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DESIGN AND DEVELOPMENT OF LOW SOLIDITY
VANED DIFFUSERS FOR CENTRIFUGAL COMPRESSORS

By

Won Joong Kim

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Mechanical Engineering

1998

ABSTRACT

DESIGN AND DEVELOPMENT OF LOW SOLIDITY
VANED DIFFUSERS FOR CENTRIFUGAL COMPRESSORS

By

Won Joong Kim

Interest has recently increased in the use of Low Solidity Vaned Diffusers.
Typically downstream of a centrifugal compressor impeller, three types of radial diffusers
are used: 1) vaneless diffuser (VNL), 2) conventional vaned diffuser (CVND), and 3)
Low Solidity Vaned Diffuser (LSVD). It is well known that a low solidity vaned diffuser
is a good compromise between the vaneless diffuser and the conventional vaned diffuser.

Four low solidity vaned diffusers (LSVDS through LSVD8) were designed for
experimental analysis. Experimental testing of a centrifugal compressor with the low
solidity vaned diffusers along with two vaneless diffusers and one vaned diffuser has
been carried out downstream of the same impeller to understand the pressure recovery
phenomena in each of the three types of diffusers, and the effect of design parameters on
performance and the results were compared with the results from numerical simulation.
The design parameters include the solidity, turning angle, vane setting angle angle, and
the number of vanes. The testing was performed at three different rotational speeds

(Mu=0.69, 0.88, 1.02). The experimental results proved the superior merits of LSVDs

relative to the vaneless and vaned diffuser. The LSVD fulfilled the high expectations
since they seemed to combine the advantages of the conventional diffuser systems by
providing a good pressure recovery over a wide flow range.

Besides steady performance analysis, pressure fluctuations were measured to
understand the instability of a compressor stage such as stall and surge using fast response
dynamic pressure transducers installed in various locations of the compressor stage. A
rotating stall was found only with the vaneless diffuser configurations. It is presumed the
progressive impeller stall is due to the destabilization of the impeller flow. This
fluctuation was added to the destabilization of the vaneless diffuser and triggered the
stage surge with high fluctuation.

Some of the experimentally tested low solidity vaned diffusers were compared
with 3-D viscous calculations to understand the flow phenomena inside the diffuser. The
effect of geometric parameters of the low solidity vaned diffuser on the flow
characteristics was also investigated by numerical calculation. The results showed that
low solidity vaned diffuser stalls when the vane suction surface separation was
accompanied by the end wall separation, and this qualitatively compared well with the

experiments.

Copyright by
Won J. Kim
1998

To all my family and all my teachers.

ACKNOWLEDGMENTS

I am very grateful to my advisor, Professor Abraham Engeda, for his guidance,
support, and encouragement throughout the course of this research work. Sincere thanks
go to Professors Craig W. Somerton, Clark J. Radcliffe, Charles R. MacCluer and Mr.
Ronald H. Aungier for their invaluable advice, suggestions, and continued interest in my
work. Mr. Aungier has been most generous with his time throughout this research work; I
have been supported in many ways by his considerable experience and special
considerations.

I wish to particularly acknowledge many helpful discussions with Mr. Chuck
Boa], Bill Hohlweg, Ken Greene, and Frank Kushner of Elliott Company. I also
appreciate the numerous criticisms, assistance, and great friendship of Dr. Jean-Luc Di
Liberti of Turbomachinery Lab., Michigan State University. I also thank Mr. Craig Gunn
for his help in preparing my thesis.

The support of Elliott Company, Trane Company, and Division of Engineering
Research is greatly appreciated. Much of the research was made possible with the
equipment provided by Elliott Company.

