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IMPELLER-DIFFUSER-VOLUTE MODELING AND FLOW
ANALYSIS TOGETHER WITH TEST VALIDATION

presented by

YINGHUI DAI

has been accepted towards fulfillment
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Ph.D. degree in Mechanical Engineering

 

 

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IMPELLER-DIFFUSER—VOLUTE MODELING AND FLOW
ANALYSIS TOGETHER WITH TEST VALIDATION

By

Yinghui Dai

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Mechanical Engineering

2004

ABSTRACT

IMPELLER-DIFFUSER-VOLUTE MODELING AND
FLOW ANALYSIS TOGETHER WITH TEST VALIDATION

By
Yinghui Dai

Although the axial flow compressor is preferred for the increasingly larger
engines which are required for aircraft propulsion, the efficiency of axial compressors
drops sharply at very low air mass flow rates and the blade is small and difficult to
manufacture accurately. Under this situation, centrifugal compressors are widely used.

One of the main objectives of turbomachinery researchers is to design a compact,
efficient and uniform circumferential pressure distribution volute. It is well known that
non-uniform static pressure variation along the impeller periphery due to the volute can
influent the flow inside the impeller and hurt the efficiency of the whole machine. And,
the non-uniform static pressure distribution also creates radial forces on the impeller shaft
and it might end up with the failure of the bearings because of too much loading. 80, the
volute study is very important for the centrifugal compressor design process.

An integrated tool that includes the volute and diffuser grids generation is
introduced in this study. For a new case, this tool can also create the sub-grid
attachment/append, boundary condition definition, initial guess, time-step selection and
post-processing automatically. Two new functions for the volute/impeller interaction

study and performance improvement are added in the integrated too], too. They are very

helpful for the volute design. It has been proved that this integrated tool is very effective
and pretty robust in the practical application.

With the help of this tool, this study presents the experimental and numerical
investigation on the matching of four different overhung volutes with four different
impellers that are used for pipeline applications. Two computational models, “stage”and
“frozen” model using the k-e turbulence model and the wall function built in the
commercially available CFD software TASCFlow, have been used to predict the internal
flow of all the compressor configurations. A good agreement between experimental data
and numerical simulation results is found. The overall/component performance and the
flow structure in the impeller, diffuser and volute are also discussed in detail.

The influences of some key geometry parameters on the compressor performance
are also investigated. Since the experiment test is only from flange to flange, diffuser stall
and volute stall phenomenon can only be explained from the CFD results. For different
cases, some suggestions have been proposed to improve the compressor performance

based on the CFD analysis.

Cepyright by
Yinghui Dai
2004

ACKNOWLEDGMENTS

I express my sincerest gratitude to my advisor, Professor Abraham Engeda at
Michigan State University, for his elaborate outline of this project, advices, assistance
and encouragement.

I would like to thank Professors Indrek Wichman, Professor Norbert Miiller, and
Professor Chichia Chiu for their suggestions, discussions and interest in this project that
made this work possible.

I am also very thankful to Mr. Michael Cave, Dr. Jean-Luc Di Libeni, Mr. Ed
Fowler, Mr. Tim David and Mr. Johnathan Bumingham at Solar Turbines, Inc. and Dr.
Fahua Cu at Concept NREC for their great help and fruitful discussions.

Thanks are also extended to Mr. Donghui Zhang, Mr. Faisal Mahroogi, Mr. Zeyad
Alsuhaibani, Mr. Mukarram Raheel, Mr. J aewook Song, and all other students at the
turbomachinery lab at Michigan State University.

Last, but by no means least, I would like to thank my wife, Xiaoling Sheng, my
parents, Shanwu Xu and Zequn Dong, my daughter, Connie Dai, whose quiet patience

and support enabled this dissertation to be prepared.

TABLE OF CONTENTS

 

 

 

 

 

 

 

LIST OF FIGURES VIII
NOMENCLATURE XII
CHAPTER 1 1
INTRODUCTION 1
1.1 HISTORY AND APPLICATIONS ...................................................................................... 1
1.2 CENTRIFUGAL COMPRESSOR COMPONENTS ............................................................... 3
1.3 THE PURPOSE OF VOLUTE STUDY ................................................................................ 4
1.4 OBJECTIVES OF THE CURRENT STUDY ......................................................................... 5
CHAPTER 2 8
LITERATURE SURVEY 8
2.1 INTRODUCTION ........................................................................................................... 8
2.2 VOLUTE ALONE STUDY .............................................................................................. 9
2.2.1 Flow model in volute .......................................................................................... 9
2.2.2 Loss mechanisms inside volute ......................................................................... 14

2.3 THE INTERACTION BETWEEN VOLUTE AND OTHER COMPONENTS .............................. 22
2.3.1 Influence of volute geometrical parameters on compressor performance ....... 22
2.3.1.3 Radial Position of the Cross Section ............................................................. 39
2.3.1.4 Tongue Geometry .......................................................................................... 40
2.3.1.5 Radial Forces ................................................................................................ 40

2.4 THE VELOCITY AND PRESSURE DISTRIBUTION IN VOLUTE ......................................... 43
CHAPTER 3 49
THEORY BACKGROUND AND THE INTEGRATED TOOL DEVELOPMENT49
3.1 COMPUTATIONAL METHODS AND CFD MODELS ...................................................... 49
3.1.1 Turbulence Model---k - 6‘ model ...................................................................... 49
3.1.2 Two CF D models for centrifugal compressors ................................................ 51

3.2 INTEGRATED TOOL DEVELOPMENT ........................................................................... 57
3.2.1 Sub-grid generation .......................................................................................... 57
3.2.2 Sub-grids attachment and append .................................................................... 58
3.2.3 Boundary Conditions ....................................................................................... 60
3.2.4 Initial guess ...................................................................................................... 61
3.2.5 Post-processing ................................................................................................ 63

3.3 CODE ROBUSTNESS AND GRID IMPROVEMENT ........................................................... 65
3.3.1 Code robustness ............................................................................................... 65
3.3.2 Two new functions in the code ......................................................................... 66
3.3.3 Grid quality improvement ................................................................................ 68

3.4 AERO TEST FACILITY ............................................................................................... 70
CHAPTER 4 73

 

vi

SOLUTION REPEATABILITY AND PREVIOUS WORK VERIFICATION ....... 73

 

 

 

 

4.1 INTRODUCTION ......................................................................................................... 73
4.2 THE STUDY FOR D3-l COMPRESSOR ......................................................................... 73
4.3 THE STUDY FOR D2 COMPRESSOR ............................................................................. 86
CONCLUSIONS ................................................................................................................ 90
CHAPTER 5 94
PERFORMANCE INVESTIGATION OF TWO DIFFERENT VOLUTES AND
SAME IMPELLER 94
5.1 INTRODUCTION ......................................................................................................... 94
5.2 THE INVESTIGATED COMPRESSORS ........................................................................... 96
5.3 TEST FACILITY AND TEST PROCEDURE ...................................................................... 98
5.4 COMPUTATIONAL METHOD ...................................................................................... 99
5.5 RESULTS AND DISCUSSIONS .................................................................................... 101
5. 5. I Compressor Performance .............................................................................. 102
5.5.2 Impeller and Vaneless Diffuser Performance ................................................ 107
5.5.3 Volute Performance ........................................................................................ 114
CONCLUSIONS .............................................................................................................. 1 18
CHAPTER 6 120
FLOW STRUCTURES INVESTIGATION AND COMPARISON 120
6.1 INTRODUCTION ....................................................................................................... 120
6.2 COMPRESSOR GEOMETRY AND COMPUTATIONAL METHOD ................................... 123
6.3 TEST FACILITY AND EXPERIMENTAL METHOD ....................................................... 125
6.4 RESULTS AND DISCUSSION ...................................................................................... 126
CONCLUSIONS .............................................................................................................. 145
BIBLIOGRAPHY 147

 

vii

LIST OF FIGURES

FIGURE 1.1 A SINGLE STAGE CENTRIFUGAL COMPRESSOR .................................................... 4

FIGURE 2.1 STRAIGHT VOLUTE MODEL IN VAN DEN BRAEMBUSSCHE EXPERIMENT (1990) 10

FIGURE 2.2 SUPERPOSITION OF VORTEX TUBES IN A VOLUTE (1990) .................................. 10
FIGURE 2.3 PARTICLE TRACING INSIDE THE VANELESS DIFFUSER AND VOLUTE (1994) ...... 11
FIGURE 2.4 SWIRL VELOCITY (A) AND TOTAL PRESSURE (B) DISTRIBUTION ........................ 13
AT MEDIUM MASS FLOW ..................................................................................................... 13

FIGURE 2.5 VOLUTE PRESSURE RECOVERY COEFFICIENT COMPARISON OF THEORY AND
DATA (AFTER JAPIKSE, 1982) ..................................................................................... 17

FIGURE 2.6 VOLUTE PRESSURE LOSS COEFFICIENT COMPARISON OF THEORY AND DATA.... 17

(AFTER J APIKSE, 1982) ....................................................................................................... 17
FIGURE 2.7 TYPES OF VOLUTES .......................................................................................... 25 '
FIGURE 2.8 PERFORMANCE WITH MINIMUM AREA (AFTER LOPEZ PENA, 1987) .................. 26

FIGURE 2.9 STATIC PRESSURE DISTRIBUTION ALONG THE VOLUTE AND DIFFUSER OF THE

STANDARD COMPRESSOR ............................................................................................ 27
FIGURE 2.10 PERFORMANCE WITH MEDIUM AREA .............................................................. 29
FIGURE 2.11 PERFORMANCE WITH MAXIMUM AREA ........................................................... 31
FIGURE 2.12 COMPRESSOR PERFORMANCE MAP ................................................................. 33
FIGURE 2.13 CROSS SECTIONS OF VOLUTES ........................................................................ 34

FIGURE 2.14 TOTAL PRESSURE RATIO OF COMPRESSOR WITH DIFFERENT VOLUTES AT
ACTUAL TIP SPEEDS OF 700 TO 1300 FEET PER SECOND .............................................. 35

FIGURE 2.15 GLOBAL PUMP CHARACTERISTICS WITH SYMMETRIC AND ASYMMETRIC

VOLUTE ...................................................................................................................... 36
FIGURE 2.16 COMPARISON OF PERFORMANCE FOR DIFFERENT VOLUTE GEOMETRIES ......... 37
FIGURE 2.17 EFFECT OF CROSS-SECTIONAL SHAPES ON SCROLL PERFORMANCE ................. 38
FIGURE 2.18 MEASURED VELOCITY AND PRESSURE FOR SMALL MASS FLOW ...................... 43

viii

FIGURE 2.19 MEASURED VELOCITY AND PRESSURE FOR OPTIMUM MASS FLOW .................. 44

FIGURE 2.20 MEASURED VELOCITY AND PRESSURE FOR LARGE MASS FLOW ...................... 45

FIGURE 2.21 LONGITUDINAL AND CIRCUMFERENTIAL STATIC PRESSURE VARIATION

CORRESPONDING TO SMALL (A), OPTIMUM (B) AND LARGE (c) MASS FLOW ................ 48
FIGURE 3.1 THE STAGE ROTOR ............................................................................................ 54
FIGURE 3.2 THE FROZEN ROTOR .......................................................................................... 56
FIGURE 3.3 BUTTERFLY GRID OF VOLUTE ........................................................................... 58
FIGURE 3.4 AVERAGED AREA AT DIFFUSER OUTLET ........................................................... 65
FIGURE 3.5 ONE EXAMPLE OF CODE ROBUSTNESS .............................................................. 65
FIGURE 3.6 ENLARGED VOLUTE ......................................................................................... 67
FIGURE 3.7 REDUCED-WIDTH VANELESS DIFFUSER ............................................................ 68
FIGURE 3.8 GRID IMPROVEMENT (1) ................................................................................... 69
FIGURE 3.9 GRID IMPROVEMENT (2) ................................................................................... 70
FIGURE 4.1 COMPRESSOR PERFORMANCE ........................................................................... 74
FIGURE 4.2 EFFICIENCY OF DIFFERENT STATIONS AT DIFFERENT MASS FLOWS ................... 75
FIGURE 4.3 TOTAL PRESSURE OF DIFFERENT STATIONS AT DIFFERENT MASS FLOWS .......... 76
FIGURE 4.4 STATIC PRESSURE AT DIFFERENT STATIONS AT DIFFERENT MASS FLOWS .......... 78
FIGURE 4.5 STATIC PRESSURE DISTRIBUTION AT THREE MASS FLOWS ................................ 81
FIGURE 4.6 RADIAL VELOCITY DISTRIBUTION AT THREE MASS FLOWS ............................... 82
FIGURE 4.7 TANGENTIAL VELOCITY DISTRIBUTION AT THREE MASS FLOWS ....................... 83
FIGURE 4.8 DIFFUSER STALL .............................................................................................. 84
FIGURE 4.9 THE CONTOUR PLOT OF RADIAL VELOCITY ....................................................... 85
FIGURE 4.10 COMPRESSOR PERFORMANCE ......................................................................... 87
FIGURE 4.1 1 EFFICIENCY OF DIFFERENT STATIONS AT DIFFERENT MASS FLOWS ................. 88

ix

FIGURE 4.12 PERFORMANCE COMPARISON OF THE TWO VOLUTES ...................................... 89
FIGURE 4.13 EFFICIENCY COMPARISON BETWEEN LARGE VOLUTE AND THE ORIGINAL ONE91

FIGURE 4.14 TOTAL PRES SURE COMPARISON BETWEEN LARGE VOLUTE THE ORIGINAL ONE

................................................................................................................................... 92
FIGURE 4.15 STATIC PRESSURE COMPARISON BETWEEN LARGE VOLUTE AND THE ORIGINAL

ONE ............................................................................................................................ 93
FIGURE 5.1 TESTED IMPELLER ............................................................................................ 96
FIGURE 5.2 SMALL AND LARGE VOLUTES ........................................................................... 97
FIGURE 5.3 COMPRESSOR CONFIGURATIONS ...................................................................... 98
FIGURE 5.4 COMPRESSOR PERFORMANCE ......................................................................... 103
FIGURE 5.5 COMPRESSOR EFFICIENCY .............................................................................. 104
FIGURE 5.6 PRESSURE RECOVERY AND LOSS COEFFICIENT AT EXIT CONE ......................... 106
FIGURE 5.7 IMPELLER PERFORMANCE .............................................................................. 109
FIGURE 5.8 CIRCUMFERENTIAL STATIC PRESSURE DISTRIBUTION AI PINCH POSITION ...... 112
FIGURE 5.9 SPANWISE AND CIRCUMFERENTIAL AVERAGED AREA .................................... 112
FIGURE 5.10 STATIC PRESSURE DISTRIBUTION AT VANELESS DIFFUSER OUTLET ............... 113
FIGURE 5.11 PRESSURE RECOVERY AND LOSS COEFFICIENT AT VOLUTE THROAT ............. 1 15
FIGURE 5.12 PRESSURE RECOVERY AND LOSS COEFFICIENT AT TONGUE POSITION ........... 116
FIGURE 5.13 STATIC PRESSURE DISTRIBUTION IN VOLUTES .............................................. 118
FIGURE 6.1 COMPRESSOR CONFIGURATIONS .................................................................... 123
FIGURE 6.2 VOLUTE GEOMETRY AT STATION 7 ................................................................. 124
FIGURE 6.3 STATIC PRESSURE AT HIGH MASS FLOW ......................................................... 130
FIGURE 6.4 MIDSPAN STATIC PRESSURE DISTRIBUTION AT HIGH MASS FLOW ................... 131
FIGURE 6.5 STATIC PRESSURE AT LOW MASS FLOW .......................................................... 134

FIGURE 6.6 MIDSPAN STATIC PRESSURE DISTRIBUTION AT LOW MASS FLOW .................... 135

FIGURE 6.7 CIRCUMERENTIAL STATIC PRESSURE DISTRIBUTION ....................................... 140
FIGURE 6.8 VOLUTE FLOW PATTERNS AT LOW MASS FLOW .............................................. 141
FIGURE 6.9 STATIC PRESSURE AT LOW MASS FLOW .......................................................... 144
FIGURE 6.10 TOTAL PRESSURE AT LOW MASS FLOW ......................................................... 145

xi

<~wvazrwmsggg>

Greek

pnewzgeuo

Nomenclature

area

area ratio

specific heat at constant pressure
specific heat at constant volume
pressure recovery ~

gravity acceleration

specific heat ratio

length, loss vector

Mach number

mass flow rate

pressure

gas constant

radius

velocity

absolute flow ngle from radial or axial
relative flow angle from radial or axial
flwo coefficient
isentropic head coefficient
efficiency
volute inlet swirling parameter
loss coefficient, impeller rotating speed
rotation speed
density

Superscripts

O

raw-1:3

Subscripts

thN—‘O

stagnation
iteration
rotor
stator
average

stagnation, tongue

inlet of impeller

exit of impeller

inlet of diffuser

grid interface between impeller and diffuser
diffuser exit

xii

TVDL

critical surface, 6 = 0

exit flange of the compressor
exit

exit cone

friction

inlet

isentropic

meridional

meridional velocity furnp loss
radial

tangential

tangential velocity dump loss

xiii

Chapter 1

INTRODUCTION

1.1 History and applications

The gas turbine has been a major driving force in the development of
compressible flow machines, both axial and radial. The multi-stage axial compressor and
the centrifugal compressor are competitors for the delivery of large volume flow rates of
air to the engine with very high-pressure ratio at the inception of gas turbine engine
development. Because the centrifugal compressor can make use of the radius change
across the impeller, it can produce a higher specific work transfer than an axial machine
at the same speed and mass flow rate. So if the pressure ratios are only up to 6, a single-
stage centrifugal compressor could replace a several-stages axial compressor. However,
since the centrifugal compressor delivers the air unhelpfully in the radial direction and
requires an exit volute, it is unattractive to build a multi-stage centrifugal compressor, at
least for aircrafi applications. Multi-stage centrifugal compressor is often used only when
size and weight are of secondary importance comparing to capacity and pressure ratio.

In the early 40’s, an enormous volume of effort was invested in the development
of gas turbines. In Germany, the major efforts were based on the axial flow compressor,
but in Britain, the centrifugal compressor was mainly developed. At the same time, the
internal combustion engine turbocharger provided a large market for small high-speed
centrifugal compressors as the centrifugal compressor had a wider margin between surge
and choke than its axial counterpart. As power requirements grew and massive projects of

research and development was invested into axial compressor in the World War II,

however, the axial flow compressor even had higher efficiencies than the turbines and
was more suitable for large engines.

By the late 503, people realized that smaller gas turbines would have to use
centrifugal compressors, and it provided the necessary impetus for timber rapid
development of the centrifiigal compressor. In the mid-60$, the need for advanced
military helicopters powered by small gas turbine engines started the serious research and
development work on centrifugal compressor again. Small turboprops, turboshafts and
auxiliary power units were made in very large numbers and nearly all used centrifugal
compressors. The reasons Why the centrifugal compressor was preferred were not only
for their suitability for handling small volume flows, but for other advantages including a
short length than an equivalent axial compressor, low maintenance demand, less
susceptibility to loss of performance by build-up of deposits on the blade surfaces and the
ability to operate over a wider range of mass flow at a particular rotational speed.

