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THESIS

7,901

 

LIBRARY
Michigan State
University

 

 

 

This is to certify that the

dissertation entitled

Investigation of the Flow Structure and Loss Mechsnlsm in n Centrifugal
Compressor Volute

presented by

Hooman Rezaei

has been accepted towards fulfillment
of the requirements for

mo. _ Mechanical Engineering
degree 1n

 

 

AEA

' D
M ajor fessor

4/12/01
Date

 

MS U is an Affirmative 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 ' I DATE DUE DATE DUE

 

minim].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 c:/CIRC/DateDue.p65—p~ 15

INVESTIGATION OF THE FLOW STRUCTURE AND LOSS MECHANISM IN

A CENTRIFU GAL COMPRESSOR VOLUTE

By

Hooman Rezaei

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Mechanical Engineering

2001

ABSTRACT

INVESTIGATION OF THE FLOW STRUCTURE AND LOSS MECHANISM IN

A CENTRIFUGAL COMPRESSOR VOLUTE

Hooman Rezaei

A spiral-shaped volute is used in many applications of compressors to collect the
rotating flow, which discharges from a diffuser downstream of the impeller, and to
deliver it into a single discharge pipe. The performance and design of volutes has not
received the detailed study given to the other components of compressors. This can be
attributed to the fact that the volute is a simple collecting device and all the necessary
difliision has been achieved in the vaned or vaneless diffuser upstream of the volute.
The volute is usually designed through the application of one-dimensional analysis. A
design objective is to achieve a uniform pressure distribution at the volute inlet. This is
usually attained at the design flow rate only; at off-design conditions the volute is either
too small or too large and pressure distortion develops circumferentially around the
volute passage. The static pressure distortions are transmitted to the diffuser exit, the
impeller discharge, and even through the inducer. Therefore, these pressure distortions

reduce the stage performance and have a direct impact on diffuser and impeller stability.

In the present study, a Trane CVHF 1280 two-stage centrifugal compressor,
which is used in air-conditioning applications, was modified to a single stage. Air
replaced the refrigerant gas and a new motor replaced the old driving system. The
compressor’s inlet and outlet components were modified to accommodate the
performance evaluation experiments. The data acquisition system was developed to
measure static, total temperatures and pressures at diffuser, volute casings, inlet and
outlet pipes. Measurements have been performed at three speeds of 2000, 3000 and 3497
RPM in order to evaluate the performance of this compressor and its volute.

In addition, Fluent 5.0 was utilized to simulate the flow in this compressor
utilizing the experimental and meanline analysis data as the boundary conditions. An
unstructured grid was generated in GAMBIT for the region of vaneless diffuser inlet to
the volute cone outlet. The simulations were performed for adiabatic flow in this flow
path to extract the flow structure and calculate the performance of the components. The
numerical results are in a good agreement with the experimental ones, which validates
the simulations. Furthermore, the flow properties were extracted for various cross
sections of the volute and vaneless diffuser from the simulation results in order to
investigate the flow structure inside these components at off design condition. These
results revealed the deviation of the volute flow from the free vortex design
methodology in all cases. In addition the compressor performance improved as speeds
and mass flow rates increases because the losses decrease for those conditions. The
losses corresponding to tongue region were inevitable and design modifications were

discussed to reduce the effect of the tongue and improve the compressor performance.

Covyright
Hooman Rezaei

2001

To my parents for all their
sacrifices throughout their
lives to enjoy this moment

AKNOWLEDGEMENT

The author deeply appreciates his advisor, Professor Abraham Engeda, for his
guidance and support throughout this research work and especially the establishment of
the experimental facility. The Turbomachinery group of Trane Company has supported
this investigation financially and provided the compressor, components, modification
designs, technical and design information of this compressor. The author would like to
thank Mr. Paul Haley as the group manager and Mr. Rick Groth for his extensive help on
behalf of the Trane Company. Sincere thanks to the Ph.D. guidance faculty members,
Professors Craig Somerton, John McGrath and Chi Chia Chiu, for their guidance,
discussions and interest in this work.

During the course of the experimental setup Mr. Roy Bailiff, the
research/instruction equipment technician of the Mechanical Engineering Department
helped significantly, for which the author is thankful. The author enjoyed and
appreciated the help and technical discussions of the members of the Turbomachincry
Laboratory at Michigan State University, Mrs. Yunbae Kim, Patrick Gayle, Steve
Barabash and Dr. Fahua Gu.

The author would like to acknowledge Professor Manoochehr Koochesfahani and
the members of the Turbulent Mixing Laboratory at Michigan State University, Drs.
Bemd Stier, Chuck Gendrich, Richard Cohn, Colin Mackinnon and Mr. Doug Bohl for

their support in extending the scientific skills required for this study.

vi

Throughout the program the author has enjoyed extensively the love and support
of his wife, Mrs. Stephanie Bonin. She had significant input in preparing this dissertation

and concluding publications, which made him more grateful of her company.

vii

TABLE OF CONTENTS

LIST OF FIGURES
NOMETCLATURE

CHAPTER 1: INTRODUCTION
1.1 Compressors
1.2 Compressor theory
1.3 Compressor components
1.3.1 Inlet
1.3.2 Impeller
1.3.3 Diffuser
1.3.4 Bend and return channel
1.3.5 Volute
1.4 A Preliminary design procedure for a two stage centrifugal compressor
1.4.1 First stage
1.4.2 Second Stage
1.5 Significance of the volute and current challenges
Figures

CHAPTER 2: LITERATURE SURVEY
2.1 Flow in compressor volutes

2.1.1 Flow mechanism

2.1.2 Static pressure distribution

2.1.3 Velocity distribution

2.1.4 Numerical analysis
2.2 Volute design

2.2.1 Volute Geometry

2.2.2 l-Dimensional Design

2.2.3 Frictionless Design

2.2.4 Design with fn'ction

2.2.5 Area ratio distribution

2.2.6 Novel ideas
2.3 Volute performance

2.3.1 Overall performance

2.3.2 Performance Equations

2.3.3 Off-design effects

2.3.4 Volute-impeller interaction

2.3.5 Volute-radial diffuser interaction

2.3.6 Parameters and mechanisms influencing performance

2.3.7 Volute Losses

2.3.7.1 Geometrical and aerodynamic effects
2.3.7.2 Loss coefficients

Figures

viii

vi

\O\OOOO\O\O\UJN

10

17
18

.20

25
25
27
29
3 l
32
33
34
35

41
42
43
43
43

45
47
47
49
49
52
6 1

CHAPTER 3: EXPERIMENTAL APPARATUS
3.1 Modification of the Trane compressor
3.2 Instrumentation of the facility
3.2.1 Overall performance instrumentation
3.2.1.1 Total temperature
3.2.1.2 Total and static pressures
3.2.1.3 Mass flow rate
3.2.2 Flow structure instrumentation
3.2.2.1 Volute pressure taps
3.2.2.2 Vaneless diffuser pressure taps
3.2.2.3 Pressure scanner
3.3 Planned measurements
Figures

CHAPTER 4: EXPERIMENTAL RESULTS AND ANALYSIS
4.1 Different approaches
4.1.1 Diffuser results
4.1.2 Volute results
4.2 Impeller one dimensional analysis
Figures

CHAPTER 5: NUMERICAL ANALYSIS SETUP
5.1 Introduction
5.2 Considerations for the numerical analysis
5.3 Geometry and grid generation phase
5.3.1 Gambit
5.3.2 Trane volute grid
5.4 Simulation phase
5.4.1 Fluent
5.4.2 Governing equations in FLUENT
5.4.3 Volute flow simulation
Figures

CHAPTER 6: NUMERICAL RESULTS AND ANALYSIS
6.1 Validation
6.2 Performance
6.3 Flow structure
6.3.1 Vaneless diffuser flow
6.3.2 Volute flow
6.3.3 Tongue effect
Figures

CONCLUSIONS

REFERENCES

ix

81
85
85
86
86
87
89
89
90
91
92
94

99

102
104
106
109

126
128
130
130
131
134
134
135
138
141

146
148
150
150
151
154
156

181

185

Figure 1.1

Figure 1.2
Figure 1.3
Figure 1.4
Figure 1.5
Figure 2.1
Figure 2.2
Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6
Figure 2.7
Figure 2.8

Figure 2.9

Figure 2.10
Figure 2.11
Figure 2.12
Figure 2.13
Figure 2.14
Figure 2.15
Figure 2.16
Figure 2.17
Figure 2.18
Figure 2.19
Figure 2.20
Figure 2.21
Figure 2.22
Figure 2.23
Figure 2.24
Figure 2.25

Figure 2.26.
Figure 2.27

Figure 2.28

Figure 2.29

LIST OF FIGURES

Schematic of a single stage centrifugal compressor with
corresponding velocity triangle and h-s diagram

Velocity triangle with slip

A typical compressor performance map

Schematic of a two stage centrifugal compressor

Stable operating range of vaneless diffusers (Jansen 1964)
Swirling flow in a volute

Superposition of vortex tubes in a volute

Static pressure distortion for high, optimum and low mass
flow

Static and total pressure variation over the volute cross
section

Circumferential static pressure distribution on the volute
wall

Swirl- and through flow velocity variation over the volute
cross section

Position of the swirl center for high, medium and low mass
flow

Formation of the volute casing from the streamline of a
vortex source ‘
Volute casing with logarithmic shape

External and internal volutes

Volutes with more subdivisions

Volute with multiple discharge point

Volute with an adjustable tongue

Volute with rectangular cross section

External volute with tapering sidewalls

Volute with circular cross section

Internal volute

Basic volute geometry

Distribution of shape coefficient of volute outer wall
Distribution of area by centriod radius over azimuth angle
Circumferential variation of cross section

Helix volute

Axial volute

Comparison of standard and modified volutes

Comparative performance maps of standard and modified
volute

Influence of the volute casing on compressor

Variation of the volute loss coefficient and the pressure
rise coefficient as a function of the diffuser outlet swirl
Loss and static pressure rise coefficients for the external
volutes

Circumferential variation of static pressure and tangential

21

22
22
23
23
62
62
63

63

3‘

65

65
66
66
66
67
67
68
68
69
69
70
70
7 1
7 1
72
72
73

73
74

74

75

Figure 2.30
Figure 2.31
Figure 2.32
Figure 2.33
Figure 2.34
Figure 2.35
Figure 2.36
Figure 2.37
Figure 2.38
Figure 3.1
Figure 3.2
Figure 3.3
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 4.9
Figure 4.10
Figure 4.11
Figure 4.12
Figure 4.13
Figure 4.14
Figure 4.15

Figure 4.16

Figure 4.17
Figure 4.18

velocity at the volute inlet

Influence of the volute size on radial compressor
performance

Reversal of meridional velocity at the impeller for low
mass flow

Pump efficiency for three impeller-volute combinations
Velocity distribution in a volute conical diffuser

Hydraulic efficiency for different volute surface roughness
Hydraulic losses K for different surface roughness

Pump head capacity relationship showing effect of volute
mixing

Asymmetrical and symmetrical volutes

Casing total loss at rotor inlet

CVHF 1280 Trane Commercial Unit

Trane two stage compressor’s cross-section

Diffuser dimensions for setting up the flow path

Probe locations on (a) Vaneless diffuser (b) Volute

Total pressure ratio for 2000 RPM operating condition
Vaneless diffuser static pressure distribution at r/r2=1.125,
2000 RPM and 0:0, 120, 180, 240, 300 degrees

Vaneless diffuser static pressure distribution at r/r2=1.27,
2000 RPM and 9:60, 180, 300 degrees

Vaneless diffuser static pressure distribution at r/r2=1.59,
2000 RPM and 0:0, 60, 120, 180, 240, 300 degrees
Vaneless diffuser static pressure distribution at 0:60 and
2000 RPM

Vaneless diffuser static pressure distribution at 9:180 and
2000 RPM

Static pressure distribution at vaneless diffuser outlet and
2000 RPM

Volute static pressure distribution at 2000 RPM

Total pressure ratio for 3000 RPM operating condition
Vaneless diffuser static pressure distribution at r/r2=1.125,
3000 RPM and 0:0, 60, 120, 180, 240, 300 degrees
Vaneless diffuser static pressure distribution at r/r2=1.27,
3000 RPM and 0:60, 180, 300 degrees

Vaneless diffuser static pressure distribution at r/r2=1.59,
3000 RPM and 0:0, 60, 120, 180, 240, 300 degrees

Vaneless diffuser static pressure distribution at 0:60 and

3000 RPM

Vaneless diffuser static pressure distribution at 9:180 and
3000 RPM

Static pressure distribution at vaneless diffuser outlet and
3000 RPM

Volute static pressure distribution at 3000 RPM

Total pressure ratio for 3497 RPM operating condition

xi

75
76
76
77
77
78
78
79
79
95
96
97
110
111
111
112
112
113
113
114
114
115
115
116
117
117
118
118

119
119

Figure 4.19
Figure 4.20
Figure 4.21
Figure 4.22
Figure 4.23
Figure 4.24

Figure 4.25
Figure 4.26

Figure 4.27
Figure 4.28
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 6.9
Figure 6.10
Figure 6.11
Figure 6.12

Figure 6.13

Vaneless diffuser static pressure distribution at r/r2=1.l25,
3497 RPM and 9:0, 60, 120, 180, 240, 300 degrees
Vaneless diffuser static pressure distribution at r/r2=1.27,
3497 RPM and 0:60, 180, 300 degrees

Vaneless diffuser static pressure distribution at r/r2=1.59,
3497 RPM and 9:0, 60, 120, 180, 240, 300 degrees
Vaneless diffuser static pressure distribution at 0:60 and
3497 RPM

Vaneless diffuser static pressure distribution at 0:180 and
3497 RPM

Static pressure distribution at vaneless diffuser outlet and
3497 RPM

Volute static pressure distribution at 3497 RPM

Impeller exit flow angle for different speeds and mass flow
rates

Impeller exit absolute velocity for different speed and mass
flow rates

Relative velocity ratio for different speeds and mass flow
rates

Vaneless diffuser

Volute casing

Complete flow path

Diffuser grid

Volute mesh

Diffuser inlet static pressure at choke

Diffuser outlet static pressure at choke condition

Cone outlet total pressure at choke condition

Volute static pressure distribution at 2000 RPM and
maximum flow rate

Volute static pressure distribution at 3000 RPM and
maximum flow rate

Volute static pressure distribution at 3497 RPM and
maximum flow rate

Volute static pressure distribution at 2000 RPM and mid
mass flow rate

Volute static pressure distribution at 3000 RPM and mid
mass flow rate

Volute static pressure distribution at 3497 RPM and mid
mass flow rate

Volute static pressure distribution at 2000 RPM and- min
mass flow rate

Volute static pressure distribution at 3000 RPM and min
mass flow rate

Volute static pressure distribution at 3497 RPM and min
mass flow rate

Diffuser pressure recovery coefficient

xii

120

120

121

121

122

122

123
123

124
124
142
142
143
143
144
157
157
158
158
159
159
160
160
161
161
162
162

163

Figure 6.14
Figure 6.15
Figure 6.16
Figure 6.17
Figure 6.18
Figure 6.19
Figure 6.20
Figure 6.21
Figure 6.22
Figure 6.23
Figure 6.24

Figure 6.25

Figure 6.26

Figure 6.27

Figure 6.28

Figure 6.29

Figure 6.30

Figure 6.31

Figure 6.32

Figure 6.33

Diffuser loss coefficient

Volute pressure recovery coefficient

Volute loss coefficient

Vorticity magnitude at different volute cross sections and
3497 RPM

Vorticity magnitude at different volute cross sections and
3000 RPM

Vorticity magnitude at different volute cross sections and
2000 RPM

Vorticity comparison for maximum flow rate and different
speeds

Tangential velocity at different volute cross sections and
3497 RPM

Tangential velocity at different volute cross sections and
3000 RPM

Tangential velocity at different volute cross sections and
2000 RPM

Tangential velocity comparison for maximum flow rate
and different speeds

Static and total pressure contours and meridional velocity
vectors for 3497, maximum flow rate and cross section
angles (a) 27, (b)117, (c)207, (d)297

Static and total pressure contours and meridional velocity
vectors for 3497, mid flow rate and cross section angles (a)
27, (b)117, (c)207, (d)297

Static and total pressure contours and meridional velocity
vectors for 3497, min flow rate and cross section angles (a)
27, (b)l 17, (c)207, (d)297

Static and total pressure contours and meridional velocity
vectors for 3000, maximum flow rate and cross section
angles (a) 27, (b)117, (c)207, (d)297

Static and total pressure contours and meridional velocity
vectors for 3000, mid flow rate and cross section angles (a)
27, (b)117, (c)207, (d)297

Static and total pressure contours and meridional velocity
vectors for 3000, min flow rate and cross section angles (a)
27, (b)117, (c)207, (d)297

Static and total pressure contours and meridional velocity
vectors for 2000, maximum flow rate and cross section
angles (a) 27, (b)117, (c)207, (d)297

Static and total pressure contours and meridional velocity
vectors for 2000, mid flow rate and cross section angles (a)
27, (b)1 17, (c)207, (d)297

Static and total pressure contours and meridional velocity
vectors for 2000, min flow rate and cross section angles (a)
27, (b)117, (c)207, (d)297

xiii

163
164
164
165
165
166
166
167
167
168
168

169

170

171

172

173

174

175

176

177

Figure 6.34 Diffuser static pressure contours for 3497 RPM and (a) 178
Max (b) Mid (c) Min mass flow rates

Figure 6.35 Diffuser static pressure contours for 3000 RPM and (a) 179
Max (b) Mid (c) Min mass flow rates

Figure 6.36 Diffuser static pressure contours for 2000 RPM and (a) 180
Max (b) Mid (c) Min mass flow rates

xiv

NOMENCLATURE

Area

Area Ratio

Speed of Sound

Passage Width

Absolute Velocity, Constant
Specific Heat Constant Pressure, Static Pressure Recovery Coefficient
Specific Heat Constant Volume
Friction Factor

Diameter

Diameter

Gravity

Enthalpy, Head loss

2

“(1)
’3

Axial Length
Mass Flow Rate
Mach number
Rotational Speed
Specific Speed
Pressure
Volume Flow Rate
Radius
Gas Constant, Center of the Volute Radius
Reynolds Number
Entropy
Blade Thickness
Temperature
Blade Velocity
Relative Velocity, Work
X-Axis
Y-Axis
Number of Blade, Z-Axis

N<xgca~m§w~owgzg§ r‘ w rmcagpgna‘mggs

GREEK

Absolute Flow Angle

Relative Flow Angle

Ratio of Specific Heats

Eficiency

Viscosity

Density

Slip Factor

Rotation Speed (Radian/sec), Vorticity
Flow Coeficient, Angle

Circumferential Angle

G‘SQ‘otaVua

‘1’

Work Coefficient

SUBSCRIPT

\OWQOU‘QNN—‘O

Ut

O

gamma"

0 a 5'-':rgaoc-§ g
i

Stagnation Condition, Ambient Condition
1" stage inlet

1‘ impeller discharge
1‘ difiirser inlet

Bend inlet

Bend outlet

Vane inlet

Vane outlet

2ml stage inlet

2“" impeller discharge
2"“ difl’user inlet
Volute inlet

Volute outlet

Average

Axial

Blockage

Compressor, Throat center
Efi‘ective Flow Area

Hub

Inner

Inlet

Meridional

Outer

Outlet

Radial

Circumferential, Tangential
Shroud, Swirl, Static Condition
Tangential, Through flow, Total Condition
Throat, Theoretical

Relative

SUPERSCRIPT

Average

CHAPTER 1

INTRODUCTION

In this chapter, a centrifugal compressor, its components and their interactions
are discussed. In order to remind the reader the governing equations and preliminary
design methodology of these compressors, steps of the design of a two stage centrifugal
compressor are described. At the end of the chapter, the reader’s attention is drawn to
the importance of the volute performance and design models in order to help exploring

the details of the next chapters.

1.1 COMPRESSORS

The major fluid mechanics problem in turbomachinery is the design of compressors.
A turbine, with its flow usually going from a high to a low pressure, always works and
with reasonable care it works at high efficiency. A compressor, particularly the axial-
flow type, may not produce a pressure rise at all. Until almost the beginning of the 20th
century, compressor isentropic efficiencies were generally less than 50 percent.

There is no record of the efficiencies of Papin’s centrifugal blowers (1705). There
appears to have been little development between that time and 1884, when Charles
Parsons patented an axial-flow compressor. Three years later, he designed and sold a
three-stage centrifugal compressor for ship ventilation. He returned to experiments on
axial-flow compressors in 1897, and made an eighty-one-stage machine in 1899, which
attained 70 percent efficiency. By 1907 his company had made or had on order forty-one
axial-flow compressors, but they were plagued by poor aerodynamics. Parsons used far
too high a spacing/chord ratio for the rotor-blade settings, and all bade rows were likely
be stalled over much of the operating range. Parsons returned to making radial-flow

compressors.

The other major pioneer working on compressors at that time was Auguste Rateau,
who published a major paper on turboblowers in 1892. However a turbocompressor he
designed to give a pressure ratio of 1.5 at 12,000 rpm and tested in 1902 gave an
isentropic efficiency of only 56 percent. Subsequently, Rateau designed and built
compressors of increasing pressure ratio and mass flow, and gradually increasing
efficiency. The continued story of compressor development is largely involved with the
long struggle to produce a working gas-turbine engine. Many attempts failed simply

because of poor compressor efficiency.

1.2 COMPRESSOR THEORY

To better understand a turbomachine’s performance, one must approach by the
means of thermodynamics and fluid mechanics. The conservation of mass, energy,
momentum and angular momentum in addition to 1St and 2"d laws of thermodynamics
are the basic laws that govern the operation of the compressor. Since the operating fluid
is air, the perfect gas and isentropic laws will be completing conservation laws. Figures
1.1 shows schematics of a single stage with components, corresponding velocity triangle
(without inlet prewhirl) and a typical h-s diagram.
As is known from thermodynamics, the shaft work input to the compressor is
transformed to build up pressure in the fluid while passing through the impeller
passages. A simple angular momentum shows that

We =uZCu2 —u,Cu1 (1.1)

On the other hand, from the first law of thermodynamics and ideal gas law

We 2,70: "hm : Cp(TO2 _T01) (12)

Equations (1.1) and (1.2) are the principles of this energy transformation. Note
that the total (stagnation) temperature in an adiabatic machine changes where the shaft
work is present, otherwise, it stays constant. Once the work input is defined, efliciency
must be defined to distinguish between the ideal and, actual work. Note that there are
various definitions of efficiency and the general definition of compressor isentropic
efficiency is

_ Idealwork _ hogs — hm
”c Actualwork ho2 - h01

1‘.
589$ H -1
P0,:n

77c —
70,014! _1

T

0,1’n

 

(1.3)

 

The efficiency defined by (1.3), although fundamentally valid, can be
misleading if used for comparing the efficiencies of turbomachines of differing pressure
ratios. Any turbomachine may be regarded as being composed of a large number of very
small stages irrespective of the actual number of stages in the machine. If each small
stage has the same efficiency, then the isentropic efficiency of the whole machine will
be different from the small stage efficiency, the difference depending upon the pressure
ratio of the machine. There are correlations to convert the isentropic efficiency to
Polytropic; however, the concept is utilized with perfect gas law to be helpfiil in
defining the properties across the stage and impeller. Having the stage pressure ratio, the

designer is able to derive the following correlation

(as—:1“

The same is valid across the impeller

 

T, P, CF”
[0-]:[ 0-] ’ (1.5)
7111 P01

Utilizing equations (1.1)-(1.5) and knowing the desired stage pressure ratio and inlet
total properties, a designer will be able to calculate the key properties at every location
in the stage.

