3.13.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1::— JETFLAOW‘ /
—_ 60 f‘
A ../ FULLY DEVELOPED l
40 I fi-DIIMENSIO‘NALI STALL
: , , w2 so TLARGE TRANSITORY STALL H‘
W1 3 g g 20 x LINE OF APPRECIABLE .
1 20 : ;-—> 29 15 STALL ,
5 E S 10
_ . ............ E § 8 \\
6
............ L X
L 4 L1 NO APPRECIABLE \\
2 l l l I ll
15 I I l 1 l 1
1 2 a 4 6 a 10 20 40 so
L/W1

Figure 3.13 Flow regime in straight wall two dimensional diffusers

They found that maximum pressure recovery occurred when a condition of transitory stall
exists. From dimensional analysis, the parameters affecting the diffuser performance are
area ratio, divergence angle, inlet Reynolds number, inlet Mach Number, aspect ratio,
and inlet blockage.

Reneau et al. (1967) have shown that the maximum diffuser pressure recovery
cannot occur at the same angle as the maximum diffuser effectiveness, but it will be

reached later at a diffuser divergence angle between 6° and 8° as shown in Figure 3.14.

47

 

-— Minimum heed toes
Mazdmum effectiveness
Peek recovery

  
 
  

 

LIW, constant
AR or 2 0

 

 

 

Figure 3.14 Representative locations of diffuser performance at constant W;

3.6 Vaneless diffuser
Stanitz (1952) showed his theoretical analysis of the flow through the vaneless

diffuser as indicated in Figure 3.15.

O

a: .13.

 

02 .7.

Figure 3.15 Flow path in a vaneless diffuser

48

The logarithmic flow path describes an arc of approximately 360° for an inlet flow angle
of 76° before discharging from a diffuser with a radius ratio of 1.8. This long flow path
results in high friction loss, and a typical static pressure recovery coefficient for a
vaneless diffuser is approximately 0.5.

According to Elder and Forster (1987), the flow in a vaneless diffuser with a
radius ratio of 2 and an inlet flow angle of 5° will rotate 400° before leaving the diffuser,
resulting in a low static pressure recovery coefficient. On the other hand, the vaneless
diffusers are well suited for off-design operation because they are compatible with a wide
range of absolute flow angle discharged from impeller and can only choke if the radial
component of the Mach number exceeds unity (VKI 1965). Dean (1976) states that
backflow into the impeller is less frequent with vaneless diffusers than with vaned

diffusers caused by vane pressure loading.

49

3.7 Vaned diffuser

Runstadler et al. (1973) demonstrated the substantial influence of inlet blockage
along with the diffuser aspect ratio on the performance of a channel diffuser. As shown in
Figure 3.16, the peak pressure recovery coefficient is a function of the aspect ratio and
the inlet blockage factor and is substantially influenced by the blockage factor with both

low and high aspect ratio diffusers.

 

090 v v r r x

080 0-02 -‘

 

Maxinmmpreeeurereeoverycoeffident
9
3
a: 1 fl ' l '

i
J

I
l

012

I
l

I
I

 

 

 

0.x 1 l 1 l A
0 1.0 2-0 3—0 4-0 5-0
Aepeciretio

Figure 3.16 Effect of throat blockage and aspect ratio on pressure recovery coefficient

50

st

 

 

This

andR

 

emf}:

 

Runstadler et al. (1975) collected the performance data of a number of channel

diffusers for a range of inlet flow conditions and created a diffuser performance map as

shown in Figure 3.17.

 

53'1'0 Man-'05

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3M1... ' ' :Vm/ ma.
5%???"
//// 1’ 1733”
E 1% /// A 1% g
g2; 7/////////°/ / d 072 35
:20“ \ fi 070
, ::j,///,///7[/ ,/ :1:
. ::////// ,// 5

 

 

 

 

 

 

l
4 5 6789101214161820
LengtiriewidthMoLWR

Figure 3.17 Channel diffuser performance map

This performance map was presented to show the effect of inlet blockage, Mach number,
and Reynolds number on diffusers with aspect ratios of 0.25, 1.0 and 5.0.
Stein and Rautenberg (1985) achieved an increase in overall pressure rise and

efficiency by reducing the passage height of a vaned diffuser by 10%. For the narrow

51

 

diffuser, the maximum efficiency is 2% higher, and the efficiency near the surge exceeds
the wide version by 4%. This effect loses the importance of the passage height at lower
speed operation. Figure 3.18 shows that the choke lines are shifted to the left in a higher
extent than the surge lines, resulting in the decreased flow range. The passage height
reduction causes the difference on the flow conditions at the diffuser inlet and thereby it
provides a good component matching. Compared to a vaneless diffuser, the narrow

version of the vaned diffuser is similar in terms of the surge flow behavior.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4.2 1 r L 1 ‘
---wideditimer ,
3.8 ~ —nemwciiiiueer ..
4- 1
K 3.4 ‘ i
0
£30 ‘ '3 5
17500\ ~\ 1 220%
i“ an i 1 1
2.2 +2oooo
3». . i |
1.8 ‘-—1'—==._. “1 t ' 18°00
‘ - n“ ; 16700
1.4 ‘ 1 4
l“ : 14600
1.0 108001,"! 112600 I . 1
mu=o.59iugle
...100
E.
g 80 ~\ P‘ \‘ 11‘
60 L I .1 Q :
g 1 ‘1 l 1 1 i T22C00
‘ i : 1 i 'm”
40 l E : 16100 18000
E 20 ' 3 '14600 I
g I 112600 I
0 10600111111 1 1

 

 

 

 

 

 

12 3 4 s 6 7 8 91011
«Inflowmemlkglel

Figure 3.18 Passage height effect on compressor maps

52

In order to find the optimum diffuser passage length to width ratio, the opening
angle always has to be taken into consideration. Thus, the maximum diffusion can be
obtained in a straight channel diffuser either with a high length to width ratio in
combination with a small opening angle or a small length to width ratio in combination
with a high opening angle.

Clements and Am (1988) tested different channel length to width ratios of
straight wedge diffusers in a turbocharger compressor and the results are shown in Figure

3.19.

 

 

‘ ' 7 r r
We! VII-d Van-h.
3-3 "' 0110111101 Cheer 0111- -
covered m m
portion «he a“
1 .1, +
e--"""’
0.7“
o 0.7“ 0.753
3.1 P fie. 746 ..
__ /0.734
O
Q 31° F e "'
3 0.711 . , .
e.
u e “(mane
/0.7tt 716

 

 

 

 

 

 

 

g 0657 '
2.. '- u
2.5 L 2
05°? ...... 11.7200011111111 mustang/s
2.4 - o—o n-ROOOr/um 111-0471111171 ~
I J l l l
0 1 z 3 4 s
Non-01111013101101 length W.

Figure 3.19 Pressure rise through the vaned diffuser passage

53

 

 

 

C1

an

int

181

CO

 

They found an optimum value of 3.7. The existence of an optimum value can be
explained by several effects. The first half of the channel length has the highest influence
concerning the pressure rise whereas the latter part contributes only a small amount of
pressure recovery. This is caused by the boundary layer growth over the channel length.
Reaching a certain thickness, the boundary layers may become unstable and the resulting
increase of blockage causes the point of separation to move towards the diffuser throat.
As indicated in Figure 3.19, the pressure gradient in the latter half of the diffuser channel
is significantly lower due to the higher throat blockage condition. Moreover, Clements
and Arrt found that a small reduction of the diffuser diameter does not necessarily lead
into a loss of stage performance. Furthermore, the minor loss in the channel pressure
recovery can be compensated in the downstream vaneless part and in the volute, which
can be explained by a higher exit dynamic head and a less distorted exit velocity profile
in the shorter channel. Falling short of a minimum diffuser diameter, stage efficiency
losses occur because the downstream vaneless part and the volute cannot compensate for
the loss of the high pressure gradients anymore, which are typical for the vaned part.
Yoshinaga et al. (1980) investigated 16 different vaned diffusers on a model
compressor rig in order to improve the efficiency of a centrifugal compressor stage. The
pressure recoveries were compared with those of two dimensional channel diffusers. His
comparison showed that the vaned diffusers reach their peak pressure recovery at smaller
area ratios and smaller length to width ratios. This peak pressure recovery was attained
for a combination of the length to width ratio around 5 .5 and area ratio around 2, which is
illustrated in Figure 3.20. The value for the given vaneless diffuser is lower because of its

smaller area ratio. The obvious existence of an optimum area ratio is coupled with the

54

fix
the

flO'ii

values for the divergence angle and the length to width ratio because a change of the area
ratio can be obtained by varying these parameters. If the divergence angle exceeds a
certain limit, separation may occur due to a high vane loading. In the case of increasing
the length to width ratio, the boundary layers grow and reduce the effective area ratio.

Both effects lead to a drop in pressure recovery and show the usefulness of a well

adjusted area ratio.

 

 

 

 

 

1
_ cu. (incompressible)
@- 0 a . 6,. 11112051
a .
2
§ 0.6 -
C r
i 0.4 -
1- .0 .
“- 0.2 » ' \
. vaneless diffuser
O i . : i
1 1.5 2 2.5 3

Area Ratio W4 / W3

Figure 3.20 Area ratio effect on the pressure recovery of diffusers

The radius ratio is a very important geometric parameter since it determines the
extent of mixing the jet and wake flow leaving the impeller. Eckardt (1976) investigated
the flow in a high speed centrifugal compressor impeller in detail. He pointed out that the

flow equalization process takes place mainly across the channel width due to decreasing

55

meridional curvature turbulence stabilization, whereas the Coriolis forces maintain a
remarkable circumferential flow distortion along the shroud wall up to r/r1 equal to 1.2.
The same value for the radius ratio was found by Jiang and Yang (1982) who tried to
improve the pressure recovery of a vane island diffuser. Applying the vane island tip at
four different radius ratios, they found that the pressure variation over the circumferential
locations was about 20% at r/rl approximately equal to 1.05 and 1.10. In order to provide
a satisfactory mixing in the vaneless space, they suggested a radius ratio from 1.15 to
1.20. This range provides a minimum of losses in combination with an optimum pressure
recovery as it can be seen in Figure 3.21. A rise in efficiency of 4% was obtained by

lifting the radius ratio from 1.10 to 1.20.

 

     

 

 

A

Do; '6-0 '-

I

g -s.0 .

‘c’

’C." -4.0 1-

01

5 -3.0 -

3

01

3,-2.0 - o rim-1.05 v-11'

.9 A f/f..1.10

E -1.0 - o r/r,-1.15 ”0'1

n 0 r/r.-1.20 n-23700rpm
o I I L I - I I I I

 

o 1 2 3 4 5 6 7 a
circumferential positions

Figure 3.21 Circumferential static pressure distribution for different radius ratios

56

As a comparison of different investigations, the number of vanes seems to be
strongly dependent on the type of diffuser.

Dean (1976) indicates that the number of vanes employed in vane island diffusers
may vary in a range of 8 to 60.

Came and Herbert (1980) could not find any significant difference in the
compressor flow range with a vane number variation.

Rodgers (1982) achieved similar results by comparing the stage performance of a
high efficiency, low pressure ratio stage with both a 13 and a 21 vane channel diffuser at
the same throat area. Figure 3.22 shows the obtained minor changes in flow ranges, head,

and efficiency on the stage.

 

013nm
I021nm.
0.9 throat area 22.8 eq in.
E 0” (9000
g 0.6 — (I q)
C
07:;- 9% Ch 0
<3C) 0.

1.0 —

M2- 0.7 ?
0.6 l l I

0.04 0.00 0.06 0.10 0.12
stage flow coefficient

 

adiabatic head
coefficient
0
Q
j
c!

 

Figure 3.22 Effect of diffuser vane number on the stage performance

57

 

 

 

 

 

rim

I'Hcic

 

Yoshinaga et. al. (1980) expected an increasing number of vanes moving the
surge limit of a centrifugal compressor to a higher flow rate. Therefore, they limited the
vane number to 27 for radial airfoil cascades for their experimental investigations.

Elder and Forster (1987) mentioned that a reduction of the number of diffuser
vanes permits the mixing of jets and wakes in the vaneless space, which prevents the
region from being blocked by low momentum flow. This argument is unimportant for a
low solidity vaned diffuser since the throat is missing. Nevertheless, Camatti et. al.
(1995) found an influence of the vane number on the performance of LSVD’s. Figure
3.23 shows that an increase of Z from 6 to 12 leads to higher efficiency but in a narrower

range of the flow coefficients.

 

 

 

 

 

 

1.3 T x
12 ? “—12UOCOSJ
. Ms
\
1.1 e.

 

1.0‘ ,7! - V‘

 

 

 

 

 

 

 

 

 

 

 

 

0.9 ’ 31 \ \\
. n“ \
0.0 \
l
0.7 . - - - , r \.
0.4 0.6 0.8 1.0 12 1.4 1.6
4’ / 1’0.

Figure 3.23 Vane number effect for rin/r2=l.106

Another point of view is to determine the number of vanes with a view to the optimum

incidence angle that leads to the best flow range and efficiency. Moreover, the

58

rotordynarnics may be important for a stable operation, i.e. the number of the impeller
blades and the diffuser vanes have to be harmonized.

The incidence angle in a radial diffuser has an important influence on the flow
range with regard to the stall and choke behavior. If the mass flow is reduced from the
design value, the radial velocity decreases in contrast to the increasing tangential
velocity. Hence, the angle of the mean absolute flow into the diffuser is inclined towards
the tangential direction, which leads to a positive increase in incidence. In the case of
transgressing a certain value for incidence, the pressure loss rises rapidly and stall
phenomena occur. Conversely, a higher mass flow than that chosen for the design point
causes the flow to enter more radially and therefore with a lower incidence angle. At a
very small incidence, the flow range is limited by choke effects.

Reeves (1976) carried out experiments with pipe diffusers and found a correlation
between the flow range and both the Mach number and the incidence angle as shown in
Figure 3.24.

0.23
0.24
0.20

..élV— 0.10

0.12
0.00

0.04

 

0

-B -7 -6 -5 4 -3 -2 -1 0 1 2 3

Ichoke Leedhgedgemaadrmiiowincidence stall 1

Figure 3.24 Effect of diffuser leading edge Mach number and incidence on range

59

At any leading edge incidence a lower leading edge Mach number corresponds to a
greater range, and the range at a constant Mach number changes with the incidence.
Reeves found an incidence angle for optimum matching that was somewhat negative, and
located near the middle of the flow range.

Kenny (1972) achieved the minimum throat blockage at the vane suction leading
edge at i=-4°.

Since the increase of the flow range is one of the major tasks in low solidity vaned

diffusers, there are already investigations that have bee made concerning the influence of

the incidence angle in LSVD.

Sorokes and Welch (1992) carried out various LSVD tests and obtained the

results shown in Figure 3.25 indicating the widest flow range for an incidence that is

slightly negative.

 

0.6

 

I
0.5 d

 

 

 

.°
5

 

 

(low range
o
01

.°
to

 

 

 

 

 

 

 

 

 

 

 

o vrv1 VIII tat! Irv 11ft T—Vlfi

-15 ~10 -5 O 5 1 O 1 5
incidence angle [deg]

Figure 3.25 Flow range versus incidence angle

Hayami et. al. (1989) achieved the maximum diffuser efficiency for i=-2° to i=-3°,
but they also point out that the best efficiency condition of the diffuser might correspond
to the choke condition of the impeller.

Hohlweg et. al. (1993) recommend the avoidance of positive incidence angles
because their test results with LSVD’s showed significant losses in efficiency and
stability for these cases. Instead of that, they recommend a negative incidence angle that

just meets the vaneless diffuser choke flow.

61

CHAPTER 4

EXPERIMENTAL TESTING WITH DIFFERENT INLETS

4.1 Experimental setup

4.1.1 Test rig setup

 

Settling Chamber & Filter

Throttling Valves

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Inlet Pipe

 

 

Conpressor

 

Figure 4.1 Schematic of experimental test rig

An integral-gear type of compressor test rig as shown in Figure 4.1 is used for the
experimental testing to obtain the compressor stage performance with two different inlet
models. 300-horse power motor with variable speed controller drives the pinion gear that
is connected to the impeller shaft with a gear ratio of 14.5. The design driver speed is
2688 rpm, which makes actual impeller rotational speed 38976 rpm. Experimental tests
are also carried out at off-design speeds of 35076 rpm (~10% off) and 42877 rpm (+10%

off). The performance characteristics of the compressor are obtained for the flow range

62

from choke to mild surge point. The compressor was tested in an open air loop. The air
entered the compressor through an air filter, a settling chamber, and an inlet pipe. The
settling chamber provides the compressor with an air supply free of the temperature
stratification, thus enabling the compressor inlet temperature to be measured accurately.
After being compressed in the impeller and the diffuser, the air passes through the volute
and is discharged to ambient air through the discharge pipe. The air in the discharge pipe
is muffled with the aid of silencer before it is discharged. The mass—flow rate through the

compressor is controlled by the throttle valve located at the discharge pipe.