A pressure ratio around 4:1 can readily be obtained from a single-stage
compressor made of aluminium alloys. If the titanium alloys that permit much higher tip
speeds would be used, the pressure ratios greater than 8:1 could be achieved in a single
stage under the advanced aerodynamics design. When higher pressure ratios are required,
the centrifugal compressor may be used in conjunction With an axial flow compressor, or
as a two-stage centrifiigal. However, as mentioned above, the latter arrangement involves
rather complex ducting between stages that is only regarded as a practical proposition
when the capacity and pressure ratio are of most importance.

In recent years, many significant improvements in the performance of centrifugal

compressor have been made, such as many new design procedures, mixed-flow design,

back swept vanes, and especially the computer aided design and analysis techniques. All
of these improvements make the centrifugal compressors not only used in the fields
mentioned above, but also employed in refrigerating plants, ventilation and in the process

industries.

1.2 Centrifugal Compressor Components

A single stage centrifugal compressor or pump consists essentially of a rotating
impeller, a non-rotating diffuser and a stationary volute. Figure 1.1 shows the various
elements of a single stage centrifugal compressor. Before the eye of impeller, sometimes
inlet guide vanes are used to guide the inlet fluid flow. Because of the whirling of the
impeller, the angular momentum of the fluid is increased which means both the static
pressure and the velocity are increased within the impeller. The diffuser is used to
convert the kinetic energy available at the impeller exit into static pressure by
decelerating the fluid. Vaneless and front-pinch diffuser is shown in Figure 1.1. A volute
that is used for collecting the fluid from the periphery of the diffuser and delivering the
fluid to the outlet pipe follows diffuser. Usually the part between station 7 and 8 has a
specific name — exit cone. The exit cone is essentially a divergent device where the fluid

in it is further diffused. In this dissertation, the exit cone is referred as one part of volute.

    

vaneless
diffuser
5

    

Figure 1.1 A single stage centrifugal compressor

1.3 The purpose of volute study

The volute surrounds the impeller, and it is well known that the fluid particles
leaving the impeller have logarithmic spiral shape. So the complicated swirling motion
inside three-dimensional volutes makes the design of the volute, matching with the
design mass flow of the impeller, very difficult. In one word, volute studies are important
for three reasons:

The first one is that the performance of the centrifugal compressor strongly
depends on the match of the impeller, diffuser and volute. The overall performance can
be completely different from any component performance, especially the impeller
performance.

Secondly, a circumferential constant pressure distribution downstream the
impeller is essential to realize a uniform energy transfer in the impeller, which is a

condition for a high impeller efficiency, because non axisymmetric pressure distributions

downstream the impeller cause flow unsteadiness and additional losses in the impeller.
So, even the impeller performance is also affected by the volute part.

Thirdly, for the same reason as above, volute can cause a circumferential pressure
distortion at off-design operation, resulting in an unsteady impeller flow and additional
radial forces on the shaft. It can significantly increase the bearings loading.

The fourth reason is that volute can influence the operating range of the
compressor by a shift of the surge line and rotating stall limit to higher mass flow. The
operating range of the compressor becomes wider with the circumferentially more
uniform static pressure distribution.

Thus, we can say that compactness, efficiency and the absence of circumferential

pressure distortion are the main design targets for compressor volutes.

1.4 Objectives of the current study

So far, many CFD companies have developed various commercial software
packages for impeller grid generation, such as Bladegen and TASCGen. However, no
commercial software is generated specifically for the volute grid generation. So,
developing a volute grid generation tool to facilitate the volute analysis is the first goal of
this study.

The second target is to use the volute grid to match different diffuser and impeller
grids and in-depth study the aerodynamic performance and interaction of the impeller,
diffuser and volute. It should be very helpful on the understanding of the flow structure in
the three components. The investigation of the effects of the different volute geometrical

parameters on the volute flow field was paid more attention.

Experiments were done in test facilities at the company that give us this project.
The experimental results are used in the verification of the simulation method. The final
purpose is to investigate the design and optimization method for volute.

This dissertation starts with a literature survey on the volute research to appreciate
the progress in this field. The main body begins fiom volute flow model, and then goes
through loss mechanisms inside volute, volute/impeller interaction, ends at the radial
force on the shaft because of the non-uniform pressure distribution circumferentially.

Chapter 3 focuses on the theory that would be used in the current study and the
integrated tool development. The theory, the first part of this chapter, would be verified
in the following chapters. The introduction for the integrated tool, the second part of this
chapter, is to clear the need for this kind of tool, the difficulty to make the tool and the
basic way to use this tool.

Chapter 4 describes an assessment of the theory background and the integrated
tool introduced in chapter 3. Theoretical and numerical analysis is employed to
investigate the performance and basic flow structures in the volutes and diffusers of two
different compressors. The numerical analysis is compared with experimental data. The
basic flow structure in diffuser and volute shown in the literature survey has been
validated in the circular overhung volutes.

Chapter 5 presents the experimental and numerical investigation on the
performance of the two different overhung volutes with flat-top circular cross sectional
area to the same centrifugal compressor impeller. Attention is paid on the agreement
between CFD results and test data, the two CFD models comparison and the effect of the

two volutes on the whole compressors. It was found that the “stage rotor” model is not so

accurate only on the prediction of the impeller performance. On the whole machine
performance, its prediction is not worse than “frozen rotor” although it cannot give the
difference exists in the two configurations at high mass flow.

Chapter 6 presents the investigation of the detailed flow structure in the impellers
and volutes. The effects of the tongue position of volute, the static/total pressure
distributions, and velocity distributions in the two volutes are the main research interest.
It reveals that the second flow strongly depends on the volute channel curvature and the
leak flow around the tongue. This phenomenon can occur either at low mass flow or at

high mass flow, or either downstream of the tongue or upstream of the tongue.

Chapter 2

Literature Survey

2.1 Introduction

The volutes—the last component of a centrifugal compressor—just captured the
turbomachinery researcher’s attention recently Since it has been proved that a good
design of volute can improve the compressor performance greatly. The reason why the
volute was neglected relative to the impeller and diffuser was primarily due to the
complex volute geometry, the strong interaction of volute with other components and the
high total cost of analysis that includes the geometry set up time, the volute grid
generation time, the analysis time, etc.

Afier more and more researches focused on the volute part recently, there are
quite a few publications for the volute part appeared in the past 20 years although they
are still small in quantities compared to the large number of papers about the other
components of the radial machines. So far, a popular way that is put forward by Erkan
Ayder divided the volute study into three groups. The first group investigates the basic
flow model in the volute and gives an insight into the sources of losses by providing
detailed information about the volute flow field. The second one deals with the influence
of global volute geometrical parameters on the overall characteristics of compressor. Its
main purpose is to predict the performance of volute. The third group is oriented towards
mechanical problems and investigates the radial force on the impeller shaft caused by the

volute. Actually, all of these three groups can be divided into two big groups. One group

focuses only on the volute study. Another one is concentrated on the interaction between
volute and other compressor components.
Basically, all the literature available would be presented in this chapter according

to the two big groups as follows.

2.2 Volute Alone Study

2.2.1 Flow model in volute

R. A. Van Den Braembussche, et a1 (1990) did the measurements of the three-
dimensional flow in a simplified model of a centrifugal compressor overhung volute at
design and off-design operations. The figure 2.1 below is the straight volute model in
Braembussch’s experiment. Since the curvature radius of volute tongue and outlet are
normally much larger than the volute cross section radius, their influences on the flow is
not importance. This is the theoretical base for the straight volute model.

Escudier, et a1. (1980) indicate that in the vortex tube the fluid enters at the
constant outer radius firstly, then move from the outer radius to the center. It results in an
increase of the radial velocity due to the conservation of momentum. The vortex tubes,
therefore, have a free vortex circulation near the walls and a forced vortex circulation in
the center. But, in Braembussche’s experiment, the flow in volute is completely different
from this theory. The fluid entering close to tongue at small radius fills the center of the
volute. New fluid enters further downstream at large radius and starts rotating around the
upstream fluid. Vortex tubes of increasing radius are wrapped around each other, shown

in figure 2.2. And, each part of the fluid remains at constant radius.

OUTLET

     
   

INLEI SECTION

 
   
  
       

  

IIII

"I” [II'LIIII

' I; III _.
8L0 DJ

INLET DUCT

AIR FROM BLOWER

Figure 2.1 Straight volute model in Van den Braembussche experiment (1990)

 
 
 
   

of'

   
 

N.-—’

r
l
l
\

 
    
 
   

\
3.0—"

$-
\/
\
\

 

 

rue

Figure 2.2 Superposition of vortex tubes in a volute (1990)

This flow model was also proved by E. Ayder (1994). Figure 2.3 is the calculated
results at medium mass flow. We can see the fluid entering the volute at a position close

to the tongue (A) remains in the center of the volute until the compressor exit. Fluid

10

entering the volute farther downstream (B, C, D) wraps around the previous one, which

confirms the volute flow model suggested by Van den Braembussche.

 

Figure 2.3 Particle tracing inside the vaneless diffuser and volute (1994)

Also, Ayder (1993) got the experimental data in a centrifugal compressor volute
with elliptical cross section. Figure 2.4 provides a clear picture of the three-dimensional
swirling flow inside an elliptic volute at different circumferential positions. It also can be
a proof of the flow model in Van den Braembussche paper. Besides the swirl velocity
distribution, this paper also showed the total pressure distribution. Firstly, the reason for
this kind of total pressure distribution was explained either from internal friction or from
a particular radial velocity distribution at the volute inlet. Finally, the detailed flow
measurements have been used to give the mechanism for the reason, which is the high

losses and low total pressure in the center of the cross sections.

11

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a??? ,

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r.
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p.
i
u
u
..
r
I
a
fi:
r
I
I

”if/{JPIM :3 \nm/

\eYlH‘I If.

I

 

12

 

Figure 2.4 Swirl velocity (a) and total pressure (b) distribution

at medium mass flow

2.2.2 Loss mechanisms inside volute

Although different configurations have different losses, the losses in volutes,
especially at off-design conditions, can be significantly high. A good understanding of
the loss mechanisms in volute can help improve the prediction accuracy of the whole
centrifugal compressor although this kind of model was put forward by neglecting all the

other component influences. The overall volute losses are modeled by J apikse (1982),

Weber and Koronowski (1986). Normally, Meridional Velocity Dump Losses (ApXJVDL ),

Friction Losses (Apj) and Tangential Velocity Dump Losses (Ap;’-VDL) are included in

the volute losses.

Usually, it is assumed the meridional velocity is lost totally, the friction losses are
modeled as pipe flow and only part of the tangential velocity can be lost. All of these
three kind of losses are expressed by following equations,

1

 

APXIVDL = EPVrfii (2‘1)
L l 2
Ap" = a) —pV, (2.2)
f f Dhyd 2
1 2
Apia/DI, = th‘Z‘O/ti — Vle) (23)

where 0), =1.

The meridional velocity is the meridional velocity at the volute inlet, which is
assumed to be lost and it is called meridional velocity dump losses. The amount of losses

is expressed by the equation (2.1).

14

"f y»;

 

The friction losses are calculated in function of the roughness of the wall, the
hydraulic diameter of the volute channel (Dhyd), the path length of the fluid particles (L)
within the volute (which is assumed to be equal to the length of the volute channel) and
the through flow velocity (V,) inside the volute. Only the through flow velocity is
considered for the fiiction losses since complete dissipation of the meridional velocity is
already accounted for in the meridional velocity dump losses. The friction coefficient

depends on the Reynolds number and relative surface roughness and can be obtained

"n-‘fl
..

from the standard friction charts for pipes (equation 2.2).
In order to calculate the tangential velocity dump losses, two assumptions are

made. Firstly if the tangential velocity accelerates fi'om the volute inlet to the volute E

 

outlet (Vt,- < Vte ), then it is assumed that no tangential velocity dump loss occurs.
However if the tangential velocity decreases from the volute inlet to the exit (Vt, > Vte ),

then the flow diffuses and it is assumed that the total pressure loss is equivalent to the
total pressure losses in a sudden expansion mixing process. See equation (2.3)

This theory has been used by Japikse (1982) to calculate the performance of a
volute, specified by means of the volute loss coefficient ((0) and static pressure recovery

coefficient Cp.

CP =———pg_p" (2.4)
p.- -p.-

in function of the ratio of volute outlet area to volute inlet area

_ _ 2
AR _ A, /A,- _ 7:1), /871r,- b,- (2.5)
and the volute inlet swirling parameter

1 = Vti/Vn' (2'6)

15

Flow is treated as incompressible and the fiction losses are neglected. The
following simple relations have been obtained in the case of accelerating tangential

velocity from volute inlet to outlet (V,,- < K, ).

 

 

For the loss coefficient a) = 2 (2.7)
1 + 11
2 2
and the static pressure recovery coefficient C p = L_!/_’:£_ (2.8)
1+ ,1
In case of decelerating through flow (V,,- > Vte)
. . 1 (A -1/AR)2
veloc1ty from volute inlet to outlet 4" = 2 + 2 (2.9)
1+1 1+1
and the static pressure recovery coefficient C p = w (2.10)
AR(1+ A )

The calculated and measured variations of C p and a) with volute inlet swirl

parameter 2. and the volute outlet to inlet area ratio AR are compared in figure 2.5 and
2.6. Measured and calculated static pressure rise coefficients agree well and it seems that
this model provides a useful basis for the prediction of volute static pressure rise but not
for the losses. The difference between the calculated and measured values of loss
coefficient for high mass flows (small ,1) can be due to neglecting the remaining swirl at
the exit of the volute in the model but not in the measurements. The assumptions of

uniform inlet and outlet flow conditions may not be satisfied.

16

- .. .‘—."'_‘1

 

._""'n"\fl !'- ?" .3 ".

 

0.2 0.4

   
 

 

 

 

DIFEUSER EXIT SWIRL PARAMETER

O

of r
E -
m
g ‘1: Solid line -
L) c? Theory
E AR _

A 0.52
goo O 0.62 -
a 9' CI 0.85 . .
3.0 E

Figure 2.5 Volute pressure recovery coefficient comparison of theory and data (after
Japikse, 1982)

 

0.4

0.3

0.2

 

VOLUTE LOSS COEFFICIENT

 

 

I L

1.0 2.0 3.0

 

DIFFUSER EXIT SWIRL PARAMETER

Figure 2.6 Volute pressure loss coefficient comparison of theory and data
(after J apikse, 1982)

17

The experimental and theoretical investigations of Weber and Koronowski (1986)
reveal 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 the internal type of volutes (R < R.). Therefore

volute
they have modified the modeling of tangential velocity dump losses.
They introduce an intermediate station in the volute channel at the 50% collection
point (where 50% of mass flow is collected by the volute). The through flow velocity at
this intermediate station (t) and at the volute exit (e) are calculated from the conservation

of mass, assuming an uniform velocity over the cross section,
V” =Q/(2Af) (2.11)
VTe = Q/Ae (2.12)

The effective theoretical velocity at the volute inlet can be calculated from the

conservation of angular momentum between volute inlet (i) and the intermediate station
(0.

VTi—f = Vyyrf /r,- (2.13)

The second value of the through flow velocity at the inlet of the volute can be
calculated from the through flow velocity at the exit of the volute and the conservation of
angular momentum between the volute inlet and exit.

VTi—e = Vtere /r,~ (2-14)
In the new model, the tangential velocity dump losses consist of two components:

If the measured tangential velocity at the volute inlet (V7?) is larger than VTH then the

18

flow is accelerating in the first part of the volute and the first component is obtained by

the following relation
0 _ 2 2
AP TVDLf - pr(VT,- —VT,-_f )/2 (2.15)

where a), = 0.5 for volutes and 1.0 for plenum.

If VT, is smaller than V“, first component of losses is calculated by

P(VTi ‘ Vti— f )2

APOTVDLf = 2

 

(2.16)

In case of measured value VT, is larger than VT”, means flow is accelerating and

the second component of the tangential velocity dump losses is given by
0 __ 2 2
AP TVDLe - prU/Ti - VTe )/2 (2.17)

and otherwise

P(VTi — Vie)2

 

APOTVDLe = 2 (2'18)
The total tangential velocity dump losses is given by

0 __ 0 0
AP TVDL — AP TVDLf + AP TVDLe (2.19)

Adding the exit cone losses to the volute losses provides a complete prediction
model for the losses between volute inlet and compressor outlet. The exit cone losses are

treated as gradual expansion and expressed by

2
(VECi ‘- VECe)

APOEC = chp 2

 

(2.20)

(0 EC depends on the total opening angle of the cone and varies from 0.15 for an

opening angle of 10 degree to a value of the order 1 for an opening angle 60 degree.

Since the opening angle of a well designed volute exit cone does not exceed 10 degree, a

19

Jmnab_t~flu fl

constant value of 0.15 is proposed by Weber and Koronowski (1986). The equation
description above mostly is referenced therein from Ekan Ayder (1993).

Based on the observations of Ayder (1994), it has been decided to solve the
problem by adding second-order dissipation and wall shear forces to an Euler solver,
rather than resorting to a more expensive and time-consuming solution of the Navier-
Stokes equations. The experimental results of Ayder have shown that the flow in volutes
is affected more by the losses in the core than by the wall boundary layer. Increased
turbulent mixing on the concave walls (Johnston, 1970) limits the growth of the boundary
layers, which are absorbed in any case by the core flow after each rotation. Boundary

layer blockage can therefore be neglected, and its influence may be limited to the shear

 

forces on the walls. The internal friction is approximated by a viscous term. The
additional momentum caused by wall friction is included by adding a term 143,1. to the

momentum equations.
d
aid," E- ”ILL/C + Qi,j,k _Di,j,k _Li,j,k = O (2.21)
and the wall shear stress can be defined by the following relation:
1 2
Twau = C f 310V (2.22)

resulting in the following components on each element of the wall:

u V W
Tx : ‘7Twall’z'y = ’l—lfl'wall’rz = TVTwalI (2-23)

and, the energy dissipation due to wall friction

— rV(S, + S y + 3,.) (2.24)

must be added to the loss vector L.

20

y )
L = ry(Sx + S, +52) (2.25)
y )

 

 

As the loss vector is calculated only on the solid wall surfaces, it influences only
the vertices of the volumes adjacent to the solid walls and creates a local velocity
gradient perpendicular to the wall.

Viscous energy dissipation, at all regions of nonzero velocity gradient (at the wall
and at the vortex center), is achieved by second-order dissipation

k21Wi—1,j,k + Wi+l,j,k + Wi,j—-l,k + Wi, j+1,k + Wi,j,k-l + Wi, j,k+1 - 6W1, j,k 1 (2-26)

The coefficient k2 is adjusted empirically to simulate the viscous terms in the
Navier-Stokes equations. Actual calculations are done with a k2 value of 0.002.