The other fact to be considered is slip factor (Figure 1.2). Even under ideal
(fiictionless) conditions, the relative flow leaving the impeller of a compressor will
receive less than perfect guidance from the vanes and the flow is said to slip. Therefore,
slip factor is defined to correct value of the energy transfer between the impeller and the
fluid. There are various correlations for slip factor in the literature, following, the below

definition has been referred by many authors to predict the best slip condition.

0w:[ggfli]:1___m (1.6)

C 20.7

u, , theory

The other characteristic of a compressor is shown in its performance diagram
(Figure 1.4), where the pressure ratio is drawn versus flow the coefficient. The diagram
has the significant information regarding the range of operation, which lies between
surge and choke lines and the area of maximum efficiency, Dixon (1998). One of the
major issues in compressor operation is surge and choke limitation. For the compressor,
efficient operation at constant NNTm lies to the right of the line marked surge. For
multistage compressors it commences approximately at the point where the pressure
ratio flattens out to its maximum value. The surge line denotes the limit of stable

operation of a compressor, where unstable operation is characterized by a severe

oscillation of the mass flow rate through the machine. The vertical portions of the
constant speed lines may recognize the choke regions of the flow. No further increase in
the flow coefficient is possible since the Mach number across some section of the

machine has reached unity and the flow is choked.

1.3 COMPRESSOR COMPONENTS
1.3.1 INLET

A well-designed inlet system, which includes a bell mouth and inlet guide vane
(IGV), will provide a uniform non-swirl flow to the impeller. To achieve high
performance, the curvature of the bell mouth should be against any separation effect at
the inlet. In some designs for better performance of the impeller, the inlet guide vanes
will provide the required flow angle at the inlet to the impeller. The most important fact
in designing the inlet system is to keep the relative Mach number as low as possible.
This will provide the required mass flow rate at the best efficiency point and minimize

the blade incidence and frictional losses in the following impeller passage.

1.3.2 IMPELLER

There is an extensive literature about the impeller design, performance and
optimizations such as Bhinder et. a]. (1987) and Palmer et. a]. (1995). The impeller is
where the energy is transferred and transformed. The fluid entering the passage will
experience Coriolis force and at the same time diffusion through the passage. As

mentioned in the previous section, losses will accompany this diffusion, which is

reflected in the efficiency concept. At the outlet of the impeller, slipping occurs, which
is the result of loss, where all equations (energy, mass, momentum) must be satisfied.

The key parameters are the angles at the inlet and outlet of the impeller and the axial
length of the impeller. One can utilize any of the optimization techniques in the
literature to design the angular variation of the passages from inlet to outlet. Blades are
designed in various types of radial, backward and forward swept blades. Radial blades
are able to create a high-pressure ratio but create significant amount of loading on the
impeller. Radial blades reduce the stress in high-pressure ratios but circulation and
separation in the rotor channels are inevitable. Forward swept blades theoretically has
the largest pressure ratio, however, current research was not able to put these impellers
in use. Backward swept blades will reduce the discharge absolute Mach number and has
a broader stable operating range. Since the streamline curvature in the blade to blade
plane is increased in these type of blades, the blade to blade pressure gradient is reduced,
therefore, the secondary flows and associated losses is avoided. However, in these types
of blades, the blockage of the flow path must be considered.

The other factor in the impeller design is the number of the blades. Based on
the impeller discharge flow angle, a zone of acceptable performance is defined for the
number of the blades, described in Wilson (1998). The higher number of blades for
certain angles, the higher blockage of the flow in the impeller passages will be created.
The lower this number, the higher blade loading will be. Meanwhile, this number is
selected in the way that half of the blades will behave as a splitter blades. These blades
will reduce the loading on the blade. More details regarding the selection of the angles

will be discussed later in the chapter.

1.3.3 DIFFUSER

Flow leaving the impeller carries kinetic energy, which is transformed inside a
radial difihser. Diffusers are classified as vaned and vaneless. If the flow leaving the
impeller has a steep angle, using vaned diffuser avoids significant losses because of the
longer residence time of the flow inside the diffuser. If the flow angle at the impeller
discharge is not large, using the vaneless diffuser will help diffuse the flow and
transform the rest of the kinetic energy left in the flow. The radial-flow component
diffuses because the area increases, and this component have a low Mach number even
when the Mach number based on the overall velocity vector is above unity. In
axisymmetric flow the pressure gradient is in the radial direction and acts on this radial
component. The tangential-velocity component diffuses because in axisymmetric flow,
and in the absence of turning vanes and wall fiiction, the tangential velocity is inversely
proportional to the radius. It is unaffected by the area change. This component of the
velocity vector can pass from supersonic to subsonic without shock since it can adjust to
direction changes from signals received through the subsonic radial component. The
governing law is the conservation of angular momentum in vaneless diffusers, which is

r3Cu3 = QC“ (1.7)

However, equation (1.7) is for the ideal case and normally there are losses due
to the friction. In addition, in the area 2-3 (Figure 1.3) there is an unsteady mixing
region, which creates its own loss.

Jansen (1964) reports the best analysis of vaneless diffusers, which has been
endorsed by many researchers (Figure 1.5). In his analysis, the performance of the radial

vaneless diffusers has been analyzed based on the Reynolds number of the impeller

discharge flow, the ratio of the discharge passage width to the radius of the impeller at
the exit, and the blade angle at the discharge. Knowing this information, the designer
will be able to have the best ratio of the diffuser radius to the impeller discharge radius

as the matter of diffusion quality.

1.3.4 BEND AND RETURN CHANNEL

There is a lack of research in this area primarily because of the complication of
the flow in this region and its inaccessibility. The flow passing through the bend,
experiences pressure gradient across the channel and this pressure gradient creates a
highly rotational flow and great pressure loss. To design these components one must rely

on empirical correlations such as those described in Aungier (1995).

1.3.5 VOLUTE

The volute surrounds the impeller, and is a spiral casing whose cross-sectional
area increases from a minimum at the cutwater to a maximum at the throat, which is the
beginning of the conic diffuser to the outlet pipe. The cutwater is the nearest component
of the casing to the impeller, and is aligned into the general direction of the flow leaving
the impeller. The cross-sectional area increases to take the volume leaving the impeller.
If the ideal flow is considered, the law of constant angular momentum will apply, and
the flow will leave the impeller on a logarithmic spiral path. In many casing designs, the
cross-sections are circular sections, and the outer wall follows an Archimedean spiral. It
is possible, using integration across each section of small elements, to evaluate the area

changes and get the correct areas for designated sections. In the governing laws, the

effect of friction is typically neglected as it has been found to affect the areas by very
small amounts. However, because of the curvature of the casing, the flow spirals inside
the volute, which requires a firll three dimensional analysis to study it. There will be a
comprehensive discussion on the volute geometry and design procedure in the next

chapter.

1.4 A TYPICAL PRELIMINARY DESIGN PROCEDURE FOR A TWO STAGE
CENTRIFUGAL COMPRESSOR

There are various ways of designing a centrifirgal compressor in one dimension
or mean radius values. The following is one of typical design procedure in which the
main goals of designing a centrifirgal compress are:
- Reducing the relative Mach numbers at the inlet to the stage in order to avoid high
losses in the impeller.
- Minimizing the kinetic energy at the outlet of the diffuser and volute.
- Enforcing the optimized geometry parameters, in order to create an optimum
performance, such as flow angles and radius ratios.

In the next sections a two-stage compressor (Figure 1.4) will be designed in
order to familiarize the reader with the methodology since this is going to be the basis of
the meanline analysis of the Trane compressor in Chapter 4. In this design procedure
fiictionless flow is considered and for explicit design the empirical correlation should be
used to consider related losses. Although the design is ideal, it can be used for a designer

to have a starting point.

10

1.4.1 FIRST STAGE

To start the design process the mass flow rate, inlet total pressure and inlet total
temperature are considered given. Suppose the desired pressure ratio for the compressor
is 7.5 where by dividing it between two stages, the first stage pressure ration is 2.8 and
the second stage is 2.7. Note that in designing a two-stage machine, either the overall
pressure ratio or work input is divided between the two stages. In order to start the
iteration process, designer should start with selecting an inlet absolute velocity C1 or
Mach number M1; correspondingly, the other parameters will be calculated knowing the
initial guesses. The absolute velocity should be selected first. Knowing the inlet

conditions, one can obtain the static temperature

C ,2

Tl :Tm_-2C_
P

(1.8)

Knowing the static pressure, the speed of sound and Mach number can be calculated

a1 2 4%?"

1.9
M129— ( )
a,

In order to calculate the relative and tangential velocities, the velocity triangles
must be obtained by calculating the corresponding the flow and impeller angles. The
inlet velocities can be assumed swirl free by using IGV, which means or, the absolute
velocity angle respect to radius, at both stage’s inlets is zero. Meanwhile, the blades are
selected to be radial at the hub and backward swept at the shroud. Therefore, [3, the angle
of relative velocity respect to radius, at the hub is zero for both stages. It is shown in

various literatures that the flow angle leaving the impeller (8:60) degree at the shroud

ll

will optimize the performance; therefore, it is assumed the same amount as the initial

guess. Having this angle, the inlet velocity triangle can be defined.

 

Wsl : Cl
COSflsl (1'10)
U51 : ClTanIle

Using the perfect gas law, total density can be calculated.

P01
R70.

 

p01 : (L11)

Having the absolute Mach number, the static density can be calculated.

&=[1+flMIZ TR] (1.12)

Q=—- (1.13)

The number of the blade Z is chosen to be 20, which puts the impeller in the
accepted region of Wilson (1998) chart. Then the slip factor can be calculated using
(1.6). It is shown in literature that selection of 60 and 45 degrees for or and B at the
impeller discharge would be good initial guesses. Therefore using the velocity triangle at

the outlet and considering slip factor the following correlation can be used.

[Cu2,ac]:{Tanfl2 +.1_}— (114)

U 2 T and:2 a
On the other hand, 'with no swirl at the inlet
Aha = U2Cu2 — UlCul : UZCuZ (1.15)

As mentioned before

12

Aho :CP(TO?__TOI) (1-16)

Using the efficiency concept (1.3) Aho can be calculated, knowing that the total
temperature stays constant from first stage impeller outlet to the inlet of the second
stage. Using (1.13) and (1.14) the tangential velocity and blade speed at the outlet will
be calculated.

Rodgers [32] showed that the specific speed of 0.8 is a good assumption to have
an optimum performance. Knowing that, the rotational speed can be calculated using the

following correlation.

3

_ 60N,(Aho)Z

2713/?

Therefore, the angular velocity can be calculated correspondingly. The diameter

N (1.17)

of the impeller at the inlet can be calculated as following

_. 2U2
a)

d2

 

(1.18)

Knowing the angular speed and (1.9), the diameter of the shroud can be similarly
calculated. To calculate the hub diameter, the result of the previous studies will be used
as was shown that a ratio of hub to shroud diameter range of 0.3-0.5 creates a reasonable
balance between the blockage and high inlet velocity, Wilson (1998). Therefore by
choosing this ratio, the hub diameter can be calculated as well. Note that using Microsoft
Excel sheets, all these parameters cab be assigned with their corresponding equations. At
the end of the calculations, a conservation law such as conservation of mass can be used
to confirm the first initial guess; otherwise, an iteration process will take place with

changing the parameters. The choices of the parameters will be used as an initial guesses

13

and based on the outcome of the design, they may be modified as the iteration goes
along.
Using the velocity triangle information at the inlet, the absolute and relative velocities

will be calculated.

 

C2 : f’wuZ
.Sma2
W142 : U2 _Cu2 (1 19)
W142 .
W, = ——
“ Sinfl2

C ,2 = C 2Cosa2
The static temperature and thus the absolute and relative Mach numbers will be
calculated similar to ( 1.7) and (1.8). Defining the thickness of the blade, the width of

the impeller discharge can be calculated by conserving the mass flow rate.

m

 

 

AflowZ : F
r2
b 2 AW; (1.20)
2 Z12
(”dz _ )
Cosfl2

The width could have been calculated from choosing a proper ratio of width to
diameter of the impeller at the discharge but (1.19) will save iteration. Knowing the

width, the blockage areas can be calculated.

 

Zt
Ab] : COSJBI (dsl —dhl)

_ th2
b2 Cosfl2

(1.21)

 

This iteration process must be implemented until the mass flow rate conserved as stated

earlier.

14

Presented in various literatures, it is shown that to have a good performance
diffuser, the ratio of the relative velocities at the impeller discharge to the inlet must be
greater than 0.6. This ratio can be a strong design condition to be conserved; otherwise,
a supersonic relative velocity will choke the flow at the inlet of the impeller. At the same
time, the size of the impeller has a direct influence on the required speed of the
compressor. The higher the rotational impeller speed, the more stress on the impeller.

Knowing all parameters at the impeller discharge, the diffuser must be designed.
In order to accommodate the mixing region at the impeller discharge, one percent of the
impeller radius can be designated for the mixing region; however, there are ongoing
researches for more accurate design of this region. In order to calculate the required
diameter of the diffuser, the absolute Mach number at the diffirser discharge is set to be
0.25, which is a reasonable value in order to guarantee the transformation of the kinetic
energy inside the diffuser as much as possible. Knowing the Mach number leads to

definition of the static temperature at the diffuser discharge.

5211—7411143 (1.22)
T, 2

Knowing the both static and total temperature and using (1.7), the absolute
velocity at the diffuser discharge can be calculated. Meanwhile, calculating the Reynolds
number at the impeller discharge and utilizing the data in Wilson (1998), one can
calculate the ratio of the diameters of diffuser to impeller. This ratio will guarantee the
acceptable performance of the diffuser.

From stage and impeller efficiencies, which are desired parameters in the design,
the total pressures at the impeller discharge and inlet to the second stage will be known.

The difference between two values is the pressure loss across the diffuser, bend, and

15

return channel. Therefore, the properties of the fluid can be calculated at every location.
On the other hand, knowing the velocities at the inlet and outlet of the diffuser, the
conservation of the mass (1.23) can be used to calculate the flow angle at the diffuser
outlet.

pzAzC,2 = ,04A4C4Cosar4 (1.23)

Note that in some designs, pinching has been used in design of the vaneless

diffuser walls but for the simplicity in this design, the width of the diffuser can be kept
constant.
In the bend section, the inner radius of the bend is kept as the average of the width at the
difluser inlet and discharge, referring to Aungier (1995). Since the width of the duct is
kept constant across the diffuser to the end of return vane, the radius of the shroud side
of the bend chosen to be equal to the two times width.

In order to adjust the flow angle for the second stage, vanes are used in the return
channel. In this design, the leading edge of the vanes in the return channel is located
where the bend is terminated. The angle of the leading edge is the same as the angle of
the flow leaving the bend. The thickness of the vanes will be equal to the width of the
duct. Since the flow at the inlet of the second stage impeller can be designed to be swirl
free, the return vanes must guide the flow to zero degree angle respect to the radius. To
accommodate this turn smoothly, the vanes are designed to be long enough in order to
avoid high pressure losses. Similar to the bend, there are ongoing research to investigate

the effect of various vanes in this section on the compressor performance.

16

 

1.4.2 SECOND STAGE

To design the second stage, the process is similar to the first stage except volute
replaces the bend and return channel. Note that all the fluid properties will be known
through the Mach numbers, total properties and velocities at the different components of
the second stage.

In the volute section, it is proven that the circular cross section has the lowest
loss (Chapter 3), therefore, in the current design circular cross section has been chosen.
To design the volute, the iteration process should be implemented to calculate the radius
and the area of the throat. The conservation of the angular momentum is valid here as
well.

rllCqu : rCCu.rh (1-24)

At the same time, conservation of mass leads to

: Cr,llbllmll

re ruck“ (1.25)

Choosing the radius of the throat and applying the conservation of mass can
calculate the throat area. Meanwhile, no blockage at the tongue has been considered,
therefore, for simplicity of the design, a linear distribution of the area has been chosen
for the volute.

For the conical diffuser, the next component attached to the volute, it is shown
that the best design is to keep 20, the divergence angle of the cone, less than 7 degree in
order to avoid stall in the diffuser. The cone’s firnction is to transform the rest of the

kinetic energy lefi in the flow to pressure as much as possible. Knowing the pressure

loss, the area ratio and the length of the diffirser at the end of volute can be calculated.

l7

1.5 SIGNIFICANCE OF THE VOLUTE AND CURRENT CHALLENGES

As mentioned previously, the primary function of a centrifugal compressor
volute is to serve as the transition from the impeller and diffuser to the pipe system.
Depending on the particular configuration, the losses in volutes especially at off-design
can be significantly high which leads to poor stage efficiency and reduction of operating
range.

It is well known, that the collecting volute of a centrifugal compressor operating
at off-design conditions, produces a peripheral pressure distortion. This pressure
distortion intensively acts back on the impeller exit, when a vaneless diffuser is chosen
and leads to a periodic throttling of the impeller flow. This results in a cyclic
acceleration and deceleration of the fluid inside each impeller channel. As a result, the
inlet flow angle and thus the incidence angle vary periodically, which is the reason for a
decrease of impeller efficiency and operating range. The varying force that acts on the
impeller blades can cause impeller failure especially when high inlet pressures are
considered.

Several simplified one- or two-dimensional models exist that predict the
peripheral pressure distortion caused by the volute. However, measurements of Van den
Braembussche and Handle (1990) and Ayder et a1. (1991, 1993) clearly show the fully
three-dimensional nature of the volute flow. The secondary flow inside the volute has a
major influence on the pressure distortion and on the distribution of the through flow
velocities. This implies that a reliable prediction method must be considered the 3-
dimensional character of the flow. Van den Braembussche et a1. (1998) present an

analytical quasi-one dimensional prediction method, which takes into consideration the

18

three dimensionality of the flow. A reasonable correspondence of the pressure
distribution and losses with the experimental results obtained at the large centrifirgal
compressor test stand of the Institute of Turbomachinery in Hanover.

Ayder et al. (1994) used a steady 3D Euler-method for the calculation of the
diffuser and volute flow of a compressor with elliptic volute. They introduced an
artificial dissipation term in their calculations in order to limit the flow quantities in the
vortex core to finite values. Generally good agreements with the measurements results
were obtained. The calculated total pressure distributions were less accurate.

There are quite few measurement results available of the flow inside the volute.
The works of Van den Braembussche and Handle (1990), Ayder et al. (1991, 1994) and
Ayder (1993) provide good insight to the flow behavior inside the volute in typical
geometries, such as circular or elliptic, at nominal and off-design operating points.
Nevertheless, Trane’s volute is a combination of rectangular and circular cross-sections,
which can affect the general flow structure and loss mechanism. Therefore we are far
from firlly understanding the flow phenomena and loss mechanism inside the volute and

further empirical data are necessary to improve the existing flow models.

19

FIGURES

20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'1

Figure 1.1: Schematic of a single stage centrifugal compressor with
corresponding velocity triangle and h-s diagram

 

 

“I

21

 

[3'22 Vane Angle ' C'ez ;1

”‘r .

[32: Average Relative ; . C
Flow Angle |

82

.‘r.

 

 

 

U

2

Figure] .2: Velocity triangle with slip

  
 
  
   

Lines of Constant
Efficiency

Maximum Efficiency

Surge Line

    

,r— Increase
N v71:
Lrnes of Constant 7: 2'

Jo

V

 

 

Figure 1.3: A typical compressor performance map

22

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Vaneless Diffuser T

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ANGLE BETWEEN STEADY-FLOII VECTOR AND RADIUS

Figure 1.5: Stable operating range of vaneless diffusers. From Jansen 1964

23

CHAPTER 2

LITERATURE SURVEY

24

In this chapter the literatures were reviewed extensively. The material gathered in
this chapter is focused on the volute design methodologies and performance analysis
performed by different researchers. Various models for losses in radial diffusers, volute,

conic outlet and their interactions with the impeller and the stage are introduced.

2.1 FLOW IN COMPRESSOR VOLUTE

As described previously, the flow leaving the impeller is collected by the volute
and delivered to the compressor outlet pipe. Circumferential volute area distribution is
designed to produce minimum static pressure distortions at minimum loss. However, in

conic diffirser, one should see a kinetic energy exchange.

2.1.1 FLOW MECHANISM

The flow leaves the impeller at a fairly constant angle over the whole periphery,
with the fluid particles following spiral trajectories. Entering the radial diffuser of the
volute, the flow is decelerated and based on the conservation of angular momentum
equation the pressure increases.

The flow inside the volute is highly three-dimensional and swirling. Described by
Ayder and Van den Braembussche (1993), the volute flow is made of layers of non-
uniform total pressure and temperature with high shear forces at the volute center.
Entering the volute, the fluid starts rotating around the cross section area, giving rise to
large velocity gradients and shear stresses. The fluid entering close to the tongue
develops a vortex flow and remains in the center of the volute as it proceeds towards the
conic diffuser. Further downstream flow wraps around the previous one, generating a

structure similar to vortex tubes of increasing radius (Figure 2.1, 2.2).

25

Turbulence mixing occurs between the high-energy fluid at the center of the
volute and the low-energy fluid in the boundary layers, resulting in mixing losses. The
boundary layer at the volute walls is absorbed by new fluid coming out of the vaneless
difiiiser after each rotation and the incoming fluid mixes with the flow already streaming
through the volute.

The amount of fluid entering the volute has an enormous effect on the flow. At
higher than optimum mass flow rate, the fluid is accelerated from the volute inlet to the
exit pipe; if the mass flow is lower than optimum, the flow is decelerated throughout the
volute. Secondary flow inside the volute occurs as the fiiction-decreased boundary layer
flow has the pressure distribution of the core flow. Therefore, the flow close to the wall
streams to the volute center mixes with the core flow and is thrown back towards the
volute wall. A twin vortex is formed in a symmetrical volute and a single vortex appears
in the asymmetrical one.

Huebl [29] measured the flow parameters of two volutes with the same
circumferential variation of the cross sectional area but different inlet positions, one
being a symmetrical and one being an asymmetrical volute (Figure 2.37). The flow in the
symmetrical volute has a completely different structure than the flow in the asymmetrical
one. Asymmetrical volutes show a higher efficiency than symmetrical volutes owing to
the formation of a single vortex in the asymmetrical volute instead of the double vortex in
the symmetrical one. The formation of the double vortex can be explained by the fact that
the sharp edge at the radial diffuser exit prevents the flow to be attached to one side of the

volute.

26

Hagelstein [29] reports that a part of the pressure developed in the radial inlet
diffuser prior to the volute, is lost in an internal volute. This is because of smaller
curvature radius of the streamlines in the volute than in the radial diffuser, resulting in
velocity increase and pressure drop. Compared to external volutes, the increase in
velocity results in higher wall fiiction losses and greater velocity reduction in the exit
conic diffuser, which contributes to the exit cone losses. Another reason for the high
losses in an internal volute is the radial velocity component of the flow at the radial
diffirser exit. Leaving the diffuser, the radial velocity component is transformed into a

swirl flow, increasing friction losses.

2.1.2 STATIC PRESSURE DISTRIBUTION

At optimum mass flow rate, there is a uniform circumferential pressure
distribution at the volute inlet, which leads to an almost uniform total pressure over each
cross section. As described by Van den Braembussche (1998) there is only a small
pressure gradient fiom the volute wall to the center due to the small swirl velocity shear
losses (Figure 2.4) and a change in the circumferential pressure distribution due to the
flow perturbation near the tongue.