Last but not least, I would like to thank my parents not only for financial support
but also for their spiritual encouragement; my wife, Jiyoung; and my son, Hanul for their
love at all times. Also I will cherish the memories with many Korean friends at Michigan

State University.

vi

TABLE OF CONTENTS

 

 

 

 

 

 

 

LIST OF TABLES - - - IX
LIST OF FIGURES - - X
NOMENCLATURE ......... XII
1. INTRODUCTION - - -- -- - - - - - 1
1.1. CENTRWUGAL COMPRESSORS AND DEMANDS ON THEM .............................................................................. I
l .2. THE IMPELLER ............................................................................................................................................. 4
l .3. THE RADIAL DIFFUSER ................................................................................................................................. 6
1.3.1. Vaneless Difi‘users .............................................................................................................................. 6
1.3.2. Vaned Diffusers ................................................................................................................................. 8
1 .4. OBJECTIVE OF THE PRESENT WORK ........................................................................................................... I I
2. THE CENTRIFUGAL COMPRESSOR 15
2.1. STEADY FLOW OF A CENTRIFUGAL COMPRESSOR ...................................................................................... 15
2.1. 1. F low Between Impeller and Difi‘user ............................................................................................... 15
2.1.2. Difiuser Design Parameters ............................................................................................................ 25
2.2. INSTABILITY OF A COMPRESSOR STAGE ..................................................................................................... 30
2.2.1. Stall in a Compressor Component ................................................................................................... 31
2.2.2. Surge ................................................................................................................................................ 39
2.3. RESEARCH STATUS ON LOW SOLIDITY VANED DIFFUSER .......................................................................... 39
2.4. Low SOLIDITY VANED DIFFUSER DESIGN .................................................................................................. 45
3. EXPERIMENTAL SETUP 48
3.1. TEST COMPRESSOR .................................................................................................................................... 48
3.2. INVESTIGATED Low SOLIDITY VANED DIFFUSERS ..................................................................................... 50
3.3. MEASUREMENT .......................................................................................................................................... 51
3.4. STEADY PERFORMANCE DATA ACQUISITION .............................................................................................. 55
3.4. 1. Instrumentation ................................................................................................................................ 55
3.4.2. Data Collection and Reduction ....................................................................................................... 57
3.5. UNSTEADY PERFORMANCE DATA ACQUISITION ......................................................................................... 64
3.5.1. Obtaining and Storing the Pressure Signal ..................................................................................... 64
3.5.2. Signal processing ............................................................................................................................. 66
3.5.3. Analysis of the Data ......................................................................................................................... 68
4. EXPERIMENTAL RESULTS OF STEADY PERFORMANCE - 72
4.1. OVERALL PERFORMANCE CHARACTERISTTCS ............................................................................................. 73
4.1. I. Effect of Solidity ............................................................................................................................... 75
4.1.2. Eflect of Vane Number ..................................................................................................................... 81
4.1.3. Efi‘ect of the Turning Angle on the Operating Range ...................................................................... 83
4.2. PRESSURE RISE IN THE STAGE WITH THE Low SOLIDn'Y VANED DIFFUSERS .............................................. 85
4.3. PRESSURE RECOVERIES IN THE DIFFUSERS ................................................................................................. 89
4.3.1. Subdivided Pressure Recoveries ...................................................................................................... 93

vii

5. EXPERIMENTAL RESULTS ON INSTABILITY IN A CENTRIFUGAL

 

 

 

 

 

COMPRESSOR STAGE 97
5. I . INSTABILITIES OF THE CENTRIFUGAL COMPRESSOR STAGE ....................................................................... 97
5.1.1. Unsteady Behavior of the Stage with the Vaneless Difi‘users .......................................................... 97
5.1.2. Unsteady Behavior of the Stage with the Vaned Diffuser ................................................................ 99
5.1.3. Unsteady Behavior of the Stage with the Low Solidity Vaned Difl‘users ....................................... 100
5.2. INDUCER STAu. ....................................................................................................................................... 110
5.3. ROTATING STALL ..................................................................................................................................... I 1 1
5.4. SURGE ................................................................................................... -- -- - - .............. 111
6. NUMERICAL CALCULATION OF LOW SOLIDITY VANED DIFFUSERS ...... 113
6.1. 3-D VISCOUS FLOW SOLVER ....................................................................................... I I3
6.2. GRID GENERA'I'ION AND BOUNDARY CONDmONs ................................................................................... I 15
6.3. CALCULATION RESULTS ........................................................................................................................... 120
6.3.1. Pressure Distributions in the Difi‘users .......................................................................................... 120
6.3.2. F low Field in the Difi‘users ............................................................................................................ 122
6.3.3. Separation at the Dijfuser Vane ..................................................................................................... 123
6.3.4. Vane Setting Angle Effect .............................................................................................................. 124
7. CONCLUSIONS AND RECOMIVIENDATIONS 140
APPENDICES 143
BIBLIOGRAPHY 147