The calculations underestimate the concentration of low total pressure at the
center of the first cross section. And the calculated magnitude of the total pressure and
static pressure over some sections are different from the measured ones for high mass
flow. The author admits the reason for this phenomenon is unkown.

The flow field measurements were carried out by Hagelstein, et a1 (2000) at the
diffuser exit and at several peripheral positions in the volute and in the exit pipe diffuser,
respectively. And, Hagelstein also use the same methods to simulate the flow in volute.
The results are compared with those obtained using the calculation method of Ayder
(1993). Again, they have the same problem. But, the author think the result should be

satisfying if one considers the complexity of the flow and the small computation time.

21

In Gu, et a1. (2001) study, they suggest that for the design and high mass flow
rates, the fi'iction loss due to the through flow accounts for more than half of the volute
losses. It implies that the assumption in Young and J apikse’s model is too pessimistic; at
least half of the inflow Meridional kinetic energy is preserved. For the low mass flow, the
friction loss only takes a small part of the total loss; it indicates that there should be some
other loss mechanisms. The obvious one is the diffusion loss, which is not considered in
the friction model. For the low mass flow, the equivalent diffuser ratio is 1.228. The flow
structure in the volute will be investigated by attempting to find out some loss
mechanisms.

One point of this paper is to show that the inlet meridional velocity component
will not totally lose; it creates the swirling flow in the volute. And at high mass flow, the
production and diffiision of the counter clock-wise vortex are believed to be an additional

source that increases the volute loss.

2.3 The interaction between volute and other components

2.3.1 Influence of volute geometrical parameters on compressor performance

There are quite a few key volute geometrical parameters commonly are
recognized in the parametrical studies in the available literature. Generally, the following

geometrical parameters are more important as Ayder’s suggested in 1993:

0 Circumferential variations of the cross sectional areas
0 Shapes of the cross sections
0 Radial position of the cross section

22

0 Positions of the volute inlet (Tangential or Central)
0 Tongue geometry
What follows will try to evaluate the actual knowledge about each of these

parameters as it appears from the literature.

2.3.1.1 CIRCUMFERENTIAL VARIATION OF THE CROSS SECTIONAL AREA

Stiefel (1972) has studied the performances of two compressors with different
volutes but with the same impellers and vaneless diffusers (fig. 2.12). Figure 2.12a shows
the volute that the pressure ratio is 3.8. Figure 2.12b presented a 30% smaller volute
performance and the pressure ratio is 6. The author explained that the wavy curves at
high pressure ratio in figure 2.12a results fiom an unsteady state. The reason for this
unsteady flow is the flow separation. The smaller volute exhibits a wider operation range
after comparison of figures 2.12a and 2.12b. And, Stiefel also pointed out that generally
the best compressor efficiency is achieved when the volute cross sectional area is 10-15%
smaller than the area calculated according to the frictionless flow.

The comparison study of the volutes with constant and circumferential-increasing
cross section area has been done by Lopez Pena (1987). All the four different volutes in
this research (figure 2.7) belong to the turbocharger compressor field and can be divided
into two types. The first type is the standard volute of a turbocharger compressor. It has a
cross section of elliptical shape and a circumferentially increasing area. The other three
volutes can be included in another type, i.e., they have a rectangular cross sectional shape
and a circumferentially constant area distribution. The differences among these three

volutes only lie in the cross section area. According to the area, the three volutes were

23

2’6' r?1_

”mm iii a: 1 ‘1'.-

referenced as minimum, medium and maximum volutes respectively. The static pressure
distributions at the impeller exit, the diffuser exit and on the volute wall have been
measured for all the investigated volutes.

The results of the first type volute and the minimum volute, which is 23% smaller
than the exit area of the first type volute, have been shown in figure 2.8a. In order to
compare the whole machine performance, four different rotation speeds have been tested.
We can see the surge line of the first type volute, or say the standard volute, is at a higher
mass flow than the surge line of the minimum volute. Figure 2.9 shows the static pressure
distributions at minimum, medium and maximum flows. It can be seen the static pressure
at minimum mass flow increases along the azimuth angle. This circumferential pressure
distortion propagated through the diffuser back to the impeller exit. It will cause unsteady
flow, initiate surge and hurt impeller efficiency. According to the author, the minimum
volute has a larger part of flow separation. This is the reason why the minimum volute
causes a lower pressure ratio and efficiency than the standard volute. Medium mass flow
is near design point. This is not the research interest. At maximum mass flow, the static
pressure decreases after 130 degrees or so. This means the air will accelerate until the end
of the volute. Before this angle, a constant pressure region can be found that indicates a
separation zone.

The results of the first type volute and the medium volute, which is 3% smaller
than the exit area of the first type volute, have been shown in figure 2.10. From figure
2.10a, the operating range of the medium volute is a little bit wider than the operating

range of the standard volute. Figure 2.1%, the curves at minimum mass flow is flatter

24

than the curves of the minimum volute. At maximum mass flow, the circumferential
static pressure distribution is more uniform than the distributions in figure 2.9.

Figure 2.11 shows the performance of the standard volute and the maximum
volute, which is 17% larger than the exit area of the standard volute. The efficiency drops
and pressure recovery losses become bigger fiom medium mass flow to maximum mass

flow. The author was also uncertain about this phenomenon.

 

 

 

 

 

 

 

(3) Increasing cross sectional area (b) Constant cross sectional area

Figure 2.7 Types of volutes

25

TOTRL EFFICIENCY

TOTRL PRESSURE RRTIO

 

0.

COHPRESSOR CHRRRCTER I ST 1 CS

— standard volute
new volute. minimum sectional area

005 01 045 02 025 03
EQUIVRLENT MRSS-FLON (KG/S)

(a) Compressor performance

Figure 2.8 Performance with minimum area (after Lopez Pena, 1987)

26

AMJ- if":

‘L9

       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N.
a? to,
E \—
<2
"0.0 90.0 180.0 270.0 360.0
0(deg)
0.0 90.0 180.0 270.0 360.0
0(deg)
m.
is.
fix.
a? In.”
E '-
<0.
‘_ Frlf' I‘T‘”:T*=aq i
"0.0 90.0 18010 270.0 360.0 '
6(deg)

Figure 2.9 Static pressure distribution along the volute and diffuser of the standard
compressor

27

{WW 3m 0! murmur. “Dung”

TOTFlL EFFICIENCY

TOTRL PRESSURE RFlTIO

COHPRESSOR CHRRRCTER 1 ST 1 CS

— sundard volute
new volute. medium sectional area

 

0.05 0.1 0.15 0.2 0.25 0.3
EOU I VRLENT MRSS-FLON (KG/S)

(a) Compressor performance

28

nuns“. mmnq
.h

3 MW»!

1.9

 

'5
of '0.
a 1.—
”. Minimum mass flow
0.0 90.0 180.0 270.0 360.0

   

0(deg)

 

 

 

 

 

Medium mass flow

 

 

 

 

 

 

 

 

 

‘2
0.0 90.0 180.0 270.0 360.0
0(deg)
°’- 1
Maximum mass flow
N.

 

 

PIP01
1.3 1,5

 

 

 

 

 

%
\,

0.0 90.0 180.0 270.0 360.0
0(deg)

 

1.1

 

 

(b) Static pressure along volute and diffuser

Figure 2.10 Performance with medium area

29

 

TDTFlL EFFICIENCY

TOTRL PRESSURE RFIT IO

COMPRESSOR CHRRRC TER 1 ST ICS

— standard volute
new volute. maximum sectional area

0.05 0.1 0.15 0.2 0.25
EOU I VRLENT MRSS-FLON (KG/S)

(a) Compressor performance

30

 

0.3

I'ms.l f“. “1.1

__ ~

 

19
>

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. / .
N.
. mm,
QEU) ‘hr'TT/A-Tq
E ‘—
02
’00 90.0 180.0 270.0 360.0
0(deg)
m.
‘— l
I\. % fit. 4- ;
.— r MW
0:510‘ [WT—INN
a. ‘—
<0.
’00 90.0 180.0 270.0 360.0
0(deg)
m.
N.
a ”<73 \ .
1- f A V
"0.0 900 130.0 270.0 360.0

6(deg)
(b) Static pressure along volute and diffuser

Figure 2.11 Performance with maximum area

31

 

 

 

 

 

 

 

 

 

 

 

 

55 [A
4.. g 1
3.5 / 1 /
. __. (2%

 

 

 

 

 

 

 

 

 

0.5 0.75 1.0 1.25 1.5 1.75
m(kg/s)

(a) Design pressure ratio 3.8

32

 

4.5

      

0.75 1 .
m (kg/S)

(b) Design pressure ratio 6

Figure 2.12 Compressor performance map

2.3.1.2 SHAPE OF THE CROSS SECTION

The effects of the chosen cross sectional shapes on the performance of the
compressor have been studied by Brown and Bradshaw (1947). The four volutes having
different cross sectional shapes and same circumferential variation of the cross sectional
area are shown in figure 2.13. The total pressure and adiabatic efficiency of the

compressor with different volutes are shown in figure 2.14. The x-axis is the corrected

33

 

load coefficient. The author concluded that the shape influence on the compressor

performance could be neglected in the four volute configurations.

WW . ..
I. :- : ”"1

 

(a) 800 asymmetrical (b) 800 symmetrical

(c) 240 symmetrical (d) 40° symmetrical

Figure 2.13 Cross sections of volutes

34

-.___.

1
1 l ‘l
Actual tip speed, U
(ft/Sec) 0 80° symmetrical (sand cast)
I 300 .1 80° do. (plaster cast)
A 80° asymmetrical
V 60° symmetrical

”'00 0 24° do.

1100

Total Pressure Ratio

 

0.08 0.12 0.16 0.20 0.24 0.23 0.32 0.36 0.40
Corrected Load Coefficient

Figure 2.14 Total pressure ratio of compressor with different volutes at actual tip
speeds of 700 to 1300 feet per second

Hubl studied the influence of the symmetric and asymmetric volute inlet on a
pump performance in 1975. The results are shown in figure 2.15. Both the volutes have
the same circumferential variation of the cross sectional area. For a symmetric volute, the
efficiency of the symmetric volute is smaller than the efficiency of the asymmetric volute
when the x coordinate is higher than 0.65. And, the maximum efficiency occurs at a
smaller mass flow than the one of an asymmetric volute. When the mass flow goes higher
further from the maximum efficiency point, the asymmetric volute efficiency becomes
better and better. The interesting thing is that the symmetric volute exhibits a higher head

at low mass flow because more energy is added to the fluid by the impeller.

35

 

 

15
l l 1 I

 

H . .
Tl. (kJ/ Asymmetric inlet
kg) M —m— ' '
0.9 . 14 as» Symmetricmlet

 

\V
t [\
V

N

13 \~
1 ° .3.

0.8. 12, ( \‘

/
11 A

 

 

 

 

 

—'*—-r
----—.4
// .
C./
,‘d

 

 

 

 

 

 

 

 

 

 

 

 

 

l
l
1
/F I
/ l h 1.
0.7:. 10. J} i \ :11
I I 1 i
l l l
9 l l l
i i 1 i
l
0.6' 8 I i l i
0. 5 0.6 0.7 .0. 8 0.9 ('1 1.0 (111%.) “1.1
I I l
0.75 0.90 v. 1.30 1.09 11.12

Figure 2.15 Global pump characteristics with symmetric and asymmetric volute

36

 

Lendorff and Meienberg (1944/1945) investigated the two symmetric volutes and
one overhung volute (figure 2.16). The data of this figure show a preference for the
overhung volute. Similar experimental results were reported by Mishina and Gyobu
(1978). Figure 2.17 shows that the losses in an asymmetric volute appear to be reasonably
insensitive to the flow angle; the losses of a volute with a circular cross section are lower
than those of a square or a rectangular cross section; a small centroid diameter appears to
deteriorate the volute performance significantly. Performance of a collector with a square
cross section was also found to have high losses. All the description in this paragraph was

referenced therein from Japikse’s book (1996).

 

80*-

Head coefficient (% design)
1

 

 

 

 

60 ' '1 1.2
1— -4 6‘
I:
.9
4o __ ~ 1.0 g
0
_ '0
" 0
.5
— 3 0.8 '13
E
O
.. -- Z

L l l l 1 l l 0.6

40 80 120 160 200

Flow coefficient (% design)

Figure 2.16 Comparison of performance for different volute geometries

 

Cr0533sectional area (nae)

 

 

 

—--1
771.6
17.9
438 438 438 I
I 17.9? i .771.“
4300 438! 439-
5-1 5-2 s-3
5-6
é
Hz
40 43g 438 438 |
‘0 I I I are.
439. 430- 4300
5-4 s-S s-7
collector
>1104
xio4 s-7
4-
a.)
t
21.
s-6
0‘ 90 180 270 300

 

 

Angle 8 (degrees)

CircunFerential area distribution
and cross-sectional shape of scrolls

0 S-1 v 55
ll 32 0 S-6

:1 s-3 0 s-7 (collector)
A34

0.8[ E ::
0.4- \\°%L‘n_n_JL__°_—o—”'

0.2-

 

Loss coefficient K

 

 

 

30 40 50
Inlet flow angle as (degrees)

Loss coefficient of scroll:

 

  
   

 

 

 

O G
° °
a a
\ \n
3,1 1.8
o :1 Diffuser Exit W?"
5 3 aEEEEEEEEEEEEEE;32=:1E33::3
m m
3 3 1.6-
‘ h
a . P250
u u lmpellerExrt
- " /
Ii; ’3 1-" Impeller on p.
+' v
m m
4- +2
x x _
1.2- Os 1
e a 05-6
3 E . 05-7
—- in
3 3.
I l l
3; 1.0" 90 180 270 31.0

Angle 8 (degrees)

Circumferential static pressure
distribution

Figure 2.17 Effect of cross-sectional shapes on scroll performance

38

 

2.3.1.3 Radial Position of the Cross Section

According to the radial positions of their cross-sectional area, volutes can be
subdivided into two groups, i.e. the external volute and the internal volute. If the radii of
all the cross-sections of a volute are larger than the radius of the diffuser outlet, this kind
of volute will be referenced as an external volute. Contrary to this definition, an internal
volute is the radii of the cross-sections of a volute smaller than the radius of the diffuser
outlet. This is only a coarse rule to distinguish all the volutes in the world. For example, a
volute can have a constant radius of outer (or say, inner) wall, which might be either an
external or internal volute because it can be an external volute at some cross-sections and
an internal volute at other cross-sections. The radial position variation of volutes depends
on their applications. Actually, it is limited by the available installation spaces and the
cost considerations.

Mishina and Gyobu studied quite a few volutes in 1978. Their results have been
shown in figure 2.17, where s-l is a circular volute while all the other volutes are
rectangular ones. The circumferential variations of the sectional areas are also shown in
this figure. We can see these curves are almost constant along the periphery. The s-2, s-4
and s-5 volutes are located at a decreasing radius. The authors pointed out that the
internal type volute (s-5) and the collector (s-7) have a very high loss coefficient for all
operating points. By moving the volute channel to a larger radius (s-4), the loss
coefficient of the volute can be decreased by 30%. Since the angular momentum is
conserved (equation 2.27), we can expect a better volute performance. Actually, the

authors of this paper have done that by giving the s-2 example.

39

'—_ Mix-1T!» rfij

 

VIE-R, = VTR (2.27)
Stiefel’s results (1972) also confirmed this theory. In his case, compressor

efficiency with the volute located at the larger radius is better than the one located at

smaller radius from low mass flow to high mass flow.

2.3.1.4 Tongue Geometry

Almost all the literatures about the tongue geometry are about pump. Lipski
(1979) has concluded that the increasing radial distance between the impeller and the

tongue by shortening the tongue but keeping the setting angle constant results in more flat

P‘s-WW ofi'Z‘T“—". 2““
.5

characteristics. Short tongues cause higher efficiencies and total head for all mass flows.

It has been observed that for mass flows smaller than the optimum mass flow the
tongue is pulled towards the impeller. The force acting on the tongue changes direction
near the best efficiency point and tongue is pushed away from the impeller for mass
flows higher than optimum one.

Keep in mind that all of these conclusions are based on pump study, not on

centrifugal compressor.

2.3.1.5 Radial Forces

The nonuniform static pressure distribution in a volute can propagate back to the
circumference of the impeller outlet. Thus, the radial force on the impeller shaft could be

created. So far, many researches focus on the source of the circumferential static pressure

variation.

40

Agostinelli, et a1 (1960) measured the radial forces. Different ratios of collector
width to impeller width and the ratios of collector outer wall diameter to impeller exit
diameter were taken into account. From his results, it shows that there is some
combinations exist to provide an effective means for minimizing the unbalanced radial
fore on the impeller shaft.

Lorett and Gopalakrishnan (1986) pointed out that the difference in momentum of
the flows entering and leaving the volute element must cause a change (if the two is not
equal to each other) in the static pressure within the length of the volute element. And,
when the static pressure is lower at the impeller periphery, the outflow radial velocity

from the impeller is higher, vice versa. Thus, the maximum radial force should be at the

Wile — xiii! WEJTT-TTR'TW1

lowest static pressure zone and in the direction from low pressure to high static pressure.
Of course, this qualitative conception should be taken into account the static pressure
forces.

Sideris (1988) shows that the continuity equation gives an uniform
circumferential distribution along the periphery of the impeller outlet regardless of the
mass flow at some volute sections. His volute’s cross section area is linearly increasing.
The radial velocity at the volute inlet is also constant. However, this is never observed in
experiment.

Fatsis, et al. (1997) conducted a numerical investigation of the centrifugal
impeller response to downstream static pressure distortions imposed by volutes at off-
design operations. The calculation of the radial force adopts two different methods. The
first one is the integration of pressure on the blade and hub surfaces of an impeller with a

coarse grid. The second one, for a fine grid, uses a control volume for the moment of

41

momentum to take into account of the momentum in and out of the control volume.
According to the authors, the two methods give the same radial load. It is also found the
circumferentially nonuniform outlet static pressure distribution results the largest
distribution of the radial force for a backswept impeller. The force is in the opposite
direction of the outlet radial momentum although it is much smaller. For the radial-
ending impeller, the total force is much smaller than the total force of the backswept
impeller. The authors explained this phenomenon from the tangential variation of

momentum since it can cause the large variation of static pressure.

. 1w MT—nT'fi‘

Flathers and Bache (1999) claimed that a viscous code is the first time to be used

in a whole compressor with all the impeller passages and the volute. Their investigation

 

predicted magnitude and direction of the radial force are in agreement with the
experimental investigation. However, significant errors existed between the CFD results

and the experimental data at low mass flow.

42

2.4 The velocity and pressure distribution in volute

40
VR(m/S)

40
Vfim/s)

2O 20

20 20

 

40 40

0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0

 

 

sz Z/D
(a) (b)
400 1.0),)
1’0”” 400
0
-400 0
-800 '400
-1200 -800
-l600 -1200
0 0.2 0.4 0.6 0.8 1-0 0 0.2 0.4 0.6 0.8 1.0
Z/D Z/D
(c) (d)

oX/L=0.1AX/L=0.3vX/L=0.SlX/L=O.7eX/L=0.9

Figure 2.18 Measured velocity and pressure for small mass flow

43

IA.