With the mass flow rate being higher than optimum, losses increase because of
large velocity gradients and shear stresses. The volute is now too small to accumulate the
flow; therefore, the flow accelerates and results in decrease of total pressure from the
volute inlet to outlet. Van den Braembussche (1998) reveals with his measurements, that
at the volute inlet sections both the static and the total pressure decrease from the volute

wall to the center. This results in a nearly uniform through flow velocity distribution. At

27

the downstream volute sections the static pressure decreases towards the center of the
volute while the total pressure increases, resulting in a through flow velocity which is
twice as large as the one at the volute inlet.

The relation between the through flow velocity and the static and total pressure

distribution is shown by the following equation:
po-p=§(v%+v§) (2.1)

The static pressure variation at high mass flow results from the swirl and the

circumferential curvature of the volute walls (2.2)

d” v: (2.2)

with the centrifugal forces due to swirl being in equilibrium with the static pressure
increase from the center to the outer walls.

At low mass flow, the volute acts like a diffuser and the static pressure increases
from the volute inlet to the outlet. A decrease of total pressure occurs at the center of the
cross-section due to internal shear stresses. The static pressure distribution at low mass
flow rates is primarily defined by the following equation, which describes the pressure
gradient between the inner and outer wall caused by the through flow velocity

distribution and the circumferential curvature RC:

0’ v
_p:p

2
_T_ 2.3
dR R. ( )

Elholm et al. (1992) and Ayder, Van den Braembussche (1993) discovered a
sudden pressure drop over the tongue at a low mass flow rate, as a result of an extra

amount of fluid entering the volute through the clearance at the volute tongue. At a high

28

mass flow rate a pressure rise at the volute tongue occurs, pushing the fluid back from the
inlet to the exit pipe. The non-uniform circumferential pressure distributions at high and
low mass flow rates lead to a periodic change in flow conditions at the impeller outlet.

This causes periodic changes in the blade load resulting in radial forces on the impeller

shaft.

2.1.3 VELOCITY DISTRIBUTION

At the impeller exit, the radial velocity is transformed into a swirling motion with
a forced vortex type of velocity distribution in the center of the volute and a constant
swirl velocity away from it. The through flow velocity in the volute follows the angular
momentum conservation equation;

R- v, = const (2.4)

The variation of the through flow velocity is due to the curvature of the volute
with the through flow velocity decreasing from the inner to the outer volute wall and
minimum through flow velocity occurring at the center of the vortex. The dependence of
swirl and through flow velocity from total and static pressure can be revealed by
equations (2.1), (2.2) and (2.3).

Van den Braembussche (1998) describes the flow in the volute consisting of
vortex tubes of increasing radius (Figure 2.2) with the swirl velocity vs at a given radial
position depending on the radial velocity of the fluid at the position where it has entered
the volute. The velocity distribution inside the volute (Figure 2.7) distinguishes itself
enormously for optimum and off-design mass flow. At optimum mass flow rate, the

velocity near the walls is nearly constant due to the constant circumferential velocity

29

distribution at the volute inlet. The uniform pressure distribution at the volute inlet with
optimum mass flow rate condition leads to an almost uniform through flow velocity at
each cross section with only a small increase towards the center of the volute. Lower
radial velocity at the volute inlet results in smaller swirl velocity throughout the volute
circumference (Figure 2.6).

Fluid entering the volute at higher than the optimum mass flow rate has a small
tangential and a large radial velocity component. Due to the negative incidence of the
flow at the volute entrance and because the volute is too small for the amount of mass
flow, the through flow velocity increases from the volute tongue to the exit. The large
radial velocity leads to a high swirl velocity formation, which increases with the cross-
section radius.

At lower than the optimum mass flow rate, the flow enters the volute with a
positive incidence leading to an acceleration of the flow around the tongue and a
deceleration towards the volute exit. This deceleration is due to the volute being too big
for the small amount of flow. The flow has a large tangential and small radial velocity
component with the volute acting like a diffuser as the tangential velocity decelerates
from the volute tongue to the exit. Near the walls, a constant swirl velocity occurs as a
result of the uniform radial velocity at the volute inlet. Due to the large tangential
velocity the static pressure distribution is mainly defined by equation (2.3).

The pressure drop at low mass flow rate and the pressure rise at high mass flow
around the tongue described by Elholm (1992) has an effect on the position of the swirl
center inside the volute (Figure 2.7). For high mass flow rate, the swirl center is pushed

firrther inside the volute and for low mass flow rate it is located closer to the volute inlet.

30

Observed by Ayder et al. (1992), the flow entering close to the tongue has a large
swirl velocity and a small through flow velocity so that the static pressure distribution in
the tongue area is primarily given by equation (2.2). As found by Ayder (1993), none of
the previously described calculation methods account for the effect of the cross flows on
the volute flow because they all assume uniform flow over a cross section. Van den
Braembussche et al. [40] have developed a method to predict the three-dimensional flow

in a compressor volute.

2.1.4 NUMERICAL ANALYSIS

Miner, Flack and Allaire (1992) calculated the velocity field in a centrifirgal pump
by using a two-dimensional potential flow analysis. The impeller and volute are modeled
with the finite element method and the results included velocity profiles for the impeller
and deterrrrination of the tongue stagnation point. Martinez-Botas, Pullen and Shi (1996)
use a 3D Navier Stokes solver to calculate the flow in a turbine volute. Their method
solves the firlly 3D Reynolds averaged Navier Stokes Equations. They conclude that by
correctly treating the boundary conditions the results of the Navier Stokes solver are
much better than the results of a free-vortex flow prediction.

Engeda (1995) examines the validity of compromise methods using 2D and 3D
viscid and inviscid solutions to describe the flow in a volute. Ayder and, Van den
Braembussche (1993) use an Euler solver added by second order dissipation and wall
shear forces to describe the flow in the compressor volute. The comparison between their
model and measured data shows a good prediction of the velocity distribution and a more

qualitative agreement of the pressure distribution. Ayder and Van den Braembussche

31

conclude, that their method, using the Euler solver with a volute adapted loss model, can
be a good alternative to a method using the solution of the full Navier Stokes equations
for which the computational effort would be much higher.

Carter (1981) solves the two dimensional Laplace equation to describe the volute
flow. The solution is obtained by using the finite element method with variational
principle, assuming ideal flow and design conditions. Carter uses the superposition
method to simplify the implementation of the boundary conditions. Initially, only the
radial flow components were considered and the tangential flow was calculated. To
obtain the total flow properties, the two solutions were added together. His results for
design flow are that the velocity follows the free vortex law except in the tongue region
that the tongue clearance has a large effect on the volute flow and that the average

velocity of the volute flow is determined by the spiral angle of the volute outer wall.

2.2 VOLUTE DESIGN

The main goal in volute design is to achieve a circumferential uniform static
pressure over the impeller outlet, Eckert et al. (1961). If this is not accomplished, the
flow inside the impeller vanes change their circulation with every rotation of the shaft
leading to a development of vortices, which results in vane vibration and lower
compressor efficiency. Therefore the fluid has to flow through the volute like a vortex
source. The volute can be designed for constant velocity at the volute inlet. For an exact
volute design it is yet necessary to account for fiiction and a change in flow density from

the volute hub to the shroud.

32

Other design targets for compressor volutes are compactness and efficiency. The
compactness is required for low cost and weight and is often in contradiction to the
volute efficiency. Aspects of limited space to install the volute have to be considered as

well.

2.2.1 VOLUTE GEOMETRY

To define the geometry of the volute, Eck [17] describes a simple vortex flow,
which is symmetrical about an axis. He substitutes a streamline of the vortex source by a
firm wall, which after a full rotation will confine the flow within the end section of the
volute (Figure 2.8).

Eckert et al. (1961) calculate the streamlines of the volute flow, and therefore the
outer wall of an external volute as logarithmic spirals (Figure 2.9). The cross-section
shape of the volute can be rectangular, circular or elliptic. The advantage of a rectangular
shape is that it is the easiest to manufacture. Most commonly used are volutes with
circular cross-sections. Van den Braembussche (1998) expressed the reason, where volute
losses are considered.

The volute cross-section can be symmetrical or asymmetrical. Asymmetrical
volutes develop only a single secondary vortex flow. Volutes can be of external or
internal type (Figure 2.10). In internal volutes, the flow undergoes a 90°-turn and is
accelerated because these volutes have a smaller radius than the impeller exit. Internal
volutes have the advantage of being much more compact than external ones. The flow
accelerates when entering the volute due to the rotation law; thus, the volute has to be

smaller than an external one. Impeller friction is smaller and the fiiction path is shorter

33

than for normal configuration. These advantages are yet balanced out by the large
increase in friction due to the greater velocity. Therefore, external volutes are preferred
because of their higher efficiency.

In addition, it is possible to subdivide the discharge section of the volute to a
number of guide blades to further decrease in the discharge velocity. For very large
volumes one can construct a volute with several subdivisions and partially profile the
guide planes [17]. This results in comparatively small units. To minimize the losses in
these volutes, Mueller [29] suggests the use of a volute casing with a number of discharge
points disposed around the circumference. This kind of volute is ofien used for aircraft
engine superchargers because of its numerous discharge points.

In order to handle mass flows at off-design conditions Eck [17] describes a volute
with an adjustable tongue and Pfleiderer [29] gives data for the position of the volute

tongue and states the tongue thickness for maximum efficiency.

2.2.2 l-DIMENSIONAL DESIGN
One of the primary equations used for the volute design is the incompressible

continuity equation.
Q = [e - dA (2.5)

c is the through flow velocity for the differential area d4 .

The predication of the continuity equation for the volute is that the mass flow in
each circumferential cross section is the same, Eckert (1961). Due to the curvature of the
volute walls, there is a rise in static pressure from hub to shroud. This results in a density

change, which is yet neglected; because the pressure rise is small the meridional velocity

34

"I

c is small compared to the circumferential velocity cu. Therefore the continuity

equation states
27r-r-b~cm:27r-r3-b3-cm3 (2.6)
with the index (3) describing the conditions at the volute inlet.
The other equation is the conservation of angular momentum equation
cu -r = cu3 -r, (2.7)
With these two equations a simple volute design can be performed. For some basic cross

sectional shapes it is possible to calculate the boundary curves of the volute

mathematically.

2.2.3 FRICTIONELESS DESIGN

Eck [17] and Eckert (1961) and Pfleiderer [29] provided mathematical solutions
for the design calculation of volutes using the continuity equation and the angular
momentum conservation equation:
- External volute with parallel sidewalls:

For parallel side walls with b 2 b3 equation (2.6) changes to

Cm : —cm3 (2.8)
r
The angle of inclination of the streamlines to the periphery is
tan a : 5'1 (2.9)

C

11

Equations (2.7) and (2.8) show that tana = tana3 and therefore that the angle of

inclination is constant and with dr and rip as the differentials of the streamline

35

 

tana = (2. 10)
r (0
Integration of equation (2. 10) results in
r c
In7=tana(¢—¢.)=f3—(<o—¢.) (2.11)
3 m

Which shows that the streamlines are logarithmic spirals. The streamline for (p, = 0 runs

through the tongue of the volute and forms the outside boundary curve of the volute

casing:
lni=fip (2.12)
’3 Cm

For volutes with parallel sidewalls that are wider than the impeller, equation (2.12)
transforms to:

r c
ln—:——

"'3 -(o--b—3 (2.13)
r3 cm b

If the flow parameters cm3 and cu3 and the geometrical parameters b3 and r3 are known,
the width b of the volute can be calculated as follows. Assuming a square discharge area
the volume of fluid exiting the volute is given by

Q = b2 ~c (2. 14)
With c is the mean velocity, which is assumed to be equal to the velocity at the point of
concentration of the discharge area, the volume flow rate at the volute exit equals to:

€143 . r3

Wis—02)

(2.15)

With Q 2 Zn . r3 ~b3 -cm3, b can be obtained from:

36

 

b=%b,fli+J(%b,3fl]+2n-r,-b,i (2.16)

€113 C113 13
- External volute with rectangular cross-section
In volutes with rectangular cross-sections the conservation of angular momentum
equation cannot be properly used here, because deviations from the law r - cu : const. are
to be expected. As an approximation for volutes with a radial extension that is not too
large with respect to the radius, Eck [17] suggests the following calculation.

With h/ b = const. the circumferential velocity at any x location becomes

Cu3'r3

 

 

Cu — (2.17)
r3 + x
Using the continuity equation and Q, = Q3¢é0 a solution for the problem can be
provided
360- c -r -h
(p° = ,"3 3 ln[1+£] (2.18)
V- h/b ’3
- External volute with tapering side walls
Using equations (2.6) and (2.7), substituting b by
b = b, + 2(r — r,)tan5 (2.19)

and solving the resulting differential equation one gets

(0: 1 ‘11—2r—3tan5jlni+2:3—[—r~—l]tan5] (2.20)
tanoz3 b3 r3 b3 r3

The logarithmic term disappears for

 

tan6= b—3 (2.21)

37

and modifies equation (2.20) to form the outer wall of a volute with tapering walls:

= 1 [L41] (2.22)
tana3 r3

- External volute with circular cross—section

 

Strictly spoken the conservation of angular momentum equation is not applicable
on volutes with circular cross sections, because they have no body of rotation with
reference to the sidewalls. Therefore the tangential force on the flow particles is existent
and equation (2.8) is invalid. However the tangential force compared to the radial force is
so small, that it can be neglected, and equation (2.8) can be used as an approximation.

A precise calculation of the volute with circular cross-section is possible but
rather complicated. Therefore Eck [17] employed a linear approximation for the volute
shape, when the diameter d of the volute section is not too large with respect to the casing
diameter. The average velocity would then be equal to the velocity at the point of
concentration of the area.

c143 . r3
0 , = — 2.23
‘“ r. +(d/2) ( )
Using the continuity equation for the flow through a cross-section at the angle (,0, the

volume flow rate Q((p) is

0

¢ 52 2
— = —d c . 2.24

With equation (2.24) the relation between (p and d can be calculated. For a solution of

the equation Eck recommends to select d approximately.

- Internal volutes

38

Eck [17] describes the design of an internal volute with rectangular cross section and
the mathematical calculation of the necessary geometrical parameters. At first there has

to be a tongue section for an angle 090. At this angle the flow will enter the rectangular

section of the volute with

I
2 0,3 b3 +b r3

                                                                              

ln — . (2.25)
cm3 b r3
internal volute is as follows:
b.
1n 1— : it; (2.26)
r3 cu, b

Eckert et al. (1961) and Pfleiderer et al. [29] do not use a linear form of equation (2.8),

but they assume its validity. With the continuity equation and equation (2.8) they receive

Q,p =[cu »dA 5.473013 -b-dr

(2.27)

                  

Using Q, = [g] + (r — r')2 = R2, equation (2.27) becomes

 

 

 

 

V3

_720-( cu3 -r3 )'j-R‘/R2—( r— —'r)2 dr_7207r-(c,3-r3)(r,_ fr'z—Rz) (2.28)
{/3 r'—R

With r' = r3 + R a solution for the radius R of the volute cross-section can be given.

The minimum radius of the cross section is Rm 2 3/ 2, due to the fact, that the

volute diameter must be larger than the impeller width. Therefore it is not possible to

39

generate a circular cross-section in the tongue region and the tongue section of the volute
has to be calculated using rectangular shapes or the method suggested by Pfleiderer [29].

Another design method suggested by Pfleiderer [29] and tested by Floerkemeier
[29] implies a shape coefficient [1 in the following equation

Ra
(p = 27:.w, -R lid}? (2,29)
”(7’) Vopt R‘

The results obtained by Floerkemeier can be seen in Figure 2.19. The highest pump

efficiency at design conditions is given for a volute with p 2 pm,“ as proposed by

Pekrun [29].

2.2.4 DESIGN WITH FRICTION

The consequence of fiiction on the walls is a decrease in total pressure in the flow
direction. A volute calculated without considering friction would have a pressure
decrease from the volute inlet to the exit and a sudden pressure rise at the tongue. In order
to achieve a circumferential uniform pressure distribution at the volute inlet, design has to
be corrected.
Since, it is not possible to calculate the friction losses exactly, Eckert (1961) takes into

account the loss head with a fiiction coefficient A :

2
dhv=/1-£—- ‘1‘
2g Dhyd

 

(2.30)

DM is the hydraulic diameter of the cross-section and c the average velocity.

Eckert substitutes ds = r, -d(p and integrates equation (2.30), receiving the

pressure losses. By increasing the final cross-section (at the throat) accordingly, from Al

40

to A,’ and subsequently the other cross-sectional areas the losses can be compensated.
The average velocity changes, following the continuity equation

C1 -A1 =cf-A,’ (2.31)
The pressure loss can be calculated with the Bernoulli equation

pl —pv +§cl2 2 pl +30;2 (2.32)

2

Using equation (2.31) and (2.32) the head loss can be written as

l’l-t—ciz-l—E:2 =i1-fil— (233)
v 2g Cr 23 A1, '

From this equation the necessary cross—sectional area A,’ can be calculated, so that the

pressure losses due to friction are compensated.

To compensate the pressure losses and to avoid a periodically unsteady impeller
flow due to non-uniform pressure distribution in the volute Eck [17] states the same
equations as given by Eckert (1961) for slightly increasing the volute cross-sectional
area. He demonstrates his method by calculating the increase in area of a conic diffirser.
Therefore he limits the validity of equation (2.33) and demands to consider the curvature

of the volute, which causes secondary flow.

2.2.5 AREA RATIO DISTRIBUTION
In order to receive uniform inlet flow conditions the cross-sectional area centriod

radius A/r must increase linearly from the volute tongue to the exit. For optimum mass

flow rate the amount of mass collected by the volute has a linear increase and the

circumferential pressure distribution is uniform.

41

Lorett (1986) gives an equation to calculate the cross-sectional area at any angle:

(fl) :Yfl’lfl (2.34)
R w gH 27:

R is the cross sectional radius, a) the angular velocity, 77 the hydraulic efficiency and

H the total head (Figure 2.20).
Japikse (1996) introduced a simple volute design based on a geometric area ratio.

The area ratio is defined by the equation:

AR=£=£
4

A,

D12

—— 2.35
27:43 -b3 ( )

where A3 and A4 are the volute inlet and exit areas. The circumferential area distribution

can be seen in Figure 2.21.

2.2.6 NOVEL IDEAS

Another volute design described by Eck [17] is the axial volute (Figure 2.23). It is
developed between two co-axial cylinders in the axial direction and has the advantage of
arising fiom cylindrical surfaces. This results in an equal distribution of the
circumferential velocity c. and the lateral boundary increases only in proportion to the
angle of admission. The lateral width b can be calculated for a given height hand an

average value of c. as follows:

b: V L (2.36)
(1.41360

 

Whitfield and Roberts [45] examined two different volute/radial diffuser systems

and compared them with a standard volute (Figure 2.24). One is designed to transfer part

42

of the diflirsion process in a conic diffuser downstream of the volute, the other design
allowed diffusion to take place in the collecting volute. For both systems the length of the
radial vaneless difiuser was significantly reduced. Due to the fact, that the pressure rise in
the shorter vaneless diffuser is lower than in a regular one. The flow velocity in the
volute of the first system is larger, leading to an increase in fiiction losses. The reduction
in pressure ratio of the stage can be seen in Figure 3.18. For the second prototype the
pressure ratio is close to that of the standard volute. However, pressure ratio and

efficiency fall rapidly with increasing mass flow.

2.3 VOLUTE PERFORMANCE
2.3.1 OVERALL PERFORMANCE

Volute performance is strongly influenced by the geometry of the volute casing,
the flow parameters and the amount of mass-flow and the volute-impeller and volute-
radial diffuser interactions. (Figure 2.26) shows the influence of the volute geometry on
the efficiency of a radial compressor Eckert et al. (1961). As to be seen, asymmetrical
volutes have a higher efficiency than symmetrical ones due to a stronger secondary flow
in the symmetrical volute. With the meanline performance prediction program, Weber et

al. (1986) describe how the losses reduce the volute performance.

2.3.2 PERFORMANCE EQUATIONS

For the evaluation of volute performance two primary parameters are calculated.

———__ (2.37)

43

C1» is the static pressure rise coefficient. The other parameter is a) , the loss coefficient.

P0. ..

(1):—

On:

— 131-0“ (2.38)
- Pm

Van den Braembussche et al. (1997) measured and predicted the static pressure
rise and loss coefficients for a compressor with an external volute and rectangular cross-
section. The results show higher losses for off-design mass flows, indicating that the
amount of mass flow affects the volute performance. The performance of a volute can be
estimated by using the following equation, combining the static pressure rise coefficient,
the loss coefficient and a term to measure the outlet kinetic energy:

—0

CP+C0+I_)° _" =1 (2.39)
Pso—Pz.

 

The dependence of the loss and pressure rise coefficients on the volute outlet flow swirl

can be seen in Figure 2.27.

2.3.3 OFF-DESIGN EFFECTS

Operation of the compressor at off-design points has a great effect on volute
efficiency. The volute is designed to have a circumferential uniform static pressure
distribution at optimum mass flow rate. However, at off-design operation the pressure
distribution is distorted and the volute efficiency decreases due to diffusion, mixing and
fiiction losses.

At smaller than optimum mass flow rate the volute acts like a diffuser resulting in
a static pressure rise from volute inlet to outlet. If the mass flow rate is too large, the flow

accelerates throughout the volute, which results in a pressure decrease between the volute

44

tongue and the conic diffuser. The effects of off-design operation on the compressor
performance are a decrease in volute efficiency due to higher losses and radial forces on

the impeller due to the non-uniform circumferential pressure distribution.

2.3.4 VOLUTE-IMPELLER INTERACTION

A circumferential uniform pressure distribution caused by a correctly designed
volute at optimum mass flow rate results in a uniform blade load of the impeller. Only the
volute tongue causes pressure and velocity distribution distortion, therefore, influences
the impeller performance. The large pressure changes in the tongue region cause noise
and vibration as well.

At off-design conditions the large velocity and pressure distortion cause variations
of velocity and pressure along the impeller periphery. The flow in the impeller channels
change periodically, causing radial thrust on the impeller shaft. The cyclic variation of
the flow in the impeller channels results in additional energy dissipation. The effect is
strong for short vaneless diffusers and almost negligible with vaned diffusers, Van den
Braembussche (1998).

As described by Van den Braembussche (1998), the volute influences the impeller
by a change in operation range and shifi surge and choking limits. Smaller volutes give
higher shut off pressure ratios and steeper performance curves than standard ones. The
influence of two different volutes on the same impeller is shown in Figure 2.30. As seen
in the figures larger volutes result in a larger operation range but have an unsteady flow at
higher-pressure ratios. The flow in the smaller volute is more stable but the volute has a

smaller range due to choking at low-pressure ratios.

45

Lorett et al. (1986) developed a computational method to express the volute-
impeller interactions. They presented numerous equations to predict the flow behavior at
off-design conditions. At very low-mass flow complete flow reversal in the impeller
channels can occur, introducing flow prerotation at the impeller inlet. Figure 2.31 shows
the distortion of the velocity field in the impeller at low mass flow and the reversal of the
velocity.

Bowerman et al. [28] measured the influence of the volute performance on the
impeller. They used three volutes with a constant axial width and the variation of the
cross-sectional area defined by the logarithmic shape of the outer wall. Using the
conservation of angular momentum equation and the continuity equation the volute is

defined by

30
R -_— R . eV (2.40)

where R and6 are the radial and angular coordinates of the volute outer wall, (6 and 1p
are the flow- and head coefficients. The cross sectional area distributions of the three
volutes result from the choice of 05 equal to 75, 100 and 120 percent of the impeller
design flow coefficient. Figure 2.32 shows the overall performance of the three-
volute/impeller combinations.

For low flow rates the volute with the smallest cross sectional area has a higher
efficiency than the other volutes, but for high flow rates the decrease in efficiency is
larger than for the other volutes. The contrary situation can be found for the volute with
the largest cross sectional area. This shows that the shape of the volute outer wall

determines the volute-impeller matching mass flow.