4.1.2 Geometric specifications of the compressor

 

(a) impeller (b) diffuser

Figure 4.2 The tested impeller and diffuser for the compressor

The tested impeller and diffuser are shown in Figure 3.2. The impeller is

unshrouded and has 17 blades with blade angles [3", Jub=46.3o, Blb_sh,=56.9° at the leading

63

edge and a backward swept blade angle sz=47.4° at the tip with reference to radial
direction. The diffuser is a conventional vaned type and has 16 vanes with constant
height 0.45” and the vane angle B3b=68.8° at the leading edge with reference to radial
direction. The geometric specifications of the compressor are listed in Table 4.1, and the

cross-section is shown in Figure 4.3.

Table 4.1 Dimension of impeller and diffuser

 

 

 

 

 

 

 

 

 

 

 

 

Dimension [in]
1' 1h 0.72447
r1, 1.70209
r2 2.82000
1'3 2.99280
r4 4.55893
b2 0.45000
11- ------------------- 4
vaned
diffuser \us
/ b2
2
/ shroud

 

 

 

 

 

 

 

 

 

 

 

///////A___::’3

Figure 4.3 Geometric specifications on the compressor cross-section

 

 

 

64

4.1.3 Geometry of the tested inlet models

The purpose of the present experimental study is to compare the compressor stage
performance with two different inlet models. The first tested inlet model shown in Figure
4.4 is a circular straight pipe with constant area of 5” diameter. This straight inlet is used
to obtain a clean flow condition upstream of the impeller for the comparison purpose.
The second tested inlet model, which is the actual design of 90-degree curved pipe, is of a
circular nozzle shape with linear area change from 6” diameter at the inlet to 5” diameter
at the exit as shown in Figure 4.5. Experimental tests for the two inlet models have been
carried out to obtain the stage performance information and to compare the results.

As has been discussed earlier in the previous chapter, the secondary flow is
developed in a curved pipe and persists far downstream after the bend section of the pipe,
depending on the intensity. Therefore, in order to avoid any inaccurate measurement due
to the presence of the secondary flow at station 1, which is the impeller inlet or the exit of
inlet system, the measurement is carried out at station 0, in which case total pressure loss

is considered in the stage performance calculation.

 

 

 

 

 

Figure 4.4 Geometry of straight inlet (‘sp’)

65

 

 

0\

di'

 

 

 

 

 

—-> ----------- i <——- 5.523-

I 27.662”

 

 

 

 

 

 

Figure 4.5 Geometry of the original bend inlet (‘bp0_no__vane’)

4.2 Experimental procedure and methodology

For the experimental testing, the steady-state compressor stage performances are
obtained using two different inlet model configurations. Several static and total
temperatures along with static and total pressures at different planes of the compressor
stage were measured in order to determine the mass-flow rate through the stage and
overall performance of the compressor stage. The mass-flow rate was measured with two

different orifice plates for the different pipe diameters of the two inlet models, which are

66

based on ASME standard flow measurement procedure. For the testing with each inlet
model, two total and two static temperatures were measured at different circumferential
positions with 180 degree and 90 degree separated respectively at the same plane before
the inlet pipe. The differential pressure across the orifice plate was measured by two sets
of static taps located at one pipe diameter upstream and half diameter downstream of the
plate (6” and 5” diameters for bend and straight inlet, respectively). The static pressure at
the orifice was also measured at two locations with 180 degree separated
circumferentially in the same plane.

The stage inlet static and total pressures were measured at two 180 degree
separated, circumferential positions. Similarly, the inlet static and total temperatures are
also measured at two different circumferential positions. Figure 4.6 shows the

configuration of the measurement and the probes for the testing.

 

 

 

 

 

 

 

 

 

station 0 and 6 orifice
'I
0 station 6
_- _______ P16 T16 A
flange orifice C
V ._ ...... .21
V : : : : :
A
cenuifugal l I l ' I l
compressor 1 : : : i
i .1 1“" ’1 i
1 l 10.5d ld I |
l l l l 1
station 1 station 0 Pa-orfz Ps-orfl Tt-orf
P11 T11 P10 T10 L—--I
Pal P30 ‘ APs-orf

 

 

 

Figure 4.6 Configuration of probes and mass flow rate measurement

67

The stage exit pressures and temperatures are measured in the discharge pipe
connected to the volute. The exit total and static pressures are measured at two
circumferential locations in the pipe at the same plane. Similarly, the exit total and static
temperatures are also measured at two locations at the same station. In order to avoid the
heat transfer effects on the temperature measurements the casing of the compressor was
covered with insulating material.

The compressor was tested at three different impeller rotating speed (-10% off,
design, and +10% off speed) for straight and bend inlet configurations. At each speed the
temperature and pressure measurements were collected from all probe locations for 12
different mass-flow rates ranging from compressor choke to mild surge in order to obtain
a complete speed line. The mass-flow rate through the compressor was controlled with
the throttle valve located at the stage exit.

At each flow point, the data were collected when the compressor stage reached
steady state condition for the pressure and the temperature. Since pressure is stabilized
quickly, the more careful attention was taken on the temperature measurement at the
stage inlet and exit. The accepted margin of temperature oscillation was within i0.1°C
for 20 minutes. Once the stage was considered stable, all the pressures and temperatures
were recorded and transferred to PC for data reduction and processing.

The data reduction and processing is performed by using EXCEL program. The
program first converts the recorded pressures and temperatures into N/m2 and K. For all
of the measurements, the temperatures and pressures at each measurement plane are
compared with each other and with downstream and upstream measurement planes. In

this way, any faulty or malfunctioning transducers can be detected, and the data from

68

them are eliminated before obtaining average pressures and temperatures at each
measurement plane. The program uses the averaged pressures and temperatures at planes
to calculate the stage overall performance. The program is also capable of plotting these
performance parameters with the mass-flow rate. This on-line plotting capability of the
program acts as a good tool to monitor the behavior of the stage and the whole system.
The overall performance parameters calculated are the flow coefficient based on the
mass-flow rate measurement, the static and total pressure ratios, the total temperature
ratio, the head coefficient, the work coefficient, and the total-to-total isentropic efficiency

of the compressor stage. The stage total pressure ratios are given by

P06
Eustage = 7,; (4-1)
Similarly, the stage static pressure ratios are given by
P 6
”nudge = F0 (4-2)

The isentropic efficiency can be calculated for the stage. Efficiency is the ratio of
work done in an ideal process to the actual work. For the stage compression process
between two stations 0 and 6, this can be expressed as a ratio of the isentropic work

representing the ideal process and the real work. In terms of enthalpy this becomes

= M (4.3)
hos ' hoo

W

_ S
"3'-

W

For an ideal gas with constant cp, the relation db = cpdT can be used to rewrite

equation (4.3) in terms of temperatures

(4.4)

In an isentropic process with constant properties, the pressures and temperatures

are related according to

11']
T063 = P—06- 7 (4.5)
Too P00

Thus, substituting into equation (4.4), the isentropic efficiency for a compression

process between station 0 and 6 can be written as

(4.6)

 

The energy transferred by the rotating blades to the gas passing through the
impeller per unit mass is defined as the compressor head. Although the compressor
produces head, it cannot be measured directly. However, it can be calculated from the
measured pressure ratio, inlet and exit temperatures and gas properties. Head in non-

dimensional form is given by

Ahos (4.7)

 

and is known as isentropic head coefficient. Using equation (4.5) the head coefficient can
be written in terms of measured quantities and gas properties for a compressor stage

between station 0 and 6.

70

 

 

Poo
Ah
111:1 0‘ = 1 (4.8)
2 2
5112 ‘U2

The work coefficient relates the isentropic head coefficient and the isentropic efficiency.
Since the impeller between station 1 and 2 is the only component where the work is
added to the fluid, the total temperature is increased in the impeller and is constant for
other components. The work coefficient is a non-dimensional value of the actual head

produced by the compressor and is given by

fl: Aho =Cp(T06_TOO)=U2Cu2—U1Cu1
1 2 1 2 1 2

-—U —U —U

2 2 2 2 2 2

 

 

 

(4.9)

The relation between the head coefficient, work coefficient and the efficiency is given by

17 = Z (4.10)
,u

The mass-flow rate through the compressor was calculated from the differential
pressure measured across the orifice based on the ASME standards. The equations used
for the calculation are given in Miller (1992). In this report the mass-flow rate is
presented in non-dimensional form known as the flow coefficient that is given by

(D=—Q—— (4.11)

It 2
—DU
42 2

71

4.3 Experimental results and discussion

A compressor stage efficiency comparison with a straight and a bend inlet at three
different impeller rotational speeds showed the significant performance difference as
indicated in Figure 4.8 to 4.13. In the case of the bend inlet, the secondary flow
developed in the bend section of the pipe is the response to the pressure gradient on the
corresponding radius of curvature and the global Reynolds number in the flow regime of

curved passage as indicated by

a V2
a—’r’=p—r— (4.12)

Equation (4.12) is valid for any stationary curved flow passage, meaning the normal
direction of the pressure gradient depends on the centrifugal force, and this relationship
also implies that the pressure gradient increases with the increase of the mass-flow rate.
Because of the presence of the secondary flow in the bend inlet, the flow properties at the
impeller inducer are unfavorable for the compressor performance and cause the
efficiency degradation. These experimental test results essentially lead to the idea that the
compressor work inputs for two inlet models have only a small difference and the stage
efficiency difference is based dominantly on the head rise difference.

Specific work input and the definition of incidence for a compressor are given as
equation (4.13) and (4.14) respectively.

Aw=U2Cu2 -U1Cu1 (4.13)

7': ,61 - flu, (4.14)
It is believed that the compressor is designed for purely axial inlet flow (Cu1=0) at an

impeller inlet to which the flow profile from the straight pipe corresponds. On the other

72

hand, the secondary flow developed in inside of the bend pipe causes the flow distortion
and results in intensified flow angle with non-uniformity. Therefore, the work input for
the bend inlet is increased by a positive incidence (-Cu.) and decreased by a negative
incidence (+Cu1) with the same degree respectively at any flow coefficient and rotational
speed since the exit flow profile of the bend pipe is exactly symmetric with reference to
the center line between the outer and the inner wall and has the opposite direction of
secondary flow, which divides the circular cross sectional area into two symmetric half
planes with the presence of twin vortices near the inner wall as shown in Figure 2.1 in
chapter 2. Figure 4.7 shows the incidence angle change based on the velocity triangle and

the possible boundary layer separation.

 

 

   

 

 

 

Figure 4.7 Incidence and boundary layer separation

73

According to equation (4-13), the symmetry of the flow profile at the impeller inlet
cancels out the work input change influenced by the corresponding incidences, which
explains the experimental test result in terms of the work coefficient shown in Figure
4.10. The work input between the bend and the straight inlet has. no significant difference
and increases only with the higher impeller rotating speed as expected. However, both
positive and negative incidence at the impeller inlet cause boundary layer separation even
at the design point and speed. Therefore, the head coefficient has the significant
difference as shown in Figure 4.9, resulting in the compressor stage efficiency
degradation as Figure 4.8 illustrates.

It is observed that the compressor stage efficiency difference between straight and
bend inlet is smaller at the higher impeller rotational speed and the discrepancy increases
at a lower flow rate for each speed. These results are reasonable since the flow in the
impeller blade passage is more vulnerable for the lower mass flow rate and speed than
under the design mass-flow rate and speed, which can be easily triggered by external
disturbance such as incidence in this case leading to more severe boundary layer
separation and possibly impeller stall compared to higher mass flow rate and speed
operating condition.

Static pressure ratio is almost identical between straight and bend inlet for all of
the three speeds. On the other hand, there is a significant total pressure ratio difference
between straight and bend inlet as shown in Figure 4.11 and 4.12. These results imply
that the distorted flow causing the incidence at the impeller inlet mainly affects the
impeller and the diffuser performance in terms of total pressure loss and does not have

severe influence on static pressure rise in the diffuser, which is to convert kinetic energy

74

to static pressure. In other words, the degree of influence by the inlet distortion is not
severe enough to lead to early diffuser stall followed by the compressor surge, in which
case the static pressure ratio would have been affected. The impact of vaned diffuser
‘ performance and operating range of a centrifugal compressor stage is critically depending
on the diffuser inlet flow conditions after the impeller discharge, such as inlet Mach
number, inlet flow angle, turbulence, blockage, and most importantly, impeller exit flow
non-uniformities (Filipenco and Deniz, 2000). Based on the results, it is presumed that
the radius ratio of diffuser inlet and impeller exit, r3/r2, coupled with the inlet distortion
effect, is small enough for the compressor to have no indication of early vaned diffuser
stall leading to the stage surge and is not large enough for the impeller discharge flow to
be mixed rapidly and uniformly in the vaneless and semi-vaneless space before the flow
enters the throat of the diffuser, which is responsible for more total pressure loss in the
diffuser in the case of the bend inlet.

Total pressure ratio and total temperature ratio are compatible with the head
coefficient and the work coefficient respectively, indicating essentially the equivalent

physical meaning.

75

-1e- Straight (40% off)

-0- Bend (-1 0% off)

-a- Straight (Design Speed)
-0- Bend (Design Speed)
-111- Straight (+10% Off)

-)(- Bend (+10% Off)

 

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Mine

Figure 4.8 Compressor stage efficiency comparison for straight and bend inlet

1.2
1.1
1.0
0.9
0.0
0.7

§ 0.6 +S1mlght(-10% off)

7 0.5 -e-eend (4016610
0-4 -a-Stralght (Design Speed)

0-3 + Bend (Design Speed)
0.2

0.1
0.0

-ill- Straight (+10% Off)

+eend (+1091. 011)

 

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
ill/4’09

Figure 4.9 Head coefficient comparison for straight and bend inlet

76

1.2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.1
1.0
0.9
0,3 -.-..2___ 4-----. __-_ -
a 0.7 J _ _
a 0.6 - -e-Stralght (40% off)
0-5 1 -O-Bend (40% off)
0-4 1 421-3111119111 (Design Speed)
0'3 i +Bend (Design Speed)
0'2 ‘ +S1reign1 (+10% 011)
0.1 .
+ Bend (+10% Off)
0.0 1 . fi fi
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
W909
Figure 4.10 Work input comparison for straight and bend inlet
1.5
l 1 l I l l l l l
1.4 . _, +Stralght «10% O") -e-Bend(-10% O")
-B-Stralgnt (Design Speed) -O- Bend (Design Speed)
1'3“ +Stralght(+10%Off) +esnd(+10%oii) *
1.2
1.1
3
E 1.0
0.9
0.8
0.7
0.6
0.5

 

 

 

 

 

 

 

 

 

 

 

 

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1 .5
W901»

Figure 4.11 Total pressure ratio comparison for straight and bend inlet

77

1.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7 l l l l I I l l
1.4 . _ -a- Straight (40% off) -0- Bend (40% off)
-a- Straight (Design Speed) + Bend (Design Speed)
"3 ‘” 41- Straight (+10% 011) -x- Bend (+10% 011) i
1.2
1.1
a
1! 1.0 »——E
2
0.9
0.8
0.7 .____- b-—
0.6
0.5

 

 

 

 

 

 

 

 

 

 

 

 

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
91909

Figure 4.12 Static pressure ratio comparison for straight and bend inlet

1.5

 

l l I l l l l l l
1_4 . . +Stralght (40% off) -0- Bend (40% off)

-a- Straight (Design Speed) -0- Bend (Design Speed)

"3 ‘“ +Sireign1 (+10% 011) -x- Bend (+10% 011) “

 

 

 

 

1.2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.7

 

 

0.6

 

 

 

 

 

 

 

 

 

 

 

0.5

 

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1 .4 1.5
9’90?