. . ‘ wall-r353 E? '
”‘1“. ‘-

4O 60
VR(In/S) V1-(m/s)

50
20

4O
30

20
20

10
a

 

 

40 O
0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0
Z/D Z/D
(a) (b)
400 paaa)
Pm) 400
0
-400 0
-300 -400
-1200 -800
c d
-l600 -1200
0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0
71D Z/D
(C) (d)

oX/L=0.1AX/L=0.3VX/I:0.5IX/L=0.7eX/I;0.9

Figure 2.19 Measured velocity and pressure for optimum mass flow

 

60

   
 
   

20

0

0 0.2 0-4 0-6 0-8 1-0 0 0.2 0.4 0.6 0.8 1.0
Z/D Z/D

(a) (b)

40

   

d

0 0.2 0.4 0.6 0.8 1.0' 0 0.2 0.4 0.6 0.3 1.0
Z/D ZJD

(C) (d)

oX/L=0.1AX/L;0.3VX/L=0.5IX/L=O.7eX/L=O.9

Figure 2.20 Measured velocity and pressure for large mass flow

Van den Braembussche and Hande (1990) presented a comparison of the

performances of compressor volute in different operations. From fig. 2.18, 2.19 and 2.20,
it is shown the swirl velocity Vr is constant in the region close to the walls and has a
forced vortex distribution in the center. And, the velocity close to the walls is decreasing
from volute tongue to outlet at minimum mass flow (fig. 2.18a). This results from a larger

Vr at the volute inlet close to the tongue, where the static pressure is low and more fluid

is aspirated. The opposite situation is clearly observed at maximum mass flow (11 g.

45

2.20a). And, the forced vortex type region occupies ahnost the 30% part of the middle
axial locations no matter how large the mass flow is.

For Vt, it shows a minimum in the volute center at low mass flow (fig. 2.18b) and
a maximum at the high mass flow operating points (fig. 2.20b). At low mass flow, a
deceleration of the tangential velocity takes place from tongue to outlet and the volute
acts like a diffuser. The swirl component keeps the fluid close to the walls and a zone of
low through-flow velocity occurs in the center. This reduces the effective cross section,

decreases the static pressure recovery and avoids flow separation at the walls. An

_ ”ml! ex“.- 2.?
x . .

opposite phenomenon takes place at high mass flow. The increasing through flow

velocity towards the center of the cross section can explained by the following relation

 

P0 — P = gm? + V32) (2.28)

The variation of static pressure over the cross sections is determined by the radial
equilibrium between the static pressure gradient and the centrifugal forces resulting from

the swirling flow

= a; (2.29)

E dP
RC
The static pressure therefore increases fi'om the center towards the walls at all
three operating points (fig. 2.180, 2.19c, 2.20c).
From equation (2.28) and (2.29), we can see a decreasing static pressure and
decreasing swirl velocity towards the center of the vortex lead to an increasing through
flow velocity towards the center (fig. 2.20b). The small difference between the total

pressure and static pressure at the center of the cross section at low mass flow results in a

low through flow velocity (fig. 2.20b).

46

The static and total pressures show nearly symmetric distributions over each cross
section with a minimum at the center. The minimum static pressure occurs close to the
volute tongue at low mass flow (fig. 2.18c) and close to the volute outlet at high mass
flow (2.20c). The largest total pressure variations are observed at low mass flow (2.18d).
These are much smaller at medium and maximum mass flow (fig. 21% and 2.20d)
where a variation between volute tongue and outlet is observed.

The measurements indicate that the large variation in maximum total pressure
between each cross section is mainly due to diffusion and fiiction in the inlet duct and
inlet section. The cross-wise total pressure variation, and only part of the decrease of
maximum total pressure are due to the swirling flow inside the volute. Friction in the
volute is the main source of the total pressure losses at maximum mass flow.

For fig. 2.21, the pressure is increasing from volute tongue to outlet at less than
optimum mass flow (fig. 2.21a). For optimum mass flow (fig. 2.21b), only a small
pressure increase was observed and the discontinuous change of pressure for 0.0<x<0.2 is
typical for the flow perturbation in the tongue region. At high mass flow (fig. 2.21c), the
volute is too small to accumulate so much fluid and the through-flow velocity is
increasing towards the outlet. This results in a static pressure decrease between volute

tongue and outlet.

47

 

Figure 2.21 Longitudinal and circumferential static pressure variation
corresponding to small (a), optimum (b) and large (c) mass flow

48

Chapter 3

Theory background and the integrated tool development

3.1 Computational Methods and CFD Models

Three-dimensional, compressible, steady flow computations were carried out for
five compressor configurations, at Michigan State University, by using the commercially
available computational fluid dynamics code, CFX-TASCflow. This code solves the
Reynolds averaged Navier-Stokes equations in primitive variable form. The k-e
turbulence model was employed for these simulations. “Wall functions” were supplied to
model the momentum and heat transfer processes for turbulent flows in the near-wall

region.

3.1.1 Turbulence Model—k -'- 8 model

It is well known that the derivation of the k- a model is made for incompressible
flows. But, the state of development of this turbulence model is such that it is also
applied, essentially unmodified, for compressible flows. Actually, the k- a turbulence
model is used throughout this dissertation.

The equations for an incompressible flow are,

6
5;(P“i)=0 (3'1)
1
a 6 6P 0 .—7
51m.)+ax—j(puiuj) = 37-53(10- + pour“ Sui (3'2)

49

where the convention that any variable without a superscript is a mean flow
variable. The term puzu} that appears in the momentum equations is identified as the

turbulent Reynolds stresses. The gradient diffusion hypothesis suggested by Boussinesq,

is used to model the Reynolds stresses for a compressible fluid as:

 

 

 

 

The turbulent viscosity ,u, is modeled as the product of a turbulent velocity scale,

—-— Bu,- auj 2 01.,
_ utu'. = __.+ —— ——+ 6.. 3.3
.0 1 j .ut(axj ax,) 301: 6x1 pt) 1} ( )
where y, is the turbulent viscosity and k is the turbulent kinetic energy defined as f“
u'-u'-
k = I I 3.4
2 ‘ ’ i
l

Vt, and a turbulent length scale, It, as proposed by Prandtl and Kolrnogorov. The constant
gives
#1 = PcpltVt (35)
Both one and two equation models take the velocity scale V. to be the square root

of the turbulent kinetic energy
Vt = J; (3.6)
The turbulent length scale is algebraically specified in a one-equation model and
determined fiom an additional transport equation in a two-equation model. In the

standard k- a two-equation model it is assumed that the length scale is a dissipation

length scale, and when the turbulent dissipation scales are isotropic, Kolrnogorov

 

determined that
3 / 2
a = kl (3.7)
t

50

where 8 is the turbulent dissipation rate.

If k and either a or 1. are known, the turbulent viscosity can be determined from
equation (3.5) and the Reynolds stresses can be computed using equation (3.3), thereby
closing the time mean averaged turbulent momentum equations, equation (3.1)-(3.2). The
remaining task is to determine the equations for k and a and the appropriate boundary
conditions.

Equations (3.5), (3.6) and (3.7) should be paid more attention because they are
needed in the initial guess for the flow field.

In this dissertation, the dependence of the solution on turbulence models has not
been studied. A comprehensive assessment has been made by Lakshminarayana on the
computation of turbomachinery flows using k - a turbulent model. So far, the results by
using this model are in a good agreement with the experimental data. And, one thing
needs to be mentioned here, all the above equations are from the TASCFlow software

user manual.

3.1.2 Two CFD models for centrifugal compressors

Because of the complex geometry of turbomachinery, usually the grid for whole
turbine and centrifugal compressor has to be divided into quite a few sub-grids, for
instance, impeller grid, diffuser grid, volute grid and exit cone grid. Undoubtedly, the
impeller grid has the relative movement to the diffuser grid. Volute grid is stationary
relative to diffuser grid. The MFR (Multiple Frame of Reference) capability in CFX-

TASCflow3D uses the Stage and Frozen Rotor concepts to catch the relative movement.

51

So the fundamental to the MFR capability is the fact that the computational domain
consists of two (or more) distinct regions that are in relative motion to each other. A
sliding interface condition is used to connect two regions together that are in different
flames of reference. The sliding interface is implemented in such a way that steady state
solutions are supported in each frame or reference. A generic sliding interface approach is
used for both Stage and Frozen Rotor interfaces; specific implementation details of the
interface condition distinguishes between the two approaches.

A sliding interface condition is used to connect control volumes together on each
side of a sliding interface. According to the ABA manual, this sliding interface condition
has the following properties:

1. The interface accounts for the change in the frame of reference.

2. The interface supports steady state predictions in the local frame of reference,
on each side of the interface.

3. Strict conservation is maintained across the interface, for all fluxes of all
equations.

4. The interface treatment is fiilly implicit, so that the presence of an interface
does not adversely affect overall solution convergence.

5. The interface accounts internally for pitch change by scaling up or down (as
required) the local flows as they cross the interface.

6. Any number of frame change interfaces is possible within a computational
domain.

It is important to note that the extent of the grid surfaces on each side of a given

sliding interface do not have to be equal. For example, the grid numbers of impeller on a

52

rotor and the grid numbers on adjacent diffuser are usually different hence the pitch
changes between the components. Unequal pitch is accounted for internally by the sliding
interface condition implementation within CFX-TASCflow3D. Conservation is
maintained in the sense that the total flow from one frame into the next scales exactly on
the surface area based on pitch ratio. So, this character makes the grid generation for the

both sides of sliding interface undependable.

3.1.2.1 Stage Rotor

, --‘-’fi“'77 T "W. "a“?

Stage rotor is one of the CFD models that are suitable for turbomachinery

 

simulation. By using this model, one or more blade passages can be solved
simultaneously with circumferential “averaging” between the impeller grid and the
diffuser grid. Steady state solutions are then obtained in each sub-grid. The stage
averaging at the sliding interface between the impeller grid and the diffuser gird incurs a
one-time mixing loss. This loss, according to the TASCFlow manual, is equivalent to
assuming that the physical mixing supplied by the relative motion between components is
sufficiently large to cause any upstream velocity profile to mix out prior to entering the
downstream machine component.

Although the unsteadiness in volute is generated by the variation of the flow at the
outlet of the rotating impeller, Hillewaert indicates that the mixing of the blade-to-blade
flow is very fast. So this is the theory base of the stage model.

Stage analysis is most appropriate when the circumferential variation of the flow

is of the order of the component pitch. Since stage model averages between blade

53

passages in terms of time average interaction effects and neglects transient interaction
effects, it is not appropriate when the circumferential variation of the flow is significant
relative to the component pitch.

Figure 3.1 is used to shown the stage interface between the impeller grid and
diffuser grid. It can be seen only one passage of impeller grid is attached with the diffiiser
and volute grid. It’s assumed that all the other passages of impeller grid experiences the
same flow as in the passage shown in the figure. And, the exit flow of the impeller is

averaged circumferentially.

    

1““ .‘
e

., \\\\‘

'1‘ 0‘“ 0‘0
\ \\\ \‘
1*“

      

 
 

17m
~ 0 n
O .0 ’l ”'I
V ‘04:;2’07
I ’I "
o o 99,014

’7,“- '

    

        

    

Figure 3.1 the stage rotor

Based on the introduction above, it is easy to understand the reason why there will

be always periodic boundary condition exists in the stage model.

54

3.1.2.2 Frozen Rotor

The flozen rotor can also be used to predict the “steady state” flow of an impeller,
a diffuser and a volute, where the impeller is solved in a rotating flame, the diffuser and
volute is solved in the stationary flame. As introduced in the TASCFlow manual, the two
frames of reference connect in such a way that they each have a fixed relative position
throughout the calculation, but with the appropriate flame transformation occurring
across a sliding interface. A steady state solution is obtained to a multiple flame of
reference problem, with some account of the interaction between the two flames. The
quasi-steady approximation involved becomes small when the through flow speed is
large relative to the machine speed at the sliding interface.

Contrary to the State Rotor, Frozen Rotor analysis is most useful when the
circumferential variation of the flow is large relative to the component pitch.

Again, transient effects at the flame change interface are not modeled. Modeling
errors are incurred when the quasi-steady assumption does not apply. Also, the losses
incurred in the transient situation as the flow is “mixed” between stationary and rotating

components is not modeled.

55

 

Fm .meii“

\
.\
:\‘~:\‘:e°

. 9 \‘¢. ,.._
\ ‘ O O

\\‘:I.'..

 

Figure 3.2 the frozen rotor

Pitch change across a Frozen Rotor interface is more difficult to quantify.
TASCF low manual explain the way to handle this kind of problem is: the flow profiles
are preserved as they cross the interface, butare scaled (stretched or compressed) in the
direction of rotation by the pitch ratio.

Figure 3.2 is the flozen case for this study. In this model, the exit flow is no
longer assumed to be uniform and flows in each passage are not assumed to be periodic
either. All the impeller passages, attached with the diffuser grid, will be simulated
together. In order to run this case, the first step is to rotate one passage of impeller grid to
get all the impeller passages, and then to attach them together, or to use another way to
make a one-block impeller grid. The latter is preferred because it is more convenient for

the grid attachment and the post processing.

56

3.2 Integrated tool development

The integrated tool includes sub-grid generation, sub-grid attachment/append,
boundary condition definition, initial guess, time step selection and post-processing. All

of these respects will be explained in detail as follows.

3.2.1 Sub-grid generation

It is well known that a lot of commercial software can be used for impeller grid

 

v I‘l Ammfii’iifi.‘j_ . ‘

generation, such as bladegen and TASC gen. However, until now there is no commercial i,
software specifically used for volute grid generation. In this study, a FORTRAN code

was made to generate “butterfly” grids for compressor volutes. The code reads in the

volute and diffuser geometry file (flom company) and a control file (self-made) first, then

writes out input files for TASCGrid, *.gdfl *.cdjf *.sdf and *.idf. Thereafter, TASCgrid,

the commercially available grid generator, can be run to generate all the sub-grids for

volute and diffuser. For the view of diffuser and volute grid, please see the figure 3.1 and

3.2.

57

 

Figure 3.3 Butterfly grid of volute

The grid of the volute is of butterfly section (see figure 3.3) to reduce the grid
skewness. The commercial impeller grid generator, TASCgen, is employed to generate
the impeller grid. In some cases, an alternative code, Fast_TASC, that was generated by
Solar Turbines, Inc, was used for the impeller grid generation. Usually the impeller grid
number is 20,000 points for one passage of the impeller, and the whole impeller grid

number can be obtained afier timing the blade numbers.

3.2.2 Sub-grids attachment and append

There is one integrated tool that has been generated for the sub-grids attachment
and append automatically. What need to do is just get the tool first, then follow the
procedures below to get the “stage” and “flozen” rotor.

If the “stage” case simulation is desired,

1. Make two new directories--“volute” and “stage”-- under one directory.

58

 

2. Copy all the files under “Tool/volute” directory and volute geometry file to your
own “volute” directory. Modify the volute control file according to the new
volute geometry file. Make your own “input.file”.

3. Run “solar.l”. Make sure you know the 2 value of the impeller [id,l,kd] node.

4. Run “subgrid” to generate the 4 sub-grids. Note: The sub-grids would not be
appended together at this time.

5. Copy “grd”(one passage grid of impeller), “gci”, “pro” to your own “stage”
directory flom your Impeller directory

6. Copy all the files under the “Tool/stage” directory to your own “stage” directory.

7. In your own “stage” directory, replace the region definition part stage. gci by the

region definition part of impeller gci file gci.

8. Run “attach_append”. Then check grid quality. If the grid quality is bad, go back
to nm the “solar.f” again after changing the parameters in volute control file.

9. Redefine the Impeller rotation speed (only the “default” speed), material
properties and inflow/outflow boundary conditions in TASCFlow GUI.

10. Give the initial guess (see part 7) and start the run flom “solve monitor”.

If the “frozen” case is desired,
1. Make two new directories-“volute” and “frozen”-- under one directory.
2. Repeat 2, 3 and 4 steps of the stage case to generate the volute and vaneless
diffuser sub-grids.
3. Copy “grd” (one passage grid of impeller) an “gci” to your own “frozen”

directory flom Impeller directory

59

9.

Copy all the files under the directory ‘Tool/frozen_smooth” to your own
“frozen” directory.

Replace the region definition part of “frozen.gci” in your “frozen” directory
by that of “gci” in your impeller directory.

Run “answer.for” to generate all the answer files for batch files. Notice: You
should keep the blade number and the blade grid size at hand before you run
the “answer.for”.

Run “Impeller.bat” file to generate all the impeller grids.

Run “attach_append” to attach all the impeller grids and all the volute sub-
grids.

Run the macro “REGION_DEF”.

10. Redefine the Impeller rotation speed (only the “default” speed), material

properties and inflow/outflow boundary conditions in TASCFlow GUI.

11. Give initial guess and run the whole compressor simulation.

Notice: So far, for flozen case, the blade number is up to 17. If you have more

blade numbers, a little bit change on “answer.for” and “solar30.mac” should be done

before you run flozen case.

3.2.3 Boundary Conditions

Inlet boundary conditions are assigned as total pressure, total temperature, flow

angles, turbulence intensity and turbulence eddy length scale. Outlet boundary condition

is defined by mass flow rate.

60

As mentioned above, equations (3.5), (3.6) and (3.7) are used for the estimation of
the turbulence parameters.

There are two sample boundary conditions files have been done respectively for
stage and flozen rotor. Just copying the two files to the working directory, all the
boundary condition will be defined automatically. Of course, material properties should

be modified manually

3.2.4 Initial guess

According to the following rule to generate the initial guess, it has been proved to
be very efficient.
1. Be sure that the design mass flow rate is selected first;
2. The velocity=.9xthe INLET velocity; align the K node direction;
3. The pressure = .65xinlet total pressure value;
4. The temperature = .85xinlet total temperature value;
5. Tu intensity and Eddy length scale are flom spreadsheet (same as
the values that can make impeller alone case converge);

6. Off-design cases use design condition converged result as initial

guess.

In some cases, this kind of initial guess still has big difficulties. Even if it
converged very well at first beginning, the solution curve waves continuously and will
never converge further when the maximum residual almost reaches the 1.0x 1 04. This is

because a bad time step has made a hurt at the very beginning already.