 

viii

LIST OF TABLES

TABLE 3-1 DIFFUSER GEOMETRIC PARAMETERS ................................................................ 50
TABLE 3-2. SUMMARY OF MEASUREMENTS AND MEASUREMENT LOCATIONS ................... 55
TABLE 3-3 NUMBER OF ROTATING STALL CELLS ................................................................. 71
TABLE 5-1 SUMMARY OF THE IMPELLER ROTATING STALL ............................................... 1 1 1
TABLE 5-2 SUMMARY OF SURGE ...................................................................................... 1 12

ix

LIST OF FIGURES

FIGURE 1 .1 COMPONENTS OF CENTRIFUGAL COMPRESSOR ................................................... 1
FIGURE 1.2 H-S DIAGRAM FOR THE CENTRIFUGAL COMPRESSOR STAGE ................................ 2
FIGURE 1.3 VELOCITY TRIANGLES FOR AN IDEALIZED IMPELLER .......................................... 4
FIGURE 1.4 EFFECT OF THE IMPELLER EXIT BLADE ANGLE .................................................... 4
FIGURE 1.5 TYPES OF VANED DIFFUSERS .............................................................................. 9
FIGURE 2.1 JET-WAKE FLOW PATTERN OF IMPELLER DISCHARGING FLOW .......................... 15
FIGURE 2.2 AN EXAMPLE OF MEASURED JET/WAKE FLOW AT THE EXIT OF IMPELLER
(ECKARDT, 1975) ....................................................................................................... 17
FIGURE 2.3 COMPARISON OF IMPELLER DISCHARGE VELOCITY (KRAIN, 1988) ................... 20
FIGURE 2.4 TRAVERSE AT DIFFUSER INLET (FISHER ET AL., 1981) ...................................... 22
FIGURE 2.5 PITCHWISE DISTRIBUTION OF ABSOLUTE FLOW ANGLE DIFFERENCE AT IMPELLER
EXIT (HATHAWAY ET AL., 1993) ................................................................................. 24
FIGURE 2.6 FLOW REGIME IN STRAIGHT WALL 2 DIMENSIONAL DIFFUSERS ......................... 26
FIGURE 2.7 LOSS MAP OF A DIFFUSER (J APIKSE, 1984) ....................................................... 27
FIGURE 2.8 CONTOURS OF TOTAL PRESSURE LOSS COEFFICIENT ......................................... 29
FIGURE 2.9 CONTOURS OF Loss OF STAGE EFFICIENCY PER UNIT WORK COEFFICIENT ......... 29
FIGURE 2.10 PERFORMANCE OF THE VANED DIFFUSERS (YOSHINAGA ET AL., 1980) .......... 30
FIGURE 2.1 1 AN EXAMPLE OF THE SEPARATED FLOW IN A 2-D DIFFUSER ........................... 31
FIGURE 2.12 INDUCER STALL DUE To HIGH INCIDENCE ....................................................... 32
FIGURE 2.13 CRITICAL CONDmONS OF INDUCER STALL (SENOO ET AL., 1979) .................. 33
FIGURE 2.14 SEQUENCE OF PASSAGE STALL IN A SINGLE PASSAGE, UNSHROUDED IMPELLER
(LENNEMANN ET AL., 1970) ....................................................................................... 35
FIGURE 2.15 CRITICAL INLET FLOW ANGLE WITH DIFFUSER WIDTH (VAN DEN
BRAEMBUSSCHE ET AL., 1980) ................................................................................... 38
FIGURE 2.16 COMPARISON OF PRESSURE DISTRIBUTIONS (SENOO ET AL., 1983) ................ 41
FIGURE 2.17 MAXIMUM SOLIDITY ...................................................................................... 47
FIGURE 3.1 COMPRESSOR TEST STAND ............................................................................... 48
FIGURE 3.2 CENTRIFUGAL COMPRESSOR IMPELLER ............................................................ 49
FIGURE 3.3 LSVD GEOMETRY NOTATION ........................................................................... 51
FIGURE 3.4 MEASUREMENT PLANES IN INLE'I‘ PIPE .............................................................. 52
FIGURE 3.5 MEASUREMENT LOCATIONS ............................................................................. 53
FIGURE 3.6 UNSTEADY FLOW SIGNAL PATH ........................................................................ 68
FIGURE 4.1 PERFORMANCE CHARACTERISTICS OF THE STAGE AT MU=1.02 ........................ 76
FIGURE 4.2 PERFORMANCE CHARACTERISTICS OF THE STAGE AT MU=O.88 ........................ 77
FIGURE 4.3 PERFORMANCE CHARACTERISTICS OF THE STAGE AT MU=O.69 ........................ 78
FIGURE 4.4 EFFECT OF SOLIDITY ON THE PERFORMANCE .................................................... 80
FIGURE 4.5 EFFECT OF VANE NUMBER ON THE PERFORMANCE ............................................ 83
FIGURE 4.6 EFFECT OF TURNING ANGLE ............................................................................. 85
FIGURE 4.7 PRESSURE RISE IN THE STAGE WITH THE LOW SOLIDITY VANED DIFFUSER ........ 87
FIGURE 4.8 DIFFUSER PRESSURE RECOVERY (CP25) AT MU=1.02 ........................................ 90
FIGURE 4.9 DIFFUSER PRESSURE RECOVERY (CP25) AT MU=O.88 ........................................ 91