Figure 4.13 Total temperature ratio comparison for straight and bend inlet

78

CHAPTER 5

NUMERICAL SIMULATIONS FOR VARIOUS INLETS

5.1 New inlet design consideration
5.1.1 Effect of the curvature radius in bend section

The experimental investigation motivated the need of a new inlet design as well
as a clear picture of the detailed flow field in the existing inlet design using numerical
simulations. New designs of different inlet systems as well as the design methods are
discussed here based on the comparison of flow properties at the pipe exit of each design.
The goal of the compressor inlet pipe design is to reduce the intensity of the secondary
flow and provide the flow as uniform as possible for a compressor with spatial limitation.

The first computational model is the original design of a 90 degree bend pipe
(‘bp0_no_vane’) as shown in Figure 4.5 in chapter 4.

For the purpose of reasonable, flow property comparison, another straight pipe
(sp_equi_bp) shown in Figure 5.1 is modeled as an ideal aerodynamic baseline that has
the circular nozzle shape with the equivalent mean line length, inlet and exit area with the

original bend pipe.

 

<—— 3524' ——>
equivalent mean line length
with the original bend inlet

9( "Lu—{)9

.1- x i

E“ ,.

Y

 

 

 

Figure 5.1 Geometry of sp_equi_bp

79

Since the spatial limitation is unavoidable, the new inlet pipes have to be a bend
shape as well within the limit. As a result, two design approaches are attempted. One is to

change the radius of curvature and the other is to insert vanes inside the pipe.

...: p_. (5.1)

The governing equation for a curved passage flow is given in equation (5.1). As it
indicates, the pressure gradient between the outer and inner wall is determined by the
radius of curvature, the density, and the velocity, which is compatible with mass flow rate
in the regime. Therefore, the pressure gradient will be increased upon the mass flow rate
increase for the same geometry and consequently, the intensity of the secondary flow will
be more severe. Similarly, the smaller the curvature radius is, the more severe the
pressure gradient is and ,hence, the stronger the intensity of the secondary flow is.
Therefore, if the geometry of the curved pipe has the shorter radius of curvature in the
bend section, it will require longer space for the flow to recover from the distortion
caused by the pressure gradient driven secondary flow after the bend section.

To investigate the effect of the radius of the curvature in the bend pipe, bp7 is
modeled with the shorter radius of curvature as shown in Figure 5.2. The comparative
numerical simulation results between pr and bp7 are shown in Figure 5 .3. For both case,
the pressure gradient between the inner and the outer wall is the maximum in the middle
0f the bend section. In case of the shorter radius of curvature, the pressure gradient is

more severe, as expected from the governing equation (5.1).

80

 

 

__.p , ......... - .............. __
f 5 E E ‘i
6.912" 5 ©

 

 

‘ ' ...........
_, .......... f 0 0771’

l I e— 9.260" —>
3.610“
—l> ----------- 4—5523-

I 27.662-
17.14- x

}——v 2
l """"""" Y V

 

 

 

 

 

 

Figure 5.2 Geometry of bp7 with shorter radius of curvature

+p Oouter wall of bp0
+ p Dinner wall of bp0
-O- p Oouter wall of hp?
-e- Olnner wall of 7

P [iii/111’]

 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized distance at bend section
Figure 5.3 Pressure gradient variations along bend section of pr and bp7

81

Figure 5.4 to 5.11 shows the qualitative numerical simulation results for bp0 and
bp7 model at the design mass flow condition obtained from the experimental testing.
Streak lines with pressure variation of the fluid particles along the wall are shown in
Figure 5.4. The low kinetic energy particles on the wall responds to the pressure gradient
in the bend section and are gathered eventually near the inner wall after the bend section,
which results in the low total pressure near the inner wall as shown in Figure 5.5. These
simulation results support the idea of using station 0 instead of station 1 for the
compressor stage performance as discussed in chapter 4. The difficulty of accurate
measurement at this location results from the non—uniform distribution of the static and
the total pressure as well as the presence of the twin vortices as shown in Figures 5.6 and
5 .7, surface vector plots and Figures 5.8 and 5.9, flow angle distributions considering the
following compressor. Figures 5.6 through 5.11 compare the simulation results for the
change of the curvature radius and clearly show that bp7 with the shorter radius of

curvature leads to worse flow profile in the regime.

82

 

 

 

1
.

 

 

 

P

9.579E+IH

9.576Efflq

9.573E+IH

9.57IE*IH

9.567Ef04

9.569510"

9.561Efflq

9.558EtOH

9.555EfIH

9.552Efflq

9.5H9E‘l9

9.5H6E+flfi

9.593Et09

9.SHIE*IH

9.537EfOH

9.5395‘09

9.531Efflq

9.528Et09

9.525E+IH

9.522E'09

9.5196‘89

 

Figure 5.4 Streak lines with pressure variation for bp0_no_vane

83

 

 

 

PTOTA].
21 9 . 601 £004

 

 

20 9 . 59713.04

 

l9 9 . 5931304

 

 

18 9 68810.04
17 9 . 584E+04
16 9 . 579E004

 

15 9 . S7S£+04
l4 9 . 570I+O4
l 3 9 . 56613404

 

12 . 9.561E+04
11 9.553904
10 9.5521304

 

 

 

 

 

 

 

 

9 9 . 548E+04
8 9.5431304
7 9 . 5391304
6 9 . 5341904
5 9 . S30£+04
4 9 . 52515104
L 3 9 . 521 RM
2 9 . 51 63104
1 9 . 51 21304

 

Figure 5.5 Total pressure distribution on the center plane for bp0_no_vane

84

 

 

 

 

 

 

 

 

 

 

Spam
3.806610l
3 .61631-01
3. 4266+01
3.2355101
3.045501
2.855501
2.6643101
2.4746101

.‘ 2.2841190]
' 2.093001

1 . 903E901
l . 71321-01
l . 52261-01
l . 33261-01
l . 14215101
9 . 5165100
7 . 613E100
5 . 7105100
3 . 8065100
I . 903E+00
0. 0005.00

 

Figure 5.6 Surface vector plot at the exit of bp0_no_vane

85

 

 

 

Spam
5. 194E101
4.9342101
4.6746101
4.4l4E+01
4.1551501
3.8956901
3.6352101
3.3766101
3. 116E101
2.856E1-01
2.597501
2.337E+Ol
2.077501
1.8172101
1.5586101
l .298E101

 

l . 0383+0 l
7 . 7916100
6 . 1 94200
2 . 597E100
0. 0006400

 

 

 

Figure 5.7 Surface vector plot at the exit of bp7_no_vane

86

 

 

 

 

 

 

 

 

 

 

 

ALFA
2.1171101

2.0113101
1.9053101
1.7991101
1.6933101
1 58715101
1.4823101
1.3763101
1.2701301

' 1.154501

1 .0581101
9 52713100
8.46812100
7 . 41 012100
6.3513100
5 .2921100
4 .23413100
3.17573100
2 . 1 1713100
1 0583100
0.0001100

 

Figure 5 .8 Flow angle distribution at the exit of bp0_no_vane

87

 

 

 

 

 

 

 

 

 

 

21
20
19
18
17
16
15

14

12
11
10

 

 

ALI-'11
2.1651101

2 .0571101

1

' 1

1

. 9491101
. 8401101
. 7321101
. 6241101
. 5161101
. 4071101
. 2981101
. 1911101
. 0821101

9 . 7451100

8 . 6621100

7 . 6791100

6.4971100

5.4141100

4.3311100

3 . 2481100

2. 1651100
1 .0821100

0 . 0001100

 

Figure 5.9 Flow angle distribution at the exit of bp7_no_vane

88

 

 

I 3 . 8061100

 

SPEED
. 8061101
. 6161101
42611-01
. 2351101
0451101
8551101

:95

DJ M (A) to (J h) (a)
. . . s

664110 1

1"
1
r1

L)

4741101

-3-

.2841101
. 0931101
. 9031101

.1
. rm wear
to M

—_

.7131101
1.5221101

r—

. 3321101

 

.—.1

.1421101
9. 5161100
7 . 61311-00

5.7101100

1 . 9031100

 

 

 

0 . 0001100

 

Figure 5.10 Velocity vector plot on the center plane of bp0_no_vane

89

 

 

L

11‘nllllli vu=nuun "I‘ll

' ' 11'

31 s 1'
1 ' I11

durum" u n 1:

 

SPEED
5.1941101
4 . 9341101
4.6741101
4 . 4141101
4 . 1551101
3 . 8951101
3. 6351101
3 . 3761101

3 . 1 161101

2.8561101

2.5971101

2.3371101

2.0771101

1. 8171101

1. 5581101

1.2981101

1 .0381101

7.7911100

5. 1941100

2.5971100

 

 

0 . 0001100

 

Figure 5.11 Velocity vector plot on the center plane of bp7_no_vane

 

5.1.2 New inlet design with vane spacing method

As has been discussed earlier, twin vortices representing the secondary flow
structure in a bend pipe are developed due to the pressure gradient between the outer and
the inner wall. The reason for the formation of twin vortices near the inner wall is that the
pressure gradient in the bend section forces fluid particles with low kinetic energy near
the outer wall to move along the wall from outer to inner and only some portion of the
particles move back upward against the pressure gradient due to the conservation of mass
while others are still dominated by the pressure gradient. Therefore, the way to reduce the
secondary flow intensity is fundamentally to lessen the degree of the pressure gradient,

which can be achieved by inserting vanes in radial direction as shown in Figure 5.12.

rm, pm outer wall
hm, pm lst vane (k=1)

<1

r:, p: last vane (k=n)
n, p: inner wall

 

Figure 5.12 Vane spacing with equal Ap in each divided flow passage

91

A simple way of design could be the insertion of vanes evenly between the inner
and the outer wall. However, a more effective way of design is that the vanes are inserted
so that each of the divided flow passage evenly shares the pressure gradient, for which a
generalized formula is derived and applied to obtain a new improved inlet design. The
simulation results are compared with all other designs based on the designated flow
parameters at the exit of the models.

The detailed derivation procedure for the formula is described in Appendix D and
only main equations are presented here. In order to simplify the design method, the flow
inside of the bend pipe is assumed to be inviscid and incompressible. The radial pressure
gradient is then calculated from equation (5.2) after being converted to the ordinary
derivative from equation (5.1) since the objective here is to find appropriate radial

locations on the cross-sectional area.

d V2
_P = p_ (5.2)
dr r

The Bernoulli equation is expressed as

P
— — = const. 5.3

P
Differentiating equation (5.3) with respect to r and substituting it into equation (5.2)

gives the variation of V with r as in

dV dr
_ = __ 5.4
V r ( )
By integrating (5.4), the free vortex flow pattern is reached as in
Vr = c (5.5)

92

The pressure variation is obtained by integrating equation (5.2) with respect to r after
substituting equation (5.5) into (5 .2).

2
pc 1 1
=— —-— + 5.6
p 2 [r12 r2] pl ( )

Here, c = Vr and pl is the pressure at rl , the radius of the curvature of the inner wall.

When n vanes are inserted, the radial location of each vane as shown in Figure 5.12 is
determined such that the pressure difference in each passage is identical using the

generalized formula (5.7) derived from the above equations (Appendix D).

k
pn-k+2 = pn+2 __(pn+2 _ P1)
n+1

= £n_+2_[(1_A2n)_(_:1_]2(1_ m]

(5.7)

1—A2 rn—k+2

where, k = 1, 2, 3,...n for each location of the vanes inside of the curved section and

r‘ , II =.E'_. With known inner and outer radii of the curvatures as well as the

’n+2 Pn+2

A:

 

corresponding static pressures, equation (5.7) can be used for the effective vane spacing,
indicating that vanes are located close to the inner wall and space grows toward the outer
wall to get an equal amount of pressure gradient in the divided flow passages. The
simulation of the bend pipe without vanes can give a good approximation for the pressure

information at inner and outer walls.

93

5.2 Computational models and specifications
5.2.1 Computational models

The computational models attempted for simulation are listed and described
briefly in Table 5.1, and those are classified with the number of vanes, the radius of

curvature, and vane spacing method.

Table 5.1 Inlet designs and descriptions

 

 

Design Description
sp_equi_bp Straight pipe as aerodynamic baseline
bp0_no_vane Bend pipe, the original design
bp0_vane_2 Original bend pipe with 2 vanes spaced from the generalized formula
bp0_vane_3 Original bend pipe with 3 vanes spaced from the generalized formula
bp7_no_vane Bend pipe with shorter curvature radius
bp7_even_space_3 Bend pipe with shorter curvature radius and 3 evenly spaced vanes

 

 

 

The shape and grid topology of the base models are shown in Figure 5.13, and the

designs with vanes are shown in Figure 5 .14.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) bp0_no_vane (b) bp7_no_vane

Figure 5.13 Grid topology of vaneless inlet models for simulation

94

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) bp0_vane_2 (b)bp0_vane_3 (c)bp7_even_space_3

Figure 5.14 Grid topology of vane inserted inlet models for simulation

5.2.2 Three dimensional viscous solver

TASCflow, a general purpose commercial CFD code widely used among
turbomachinery industry, is used for numerical simulation of all of the models.
TASCflow solves three-dimensional Reynolds-stress-averaged N avier-Stokes equations
with mass-averaged velocity and time-averaged density, and pressure and energy
equations. The mean form of the governing equations, expressed in a finite-volume

formulation that is fully conservative, include the following.

1. conservation of mass

8p 3
3‘...an j)

II
C

(5.8)

95

2. conservation of momentum
a a _a_p+ 3 Bu Bu!-
. =_ — S 5.9
at —(ml)+ axj —(Wj .u‘) a: +ax —-;-x{luefl[a; + axi ]}+ at ( )

where pefl = p + p,. S u,- is the momentum source term, which is zero for the simulations

of the inlet models in this section since the models are in a stationary frame.

3. energy equation

a 31’ a 3 3T [1 3h
—- H —— — -H =— ,1 t s
) + ) axj[ BXj+Prt axj]+ E

+__a__ u. ” £4.31}. _2 9&6”
ax, ‘ ‘axj 8x,- 3”‘ax, '1

where the total enthalpy is defined by H = h + gain,- + k .

 

(5.10)

The second order discretization scheme is used for the simulation and standard 1(-
8 model is adopted as a turbulence model combined with wall function approach that
eliminates the necessity of discretely resolving the large gradients in the thin, near-wall
region. The grid size ranges from 60,000 to 80,000 depending on the geometry and the
grid t0pology of each model. The convergence criterion was set to the maximum residual
of 9* 10'5 for u, v, w and p. The inflow boundary condition includes uniformly distributed
total temperature and total pressure, which are adopted from the average values of
experimental study in chapter 4. The inflow is assumed to be normal to the inlet surface
and the mass flow boundary condition is imposed on the exit surface. The wall is

modeled as hydraulically smooth with adiabatic condition.

96

5.3 Simulation results and discussions
5.3.] Flow structure affected by bend curvature

As discussed earlier in chapter 2, Kajishima (1989) carried out a numerical
simulation and showed the flow structure recovery downstream in case of laminar flow in
curved rectangular channel. The conclusion from his study is that the pressure loss in the
bend section corresponds to that in the same cross sectional area of straight duct with a
length of 6 diameters and that flow upstream of the duct is also influenced by the bend
curvature while the downstream condition seriously affects the development of secondary
flow.

The most important aspect of his study associated with the present work here is
that the developed vortices in the bend section persist far downstream after the bend
curvature and the most intensive secondary flow occurs in the middle of the curved duct
where the pressure difference between the inner and outer wall is the maximum. Since
the inlet distortion is established by the inevitable spatial limitation for the configuration
of the compressor stage, it is worthwhile to follow his study to investigate the flow
structure after being affected by the bend curvature for the present study.

Figure 5.15 shows the numerical simulation result for the original design of the
bend inlet attached with 40 diameter pipe length after the exit. Flow structure in (d)
corresponds to the exit of the bend inlet or the impeller inlet, which has severe flow
distortion near inner wall. The distorted flow structure is eventually almost recovered
downstream at the location of 20 diameter after the exit. This simulation result implies
that the possibility of the pipe length extension is not applicable to obtain clean flow

profile for the following compressor in the practical situation.