61

Usually, in commercial CFD software, such as StarCD and Fluent, there is a
relaxation factor that can be used to help converge. However, in TASCFlow, there is no
such a kind of parameter to control the convergence. The converge process in TASCF low
strongly depends on the initial guess and time step selection. Once the initial guess is set
appropriately, the rest thing is how to choose a appropriate time step to make the
simulation converge. Fortunately, there is a similar function parameter in TASCflow to

6

control the relaxation— ‘dtime”. When obtaining steady state solutions, the time step by
using this parameter effectively provides relaxation to the solution procedure. Relaxation
is necessary because the CF X flow code is solving a set of non-linear equations as a
sequence of linear problems. The role of the time step becomes more important as the
problem non-linearity increases. So the best way to make the impeller, diffuser and

volute case converge is to set the initial guess as mentioned above first, then use the

“dtime” instead of the “etfact” parameter to control the converge process as follows,

1x10-5

1. Set the dtime = ;
RotationSpeeda)(r / s)

 

II. If it looks converge and the trend is pretty good after 30-50 steps, set

—4 —6
dtime = 1x 10 (Otherwise set dtime = 1 x 10

RotationSpeedco(r / s) RotationSpeeda)(r / s)

 

 

111. If everything is ok after another 20 steps, ten times the old dtime parameter again.

IV. The correct method should increase dtime in this way until the solution converged
and finally the dtime can be as big as 1000. But, since the parameter etfact has
been proved to be accurate enough to guarantee a correct solution, feel flee to
change the parameter flom dtime to etfact when the trend is pretty good. Thus, we

can leave the computer run overnight, no need to sit in flont of it to modify the

62

--- --. 2,1

 

dtime value flom time to time. Usually, the etfact should be set around 5. 3 is
prefered. This is a worry-flee value.
Two cases that cannot converge even set the eq’act as 1 for the same initial guess

has been made converged by using this method.

3.2.5 Post-processing

9

A postprocess macro— “solar30.mac’

 

is also ready for use. The specific heat at
constant pressure, specific heat ratio, blade numbers, tip diameter of impeller and I grid
number at pinch position would be asked for input while you are running the macro.

The following five equations were built in the macro for the performance
prediction. The equation (3.8), (3.9) and (3.10) are flom the technical handbook at Solar

Turbines, Inc.

(1): Q1

71' 2

 

(3.8)
:1

P2
Hisen=778.3xCpr1x F —1 (3.9)

l
Wiser: = 6334)‘ Hi“; (3.10)

Utip
Cp = fl (311)
P04 "P4

63

w=£0_4___pfl. (3.12)
P04 ’P4

Equation (3.11) and (3.12) are for the pressure recovery coefficient and total
pressure loss coefficient calculation. The subscript 4 means the pinch position and 0
means total properties.

After reading the “solar30.mac” in, run “initialize” first, then follow the screen
output to get the desired output. In order to get the tablet output, please run the
“volute_post”.

The impeller output is in the “Inflow & outflow of Impeller” block. Here the
impeller outlet is at the pinch position. If a different position would be selected as the
impeller outlet, please input the desired I grid number when answering the question
“Please input the I grid number at the pinch position” while running the “volute_post”.

The results in “Flow Properties in Vaneless Diffuser Outlet”, “Flow Properties in
Volute Throat” and “Exit Cone Flow Properties” are 360—degree circumferential averaged
value.

The results in “Circumferential Flow Properties in VOLUTE” are radial (flom
diffuser outlet) mass averaged result. The radial area position (K direction) starts flom 11
and the step is 10. The last station in this block is at the tongue position. However, if
different circumferential K size was defined in the volute control file, corresponding
modification should be made in the “solar30.mac’.

The results in “Circumferential Flow Properties at Diffuser Outlet” are mass
averaged in two adjacent circumferential K grids, see the rectangular enclosed by thick

lines in figure 3.4.

64

 

Figure 3.4 Averaged area at diffuser outlet

The actual circumferential angle for the two circumferential flow properties
depends on the tangential node distribution. If some important position was missed,

please modify the macro to satisfy the requirement.

3.3 Code robustness and grid improvement

3.3.1 Code robustness

     
   

    
  
 
 

1.» .
Neel.
~ \\\‘\t‘~‘vt*\‘i

\§§\\\\N\\§QM(

 
     
      

  
 

  

   

   

Figure 3.5 One example of code robustness

65

At very beginning, the code for volute and diffirser grids generation has many
bugs in it. For one case, maybe the code works fine, but, there are always a lot of
problems for grid generations if the volute and diffuser geometry file was changed. One
example of the problems is shown in figure 3.5. In this figure, the problem is flom the
starting point of exit cone sections are different from the ones of volute section in the
geometry file. We can see that there are many cross grids occur near the tongue position
in the left figure in figure 3.5. This kind of grid will incur quite a few negative control
volumes in the volute grid, so it even cannot be read in by TASCF low. After debugging
the code, the right one is shown in the right figure in figure 3.5. It can be seen all the
control curves near tongue position are parallel now.

And, many other problems are also solved by making the code robust. For
example, the code is no longer sensitive to the data sequence in the volute and diffuser
geometry file, point numbers on the half circle at the volute/diffuser interface and the
distance of adjacent points.

In one word, this code is very robust for the routine use for the volute and diffuser

grid generation.

3.3.2 Two new functions in the code

Besides generating the grids according to the original geometry file, there are
another two new functions added in the code.
The first one is the volute volume can be changed fleely. Figure 3.6 shows an

enlarged volute (outside contour) based on the original one (inner contour). The butterfly

66

grid control curves are in the middle. Of course, the volute volume can also be decreased
in the same way. Thus, the effect of volute volume on the performance of the whole
compressor can be investigated because this new function makes the volute volume
change as many times as you want. However, because the exit cone keep unchanged in
this process, it is inevitable to meet a geometry “step” on the connection surface between
volute and exit cone. Another disadvantage is there is no experimental data to validate the
CFD result of the modified volute since there is no such a volute exist at all. So this
fimction is only for research interest, or for the numerical test at the beginning of a volute

design.

 

 

Figure 3.6 Enlarged volute

The second function is that the shroud wall of the vaneless diffuser can be moved
to or away flom the hub wall. Since the diffuser is the component that connects the
impeller and volute, any grid combination of volute and impeller is possible if the width

of the diffuser can be changed randomly. So this new function can be used to investigate

67

any combination of current volutes and impellers. For this method, the experimental data
are always available for the CFD results validation because we can use same way to build .
up a test rig at the Aero Test Facility. Figure 3.7 is the example to move the shroud wall

of the diffuser to hub wall. This analytical method was adopted in Chapter 5 and 6.

 

(a) Original diffuser (b) reduced-width diffuser

Figure 3.7 Reduced-width vaneless diffuser

3.3.3 Grid quality improvement

Even if the volute and diffuser grids can be generated successfully, there are a lot
of jobs to do on the grid volume, skew and aspect, i.e. grid quality. In figure 3.8, it can be
seen that the half circle became smoother and grid angle increased a lot flom the left
figure to the right figure. Since the skew angle in TASCFlow requires more than 20

degrees, this improvement reduce a great deal of warnings, even errors.

68

 

Figure 3.8 Grid improvement (1)

Figure 3.9 shows the twist grid control curves flom the last volute section to the
first exit cone section. Notice, here only the control curves are plotted in order to give a
clear view. Sometimes, TASCF low would not give any warnings for this kind of grid.
However, it will take a much longer computer time to get a converge solution based on
this kind of grid. So to correct this defect is profitable. The figure of 3.9 (b) is the
corrected control curves. It looks much better now. And, the new grid only took one third

of total time of the 01d grid to get the final converge solutions.

69

 

(a) twist control curves (b) straight control curves

Figure 3.9 Grid improvement (2)

3.4 Aero Test Facility

The Aero Test Facility is located at Solar Turbines, Inc. Keamy Mesa Facility,
San Diego, California. From the test report prepared by Dr. J ean-Luc Di Liberti, we can
get a clear conception of the experiment.

The test article and closed loop piping are indoors. Air or nitrogen can be the test
gas. A gearbox coupled with an electric motor drives the test article. Oil and seal gas is
supplied to the compressor and gearbox with facility resources.

Two valves in parallel operation control compressor flow. The valves are located
downstream of the discharge flange. The discharge gas is cooled by water/ gas heat

exchangers.

70

The heat exchangers use plant resources for cooling water. Auxiliary pumps,
coolers and valves are used to control the electric motor, loop pressure and temperature
and seals.

Flow was determined using a bellrnouth venturi located upstream of the
compressor inlet flange. Four temperatures, four total pressures and four static pressures
are measured at the venturi, compressor inlet and compressor discharge ports so there is
sufficient instrumentation to determine flow, head and efficiency. Four measurements
provide sufficient instrumentation for redundant practice and assess the flow field.

At the compressor flanges, the 4 probes are located 90 degrees apart and at 4
different irnmersions satisfying equal areas.

The data acquisition system is proprietary software purchased/designed by Solar
Turbines, Inc. Pressures are required with a pressure systems Inc. (PSI) system. All
measured pressures are referenced to ambient pressure and calibrated on line during the
test.

A SCXI temperature system incorporating type T thermocouples was used to

measure temperatures. The thermocouples are calibrated with a reference RTD and

calibration coefficients are developed to provide an accuracy of i 02’ F in the
anticipated temperature range.

Raw data was reduced online with the proprietary software. Three files: pressures,
temperatures and reduced data are stored at the end of each test.

The facility, or system stability is a result of the interaction of: suction pressure
and temperature control systems, test article thermal inertia, oil supply temperature, seal

leakage, and the loop and instrumentation plumbing. Gross values such as speed, flow

71

and suction values stabilized within 3-Sminutes after a flow change. The system averaged
consistent fluctuations of approximately i 0.5 Psi, and i 1 0' F .

In the experiments, the data quality was very good. When data is averaged a

minimum of 25 seconds, the standard deviation of efficiency is usually within i 0.1

points.

—--T- .u... “aunt's,
1
,.

 

72

Chapter 4

Solution repeatability and previous work verification

4.1 Introduction

Two single-stage centrifugal compressors were simulated in this chapter. There
are two reasons to run the cases. The first one is to check the solution repeatability, i.e.
the reliability of the CFD method. The second one is to verify the basic flow structures in
diffusers and volutes that have been given in the papers mentioned in chapter two.

All the information about the theory background of the CFD method and the test
facility has been introduced in chapter 3. And, since this chapter is not focus on the
comparison research of the compressors, the compressor geometries and the test
procedures are not discussed here. What we are interest in is to take a look at the match
between the CFD results and the experimental data, and to understand the flow

phenomenon based on the CFD analysis.

4.2 The study for D3-l compressor

The performance figure (figure 4.1) is for the D3-1 case at Solar Turbines, Inc.
The impeller is a shared one for D3—1 and E2 stage compressor. The difference between
the two compressors is the widths of the two diffusers. Here, six points including the
design condition were run for the comparison with the test data. The test data were read
flom the figures in the D3-1 test report that was written a few years ago. It shows that the
CFD results match the experimental data very well. The CFD points are above the

experimental curve mainly due to the fact that the CFD model did not incorporate the

73

leakage flow in the labyrinth between the shroud outer wall and the machine case, and the

back surface friction of the impeller was also not taken into account.

 

1.4

 

1.3 _-____

1.2 :- --——<— — — __._#_fl__- m~- fl- -‘_-_ ____

1.1
1

 

0.9 :
0.8 ~

 

 

 

0.7 1

 

 

0.6

Relative lsentropic Head Coefficlent

0.5 ~-—- - ‘ v - —

 

 

 

0.4

 

0.6 0.8 1 1.2 1.4
Relative Flow Coefficient

Figure 4.1 Compressor performance

The efficiency at different locations in the D3-l stage case is shown in Figure 4.2..
From this figure, it can be seen the design mass flow always has the best efficiency.
Apart flom the design mass flow (75% vs. 125% design mass flow; 86.8% vs. 110.4%
design mass flow), the high mass flows have a good performance. For low mass flow
cases (75% and 86.8% design mass flow) the loss in diffuser is big and the loss in the
volute cone part is small. For design mass flow and high mass flow, the loss in vaneless
diffuser is kind of small. However, it becomes very big in the volute cone part. Note that

the volute cone part is from station 7 to station 8.

74

.1:

 

0.95

position 1: Impeller

position 2:

position 4: vaneless diffuser
position 5: vaneless diffuser
position 7:

position 8: discharge

0.90 =~\ —

0.85 \ ;

 

 

Adiabatic Efficiency

+ 75% design mass flow

0'80 -_. + 100% design mass flow ..
+125% design mass flow

+ 86.8% design mass flow

+ 131.5% design mass flow

+ 110.4% design mass flow
0.75 l I l i

0 2 4 6 8 1 0
position

 

 

 

 

Figure 4.2 Efficiency of different stations at different mass flows

This trend can also be proved from figure 4.3. It shows that the total pressure
drops more at low mass flow than at high mass flow in the vaneless diffuser. And this

situation reversed in volute cone part.

75

22

21

20

19

18

17

16

Total Pressure(psl)

15

14

13

12

Figure 4.3 Total pressure of different stations at different mass flows

According to the static pressure map, figure 4.4, the static pressure at low mass
flow is always higher than the static pressure at the high mass flow at the same station.

This result can also be found numerically from figure 4.5. For instance, at the volute

 

 

 

position 1: Impeller Inlet

position 2: Pinch

position 4: Vaneless diffuser inlet
position 5: Vaneless diffuser outlet
position 7: tongue

position 8: discharge cone

 

 

 

 

 

ti

 

 

 

 

 

w
4 F +——I
+ h
+
4 111— i,

 

 

 

+ 75% design mass flow
+ 100% design mass flow
+125% design mass flow

 

+ 86.8% design mass flow
+ 131.5% design mass flow
+ 110.4% design mass flow

 

 

 

 

I I

4 5 6 7 8
position

-1
-1
-l

76

 

inlet, the static pressure is 2.215E2 at 75% mass flow, 2.162E2 at design mass flow and
2.071E2 at 125% mass flow.

At high mass flow (110.4% and 125% design mass flow), the volute is too small
to accumulate so much fluid and the through-flow velocity is increasing between vaneless
diffirser outlet (station 5) and tongue (station 7). This results in a static pressure decrease
between volute tongue and compressor outlet. From the tongue to the volute outlet, the
static pressure recovered a little bit and increased again because the cross section area of

the exit cone becomes bigger.

77

 

22

position 1: Impeller
position 2:

 

21

position 4: vaneless diffuser
position 5: vaneless diffuser
position 7:

 

N
0

position 8: discharge

 

 

 

.3
(O

 

 

 

.5
m

 

 

 

Static Pressure(psl)
a :1

 

 

 

—L
0'!

+75% design mass flow
+100% design mass flow

 

.—L
.b

+125% design mass flow
—>+— 86.8% design mass flow
+ 131.5% design mass flow

 

13

 

+110.4% design mass flow

 

 

 

 

12

I I I l I I l

2 3 4 5 6 7 8

position

Figure 4.4 Static pressure at different stations at different mass flows

78

And, from the figures 4.6 and 4.7, it can be found that the radial velocity is
7.749132 at 75% mass flow, 1.217E3 at design mass flow and 1.469E3 at 125% mass flow
at the volute inlet part. For tangential velocity, it is —2.396E3 at 75% design mass flow, -
2.52E3 at design mass flow and —6.336E2 at 125% design mass flow.

The higher static pressure at low mass flow (figure 4.4) should lead to a lower
radial velocity and higher tangential velocity. This means the radial velocity is lower at
low mass flow than the radial velocity at high mass flow. The small radial and large
tangential velocity at the impeller outlet means the fluid would move a longer distance
from the impeller outlet to the volute inlet. Long distance (long pathline) flow leads a
bigger friction loss in the diffuser. It will lead an adverse pressure gradient in the
boundary layer and the separation occurs in the hub wall. Figure 4.8 shows the
phenomenon. This is the reason why the loss in the vaneless diffiiser is bigger at low
mass flow. So we can expect it will be much helpful to shorten the length of vaneless
diffuser at low mass flow and lengthen the length at high mass flow.

One interesting phenomenon is that the CFD results indicate the tangential
velocities are also low in low mass flow. This is also can be explained fi'om the high
diffusion and high friction losses because of the long pathlines of the fluid particles.

It is common now to expect a large radial velocity at high mass flow. Observing
the figure 4.7 at 125% design mass flow carefully, it can be found the radial velocity hit
the shroud wall is so severely that it leads to a reverse flow in the hitting part (green
contour line part which means a positive value) when the radial velocity is big enough.
This is the reason why the losses in the volute are relative bigger when the mass flow is

higher than the design mass flow. We can call this phenomenon as a volute stall.

79

This phenomenon can also be obtained from the figure 4.9. In all of these figures,
radial velocity evolved into the swirl velocity after the fluid flows into the volute. A low
static pressure at the impeller outlet leads to a large radial and a small tangential velocity
at the volute inlet and therefore a strong swirling motion occurs inside the volute channel.
So the swirl velocity in the volute is related to the radial velocity component at the volute

inlet. The bigger radial velocity at high mass flow is, the bigger the loss in the volute

would be.

80

 

125% design mass flow

 

 

 

 

225.3

223.4

221.5

219.1

217.6

215.7

207.1

206.2

205.2

204.3

203.3

202.5

 

100% design mass flow

Figure 4.5 Static pressure distribution at three mass flows

 

 

218.5

217.2

216.2

2146

2133

2120

254J

1560

7743

-1014

   

-7952

 

 

75% design mass flow 100% design mass flow

3584
2409
1469

-294.6

 

-6452

 

125% design mass flow

Figure 4.6 Radial velocity distribution at three mass flows

82

 

 

2852

2034

1217

399J

-4l8J

 

 

 

 

 

. 10850
101° x 3742
6437 i if; X1
1 l i , '.
‘| ’ / “l 5926
1'4 / i .
' l 1 ,»»~"" f .
3492 2’5 /"/ 31 1 1
\ . ,.. :.
41‘ /// f
\\ K“- ‘ 'K \ «"11/
543-3 ‘:~~:.>;;e_.~..4__ .«w 295.5
1
‘2396 2520
75% design mass flow 100% design mass flow

10170

8151

5448

2069

-633.6

 

 

 

-2560

125% design mass flow

Figure 4.7 Tangential velocity distribution at three mass flows

83

 

 

 

\

 

_ C‘ - ‘
Os: \“ ‘ ‘ '
I
j .
\- _ . - \. ‘ \ ‘ ,-
g ._ . .
1’.
u»... . \
~ ‘ , .- . L ‘ \
‘ .
‘\
. l
I 8
.\ . x
‘I
I. I
a \
I“ x.
S." ‘
r “
K
)

l ‘.

1 \
\
\ .
I. S
0' \
.‘b ‘
\ \
\«
, _ x
\
K \
x
\. ‘
\
I
\ "s
x s
\

Figure 4.8 Diffuser stalll

84

 

in"? 55 55“ ‘ ..

(a) Radial Velocity

(a) Radial Velocity

‘ IK{ ,W 1.
, r :
, i
' » ;
'_.,Ii 7
If
t \ /'

(a) Radial Velocity

2737

2148

1560
't : 971.2
382.4
-206.4

-795.2

 

 

(b) Tangential Velocity

75% design mass flow

3057

2443

1830

1012

399.1

-214.2

 

-1000

3584

2879

2174

' 1234

529.6
—l75.3

-880.2

 

é .
i; 2-._._~._‘._.. 2..“

.72 ‘ .‘
s .
1 ’1
4 I
1 I _
.‘I '
I, 'l
3 —~' / .
v "I _
7
e r;
l
J

(b) Tangential Velocity

100% design mass flow

(b) Tangential Velocity

125% design mass flow

Figure 4.9 The contour plot of radial velocity

85

 

10850

8546

6437

4229

2020

-l87.8

-2396

 

 

 

3057
2443
1830
1012
399.1
-214.2

-1000

3584
2879
2174
1234
529.6
-l75.3

-880.2

4.3 The study for D2 compressor

The volute and diffuser grids were generated by the same way of the self-coded
program as the one in the chapter 3. After two cases, the program for grid generation has
been improved greatly. It won’t be sensitive to the volute geometry file so much as
before.