FIGURE 4.10 DIFFUSER PRESSURE RECOVERY (CP25) AT MU=0.69 ...................................... 92

FIGURE 4.1 1 SUBDIVIDED PRESSURE RECOVERY IN THE DIFFUSERS AT MU=1.02 ................ 94
FIGURE 4.12 SUBDIVIDED PRESSURE RECOVERY IN THE DIFFUSERS AT MU=0.88 ................ 95
FIGURE 4.13 SUBDIVIDED PRESSURE RECOVERY IN THE DIFFUSERS AT MU=0.69 ................ 96
FIGURE 5.1 POWER SPECTRUM OF THE STAGE WITH THE VNL2 ........................................ 103
FIGURE 5.2 POWER SPECTRUM OF THE STAGE WITH THE VNL1 ........................................ 104
FIGURE 5.3 POWER SPECTRUM OF THE STAGE WITH THE CVND ....................................... 105
FIGURE 5.4 POWER SPECTRUM OF THE STAGE WITH THE LSVD5 ...................................... 106
FIGURE 5.5 POWER SPECTRUM OF THE STAGE WITH THE LSVD6 ...................................... 107
FIGURE 5.6 POWER SPECTRUM OF THE STAGE WITH THE LSVD7 ...................................... 108
FIGURE 5.7 POWER SPECTRUM OF THE STAGE WITH THE LSVD8 ...................................... 109
FIGURE 5.8 TEMPERATURES IN THE DIFFUSER ................................................................... 1 10
FIGURE 6.1 COMPUTATIONAL MESH OF LSVD5 (105 X 50 x 17) ..................................... 1 17
FIGURE 6.2 PRESSURE RATIO CURVES OF THE STAGE WITH THE FLOWS USED FOR THE
NUMERICAL CALCULATION ....................................................................................... 118
FIGURE 6.3 PRESSURE RISE IN THE STAGE WITH THE LSVD5 ............................................ 1 19
FIGURE 6.4 GEOMETRY OF THE LSVD5 ........................................................................... 1 19
FIGURE 6.5 PRESSURE DISTRIBUTION AT DESIGN FLOW & MU=0.69 ................................. 126
FIGURE 6.6 PRESSURE DISTRIBUTION AT NEAR SURGE FLOW & MU=0.69 ......................... 127
FIGURE 6.7 PRESSURE DISTRIBUTION AT NEAR CHOKE FLOW & MU=0.69 ......................... 128
FIGURE 6.8 FLOW PATTERN AT DESIGN FLOW & MU=0.69 ................................................ 129
FIGURE 6.9 FLOW PATTERN AT NEAR SURGE FLOW & MU=0.69 ........................................ 130
FIGURE 6.10 FLOW PATTERN AT NEAR CHOKE FLOW & MU=0.69 ..................................... 131
FIGURE 6.1 1 FLOW FROM LEADING EDGE PATTERN AT DESIGN FLow & MU=0.69 ............ 132
FIGURE 6.12 FLOW FROM LEADING EDGE AT NEAR SURGE FLOW & MU=0.69 ................... 133
FIGURE 6.13 FLOW FROM LEADING EDGE AT NEAR CHOKE FLOW & MU=0.69 ................... 134
FIGURE 6.14 LSVD5+2FORNEARCHOKE mow AT MU=0.69 ........................................... 135
FIGURE 6.15 LSVD5+2 FOR NEAR SURGE FLOW AT MU=0.69 ............................................ 136