46

2.3.5 VOLUTE-RADIAL DIFFUSER INTERACTION

Pressure and velocity distributions in the volute affect the radial diffuser
efficiency as they cause velocity distortions in the radial diffuser. Figure 2.33 by Mueller
[29] shows the velocity distribution in the radial diffuser caused by the volute. The volute
tongue causes a wake, which propagates itself in the radial diffuser and contributes to the
radial diffuser losses as measured.

The secondary flow in the volute greatly influences the radial diffuser flow
leading to a non-uniform pressure distribution in the radial diffuser cross-section. Mueller
[29] noticed that the secondary vortex flow transports boundary layer material in the core
flow of the radial diffuser causing mixing and diffusion losses. With an asymmetrical

design of the volute, it should be possible to reduce the radial diffuser losses.

2.3.6 PARAMETERS AND MECHANISMS INFLUENCING PERFORMANCE

A high inflow velocity 0 affects the volute performance negatively, as it increases
the volute wall fiiction losses, which are function of the volute Reynolds-number.
Following the pipe fiiction loss-model, the pressure losses due to wall friction are also a
function of the volute surface roughness.

Varghese (1978), describes in his work the influence of the volute surface
roughness on compressor performance. As expected the hydraulic losses increase with
increasing surface roughness, as shown in Figure 2.34. The experimental results shown in
this figure are in agreement with the empirical equation given by Varghese for the volute

efficiency:

([30 = 2.1605 . 112—00738 — 0.029111%?) (2.41)

47

Varghese observed that with increase in surface roughness, the best efficiency
regime shifts to smaller discharges. The hydraulic losses in the volute however are not
mainly influenced by the surface roughness, but by mixing losses, which are dependent
on the Reynolds number (Figure 2.35). The results show the mixing process plays a more
predominant role in deciding the volute losses than the surface roughness. The losses can

be described by the following equation:

K _ —— (2.42)

where (H 1 — H) is the difference between the virtual and the total head developed by the

pump. K can be expressed as
d
K =f[Re,Z,R] (2.43)

and can be calculated empirically.

Iversen et al. (1960) assumed that the mixing of the fluid exiting the impeller with
the fluid already in the volute influences the volute pressure distribution. In order to
describe the relation between the mixing and radial forces on the impeller as well as head
losses, Iversen developed a program. Additionally he performed experiments with a
centrifirgal compressor to compare his findings with the program. Figure 2.36 shows the
results and comparison.

The influence of the volute inflow angle a, is described by Van den
Braembussche (1998) and Huebl [29]. If the inflow angle is too large with respect to
tangent, the flow has a large radial and a small tangential velocity. This occurs, if the
volute operates at larger than optimum mass flow rate. Due to the large radial velocity the

formation of secondary flow vortices increases having a negative effect on volute

48

efficiency. For a small inflow angle the radial velocity is small compared to the tangential
velocity, resulting in a small vortex formation.

Cohen et al. (1987), describe the effect of high Mach numbers on volute
performance. High Mach numbers at the volute inlet are to be avoided, as they cause
shock losses. They also imply high air speeds and large pressure gradients leading to a
circumferential variation of static pressure. To reduce the relative velocity at the impeller

inlet and hence the Mach number Cohen suggests to use inlet guide vanes.

2.3.7 VOLUTE LOSSES
2.3.7.1 GEOMETRICAL AND AERODYNAMIC EFFECTS

The volute itself has a direct influence on the performance of the compressor
because of the non—isentropic deceleration of the fluid inside the volute, Van den
Braembussche (1998). The overall performance of the volute is influenced by the volute
cross-sectional shape and its radial position, the circumferential variation of the cross-
sectional area, the tongue geometry and the shape of the conic diffuser, Elholm et al.

(1992)

- Aerodynamic effects influencing performance

Because of the curvature of the volute, boundary layers of the volute flow are
decelerated and as they have the pressure distribution of the core flow, they produce a
secondary flow on both sidewalls of the volute. The boundary layers follow the pressure

gradient from the surface to the core of the volute, mix with the core flow and are thrown

49

back towards the volute surface. A twin vortex is shaped which produces pressure losses
(Figure 2.37). The twin vortex can be reduced to a simple vortex designing the volute
asymmetrical, Eck [17].

- Influence of the cross-sectional shape and volute size

The cross-section shape and its radial location have an important influence on the
volute losses. Circular cross-sections have a smaller wetted surface and therefore show
smaller fiiction losses, Van den Braembussche (1998). Although it is quite imaginable,
the swirling flow in rectangular cross sections does not cause higher losses than in
elliptical or circular ones, as the flow approaches the comers tangentially and does not
undergo a 90° - turning.

Volutes with elliptic cross-sections show higher diffusion and mixing losses than
circular ones, because of the periodic increase and decrease of the swirl velocity Vs
following the conservation of angular momentum equation. Asymmetrical volutes have a
higher efficiency than symmetrical volutes, because of the formation of a single vortex in
the asymmetrical one instead of the double vortex in the symmetrical volute.

The size of the volute also has major effects on the performance of the compressor-
volute system. Larger volutes give lower shut ofl pressure ratios and flatter performance
curves, while smaller volutes result in higher shut off pressure and steeper performance
curves than standard ones, Van den Braembussche (1998). There is only one amount of
mass flow rate for which the volute has a circumferentially uniform pressure distribution
and therefore the least losses. If the mass flow rate is smaller than at the optimum, the

flow is decelerated inside the volute and a static pressure rise from the volute inlet to the

50

outlet occurs, resulting in diffusion losses. Small radial velocity causes a rise of swirling
motion, which is dissipated by internal shear and wall fiiction.

For larger than optimum mass flow rate the volute is too small, thus the flow is
accelerated inside the volute resulting in a pressure decrease from the volute inlet to the
outlet. This results in a circumferential pressure distortion at the radial diffuser and
impeller exit and extra losses due to a partial destruction of pressure rise, which took
place in the radial diffuser, Van den Braembussche (1998). Internal volutes show a lower
efficiency than external ones, due to an increase in through flow velocity because of a
decreasing average radius.

The acceleration of the fluid destroys the static pressure rise achieved upstream in the
vaneless diffuser. Therefore the static pressure decreases from the vaneless diffuser exit
to the volute exit. Another reason for the low efficiency of internal volutes is an
accumulation of low energy fluid at the inner wall and the existence of an anti clockwise
vortex in the hub inner-wall comer, Van den Braembussche (1998).

- Influence of the tongue geometry

The tongue is a major contributor to the casing losses, Chen (1986). Especially in
turbine volutes the tongue losses are not to be neglected, as the flow around the tongue
generates a wake, which leads to additional diffirsion and mixing losses. In compressor
volutes impact losses occur at the tongue at off-design operation, as the flow angle off the
impeller does not match the volute-opening angle [29]. An increasing opening angle at a
given mass flow leads to flatter loss curves, with the point of minimum losses moving to

greater flow coefficients.

51

The volute performance is also influenced by the necessary clearance between
impeller and volute tongue. Parts of the flow will stream through this gap and produce
losses, as they have to rotate around the impeller again. The clearance can be modified
either by changing the tongue angle or the length of the tongue. To change the tongue
angle, the volute can be designed with a pivoting tongue (Figure 2.13). A larger clearance
leads to a decrease in compressor efiiciency and a more narrow operating range. The
tongue length afi‘ects the overall efficiency with a shorter tongue causing higher
efficiency than a longer, Ayder (1993). Pfleiderer and Peterrnann [29] recommend that
the tongue should be of a certain thickness and well rounded to minimize a decrease in
efficiency at off-design operation.

- Influence of the exit diffuser

A major contributor to the volute losses is the secondary flow in the exit conic
diffuser. The intense vorticity generates strong local shear resulting in turbulent and
viscous dissipation. From their numerical calculations Li et al. [27] developed, that the
swirling motion of the fluid particles in the curved conic diffuser is more intense than that
in the straight diffirser, therefore leading to higher losses in the curved diffuser. They
conclude, that the losses in the diffuser can be reduced by improved design, such as a
straight diffuser. Pfleiderer [29] claims the opposite. He says that the curved diffirser can

have a higher efficiency than the straight diffuser.
2.3.7.2 LOSS COEFFICIENTS

There are several models describing the losses in the compressor volute. One of

them is the model by Weber et al. ( 1986), which is further described by Van den

52

Braembussche et al. (1992, 1998). It was generated for use in meanline performance
prediction programs (MLPPP). The model describes the four main sources of losses:
1. Meridional velocity dump loss

It is assumed that the head associated with the meridional velocity at the volute
entrance is lost. The reason for this, intuitively given by Weber et al. (1986), is that the
meridional velocity entering the volute becomes a spiraling velocity component in the
volute does not contribute to the transport of the fluid through the volute. The amount of

loss is expressed by the equation

1
Apgfl’DL : 5p ' vrzzs (2-44)

2. Skin fiiction loss
The fiiction loss is a firnction of the surface roughness of the wall, the volute’s

hydraulic diameter Dhyd, the average path length of the fluid particles L within the

volute and the volume flow entering the volute, represented by the through flow velocity

v,.

 

lp- VT (2.45)

The friction coefficient a), is a function of the Reynolds number and the relative
surface roughness and is obtained by making use of the standard friction charts for pipes.
3. Exit cone loss

Having been calculated during the past as a simple, sudden expansion loss, the exit
cone loss is now calculated using the standard gradual expansion model from pipe flow

analysis, Van den Braembussche (1998).

53

2
1ng = m. -C - p97“)— (2.46)

With v4 as the velocity at the radial diffuser entrance and v5 as the exit velocity.

21ng depends on the total opening angle of the cone and varies from 0.15 for an

opening angle of 10° to a value of the order of 1 for an opening angle 60°, Van den
Braembussche (1998). Weber et al. (1986), propose a constant value of 0.15, since the
opening angle of the volute exit cone should not exceed 10°.
4. Tangential velocity dump loss

Two assumptions are made, in order to calculate the tangential velocity dump loss:

If the tangential velocity accelerates from volute inlet to volute outlet (v,3 < V”), it is

assumed that no tangential velocity dump loss occurs.

If the tangential velocity decreases from the volute inlet to the volute outlet (VT3 > v“),

then the flow diffuses and the appearing total pressure loss is equivalent to the total

pressure loss in a sudden expansion mixing process.

Apgmr. : pr@£:2_vT‘4—) ' (2-47)

where a), = 1 .

Van den Braembussche (1998), points out that the modeling of the tangential
velocity dump losses without taking into account the variation of the central radius of the
volute channel causes an incorrect prediction of the losses especially for internal volutes.
Therefore, the modeling of the tangential velocity dump loss has been modified by
introducing an intermediate station in the volute channel at the point where 50% of the

total mass flow is collected by the volute. In this new model the loss consists of two

54

components: If the tangential velocity at the volute inlet v” is larger than the tangential
velocity at the 50% collection point v,3_f the flow is accelerating in the first part of the

volute and the first component of the loss is calculated by

(”73 _ V734);
2

 

 

Apgl'DL—f : pr (2-48)
If v,3 is smaller than v,,_ f the first component states
0 (vrs _ Vr3~ [)2
ApTVDL— f = .0 2 (2.49)

In case of v” is larger than v,4 the flow is accelerating and the second component of the

tangential velocity dump loss is given by

(VT3 _ VT4)2 (250)

Apgl-DL -4 Z (or p 2

Otherwise,

.3

‘-

(vT3 _vT ) (251)

AngDL—‘t = ,0 2

The total tangential velocity dump loss is the given by adding the two components:
Apgr’m : Apgl’DL- f + Apia/0&4 (2- 52)

Another model describing the losses in compressor volutes is the one by Decker [29].
From his measurements of the flow in a compressor with different impellers and volutes,
he specified three different types of losses:

1. Wall fiiction loss
Similar to Weber et al. (1986), Decker describes the wall friction loss in analogy to

the pipe fiiction loss model.

55

2
- C
W... = ——°’°'SP, 5” (2.53)
”2

with cs}, as a characteristic velocity of the volute, here the average velocity in the 360

degrees cross section.

Taking into account the continuity equation the wall fiiction losses can be written as

Wurb : Crb,SP [Aijwf (2 54)
SP

2. Decker assumes that the flow performs according to the angular momentum equation.
This implies, that the volute can only have the correct size for one flow coefficient

(onopnsp , which represents the proper amount of flow.

The volute is either too large or too small for all other amounts of mass flow, so
that the flow angle off the impeller is not according to the volute tongue angle. This

results in impact losses, which can be written as

WVJLSP : 43:,SP[::i] ((0, — ¢r,opt,SP) (2-55)

with (pmmsp as the optimum mass flow coefficient.
3. The combination of a rotating impeller and the non-rotating volute implies a certain
link between impeller and volute tongue.

This distance implies that a small part of the fluid flows through the gap between

impeller and tongue and is forced to revolve around the impeller again, leading to a so-

called kink-loss 01,, SP1 which is a linear dependence of the theoretical pressure

coefficient 01,, .

56

stSP : Ksy/th (2‘56)

From his experimental and computed results, Decker assumes a linear dependence of the

cross-section rate ASP / A2 for the fiiction- and impact coefficient:

A. A
€10,513 : krb "Ab—P; €51.51) : ks! ASP (2.57)

 

For the volutes used by Decker the coefficients k, , k, and k, are constants.
The total volute losses are the sum of the three loss types:

Wasp : (”wasp + Wursp + l/’1-1,5P (2-58)

Huebl [28] introduced another model. He describes the losses in the volute consisting of

two parts, the wall fiiction head loss and the interior fiiction head loss.

1. The wall fiiction head loss is the difference between the squared in-flow velocity c0

and the squared velocity on the volute surface cs:

h: . (2w)

 

2. The tangential velocity in the volute is reduced by wall fiiction.
3. The difference between the fiiction induced reduction of the tangential velocity head

and the original tangential velocity head is called interior fiiction head loss.

 

aw)

Summation of the two loss types results in the local head loss for any location in the
volute casing.

mzmfim am)

57

The loss model given by Eck [17] contains of radial diffuser losses and fiiction losses.
The radial diffuser losses developed due to the retardation of the flow in the radial
diffirser. With the entry velocity into the volute is C3 and the discharge velocity ca, the

losses can be written as
Apt. -- (0.1— 0.2)(p/2)lc§ — of] (2.62)
In case that the casing width 8 is greater than the impeller width b an additional
shock loss occurs, as the meridian velocity c2”, will change to c3," following the

continuity equation. The resulting loss can be described as follows:

B

Apt. = (p/2)(c§,. — c§,)=(p/2).,2,[1_[£)] (2.63)

Eck describes the friction losses as throughout the dynamic pressure of the meridian

velocity in the radial diffuser.

loss,total : (p/z) 622»: (264)

Relating the total loss coefficient to the dynamic pressure of the entry velocity, the

friction losses are

Aploss,total : C gcg (265)

and for the loss coefficient one can obtain

2
Aplosstoral C ° 2
4 =——————: = __21»_ =srn 012 (2.66)
(p/:Z')'c22 cz

Lorett et al. (1986), has a simple loss model consisting of mixing losses and pressure

drops caused by wall friction. He describes the energy losses of the volute as the

58

difference between the flow energy at the impeller exit and the energy at the volute
outlet, without distinguishing single loss types.

The energy contributed by the impeller at each section of the volute, is given by Lorett

 

as:
c2
AE, = AQ,[HS, + 2’] (2.67)
28
The energy at the volute exit is
(:2
AEN : Qror [Hay + A] (2-68)
2g

The total volute loss can now be obtained by subtracting equation (2.67) from equation
(2.66):

L = ZAE, — EN (2.69)

Eckert’s loss model only takes into account the wall fiiction losses and gives

equations to compensate them for volute design. He describes the head loss dhv in

relation to the friction coefficient xi :

2
dh, = 2°— d‘
2g Dhyd

 

(2.70)

Substituting dsbyds : rs -d(p and integrating equation (2.70) the pressure loss for a
volute section can be written as

4’1 2
11, :JL ’i—C—da (2.71)
2g 11. Dhyd

Eckert uses the circumferential velocity at the centriod c as an approximation for the

cross-sectional velocity. DM is the hydraulic diameter of the cross-section.

59

Ayder et al. (1993) described another three-dimensional model, which numerically
calculates the volute losses by adding second order dissipation and wall shear forces to an
Euler solver. They justify their method with the fact that the simplified one and two-
dimensional prediction methods found in the literature are of limited interest, since the
volute flow is highly three-dimensional. The flow in volutes is more affected by the
losses in the core flow than by the losses at the wall. However because it is quite difiicult
to determine the core losses numerically and shear forces are calculated only on the walls
and the internal fiiction is approximated by a viscous term. The wall shear stresses are

given by

1'

wall

= c, g p . v2 (2.72)

and its components are added to the loss vector, taking into account the energy
dissipation due to wall friction. The viscous energy dissipation is achieved by the second
order dissipation. The equations are not given here due to their complexity, they can be
found in Ayder et al. (1993). They conclude that their model using an Euler solver with a
loss model can predict the volute flow and losses accurately and causes a smaller

computational effort than a solution of the full Navier Stokes equations.

60

FIGURES

61

 

_.—---'I""‘\
I \\
-——*“'”"’~‘ I \
I \ I ‘
I I ‘ l .
‘_~¢.’.-\ ‘ l \
F. ’I I \ I I .
.. l \ 1 I I '
--"' ' 1 \ I ‘ l ‘ ‘ 4
. 1 1 1 . r 1 ‘ 1 I
,..4.~~ , 1 1 \ a \ \ ’1 \\ , 1
'-- i ‘1 ‘ ‘ ) ‘11 ‘s I" \ ‘x I" ‘ I’ ‘
nvké.‘ 1" \V“ ‘Ij als“"’ ) —‘.~'V’ ’4 -fi‘:-’ :
I
1' 1 ’ : :
I ‘ .
‘ ~“-.--J ‘-_----' ~-~i--- -*--—-- —-"-.

 

 

62

 

 

 

 

Figure 2.3: Static Pressure Distortion for High, Optimum and Low Mass Flow

 

Figure 2.4: Static and Total Pressure Variation (Pascal) over the Volute Cross

63

 

1 1

1 1

1 l

1 1

1 1

low mass flow 1.

1 /1\
1 1

 

 

 

\ .
g 1 \. /1/ I \\
g; 1 ,\\._//optimum mass flow “
e \ 1‘1/ ‘\
EL: 1r m5 i 1
"g : KT igh mass floj~
(‘5 1 l I

1 1 1

' 1 1

l

1 / 1 \\ 1

1/ 1 ‘ 1

1 1 1

1 1 1

0 180 360

Azimuth Angle (deg)

Figure 2.5: Circumferential Static Pressure Distribution on the Volute Wall

 

Figure 2.6: Swirl- and through flow Velocity Variation
(m/s) over the Volute Cross Section

 

 

 

 

 

.1,
O p .o- ’ ’ -.. ’1 - - o _.o
- d - -- — - -— . n "
a i ’1' / a, x \
’ ' i'. o- — - / I" 5 ~. ‘\ ' . \ .\ \
. " I ' I I —
/ i ‘ . r I ‘ '. r ‘ ‘ ’ " I
\ ' '
.- l _ I . I I 0' . I / I
F I I 1' " I. .' $ \
' I ’ g I I ‘ \ \ — I. / I
I .’ l
l . , . / .. . .. , '1 ,1 1 \ _ .4 I. ,
I ‘ \ ' I ‘\ / “ \
.l . a' l- ’ 1 ‘ a ’ , _ _. .J' ’
$ ‘\ ‘ s I \ \
'0 ‘ 0' "f A K .r a
“1. “~ "" x K --. ‘r‘ x. \ “ ""
_\ ,_.\- —~-- I \ a — __’ ‘. -_ - - -
C‘ --

 

 

 

 

 

 

Figure 2.7: Position of the Swirl Center for High, Medium and Low Mass Flow

64

 

 

 

Figure 2.8: Formation of the Volute Casing from the Streamline of a Vortex Source

Throat

 

 

 

Figure 2.9: Volute Casing with Logarithmic Shape

65

 

 

 

 

 

Figure 2.12: Volute with Multiple Discharge Points

66

 

Figure 2.13: Volute with an Adjustable Tongue

b(f)

 

 

 

 

 

 

Figure 2.14: Volute with Rectangular Cross-Section

67

 

 

 

 

 

1"" ‘

b/Ztard 1

Figure 2.15: External Volute with Tapering Side Walls

 

Figure 2.16: Volute with Circular Cross Section

68

 

 

 

 

 

 

Figure 2.17: Internal Volute

 

 

 

 

 

 

 

 

 

 

Figure 2.18: Basic Volute Geometry

69

 

‘5:

 

Pfleiderer

 

Incorll(0.9,1.1.1)

 

 

 

 

 

\‘~\.. Pekrun
\u‘ A
~-\.. N”-.. --m<or=m...
\\ \-.\..‘ “ .- m(o) m
‘x. :sz .... , “1"“
s _—‘ " .‘.. _
\ N“ ______ 1 __-- / 1 ,».<__ __ —m(Q)_mw
/ / ‘-.‘
\ A/A’
EI—r Steganofi

 

---- m(Q)= 111 Step

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.19: Distributions of Shape Coefficient of Volute Outer Wall

 

  
    

Cl Casing A
B Casing B
Q Casing C

A/r

 

 

 

\J

0 120 240 360
Azimuth Angle (deg)

Figure 2.20: Distribution of area by centriod radius over azimuth angle

70

 

A / ADiff outlet

 

 

 

O)

 

\

 

 

 

 

 

 

 

 

1

J 3 4 Crosls Elections
*1”; :
1

100 200 300 400 500
Azimuth Angle (deg)

Figure 2.21: Circumferential Variation of Cross Sectional Area

 

 

Figure 2.22: Helix Volute

71

 

Standard Volute

A

>/’“‘“\\ R

 

Figure 2.23: Axial Volute

 

 

 

 

Standard
P2
_Standard
Diff. Exit
Diff. Exit __
_ _ 311:: _P_ _ _,P_‘l ___ _
Diff. Exrt
Azimuth

Figure 2.24: Comparison of Standard and Modified Volutes

72

2.5 —~

S
1

Static pressure ratio

1.5——

 

— — — Standard Volute

 

P1 Volute ,

Sbkrev/min

  
  

52.5 k rev / min

 

42 k rev/ min

 

111711111
123456789

Non-dimensional mass flow

Figure 2.25: Comparative Performance Maps of Standard and Modified Volute

Relative Drucmhl y

 

3
.c:

1.1
1.0

0.9 g

0.8 E

0.7
a:

0 20 40 60 8010012014016018020096]
ReiativeLieferzahl 1’

Figure 2.26: Influence of the Volute Casing on Compressor

73

 

 

 

 

 

 

 

 

 

 

2.0
l — (a) + 5,.)
1.0 47/

/

0 \
-1.0

Q»
-2.0
0 0.3 0.6 0.9 1.2
VR IVT

Figure 2.27: Variation of the Volute Loss Coefficient and the Pressure Rise
Coefficient as a Function of the Diffuser Outlet Swirl

 

low med max
Mass Flow

 

t ----- Measured ——Calculated ]

 

Figure 2.28: Loss and Static Pressure Rise Coefficient
for the External Volute

74

 

 

 

 

Static Pressure

 

 

 

 

 

 

 

 

 

 

\ E 119;“
\ ,2, z/ \
\ high E, flfmk
/ ,2 \f A
\/’ Iowv

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 60 120 180 240 300 360 0 60 120 180 240 300 360
Q0 Q0

Figure 2.29: Circumferential variation of static pressure and tangential
velocity at the volute inlet

 

 

 

 

6.0 1 1 1 6.5 r I 1 i
0 Impeller - vaneless diffuser - volute o Impeller - vaneless diffuser - volute
_P5_ Volute designed for PSIP,=3.8 I f; Volute designed for P5/P,=6.0
0 I 0 6.0 ' ‘
P. 5.5 , P.