97

(a)

Level all:

-
$9
00

   
 

 

9?”???9fl?
ooooooooo

 

 

'—
I

-wuao-a---~
‘UUIVO‘ ;
_sa-_

9N9999N9993 E

00000000000

 

 

 

 

(a) pipe inlet (h) before the bend (c) after the bend (d) pipe exit (e) 10d downstream
(0 20d downstream (g) 30d downstream (h) 40d downstream (i) mesh structure

Figure 5.15 Flow structure of the original inlet with 40d pipe length extension

5.3.2 Mass flow rate weighted averaging of exit flow parameters

Normal velocity and its standard deviation, flow angle and its standard deviation,
total vorticity, and normal vorticity are considered as the measurement of the intensity of
secondary flow and the uniformity of the flow condition at the pipe exit. The nozzle
efficiency and total pressure loss information of the pipe systems are also considered as
supplemental criteria. For the quantitative simulation result comparison, mass flow

weighted average and standard deviations are taken for the selected parameters to reflect

98

 

        

..4

_ a
9~9999~9.w

 

 

 

 

    

the non-uniformity of the flow condition at the exit of each inlet model. The quantitative
numerical simulation results are summarized in Figure 5.16 to 5.18, which correspond to

three different operating points that are at near surge, design and near choke.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

600
a
.2
i 500
2
n. g, 400
h
i. a
Q a
> O
< z
3 a 200-
o
E
3 mo-
0
2
0-
sp_equl_ bp0_no_ bp0_vano bp0_va bp7_no_ bp7_e
l bp van. _2 _3 vane _spaeo_3
DVn [mls] 26.595 26.613 26.554 26.664 26.605 26.525
D 5.0. Vn [mic] 2.330 2.654 2.504 2.954 3.003 2.464
I Alta [639] 0.529 3.236 1.652 1 .506 3.459 1.409
I?! 8.0. Alta [deg] 0.003 0.060 0.027 0.023 0.065 0.016
ITotal Vortlcity [rad/s] 264.966 366.066 404.522 473.050 377.045 400.076
lNormal Vorticlty [rad/s] 0.932 146.266 104.595 66.306 146.247 61.713
IPt Loss [26] 0.0313 0.0424 0.0613 0.0994 0.0523 0.0621
I Nozzle Efficiency [96] 93.200 91.461 66.325 61.670 69.637 64.532

 

 

 

 

 

 

 

 

Figure 5.16 Mass flow averaged flow properties at inlet model exit for near surge point

As indicated in Figures 5.16 to 5.18, it is obvious that the straight pipe,
sp_equi_bp, exhibits the most uniform exit flow. For all of the designs, the exit flow
becomes more non-uniform as the mass flow increases from near choke to near surge
flow condition. This is due to the fact that higher velocity produces accelerated normal

vorticity, equivalently stronger secondary flow, and higher friction loss in the flow field.

99

 

 

 

 

 

 

 

 

Mass Flow Averaged Properties
0 DP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

200-
100-
0-
ep_equl_ bpo_no_ bp0_vane bp0_ve bp7_no_ bp7_even
1 bp vane _2 _3 vane _epeee_3
DVn [In/e] 30.699 30.941 30.693 30.967 30.959 30.676
D 8.0. Vn [In/e] 2.667 3.173 2.906 3.309 3.443 2.670
I Alta d 0.460 3.002 1.649 1.439 3.332 1 .561
D 5.0. Alta [deg] 0.003 0.059 0.026 0.025 0.063 0.017
ITotal Vortlelty [rad/e] 321.566 434.622 469.012 546.125 444.122 466.471
I Normal Vortlclty [rad/e] 0.915 169.612 120.156 99.611 167.035 93.014
I Pt Lose [36] 0.0410 0.0559 0.0611 0.1 320 0.0667 0.1093
I Neale Etllclency [96] 93.426 91 .749 66.275 61 .967 90.120 64.537

 

 

 

Figure 5.17 Mass flow averaged flow properties at inlet model exit for design point

The effect of the boundary layer is represented by the total vorticity, while the
normal velocity and the flow angle are the direct indication of the intensity of secondary
flow. In the case of the bend pipe with shorter curvature radius, (bp7_no_vane) exhibits
the worst exit flow condition as expected. In the case of the bend with shorter radius of
curvature, (bp7_even_space_3) the minimum of the exit flow angle, its deviation, and
normal vorticity is achieved. However, the flow distortion is concentrated on the inner
wall as indicated by the twin vortices, and it is predictable that the degree of concentrated

flow distortion near the inner wall will be increased with sharper bend curvature.

100

 

 

 

 

 

 

If.“

 

 

Mass Flow Averaged Properties
6 Near Choke

600
500
400
300
200
100-
“I ll lfllu I

 

 

      

 

 

 

 

 

ep_equl_ bp0_no_ bp0_vene bp0_ve - bp7_no_ bp7_even

1 bp vane _2 _3 vane _speoe_3
El Vn [In/e] 41.937 41 .961 41 .906 42.075 41.991 41 .679
C] 8.0. Vn [mle] 3.620 4.355 3.697 4.570 4.653 3.650
I Alta [deg] 0.516 3.052 1.607 1.432 3.304 1.399
El 8.0. Alta [d_eg] 0.003 0.056 0.026 0.023 0.062 0.017

 

ITotal Vortlclty [rad/g] 444.522 576.016 626.241 730.727 566.435 620.021
INormal Vortlclty [rad/s] 0.601 227.914 160.626 132.563 224.699 124.593
In Less [96] 0.0631 0.1006 0.1436 0.2370 0.1235 0.1965
INozzle Efficiency [96] 97.474 91.641 66.559 62.449 90.316 65.013

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5.18 Mass flow averaged flow properties at inlet model exit for near choke point

Figure 5.19 to 5.22 clearly show the flow structures at the exit of the models in
terms of secondary-flow vectors, contours of normal velocity, flow angle, and normal
vorticity. The designs of the original bend with 2 and 3 vanes, (bp0_vane_2 and
bp0_vane_3 respectively) show significant improvement over the original bend inlet,
bp0_no vane. As the surface vector plot in Figure 5.19 indicates, the strong twin-vortices
that exist in the case of bp0_no_vane and bp7_no_vane, do not appear with the vane
inserted models. The velocity profiles and flow angle distributions shown in Figure 5 .20

and 5.18 are a great deal more uniform for the vane inserted models, and in the case of

101

bp0_vane_2, the flow angle is decreased to 2 degree at its maximum compared to the
original bend inlet, (bp0_no_vane) that has the highly concentrated flow angle at near
inner wall up to 20 degree. This is a result of blocking the secondary flow path that is
tangential to the main flow direction. By dividing the flow passage, the secondary-flow
intensity reaches its minimum since the pressure gradient is also divided equally based on

the number of vanes inserted for each flow passage.

102

   

bp0-vane-2

sp-equi-bp

    

I..I\\\§OID".‘
IOII‘\§.IOOII
IIIOQQIIIOIIU
66.999.00.000

0000000006...
9696000000990
IOII'I'009000

 

u
e ‘ ‘ "ill

666000096600 '0‘

0 II!

III...

eeeeee

......
000000000000.
000000000000

 

'0
'00
'0

bp0-vane-3

bp7-even-space-3

oooovlllllill
neellllIIIIII

 

OUTER

e - eeOOOII'III”

6660060;”{\ :

 

e e 066\\\\“\

pr-no-vane
bp7-no-vane

 

O 0..
no;
I I’ll.-

0
00
0 I
O "0" “‘91

 

0 0 |"”’-

.
\ 9
e 9460-

 

 

 

 

Figure 5.19 Surface vector plots for all of inlet models
103

sp-equi-bp

 

 

Figure 5.20 Normal velocity contour plots for all of inlet models

 

 

 

 

 

 

 

 

 

 

 

 

 

Level vn
13 36.0
1 1 30.0
9 24.0
7 1 6.0
5 12.0
3 6.0
1 0.0
[WI/31
Level vn
1 3 36.0
1 1 30.0
9 24.0
7 16.0
5 12.0
3 6.0
1 0.0
[In/8]
Level vn
13 36.0
1 1 30.0
9 24.0
7 16.0
5 12.0
3 6.0
1 0.0
[In/8]

pr-va ne-2

 

 

104

 

 

 

 

 

 

 

 

 

Level vn
13 36.0
11 30.0
9 24.0
7 16.0
5 12.0
3 6.0
1 0.0
[mlsl
Level vn
13 36.0
11 30.0
9 24.0
7 16.0
5 12.0
3 6.0
1 0.0
[this]
Level vn
13 36.0
1 1 30.0
9 24.0
7 16.0
5 12.0
3 6.0
1 0.0
{this}

 

 

 

sp-equi-bp

pr-no-vane

 

 

 

Levelana
11 0
9

 

amour
ppprrw
06-00mm

 

 

 

 

 

 

 

 

 

[deg]
Level ana
21 200
19 160
17 160
15 140
13 120
11 100
9 60
7 60
5 40
3 20
1 00
[deg]
melmm
21 200
19 160
17 160
15 140
13 120
11 100
9 60
7 60
5 40
3 20
1 00
Ides]

 

OUTER

 

pr-vane-2

bp0-vane-3

  

Figure 5.21 Flow angle contour plots for all of inlet models

105

 

 

 

 

 

 

 

 

 

 

Lamlmm
21 200
19 180
17 160
15 140
13 120
11 106
9 60
7 60
5 40
3 20
1 00
[deg]
Lam mm
21 200
19 160
17 160
15 140
13 120
11 100
9 60
7 60
5 4D
3 20
1 00
[deg]
Level aHa
21 200
19 180
17 160
15 140
13 120
11 100
9 60
7 60
5 40
3 20
1 00
[deg]

 

 

 

sp-equi-bp

11\

     

 

 

LeveNorticity‘
21 1000.0

 

 

 

 

 

 

 

 

 

LeveNonicityl
21 1000.0
19 600.0
17 600.0
15 400.0
13 200.0
1 1 0.0
9 -200.0
7 -400.0
5 -600.0
3 -800.0
1 -1000.0
LevelVonicity,
21 1000.0
19 600.0
17 600.0
15 400.0
13 200.0
11 0.0
9 -200.0
7 -400.0
5 -600.0
3 -600.0
1 -1000.0

 

 

 

 

pr-va ne-2

 

 

 

 

 

 

 

 

 

 

 

LeveNorticityz
21 1000.0
19 800.0
17 600.0
15 400.0
13 200.0
1 1 0.0
9 -200.0
7 -400.0
5 -600.0
3 -800.0
1 1000.0
LeveNorticity,
21 1000.0
19 600.0
17 600.0
15 400.0
13 200.0
1 1 0.0
9 -200.0
7 -400.0
5 -600.0
3 -600.0
1 -1 000.0
LeveNonicity,
21 1000.0
19 600.0
17 600.0
15 400.0
13 200.0
1 1 0.0
9 -200.0
7 -400.0
5 -600.0
3 -800.0
1 -1000.0

 

Figure 5.22 Normal vorticity contour plots for all of inlet models

 

5.3.3 Total pressure loss contribution to the stage efficiency

Although the vane-inserted designs indicate the reduced secondary flow effect
and more uniformin due to the smaller pressure gradient in the divided flow passage, the
increased surface area causes more friction loss. To be able to appreciate the friction loss
contribution to the compressor stage efficiency, total pressure loss is quantified
associated with the stage efficiency in this section.

Total pressure loss in an inlet pipe, which has essentially the same aspect with
nozzle efficiency, can be another criterion as an important aerodynamic parameter. The
total pressure losses increased with vanes inserted due to the increase of the friction
surface. To have a clear appreciation of the total pressure loss in the inlet model in
relation to the contribution of stage performance, the compressor efficiency is calculated
between station 0 (inlet of the inlet model) and station 6 (compressor stage discharge),
and between station 1 (exit of the inlet model or impeller inlet) and station 6, which
includes and excludes the total pressure loss in the inlet model respectively. For the
calculation of the efficiency between station 0 and 6, the quantity from the tested data
with the original bend inlet is used. For station 1, the mass averaged numerical simulation
results are adopted for each computational model. As listed in Table 5 .2, the total
pressure losses in the inlet systems do not have significant influences on the compressor
efficiency that is dropped less than 0.3% of for all the designs.

Therefore, the increased total pressure loss by having vanes inside can be
considered as only a minor effect compared to the potential compressor performance

improvement from the reduced secondary flow effect and the more uniformity of the

107

flow. With all of the preceding discussions and the manufacturing point of view, the

design of bp0_vane_2 is most favorable.

Table 5.2 Contribution of inlet model total pressure loss to stage efficiency

 

 

 

 

 

 

Geometry (1116'006)/7106* 100

[%l
sp_equi_bp 0.09
bp0_no_vane 0. 12
bp0_vane_2 0.18
bp0_vane_3 0.29
bp7_no_vane 0.15
bp7_even_space_3 0.24

 

108

CHAPTER 6
STEADY STATE COMPRESSOR STAGE SIMULATION

6.1 Necessity of 360 model with whole passages

As has been shown and discussed in the previous chapters, the nature of the bend
passage leads to the secondary flow consisting of twin vortices, which results in severely
distorted flow, and the secondary flow effect continues with a very slow mixing process
radially and circumferentially in the flow regime, even far after the bend curvature as
shown in Figure 6.1. When a bend inlet system is used for a compressor stage with spatial

limitation, the degradation of efficiency and head for a compressor stage is inevitable

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

(Kim 2001).
outer wall
outer wall ”I”...
\\
- inner wall

 

Figure 6.1 Secondary flow structure in a bend inlet

Since the distorted flow caused by the bend inlet system is not circumferentially
axisymmetric, it is necessary for the compressor to be modeled with whole passages,

although the computation time and effort is excessively required.

109

6.2 Computational model and specification
6.2.1 CFD model description

TASCflow is a general purpose, commercially available CFD code, widely used
among turbomachinery industry. For the present study, TASCflow is used for steady-
state compressor stage numerical simulation. The validation of this code for the
configuration of centrifugal compressors can be found, for example, in the work of
Flathers (1994, 1999). TASCflow solves three-dimensional Reynolds-stress—averaged
Navier—Stokes equations with mass-averaged velocity and time-averaged density and
pressure and energy equations. The mean form of the governing equations, expressed in a

finite-volume formulation that is fully conservative, include the following.

1 . Conservation of mass

8p 8
_ _ . = 6.1
at +an J) O ( )

2. Conservation of momentum

a 6 ap a an, an,-

—— - +—— -u- =-—+— —+— +S- 6.2
Where fleflr = ,u + [1,. Sm. is the momentum source term for the impeller in the rotating

frame of reference. The effect of Coriolis and Centn'petal forces are modeled in the code

by including

“

s -—2§2xr7-r”2x(fzx7) (6.3)

ui"

110

3. Energy equation

d 31’ a 3 8T ,1! 8h
_ H __ _ -H =___ ,1— _L__ S
(p ) at+BX' u} ) axj'[ an+PrtBXj]+ E

+3... u. EEL+§EL -2.” 9.116..
3x!- ‘fl‘ 8x}- ax, 3 ‘ax, '1

where the total enthalpy is defined byH = h+-;-u,-u,- +k. In the rotating frame of

(6.4)

2 2

 

reference, the rothalpy I = H — a) is advected in the energy equation in place of the

total enthalpy. (.0 is the rotation rate, and R is the local radius.

For the sliding interfaces between stationary(inlet and diffuser) and
rotating(impeller) components, two models are available : one is the “frozen rotor model”
and the other is the “stage model”. The stage model circumferentially averages the fluxes
at the interface before the interpolation of the flow variables across the different frame of
reference although the pressure distortion caused by any perturbation, for example the
impeller and the diffuser leading edge, is still allowed. For axisymmetric inlet flow
Condition, the stage model can be used with the advantage of modeling one or two
passages having a periodic boundary condition for the tangentially-neighbored blade
Passages instead of modeling fully 360 degree passages, which is significantly
economical for computation time and effort.

On the other hand, the frozen rotor model achieves a frame change across the
interface without a relative position change over time as well as without any interface
averaging of flow variables. The details of the numerical algorithm and methodology can

be found in Galpin et al. (1995). This model is an exact representation of the case when

111

the Strouhal number is zero, in which case either the sound speed is infinite or the
impeller rotating speed is zero. Therefore, when the Strouhal number is small enough
such as the compressor stage simulation presented here (St is between 0.1423 and 0.1431,
depending each inlet models), the predicted simulation result is an approximation of the
real situation. Flathers and Bache (1999) used this model to predict the radial force of an
impeller. In the case of the frozen rotor model, all of the passages have to be modeled and
this model is adequate to investigate the influence of the distorted flow caused by the
bend inlet along the compressor stage flow passages since local flow features are allowed
to transport across the interface, and thus, the non—uniformities of flow variables among
the passages can be predicted, which results in different flow conditions at the

compressor stage exit.