FIGURE 6.16 LSVD52 FOR NEAR CHOKE FLOW AT MU=0.69 ............................................ 137
FIGURE 6.17 LSVD52 FOR NEAR SURGE FLOW AT MU=0.69 ............................................. 138
FIGURE 6.18 THE FIRST DIFFUSER EFFICIENCY .................................................................. 139
FIGURE 6.19 THE SECOND DIFFUSER EFFICIENCY .............................................................. 139
FIGURE A.1 H-s DIAGRAM IN A DIFFUSER .......................................................................... 144

xi

NOMENCLATURE

passage width from hub to shroud
absolute velocity

specific heat at constant pressure

pressure recovery pr = (P6 - P, )/ [é- plU§ l
/

conventional vaned diffuser
incidence angle

low solidity vaned diffuser
Mach number

impeller tip Mach number
pressure, pitch

pressure side

radius

suction side

pitch

temperature

impeller tip speed

vaneless diffuser

vane number

axial coordinate

flow angle with respect to tangent

vane angle with respect to tangent

 

M 2
inlet flow coefficient ¢ = ’h/[PIUz 42 1
/

ratio of specific heats

efficiency 775 = fiI-Thm 5 ((50,145 V" ‘ IJ/(Tma _ 1)

h06 01

xii

Subscripts

_cp(T06-T0,)

 

work coefficient

% U 22
pressure ratio 710.16 = 06 /P01
blade turning angle
density
temperature ratio 10,6 = 06 /T0,
solidity
loss coefficient 5 = (P03 — P06 )/(% plU 22)

head coefficient w = Ahoy Ayn/,2) a cme R0,”... )(”'4) — 110w;

total condition

stage inlet

impeller exit

impeller exit - measurement station

vane leading edge station based on LSVD
vane trailing edge station based on LSVD
diffuser exit

stage exit

compressor Stage

radial component

isentropic

total-to-total

total-to-static

circumferential component

axial corrtponent

xiii

 

 

 

1. INTRODUCTION

1.1. Centrifugal Compressors and Demands on Them

A turbomachine is a device which adds energy to a fluid (pump, compressor) or
extracts energy out of it (turbine) by means of fast-moving blade. In the cylindrical
coordinate system, the energy transfer through turbomachinery is governed by the rate of
change of the angular momentum (UCu). The function of turbomachinery involves the
exchange of significant levels of kinetic energy. Among turbomachinery, a pump uses

liquids for a working fluid, while a compressor uses gases. For a compressor, three

 

 

 

 

 

 

 

 

Figure 1.1 Components of centrifugal compressor

different terms (a fan, a blower, and a compressor) may be used depending on the
pressure ratio or the pressure rise achieved. Furthermore, depending on the discharge flow
direction, a compressor can be classified as axial, centrifugal (or radial), or mixed flow.