 

/1( {/1
5.0 \ (

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[I
4.5
[AK 4.5 1Z2 /
4.0 I! 1 / /
1.... fl / 4.0 I I
3.5 l/k /
/ )>// 3.5 /
3'0 Z? I 3.0 biz
/
2.5 y I! k 2.5 ’4'“
a % / l
2.0 2.0
0.5 0.75 1.0 1.25 1.5 1.75 0.5 0.75 1.0 1.25 1.5 1.75
Q(kg/S) Q(kg/S)

Figure 2.30: Influence of the Volute Size on Radial Compressor Performance

75

 

+
N

 

f.

\
l
I

/

F

 

Meridional Velocity cm (m/s)
\
\
/

 

 

 

I
k

 

O

180 360
Angular Coordinate

Figure 2.31: Reversal of Meridional Velocity at the Impeller for
Low Mass Flow

 

 

0‘ ..H‘°\
”Ax

.7' >5
['7 '- \\
,-I '.
.’/

.,- i
/’ \ '21
I 2‘
.I/ l 1‘

7i 1 i
I —75% Volute Combination :

—J—~ -- ~ «100% Volute Combination
)4 _. __1 20% Volute Combination
i

O

 

 

 

 

 

 

 

 

Pump Efficiency ——->

 

 

 

 

 

 

 

 

 

 

Flow Rate Coefficient ——~>

Figure 2.32: Pump Efficiency for three Impeller — Volute
Combinations

76

sz

1

1 .0

0.5
0

Geschwindigkelt c

 

0 0.25 0.50 0.75 1 .00
innen ausser
relative Breite le

Figure 2.33: Velocity Distribution in a Volute
Conical Diffuser

 

Hydraulic Efflcnency —’
> i
/7

 

8. Painted Surface
Impeller Flow Coefficient —>

 

 

 

Figure 2.34: Hydraulic Efficiency for Different Volute
Surface Roughness

77

 

\ 1. Natural Surface
?:\\‘ 2. D=1.200 mm
35 \f . 3. 0:0 815 mm
f‘i-‘x 4. 0:0 475 mm
\\ \\\ 5. 0:0.260 mm
\ ii} §§ 6. 0:0 150 mm
' .73. ‘55:; ‘\5.\ 7 D=0.080 mm

T * “\\ \E-l;;.:\fi~“‘\\\~\ 8 Painted Surface

 

 

 

 

 

Re—>

Figure 2.3 5: Hydraulic Losses K for Different Surface Roughness

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

60
Euler
50 \\ ’/
... Stodolai \
8 40 \\
i’ 30 \ x \\ \
x
“’5‘ \ V\\
20 a
\ \ \
; \
10
‘l
\ \
0 l \
0 100 200 300 400 500

Capacity - GPM

Figure 2.36: Pump Head-Capacity Relationship
Effect of Volute Mixing Losses

78

Total Pressure Loss

 

Figure 2.37: Asymmetrical and Symmetrical Volutes

 

0.10
Experimental Data from Reference (4)

0.08 + Pressure Ratio = 1.50 design point

— Pressure Ratio = 125 design point
0.06
0.04
0.02
0.00

0 60 120 180 240 300 360
Azimuth Angie (deg)

Figure 2.38: Casing Total Pressure Loss at Rotor Inlet

79

CHAPTER 3

EXPERHVIENTAL APPARATUS

80

In this chapter, the details of the experimental facility setup and modifications
are discussed. The initial measurement strategy and fiirther changes were described.
Note that because of the confidentiality of the compressor geometry, the author was not
permitted to provide the details of the compressor geometry and they are not presented

in this dissertation.

3.1 MODIFICATION OF THE TRANE COMPRESSOR

Trane Company donated a two-stage centrifugal compressor to Michigan State
University (MSU) for this study. The unit operates with refiigerant gas R123 and is
driven by hermetic motor (Figure 3.1). An electrical motor is installed on the casing and
shares single shaft with the compressor (Figure 3.2).

In order to prevent working with refrigerant and high-pressure ratios in laboratory
environment, air was selected as working fluid and modify the unit to a single stage
compressor. The original modification plan suggested by Trane Company included the
following (Figure 3.3):

1. Disassemble the compressor completely

2. Design and manufacture a new shaft to accommodate an external driving motor

3. Replace the 1St stage impeller by a spacer on the shaft

4. Provide a straight inlet to the second stage by placing a pipe inside the casing and
block the 1fit stage return channel

5. Reassemble the unit completely
Afier studying the design carefully and evaluating the resources, several

modifications were performed as following:

81

1. The compressor was disassembled completely following the disassembly manual

2. The new shaft was designed and manufactured by a company outside the state

3. A pair of thrust bearing at the driver side and a journal bearing at the impeller side
lubricated continuously during the compressor operation and the lubricant is gravity-
drained back to the oil reservoir through the passages inside the casing and external
piping. Trane Inc. provided a new pair of thrust bearing because the old ones were
completely damaged. The old journal bearing was used in reassembling after passing the
required inspection. The new thrust bearings were oven heated prior to the installation
and installed on the shaft with respect to the required installation procedure. The journal
bearing was installed after the shaft was located and aligned inside the casing. The
bearing cover rings were bolted after inspecting the required tolerances.

4. Having the shaft assembled in the first step, it was decided to couple the shaft to the
external motor’s shaft and run the external motor in order to perform the vibration
analysis and balancing before adding the 2"d stage impeller and the diffuser casing.

5. A stand was designed and built on the compressor platform to have a 300hp electric
motor replace the original driver. The new shaft was designed longer than the original
one in order to extend beyond the casing cover and be coupled to the new motor’s shaft.
The back cover plate of the motor casing was modified to let the shaft passes through
and a new seal ring was provided to seal the oil coming from the thrust bearings. The
motor was coupled to the shaft using a RING-flex Disc Couplings. This coupling
provides reasonable tolerance for vibration analysis. A local company aligned the motor
shaft with compressor shaft with the required coupling tolerances. The male and female

coupling casings were bolted together to complete the coupling procedure.

82

6. The power line in the lab is 410 volts and a frequency controller provides the
required power to run the motor with variable RPM, therefore, the motor was wired
from the frequency controller at it’s new location.

7. In the commercial setup the control box on the compressor’s platform has various
control instruments for operating the whole unit. The controlling process includes
warming the oil prior to the operation in order to overcome the cooling effect from
refrigerant and provide proper viscosity. In the modified setup, the control box was
equipped with a transformer to provide the power to the oil pump and heater, an alarm
for the required initial pressure in the oil supply line, and monitoring devise to control
the maximum oil temperature. In the commercial setup the heat generated by friction
was balanced with the refrigerant cooling and in the new design, the unit was cooled
naturally by air. Therefore, the oil temperature rises naturally and there is no need for
prior heating. In fact, the natural heating would be limiting because if the temperature of
the oil increases more than 250 Fahrenheit, the lubrication process will fail. Hence, an
alarm was provided to notify the maximum limit of the operation by monitoring the oil
temperature in side the oil tank. It was found that there would be a window of one-hour
experiment duration depending on the RPM.

8. After testing the coupling between the motor and compressor, the 2nd stage impeller
was installed and the same procedure (4) was successfully repeated. Finally, the diffuser
casing was installed and a Trane specialist approved the assembling process after
performing the last vibration analysis.

9. Instead of reassembling the rest of the compressor components, a new inlet was

designed in order to simplify the reassembling process and make the test rig practical for

83

adding any other parts for fiiture investigations. In the previous plan, parts had to be
assembled and reassembled very often and their extensive weight and size would make
the process very expensive in time and labor. Therefore, after the seal ring of the 2nd
stage impeller was installed, instead of installing the 18t stage return channel, a metal
sheet was rolled into the casing opening of the 2"d stage impeller. Rather than installing
the 1“t stage return channel, the roll was designed to have ears on the side in order to bolt
the roll to the casing. Because of the large size of the 2"d stage inlet, a reducer with a 12-
inch diameter flange was welded to the roll afterwards. Consequently a 12-inch flange
was welded to the reducer in order to use 12-inch diameter PVC pipes at the inlet.
10. The conical outlet of the commercial unit was connected to another pipe that carries
the refiigerant to the heat exchanger unit. In the current design, the outlet conic was
reduced to 12-inch flange by blocking it with a plate, which had a 12-in flange cut out.
In the next step, a 90-degree PVC elbow was used to turn the flow to horizontal and a
12-inch diameter PVC pipe carried the flow to the flow control valve. The valve was
providing different loading conditions for the compressor. In order to save lab space, the
outlet flow was turned around the test rig by using more PVC 90-degree elbows and
proper supports welded to the stand in order to cany the weight of the fittings and hold
the pipes horizontal. Note that no silencer used at the outlet and the flow was exhausted
into the laboratory directly after passing through the valve.

During the modifications, there were various challenges regarding to the
assembly details and limited equipment resources in the laboratory. Parts were rusty
because the compressor casing was made of cast iron and exposed to humidity in the

atmosphere. One important fact about the installation was since the machine was

84

centrifugal; there was no need for the platform to be bolted to the floor. Contrary to
reciprocating machines where forces make the machine “walk”, in the centrifiigal
machines, if all the rotating parts are balanced, there will not be any motion since the
forces are canceling each other. However, in this setup special rubber pads were located
underneath the platform that provides enough fiiction to prevent any small motions.

In addition, there was a minor change in the lubrication. In the commercial setup,
the oil shoots out of the journal bearing and is mixed with the refrigerant. Down stream
this oil is separated from the stream and returned to the oil tank. In the current setup,
when the compressor was running at higher than 2000 RPM oil leaked from the bearing
but the amount depend on the load of the compressor. In order to avoid or at least reduce
the amount of leak, more breath room was provided to the oil gravity drained loop by
adding a “T” on the top of the oil tank. One side of the “T” was guided to the side of the
compressor for breathing and refilling the tank and the other side was bolted to two
flanges on the old motor casing. This return would provide the atmospheric pressure
inside the motor casing. This modification reduced the leak significantly, however, oil

was detected at the volute outlet at high speeds.

3.2 INSTRUMENTATION OF THE FACILITY
3.2.1 OVERALL PERFORMANCE INSTRUMENTATION

As previously explained, for performance analysis, the values of total and static
pressures, temperatures and mass flow rate at the inlet and outlet of the compressor are

of importance. Therefore, the following describes them individually:

85

3.2.1.1 TOTAL TEMPERATURE

The total temperatures were measured utilizing two United Sensor TCS-lZ-K-
36-C-1-F temperature/thermocouple probes at the inlet and at the outlet. These probes
are used to measure total temperature of air, gas or liquids in industrial application.
These probes measure temperatures up to 2000°F in velocities from 100 to 2000 ft/sec.
A variety of complete line of exposed-loop, insulated junction, radiation shielded,
stagnation shielded and aspirated shielded is available and all are constructed of stainless
steel. The type TC is commonly used in all types of compressors for efficiency

measurements and up to 500°F.

3.2.1.2 TOTAL AND STATIC PRESSURES

Two United Sensors Kiel probes KBC-8 were utilized in order to measure the
total pressure at each side of the impeller. These probes are used to measure total
pressure in a fluid flow where the direction of flow is unknown. They can measure
pressures in flows up to Mach 1.0 with some considerations for pitch and yaw angles.
The outstanding advantage of Kiel probes compared with other total pressure probes is
complete insensitivity to direction of the flow within certain limits. Their yaw and pitch
characteristics are generally the same although stem interference on some designs will
change one from the other.

The probes were setup in this test rig such that the average values of pressure
were obtained by connecting the probes to each other by a “T” and reading the value at

the outlet of the “T”. Note that in both total temperatures and pressures, the probes were

86

installed in the direction of the mean flow path and immersed into the flow 1/3 of
diameter of the pipe based on ASME standards for flow measurement.

Four steel capillary static pressure taps with an outer diameter of 1/16 inch were
inserted at 90-degree intervals into the 12 inch diameter PVC pipe at the inlet and outlet.
Static pressures were measured by averaging the readings from the four pressure taps.
The surface of the taps were sanded and flushed to the surface in order to reduce the
error in reading the static pressures. The average measurements of the three taps on the
top and sides of the pipe surface were utilized because the leaking oil collected on the

bottom surface of the pipe, making the tap at that location unusable.

3.2.1.3 MASS FLOW RATE

In this investigation, a thin plate orifice was used at inlet to compressor in order
to measure the mass flow rate. An orifice is considered an obstruction of the flow in the
basic duct of diameter D, where the flow is forced through an obstruction of diameter d.

The B ratio of the devise is the key parameter

fl=— (31)

After leaving the construction, the flow may neck down even more through a
vena contracta of diameter D2 < (1. Applying the Bernoulli and continuity equations for
incompressible steady frictionless flow to estimate the pressure change will result in an
ideal volume flow rate. However, the effect of the vena contracta and fiiction in the flow
forces to calibrate the idea mass flow rate considering a discharge coefficient to fit

relation

87

 

 

where subscript t denotes the throat area of the obstruction. The discharge coefficient Cd
accounts for discrepancies in the approximate analysis. By dimensional analysis for a

given design it is expected
Cd =f(,B,ReD) where ReD =— (3.3)

Indices 1 and 2 indicate the inlet and outlet of side of the orifice and multiplying (32) by
the density of the air, the mass flow rate will be calculated.

The thin plate orifice can be made with B in the range of 0.2 to 0.8 where the
hole diameter (1 should not be less than 12.5 mm. To measure P1 and P2, three types of
tappings are commonly used:

1. Corner taps where the plate meets the pipe wall

2. D: '/2 D taps: pipe wall taps at D upstream and ‘/2 D downstream

3. Flange taps: 1 inch upstream and 1 inch downstream of the plate, regardless of
the size of the pipe

In this investigation type 2 which ASME standards recommends the following

correlations resulting from curve fit:

4
C, = f(,6)+91.71fl2'5 ReD‘O75+-(—i—'-g—9fl’6—4—E 4033713317,

f(,B) : 0.5959+0.0312,B“ —o.1s4,38 (3.4)

where the correction factors F1 and F2 for this type of orifice are 0.4333 and 0.47.
Mass flow rate was measured by installing a ‘A inch thick orifice plate with

[3:063 between two flanges at the inlet based on ASME standards for flow

88

measurements. Eight static taps were put on 1.5D and 2.5D across the orifice, four on
each side, 90 degrees apart. The ambient temperature and pressure were used to
calculate the density of the inlet flow. The standard mass flow rate measurements were
performed utilizing these static pressure taps and calculated density, White (1999).

Note that the pressure measurement across the orifice was used to determine the
operating condition of the compressor from surge to choke by monitoring the flow
oscillation at surge in the inlet. For all the pressure measurements, handheld OMEGA
pressure sensors were initially utilized but as will be described later, the Scannivalve

pressure scanner replaced the handheld sensors.

3.2.2 FLOW STRUCTURE INSTRUMENTATION

The flow structure was studied by measuring the static pressure distribution over
the inner surfaces of the vaneless diffuser and volute. Because of the high magnitudes of
velocity and pressure, instruments such as hot-wire could not be used. Optical
techniques were not useful either since providing optical access would be very

expensive for a machine with the size of the Trane compressor.

3.2.2.1 VOLUTE PRESSURE TAPS

In the first step, 'when the volute inner surface was accessible during the
reassembling process, a fixture was designed to hold a Magna drill on the volute’s
flange in various orientations. Because the volute casing was an inch thick, the fixture
would help to hold the drill in an orientation that the drill bit was perpendicular to the

casing in any angle with respect to the compressor shaft axis.

89

On the casing of the volute 3/8 inch holes were drilled at 45 degree intervals
circumferentially and in different axial locations. The holes were first tapped and filled
with epoxy and later the dried epoxy was drilled for 1/16-inch O.D. static pressure tap
inserts. Similar to the taps at the inlet and outlet, the steel pipe inserts were cut and
sanded on the tip. The epoxy on the volute casing was sanded from inside prior to

drilling and the steel capillary pipes were inserted to be flush with the surface.

3.2.2.2 VANELESS DIFFUSER PRESSURE TAPS

In the diffuser, the same strategy was followed with minor changes. Holes were
drilled every 60 degree circumferentially on the diffiiser cover at different radial
locations from impeller exit to before the diffuser bend. The desired locations were as in
the volute but because of the structure of the diffuser cover casing, it was impossible to
drill holes at every 45-degree. The casing had bases on the back in order to carry the
vanes inside the return channel after the first stage. The holes were drilled for 3/16-inch
I.D. steel pipe inserts and similar to inlet and outlet static taps, the tips were sanded and
inserted flush to the surface of the diffuser cover.

There were pressure taps on the surface of diffuser cover that were initially used
in Trane’s design experiments. These taps were distributed at every 120 degrees at the
inlet and outlet of the diffuser. Pressure taps were provided in addition to the Trane taps
so that overall distribution included two taps installed at each 0, 120, 240 degrees and
six at each 60, 180, 300 degrees and different radial locations. In addition, there were

three total pressure taps were provided by Trane at every 120 degrees and depths of 25,

9O

50 and 75 percent of the diffuser width. Note that Tygon tubes were utilized to connect

both volute and vaneless diffuser’s pressure taps to the pressure scanner’s ports.

3.2.2.3 PRESSURE SCANNER

Due to the large number of the points on the volute and vaneless diffuser to be
measured, two 16-channel differential Scannivalve DSA3017 pressure scanners were
purchased. The DSA3 000 series pressure acquisition systems represent the next
"generation of multi-point electronic pressure scanning. Model DSA3017 Digital Sensor
Array, incorporate l6-temperature compensated piezoresistive pressure sensors with a
pneumatic calibration valve, RAM, 16-bit A/D converter, and a microprocessor in a
compact self-contained module. The result is a network ready intelligent pressure-
scanning module.

The microprocessor compensates for temperature changes and performs
engineering unit conversion. The microprocessor also controls the actuation of an
internal calibration valve to perform on-line zero and multipoint calibrations. This on-
line calibration capability virtually eliminates sensor thermal errors with a long-term
system accuracy of 1.005% full scale (F S). Pressure data are output in engineering unit
via Ethernet using TCP/IP protocol.

The DSA3017 Digital Sensor Array is ideal for flight and turbine engine testing
applications where ambient temperatures vary. It is also ideal for industrial pressure
measurement where long calibration intervals are required or temperature can vary
greatly. The DSA temperature compensated pressure sensors are more than ten times

less sensitive to temperature than typical piezoresistive pressure sensors. They are not

91

attitude sensitive, so the units may be close coupled to the pressure sources to be
measured. When further temperature stability is required or for use below 0°C, it is
recommended that the Model DSA3018 to be used. The DSA3018 is basically a
DSA3017 placed in an insulated, thermostatically controlled environment box.

With the initial experiments at 3600RPM, the pressure range of 2.5 PSID was
selected for the units. Note that these units measure the pressures with respect to a
common reference. Handheld pressure sensors were utilized to read pressures at the inlet
and outlet initially but because the range of the pressures at these locations were in the
range of the pressure scanners, it was decided that the pressure scanners take over the

handheld sensors as well.

3.3 PLANNED MEASURMENTS

The initial goal was to find a design point for the operation of this compressor
and compare the overall and component performances with an off-design condition. The
design speed would determine the maximum mass flow rate that the size of the
compressor could handle; therefore, the first objective was to find a design speed and the
peak total-to-total efficiency point for that speed. At a certain speed, the amount of load
on the compressor defines a datum point, which depends on the amount of mass flow
rate that is being compressed. In the current setup, the exit valve was responsible for
varying the mass flow rate from “Choke” (maximum flow rate) to “Surge” (minimum
flow rate) where the compressor stalls.

The experiments were planned to evaluate the overall and component

performances of the compressor at three speeds of 2500, 3000 and 3600 RPM. As

92

mentioned in previous sections, there were two limiting factors for not performing
experiment in higher RPM. The first factor was the oil leakage at higher speeds and
second was the air-cooled compressor. Hence, the performance experiment was
performed at 2000RPM initially in order to avoid the higher RPM and to evaluate the
efficiency of this compressor and consequently the design point. The result of the first
set of experiments failed to show the general characteristics of a compressor on
efficiency and pressure ratio diagrams. After checking the Excel spreadsheet’s
calculation for accuracy, a second set was performed but failed again. One of the main
reasons for the failure was the outlet temperature variation that made the efficiency
calculations wrong. In turbomachines, the thermal stability is essential and the larger the
compressor is the longer the stability duration will be therefore; in the next set of the
experiment data were. collected every 15 minutes for every point. After obtaining initial
data points, it was found that the waiting period should be longer since the temperature
was still varying.

After observing the above, it was decided to change the strategy and take
advantage of the physics of the flow inside the vaneless diffusers, as described in the
theory, to find the design point of this compressor. The strategy was based on pressure
measurement inside the vaneless diffuser and will not consider the total—to-total
efficiency, which requires temperature measurement. Therefore, the pressure scanners
were a great advantage in making the duration of the experiment shorter and collect
more accurate data. The experiments were performed at speeds of 2000, 3000 and 3600

RPM and the data was analyzed to study the performance of this compressor.

93

FIGURES

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CHAPTER 4

EXPERINIENTAL RESULTS AND ANALYSIS

98

In this chapter different approaches are described for the experimental analysis of
the compressor performance. The experimental results for the vaneless diffirser and
volute are analyzed. Results of the meanline analysis of the compressor impeller are
presented. A few design modifications are suggested for future investigations on this

compressor.

4.1 DIFFERENT APPROACHES

As mentioned previously, the first objective was to evaluate the compressor’s
performance curve with air as the working fluid. In order to achieve this goal, various
experiments were performed to evaluate the isentropic efficiency of the compressor for
different loads and speeds utilizing total pressures and temperatures at the inlet and
outlet. At every speed, one load would determine the optimum operating point of the
compressor.

After preliminary experiments, efficiencies were evaluated close to 100%, which
were very unrealistic. The primary reason for such results was that the thermal
equilibrium plays a major role in the performance calculation of turbomachines. The
larger and the higher speed of the machine, the longer the time to reach thermal stability.
Therefore, in this situation, the data should ideally be collected over a longer time frame
and with compressor being air-cooled. This procedure was impossible due to the limited
available running time because of the oil temperature rise in this setup. Therefore, an
alternative approach had to be taken to evaluate the design point.

Meanwhile, possible oil droplets in the exit flow might have cooled the

thermocouples as well. The reason for droplets existence was the design of the bearing

99

seals based on the pressure difference across the seal. In the commercial, unit the mass
flow rate and the number of stages were different, therefore, the pressure difference
across the seal is different than the new operating condition. This fact would lead to oil
leakage in the current standard journal bearing sea]. In order to improve the performance
of the seal, portion of the seal was machined and a rubber shaft seal was added in front
of the old seal. Adding the rubber seal increased the fiiction on the shaft and frequency
controller, which provided the driving power to the electrical motor, couldn’t sustain the
required initial torque to start the compressor. Thus, running the compressor for the next
set of investigations is due to adjusting the fiequency controller for the initial required
torque in the new configuration. However, the addition of the rubber seal happened
when all the experiments of the alternative approach were performed. A better way to
stop the oil leakage is to redesign the bearing seals by the company for air as the
medium.