As far as the CFD model and boundary conditions, same methods were used as
the models in the chapter 3.

One more thing I want to mention is that only stage case was run for this case.

In figure 4.10, the difference between the experimental data and calculation data
is kind of big. The reason is that there is no “actual” experimental data available for this
case. The experimental data for comparison in this figure is from the prediction value.
And, another possible reason is the geometry data of this volute at a few critical stations
are not available. The author only can measure them fiom one drawing from the company
and calculate the actual value from a scale factor. However, the error exist in this model
won’t affect the final conclusion.

From figure 4.11, the trend is the same as the analysis of the D3-l case. But, we
can find the adiabatic efficiency became very bad when the mass flow is higher than
design mass flow (125% design mass flow). It gave us a hint that we might need a big
volute for the impeller that is used in this compressor.

Since it has been proved the diffuser length and tongue position have strong
influences on the performance of a centrifugal compressor at off-design conditions, the

diffuser and tongue position of volute will be kept unchanged in our numerical

86

experiment. Because the axial position of the volute can affect the centrifugal compressor
performance and the flange position limits axial position of the volute, the axial position
of the volute will also be kept the same as the original volute.

Thus the method to enlarge the volute is just to enlarge the volute volume before
the tongue position, at the same time the cone part was kept unchanged. Figure 3.6 shows

the way how the volute volume was enlarged.

1.4

1.2 \‘5

 

 

 

 

0.8 \ \

Relative lsentropic Head Coefficient

 

 

 

0-6 “‘— +CFD@cone —
+experiment@cone
0.4 1 r .
0.6 0.8 1 1 .2 1 .4

Relative Flow Coefficient

Figure 4.10 Compressor performance

87

 

1.00

position 1: pinch

position 2: vaneless diffuser
position 3: vaneless diffuser
position 4: tongue

0'95 position 5: discharge

\

 

 

9
co
0

 

0.85

Adiabatlc Efficiency

+75% design mass
flow

+100% design mass

 

flow

0-80 “* flow
+125% design mass \

 

 

0.75 . 1 r I l

O
.5
N
00
A
01

positlo

Figure 4.11 Efficiency of different stations at different mass flows

88

 

 

1.4

 

1.2

 

 

0.8 \' \

O 67— +CFD@cone
' +CFD@cone discharge with
+experiment@cone

Relative lsentropic Head

 

 

 

0.6 0.8 1 1 .2 1 .4
Relative Flow

Figure 4.12 Performance comparison of the two volutes

Figure 4.12 shows the compressors performance with the enlarged volute and the
original volute. From this figure, we can see that at the design and high mass flow, the
isentropic head improved a little bit in the enlarged volute configuration. However, at low
mass flow, this change hurt the performance a little bit.

Figure 4.13 can make this idea more clear. The efficiency is almost the same for
the design and low mass flow (around 0.5% up in design mass flow and 0.5% down in
low mass flow). But, at high mass flow, the efficiency increased by 3%!

Figure 4.14 and 4.15 give the total pressure and static pressure comparisons for
the original volute and the enlarged volute. At design and low mass flow, the two

configurations have the similar total and static pressure distributions. At high mass flow,

89

both the total and static pressures were improved a lot in the enlarged volute
configuration.

This means that if the volute volume is enlarged without changing the tongue
position, diffuser width/length and the volute axial position, a 3% efficiency gain can be
expected at least at high mass flow for this volute and impeller configurations. At the
same time, the compressor performance will almost keep the same as the original
compressor performance at design and low mass flow.

This method indicates a way to improve the performance at high mass flow

without hurting the low mass flow performance.

Conclusions

From the analysis above, quite a few conclusions can be deduced.

The integrated tool introduced in chapter 3 is very robust and reliable for the
compressor performance prediction.

For this kind compressor configuration, circular volute/vaneless diffuser with
backswept impeller, the diffuser stall usually occurs at the hub wall around the volute
inlet station.

Volute stall usually occurs at the shroud wall near the volute inlet region at high
mass flow.

Large radial velocity at the impeller outlet is the main reason for the big swirl loss
in the volute.

The ftmction to change a volute volume freely is very useful for performance

improvement, especially in the beginning of a volute design.

90

Adiabatlc Efficiency

1.00

 

position 1: pinch
position 2: vaneless diffuser

 

0.95

0.90

position 3: vaneless diffuser
position 4: tongue position
position 5: discharge cone

—-——4

 

 

0.85

0.80 7

_—

 

0.75

 

+ 75% design mass
flow

+100% design mass
flow

+125% design mass
flow

 

—-><— 100% design mass
flow with large

—o— 75% design mass
flow with large

+125% design mass
flow with large

 

 

I I

1 2

I I I

3 4 5

position

Figure 4.13 Efficiency comparison between large volute and the original one

91

22

 

position 1: impeller inlet

position 2: pinch

position 4: vaneless diffuser

21 position 5: vaneless diffuser —
position 7: tongue

position 8: discharge cone

 

20

 

 

 

 

 

 

: f: N—

16 —o— 75% design mass flow —
+100% desrgn mass flow
+125% design mass flow

+ 100% design mass flow with large
+125% design mass flow with large
+ 75% design mass flow with large

Total Pressure(psi)

 

 

 

15 I

 

 

 

14 I i I l T l I 1
o 1 2 3 4 5 6 7 8 9
position

Figure 4.14 Total pressure comparison between large volute and the original one

92

 

 

 

 

 

 

 

 

 

 

 

 

 

 

24 position 1: impeller inlet _
position 2: pinch
position 4: vaneless diffuser
position 5: vaneless diffuser
position 7: tongue
22 position 8: discharge cone —‘
20
'6
a.
E
3 18
01
in
o
I-
a
.2
1'6 16
no.0
(D
14 ..
+ 75% design mass flow
+100% design mass flow
12 +125% design mass flow _
—x— 100% design mass flow with large
+125% design mass flow with large
+ 75% design mass flow with large
1 0 r 1 1 1 1 1 1 1
0 1 2 3 4 5 6 7 8 9

position

Figure 4.15 Static pressure comparison between large volute and the original one

93

Chapter 5

Performance investigation of two different volutes and same impeller
5.1 Introduction

Volutes are widely used in industrial compressors as the transition from the
impeller-diffuser to the pipelines, because of their simple structure, easy production and
wide operating range. However, there are only very few documented data on internal
flow measurements in volutes.

Volute, conic diffuser and sudden expansion discharge loss account for 4-6 points
of efficiency decrement in a typical centrifiigal compressor stage. The flow in a volute is
highly complex. It is strongly believed that understanding of the detailed flow structure in
a volute will provide insights on minimizing the losses by isolating the mechanisms that
contributes to entropy generation. The result will be a more efficient centrifugal
compressor product for customers and users and a product at higher profitability levels
for manufacturers.

Lendorff and Meienberg have investigated two symmetric volutes and one
overhung volute. The results indicate that the overhung volute has a better performance.
Mishina and Gyobu presented a detail test results about different shape volutes in 1978.
The data show a preference for circular cross section volute if the centerline diameter is
not small. Fahua et a1 has studied the flow in overhung volute by using one passage grid
of impeller to attach with a volute/diffuser grid. This paper limits the discussion to the
flow axial distortion since the exit flow at impeller exit was averaged. Ayder et al.

measured and simulated the elliptic cross section volute, and, compared the performance

94

at high, medium and low mass flow. Hagelstein et al. tested a rectangular volute at high
mass flow. Euler method with a correction for friction effects is used in this paper.
According to Hagelstein, this method predicts the tendency of the losses and the pressure
rise, but less accurate to predict the volute performance. The unsteadiness in volute is
generated by the variation of the flow at the outlet of the rotating impeller. But, the
unsteadiness decreases very soon because of the rapid mixing of the blade-to-blade flow.
So only a small error can be anticipated if the flow in volute is assumed to be steady
(Hillewaert).

This chapter presents the experimental and numerical investigation on the
performance of the two different overhung volutes with flat-top circular cross sectional
area to the same centrifugal compressor impeller. The experimental data were measured
from flange to flange firstly, then three Kiel probes were installed at pinch position
circumferentially. At the same time, a detailed numerical simulation of the performance
of the two volutes has been carried out. Two computational models, stage and frozen,
using the k-e turbulence model and the wall function, has been used to predict the internal
flow of the both volutes. A good agreement between experimental data and numerical
simulation results was found. The overall performance of the two volutes was also
discussed in detail. Attention was focus on the effect of different volutes on the impeller,
diffuser and the whole compressor performance, and the comparison of the two CFD
simulation methods. The objective to predict the compressor performance followed by a
volute through an inexpensive, fast and reliable way is achieved after the experimental

data validation.

95

5.2 The Investigated compressors

The same impeller with two different exit components (small volute vs. large
volute) is scaled from the product of the Solar Turbine, Inc. The two configurations are as
follows:

The first configuration consisted of the scaled impeller with the scaled volute that
was designed for this impeller at Solar Turbines, Inc. This volute will be marked as small
volute.

The second configuration used the same impeller as the one in the first
configuration, but another scaled volute from another compressor was used as the exit

component this time. This volute will be referenced as large volute.

 

Figure 5.1 Tested impeller

96

 

Figure 5.2 Small and large volutes

The shrouded impeller with 13 blades (figure 5.1), which the tip/diameter ratio
(b2/D2) is 0.036, is same in the both compressor configurations. The exit blade angle is -
60 degree from radial direction.

The vaneless diffuser is pinched 40%, which means the pinch ratio (b3/b2) is 0.60,
at a radius of R3=l.10xR2. The width of the vaneless diffuser is also same for the both
configurations.

The large volute was generated by increasing the axial position and decreasing the
diffuser length of the small volute a little bit. The figure 5.2 shows the outside view of the
two volutes. The contour of the two volutes at tongue position (station 7) is shown in
figure 5.3 (a). Circumferentially, the other cross-sectional area ratio of the two volutes is

same as the ratio in the tongue position. For the cone part, the area ratio of the two

97

volutes at the same axial position is 1.25. And, the circumferential angle distribution of

volute and the position of station 7 and 8 can be found in figure 5.3(b).

 
 
 

__.Large Volute
- - - Small Volute

 

 

 

 

(a) contour at tongue position (b) circumferential angle distribution

Figure 5.3 Compressor configurations

5.3 Test Facility and test procedure

The Aerotest Facility, as introduced in chapter 3, is located at Solar Turbines, Inc.
Keamy Mesa Facility, San Diego, California. The test article and the closed loop piping
are indoors. Air was the test gas for all the two compressor configurations. As far as the
instrumentation, please reference the test report prepared by Dr. Jean-Luc Di Liberti for
detail.

A bellrnouth venturi located upstream of the compressor inlet flange was used to
measure the flow. All pressures are referenced to ambient pressure and calibrated on line
during the test. Solar Turbines, Inc. has an SCXI temperature system incorporating Type

T thermocouples was used to measure temperatures. The thermocouples are calibrated

98

with a reference RTD and calibration coefficients are developed to provide an accuracy
of i0.2°F in the anticipated temperature range.

In the flange-to—flange rig tests, the compressor stage was insulated and equipped
with 4 total pressures, 4 static pressures and 4 total temperatures at the compressor inlet
and discharge port. At the compressor flanges, the 4 probes are located 90 degrees apart
and at 4 different immersions satisfying equal areas. And, for each speed line, a minimum
of eight flow set points were obtained. From the pressures and temperatures measured
above, the flange-to-flange performance and components static pressure recovery can be
calculated.

After completion of a flange-flange test, Kiel probes were installed at pinch
position at a fixed angle and the volute backface was not insulated any more. The Kiel
probes were located at three different circumferential locations (F, N and V, see 11 gure
5.3 (b)) for the both volute configurations. So the impeller performance can be estimated
from the measurement of these probes since the pinch position is only 10% downstream
of the impeller tip.

A few rotation speeds, 13,100rpm, 16,030rpm, 19,240rpm, 20,640rpm and
21,865rpm, were measured for the two compressor configurations at Solar Turbines, Inc.

In this paper, only the 19,240rpm rotation speed was analyzed.

5.4 Computational Method

Three-dimensional, compressible, steady flow computations were carried out, at
the Michigan State University, by using the commercially available computational fluid

dynamics code, CFX-TASCflow. This code solves the Reynolds averaged Navier-Stokes

99

 

equations in primitive variable form. The k—e turbulence model was employed for these
simulations. “Wall functions” were supplied to model the momentum and heat transfer
processes for turbulent flows in the near-wall region.

The impeller grid was generated from the commercial impeller grid generator,
TASCgen. TASCgrid was used to generate the volute and diffuser grid. However, all the
complicated input files for this software were produced from a self-made FORTRAN
code at the turbomachinery lab at Michigan State University. The volute grid is of
butterfly section so as to reduce the grid skewness because a bad grid skewness might
cause the converge problem (figure 3.3). The Multiple frame of reference (MFR)
capability in CFX-TASCflowBD uses the “stage” and “frozen” rotor concepts. A sliding
interface is implemented in such a way that steady state solutions are supported in each
frame. Two flow models in the MFR frame, stage rotor and frozen rotor, were adopted
for the simulation.

For stage cases, please reference to 3.1.2.1 for theory detail. For the whole
compressor “stage” grid, please see figure 3.1. The basic idea for this model is that it’s
assumed that all the other passages of impeller grid experience the same flow as in the
impeller passage shown in the figure 3.1. And, the exit flow of the impeller is averaged
circumferentially. 80 only one passage was modeled here and the periodic condition was
defined for this impeller passage.

For frozen rotor, see 3.1.2.2, all impeller passages are simulated together. The exit
flow of impeller is no longer assumed to be uniform and the flows in each passage are not
assumed to be periodic either. Thus, frozen rotor analysis can be used to investigate the

circumferential variation of the flow. Same as in the stage case, the transient effects at the

100

 

interface between impeller and diffuser are not modeled. Please go to figure 3.2 for the
whole frozen model grid.

For each impeller passage, the grid size is 36,860 points. So the whole impeller
has 479,180 points. The volute size is 145,535 points.

The inflow boundary conditions were based on the total pressure, total
temperature, inflow velocity direction, turbulent eddy length scale and turbulent intensity.
The mass flow was used as outlet boundary condition. Experience shows that this kind of
boundary conditions are very robust in the simulations.

The calculation was considered to be converged when the nondimensionalized

maximum residuals are reduced to 1.0x104, and it was also confirmed that the final
solutions were unchanged after further iterations reduced these errors to 1.0x10'5 or
1.0x10'6.

Since the purpose of this chapter is to focus on the compressor performance, such
a kind of compressor grid is fine enough (On). The influence of the turbulence model and

the wall function used in this paper has not yet been studied.

5.5 Results and discussions

For stage case, design and 6 off-design conditions were run for each volute. For
frozen case, because of time-consuming, 3 off-design conditions plus the design
condition were run for each volute. The design condition was always the first point to run
for each simulation. Thereafter, the result of design condition was used as the initial
guess of the off-design conditions in the same model. For all the simulations, the machine

mach number is 0.66.

101

 

5.5.1 Compressor Performance

The compressor performance, i.e. from impeller inlet (station 1) to cone diffuser
outlet (station 8), is given in figure 5.4. Firstly, it can be seen the CFD simulation results

match the experimental data very well except at high mass flow. The biggest error is in

 

r-
small volute that is near 10% at high mass flow. Second, as far as the head coefficient is E
concerned, the difference between the “stage” and “frozen” case of same volute can be
neglected. Thus, the stage case is preferred if only the flange to flange performance is
interested since it takes much less computer time than frozen case. Third, the CFD 1;:

simulation did not incorporate the leakage flow in the labyrinth between the shroud outer
wall and the machine case. Moreover, the “smooth” wall was an assumption in the
simulation. So the CFD lines are always above the experimental data lines. It can also be
noted, for small volute, the difference between CFD points and experimental points
become bigger and bigger from low mass flow to high mass flow. But, for large volute,
the difference is almost constant. Since the leakage flow is always there, this might
because the surface roughness has more effect in small volute. Fourth, the small volute
performance is better when the normalized flow coefficient is lower than 0.86; the profit
lies on the large volute if the normalized flow coefficient is bigger than this value. The

same cross-point is around 1.0 in the stage and frozen case.

102

 

1.2

 

 

1.1

 

0.9

 

0.8

 

 

 

 

. \
0.7 5.;
+ frozen case of large volute X \
06 __ -—I— frozen case of small volute
+ stage case of large volute ' X

lsentropic Head Coefficient iii/1PM

-~+t’-- stage case of small volute
X experimental data of large volute

0 experimental data of small volute
0.4 . a

0.5 0.75 1 1.25 1.5

Inlet Flow Coefficient OIO ref

0.5 5—

 

 

 

 

 

Figure 5.4 Compressor performance

The flange-to-flange (from station 1 to station 8) isentropic efficiency is presented
in figure 5.5. From this figure, we can see the frozen case can predict the efficiency
“trend” very well. At high mass flow, as shown in this figure, the large volute improved
the efficiency significantly. At low mass flow, the harrnfulness to efficiency of large
volute is kind of small. For stage case, the benefit of large volute is not so obvious
because the exit flow of impeller is averaged circumferentially. This figure can be used as
a proof to explain how big the non—uniform circumferential pressure affects the
compressor performance. Another interesting thing is the peak efficiency is almost same
for both volutes. This phenomenon is very clear no matter in experiment, stage case or
frozen case. The difference between the experimental data and CFD results is that the
peak efficiency of small volute is at a lower mass flow than the one of large volute in

experiment, but, for CFD results, they’re almost on same flow coefficient.

103

 

1.1

l

 

 

.°
9
5,

 

 

 

.°
o
i

 

.0
q

 

 

—O—frozen case of large volute O
._ +frozen case of small volute
+stage case of large volute
«5535:55- stage case of small volute
“*— X experimental data of large volute ——0—
. experimental data of small volute

.0
a1

 

lsentropic Efficiency tin/VIM“)

P
or

 

 

0.4

 

0.5 0.75 1 1.25 1.5

Inlet Flow Coefficient 43/0...

Figure 5.5 Compressor efficiency

From figure 5.4 and 5 .5, we can find frozen case can predict the differences
existing between the two volute configurations at high mass flow although there is an
almost 10% error for the small volute case at high mass flow. Stage case, no matter head
or efficiency, cannot predict the differences between the two volute configurations that
have been shown by experimental data. So, as far as the “trend” is concerned, the frozen ‘
case looks better. However, from accurate point, stage case is not worse than frozen case
in the whole compressor performance prediction.