The centrifugal compressor, shown in Figure 1.1, is made up from four basic
components: (1) a stationary inlet casing, (2) a rotating impeller, (3) a stationary diffuser
of the vaneless or vaned type, and (4) the collector or volute.

The contribution of each component of the compressor is Shown in Figure 1.2.
The fluid is drawn in through the inlet easing into the eye of the impeller parallel to the
axis of rotation. In order to add angular momentum, the impeller whirls the fluid
outwards and turns it into a direction perpendicular to the rotation axis. As a result, the
energy level is increased, resulting in both higher pressure and velocity. The purpose of
the following diffuser is to convert some of the kinetic energy of the fluid into static

pressure. Outside the diffuser is a scroll or volute whose function is to collect the flow

 

 

 

 

 

 

 

 

 

 

P
4* 02 m 05 /P05
P5
5
s / c
Q P.
55 058 4
III / p
58 J 2
/ 2
4s
/
{3 PM
00‘
P, I c ,2/2
1
‘13 I I
I o I
I
I I -: 8 i
Iniet : l r. 3' Diffuser .
casing. Impeller I g 0 Lebannci I _

 

 

 

Entropy

 

 

 

Figure 1.2 h-s diagram for the centrifugal compressor stage

from the diffuser and deliver it to the discharge pipe. It is possible to gain a further
deceleration and thereby an additional pressure rise.

Because of the advantages of higher-single stage pressure ratio and the wider
stable operating range over axial compressors the centrifugal compressor has been widely
used. Centrifugal compressors are found in small gas turbine engines, turbochargers, and
refrigeration systems, and are used extensively in the petrochemical and process industry.
The other advantages of centrifugal compressors are that they are reliable, compact, and
robust; have better resistance to foreign objects; and are less affected by performance
degradation due to fouling.

This wide range of demands on centrifugal compressors brings many design
considerations. Most of the design requirements need solutions to two major problems:
stress and aerodynamics. The stress problems are caused by the material strength
limitations and the capability to accurately predict blade and impeller steady state and
vibrational stress for complex impeller Shapes and at high rotational speeds. The
aerodynamic problem is to efficiently accomplish large air deflections and diffusion at
high flow velocity, with the added difficulty of very small passage flow areas required to
get good efficiency and high pressure ratio. Even though the individual components of the
compressor are capable of achieving high efficiency, it is the efficiency of the whole stage
that is of great importance. Thus, component matching is an essential aspect of design. It
is often required to redesign one or more components of the compressor due to improper
matching and sometimes the efficiency of a component is sacrificed to achieve good

matching.

1.2. The Impeller

The impeller is the rotating component of the centrifugal compressor stage, where

energy transfer of the compressor stage occurs.

AhoC=h05-ho, =h02—ho, (1-1)
The specific energy transfer can be derived from the velocity triangle at inlet and
outlet from the impeller (Figure 1.3). The rate of change of angular momentum will equal
the sum of the moments of the external forces, TQ. When applied angular momentum

theorem to an impeller, the torque, TQ, is given by

romance —r.C..> (1-2)
The energy transfer is given by the product of angular velocity and the torque,

given by the Euler equation

mAhOC = —W= wTQ= Mug", —U,Cu,) (1-3)

Applying the law of trigonometry to the velocity triangles of exit and inlet of the

 

 

 

 

 

 

 

 

 

 