6.2.2 Grid generation and boundary condition

The compressor stage models used for numerical simulations include 17 impeller-
blade passages and 16 diffuser-vane passages as a fully 360 degree compressor model,
With the attachment of three different inlet models : sp_equi_bp, pr, and bp2, which are
developed and used for the numerical simulation in chapter 5. The model, sp_equi_bp, is
used for the baseline of the compressor aerodynamic performance comparison without
the secondary flow and the distortion effect, and pr is the original bend inlet. Since the
actual compressor system includes an inlet casing as a part of the volute casing between
the inlet and the impeller, the grid of each inlet is generated with the inlet casing as a
Whole block. An inlet casing is essentially a nozzle, and the purpose of having the inlet

Casing is to make the boundary layer blockage thinner for the flow before the impeller

112

and to improve mainly the velocity profile at the impeller shroud. However, in the case of
the compressor with bend inlet system, the further acceleration of the flow in the inlet
casing after the distortion upon the bend curvature aggravates the flow distortion and
cause more incidence at the impeller leading edge.

In order to properly model the proposed new inlet, bp2 in chapter 5, the
compressor stage simulation with pr is carried out first and the static pressures at the
bottom and the top wall of bp0 inlet model are evaluated to find the radial location of the
vanes to be inserted in the bend passage using the generalized formula (equation 6.5)

developed in chapter 5.

r...:, p.62 outer wall
rm, pm 1st vane (k=1)

9)

r:, p. last vane (k=n)
n, p. Inner wall

 

Figure 6.2. Vane spacing for the location of each vane to be inserted in bp2 model

It
Pn-k+2 = Pn+2 — _(Pn+2 ‘ P1)
71 +1

=.131112_[(1_A2n)_[_’1_]2(1 41)]

(6.5)

1 - A2 rn-k+2

113

where, k = l (the first vane) and 2 (the second vane) for bp2 inlet model

 

A=r_1, n = I" (r4 and r1 are the radial locations of the top and the bottom
r n+2 pn+2

wall, p4 and p1 are the static pressures at the top and the bottom wall)

The grid of the three inlet models is shown in Figure 6.3. For the inlet model, bp2,
two vanes are modeled with zero thickness, for which the grid block boundary is used, to
avoid disturbance on the flow regime. For each of the three inlet models, an inlet casing
is attached at the end as a whole block. The convention of the stations used for the
compressor stage performance calculation is indicated in Figure 6.4. Station 1 and 2 are
the impeller leading and trailing edge, and station 3 and 4 are the diffuser leading and

trailing edge, respectively. Station 0 is the inlet of each inlet model as a compressor stage

inlet.

  
 

Vanes based on the formula

 

(a) pr (original bend inlet) (b) bp2 ( two vane inserted model)

114

.e‘
,a

' 1

 

 

(c) sp_equi_bp

Figure 6.3 Grid of inlet models used for compressor stage simulation

 

 

 

 

 

 

shroud

 

hub

mug;

Figure 6.4 Convention of the stations on compressor cross-section

 

 

 

 

 

 

 

 

 

 

 

 

Table 6.1 summarizes the grid sizes for each component and entire stage. The
node indices, 1, J, and K for the impeller and the diffuser are along the meridional,
Circumferential(pitchwise), and radial(spanwise) direction. The grid of the full impeller

and diffuser passages at mid span is shown in Figure 6.5

115

Table 6.1 Grid size of each component and entire stage for numerical simulation

 

 

 

 

 

Inlet Model with Inlet Caslng lixK One Passage Model lixK Z Entlre Stage
sp_equi_bp 263460 impeller 47x17x15 17 670245
bpo 281880 diffuser 47x18x15 16 688665
bp2 251696 658681

 

 

 

 

 

 

  
  
 
 
     
  

   
  
   

1:1’; 'Oo.‘
,;;'Il,;'o”'
q, r0,",

1,, 'I’II/ /

  
      
      

-, —.,

        
     
 
   

  

.-
‘r...
..
‘6
-
«3.x —

‘
‘
\\\

  
   

“‘
'- \\s

a \
\\\““ ‘_—
~. xx‘

~.\

    

  
 
  
  

 
  

, o

a - o

. , - o o,

,- - o o. 3

-..:.:.,.,o.:-.
‘ O O O .. '.
.‘~~. 0...,‘

Figure 6.5 Grid of 360 degree impeller and diffuser

The second order discretization scheme is used for the simulation and standard k-
8 model is adopted as a turbulence model combined with wall function approach that
eliminates the necessity of discretely resolving the large gradients in the thin, near-wall

region. The convergence criterion was set to the maximum residual of 104 for u, v, w,

116

 

and p. The inflow boundary condition includes uniformly distributed total temperature
and total pressure, which are adopted from the average values of experimental study in
chapter 4. The inflow is assumed to be normal to each of the stage inlet surface, and the
mass flow boundary condition is imposed on the diffuser exit surface. The wall is
modeled as hydraulically smooth with an adiabatic condition. Frozen rotor models are
adopted at the interfaces between the stationary and the rotating frame of reference : one
at the interface between each of inlet model and the impeller, the other between the
impeller and the diffuser, which allow the inlet distortion influence to be propagated
across the different frame of reference and the pressure distortion due to the perturbation
caused by the impeller blade and the diffuser vane leading edge as described in the

previous section.

6.3 Impeller-diffuser interaction

The interaction between an impeller and a vaned diffuser is essentially an
unsteady phenomenon caused by the perturbation due to the diffuser vane leading edge,
which causes non-uniformities of the flow properties upon the different mass flow
distribution and, thus, large circumferential distortion among the impeller and the vaned
diffuser passages at instantaneous circumferential passage alignment between the
impeller and the vaned diffuser.

Fisher and Inoue (1981) investigated the impeller-diffuser interaction
experimentally with a low speed centrifugal compressor for four different diffusers. They

observed large pitchwise variation among the passages at the impeller exit and concluded

117

that the interaction between the impeller and the vaned diffuser is dependent on the
leading edge of the diffuser vanes.

Dawes (1995) carried out a numerical study to capture the unsteady interaction
between a splittered centrifugal impeller and a vaned diffuser and observed very large
periodic variations of velocity and flow angle in the entry zone to the diffuser. From the
comparison between the unsteady time-averaged flow and the steady-state flow, the
principal cause of the rather high loss levels observed in the diffuser is due to the strong
spanwise distortion in swirl angle at the inlet, which initiates a strong hub corner stall
rather than the unsteady effects.

Shum et. al. (2000) conducted a study of unsteady effects on impeller-diffuser
interaction using numerical simulation for three different radial locations of the diffuser
vane leading edge. They identified the consequent changes at the impeller exit with
increasing interaction for smaller radial gap between the impeller exit and the diffuser
vane leading edge. They concluded that the interaction can be mainly characterized as
reduced slip, reduced blockage, and increased loss with the smaller radial gap and when
the diffuser vane leading edge is getting closer to the impeller than the optimum gap, the
increased loss overcame the benefits of the reduced slip and blockage. Although the
changes in loss, blockage, and slip are due largely to unsteadiness, the consequent
impacts on performance are mainly one-dimensional and the influence of flow
unsteadiness on diffuser performance is found to be less important than the upstream

effect.

118

flu

 

 

 

Fatsis et al. (1995) suggested the use of the acoustic Strouhal number in the case
of compressible flow to quantify the relative effects of the rotation and pressure wave

propagation. The acoustic Strouhal number is defined as
St = E (6.6)

Here, L is defined as the average length of a impeller blade passage, f is the number of
rotations per second times the number of perturbation waves around the circumference.
After the compressor stage simulations, the Strouhal number is evaluated with the
sound speed based on the average static temperature in the impeller passage and is shown
to be between 0.1423 and 0.1431, depending on the inlet models at design flow rate when
f is replaced by rotation frequency, which indicates that the pressure wave propagation is
much faster than the rotation of the impeller. In other words, the pressure perturbation
finishes traveling over the passage almost at the same time as when the impeller moves to
a new position. Therefore, the frozen rotor model can be used for the compressor stage
simulation presented here to include the pressure distortion and the impeller-diffuser
interaction influence on the calculation of flow variables, which is due to the diffuser
vane leading edge of non-periodic passage alignment between the impeller and the

diffuser.

6.4 Simulation results and discussions

The compressor stage simulation results are presented based on circumferentially
mass flow rate weighted averaging of flow variables at four stations for three different
flow rates. The influence of each inlet model on the stage efficiency, the head coefficient

as well as on the axial distortion between the impeller exit and the diffuser inlet are

119

quantitatively compared. In addition, total pressure loss coefficient and pressure recovery
coefficient for the diffuser are evaluated from the simulation results for each of inlet
models.

Stage performance is compared for each inlet model based on three different flow

coefficients that are defined as

It 2
—DU
42 2

and the isentropic head coefficient between stage inlet and diffuser exit is given by

 

 

7_—l
P
C p700 {—01} 7 -1
P 00
ll’o—4 = 1 2 (6-8)
—U2
2
The stage efficiency calculation is based on
:1
[Pi 7 -1
P
176.. = 0", (6.9)
i _
Too

Figures 6.6 and 6.7 compare the head coefficient and the stage efficiency from the
numerical simulation for three inlet models with the experimental test results from the
work of chapter 4. As it indicates, the bp2 model with two vanes inserted, based on the
generalized formula, improved the efficiency by 3.11% at higher flow rate, 2.88 % at the

design flow rate, and 2.17% at lower flow rate.

120

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2
fi—-————-‘\‘
1.0 ~~——~ ———+ ~— -~
r 3. u ‘H \
0.8 .__- — \
0.6
0 4 q +SP (EXP wl volute)
+ BP (EXP wl volute)
0 2 +SP_EQUI_BP (CFD)
' + 3P0 (CFD)
-— BP2 (CFD)
000 T U I T
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
What
Figure 6.6 Head coefficient comparison
1.2
1.0 J——
Bah-H
0.8 ~ ‘\
0.6 ____. \
0 4 4 +SP (EXP wl volute) \\
+ BP (EXP wl volute)
0 2 +$P_EGUI_BP (CFD)
' + 990 (cm)
... BP2 (cm)
0.0 r . . .
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
W910

Figure 6.7 Stage efficiency comparison

121

... -.

."

 

 

The reason for more efficiency improvement at higher flow rate is due to the fact
that the flow distortion caused by the secondary flow in the case of the original bend inlet
becomes more severe for higher mass flow rate and by inserting two vanes in the bend
curvature, the secondary flow effect has been significantly reduced, which results in
relatively more efficiency improvement. The discrepancies of the stage efficiency and the
head coefficient between the experimental and the numerical simulation results are due to
the volute effect, where more total pressure loss occurs, especially at the off-design point,
since the volute is not modeled for the numerical simulation for the work of this chapter.

In order to investigate the diffuser performance influenced by the inlet distortion,
total pressure loss coefficient and diffuser pressure recovery coefficient between stations
3 and 4 are calculated and presented in Figure 6.8 and 6.9. Total pressure loss coefficient

based on the diffuser inlet dynamic pressure is given by

 

Y3_4 = RB _ B4 (6.10)
P23 "' 1[’3
and the diffuser pressure recovery coefficient is defined as
P4 — P3
C p 3_4 = (6.1 1)
P13 " P 3

Total pressure loss comparison indicates smaller magnitude in the diffuser in the
case of bp2 model compared with bp0 model as shown in Figure 6.8. As a consistent
result , the improvements are made relatively more at higher flow rate upon the reduced
secondary flow effect and thus, smaller incidence at the diffuser leading edge. This
tendency also appears in the comparison of diffuser pressure recovery coefficient as

shown in Figure 6.9.

122

In the case of pr, as shown in Figure 6.10, flow angle is remarkably reduced,
implying severe incidence especially at the hub region of the impeller. Clearly, the bp2
model reduced this effect considerably and improved flow angle in terms of the
magnitude as well as the uniformity at both hub and shroud region.

Mach number comparison at design flow is shown in Figure 6.11. The
discrepancy of Mach number between pr and bp2 model implies that total pressure loss
is smaller in the impeller in the case of bp2 model. The higher Mach number near the
shroud region is caused by locally low static temperature upon relatively high radial

velocity.

0.5

 

 

 

 

 

 

0.4 + SP_EGUI_BP -0- 8P0 + BP2

 

 

 

 

 

0.3

0.2
\M”:

0.0
0.80 0.90 1.00 1.10 1.20 1.30

MM

 

 

 

 

 

 

 

 

 

 

 

 

Figure 6.8 Total pressure loss coefficient comparison

123

 

0.80

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.70 + SP_EOUI_BP + 8P0 + BP2
Mafia 7“ \_-______
g: \
o 4%
0.50 d————r~~— \
0/
0.40 «~——— ——
0.30
0.80 0.90 1.00 1.10 1.20 1.30
(ll/(Par
Figure 6.9 Diffuser pressure recovery coefficient comparison
80
g %
7o -
Iggy-I"
gfi /
50 x
a. /
o 1: :1:
0
g. 50
‘5‘
40
+ SP_EOUI_BP CSTATION2 +SP_EQUI_BP 08TATION3
30
+ 8P0 GSTATION2 + 8P0 OSTATIONS
-O- BP2 08TATION2 -II- BP2 CSTATION3
20 I V f I I I I I I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
hub - shroud

Figure 6.10 Flow angle comparison

124

0.70
0.65
0.60
0.55
0.50

0.45

Mach GDP

0.40
0.35

0.30 + SP_EOUI_DP QSTATIONZ + SP_EQUI_DP GSTATION3
025 + 8P0 OSTATION2 -l- 8P0 OSTATION3
+ BP2 OSTATIONZ -0- BP2 OSTATIONI!

 

0.20
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

hub - shroud

Figure 6.11 Mach number comparison

125

CHAPTER 7

EXPERIMENTAL TESTING WITH VARIOUS DIFFUSERS

7 .1 Specifications of the tested diffusers

Three different diffusers are tested to investigate the contribution of diffuser
performance to the compressor stage performance downstream of the same impeller,
combined with two different inlet pipes at three different impeller rotating speeds. The
experimental test rig setup and the procedure are mostly similar to what has been
previously presented in chapter 4. With each inlet system, three different diffusers are
installed alternately on the compressor test rig and each diffuser is tested at three different
impeller rotating speed. The detailed specifications of the three diffusers are summarized

in Table 7.1.

Table 7.1 Specifications of three different diffusers (angle based on tangential)

 

 

 

 

 

D'FFUSER TYPE 91’”: l' 3" 2 '4" 3 WM: 536 546 29: '- '3 (=53: " as) Z 0
CVND #1 I flat-cambered 1.0 1.07143 1.4881 2.4 21.20 35.68° 11° 0.2793 0.25 16
CVND #2 I airfoil-cambered 1.0 1.07143 1.4881 " 21.2o 35.68° 11° ' ' 16
LSVD I flat-straight 1.0 1.07143 1.1447 - 7 ° ° - - 16 0.613

 

 

 

 

 

 

 

 

 

 

 

 

 

CVND#2 differs geometrically from CVND#l in terms of the vane leading edge
radius and vane thickness distribution for the purpose of improving structural integrity.
CVND #2 has a smaller vane leading edge radius and an airfoil shape of blade thickness
distribution. Both of CVND #1 and #2 are cambered with blade angle 21.2° at its leading
edge and 35.68° at its trailing edge with reference to tangential direction. LSVD has a

solidity equal to 0.613 and is designed for the smaller stage of compressor than the one

126

used for the present study. The experimental testing purpose for LSVD is to see the
performance contribution to a larger compressor stage and was expected to possibly
result in efficiency sacrifice with wider stable operating range. The actual vane shapes of

the three diffusers are shown in Figure 7.1 to 7.3.