Another alternative approach could have been obtaining the performance curve
of this compressor based on the definition of the efficiency but with different
perspective. As noted before, the isentropic efficiency is the division of the ideal power
by real consumption power in compressors. The real consumption power is calculated
from first law of thermodynamics, which leads to total temperature ratio term in the
efficiency calculation (1.3). The ideal power is obtained during an isentropic
compression and by using the isentropic relations and the first law of thermodynamics;
the total temperature ratio is converted to the pressure ratio term in the efficiency
calculation. The mechanical power is impossible to measure in compressors; therefore,

thermodynamical definition of power is used, which can be calculated from measuring

100

the fluid properties at the inlet and outlet of the compressor. If the braking power were
measurable, the efficiency of the compressor would have been obtained utilizing those
techniques similar to the internal combustion engines techniques for measuring the
efficiency.

In this compressor, however, the input power could be measured by the electrical
power input to the compressor. Having a constant voltage provided to the motor and
measuring the consumption current, the electrical power input to the compressor motor
could be calculated. There are losses in the frequency controller and power transmission,
which have to be included to obtain the net power consumption in the compressor
operation at every load. This power could replace the total temperature ratio term in the
denominator of the efficiency definition (1.3.) and the pressure ratio term in the
numerator represents the ideal work input to the compressor, hence emciency could be
calculated for every load. There would be a small error in this method, which is due to
the neglecting the electrical losses.

In this investigation, this technique was not utilized to find the best operating
point of the compressor, instead the load with highest pressure ratio was referenced as a
point with mid mass flow rate for the analysis. The reason behind such a selection was,
even though the compressor works at off design, the operating conditions at the largest
pressure ratio will be the closest to the optimum conditions when efficiency data can not
be utilized. Since the focus of this investigation was performance of the volute as a
component, evaluation of the stage performance left for the next investigation on this

test facility utilizing the technique discussed above.

101

 

4.1.1 DIFFUSER RESULTS

In this investigation, the diffuser behavior was initially the essential component
for defining the operating point. As described in Chapter 2, at a lower mass flow rate
than the optimum point, there is not enough mass flow to fill the space, hence diffusion
occurs. On the other hand, at higher flow rates, only by acceleration in the flow will the
mass flow be conserved. Therefore, there would be a balance point between the two
cases, which provides the highest efficiency of the compressor. Collapse of these points
for a certain mass flow rate indicates a uniform circumferential pressure distribution at
the diffuser exit and guarantees the best operation of the whole stage. In this condition
the components are “matched” with each other.

To study this fact, the vaneless diffuser static pressure distribution was mapped
by the pressure taps provided radially and circumferentially (Figure 4. la). Hand held
pressure sensors were initially utilized but with evaluation of the pressure range in the
experiments, they were replaced with pressure scanners because of higher accuracy in
their pressure range. Therefore, all the pressure taps on diffuser cover, inlet, and outlet to
the stage were connected to the pressure scanners and measurements were repeated for
the speeds of 2000, 3000 and 3497 RPM, which was the highest speed that the motor
could reach. Figure 4.2 shows total pressure ratio versus flow coefficients fi'om choke to
close to surge at 2000 RPM. Figures 4.3-5 shows circumferential pressure distribution at
different radius ratios on the vaneless diffuser shroud wall. The data points in each plot
present the circumferential static pressure distortion for every radius ratio. As motioned
before, at one flow coefficient point, the data points should have collapsed to represent

the balancing point in the operation of the diffuser. Collapse of these points would have

102

shown zero circumferential static pressure distortion at each radius ratio. The numerical
analysis will show that this distortion is because of the tongue effect in Chapter 6.

Figures 4.6-7 show the diffuser radial pressure distribution for the same flow rate
coefficients at 60 and ISO-degree angles with the reference to 12 o’clock facing the front
of the compressor (Figure 4.1). These results show the radial diffusion inside the
vaneless diffuser. Note that with increase in speed and mass flow rate, the rate of
diffirsion decreases. As described in Chapter 2, for mass flow rates above design point,
acceleration will occur because the diffuser will be too small and flow has to accelerate.

Figure 4.8 represents the diffuser circumferential outlet pressures for the same
flow coefficients as of previous plots. It is clear that the tongue region (0:240) has
significant effect on the performance of the machine by creating distortion in the
circumferential static pressure distribution at the diffuser outlet. This sudden drop in the
static pressure at tongue region could have a direct effect on the flow back to the inducer
and impact the bearings with unbalanced circumferential loads. The performance of the
vaneless diffuser is similar to ones from other researchers presented in Chapter 2. The
maximum and minimum pressure drops at the tongue region with respect to the average
pressure at the diffuser outlet are 8.4% and 6.9% for this speed. Figures 4.10-16 and
4.18-24 are the similar results for the speeds of 3000 and 3497 RPM. Comparing Figures
4.2, 4.10 and 4.18 it is concluded that for air this compressor provides larger pressure
ratios at higher speeds.

In the next chapter, three points were selected for the numerical analysis with
minimum and maximum flow rates and a point with the largest pressure ratio (Figures

4.2,10,18) as the mid mass flow rate. The maximum and minimum pressure drops at the

103

tongue region are 11.8% and 8.0% percents for 3000 RPM and 12.1% and 8.3% for
3497 RPM respectively. This shows that at higher speeds and mass flow rates the impact
of the tongue is less significant. Figure 4.20 shows that the compressor is close to the
point where the data points will collapse at one mass flow rate. To reach the best
operating point, where the components are matched, requires running the compressor at
a speed higher than 3497 RPM, which is impossible with the current driver.

Note that the radius ratio of 1.125 is very close to the impeller tip, which implies
that this point might be close to or in the unsteady impeller wake region of shear zone
off of the impeller. In order to study the flow in this region unsteady pressure

measurement equipments should be utilized for future experiments.

4.1.2 VOLUTE RESULTS

In order to map the static pressure distribution in the volute, pressure taps were
provided as far as the geometry of the volute cross sections allowed. These taps were
located on the flat portions of the volute casing, where normal drilling on the surface
was possible. Therefore, depending on the circumferential locations on the volute
casing, one to three taps were provided. These pressure ports were scanned for similar
mass flow rates and speeds as the diffuser experiments. Results were averaged axially
for every cross section at every operating point and shown in Figures 4.9, 4.17 and 4.25.
Note that the reference of the angle in these plots is the tongue location, Figure 4.1.

The volute static pressure contours in numerical results and experimental data
collected from each tap show that the axial variation of the static pressure on the volute

casing on the outer diameter region of volute cross sections is not large. Therefore, this

104

averaging can be a good representative to compare the static pressure at different volute
cross sections. However, the pressure distribution inside the volute may vary radially,
which affects the flow structure inside the volute.

Reviewing the plots, the reader clearly observes that the performance of the
volute is improving with increase in mass flow rate and speed. Diffusion occurs sharply
in the cross sections with smaller areas and decreases as the flow enters the cone inlet.
One primary conclusion would be that this volute is performing at off design condition.
As was described before, the pattern of diffusion in the volute shows that the volute is
too large for these mass flow rates. Experiments show that this is true for all speeds and
mass flow rates.

The ideal volute performance is collecting the flow leaving the diffuser and
providing uniform circumferential pressure distribution at vaneless diffuser exit. As
stated previously, the uniformity of the pressure will improve the impeller and vaneless
diffuser performances. Having mentioned the above, there is a large pressure drop at the
tongue region between the cone and tongue entrances, which forces the flow to reenter
the volute. Because of the curvature of the scroll casing the reentry flow creates a
circulation region at the beginning of the scroll and corresponding losses within the
volute. The CFD results will reveal this fact by calculating the vorticity magnitude at the
first volute cross sections and presenting the velocity vectors in this region (Chapter 6).
The flow circulation region at the beginning of the volute creates a region of low
pressure and pressure recovers further downstream inside the volute.

On the other hand, the wavy shape of the plots for 2000 RPM speed indicates the

nonuniform circumferential distribution of the static pressure in addition to the pressure

105

drop across the tongue region. Increasing the speed and mass flow rate, improves the
uniformity of this pressure distribution and therefore reduces the loss in the stage
operation. However, the pressure drop across the tongue region is inevitable and
depends on the design of the tongue. Note that the reentrance of the flow to the volute at
the tongue region could help reduce and balance the circumferential pressure drop at
tongue region.

In the design of the tongue for this model, if the distance between the tongue and
scroll is reduced, the length of the sharp pressure gradient region decreases and would
reduce the nonuniforrnity of the circumferential pressure distribution. Flow could be fed
to this region by a return supply line from the cone outlet to balance the pressure
circumferentially. A valve can be utilized at the supply line to adjust the inlet pressure
and mass flow rate to this region dynamically. This modification could improve the

volute performance significantly in both the laboratory and commercial models.

4.2 IMPELLER ONE DIMENSIONAL ANALYSIS

Having the mass flow rate and impeller geometry information, a one-
dimensional analysis of the impeller was performed for various purposes. In order to do
the numerical simulation, boundary conditions had to be provided for diffuser inlet and
cone outlet. Having only experimental static pressure data at the diffuser inlet was not
sufficient for the simulation. Therefore, this analysis would provide the absolute velocity
and angle of the flow leaving the impeller, which were sufficient for the inlet boundary

condition.

106

In addition, the relative velocity ratio inside the impeller was to be evaluated. If
this ratio is too small, there will be a strong pressure gradient inside the impeller
passages, which leads to flow separation. At the same time, having the velocity
information enables evaluation of the vaneless diffuser stability based on performance of
the diffuser in Jansen chart.

Figures 4.26-27 present the results of this study utilizing the design methods
described in Chapter 1 for speeds of 2000, 3000 and 3497 RPM and corresponding mass
flow rates. In this analysis, absolute flow angle was calculated with respect to the radial
direction. Figure 4.26 shows that the flow angles decreases as the mass flow rate
increases. The cobra probes were installed on the vaneless diffuser for measurement of
these angles for the firture investigations. In these results C2, absolute velocity leaving
the impeller, follows the same trend of the absolute flow angle. Note that these results
are based on meanline analysis and no loss was included in the analysis. However,
performing the numerical simulations based on these boundary conditions led to results
with good agreement with the experimental results (Chapter 6).

Referring to Jansen chart, Wilson (1998), and calculating the average Reynolds

number of 2 x106 for the flow leaving the impeller, the diffuser was stable with the flow
angles between 70-75 degrees respect to radial direction. In low mass flow rates where
flow angles are more than 75 degrees respect to radial direction, the vaneless diffuser
becomes unstable and rotating stall occurs inside the diffuser. In general, centrifiigal
impellers are designed for the range of 60 to 65 degrees of absolute flow angles at the

impeller exit, which is lower than the calculated range.

107

Figure 4.28 depicts the variation of relative velocity ratio versus mass flow rates,
in which W2/W1 increases with increase in mass flow rate. Small relative velocity ratios
mean large diffusion rate inside the impeller passages, which lead to separation of the
flow and impeller stall. In order to prevent separation or reduce the separation losses
inside the impeller passages, impellers are designed for relative velocity ratio W2/W1
about 0.7. The meanline analysis of the Trane impeller produced a maximum ratio of
0.4, since it is operating in low mass flow rates, (Figure 4.28). This predicts that the flow
might be separated inside the impeller in all cases of the experiments and separation
losses should be considered depending on its intensity. In comparing the cases, the loss
is predicted to be the least in 3497 RPM case and increase as the speed and mass flow
rate decrease. Note that the compressor’s impeller was designed for a prewhirl flow at
the inlet to the stage where in current investigation no inlet guide vanes were utilized.
The meanline analysis was performed for uniform flow at the inlet as was in the
experiments.

For the next set of experiments on this compressor, inlet guide vanes can be
installed and the effect of the prewhirl flow at the inlet to the stage investigated.
Numerical simulations can be performed for the flow inside the impeller as well in order
to investigate the flow structures for such low relative velocity ratios. It is predicted that

separated flow regions should be diagnosed inside the impeller passages.

108

FIGURES

109

 

6=342 6=297 9=252

 

Figure 4.1: Probe Locations on (a) Vaneless Diffuser (b) Volute

110

Total Pressure Ratio

P (PSIG)

 

1.043
1.048 -

 

 

 

 

0.015 0.020 0.025 0.030 0.035 0.040 0.045

Figure 4.2: Total Pressure Ratio for 2000RPM Operating Condition

00 [360 A120 0180 X240 .300

 

0.50 . _ ‘ ‘

0,5 . .............................. .................. ................ .............................. .............................. .............................

0.0. ........ 3 ................. 38

0,35 . ........ g . .. g . _. ._

0,30 . x , o .3 ......... .. ..............

020 . ................. , ........... ................. .............. .............. _ ........ x ................. e .......... ..8 ......................
. . . . . .

0_ 5 . ........................... ............. .............................. g .............................
1 2 z a z s X

 

 

 

0.10
0.015 0.020 0.025 0.030 0.035 0.040 0.045

Figure 4.3: Vaneless Diffuser Static Pressure Distribution at r/r2=1.125, 2000RPM and
0:0, 120, 180, 240, 300 Degrees

111

P (PSIG)

060 13180 A300

 

 

 

 

0.015 0.020 0.025 0.030 0.035 0.040 0.045
11

Figure 4.4: Vaneless Diffuser Static Pressure Distribution at r/r2=1.27, 2000RPM and
0:60, 180, 300 Degrees

00 1360 A120 0180 X240 0 300
0.54

. .
049. ....................................................................................................................................................................................

E 0 s 9 . 2 ;
044 .1 ............................. x .............................. ',......... , ............................... ...............................
x i . i E

I ‘ x . ‘
v I L I 0
I I x I .

034 - .............................. ...................... X”; ................. 8 ..............................
x 3
029 _ .............................. 4 .............................. ............................... . ............................. .......... . ................... ‘, ..........................

0.24 ;
0.015 0.020 0.025 0.030 0.035 0.040 0.045

 

 

 

 

Figure 4.5: Vaneless Diffuser Static Pressure Distribution at r/r2=1.59, 2000RPM and
0:0, 60, 120, 180, 240, 300 Degrees

112

P (PSIG)

 

OChoke I2nd A3rd X4th 35th 06th +7th OSurge

0.30 4 .......................... EMA .................. g ................ I ....... .......................... g. ........................ ......................... .............................

0.25 , .......................... 2,... ............... 6 .......................... ......................... .......... . ............... ........................ ......................... ,

 

 

0.20
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

 

r/r2

Figure 4.6: Vaneless Diffirser Static Pressure Distribution at 0:60 and 2000RPM

OChoke l2nd A3rd 04th 15th 06th +7th XSurge

 

0.55

..............................

+X

0.50 , .......................... ........................ ............ . .......
. .................. . ....... ...................... . .................... e ..........................
0.45 E 3 x , :5 + .3 x -.
: E + i : :
z x x: : . : :
0'40 . .......................... ,....+ .............. +, ................ ........E ....... X ............... x ................. . ..... , .................... 0..., .........................
e 3 0 5 A 5
035 .. .......................... ....x A ' _
030 . .......................... ...................... A. ...................... ....... l ............... I .................... .................... . ........................
020 _ .......................... . .......................... .......................... ..................... . .....
0.15

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7
r/r2

Figure 4.7: Vaneless Diffuser Static Pressure Distribution at 0:180 and 2000RPM

 

 

 

113

+ Choke —I— 2nd —A— 3rd —x— 4th + 5th + 6th + Surge +7th

 

0.6

 

 

 

 

 

 

 

 

 

 

 

 

P (PSIG)

 

0.1

 

 

 

0.0
0 50 100 150 200 250 300

Figure 4.8: Static Pressure Distribution at Vaneless Diffuser Outlet and 2000RPM

+Choke +2nd +3rd +401 +5th +6111 —t—-7th —-—Surge

P (PSIG)

 

400 450

100 150 200 250 300 350

Figure 4.9: Volute Static Pressure Distribution at 2000RPM

114

 

1.110

1.108-

1.106 d

1.104-

Total Pressure Ratio

1.098 -

 

 

 

I I

 

1.096

0.020

0.035

1 I
. v

0.025 0.030 0.055

0.040 0.045 0.050

Figure 4.10: Total Pressure Ratio for 3000RPM Operating Condition

00 D60 A120 0180 X240 .300

 

1.05

0.85 1

0.65 _

0.45 4

P (PSIG)

0.25 -

1 .
, . . 1 1
. . . . ,
. . . . .
1 1 1 . .
. 1 . .
.1 .......,,...., ......................,.. ............
. 1 1 1 .
i
1
. .

.................................................................................................................

 

 

 

-0.15

0.020

Figure 4.11: Vaneless Diffuser Static Pressure Distribution at r/r2=l . 125, 3000RPM and

7 I I

0.035 0.040 0.045

r i

0.025 0.030 0.055

0.050

0:0, 60, 120, 180, 240, 300 Degrees

115

P (PSIG)

060 D 180 A300

 

DDO

>00

0.6 2. . A ................. i 3
O4 2. .. .. . . . . .. a ......................... 2: ......... . .................

1 1 1 1 1 v
1 1 1 1 1 i
1 1 1 4 1 a
. 1 1 . 1 1
q ............... . ....... ...-.2 .......................................... 2 .............................................................................................................
. . . . . 1
' 1 r 1 . 1 .
1 1 ~ . . i
1 . . . 1 1
2 . . . 1 1
1 1 1 - q
1 1 1 . O 0
1 1 1
.

 

 

 

0.0 ;
0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Figure 4.12: Vaneless Diffuser Static Pressure Distribution at r/r2=1.27, 3000RPM and

P (PSIG)

0=60, 180, 300 Degrees

00 D60 A120 0180 X240 .300

 

1.2

10. ........... 8 ........... 3 .A

0.8 , . X .............. 9' ,
X
06 2 ,2 ......... 3.2,: ........................... .........................

I Z I 2 2 1
f E I E i i
04 4.1...) ............ W} ............ ..220222. ......u: .......................... .1

............................................................................................................................................................................................

0.2 ~

 

 

 

0.0
0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Figure 4.13: Vaneless Diffuser Static Pressure Distribution at r/r2=1.59, 3000RPM and
0:0, 60, 120, 180, 240, 300 Degrees

116

P (PSIG)

P (PSIG)

OChoke I2nd A3rd X4th XSth 06th +7th OSurge

 

1.2

o ubixxog-i-o

.......................... ......... ...................... a. ..........
1'0 2 g 2 ¥ 3+
' b

 

 

0.0
1.0

1.1

r/r2

t
............. 4...“......................3......-..................
' o ':
................................ x
X 2
...-HA;-
I
°
. .9,
. ;

 

1.5 1.6 1.7

Figure 4.14: Vaneless Difluser Static Pressure Distribution at 9 =60 and 3000RPM

1.2

 

l.0~

0.8 ~ ............

0.4 ~

 

0.0

02 2 ............ ....... , .................... ..

OChoke I2nd A3rd 04th XSth 06th +7th XSurge

xo§+x

................................................................

o+§x

 

 

1.0

r/r2

Figure 4.15: Vaneless Diffuser Static Pressure Distribution at 0=180 degree and

3000RPM

117

P (PSIG)

+Choke +2nd +3rd +4th + 5th +6th —+—Surge —O—7th

 

 

 

 

 

 

 

 

 

 

 

 

O4 ..............

(12 .............................. éHm“W-W-W-W-W3W-W-WWW-W-Wém-W-WWW“m-m-3-WHW-W-m2m-é ............................

0.0 . 1
0 50 100 150 200 250 300

Figure 4.16: Static Pressure Distribution at Vaneless Diffuser Outlet and 3000RPM

P (PSIG)

+Choke +2nd +3rd +4th +Sth +6th —i—7th —-—Surge

 

L2

 

0.0

 

 

 

I I
l l r

 

 

 

 

 

 

 

 

 

 

 

 

 

 

450

0 50 100 150 200 250 300 350 400
6

Figure 4.17: Volute Static Pressure Distribution at 3000RPM

118

Total Pressure Ratio

1.

l.

l.

l.

l.

1.

l.

l.

l.

P (PSIG)

 

150
146 1 I
144 2...-......
142 . ..
140 «
138 .. .

136 <

 

 

 

 

134 4
0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Figure 4.18: Total Pressure Ratio For 3497RPM Operating Condition

00 060 A120 0180 X240 .300

 

13 3 E E E E E

1.1 . ......................... 3 ........... ...........................
09 ..................... ........................... ...........................
0,7 x .................... x ........ . ............. ,. ................ I _ ......................

s a s X 2 1 1
' ' ' ‘ . ' z
X

1 . 1
1 1 1 1
1 1 1 1
1 1 1 1
.1 ................................................................................. . ...................................
u 1 v 1 1
1 1

.
01 .1 1 .X .............
- : : ' : : :

_0] - .. . .... .. .. ... .. . ................
I l

 

 

 

o3 51 , i
0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Figure 4.19: Vaneless Diffuser Static Pressure Distribution at r/r2=1. 125, 3497RPM and
0=0, 60, 120, 180, 240, 300 Degrees

119

P (PSIG)

0.8 .

0.6 ~

0.4 -

0.2 -

0.0

060 0180 A300

 

 

D
DElO

mo
0

.....................................................................................................................................................................................

 

 

0.020

Figure 4.20: Vaneless Difi‘user Static Pressure Distribution at r/r2=l.27, 3497RPM and

P (PSIG)

Figure 4.21: Vaneless Diffuser Static Pressure Distribution at r/r2=1.59, 3497RPM and

0.025 0.030 0.035 0.040 0.045 0.050 0.055

0:60, 180, 300 Degrees

00 060 A120 0180 X240 .300

 

1.6

l.4~

1.24-

m -

0.8 «

 

 

 

0.0

I I I l I

0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

0:0, 60, 120, 180, 240, 300 Degrees

120

P (PSIG)

P (PSIG)

o Choke I 2nd A 3rd X 4th
I .6 , . _ ‘ <H‘ a An" 4- 7““ AQnrno

.4 . .......................... .......................... ........................... ....................
1.2 . .......................... ....................... 4 3 3
.0. .......................... i._.__... ............ .
0.8 « 3

()31 2 .......................... 3 ...................... 1:32.”.H.MU.2.HH.U.3 ...... I. ............... ii. . 2.2.“.nu.nu ....................
3 5 o b 5

......................................................................................................................................................

0.2

 

 

0.0 3 3 3 3 3 3
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7

 

r/r2

Figure 4.22: Vaneless Diffuser Static Pressure Distribution at 0:60 and 3497RPM

OChoke I2nd A3rd 04th XSth 06th +7th XSurge

 

1.6
.4 . ......... .................. , .......... ............................. ..............................

12 2 1 .. x ..................... ......T ....................... . ..... . ...... . .....................
x X: +
o3 .

0_3 - ....................... ,3 ...... C ...................... 3, ...... . ........... xx ............................

0.6 2 ............................... .................. o-......... ....... o. 2 ...................... .‘u-

5 . 3 A § 5
0.4 - ............................... ._ .................. A .................... . ........ I

.. .......................................................... ' ..................... . ................ .. ................................................................................
. . O . .
.1 . . .

 

 

9 I
4

 

0.0 i
1.0 1.1 1.2 1.3 1.4 1.5 1.6

Figure 4.23: Vaneless Diffuser Static Pressure Distribution at 0:180 degree and
3497RPM

121

Pressure (PSIG)

P (PSIG)

+ Choke em 2nd + 3rd —x— 4th *7!— 5th + 61h + Surge —-B—7lh

 

Figure 4.24: Static Pressure Distribution at Vaneless Difiuser Outlet and 3497RPM

+Choke +2nd + 3rd +4th + 5th +6th —l—Surge

 

Figure 4.25: Volute Static Pressure Distribution at 3497RPM

122

C2 (HI/S)

- -O-- 2000-~I~ ' 3000-i- 3497

 

. .
. x
.
.
. .