At Solar Turbines, Inc., the pressure recovery from diffuser outlet to volute throat
at design condition was set as zero in the process of volute design. Thus in this paper the
diffuser outlet was chosen as the reference station to do the pressure recovery and loss
coefficient calculation. In order to get the whole idea of the compressor performance,

equations (5.1) and (5.2) were used to compute the pressure recovery and loss coefficient

104

‘ ‘. 1" {KM-T:

1. m“. -WS‘S' .021? n.’

 

between station 4 and station 8 respectively. And the results are given in figure 5.6. The

pressure recovery and loss coefficient between station 4 and 5 will be shown later.

 

 

 

 

 

 

Cp = __p_"£4_. (5,1)
P04 - p4
w=——p°4—p° (5.2)
P04 - P4
0.8 it
+ Cp of large volute ii
0 7 __ +Cp of small volute
' + (not large volute
""372"- (Dof small volute
L-

 

 

 

 

 

 

 

 

 

0.5 0.7 0.9 1.1 1.3 1.5
Inlet Flow Coefficient $10...

(a) Frozen Case

105

0.8

 

+Cp of large volute
+Cp of small volute
+ (1) of large volute
wit—5» (1) of small volute

0.65 -— ._‘_._ 2 fl_,

 

0.7

 

 

30.5 '1
O

0.4 5

 

 

0.3 5’

 

 

 

0.2

 

I I

0.5 0.7 0.9 1.1 1.3 1.5
Inlet Flow Coefficient with...

—. u..-" —_-. .ZL -

 

 

(b) Stage Case

Figure 5.6 Pressure recovery and loss coefficient at exit cone

At same flow coefficient, the frozen case 5.6 (a) and stage case 5.6 (b) give same
value. So we can use either map to discuss the result. When the normalized coefficient is
1.03, the pressure recovery Cp is same for both volutes. The loss coefficient (1) is same
when the normalized coefficient is around 1.13. When the flow coefficient is lower than
1.03, the pressure recovery Cp of large volute is lower and the loss coefficient to of large
volute is higher. But, when the normalized flow coefficient continuous decreases, the
properties differences between the two volutes become smaller. When the flow
coefficient is higher than 1.13, the benefit lies on large volute. Furthermore, the
differences become bigger and bigger when normalized flow coefficient goes way to
choke side. It means the large volute performance will be better and better when the mass

flow is higher and higher. The author has the experience that enlarged volute can improve

106

the compressor performance at high mass flow and impair the performance at low mass
flow. In figure 5.6 (a), after comparing the two points where normalized flow coefficient
is 0.65 and 0.75, we can find the difference between the two volutes is a little bit smaller
at 0.65 that means the performance of large volute recovered a little bit. This is more
obvious in figure 5 .6 (b) since more points were run for the stage cases. The biggest
difference for the two volutes at low mass flow is around 0.85. At a “lower” mass flow,
the recovered performance of large volute can be seen by eyeball. At low mass flow, the
reason that the performance of large volute get bad first, then recovered a little bit at a
“lower” mass flow is from the truncated diffuser, see figure 5.3 (a). A shorter diffuser can
make the fluid particle flow path inside the vaneless diffuser shorter so as to reduce the
friction loss that is the main loss in diffuser at low mass flow. From this figure, it can be
found how big the effect of diffuser length on the low mass flow performance since
radius radio of the two diffuser outlets is only 1.05. The reason why the large volute
performance is better and better when the flow coefficient approaches the choke side is
due to the small volute volume is too small. At high mass flow, this disadvantage can
produce an accelerating flow that can cause a strong non-uniformity in the volute that can

propagate back to upstream. We can see this result pretty clear in later discussion.

5.5.2 Impeller and Vaneless Diffuser Performance

The performance from impeller inlet (station 1) to pinch position (station 3),
shown in figure 5 .7, was used as the estimation of the impeller performance in order to

compare CFD results with experimental data. The experimental data were from the three

107

probes installed on pinch position circumferentially, where V probe is on 72 degree, N
probe on 180 degree and F probe on 288 degree (see figure 5.3 (b) for the three positions).
The experimental data were from the average value of these three probes. Since the

pinch position is located only 10% downstream of impeller outlet, this performance is
referred as impeller performance. It can be seen that the experimental data of the two
volutes are pretty close except a little bit difference exists at low mass flow. The CFD
results, especially the frozen case result, match the experimental data very well from

surge side to choke side. The discrepancy between stage case and experimental data is

It! 2L1“.L ‘IAmfl

bigger only when the normalized flow coefficient is around 0.75. This can be understood

from the assumption of the stage case. As mentioned above, the exit flow at the impeller j

 

outlet was averaged circumferentially for stage cases. So this phenomenon (big difference
between stage case and experimental data exists at low mass flow) gave us a strong hint
that there is a severe circumferential pressure distortion for both volutes at low mass flow

which stage case cannot catch.

108

 

1.5

1.34 ——-—~- — -~

 

1.1«~— 5— —-—~ - — ~ 5—

0.9 ~~ - --—-—

 

 

 

—e—frozen case of large volute
—I— fozen case of small volute
0.7 ~-— +stage case of large volute
555* stage case of small volute
x experimental data of small volute
0 experimental data of large volute ;

lsentropic Head Coefficient III/Wm

 

 

 

0.5

 

I

0 0.5 1 1.5
Inlet Flow Coefficient ole...

Figure 5.7 Impeller performance

Figure 5.8 is the circumferential pressure distribution of both volute
configurations at pinch position in frozen cases. All circumferential mass averaged results
(b). These averaged results are based on the averaged area shown in figure 5.9. The
rectangular area enclosed by think lines along the radial direction is used for the spanwise
average and the radius ratio is only 1.01. The rectangular area enclosed by thick lines
along the pinch position is for the circumferential average and it only occupies 1.54
degree circumferentially. So please keep in mind that the circumferential average also
includes spanwise average. The small spanwise area (along the radial direction) is exactly
on one circumferential angle. However for 5.8 (b), the averaged circumferential angle of

the small rectangular area along the pinch position was used for the circumferential

109

location. The first reason to do such a kind of circumferential average is because there is
spanwise variation exists. Second, all the data are mass averaged value and there are
more mass flow go through this face relative to the spanwise averaged area. What’s more,
the author also has interest to take a look at the results of different averaged methods. As
far as what’s the spanwise variation, please see the reference 3 for detail. Nowadays, it is
well known that the uniform circumferential pressure distribution at impeller outlet is one
design objective of turbomachinery. Here, the pinch position was selected instead of

impeller outlet due to the same reason as before. It can be noticed that the figures 5.8 (a)

_' . .__fig‘4 3;“!qu

and 5.8 (b) gave the same trend throughout the low, design and high mass flow no matter

what averaged methods were used. And, no matter in 5.8 (a) and 5.8 (b), the static

 

pressure distribution curves for two volutes have same trend at design and low mass flow.
The only difference between the two mass flows is the low mass flow has more non-
uniform distribution. Especially from 300 degree to 80 degree, the static pressure
distortion is more severe, where is near the tongue position. This is the reason why the
frozen cases have a better impeller isentropic head prediction than stage cases. Between
360 and 80 degree, the small volute has a better distribution than large volute at low mass
flow. So the impeller matched with small volute has a little bit better performance than
the one with large volute when the flow rate is lower. At high mass flow, the static
pressure distribution has the opposite trend for large and small volute, i.e. the static
pressure decreases for small volute and increases for large volute when the azimuth angle
is less than 300 degree, and increases for small volute and decreases for large volute

between 300 and 360 degree. And, the large volute has a flatter curve than the small

110

volute has at high mass flow. If compare the high and low mass flow, it also can be

found that the pressure distortion level is more severe at low mass flow.

 

 

 

 

 

 

 

 

1.08
[gg‘,&_.;,,2.,:¢-.b;w;+-—9.q-52r—,~ts-—,gfi3\

1.04 4 __ .
"’ ‘ '°’ MA
5 , q,

0.98 5%

0.96 - -_

7' m
0.94 . . .

 

 

 

0 1 00 200 300 400

Circumferential Angle

+ low mass flow of Iar e volute
+design mass flow 0 arge volute
—-—hrgh mass flow of Iar e volute
”-5355“ low .mass flow of sma l volute
+ desrgn mass flow of small volute
+ high mass flow of small volute

(a) spanwise average

111

 

1.08

 

1.06 -2 ~17 47
My... »%AWIAWW\

1.04- .#

0.98-4 4 7 7 , .74 47 7

 

 

 

0 100 200 300 400

Circumferential Angle

+low mass flow of Iar e volute
+design mass flow of arge volute
—-—high mass flow of large volute
low mass flow 0 small volute
+design mass flow of small volute
+high mass flow of small volute

(b) circumferential average

Figure 5.8 Circumferential static pressure distribution at pinch position

 

Mesh at pinch position

._____ $4 .‘a rise-4175’s?

55$ {fl—m;

    

Figure 5.9 Spanwise and circumferential averaged area

112

The circumferential static pressure distribution at vaneless diffuser outlet is given
in figure 5.10. Just like the phenomenon at impeller outlet, at low and design mass flow
the large and small volute almost have same static pressure distribution from 30 degree to
300 degree. Near tongue position, i.e. from 300 degree to 360 degree, the large volute
shows a little better distribution. This tendency is more obvious at high mass flow at the
tongue position where the static pressure in large volute is 181% higher than the one in
small volute.

According to common sense, the fluid left the impeller outlet will follow a
logarithm spiral path. But, compare figure 5.8 and 5.10, we didn’t find the range of
pressure distortion enlarged, shrinked or shifted when the pressure distortion propagated
from diffuser outlet to pinch position. It needs to be investigated further whether or not
this phenomenon is from the use of a narrower diffuser, computational model or

something else.

1.2

 

 

+low mass flow of large
volute

_ +design mass flow of large

2 volute

E, 0-5 ‘L—— —— high mass flow of large

0- volute

w-ae- low mass flow of small

0-4 ‘— volute

+design mass flow of
small volute

0‘2 ‘———— + high mass flow of small

volute

0.8 -—

 

 

 

 

 

 

 

0 50 100 150 200 250 300 350 400
Circumferential Angle

Figure 5.10 Static pressure distribution at vaneless diffuser outlet

113

‘ . 3.1“. ”MW-
.

 

5.5.3 Volute Performance

As mentioned above, the pressure recovery between diffuser outlet and volute
throat was chosen as zero at the design mass flow in the volute design process. The flow
properties at the diffuser outlet (station 4) and volute throat (station 5) are circumferential
(360 degree) mass averaged, and tongue position (station 7) is radial mass averaged.
Again pressure recovery and loss coefficient relative to station 4 were calculated by using
the equation (5.1) and (5.2). The results are shown in figure 5.11 and 5.12 respectively.

As show in figure 5.11, the pressure recovery increases and loss coefficient
decreases in both volutes when flow coefficient becomes bigger. The difference between
loss coefficients of the two volutes at surge side is kind of bigger. At the choke side, the
difference become smaller and smaller. Accordingly, the differences between the
pressure recoveries of the two volutes become bigger at choke side from (b) since stage
case has more points. This means the enlarged throat of the large volute make a detriment
on surge side, but benefit on choke side. In both volutes, the design criterion of zero
pressure recovery coefficients at the beginning of volute design is not satisfied. Anyway,

both volutes exhibit a desired performance at throat position.

114

 

0.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q45 ._ +Cp of large volute
—l— Cp of small volute
0.4 _ + (r) of large volute
~--’»<~-- (1) of small volute
0.35 ~
8
0.3 5 5
8
0.25 5
0.2
0.15 5
0.1 55~———— 44 . .54
0.05 . . . ,
0.5 0.7 0.9 1.1 1.3 1.5
Inlet Flow Coefficient OM...
(a) Frozen Case
0.5
+C of la e volute
0-45 7— +CE) of srrrtgall volute
+ of large volute
0.4 «— ”‘14- (Dof small volute
0.35 1’
0.3 * /'
8 \ /l/
a 0.25
o
0.2 -__'/¢§S(:\‘\
0.15 4%“ “M... .. fl
0.1 ...-1; ......,_...- 2.2.;- _ "1' ,' ;
0.05
o T I T r
0.5 0.7 0.9 1.1 1.3 1.5

Inlet Flow Coefficient WC...

(3) Stage Case

Figure 5.11 Pressure recovery and loss coefficient at volute throat

115

 

0.6

0.4 1

 

 

 

 
  

 

+Cp of large voltue
—l— Cp of small voltue
'04 '——' + (1) of large volute
"735’:‘7 (r) of small volute

 

 

 

-0.6
Inlet Flow Coefficient W0...

(a) Frozen Case

 

0.6

0.4 5

 

0.2 5-

 

 

0

Cplfr)

015 0.75 1 1.25 115

 

-o.2 «—
+Cp of large volute

+Cp of small volute
.04 1—- + moi large volute
minim (Dof small volute

 

 

 

 

-0.6
Inlet Flow Coefficient WC...

(b) Stage Case

Figure 5.12 Pressure recovery and loss coefficient at tongue position

The pressure recovery coefficient and the loss coefficient at station 7 relative to

station 4 are shown in figure 5.12. We can see in this part the performance get worse. The

116

loss coefficient is very high. And, pressure recovery coefficient goes down continuously
for both volutes. Especially for small volute at high mass flow, the loss coefficient goes
up dramatically and pressure recovery coefficient goes down to negative when the
normalized flow coefficient is large than 1.1. When mass flow is less than design mass
flow (around 1.0), the performance of the large volute at tongue position is even much
better than the performance of small volute. So, great attention should be focus on this
“performance neck” —tongue position——in volute design.

The circumferential static pressure in volutes is also calculated by using mass
averaged method. The results are given in figure 5.13. We can see the large volute and
small volute match each other very well at design and low mass flow except only some
differences exist near tongue position. At high mass flow, the static pressure in small
volute always goes way down throughout the flow. But, large volute presents a desired
performance. It seems the small volute volume can only accelerate the fluid in it. So it
leads a pressure drop that is the source of non-uniform pressure distribution at diffuser
outlet and pinch position. This proves the theory in Ayder et al paper.

Compare figure 5.10 and 5.13, we can find that the static pressure distribution at
diffuser outlet and in volute can be completely different. The volute acts back on diffuser
outlet only through the volute throat. So future research is urgently needed on the throat

radial position, angle and size.

117

 

 

1.2
+ low mass flow of Iar e volute
+design mass flow of arge volute
+ high mass flow of large volute
1 15 .. w5:35»- low .mass flow of small volute

' +desrgn mass flow of small volute
+ high mass flow of small volute

 

   

 

1.1 H .

PIP...

 

 

 

 

1.05
1 M
0.95 . . .
0 100 200 300 400

Circumferential Angle

Figure 5.13 Static pressure distribution in volutes

Conclusions

Two volutes with same impeller are investigated by using frozen case and stage
case in this paper. The CFD results have been compared with the experimental data.

0 From the analysis above, it has been shown the results of frozen
and stage method in CFD code “TASCflow” match the experimental data very
well except for the whole compressor performance at high mass flow. And, only
frozen case can predict the performance difference exists at high mass flow for
the both volute configurations.

0 For impeller performance, frozen method is preferred because of

the assumption of stage case. For the same reason, frozen method should be

118

selected if the circumferential distortion downstream of impeller outlet is
interested.

o The large volute almost has the same maximum efficiency as the
small volute has. From experiment data, the peak efficiency for different volutes
lies in different flow coefficient. But, CFD results didn’t catch this characteristic.

0 The volute volume plays an important role in compressor
performance at high mass flow. If combined with an improved diffuser, a little bit
shorter diffuser used here, large volute won’t impair the performance much at low
mass flow.

0 The zero pressure recovery from diffuser outlet to volute throat in
the volute design was not satisfied; and an enlarged throat is benefit for the static
pressure distribution at vaneless diffuser outlet at high mass flow.

0 No pressure distortion shift was found between pinch position and
diffuser outlet by the two computational models.

0 For small volute, the performance is very bad at tongue position at
off-design condition. A large volute improves the performance at tongue position
even at lower mass flow than design point.

Future work of the two configurations should be focused on the effect of the
volute throat part and tongue position on the whole compressor, the impeller/volute

interaction, and the flow structures inside the impellers, diffusers and volutes.

119

Chapter 6

Flow Structures Investigation and Comparison

6.1 Introduction

Volute is an important component whose function is to collect the flow from the
periphery of the diffuser and deliver it to the outlet pipe. Even in low-speed compressor
and pump applications where simplicity and low cost count for more than efficiency, it is
the diffuser not the volute that can be omitted. Nowadays, one popular design objective
for volute is to achieve a uniform pressure distribution at the volute inlet because the
circumferential distortion that occurs inside the volutes would propagate back to
upstream and cause flow fluctuation among impellers. This would make the efficiency
drop of the whole machine.

Recently, the study on volute/impeller interaction caught more and more interest.
T. Elholm, et al. investigated the three-dimensional velocity distributions in two different
cross sections of a pump volute by means of LDV. He found that the leakage flows in the
tongue region could increase or decrease the flow in the volute and therefore influence
the circumferential pressure distribution. Ayder, et al. showed by measurement that the
variations of the total and static pressure distribution at the different volute cross sections
and at the vaneless diffuser exit in a centrifugal compressor with a volute of elliptic cross
sections. The centrifugal forces due to the swirl velocity in the volute cross section was

believed to have more influence on the static pressure distribution. Hillewaert, et al.

120

simulated a volute/impeller interaction by an unsteady flow calculation in the impeller
and a time-averaged flow calculation in the volute. There is no average total pressure
reduction found in his calculation method that was explained as no mix out in the diffuser,
contrarily to the rapid mixing at the impeller exit. Fahua, et al. has studied the flow in
overhung volute by using one passage grid of an impeller to attach with a diffuser grid.
This paper limits the discussion to the flow axial distortion since the exit flow at impeller
exit was averaged. Thus, this paper investigated the volute/diffuser interaction axially
only. Fatsis, et al. suggested using the acoustic Strouhal number to quantify the relative
effects of the rotation and pressure wave propagation in order to decide whether or not
the flow in volute can be modeled as a steady flow. According to the suggestion in this
paper, the pressure wave propagation in the two compressor configurations investigated
here is much faster than the rotation of the impeller. That means the pressure perturbation
finishes traveling over the passage at almost the same time as when the impeller moves to
a new position. Thus, the steady model can be used to study the pressure distortion due to
the volute.

The performance prediction and CFD/TEST data comparison of same impeller
with two different volutes have been done in chapter 5. So there is no performance
comparison in detail in this chapter. In this chapter, the interaction of the impeller with
the two overhung volutes and the flow structures in the two compressor configurations
would be investigated by using the CFD result from the “frozen rotor” because no
circumferential averages were made in this model. The k-e turbulence model and the wall
function built in this model were used to predict the internal flow of both the volutes. The

reliability of the model has been validated in the last chapter, too. For the study presented

121

in this chapter, attention was focused on the effect of volute tongue, volume and cross
section channel curves on the impeller and the compressor performance, especially at off
design condition. The research has been divided into two parts. Firstly, this chapter
concentrates mainly on the effect of volute tongue on different impeller passages. The
second part of this chapter describes the flow structure in the parts of volute that makes
the differences in the two different volutes.