 

Figure 7.1 Vane shape of CVND #1

 

Figure 7.2 Vane shape of CVND #2

127

 

Figure 7.3 Vane shape of LSVD

7.2 Design procedure of a conventional vaned diffuser

The design procedure for the tested conventional vaned diffuser is presented in
Aungier (1997) and the geometry of the vaned diffuser design is shown in Figure 7.4.
The leading edge radius at diffuser inlet is estimated by

r3/r2=l+a3/360+M22/15 (7.1)

Equation (7.1) provides additional vaneless space to diffuse high Mach number flows
from impeller before entering diffuser inlet. The discharge radius is based on the vane
passage length, L3, the equivalent divergence angle, 296. the vane loading, L, and the area

ratio, A3, with constant vane height (b3 = b4).

r dr '
LB - risin ,3 (7.2)

’3

 

128

tan 0c = ”(r4 Sin fl4 - r3 Sln fl3)/(ZLB) (7.3)

 

L = 27Z'(T3C93 — T4C94)

 

 

 

 

 

 

 

 

 

 

 

(7.4)

ZLB (C3 " C 4 )
AR = r4 8111 54 /(r3 Sin £3) (7.5)

. 04
re T
Figure 7 .4 Geometry of conventional vaned diffuser design

Since the vane height is fixed to be constant

AR = W4 /W3 (7.6)
Where W is the effective passage width and is given by

W = (2msin ,B)/Z (7.7)

129

 

Relating equation (7.7) with equations (7.3) and (7.5) yields
20, = 2tan'1[(W4 —W3)/(2LB )] (7.8)

Vane loading is evaluated after the average vane-to-vane velocity difference is computed

from potential flow theory, related with the change in angular momentum.
_ L
ACLB = f(Css - CPS )d6 = 275(73C93 " T4C94)/Z (7.9)
0

Since the inlet and discharge flow angles for a vaned diffuser are approximately match

the corresponding blade angles at the design flow

 

X? = C3W3 [cot 133 - (r4 /r3)C,4 cot 04 IC,3 ]/ LB (7.10)

Finally, the vane loading is obtained as

L: AC (7.11)

 

Since a vaned diffuser has its diffusion limit to avoid possible stall and at the same time

needs to achieve its maximum static pressure recovery, the limit criteria are set as
26C 511” (7.12)

l
Lg_ 7.13
3 ( )

As equation (7.11) indicates, the vane loading is an approximation to the ratio of the
average vane-to—vane pressure difference to the inlet-to-discharge pressure difference
based on incompressible flow analysis. The vaned diffuser performance is then evaluated
With static pressure recovery coefficient as a measure of the conversion of kinetic energy

to static pressure between the inlet and discharge of the passage.

CP = M (7.14)
P13 " P3

130

7.3 Design procedure of a low solidity vaned diffuser
7.3.1 Singularity method

The singularity method has been applied successfully by Kannemans (1977) to
analyze the flow in curved vane diffusers. The method is based on a source, Q, and a
vortex, F at the center in order to allow an easy generation of the diffuser inlet flow

conditions.

 

Q = Cr22flr2 (7-15)

F = C92 27172 (7. 16)

The influence of the vanes is implemented by vortices on the camberline or on the

contour. Van den Braembusche (1990) gives the velocity component C, and C9 in each

point of the flow field in r-0 coordinates by equations (7.17) and (7.18).

z - 7019’) sin[z - (0-0’)] ds,+ .2.
4m cosh[z - ln(r’/ r)] — cos[z - (6 - 6')] 2m

 

C,(r,6) = -§ (7.17)

C (r 0) 9127026,) Sinlz'lnwr’” ds’+—l:— (7 18)
a ’ 470' cosh[z - ln(r’/ r)]—cos[z - (0 —0')] 2m“ .

 

where r' and 6' are the local coordinates at the single vortices 7(r',6') that can be

defined by imposing that the flow is tangential to the vane or to the camber line.

131

 

 

 

 

Figure 7.5 Singularity method

7.3.2 Conformal mapping

As the flow in a radial turbomachine is much more complicated than in an axial
machine, no satisfactory calculation method exists for the radial cascade. Therefore, it is
advantageous to use the experience of axial machines by transforming the radial cascade
into an axial one and determining the required data, after which these data can be
converted by retransformation. The geometric approach that is based on complex
numbers is called conformal mapping and leads to geometrically similar triangles, which
means the same angles but distorted distances. Figure 7.6 shows an example of conformal

mapping of a radial cascade into an axial cascade.

132

Axlaleaseade
z-plane

(

 

 

 

 

 

 

 

 

 

 

Figure 7.6 Conformal mapping of a radial cascade into an axial cascade

Schlichting (1954) distinguishes two kinds of problems that appear most frequently.

Indirect problem :

The known quantities are the directions of the inflow and the outflow (e. g. the
velocity diagram), and the unknown quantities are the geometry of the cascade and
the geometry of the vane section as well as the pressure distribution on the vane.
Direct problem :

The known quantities are the geometry of the cascade and the geometry of the vane
profile, whereas the unknown quantities are the resulting aerodynamic force on the
vane, the pressure distribution, and the direction of the outflow, all of which are

functions of the direction of the inflow.

133

 

In other words, in the case of the indirect problem, the aerodynamics of the cascade are
given and the geometry is required, while the direct problem is the reverse of the indirect
problem. Faulders (1954) presented detailed mathematics of conformal mapping for
conventional cascades. Using the Cartesian x-y coordinates in the z—plane and the polar r-
0 coordinates in the C-plane that are related by equation (7.19) and (7.20). One can

achieve the simple transmitting function (7.21), adopted from Koppenfels et. a1. (1959).

¢ = y (7.19)
r = eJr (7.20)
g = e2 (7.21)

Faulders also gives information on how to calculate the velocity and the pressure
distribution. Smith (1970) corrects the presented transformation for compressible flow by

implementing the Mach number.

7.3.3 Geometric relations

The geometry and the design parameters of a LSVD with straight vanes are
shown in Figure 7.7. The design method is based on the maximum solidity which means
the highest possible solidity without forming a throat.

The difference of [33 and [34 results in the vane turning angle 0, which is given by
9 = fl4 - fl3 = a4 "'a3 (7.22)
In a radial cascade, B3 is called the stagger angle. By applying the cosine law to get an

expression for 1]

r32 = 52 + r32 — 2r3scosn (7.23)

134

 

s = 2r3 cosn (7.24)

z -1 _.._ . -1 - 92
77 cos [2’3] cos [srn[ Z ]] (7.25)

where the inlet radius, r3, and the number of vanes, Z are known.

 

 

Figure 7.7 Geometry of a LSVD design with maximum solidity

Equation (7.26) gives the angle, 1; that is needed to calculate the throat, t, and vane

length, l, by simple sine and cosine relations in equations (7.27) and (7.28).

C = fig + (90" -n) (7.26)

135

 

= s - sin 4' (7.27)
l = 5 ~ cos C (7.28)
The outlet angle, [34, and the outlet radius, r4, are given in equations (7.29) and (7.30) by

using the sine law.

P -

 

 

 

 

. [180)
23111 7 t
-1 bl
= tan tan + - 7.29

fl4 '63 cos ,8, 2r3 sin ,63 ( )

where tb, is the vane thickness at the leading edge of the vane.
,4 z ,3 005 133 (7.30)

cos 6,,

The exact vane geometry is shown in Figure 7.8. It shows the diverging shape of the vane

with the leading and trailing edge in detail.

 

trailingedge _________ _ ____ _
’pressuresurface

  
 
  
  

 

suction surface
straight line

/"7rr“7~

 

’

'\ \\I

Figure 7.8 Exact vane geometry of flat plate LSVD vane

 

 

 

136

As the vane contour does not form a single line, the vane length has to be corrected by

introducing the adjusted vane length, lad]. , that is given by

‘61
l . =l+ 7.31
adj 213nfl3 ( )

 

With pitch or space, s , from the previous calculation, the maximum solidity can be

obtained.

_ lad}
S

0' (7.32)

7 .4 Throat area variation in a varied diffuser

As has been discussed earlier, a vaneless diffuser is used for a wider operating
range for a compressor stage because of the absence of a throat. However, the long
logarithmic spiral path of the particle leads to great friction loss and reduced efficiency
for the compressor stage. To enhance the pressure recovery and the stage efficiency, a
vaned diffuser is used at the expense of the flow range. The reduced flow range at higher
mass flow rate results from the formation of aerodynamic throat area including a
blockage effect due to the local boundary layer. Since a vaned diffuser is typically
designed to have a smaller throat area than the impeller does, the aerodynamic throat area
of the diffuser determines the maximum flow rate, indicating that the Mach number based
on the local absolute velocity reached one at the throat.

The flow angle at the diffuser inlet can be used to explain the relationship
between the variation of the throat area and the flow range in detail since the flow angle
is the aerodynamic parameter depending on the radial velocity component of the local

mass flow rate. Figure 7 .9 shows the throat area variation based on the flow angle change

137

at the diffuser inlet. a", is the flow angle with reference to the radial direction and based

on the flow direction following the centerline of a diffuser passage.

 

that

   

passage centerline
/ vaneless space
// /' \ semi-vaneless space

i

\

 

 

 

Figure 7.9 Throat area variation upon inlet flow angle change in a vaned diffuser

If the flow angle becomes larger than amf , which is the case of near stall point, the
throat area will increase causing flow deceleration and thereby increase pressure recovery
in the semi-vaneless space before the throat area. On the other hand, if the flow angle
becomes smaller than are}. , which is the case of near choke point, the throat area will
decrease, which causes flow acceleration in the vaneless space after the exit of impeller.
When the effect is excessive, it will lead to choke as a maximum flow rate for the

compressor stage. In this case, the pressure recovery will be reduced significantly

because of the reduction of the static pressure rise due to high acceleration of the flow.

138

 

Therefore, if the flow angle in a diffuser is designed to be larger, equivalently
more tangential inlet flow angle in a diffuser, the operating range will increase since the
choke will happen at a higher mass flow rate, which indicates that the velocity at the
throat reached sonic only with the magnitude increase in the same direction.

A low solidity vaned diffuser is recently used widely for the advantages of the
competitive efficiency with a vaned diffuser and the compatible operating range with a
vaneless diffuser for a compressor stage. A low solidity vaned diffuser is designed
without having a throat area (“maximum solidity”) and the lack of a throat makes a wide
operating range possible. In this case, the compressor choke limit is determined by the
impeller throat area when the Mach number based on the local relative velocity reaches
one, which allows the choke limit to move with a different impeller rotating speed more

than the case that the limit is controlled by a conventional vaned diffuser.

‘ 7 .5 Experimental results and discussions

All of the experimental test results shown in Figure 7.10 to 7.33 are based on the
compressor stage performance only and the measurement of flow range from choke to
mild surge point. Although the detailed measurement for individual diffuser performance
has not been carried out, one can clearly see the contribution of each diffuser on the

performance of the compressor stage by comparing the results in detail.

7.5.1 Comparison of choke limit

The compressor choke limit difference with the three types of diffusers at the

design speed are indicated in Figures 7.28 to 7.33.

139

Comparing CVND#l and CVND#2, the choke limit is shifted to somewhat higher mass
flow in the case of CVND#2. This difference is caused by the smaller leading edge radius
and the thinner vane thickness distribution for CVND#2 at the inlet as shown in Figure
7.1 and 7.2. In the case of LSVD, the choke limit is significantly changed since the limit
is controlled by the impeller throat while CVND#l and CVND#2 are controlling the
choke limit with their throats. It can also be noticed that the choke limit change is
distinctive upon the rotating speed change in the-case of LSVD compared to CVND#l

and CVND#2.

7.5.2 Comparison of mild surge limit

Surge is an unstable system phenomenon, and the indication is that the unstable
flow in the compressor starts making noise upon its periodic oscillations in the entire
system. At small mass flow rate, the reduction of flow necessitates a lower pressure
production by the compressor, and instantaneously, the back pressure is higher than the
delivery pressure. The flow will then stop because the delivery cannot be maintained
against the adverse pressure gradient and the load in the compressor will be cleared,
resulting in lowering back pressure and starting the delivery again. This periodic and
reversed flow may take place gently with the instability of pressures, which is known as
mild surge, and violently with frequent loud noise and high fluctuation of pressure, which
is known as violent surge and can cause structural damage on the machine. Surge can be
precipitated by either impeller stall or diffuser stall, depending on the design of

compressor. Aungier (1997) stated that vaned diffuser stall is almost inevitably closely

140

followed by compressor stage surge for the stage pressure ratio above 1.7, which is the
case of CVND#l and CVND#2 for the present study.

Since the violent surge limit is not measured on a strict basis and the measurement
is limited only to mild surge to avoid possible structural damage on the machine, the
behaviors of the compressor with CVND#l and CVND#2 at different rotating speed are
not clear enough to explain the tendency in terms of rigorous surge lirrrit. However, by
comparing CVND#l and CVND#2, it can be seen clearly that the surge limit is improved
somewhat in the case of CVND#2 at the expense of somewhat lower efficiency and head
than those from CVND#l. The results for LSVD as shown in Figure 7.22 implies that
surge is not controlled by LSVD but by the impeller for all of the three rotating speed
while the results with CVND#l and CVND#2 indicate that the control of surge is on the
diffusers. Therefore, the tested low solidity vaned diffuser is successful in terms of the
wide flow range without indication of diffuser stall up to mild surge point and with the

increased choke limit for the absence of a throat.

7.5.3 Comparison of stage performance

All of the experimental results showed the stage performance difference between
straight and bend inlet. As discussed in chapter 4 and 5, the stage performance difference
is caused by the intensified flow angle, and thus incidence due to the pressure driven
secondary flow upon the bend curvature of the original inlet before the impeller inducer.
The efficiency difference is dominantly based on the head rise difference between
straight and bend inlet while the work input difference has only minor influence on the

stage performance and shifted upward with higher impeller rotating speed as one can

141

expect. This tendency appears for all of the three diffusers and the head rise difference is
significant in the order of CVND#l, CVND#2 and LSVD as clearly shown in Figure
7.29. Considering the geometric difference among the three diffusers, these results imply
that the total pressure loss in the diffuser is influenced by the throat area of the diffusers.
In the case of CVND#l with smallest throat area, the head rise difference between
straight and bend inlet is indicated by the largest value among the three diffusers, and the
difference is the minimum in the case of LSVD.

The static pressure ratio differences between straight and bend inlet for three
different rotating speed are shown in Figure 7.14, 7.20, 7.26, 7.32. The static pressure
ratio between straight and bend inlet is identical for CVND#l, and almost identical for
LSVD for all of the three different rotating speed. On the other hand, the static pressure
ratio increases gradually with the decrease of the mass flow rate and the increase of the
rotating speed for the bend inlet in the case of CVND#2.

Overall stage efficiency comparison at the design speed as shown in Figure 7.28
indicates that CVND#l has the maximum peak efficiency with the minimum flow range
and CVND#2 has nearly the same performance with the advantage of wider flow range
both at mild surge and choke points for its smaller leading edge radius and thinner vane
thickness distribution at its throat. Although LSVD has the minimum performance, the
flow range is significantly widest among the three diffusers for the absence of a throat

with reasonable efficiency for not having a stall leading to the compressor surge.

142

1.2
1.1
1.0
0.9
0.8
0.7

,3 0.6- -e-srreigni (4016611)

0.5 1 -e-Bend (4096011)

 

 

 

 

 

 

 

 

”1'1

 

 

 

 

 

 

 

 

 

 

 

 

E

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0-4‘ —a—Stralght (Design Speed)

0-3‘ +Bend(Deslgn Speed) \

0'2“ +Simigni 01016011) L

3': +Bend(+1096011)

.030 0.46 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.90
11191.1

Figure 7.10 Stage efficiency for straight and bend inlet with CVND#l

 

1.2
1.1
1.0
0.9
0.8 \
0.7

g 0.6 + +Stralght (-1096 off)

3 0.5 . -e—Bend (4096011)

0-4 1 -a- Straight (Design Speed)
03 ‘ -e- eend (Design Speed)
0'2 4 err—Straight (+1096 011)

0.1 .
-x— Bend (+1 096 011')
0.0 .

0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80
Wm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 7.11 Head coefficient for straight and bend inlet with CVND#l

143

1.50

 

1.35

 

1.20 ~——~-

 

 

 

1.05

0.90

 

 

 

 

 

 

 

 

I
i 0.75 4 +Straight (4096011)

 

0.60 . -e-Bend (-1096 011)
0.45 , -a—Stralght (Design Speed)

 

 

 

 

 

 

 

 

 

 

 

 

0 30 ‘ —e—Bend (Design Speed)
0 15 +Stralght (+1096 011)
-x— Bend (+1096 011)
0.00 . . . . .
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

Mini

Figure 7.12 Work coefficient for straight and bend inlet with CVND#l

1.5

1.4 +Sln|9hl (4096011) -e-Bend(-10% off)
-a— Straight (Design Speed) + Bend (Design Speed)
"3 +Straigni (44096011) -x—eend (+10%
1.2
1.1
I
e 1.0
It
0.9
0.8
0.7

0.6

 

0.5
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

Mini

Figure 7.13 Total pressure ratio for straight and bend inlet with CVND#l

144

0" I.