 

 

 

72

1.5 2.0 3.5

Mass Flow Rate (Kg/s)

0.0 0.5 1.0

Figure 4.26: Impeller Exit Flow Angle For Different Speeds and Mass Flow Rates

— o— 2000 -- -- I -- «3000 A 3497

 

120
110 - .................................................................
100 —

90-

................................................................................................

.................................................................

80 -

 

 

 

40
0.0 1.5 2.0 2.5 3.0
Mass Flow Rate (Kg/s)

3.5

Figure 4.27: Impeller Exit Absolute Velocity For Different Speed and Mass Flow Rates

123

mm.

+ 2000 RPM + 3000 RPM + 3497 RPM

 

0.45 3
0.40 , ,

0.30 - ' .

025 2............
0.20 -
0.15 1
0.10 3
0.05 3

 

 

 

0.00 4
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Mass Flow Rate (Kg/s)

 

Figure 4.28: Relative Velocity Ratio For Different Speeds and Mass Flow Rates

124

CHAPTER 5

NUMERICAL ANAYSIS SETUP

125

In this chapter, various approaches in performing numerical analysis for this
investigation are discussed. Advantages and disadvantages of each approach were
described in detail. Later in the chapter, the numerical setup of this investigation was
presented step by step. The author was not permitted to present the detail of the
geometry graphically because of the confidentiality agreement with Trane Company;
however, the final grid for the complete flow passage is presented as the conclusion of

this chapter.

5.1 INTRODUCTION

With recent software development, Computational Fluid Dynamics (CFD) has
become more reliable in flow analysis in fluid mechanics and aerodynamics. In thermo-
fluid research area, CFD predictions have been utilized for analysis because of their
reasonable accuracy. However, there are still cases such as turbulence modeling and
industrial applications, which challenge this tool. There are ongoing developments in
simulating the flow structures inside turbomachines utilizing commercial and in-house
codes and the results are comparable up to certain accuracy. In blade design, either axial
or radial, CFD is becoming very reliable tool, however, researchers have not been able
to model the losses properly utilizing this tool.

Recent research areas are based on how to polish the physics and optimization of
designs such as blade cooling and passage configuration. Generally, the overall size and
geometry of turbomachines are large and complicated in comparison to the benchmark

problems that have been solved to approve the credibility of the CFD analysis.

126

Simulation of the volute flow in centrifiigal compressors is still a major challenge for
CFD vendors because of the complexity of the flow path topology.

In addition, current commercial solvers utilize various turbulence models, which
have their own arguments as to how accurately they can predict a three-dimensional and
highly rotational volute flow. Often because of the size of the geometry and to avoid
memory expenses, there are simplifications made to the geometry and meshing schemes,
which reduce the accuracy in flow prediction. Therefore, the results are reliable only for
qualitative flow structure.

Most of the turbomachinery companies have developed in-house solvers, in
which inviscid theory for flow analysis and empirical correlation for loss mechanism
inside the volute are utilized. This approach reduces the cost of the simulations and the
design analysis is obtained in a shorter time than solving the filll Navier-Stokes
equations. This will enable the designers to perform optimization analysis of their
designs in a shorter time and make the development process cheaper. However, these
approaches cannot be sophisticated tools for various configurations because they can
vary from case to case and geometry to geometry.

Despite all the facts mentioned above, CFD can still be a supplement to
experimental analysis. CFD can provide reasonable insight to the problem despite its
reduced accuracy. With the current developments, CFD have found its place among the
designers and researchers and increased their analysis capabilities extensively. However,
complete replacement of expensive experiments by CFD analysis is still questionable

and to be answered in future.

127

5.2 CONSIDERATIONS FOR THE NUMERICAL ANALYSIS

In this investigation, initially CFX-TASCFLOW solver, which is designed for
turbomachinery applications, was going to be utilized for the numerical analysis. This
solver is a structured based solver and specifically designed for turbomachinery
applications. Anormous amount of work is facing the designer to generate grid for a
complex topology such as volutes. However, in different cases this solver has presented
reasonable results for the impeller geometries and predicted these flows more accurately
than the other vendors.

There are ongoing developments in CFD grid generators and solvers for flow
inside the volute geometry. A code has been developed at MSU that generates grid for
all types of volutes with certain modifications, Gu (2000). In this code instead of
generating grid for the complete volute volume, it is broken up to 40 cross section
profiles, which are connected to each other linearly. Utilizing the butterfly technique,
planar grid is generated for each profile and a volume mesh is generated utilizing linear
interpolation consequently. The butterfly technique improves the quality of the mesh and
increases the convergence rate of the simulation iterations. Note that this technique is
popular among TASCFLOW users because it is the only way to generate structured grid
for such geometries. In addition, it has been proven that the simulation converges faster
for a structured mesh and the post-processing would be much easier than the
unstructured grid. Meanwhile, for the same accuracy in results, the number of required
structured mesh is less than unstructured one. Therefore, there is a significant advantage

of using the structured grid in reducing the cost of the numerical simulations.

128

Profile technique requires some simplifications in the geometry especially in the
tongue region. The configuration of the tongue region in the Trane compressor, forces
the flow to reenter the scroll partially. Because of incompatibility of the cross sections in
this region with the rest of the volute geometry, the profile technique cannot be
successful in predicting the reentry flow. Thus, by ignoring this region the designer has
to compromise portion of the geometry in order to have structured grid inside the volute.
In addition, if the curvature radius of the volute casing is small, then a line replaces the
curvature and its length depends on the number of the cross sections in the volute
volume. Therefore, this meshing scheme and CFX-TASCFLOW solver cannot handle
many industrial problems and for the same reasons vendors created unstructured solvers.
FLUENT Corporation performed this conversion in order to adapt itself to the variety of
the industrial applications.

In this investigation there was another reason for the choice of the commercial
CFD software and that was the rotating frame in the turbomachinery applications. CFX-
FLOW has shown very good performance in simulating the flow inside rotating impeller
passages. However, since the volute casing is stationary, this simulation could be
performed almost with any solver. The only limitation was if the grid generator could
handle grid generation of this volute.

However, many researchers believe that in order to have more accurate
simulation results in centrifirgal compressor flows, one must perform the simulation for
the complete stage in order to include the interaction between the impeller and diffuser.
To do such an analysis, it requires strong computation wealth, which is not available

extensively in academic level.

129

In all grid generation techniques, the first requirement is to have the CAD
drawing or profiles of the volute geometry. Since the CVHF 1280 compressor was one
of the older T rane designs, the only available geometry information was an AutoCAD
file, which was drawn for casting purposes. It was possible to extract profiles geometry
out of the CAD file but the information had to be transformed to a group of coordinates
for every cross-section and that required an AutoCAD professional. In addition, cross-
sections of the vaneless diffuser geometry at the same angles as the volutes had to be
extracted in order to complete the flow path.

Having studied FLUENT 5.0 capabilities and the geometry, it was decided to
utilize this software for numerical analysis portion of this investigation. Although
FLUENT 5.0 is capable of reading grid files from various grid generator software
GAMBIT, the default grid generator for FLUENT 5.0, was utilized to generate mesh for
this geometry. Note that this simulation has been the first successful attempt in utilizing
FLUENT for such geometry among other FLUENT’s applications, to the best

knowledge of the author.

5.3 GEOMETRY AND GRID GENERATION PHASE
5.3.1 GAMBIT

GAMBIT is a single, integrated preprocessor for CFD analysis. It has ACIS solid
modeling capabilities, which enable the user to import CAD solid model files directly. It
has the capability of reading -IGES CAD format, which has only the information of the
vertices and surfaces. GAMBIT enables the user to cleanup and modify the geometry for

grid generation purposes. This sofiware can generate mesh for all FLUENT solvers

130

including F IDAP and POLYFLOW. It enables the user to generate a grid in structured
and unstructured hexahedral, tetrahedral, pyramid, and prisms and assign boundary

zones to the grid.

GAMBIT provides a strong set of solid modeling-based geometry tools. Top
down geometry construction using 3D primitives allows user to create geometries fast,
without the complexity of a full-fledged CAD package. Different CFD problems require
different mesh types, and GAMBIT gives user all the options needed for these
applications. Meshing toolkit in GAMBIT lets user decompose geometries for structured
hex meshing or perform automated hex meshing with control over clustering. Triangular
surface meshes and tetrahedral volume meshes can be created within a single

environment, along with pyramids and prisms for hybrid meshing.

5.3.2 TRANE VOLUTE GRID

As mentioned previously, Trane Company provided the AutoCAD file of the
volute casing design, which was in solid model format (ACIS). This file included a solid
volume of the volute that showed the casing with its wall thickness, oil passages and
holes for bolting the flanges on the compressor casing. Note that in the first attempt, an
IGES format, which had the surfaces information, was utilized but the universities

UNIX workstations were not capable of handling the large size of these files.

Afier importing the ACIS file, the volume was deleted and only the inner shell of
the volute was kept (Figure 5.2). In the next step, the vaneless diffuser was generated in

the same volute file. An attempt was made to attach both geometries but it was not

131

possible due to the geometry mismatch at the interface of the two (Figure 3.4). After
studying GAMBIT capabilities, the vaneless diffuser and volute volumes were generated
and meshed in two separate files. Later in Fluent, the non-conformal meshing technique

was utilized to attach the two meshes in a single file.

In order to create the volume mesh, the geometry must be a closed area in order
to be recognized by GAMBIT as a volume. Therefore, the volute shell had to be covered
by an interface surface between volute and the vaneless diffuser exit. Having the
dimensions of the vaneless diffuser (Figure 3.4), it was created in a separate file and the
outlet face was mapped over the volute shell in order to create the required interface.
Note that in the tongue region, the diffuser outlet was blocked by a portion of the casing
wall, which created a passage between the tongue and beginning of the scroll. At the
same time, the outer flanges of the diffuser and volute were offset. Hence,
considerations were applied to accommodate the mismatch. These details were

challenging at every step, however they contributed to a more accurate flow diagnosis.

In defining the volute volume, it was found that since the scroll surface of the
volute was defined in multiple long spiral pieces, GAMBIT was unable to recognize the
surfaces after closing the volume. It was recommended that all long surfaces be broken
into small surfaces in the original CAD file, which meant that the volute had to be
redrawn. Having that modification, GAMBIT would have been able to generate an

structured mesh for the volute.

In order to avoid additional work for an older design, it was decided to continue

with the same file and create an unstructured grid for the volute. Having tried various

132

ways to resolve the volume recognition in GAMBIT, it was found that by generating the
grid on the surface prior to defining the volume, GAMBIT could recognize the volute
volume. This was due to the fact grid nodes on the surfaces would define more
coordinates over the curved and spiral surfaces and function in a similar way if the

surfaces had been redefined in pieces.

The configuration of the spiral surfaces in few pieces was a disadvantage to the
quality of the grid. Hence, by using the virtual geometry in GAMBIT, those surfaces
were merged into cleaner surfaces. Though, virtual geometry would increase the level of
difficulty of attaching the surfaces and defining the volume. In addition, generating the
grid on the long virtual surfaces wouldn’t allow any Boolean operation between the
surfaces. Once the grid was generated, changing the parameters was not possible and
forced GAMBIT not to recognize the volume. Therefore, certain precautions had to be

considered in merging the surfaces in order to avoid volume recognition problem.

Having the above as obstacles, the volute volume was generated with all surfaces
and solid edges. Note that in this study the only geometry simplification was the step at
the connecting flanges of the two volumes, which was modified to an inclined
connection. The height of that step was 0.182 inch, which was very small in comparison
to the overall size of the volute. Other than that, there was no other simplification in the
geometry and entire the casing art effects were included in the domain as far as the

accuracy of the drawing software would permit.

The first tetrahedral grid meshes were generated for both diffuser and volute with

1 inch spacing. After the first simulation, it was found that finer grid would provide

133

better convergence rate. Meanwhile, at some areas such as tongue region, the initial size
of the mesh was not sufficient to cover the flow path. Therefore, a second grid set was
generated with 0.25 inch grid spacing, which converged the simulation faster than the

initial grid.

Upon creating totally 140,000 grid nodes for volute and diffuser in two separate
files (Figures 5.4-5), boundary zones were defined in order to extract data over any
desired surface in post-processing phase. There were multiple ways to merge the two
grid files into one. In this study “TGRID”, which is one of the FLUENT’s older grid
generator software, was utilized to do so. However, the diffuser and volute interfaces
were assigned “Interface” zone prior to merging the files in order to be recognized in

non-conformal technique.

5.4 SIMULATION PHASE

5.4.1 F LUENT

FLUENT provides a wide variety of physical models for turbulence, combustion,
and multiphase applications. The fully unstructured mesh-based technology in FLUENT
5.0 has proven over time by multiple validations in benchmark problems. FLUENT
turbulence models include simple k-e modeling to second-moment closure Reynolds
stress models and large eddy simulation. Species transport and chemical reaction models

with materials and reaction database are available as well.

Mesh quality can be the primary factor in CFD solution accuracy. FLUENT lets

the user improve the mesh as part of the solution process by examining the preliminary

134

solution using FLUENT tools for solution-based mesh adaptation to get a more accurate
result. A set of solver algorithms are existing in FLUENT, which is tuned to specific
problem physics, such as advanced coupled solvers for compressible and incompressible

flows, and segregated solvers for the complicated numerical tasks.

Parallel processing is the key to fast turnaround of CPD calculations. FLUENT
has the capability of parallel computing, with all the interactive tools one needs. By
taking advantage of the user-defined firnctions capability in FLUENT, user can create a
custom version of the software that suits his/her needs. This flexible capability lets user
specify volumetric sources, reaction rates, custom physical properties, boundary
conditions, scattering phase functions for radiation modeling, and body force, drag, and
source terms for discrete phase modeling. One can also create custom post-processing

variables and define own scalar transport equations.

5.4.2 GOVERNING EQUATIONS IN FLUENT

There are various governing equations available in FLUENT that depending on
the flow regimes any of them can be selected. In this investigation the flow regime is
turbulent and the momentum equation should be companied with a turbulence model. As
was stated previously there are various models available, however, the simplest one (k-

8) was selected to perform this simulation.
The governing equations in this model in mean form are as following

Conservation of mass:

135

8p 6

_ —— . .—. 0 5.1
at ”Lax, ('0 u’) ( )
Momentum:
a 8 6P 6 611. 5U,-
_ , +_ . . =_—+——— ——’+— 5.2
61(p 11,) ax]. (pujur) axi 6x]. {#Gfl-[axj axi ]} ( )
Where: #47 = .11 4“,“:

The turbulent (eddy) viscosity term is defined based on the (k-e) model:

k2
”I : pcp? (5'3)

where a is the dissipation rate of the k, turbulent kinetic energy. The amount of k per
mass and time converted into the internal energy of the fluid by viscous action. C,l is the

model constant which is equal to 0.09.

Local values of k and a are obtained from the solution of the following semi-

empirical transport equations:

 

at 6x. 6x.

I

a(pk)+6(pu,-k)= a[ 5k

 

at ax 6x

1

6(pa)+a(,0u,~€): 6 [ as

where the diffusion coefficients are given by,

136

 

I", = [u +
0k
(5.5)
I} = p + ,u,
05
The production rate of turbulent kinetic energy Pk is given by
62:. Bu . .
p,=,, 1+ , a“! (5.6)
6x}. 6x'. 6x].
and the model constants are given
cs, 2 1.44
cg2 = 1.92
(5.7)
0,, = 1.0
a, 21.3

In this investigation for simplicity, the standard k-e model with wall function
was utilized as the turbulence model. The k-e default constants were used, however, they
can be modified with in FLUENT. The simulations were performed for steady state
condition, in which the transient terms of the governing equations were eliminated. The
convergence criterion was chosen 1E-4 for the residual and default algorithms were
utilized for discretization of the governing equations. The default schemes are first order
upwind for momentum and turbulence kinetic energy and SIMPLE for pressure-velocity

couphng.

137

5.3.3 VOLUTE FLOW SIMULATION

The grid generated in GAMBIT was imported into FLUENT 5.0. The boundary
conditions and materials had to be defined prior to the simulation. There are various
ways of defining boundary conditions for a simulation in FLUENT. For momentum
boundary conditions, total and static pressures, mass flow rate at the inlet and outlet are
among the choices. The boundary surfaces are named after the type of condition
provided there, such as “Pressure Inlet” or “Inlet Mass Flow”. Depending on the
additional equations engaged in the simulation, such as energy equation, one could
define the corresponding variables at the boundaries. If the momentum equation is
companied with energy equation, flow temperatures must be provided in addition to the

momentum boundary conditions.

Initially in the simulation, the energy equation was employed and in the material
section, air with ideal gas status was chosen as the working fluid. This choice would let
the density of the air vary with the pressure and temperature along the flow path.
However, experimental results showed later that the compressor has low pressure ratio
and flow at the impeller exit has low Mach numbers. Therefore, the assumption of
constant density would suit the flow simulation fiom impeller exit to the conic outlet.
Meanwhile, the previous temperature measurements were not reliable for boundary
conditions because of the thermal stability of the compressor as was described in
previous chapters. Hence, it was decided to eliminate the energy equation and perform

only momentum simulation.

138

To define the momentum boundary conditions, the combination of “Inlet Mass
Flow Rate” and “Static Pressure” at the outlet was considered initially but the flow angle
at the diffuser inlet would have been neglected. Therefore, velocity magnitude and flow
angles with respect to radial direction at the vaneless diffuser inlet, which were
calculated from the impeller meanline analysis, were provided as the inlet condition.
This boundary condition included both the mass flow rate information and flow angles

at this face.

As mentioned in the introduction section of the chapter, if the simulations were
performed for the stage, the velocity and flow angle distributions could have been
extracted at the vaneless diffuser inlet. Circumferential and axial variation of the
velocity vectors and flow angles at this face, would have determined the interaction of
the impeller and the vaneless diffiJser. However, the results in the next chapter shows
that assigning uniform velocity and flow angle distribution in this region has provided

reasonable performance results for these components.

In the case of simulation without the impeller, the best inlet boundary condition
was to measure velocity magnitudes and flow angles at different circumferential and
axial locations at the vaneless diffuser inlet, Ayder (1991). A profile that included
circumferential and axial velocity distribution could be provided in FLUENT. For the
future investigations on this compressor, the Cobra probes are utilized to perform these

measurements.

For the conic outlet, the experimental measurements of static pressure were

provided as the boundary condition. FLUENT provides the option of correction of the

139

flow at the outlet with respect to the upstream condition. This means that if the flow
upstream becomes supersonic or separated, the outlet flow properties would be

extrapolated from the results upstream.

In addition to definition of the working fluid, the wall material had to be defined
in order to include the effect of surface roughness. In the initial simulation smooth wall
was chosen for the volute casing and after validation of results, the next simulations

were performed with the same smooth wall material.

140

FIGURES

141

 

Figure 5.1: Vaneless Diffuser

 

Figure 5.2: Volute Casing

142

 

Complete Flow Path

3

5

igure

F

 

Figure 5.4: Diffuser Grid

143

 

: Volute Mesh

Figure 5.5

144

CHAPTER 6

NUMERICAL RESULTS AND ANALYSIS

145

In this chapter, the simulation results are validated by comparing them to the
experimental results. In addition, performance, flow structures, and loss mechanisms for

the vaneless diflirser and volute are discussed in detail.

6.1 VALIDATION

The simulations were validated by comparing the overall properties in the
simulation to those in the experiments results. The properties obtained experimentally
were averaged circumferentially (vaneless diffuser) and axially (volute) at every desired
cross section of the flow. The properties obtained numerically were mass averaged over
the cross section, which is a popular technique among numerical analysts because of its
accuracy.

As mentioned in the previous chapter, the boundary condition at the diffuser inlet
includes the velocity magnitude and flow angle extracted from the meanline analysis.
Figure 6.1, compares the diffuser inlet static pressure for different speeds and maximum
mass flow rates obtained from experiments and CFD analysis. Note that static pressure
was not the boundary condition at this cross section and could vary from the impeller
meanline analysis. There is an offset between the two static pressures, which propagates
in the next results as well, Figures (6.2-3). Without including impeller flow in the
simulation, CF D cannot predict accurately the boundary layer development at the
beginning of the vaneless diffuser. The development of the boundary layer on vaneless
diffuser walls increases the entrance speeds and reduces the static pressure at the diffuser
inlet. In order to prevent this situation, the measured mass flow rate at the vaneless

diffuser entrance could be utilized as the boundary condition for each case. Simulations

146

had to be repeated with different flow angles until the CFD and experimental static
pressures at this face were matched. This matching between the two values concludes the
most accurate flow angle for the flow at the vaneless diffuser inlet. Another alternative
would have been to provide experimental values for the flow angles and speeds at the
vaneless diffilse inlet, which were described in the previous chapter. However, with the
provided boundary conditions, the CFD and experimental results are in good agreement.
The minimum and maximum offset for results in Figures (6.1-3) are 0.35% and 2.4%,
which are reasonable.

Figures 6.2-3 compare the diffuser outlet static and total pressures at different
speeds and maximum flow rate. The CFD prediction has a small ofi‘set and follows the
same trend as the experimental results. As rotational speed increases, both static and total
pressures at vaneless diffuser exit increase. Note that similar results for different mass
flow rates were available, however, for validation purposes maximum, minimum, and
intermediate mass flow rates were selected.

Figures 6.4 through 6.12 present the volute static pressure distribution at different
volute cross-sections where the static probes are located in the experiments (Figure 4.1).
These results show the behavior of the volute at different speeds and mass flow rates.
Numerical simulations predict the initial diffusion at the beginning of the scroll with the
same trend and rate of the experimental results. They confirm the near uniformity of this
pressure distribution downstream of the scroll, however, there are also diffusion patterns
in this region for all cases.

In all cases the experimental and numerical results are in good agreement with

each other, which indicates the validity of the simulations.

147

6.2 PERFORMANCE

Figures 6.13-14 show the static pressure recovery and loss coefficients (2.37-38)
for the vaneless diffuser. Clearly the vaneless diffuser raises the static pressure more in
higher mass flow rates and speed. Losses in the vaneless diffuser decrease as the mass
flow increases because the flow obtains the momentum to overcome the adverse pressure
gradient. The largest losses in the vaneless diffuser occurred at low mass flow rates and
2000 RPM due to the flow separation in this component.

Figures 6.15-16 show the static pressure recovery and loss coefficients for the
volute and cone. This plot presents the overall performance of these two components
together. The static pressure recovery of the volute and cone decreases with increase in
the mass flow rate and speed. Generally at off design condition, flow is decelerated inside
the volute, resulting in a slight pressure rise inside the volute. However, larger mass flow
rates in the volute reduce the diffusion inside this component. The conic diffuser
transforms the kinetic energy left in the flow to pressure regardless of the volute
performance, unless the flow separates inside this component. Figure 6.16 shows that the
loss at 3000 RPM decreases with increasing in mass flow rate while the 3497 RPM
remains almost constant in that flow range. 2000 RPM and minimum mass flow rate has
the maximum loss, which indicates worst operating condition of the compressor.

The radial component of the velocity at the vaneless diffuser outlet generates a
strong rotational flow in smaller areas of the volute, which is in the form of a forced
vortex flow. Further downstream, fresh fluid wraps around this rotational flow and as the
volute area increases a counter vortex is generated, as was described in Chapter 2.