It’s better to emphasize that the large volute was generated by increasing the
cross-sectional area of the small volute through increasing the axial position of the small
volute.

An experimental test of the performance of the two configurations was carried out
at Solar Turbines Inc. A good agreement between experimental data and numerical
simulation results was found and shown in chapter 5.

Corresponding improvements for volute design based on the CFD analysis in this

chapter and the test data were also presented.

122

 

     

volute

vaneless
diffuser

Figure 6.1 Compressor Configurations

6.2 Compressor Geometry and Computational Method

The geometries of the two compressors have been introduced in chapter 5.
However, there are four new stations that were added in the wheel, which has 13 blades,
namely, station 1, 2, 3 and 4 (see figure 6.1). Therefore, the flow field among the blades
can be investigated in detail. Note: the nomenclature in this chapter is a little bit different
from the ones used in previous chapters. In this chapter, the station 4 is near the impeller
tip, station 5 at pinch position, and station 6 at the vaneless diffuser outlet. The large

volute was generated mainly by increasing the axial position and decreasing the diffuser

123

length a little bit of the small volute. The tongue position of both the compressor
configurations starts at zero azimuth angle. The contour of the two volutes at tongue
position (station 7) is shown in figure 6.2 again because here volute wall has been divided
into four parts to facilitate the later description. There is no clear dividing points between
the different walls (for example, between the outer wall and the shroud wall). These wall
concepts are only qualitative. One thing need to be mentioned is circumferentially the
other cross-sectional area ratio of the two volutes is the same as the ratio in the tongue
position. For the cone part, the area ratio of the two volutes at the same axial position is
1.25, the differences between the two configurations are that the large volute has a larger
volume and bigger throat. The vaneless diffuser length is just a little bit shorter; the

radius ratio of the two vaneless diffuser outlets is 1.05.

 

Large Volute
- - - -SmallVolute outer

 

 

 

Figure 6.2 Volute geometry at station 7

The impeller grid was generated from the commercial impeller grid generator,
TASCgen. TASCgrid was used to generate the volute and diffuser grids. The volute grid

consists only of butterfly sections so as to reduce the grid skewness because small grid

124

angles can make the convergence difficult. A sliding interface between impeller and
diffuser grid is implemented in such a way that steady state solutions are supported in
each frame. There is no need to keep the impeller grid number and shape the same as the
diffuser grid number and shape at the connection interface.

All impeller passage grids, diffuser grids and volute grids have been shown in
figure 3.2. The exit flow of impeller can be non-uniform and the flows in each impeller
passage are not assumed to be periodic. Thus, this analysis method can be used to
investigate the circumferential variation of the flow. The transient effects at the interface
between the impellers and the volutes weren’t taken into account in this model.

For each impeller passage, the grid size is 36,860 points. So the whole impeller
has 479,180 points. The size of volute and diffuser is 145,535 points.

The inflow boundary conditions were based on the total pressure, total
temperature, inflow velocity direction, turbulent eddy length scale and turbulent intensity.
The mass flow was used as the outlet boundary condition. Experience shows that this
kind of boundary conditions are very robust in the simulations.

These calculations was considered to be converged when the nondimensionalized

maximum residuals are reduced to 1.0X104, and it was also confirmed the final solutions

were unchanged after further iterations reduced these errors to 1.0><10'5 or 1.0X10'6.

6.3 Test Facility and Experimental Method

The Aerotest Facility is located at Solar Turbines, Inc. Keamy Mesa Facility, San
Diego, California. The test article and the closed loop piping are indoors. Air was the test

gas for all tests. The compressor stage was insulated and equipped with four total

125

pressures, four static pressures and four total temperatures at the compressor inlet and
discharge port in order to determine the machines head, efficiency and flow. After
completion of the flange-flange test, Kiel probes were installed at pinch position at a
fixed angle and the volute backface was not insulated any more. The Kiel probes were
located at three different circumferential locations (V, N, and F in figure 5.3 (b)) for both
the volute configurations, which means the impeller performance can be estimated from
the measurement of these probes since the R5 is only 1.1 times of the R4. Flow enters
through an inlet guide vanes (IGV’s). The IGV deswirled the inlet flow and provides
flow with zero swirl to the impeller eye.

As far as detailed test instruments and test procedure, please reference chapter 5

for detail.

6.4 Results and discussion

For both the configurations, design and three off-design conditions have been run
by using the “frozen rotor” model when the machine Mach number is 0.66. In this
chapter, only the 75% design mass flow and 125% design mass flow conditions were
taken out as the representation of the low mass flow and high mass flow. And, the
discussion begins from the impeller analysis, and then go through the vaneless diffuser,

ends at volute structure investigation.

126

 

Flow Analysis in Impeller:

 

  
 
 

 
 
   

Station 2:

S S
Large h u b

”’7' :\
”M“ \\:"
7 "’17...” :3?.:::f\ \\\ \\ W"

Small
Station 3:

  

  

‘2 —14 ’5-15

 

Small

127

Station 4:

 

 

 

 

 

Small
Large Volute Small Volute

(a) Nearest to the tongue

Station 2:

 

Large

128

 

Small

Station 3:

-—:’ s -—1—, 10—112——14

    

1
I

. —'l4
—1.—6 8—{10—I'12
.——'-1—4 z , l ‘ ' ;
.111
g/

2 / 1 1 1’; 1'! I '
l .5 . r ,« s
x , ."I 1" ,3“ ...! .-‘ > V 1‘ I

   

Small

Station 4:

 

 

129

 

\ 14 -
55-. 7 ll 71
‘\ /
/

\\ f/ x [(18
\ ,r/ {f 511

(b) Farthest away from the tongue

   

Small

Figure 6.3 Static pressure at high mass flow

1.16

 

1.14 ~~

 

 

1.12

1.1 5~

 

 

 

 

1.08 -

PlPref

1.06

 

 

 

 

 

 

1.04

 

1.02

 

 

 

azimuth angle

+ nearest tongue with large volute
—I—- nearest tongue with small volute
+277-305 deg with large volute
-)(—277-305 deg with small volute

(a) station 3

130

 

 

PlPref

 

 

 

 

 

SS azimuth angle PS

+nearest tongue with large volute
+nearest tongue with small volute
+277-305 deg with large volute
—)(—277-305 deg with small volute

(b) station 4

Figure 6.4 Midspan static pressure distribution at high mass flow

Station 2:

 

Large

131

 

Small

Station 3:

 

 

 

Large
2—3—T5 3.18—1j11514—m17'1819“
. 1 . 2‘ ; - ,
\l‘l'll“
" 6 . 1
. 1 -.
if I 1" Ii '1 \1
4 7 3 II "1 1 l3 ‘. \\
I I 5 1 ‘. . '\
* 7 9 - 10 —— 12 —_;-_ 15
Small
Station 4:

 

 

132

 

Small

 

Station 2:

 

Large

 

Small

133

Station 3:

 

3—4—5—6

\2\\

    

Small

 
  

Station 4:

 

5-8—“__'_”_“"—V17

K 7I14
I
:ggil: \\ J11”

Il/Il

 

Small

(b) Farthest away from the tongue

Figure 6.5 Static pressure at low mass flow

134

 

1.21

 

 

1.18 ~

1.15 5

 

 

PlPref

 

1.12

 

 

 

 

SS azimuth angle PS

+ nearest tongue with large volute
-l— nearest tongue with small volute
+277-305 deg with large volute
+277-305 deg with small volute

(a) station 3

 

 

 

PlPref

 

 

 

 

 

1.26 . w . .
SS azimuth angle PS

 

+ nearest tongue with large volute
-—-I—- nearest tongue with small volute
+277-305 deg with large volute
+277-305 deg with small volute

(b) station 4

Figure 6.6 Midspan static pressure distribution at low mass flow

135

. 1 -..-....'Fflm1n_...~;-<ouuulh'
'5

 

 

Figure 6.3 represents the static pressure distribution among the impellers at high
mass flow, the part (a) is nearest to the tongue and part (b) is farthest from the tongue. All
the four sides have been marked in the first figure at station 2 in figure 6.3 (a), where
“large” means in large volute configuration, and “small” means small volute
configuration. All the other stations have the exact same border definition as in this
station. So they are not tagged any more.

For both volutes, they exhibit similar trends at the three stations. The static
pressure at station 2 nearest to the tongue region (Fig. 6.3 (a)) shows a gradient in the

shroud-to-hub direction due to the high centrifugal acceleration at large mass flow. At

n. -— '.'.s.' f7 . 5“! . fut—3311.101.”

this station the pressure on the suction side is higher than on the pressure side. So the

 

impeller has a negative loading on the leading edge at high mass flow. And the low-
pressure region is also located at the shroud/pressure-side corner. At station 3, the
pressure gradient is no longer shroud-to-hub. Moreover, blade loading becomes positive
at this station, and the low-pressure region changes to shroud/suction-side comer. At
station 4, the pressure exhibits an almost symmetry distribution. The low-pressure region
is on both shroud/suction-side and hub/pressure-side corner.

However, except the same trend shown above, there are also some differences
exist between the two compressor configurations. Regardless to which station, at the
same location, the pressure in. the large volute is lower than the pressure in the small
volute. The largest adverse pressure gradient of the static pressure between station 2 and
3, or between 3 and 4 is on the shroud/pressure-side comer and hub/suction-side when

fluid flows from station 2 to 3. This pressure gradient is more than two times than other

136

 

comers at least. This pressure rise occurs as the fluid turns through the bend while
reducing the relative velocity.

The flow field among blades farthest from the tongue at high mass flow was
shown in figure 6.3 (b). It can be seen the impeller also has a negative loading at station 2
and the pressure gradient also becomes pressure-to-suction direction at station 3 and 4.
However, it can be found that the two volutes exhibit almost same trend and same
magnitude in all three of the stations. That’s means the tongue effect can be neglected
around this location.

Since the pressure gradient is pressure-to-suction side at station 3 and 4, the
midspan pressure distributions at these two stations should be representative of the field
pressure distribution among blades. Because of too many lines (13 lines among 13
blades), only two lines, minimum and maximum pressure curves, are shown in figure 6.4
for each configuration. All the other pressure distribution curves fall into this range
limited by the two extreme curves. For large volute configuration, the minimum pressure
distribution between neighbor blades is nearest to the tongue position; the maximum
pressure distribution is between 277 degrees and 305 degrees. For small volute, the
phenomenon reversed, the maximum pressure distribution is nearest to the tongue
position; the minimum pressure distribution is between 277 degrees and 305 degrees. The
minimum pressure distributions for both configurations are nearly the same. The
discrepancy between maximum curves becomes bigger when the flow goes way to
impeller exit from station 3 to 4. Also, the small volute configuration has a wider
pressure distribution range that means a more non-uniform pressure distribution

circumferentially. Thus at high mass flow, the tongue position gives rise to a more severe

137

 

pressure distortion among impellers in small volute configuration. And, one extreme is
always nearest the tongue position; another extreme is always around 290 degrees (i.e.
upstream of the tongue). This means that the minimum pressure at high mass flow is not
always located upstream of the tongue as Hagelstein et al. pointed. The position
(minimum pressure) also depends on the volute volume and throat because those two
factors are the only differences exist between the two investigated compressors. It’s well
known nowadays that the circumferential distortion among blades is caused by the
distortion in volute. Therefore this problem will be discussed in the upcoming volute part
section.

At low mass flow, the static pressure gradient at station 2 is not shroud-to-hub
direction any more (figure 6.5) throughout the impeller flows. At station 3 and 4, the
tendencies are the same as the one at high mass flow. Far away from the tongue, both
configurations exhibit almost same pressure distribution. Nearest to the tongue position,
the tendency is the same, but the pressure in impeller with large volute is a little bit
smaller than the pressure in impeller with small volute at same position.

Figure 6.6 shows the midspan pressure distribution at station 3 and 4 at low mass
flow based on the same reason mentioned above. It can be seen the minimum pressure
distribution is nearest to the tongue position for both volutes this time. Also, for both
volutes, the maximum pressure distribution is between 277 degree and 305 degree. From
the figure 6.6 (b), it can be seen the small volute cause less severe pressure distortion
among the blades because the range between maximum and minimum pressure is smaller

at low mass flow.

138

From a comparison of figures 6.4 and 6.6, it can be concluded that the distortion
in different impeller passages at low mass flow is more severe than the distortion at high

mass flow.

Flow analysis in vaneless diffuser

 

 

 

 

 

 

 

 

1.08

1.06 ”My”? 4““:th

1.04 4’ 6*“7
51-02 M
5 1

0.98 5

0.96 5 .— .. ...... .

0.94 r ' '

 

 

0 1 00 200 300 400

Circumferential Angle

+ low .mass flow of Iar e volute
—l— desrgn mass flow 0 arge volute
—— high mass flow of lar e volute
wee—~— low .mass flow of sma | volute
+ desrgn mass flow of small volute
+ high mass flow of small volute

(a) At pinch position

139

0.4

0.2

 

Al—————-——

41————_———

.h———

‘— + high mass flow of small

+ low mass flow of large

 

 

volute
—-I— design mass flow of large
volute

 

--- high mass flow of large
volute

--~_:~<---~ low mass flow of small
volute

+ design mass flow of
small volute

 

volute

 

e—v’fil-

 

 

0 50 1 00 1 50 200 250 300

Circumferential Angle

(b) At vaneless diffuser outlet

350 400

Figure 6.7 Circumerential static pressure distribution

140

Figure 6.7 is a mass averaged pressure value distribution at the pinch position and
at the diffuser outlet. The most severe pressure distortion is between 270 and 360 degrees.
In the figure 6.7 (a), it can be found that the trend for both volutes at low mass flow is the
same and the trend is opposite at high mass flow. Especially at high mass flow, from 270
degrees to 360 degrees, the range of pressure change is consistent with the trend among
impellers (fig. 6.4 (b)). So from the pinch station to the stations inside the impellers, no
pressure distortion shift is found although circumferential pressure distribution inside the
impellers is more non-uniform. Just like the phenomenon at the pinch position, at low and
design mass flow, the large and small volute almost have the same static pressure

distribution when the azimuth angle is less than 270 degrees at the diffuser outlet. Near

tongue position, i.e. from 270 to 360 degrees, the large volute shows a little better
pressure distribution. This tendency is more obvious at high mass flow at the tongue
position where the static pressure in the large volute is 181% higher than the pressure in
the small volute. Again, the position with severe distortion is the same at the pinch and
among the impellers. No phase shift can be found by the frozen case.

Flow structure in volutes:

270 degrees

   

357 degrees

   

(a) Large volute (b) small volute

Figure 6.8 Volute flow patterns at low mass flow

141

It is well known that the swirling flow exists over all the sections of volute. Gu, et
al. indicates that the high energy loss at high mass flow is because of the existence of a
twin vortex downstream of the tongue which is induced by the low radial velocity at the
shroud side; at low mass flow the high loss is from the recirculation upstream of the
tongue that is because the fluid at the hub side cannot exit the volute. According to the
impeller analysis, the zone between the blades that is affected most by volute is from 277
to 360 degrees. Thus the comparison of the swirling flow of the two volutes at low mass
flow in this range is shown in figure 6.8 first. Ayder, et al. shows that the second flow
exists in the inner-hub wall comer in their rectangular volute. Here the volute cross-
sections between 270 and 357 degrees are selected to show in figures. At low mass flow
the twin vortex exists at 357 degrees (upstream, not downstream of the tongue) in both
the volutes. And the position is around the interface of the inner-shroud wall. At 270
degrees, the twin vortex occurs only in the large volute, not in the small volute. No twin
vortex flow is found for either volute at high mass flow (didn’t shown here) because of
the large radial velocity at volute inlet. This proves that the twin vortex is not relative to
how big the mass flow is (Gu, et al. found twin vortex at high mass flow). It strongly
depends on the flow structure in the volute that is affected by the volute channel
curvature and the leak flow around the tongue.

Figures 6.9 and 6.10 show the static and total pressure distributions in the same
cross-sections at low mass flow respectively. The pressure in the large volute ranges from
numbers 26 to 36 at 270 degrees; number 33 to 37 at 357 degrees. The distribution is
more uniform than the distribution in the small volute that is from number 24 to 40 at 270

degrees and from numbers 34 to 40 at 357 degrees. From a comparison of the two volutes

142

at 270 degrees, it can be found that the pressure gradient is bigger in the small volute.
This is because the sharp cross-section curvature of the volute is “strong” enough to make
a pressure gradient that is distributed in the inner-outer wall direction. This is helpful to
suppress the secondary flow——twin vortex. Around the tongue, i.e. at 357 degrees, neither
volute curvature can keep this pressure gradient. This is the reason why the twin vortex
occurs from the shroud-inner wall interface. So it should be a good idea to change the

large volute cross section curvature from 270 degrees according the small volute shape to '

' .W‘. _~

get better performance at low mass flow since no twin vortex occurs in the small volute at

high mass flow. It will be harmless to high flow performance by this improvement. From

 

the analysis above, it is not hard to understand the reason why the total pressure in the

 

large volute is lower than the total pressure in the small volute at low mass flow.

 

 

 

 

270 Degrees ”PM.

40 1.3952

38 1.3933

36 1.3923

34 1.3914
, 36:7 32 1.3904
7:64—57 35 30 1.3895
'/—*-~ 34 28 1.3876
:. 26 1.3866
‘ 24 1.3856
22 1.3847

20 1.3837

18 1.3828

16 1.3809

14 1.3799

12 1.3789

10 1.3780

8 1.3770

6 1.3751

4 1.3742

2 1.3732

1 1 0700

 

 

 

143

357 Degrees

   

(a) Large Volute (b) Small Volute

Figure 6.9 Static pressure at low mass flow

 

270 Degrees 30 1.3889

 

 

 

 

357 Degrees

 

 

(a) Large Volute (b) Small Volute

Figure 6.10 Total pressure at low mass flow

Conclusions

This chapter has investigated the flows inside impellers, diffusers and volutes in
detail. The frozen method build in CFD code TASCFlow was the tool to do the study. A
few conclusions based on the analysis in this chapter are as follows,

No distortion position shift from the vaneless diffuser outlet to fluid interior the
blades was found by using the steady state frozen method.

At high mass flow, negative blade loading was found in the blade leading edge.

The distortion in different impeller passages at low mass flow is more severe than
the distortion at high mass flow. Same phenomenon can be found at the pinch position.

At high mass flow, the large volute throat benefits the performance more.

145

For flat-top circular overhung volute, the secondary flow usually starts from the
inner-shroud interface. And, the secondary flow strongly depends on the volute channel
curvature and the leak flow around the tongue. This phenomenon can occur either at low
mass flow or at high mass flow.

The twin vortex flow can occur not only at downstream of the tongue as a few
papers indicated, but also at upstream of the tongue. A sharp curvature can help to
eliminate this phenomenon in volute. At high mass flow, no twin vortex was found in
volute, however, as the analysis in chapter 4, it will give rise the volute stall around the

volute inlet region.

146

10.

ll.

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