 

“5 1 4 I 1 i 1 l I I
1.4 _. +Stralght (4096011) -e—Bend (4096011)

-a- Straight (Design Speed) + Bend (Design Speed)
—rir— Straight (+1096 011) —x— Bend (+1096 011)

 

1.3 1-

 

 

1.2

 

 

 

 

1.1 -~——-+-

'2
1.31.0
E

 

 

 

0.9

 

 

 

 

 

0.8

 

 

0.7 ——

 

 

0.6

 

 

 

 

 

 

 

 

 

 

 

 

0.5
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

MM

Figure 7.14 Static pressure ratio for straight and bend inlet with CVND#I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.5
I l l l I l I I I
1_4 .. +Stralght (-1096 01‘!) +Bend (-1096 011)
-B- Stralght (Design Speed) -e- Bend (Design Speed)
"3 ‘“ +Sireigni (+10960fl) -x—Bend (+1096011)
1.2
1.1
I
130-
g 1.0 T
0.9
0.8
0.7
0.6
0.5
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80
We:

Figure 7.15 Total temperature ratio for straight and bend inlet with CVND#l

145

1.2
1.1 —
1.0 ‘—--—- -—
0.9 -—— —~
0.8 — a.___
0.7
1} 0.6 - +Streigni(-10% all)
r.- 0.5 . -9- Bend (-1096 oil)
0-4 ‘ -a- Straight (Design Speed) 7

0'3 ‘ +Bend (Design Speed)
0.2 «

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+Straight (110960")
0.1«
-x—Bend(+1096010
0.0 I I I T
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

91910

Figure 7.16 Stage efficiency for straight and bend inlet with CVND#2

1.2
1.1
1.0
0.9
0.8
0.7

\5 0.6~ +Stralght (4016611)

5 0.51 -e-Bend (4096011)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0-4~ -a—Stralght (Design Speed)
03} +Bend(Deslgn Speed)
0'2 +Stralght (11096011)
0.1-
-x—Bend(+10960fl‘)
0.0 . . . .
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.60

9,910

Figure 7.17 Head coefficient for straight and bend inlet with CVND#2

146

{‘OV‘

 

1.50

 

1.35 «~—

 

 

1.20 ——

 

 

 

1 .05

0.90

 

 

 

 

 

 

 

 

I
i 0.75 1 -6- Straight (-1096 011)
0.60 . -9- Bend (-1 0% Off)
045 4 -a— Straight (Design Speed)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

030‘ +Bend (Design Speed)
+Stral ht +1096
0.151 9 ( Off)
+Bend(+10960fl)
Dem I I fi I I
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

91910

Figure 7.18 Work coefficient for su‘aight and bend inlet with CVND#2

1.5

1.4 +3991“ (4096011) -e-eend (401601)
-a- Straight (Design Speed) + Bend (Design Speed)
+ (+1096 0") —x— Bend (+1096 011)

1.3
1.2
1.1

I
i! 1.0

E
0.9
0.8
0.7

0.6

 

0.5
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

(W10

Figure 7.19 Total pressure ratio for straight and bend inlet with CVND#2

147

 

1.5

1.4 -a— Straight (-1 096 off) . —0- Bend (-1096 off)
—8- Straight (Design Speed) —0— Bend (Design Speed)
* +10% Off) -x—Bend (+10%

1.3
1.2
1.1

'2
131.0

I:
0.9
0.6
0.7

0.6

 

0.5
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.85 1.80

91910

Figure 7.20 Static pressure ratio for straight and bend inlet with CVND#2

1.5

1.4 -e- Straight (-1 096 off) -9- Bend (-1096 off)
-a- Straight (Design Speed) + Bend (Design Speed)

"3 + +10% —x—eend +10%

1.2
1.1
I
13’ 1.0
3'
0.9
0.8
0.7

0.6

 

0.5
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

91910

Figure 7.21 Total temperature ratio for straight and bend inlet with CVND#2

148

 

1.2

 

 

1.1

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0
0.9
0.6 __r
/
I 0.7 .. l1
1: 0.6
E- 0 5‘ +Stralght(-109601‘f) \\
' -e— Bend (4096611) \L
0.4 «
o 3 - -a—Streight (Design Speed) \\ \ \
' + Bend (Design Speed) \\
0.2 -
+Stralght(+10960fl) 1L 3),
2'; ‘ -x- Bend (+10% 011)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9,910

0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

Figure 7.22 Stage efficiency for straight and bend inlet with LSVD

1.2

 

1.1

 

 

1.0
0.9

 

0.8

 

 

 

 

 

0.7

 

 

 

 

 

I

2- 0.6 1

a
0.51
0.4 1
0.3 1
0.2 1
0.1 1

 

0.0

-e- Straight (4091. on)

-e- Bend (40% 011)

-a- Straight (Design Speed)
-e- Bend (Design Speed)
+ Straight (+10% 011)

-x— Bend (+10% 011)

 

 

 

 

 

 

 

ll

\

 

 

 

 

 

 

 

 

11.11%—

 

 

0.30 0.45 0.60 0.75 0.90

1.05
9,910

1 .20

1.35

1.50

f

1.65

1.80

Figure 7.23 Head coefficient for straight and bend inlet with LSVD

149

1.50

 

1.35

 

 

 

1 .20

1.05

 

 

0.90

 

 

 

 

 

 

 

 

 

'E
i 0.75 1 +Straight (~1096 011)
0.60 J -e- Bend (40% off)
045 ) -B—Stralght (Design Speed)

 

 

 

 

 

 

 

 

 

 

 

 

 

0 3O 4 -e—Bend (Design Speed)
+Strai ht +1096
0.15 1 9 ( OH)
-x— Bend (+1096 011)
0.00 . . . .
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

91910

Figure 7.24 Work coefficient for straight and bend inlet with LSVD

1.5

1.4 +Sml9ht (4096011) -e—,Bend (409601)
-a- Straight (Design Speed) —e— Bend (Design Speed)
‘1'" +10% -X- Bend (+1096

1.3
1.2
1.1

r

9' 1.0

it
0.9
0.8
0.7

0.6

 

0.5
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

91910

Figure 7.25 Total pressure ratio for straight and bend inlet with LSVD

150

1.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.80

I I L I I I I I I l

1.4 .. +Straight (4096011) -e-Bend (4096011)

—a— Straight (Design Speed) -e- Bend (Design Speed)
‘13” +St1aight (+109601f) —x—Bend (+10960fl)
1.2
1.1

$1.0 :FF
0.9 rme_.a_afifii=fittofi
0.8
0.7 k m
0.6 1~—~
0.5
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65
M10

Figure 7.26 Static pressure ratio for straight and bend inlet with LSVD

1.5
1.4
1.3
1.2
1.1
I
13’ 1.0
B
0.9
0.8
0.7
0.6

0.5

0.30 0.45 0.60 0.75 0.90

-e— Straight (-1 096 off)
-a- Straight (Design Speed)
+ +1096

1.05
9,910

1.20 1.35

1.50

-9- Bend (-1 096 011)
-e- Bend (Design Speed)
-x— Bend (+1 096 Off)

 

1.65

1.80

Figure 7.27 Total temperature ratio for straight and bend inlet with LSVD

151

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2
1.1
1.0
59”
0.9 ——e
0.8 we
><//’r V,
E 0.7 \
E 0.6
1.- 0 5 -e— Straight CVNDiii
0.4 -e— Straight CVND#2
0.3 -a-Straight LSVD \
0‘2 -e- Bend CVND“ \\
' + Bend CVND#2 ii,
0.1 «
-)t- Bend LSVD
0.0 .

 

 

 

 

 

 

0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

11910

Figure 7.28 Stage efficiency with three diffusers at design speed

1.2
1.1
1.0
0.9
0.8
0.7

I
g 0.6
5-
0.5
0.4
0.3
0.2
0.1

0.0

0.30 0.45 0.60 0.75 0.90

-e- Straight CVND“

-e- Straight CVND#2
-a- Straight LSVD
+ Bend cqusi
+ Bend CVND#2
+ Bend LSVD

 

1.05 1.20 1.35 1.50 1.65 1.60
91910

Figure 7.29 Head coefficient with three diffusers at design speed

152

 

1.50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.35
1.20 3*
1.05
0.90
I
i 0.75 1 +StraightCVND#1
0.60 . -O-Stralght CVND#2 _
0.45 . -a-Stralght LSVD
0.30 ‘ +Bend CVND#1
+ Bend CVND#2
0.15 1
-x— Bend LSVD
0.00 . f . .
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

i
e-
E

91910

Figure 7.30 Work coefficient with three diffusers at design speed

 

"5111111111

1.4 1 1 -&- Straight CVND” -e— Straight CVND#2 -B-$tra|9ht LSVD

 

1.3 1* + Bend CVND“ + Bend CVND#2 -)(— Bend LSVD

 

 

1.2

 

 

1.1

 

1.0

 

 

0.9

 

 

 

 

0.8

0.7 \
, it)...

0.6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.5
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

9191.1

Figure 7.31 Total pressure ratio with three diffusers at design speed

153

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.5
I I I I I I I J I

1.4 -I -e—St1aight CVND#1 -e—Stralght CVND#2 -a-St1aight LSVD
1.3~~ +send CVND“ +eend CVND#2 -x—Bend LSVD
1.2

1.1

'2

131.0 x:

E

0.9

0.6 \

0.7 \99

0.6

0.5
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.60

N910

Figure 7.32 Static pressure ratio with three diffusers at design speed

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.5
I I I I I l I I I
1.41~-e-Straight cquiii +Stralght cqusz -a-Straight LSVD 1
1.3- -e-BendCVND#1 +eend CVND#2 -x-eend LSVD 1

1.2
1.1 T—-—
‘E x—
1: 1.0 —«
3 ~"El
0.9
0.8
0.7
0.6
0.5 *1 1
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1.50 1.65 1.80

91910

Figure 7.33 Total temperature ratio with three diffusers at design speed

154

CHAPTER 8
CONCLUSION

As has been presented, in the curved section of a bend pipe, secondary flow is
developed due to the pressure gradient, more fundamentally caused by the difference of
the centrifugal force between the inner and the outer wall and results in distorted flow
profile, non-uniform intensified flow angle for the following compressor as well as more
frictional loss compared to the equivalent mean line length of straight pipe.

In the experimental test part in chapter 4, the compressor performance
degradation is clearly shown and discussed with the comparative test results between the
two different inlet configurations. The conclusion from the experimental study is that the
flow distortion from the bend inlet influences significantly on the compressor stage
performance by having non-uniform flow angle distortion at inducer and non-uniform
total pressure distribution in the blade passages. These cause incidences, boundary layer
separation, and possibly impeller stall for the compressor, especially at off design
condition. As a result, head rise is deteriorated significantly compared to the straight inlet
configuration although the work inputs for two inlet models remain essentially the same,
which finally results in the efficiency degradation.

In the numerical simulation section in chapter 5, the simulation results are
presented to understand the detailed flow structures of the inlet pipes and the mechanism
of the flow distortion in the bend inlet. Based on the conclusion that the work input
difference is very small between the two inlet configurations from the experimental part,
the new design of inlet models having vanes inside have been proposed with the

simulation results, which clearly indicate the improvement for the designated flow

155

 

properties compared to the original bend inlet at the exit of the model. A generalized
formula has been developed to obtain an effective design of the inlet in terms of the
location and the number. Twin counter rotating vortices in the original design of bend
inlet vanished, and the flow becomes more uniform for the vane inserted models.
Especially, the two-vane inserted design on the basis of the original bend inlet and the
generalized formula showed the advantages among other designs. The expectation from
the new design is to bring head rise improvement and hence efficiency recovery from the
original bend inlet configuration.

In chapter 6, steady-state compressor stage simulations are carried out with three
different inlet models to investigate the effectiveness of the proposed inlet model on the
improvement of the stage efficiency as well as the flow profiles in the vaneless space
between the impeller exit and the diffuser leading edge. The conclusion from the stage
simulation is that the proposed inlet model indeed improved the stage efficiency about
3% for three different flow rates compared to the results with the original inlet model.

In chapter 7, additional experimental tests are carried out to investigate the
contribution of three different diffusers to the compressor stage performance as well as
the influence of the inlet distortion on the performance. CVND#l indicated the maximum
peak efficiency while the flow range is relatively narrow compared to CVND#2.
Comparing CVND#l and CVND#2, the choke limit is shifted to higher mass flow in the
case of CVND#2, which results from having the smaller leading edge radius and the
thinner vane thickness distribution at its throat area. LSVD showed widest flow range for
the absence of an aerodynamic throat with reasonably good efficiency compared to

CVND#l and CVND#2. The experimental results indicated that the surge limit is

156

controlled by the diffuser in the case of CVND#l and CVND#2 and by the impeller in
the case of LSVD.

For all of the diffusers, the inlet distortion influence are shown clearly for the
stage performance, which is dominantly based on head rise difference while the work

inputs for all of the diffusers have only a minor difference.

157

BIBLIOGRAPHY

Anwer, M. and SD, R., 1993, “Swirling turbulent flow through a curved pipe, Part I:
Effect of swirl and bend curvature”, Experiments in Fluids 14, pp. 85—96.

Ariga, 1., Kasai, N., Masuda, S., Watanabe, Y. and Watanabe, 1., 1982, “The Effect of
Inlet Distortion on the Performance Characteristics of a Centrifugal Compressor”, ASME
Paper 82-GT-92.

Ariga, I., Masuda, S. and Ookita, A., 1986, “Inducer Stall in a Centrifugal Compressor
with Inlet Distortion”, ASME Paper 86-GT-139.

Aungier, R., 1988a, “A Systematic Procedure for the Aerodynamic Design of Vaned
Diffusers”, ASME FED-Vol. 69, pp. 27-34.

Aungier, R., 1990, “Aerodynamic Performance Analysis of Varied Diffusers”, Fluid
Machinery Components, ASME FED-Vol.101, pp. 27-44.

Aungier, R., 1993, “Aerodynamic Design and Analysis of Vaneless Diffusers and Return
Channels”, ASME Paper 93-GT-101.

Aungier, R., 1997, “Design of Centrifugal Compressor Stage for Enhanced Operating
Range and Head Rise”, a report by Aungier, made available for the work in this
dissertation.

Cain, SA. and Padmanabhan, M., 1999, “Numerical Simulation of Flow Distribution and
Swirl due to a Combined Pipe Bend”, ASME/ISME Joint Fluids Engineering
Conference, FEDSM99-7217. '

Camatti, M., Betti, D. and Giachi, M., 1995, “Vaned Diffusers Development using
Numerical and Experimental Techniques”, ASME Paper No 95-WA/PID-4.

Came, P. and Herbert, M., 1980, “Design and Experimental Performance of Some High
Pressure Ratio Centrifugal Compressors”, AGARD-CP—282.

Casey, M. and Marty, F., 1986, “Centrifugal Compressors - Performance at Design and
Off-Design”, Proc. of the Institute of Refrigeration, London, pp.7l-80.

Cheng, KC. and Lin, RC. and Ou, J.W., 1975, “Fully Developed Laminar Flow in
Curved Rectangular Channels”, ASME Paper, 75-FE-4.

Clements, W. and Ant, D., 1987, “The influence of diffuser channel geometry on the

flow range and efficiency of a centrifugal compressor”, Proceedings, Institution of
Mechanical Engineers, Vol. 201, No A3.

158

 

Clements, W. and Arrt, D., 1988, “The influence of diffuser channel length-width ratio
on the efficiency of a centrifugal compressor”, Proceedings, Institution of Mechanical
Engineers, Vol. 202, No A3.

Cumpsty, N.A., 1989, Compressor Aerodynamics, University of Cambridge, Longman
Scientific Technical, UK.

Dawes, W., 1995, “A Simulation of the Unsteady Interaction of a Centrifugal Impeller
with its Vaned Diffuser : Flow Analysis”, ASME Journal of Turbomachinery, Vol.117.

Dean, R., 1976, “The fluid dynamic design of advanced centrifugal compressors”, Creare
Inc., TN-244.

Deniz, S, Greitzer, E. and Cumpsty, N., 2000, “Effects of Inlet Flow Field Conditions on
the Performance of Centrifugal Compressor Diffusers: PartZ-Straight Channel Diffuser”,
ASME Journal of Turbomachinery, Vol. 122.

Eckardt, D., 1976, “Detailed Flow Investigations Within a High-Speed Centrifugal
Compressor Impeller”, ASME Journal of Fluids Engineering, pp.390-402.