Figures 6.17-20 show the average vorticity magnitudes at the volute cross-sections for

148

2000, 3000, 3497 RPM and maximum, medium and minimum mass flow rates. In all
cases, high vorticity levels are observed at the beginning of the scroll and stay at a
constant level fithher down stream. The primary observation is that the trend is
independent of the mass flow rates and speeds. Further in the chapter the flow structure
will describe the reasons for this tendency. Note that in all case, the minimum mass flow
rates are generating slightly different vorticity distribution in upstream of the volute due
to the strength of the initial vortex flow. In lower mass flow rates, the radial velocity
component. at diffuser outlet is smaller than higher mass flow rates; therefore, the vortex
flow is weaker. Figure 6.20 presents a comparison of the same flow property for different
speeds at maximum mass flow rate. There is a decrease in vorticity at 2000 RPM due to
smaller radial velocities the volute inlet as compared with the other two speeds

Figures 6.21-23 show the tangential velocity distribution inside the volute for
different speeds at varying mass flow rates. It was observed that the flow goes through
acceleration and deceleration in the smaller cross sections and minimum mass flow rates.
In higher mass flow rates, diffusion decelerates the flow inside the volute and the
tangential velocity decreases. The tangential velocities decrease more when the flow
arrives inside the conic diffuser because of the larger diffusion rate in this component.
Note that in 2000 RPM cases, the flow decelerates so much that might not be able to
recover from the adverse pressure inside the volute. Therefore, boundary layer on the
volute walls may become separated and reversed flow occurs. In addition, the convex
surface of the inner wall of the volute could contribute to this phenomenon as well.
Figure 6.24 compares the tangential velocity distribution for three speeds and maximum

flow rates.

149

6.3 FLOW STRUCTURE
6.3.1 VANELESS DIFFUSER FLOW

Figures 6.25-33 present the static and total pressure contours and meridional
velocity vectors in the volute cross-sections at 27, 117, 207 and 297 degrees for 3497,
3000 and 2000 RPM and varying mass flow rates.

At the diffuser inlet, the static pressure is constant over the diffuser width because
the boundary condition at this face is uniform absolute velocity and angle. The static
pressure increases radially towards the diffuser exit. The 90 degree bend on the hub wall
affects the upstream flow and results in separated flow on this wall. Decrease in mass
flow rate, decreases the radial component of the velocity inside the vaneless diffuser,
which reduces the momentum of the flow to overcome the existing adverse pressure. In
2000 RPM and minimum mass flow rate, the radial component of the velocity is so small
that the separated regions cover the whole wall. This due to the fact that the flow angles
at this condition is very large and it is predicted that the diffuser stalls.

If the impeller were included in the simulation, the mixing region between the
impeller and the vaneless diffuser would wash out the nonuniforrnity of the velocity
profile of the flow leaving the impeller. Therefore, considering a uniform velocity
distribution at the vaneless diffuser inlet was not far from reality. In addition, more flow
exits the impeller on the shroud side in lower mass flow rates, while more flow exits from
the hub side of the impeller at higher mass flow rates. This is due to the nature of the
centrifugal flow, which forces inevitable secondary flows inside the impeller passages.
Thus, this lack of momentum on the hub wall would have been superimposed on the

current simulation results.

150

The contours of the total pressures confirm the flow separation on the hub wall as
well. In lowest mass flow rate (Figure 6.33), a pattern of an almost returned flow can be
observed on the hub wall and the separated region is very close to the impeller. This
suggests the possibility of the stall inside the vaneless diffuser. Note that these are steady
state results and unsteady simulations would predict oscillation patterns in these regions.

It is concluded that the vaneless diffuser is too large for these mass flow rates and
the hub wall has to be pinched in order to prevent this separation. Pinching the diffuser
increases the speeds and provides the required momentum to overcome the adverse

pressure.

6.3.2 VOLUTE FLOW

In general, the flow from the diffuser is turned from a radial to a horizontal in the
90-degree bend between the difl’user and the volute. The radial component of the velocity
entering the volute, initiates a rotating flow inside the volute. The curvature of the volute
casing contributes to this flow structure as well. The vortex is initially formed in smaller
areas and expands firrther downstream. Downstream in the volute, a counter vortex is
formed in lower pressure region inside the volute, which shows the reason for vorticity
magnitude decay in the vorticity plots. Those plots show the resultant vorticity
distribution in the cross sections.

The rotational velocity of this vortex flow increases from zero at the center to a
higher value radially out. The velocity distribution at the vortex core has linear
distribution to some radial distances, thereafter the distribution is affected by the

geometry of the volute cross section. Ayder (1993) observed more or less linear

151

distribution of swirl velocity outside the vortex core for elliptical volute cross section,
which indicates that the flow has a solid body rotation regime. However, Hagelstein et al.
[23] reported a constant velocity distribution outside the'vortex core for a rectangular
volute cross section. In this case, the vortex losses primarily occur in the transition region
between the frictionless solid body core and the outer shell in which small velocity
gradients predominate.

Similar forced vortices are detected in the Trane volute cross sections, however,
since the mass flow rates are much lower than the design point, the intensity of these
vortices are not as much as the above cases. Therefore, outside core flow is swept away
by the through flow, which impacts the velocity distribution. Note that in the 2000 RPM
case, the twin vortex is never formed, instead, the single vortex has occupied a large
region downstream of the volute. Existence of these vortices results in larger radial
velocities at the walls, which increase the fiiction losses inside the volute. Another
important observation is the rotational flow close to the volute hub wall, returns to the
vaneless diffuser in case of 2000 RPM and minimum mass flow rate, (Figure 6.33). This
is due to the fact that separated flow on the diffuser hub wall created a pressure sink in
the flow path, which causes the flow return.

Observing the static pressure contours in Figures 6.25-33 shows that the axial
variation of the pressure on the outer casing of the volute is not significant and validates
the averaging method utilized in the experimental measurements, described in Chapter 4.
As predicted previously, the flow decelerated inside the volute and the expansion of large
static pressure areas further downstream indicates the fact. In other words, the

compressor is working off design and the volute is too large.

152

The static pressure variation over the cross section results from swirl and the
circumferential curvature of the volute channel. The centrifugal forces due to swirl are in

equilibrium with the static pressure increase from center toward the walls:

dP VS2
._ : p _—
dr r

C

(6.1)

where rc is the curvature radius of swirling component velocity and r is radial distance
from the swirl center. In the Trane volute this happens only in small area cross sections,
where the intensity levels are high. In larger area cross sections the intensity of the
vorticity decays, therefore, it doesn’t impact the static pressure distribution. Thus the
through flow velocity and circumferential curvature create a pressure gradient between

the inner and outer wall:

ELIE
fl—pR on

which can be observed in the figures. Van den Braembussche et al. (1990) show how the
variation of through flow velocity over the cross section results from the static and total

pressure distribution:
P0 — P 2 gm? + V52) (6.3)

At the volute inlet sections both total and static pressures decrease from the volute
wall toward the center resulting in a nearly uniform through flow distribution. In Trane
volute at the downstream sections and minimum mass flow rates, forced vortex cores are
extended resulting in more uniform total pressure distribution. The total pressure contours

in Figures 6.25-33 show a strong total pressure gradient zone at small areas of the volute

153

indicating that the total pressure loss primarily happens in the areas immediately
downstream of the tongue.

In addition, the periodic increase and decrease of swirl velocity during rotation
around the volute cross section periphery results in extra diffusion and mixing losses.
Increased turbulence mixing between the low energy fluid in the boundary layers and the
high energy fluid at the center due to the curvature of the walls, and the fact that after
each rotation the boundary layer is absorbed by the new fluid coming out of the diffuser,
firrther contribute to a distribution of total pressure losses over the volute cross section.
The total pressure over the volute cross section is lower than of the incoming fluid and
gradually decreases toward the volute outlet.

Note that the single vortex and twin vortices have moved axially firrther fiom the
wall in the lowest mass flow rate (Figure 6.33). It can be observed that the strength of
these vortices decreased downstream and the center of the rotational flow is carried away
from the hub wall to the shroud wall. The low-pressure region in volute has expanded
more than the 3497 RPM case, which can contribute to this process as well. However, it

is not possible to exactly predict the location of these vortices.

6.3.3 TONGUE EFFECT

Figures 6.34-36 show the static pressure contours on the shroud side of the
vaneless diffuser for different speeds and mass flow rates. The tongue region is shown
with a radial dashed line to observe its effect on the pressure distribution. In all cases,
constant pressure contours are broken up between the tongue and volute beginning,

which creates a distortion in the circumferential static pressure distribution. In addition,

154

this region creates a sharp circumferential static pressure gradient between volute outlet
and inlet. Existing of such gradient forces the flow at the volute outlet to “leak” back into
the volute. As the flow rate increases, the distortion shrinks due to pressure build up at
the tongue because of the blockage effect. On the other hand, overall the intensity of the
radial pressure gradient inside the vaneless diffirser increases as the mass flow rate

decreases, which leads to the separated flow in this component.

155

FIGURES

156

Absolute Pressure (KPa)

Absolute Pressure (KPa)

 

2 —-O— CFD —I— Experiment
10 .

100 ~

 

 

98~

96 . ....................

92 - ................................... .................... .................................. ..................................

 

 

1500 2000 2500 3000 3500 4000

 

Figure 6.1: Diffuser Inlet Static Pressure at Choke

+ CFD -I— Experiment
106 ,

 

104~

102 .

 

 

 

100 4
9,. ................................ ........ , .......................... .............. , .............. ....... ‘ .......................

92. .................................. .................................. ', .................................. l .................................. j ..................................

 

 

 

90 4
1500 2000 2500 3000 3500 4000
RPM

Figure 6.2: Diffuser Outlet Static Pressure at Choke Condition

157

Absolute Pressure (KPa)

Absolute Pressure (KPa)

106

 

104

102

100

984

92«

90

+ CFD_Cone + Exp eriment_0ut let

 

 

 

.

..............................................................................................................................................................................

 

 

104

1500 2000 2500 3000 3500 4000

Figure 6.3: Cone outlet Total Pressure at Choke Condition

+ CF D -l— Experiment

 

102 -

100 .

984

94~

924

 

 

 

. . .
.............................................................................................................................................................................

 

90

 

 

0 50 100 150 200 250 300 350 400 450

Figure 6.4: Volute Static Pressure Distribution at 2000 RPM and Maximum Flow Rate

0

158

 

Absolute Pressure (KPa)

Absolute Pressure (KPa)

+ CFD —I-— Experiment

 

94

 

. .
. .
l i .
.
.
.

 

90

 

 

 

 

 

...............................................................................................................................................................................

 

 

Figure 6.5: Volute Static Pressure Distribution at 3000 RPM and Maximum Flow Rate

50 100 150 200 250 300 350 400 450

 

106

104‘

102 -

100 ~ Q

964

94~

92‘

 

+ CFD + Experiment

 

 

 

 

 

 

................................................................................................................................................................................

 

 

90

0 50 100 150 200 250 300 350 400 450

Figure 6.6: Volute Static Pressure at 3497 RPM and Maximum Flow Rate

159

Absolute Pressure (KPa)

Absolute Pressure (KPa)

+ Experiment + CFD

 

102 <

98«

94*

................ .‘......I............,....n.............,...........h .............._.........,... . ............,4 .......................................................

.........................................................................................................................................................................

 

 

 

 

 

. . I I I . I I
. I . I I I I I
I I I I I I I I
. . l I I . I .
. I I I l I I I
_J I I I I I . I I
..................5........,..... .. .... ....4.....4....,......... .......r‘...................,....................'...............I...‘I...........I.......,...........I......
I
I I I I
I l I l I
I I I

 

 

 

90

O 50

100

 

150 200 250 300 350 400 450
0

I I T

Figure 6.7: Volute Static Pressure Distribution at 2000 RPM and Mid Mass Flow Rate

106

 

104*

102 .

100 ~

98‘

94~

92‘

 

90

 

 

+ Experiment -I— CF D

 

 

 

 

 

 

I . . . I
I I I I I I I I
I I . I I I . I
I . I . I . I .
I I I I I I . I
I I I I I . . .
.4.....—.............4...........-..... ................4....~...........4......J........I.........4-.........I.»..4..4—.4..V..............I...... .1........qsfl........4.......
I
I

 

L

 

T

50

I

100

150 200 250 300 350 400 450
0

Figure 6.8: Volute Static Pressure Distribution at 3000 RPM and Mid Mass Flow Rate

160

 

106

1041

100 4

98‘

96‘

Absoulte Pressure (KPa)

94~

92«

 

90

+ Experiment —I— CF D

 

 

..............................................................................................................................................................................

.,,_,,-.-- ...................

...............................................................................................................................................................................

 

 

Figure 6.9: Volute Static Pressure Distribution at 3497 RPM and Mid Mass Flow Rate

104

+ Experiment + CF D

 

1024
1004
98«
96-

94~

Absolute Pressure (KPa)

 

 

92 ..I.......,‘....., ‘..... , .,',...-,.-..
90 I I I l T T I I

 

 

...............................................................................................................................................................................

...............................................................................................................................................................................

....I.............I.M.....................,........... ..,...,......... . ‘..-..,. ......................................

 

 

Figure 6.10: Volute Static Pressure Distribution at 2000 RPM and Min Mass Flow Rate

50 100 150 200 250 300 350 400 450

161

110

+ Experiment —I— CFD

 

108
106 4
104 -
102 d
100 ~
98 ~
96 4
94

92 1
90

Absolute Pressure (KPa)

.I ............................................................................ .-......-.... .....W ......................

 

 

  

 

...............................................................................................................................................................................

...............................................................................................................................................................................

 

 

0 50 100 150 200 250 300 350 400 450

Figure 6.11: Volute Static Pressure Distribution at 3000 RPM and Min Mass Flow Rate

115

110‘

. I I I I I I
I . I I I I I I
I I . I I I I I
I I I I I I I I
l I I I I I
l l t l ‘
v C ' '
I l ‘ ' 1
I I I I I I I
. . . I I I I I
I . I I I I I I

, , , I I . I
I I I I I
- I I I I
u I ' ‘
I v I l I r l
I I I I I I I .
I I I I I I I I
I I I I I I a
I I I I I I I
I I I I I I I I
I I I I I I I I
I I I I - I ' -
I I I I I I - v
105 ' ' ' ' ' ' ' '
...............................................................................................................................................................................

l I I u ' ' '
I I I I I I I
I . . I I I I
I I I I I I I
, , , . I I I
. . I I -

I I I

I I I

. I I

I I I I

I
I I
I I I

100 .

Absolute Pressure (KPa)

\0
L10
1

90

Figure 6.12: Volute Static Pressure Distribution at 3497 RPM and Min Mass Flow Rate

+ Experiment + CFD

 

 

 

 

 

 

 

0 50 100 ISO 200 250 300 350 400 450

162

(I)

0.55

 

0.50 I

0.45 I ~ ~

0.40 4

0.35 4

0.30 .

0.25

 

0.20

+ 3497 RPM + 3000 RPM +2000 RPM

 

..............................................................................................................................................................................

 

 

0.5

0.00 0.01 0.02 0.03 0.04 0.05 0.06

Figure 6.13: Diffuser Pressure Recovery Coefficient

+ 3497 RPM + 3000 RPM +2000 RPM

 

0.4 ~

0.3 <

0.2 -

0.1 4

0.0

 

 

 

 

0.00 0.01 0.02 0.03 0.04 0.05 0.06

4>
Figure 6.14: Diffuser Loss Coefficient

163

+ 3497 RPM -I- 3000 RPM +2000 RPM

0.6

 

 

 

02 I ...........

0.1 ~

 

 

0.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06
¢

Figure 6.15: Volute Pressure Recovery Coefficient

 

+ 3497 RPM + 3000 RPM +2000 RPM

 

0.6

0.5 ~

0.4 -

 

: : 1 : :
02 4.. ........ . ............................. '. ............................

I I I I I
I I I I I
I I I I I
I I I I I
I I I I I
I I I I I
-I ...............................................................................................................................................................................
o I I I I I
I I I I I
I I I l I
I I I I I
I I I I I
l

 

 

 

0.0
0.00 0.01 0.02 0.03 0.04 0.05 0.06

Figure 6.16: Volute Loss Coefficient

164

a) (l/sec)

-0-hdaxhdass -4I-hdklbdass-1&-hdu1hdass

 

 

 

 

 

 

 

 

 

 

 

 

2500

2000 - -------------
A 1500 < IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
§
5 1000 I ...................... i .......... . E, ............

500 I ,. L ...... ._ ..............
Nazi.» . "fl
0 l ‘ i I I I
0 50 100 150 200 250 300 350 400 450
9

Figure 6.17: Vorticity Magnitude at Difi‘erent Volute Cross-Sections and 3497 RPM

-C-hdax_hdass -l|-hdk1hdass -1§-hdhihdass

2500
2000
1500 .. . E , . ................ .. ..

1000

 

500

  

0L” I_e
0 50 100 150 200 250 300 350 400 450

Figure 6.18: Vorticity Magnitude at Different Volute Cross-Sections and 3000 RPM

165

w (Um)

(I) (l/sec)

I400

+Max Mass +Mid Mass +Min Mass

  

   

1200

l 000

800

 

600

400

200

0 50 100 150 200 250 300 350 400 450

Figure 6.19: Vorticity Magnitude at Difl‘erent Volute Cross-Sections and 2000 RPM

+ 3497 RPM + 3000 RPM +2000 RPM
2500
2000
1500
1000

500

 

Figure 6.20: Vorticity Comparison for Maximum Flow Rate and Difi‘erent Speeds

166

Vt (m/soc)

VI (In/see)

+Max Mass +Mid Mass + Min Mass

70

    

60
50
40
30

20 ............

Figure 6.21: Tangential Velocity at Different Volute Cross-Sections and 3497 RPM

Tangential Velocity at Different Volute Cross Sections and 3000 RPM

+MaxMun +Mide +MinMus

 

Figure 6.22: Tangential Velocity at Different Volute Cross-Sections and 3000 RPM

167

 

+ Max Mass +Mid Mass +Min Mass

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 6.23: Tangential Velocity at Different Volute Cross-Sections and 2000 RPM

+ 3497 RPM + 3000 RPM +2000 RPM

 

Vl (m/sec)

 

Figure 6.24: Tangential Velocity Comparison for Maximum Flow Rate and Different
Speeds

168

Ps (KPa)

Ml

—¢:‘~
*:::i- : {3:12—31

 

(i)

mm

 

,(
in
I
5' I '
A 1 '
'1. MI \ ‘ luv
‘1, ”1‘H‘I ’1le,
. m u“! I t
linuhm I :1"
In”,
”"1!
IH
1,1,!
11'

(1) {hm

 

I

1 I
‘ \\ \

1 1 ‘1‘ I \V n, H

‘ \ i‘ N1 "N

%\‘\\E\“ Q) £1111"

i «a;
(k) w

 

 

Figure 6.25: Static and Total Pressure Contours and Meridional Velocity Vectors for
3497 RPM, Maximum Flow Rate and Cross Section Angles (a) 27, (b)117,(c)207,
(d)297

169

Pt (KPa)

   

(8) (6) (i) 5;,”

   

 

1 )1 v
I‘fl ‘\ ‘ I",
h 1 in
Saiii‘ris‘tur. I '

(i) zlw'

 

 

13;. \‘I

it 3‘ M
“"3011 ”’[1442' £111:
1
00 SW"

 

 

Figure 6.26: Static and Total Pressure Contours and Meridional Velocity Vectors for
3497 RPM, Mid Mass Flow Rate and Cross Section Angles (a) 27, (b)117,(c)207,
(d)297

170

-
‘5

(i) 53'"

/I R\\\
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(d)297

171

 

Figure 6.28: Static and Total Pressure Contours and Meridional Velocity Vectors for
3000 RPM, Max Mass Flow Rate and Cross Section Angles (a) 27, (b)117,(c)207,
(d)297

172

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177

 

Figure 6.34: Diffuser Static Pressure Contours for 3497 RPM and (a) Max (b) Mid (0)
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Figure 6.35: Diffiiser Static Pressure Contours for 3000 RPM and (a) Max, (b) Mid, (c)
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180

CONCLUSIONS

In this investigation there were two primary objectives were considered:

1) To establish an advanced experimental facility, which enables understanding of the
detail flow characteristics inside a volute geometry.

2) At the same time develop a numerical scheme that can predict and analyze the flow
inside the volute.

With these two procedures, theory and experiments are complementing and
supplementing each other in design and analysis of the volute flow. Hence, a designer or
flow analyst is able to understand the losses and flow mechanism inside the volute,
which results in design of an efficient volute.

An advanced testing facility with the capability of analyzing the flow in a
centrifugal compressor was established. A CVHF 1280 Trane two stage compressor was
modified to a single stage. This unit operates with refrigerant gas in commercial settings
and after modifications air replaced the refrigerant. This facility is designed and
modified for investigation of the performance, flow structure and loss mechanism in the
stage and components. The vaneless diffuser and volute are utilized with static pressure
taps to map the static pressure field in these two components. This compressor is utilized
for measuring velocity vectors inside the diffuser and volute with five-hole and cobra
probes in future. This unit can operate with the academic laboratory standards and its
reassembly will enable the future researchers to modify the parts and convert it to a two-

stage unit and perform investigation in any component of this compressor.

181

In this dissertation, the performance of the compressor at three speeds of 2000,
3000, 3497 RPM was evaluated. Upon calculating the mass flow rates in these speeds
and comparing to the design conditions, it was found that the compressor is operating at
off design condition. In the experimental results, the nonuniform circumferential static
pressure distribution was observed in all cases. This was due to the effect of the tongue
region on the compressor performance. There is a large circumferential pressure gradient
between the volute outlet and inlet, which forces the flow to reenter the volute.

A meanline analysis of the impeller was performed with the experimental data in
order to evaluate the performance of the impeller and provide diffuser boundary
conditions at the diffuser inlet. It was predicted that the diffuser performance at lower
speeds and mass flow rates results in stall because of the large flow angles entering the
vaneless diffuser.

For the first time, to the best knowledge of the author, F LUENT has been
utilized to perform flow simulation inside volute geometry. Currently in the
Turbomachinery industry CFX-TASCFLOW is utilized for design and analysis of the
flow in centrifugal compressors. This solver is a structured based in which creating the
grid requires time consuming techniques. In contrast, the unstructured F LUENT solver
was able to import CAD files directly and with the efficient grid generation schemes of
GAMBIT, an unstructured mesh was generated for the vaneless diffuser and volute.
Although the grid was unstructured, the results were in good agreement with
experimental ones. Vortices were diagnosed inside the volute that contributes to higher
losses. There is a large vorticity magnitude at the beginning of the scroll that decreases

further downstream of the tongue. The decrease in this magnitude is due to the

182

formation of the counter vortex to dissipate the original vortex. This will result in
dissipation of the kinetic energy inside the volute. In addition, the friction losses
increase because of the large radial component of velocities produced by these swirling
structures.

Flow at the inlet of the diffuser is uniform axially but the axial distribution
deforms in the diffuser outlet because of the bend section. In lower mass flow rates, the
momentum of the flow cannot overcome the large radial pressure gradients inside the
vaneless diffuser and the flow separates. The separation of the flow becomes more
pronounced with decrease in the mass flow rate. At 2000 RPM and minimum mass flow
rate, the flow completely separates on the hub wall and extends back to the impeller
region. It was observed that in this case, flow reenters from volute back into the vaneless
diffuser. Overall pressure distribution contours showed that the volute is too large for
these mass flow rates, which result in diffusion pattern circumferentially inside the
volute.

One of the primary interests of industry in volute investigation is development of
a methodology to perform optimization study for volute geometries. This dissertation
presented an efficient technique to analyze the flow inside the volute with an optimum
approach. All in-house codes can perform meanline analysis for the stages of a
compressor in order to provide the inlet boundary conditions. With outlet boundary
conditions obtained from a performance test, simulation can be performed for all cases.
However, grid generation is always the difficult part of the simulation. If the original

CAD file was drawn with shorter surfaces, GAMBIT could have handled the volume

183

grid generation easier and faster. In this approach generation of structured grid for

profiles and interpolation of the surfaces, which is very time consuming, is not required.

184

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185

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