Eckardt, D., 1980, “Flow Field Analysis of Radial Backswept Centrifugal Compressor
Impellers - Part 1: Flow Measurement Using Laser Velocimetry”, in Performance
Prediction of Centrifugal Pump and Compressors, ASME Fluid Conference.

Elder, R. and Forster, C., 1987, “Flow in Centrifugal Compressor”, VKI Lecture Series
1987-01.

Fatsis, A., Pierret, S., Van den Braembussche, R., 1995, “3D Unsteady Flow and Forces
in Centrifugal Impellers with Circumferential Distortion of the Outlet Static Pressure”,
ASME Paper 95-GT—33.

Fauldcr, C., 1954, “An Aerodynamic Investigation of Vaned Diffusers for Centrifugal
Compressors”, MIT Gas Turbine Lab.

Filipenco, V., Deniz, S, Johnston, J ., Greitzer, E. and Cumpsty, N., 2000, “Effects of Inlet
Flow Field Conditions on the Performance of Centrifugal Compressor Diffusers: Part1-
Discrete-Passage Diffuser", ASME Journal of Turbomachinery, Vol. 122.

Fisher, E. and Inoue, M., 1981, “A Study of Diffuser/Rotor Interaction in a Centrifugal
Compressor”, Journal of Mechanical Engineering Science Vol. 23.

Flathers, M., Bache, GE, 1999, “Aerodynamically Induced Radial Forces in a

Centrifugal Gas Compressor: Part 2-Computational Investigation”, ASME Journal of
Engineering for Gas Turbines and Power, Vol. 121, pp. 725-734.

159

 

Flathers, M., Bache, GE. and Rainsberger, R., 1994, “An Experimental and
Computational Investigation of Flow in a Radial Inlet of an Industrial Pipeline
Centrifugal Compressor”, ASME Paper 94-GT-134.

Ghia, K.N. and Sokhey, IS, 1977, “Laminar Incompressible Viscous flow in Curved
Ducts of Regular Cross-Sections”, ASME Journal of Fluids Engineering, pp. 640-648.

Hayami, H., Senoo, Y. and Utsonunriya, K., 1989, “Application of a Low Solidity
Cascade Diffuser to Transonic Centrifugal Compressor”, ASME Paper No 89-GT-66.

Hohlweg, W., Direnzi, G. and Aungier, R., 1993, “Comparison of Conventional and Low
Solidity Varied Diffusers”, ASME Paper No 93-GT-98.

Hunziker, R. and Gyarmathy, G., 1994, “The Operational Stability of a Centrifugal
Compressor and its Dependence on the Characteristics of the Subcomponents”, ASME
Journal of Turbomachinery, Vol. 116.

J apikse, D., 1996, “Centrifugal Compressor Design and Performance,” Concepts ETI Inc.

Jiang, T. and Yang, T., 1982, “Improved Vane-Island Diffusers at High Swirl”, ASME
Paper No 82-GT-68.

Johnson, M.W. and Moore, J., 1983, “Secondary Flow Mixing Losses in a Centrifugal
Impeller”, ASME Journal of Engineering for Power, Vol.105, pp.24-32.

Johnson, M.W., 1978, “Secondary Flow in Rotating Bends”, ASME Journal of
Engineering for Power, Vol. 100, pp.553-560.

Kajishima, T., Miyake, Y. and Inaba, T., 1989, “Numerical Simulation of Laminar Flow
in Curved Ducts of Rectangular Cross Section”, JSME Series II, Vol. 32, No. 4, pp. 516-
52.

Kannemans, H., 1977, “Calculation of 3D Incompressible potential flow by means of
singularities in mixed flow machines” VKI Project Report 1977-01.

Kenny, D., 1972, “A Comparison of the Predicted and Measured Performance of High
Pressure Ratio Centrifugal Compressor Diffusers”, ASME Paper No 72-GT-54.

Kim, Y., Engeda, A., Aungier, R. and Direnzi, G., 20006, “The Influence of Inlet Flow
Distortion on the Performance of a Centrifugal Compressor and the Development of
Improved Inlet Using Numerical Simulations. Part I - Experimental Test Comparison for
Compressor Stage Performance”, ASME IMECE, PID-Vol. 5, pp. 109-1 15.

Kim, Y., Engeda, A., Aungier, R. and Direnzi, G., 2000b, “The Influence of Inlet Flow

Distortion on the Performance of a Centrifugal Compressor and the Development of
Improved Inlet Using Numerical Simulations. Part II —- Development of Improved Inlet

160

for a Centrifugal Compressor Using Numerical Simulations”, ASME IMECE, PID-Vol.
5, pp.l39-146.

Kim, Y., Engeda, A., Aungier, R. and Direnzi, G., 2001, “The Influence of Inlet Flow
Distortion on the Performance of a Centrifugal Compressor and the Development of
Improved Inlet Using Numerical Simulations, IMechE Part A, Journal of Power and
Energy, Vol. 215, pp.l-16.

Kline, S. J., Abbott, D. E., and Fox, R.W., 1959, “Optimum Design of Straight Walled
Diffusers”, ASME Journal of Basic Engineering, pp. 321-331.

Krain, H., 1981, “A Study on Centrifugal Impeller and Diffuser Flow”, ASME Journal of
Engineering for Power, Vol.103, pp.688-697.

Krain, H., 1988, “Swirling Impeller Flow,” ASME Journal of Turbomachinery, Vol. 110,
pp.l22-128.

Lakshminarayana, B., 1995, “Fluid Dynamics and Heat Transfer of Turbomachinery”,
Wiley-Interscience Publication.

Moore, J. and Moore, J., 1979, “A Calculation Procedure for Three-Dimensional,
Viscous, Compressible Duct Flow. Part I — Inviscid Plow Considerations”, ASME
Journal of Fluids Engineering, Vol.101, pp.415-422.

Moore, J. and Moore, J., 1979, “A Calculation Procedure for Three-Dimensional ,
Viscous, Compressible Duct Flow. Part II- Stagnation Pressure Losses in a Rectangular
Elbow”, ASME Journal of Fluids Engineering, Vol.101, pp.423-428.

Osborne, C. and Sorokes, J., 1988, “ The Application of Low Solidity Diffusers in
Centrifugal Compressors”, Flow in Non-rotating Turbomachinery Components, ASME
FED-Vol. 69, New York.

Reeves, G., 1976, “Estimation of Centrifugal Compressor Stability with Diffuser Loss
Range System”, ASME Gas Turbine Conference.

Reneau, L., Johnston, JP. and Kline, S., 1967, “ Performance and Design of Straight,
Two Dimensional Diffusers”, ASME Journal of Basic Engineering.

Roberge, LA. and Mathisen, RR, 1999, “Sensitivity Analyses to Assess the Use of CFD
to Predict the Occurrence of Vortices near Pump Intakes”, ASMFJJSME Joint Fluids
Engineering Conference, FEDSM99-7224.

Rodgers, C., 1978, “A Diffusion Factor Correlation for Centrifugal Impeller Stalling”,
ASME Journal of Engineering for Power, Vol. 100, pp. 592-602.

161

 

 

Rodgers, C., 1982, “The Performance of Centrifugal Compressor Channel Diffusers”,
ASME Paper No 82-GT-10.

Runstadler, P., and Dean, R., 1969, “Straight Channel Diffuser Performance at High Inlet
Mach Numbers,” ASME Journal of Basic Engineering, Vol. 91, pp. 397-422.

Schlichting, H. 1987, “Boundary Layer Theory”, translated by Kestin, J., McGraw-Hill,
7‘h edition.

Seidel, U. and Rautenberg, M., 1994, “Method for Predicting Choke Flow in Varied
Radial Diffusers based on Thermodynamics and Gas Dynamic Criteria, ASME Paper,
94-GT-157.

Senoo, Y. and Kinoshita, Y., 1977, “Influence of Inlet Flow Conditions and Geometries
of Centrifugal Vaneless Diffusers on Critical Flow Angle for Reverse Flow”, ASME
Journal of Fluids Engineering, pp.98-103.

Senoo, Y. and Kinoshita, Y., 1978, “Limits of Rotating Stall and Stall in Vaneless
Diffuser of Centrifugal Compressors”, ASME Paper 78-GT-19.

Senoo, Y., 1984, “Vaneless Diffusers”, Flow in Centrifugal Compressors, VKI Lecture
Series 1984-07.

Shum, Y., Tan, C. and Cumpsty, N ., 2000, “Impeller-Diffuser Interaction in a Centrifugal
Compressor”, ASME Journal of Turbomachinery, Vol. 122.

Smith, V., 1970, “A Review of the Design Practice and Technology of Radial
Compressor Diffusers”, ASME Paper No 70-GT-116.

So, R. and Anwer, M., 1993, “Swirling turbulent flow through a curved pipe, Part H:
Recovery from swirl and bend curvature”, Experiments in Fluids 14, pp. 169-177.

Sorokes, J. and Welch, J ., 1992, “Experimental Results on a Rotatable Low Solidity
Vaned Diffuser”, ASME Paper No 92-GT-19.

Stein, W. and Rautenberg, M., 1985, “Flow Measurement in two Cambered Vane
Diffusers with different Passage Widths”, ASME Paper No 85-GT-46.

Stodola, A., 1927, “Steam and Gas Turbines. McGraw-Hill Inc.
TASCflow Version 2.9 Users Manual, 1999, Advanced Engineering Computing.

Van den Braembussche, R., 1984, “Surge and Stall in Centrifugal Compressors” VKI
Preprint 1984-15.

162

 

Van den Braembussche, R., 1990, “Design and Optimization of Centrifugal
Compressor”, VKI Course Note 141/T U.

Wiesner, F., 1967, “A Review of Slip Factors for Centrifugal Compressors”, ASME
Journal of Engineering for Power, pp.558-572.

Wilson, D., 1993, “The Design of High-Efficiency Turbomachinery and Gas Turbines,”
The MIT Press, 6th edition.

Yoshinaga, Y., Gyobu, I., Mishina, H., Koseki, F. and Nishida, H., 1980, “Aerodynamic

Performance of a Centrifugal Compressor with Vaned Diffusers”, ASME Journal of
Fluids Engineering, Vol.102, pp.486-493.

163

APPENDIX A

Representation of non-uniform flow promrtx distribution over cross-sectional area
1. Mass flow weighted average

X= . (Al)
2’";

 

2. Mass flow weighted standard deviation

EKXi'YMiP

Wiz
I

 

(A.2)

 

APPENDIX B

Definitions of the efficiency used

1.Nozzle efficiency (total to static between station 0 and 1)

_ boo-hr _ Too (13.1)

2. Compressor stage efficiency including inlet model total pressure loss (total to total

between stations 0 and 6)

wit-1151*
hos P00 (3.2)
no 6: ”06‘h00 O6

[is]

164

3. Compressor stage efficiency excluding inlet model total pressure loss (total to total

between stations 1 and 6)

Lil
_"063 "'01_ P01

3.3)
’71 — 6 (
h06 ”'01 [T06 ]_1

701
For all of the efficiency calculation, mass flow averaged values at the exit of each pipe

[stationl] from numerical simulation are used to consider the non-uniformity of the flow.

APPENDIX C

Exit flow rofile location and flow an e definition used

 

l
outer wall a = tan"[(u2 + v2); lw]

\ (u2 +v 2)3

(1.
normal axis
. / exit surface for the reference of
inner wall flow property comparison
X [u]

 

 

L Z[w]

Y [v]

Figure C.1 Location of exit flow profile and flow angle definition

165

 

APPENDIX D

Derivation of a formula for effective vane spacing in curved Pipe

The vertical location of the vanes inside of the curved section of the pipe is based
on the formula developed here. The purpose of the idea with vane spacing calculation is
to make the pressure gradient equal for each of vertically divided flow passage by the
vanes. Although the final equation is only approximate with the assumption that the flow
in the pipe is incompressible, inviscid, ignorable secondary flow effect with the proper
spacing of vanes to obtain simple and possible solution, the numerical simulation result
showed that the equation developed here works reasonably well for the case of relatively
large radius of curvature. Since the equation used here only for the cross—sectional area in
the curved section of the pipe, the partial relationship for the pressure and the velocity
can be transformed to the ordinary derivative with the function of the radius of

curvature(r) only.

2 2

9513: Z;—=const. =>%=p1r- (DJ)
1 2

p, = p+-2-pV = const. (D2)

Taking derivative of (2) with respect to r gives,

_+pV-—:O (D'3)

166

 

 

From (1) and (3),

2
V dV => V _d.___V =_d_Z=—§I-=> ln(Vr) =C0nSt.:-°-V =2 (1)-4)
r dr r dr V r r

‘9
|
u

1':

<
l
|
u

Therefore, the flow over any cross—sectional area in the curved section is free vortex.

From (1) and (4),
_p_p_c2__c =Idp-J—c dr=' p-c __c2 (D5)
dr r3 r3 r3 H I r2 .

Rearranging of (5) to get c1, c; with the boundary values of the pressure at r1, r2 gives,
rlzplzrlzcl—c2 4: p=platr=rl (D.6)

rzzp2 = r226l —c2 <2 p = p2 at r = r2 (D.7)

 

(7)—(6) to getcl; c,(r22—rlz)=r22p2 -42“ , C1:

167

For simple representation,

 

_ 2
cl=p2(l A2“) ,whereA=—r'—, I'I=-p—'
l-A r2 p2
To get c2, substitute (8) for c, of (7) and eventually get,
c2=r12p2 _1_-_l'_:. ,whereA=-r!-, =31-
l—A r2 p2
Substitute (8) and (9) for c1 and cz of (5),
r 2 r
.-.p=-£Z-2— (1—A2n)— —' (l—II) ,whereA=—‘, n=1’—'-
l—A r r2 p2

(D8)

(D9)

(D. 10)

With the known geometric information for n and r2, the equation above can be used with

p; and p; which can be obtained either from the simulation of the curved pipe without

vanes inside or from the measurement at the location of the end of the curved section

with static tabs.

Casel : Vane spacing with 2 vanes inside (4 = outer, 1 = inner).

1'4, p4
1'3, p3
r2, p2
1'1, p1

 

 

1
P4‘P3 =P3—P2=P2-P1=§(p4-Pl)

168

(<=p1&p4,r1&r4areknownand A=-r-'-, H=-El-)

r4 174

For 1'3, [)3

1
P4—P3 =§(p4—pl)

 

2

1 r

p3=p4--(p4-pl)= p42 (1-A2H)- —‘ (l-H) =>getr3,p3
3 l-A r,

For r2, pg

1
p3 -p2 =§(p4-p.)

 

2
l 2 r
P2 = P3 _§(p4 ‘17:): P4 "§(P4 "P.) = 1 p22 [(1’A2H)-['—L] (1—I'I):l => get 1'2,

Case2 : Vane spacing with 3 vanes inside (5 = outer, 1 = inner).

l
P5_P4=P4"P3=P3"P2 :Pz‘Pi =Z(Ps-Pi)

 

(<=p1&p5,r1&r5areknownandA=r—', H=-p—l)
’5 P5
For r4,p4
1
Ps-P4=Z(P5—P1)
1 P5 2 r1 2
p4=p5-—(ps-p1)= 2(1-AU)- — (1‘11) ”8619434
4 l-A r4
For r3, P3

1
P4—P3 =Z(P5—Pl)

169

 

2
l 2 p r
p3 = p4 —-‘—"—(p5 —pl): p5 —Z(p5 —pl)=1_:32|:(1—A2H)-(i) (1—1'I)] => gCII'3,p3

For r2, pz

1
P3 "Pz =Z(P5 _p|)

 

2
1 3 p r
102 = p; -Z(p5 -p.) = p5 ‘ZU’S -p1)= l_22l:(1—A’-II)—[i] (141)] => get r2, p2

Case3 : Vane spacing with n vanes inside (n+2 = outer, 1 = inner).

rm», pm outer wall
rm, pm lst vane (k=1)

0

n, p: last vane (k=n)
n, p: inner wall

 

The generalized formula to obtain r2, p; to rm], pm] is

 

2
k p +2 2n ’1 H
12..-,” pm n+1(p”+2 p') l—AZ [( ) [new] ( {I ( )

where, k = l, 2, 3, n for each location of the vanes inside of the curved section.

’1

 

 

A = , II = p, from the known values of r1, r“... and p1, pm.
r

n+2 pn+2

170

IIIIIIIIIIIIIIIIIIIII

rIIliulrwzlwmzlllmw[I