 

impeller yields
02 U2=or2
C .
l
W 3,. int/,2 flb>90°(Forwarti—curved)
1 fia=90°(Radiai)
R. 52690" (Backward-curved)
CW2
Figure 1.3 Velocity triangles for an idealized Figure 1.1 Effect of the impeller exit
impeller blade angle

 

U2Cu2 =%(U22+C22-W:2) (1'4)

UlCui = ”(U12 +(:12 -W12) (1'5)

Combining (1-3), (1-4), and (1-5) results in the enthalpy rise in terms of velocity

relations

Ah... =%l<U§ —UE)+(W,2 —W§)+(C§ —CE)J (1-6)
The sum of the first and the second terms on the right hand side represents the
increase in Static pressure and the kinetic energy increase is Shown in the last term. In an
axial compressor machine, there is no impeller tip speed variation (U 2 = U , =constant)

explaining a higher enthalpy rise in a radial compressor.
If we neglect inlet angular momentum, which is generally acceptable, the

theoretical enthalpy reduces to

Ahoc =—=U2Cu2 (1'7)

Then the effect of impeller exit blade angle, [32b on the theoretical enthalpy rise

becomes
W C
T=U22(1-—'z'cotflzb) (1'3)
m U2

For a given value of impeller exit blade angle, [32b there is a linear relationship

between specific energy transfer and flow rate (Figure 1.1). Theoretical enthalpy of

impeller backward-curved blades decreases as the flow rate increases while that of

impeller with the radial blades remains constant The positive-slope condition can be
unstable and cause surge. For this reason a backward-curved blade impeller is generally

preferred.

1.3. The Radial Diffuser

Diffusion occurs where velocity reduction occurs. Velocity is a vector quantity
having both magnitude and direction. In other words, diffusion can occur on an isolated
surface or in a duct.

In centrifugal compressors, energy is transferred to the fluid by the impeller. Even
though centrifugal impellers are designed for good diffusion within the blade passage,
approximately half of the energy imparted to the fluid remains as kinetic energy at the
impeller exit. Therefore, for an efficient centrifugal stage, this kinetic energy must be
efficiently converted into the static pressure. Thus, a diffuser, which is stationary and is
located downstream of the impeller, is a very important component in a centrifugal
compressor.

Since over the years the demands on the centrifugal compressors increased for
higher pressure ratios and efficiency, different types of radial diffusers have been
developed. These different types of radial diffusers can be classified as the vaneless

diffusers, the vaned diffusers, and the low solidity vaned diffusers.

1.3.1. Vaneless Diffusers

Vaneless diffusers consist of two radial walls that may be parallel, diverging, or

converging. The flow entering a vaneless diffuser has a large amount of swirl; the swirl

angle (a = tan‘l (C, /C,)) is typically between 10° - 30°. Thus, the tangential component
of momentum at low flow rates can be more than twice the radial component. The radial
component of the flow diffuses due to the area increase (conservation of mass), and the
tangential component diffuses inversely proportional to the radius (conservation of
angular momentum). However, the radial component has to surmount the radial pressure
gradient for the tangential component to diffuse continuously. When reverse flow of the
radial boundary layer occurs, it is not possible for the tangential component to continue
diffusing, as this would imply a pressure increase in one component and not in the other.
Therefore, in such cases the breakdown of flow occurs, and this can cause the diffuser to
stall and produce other flow instabilities such as surge or stall. However, backflow into
the impeller is less frequent with vaneless diffusers than with vaned diffusers where local
pressure disturbs caused by vane pressure loading.

The vaneisess diffuser is widely used in automotive turbochargers because of the
broad Operating range it Offers. It is also cheaper to manufacture and more tolerant to
erosion and fouling than the vaned diffusers. However, the vaneless diffuser needs a large
diameter ratio because of its low diffusion ratio. The flow in a vaneless diffuser follows
an approximate logarithmic Spiral path. The flow in a vaneless diffuser with a radius ratio
of 2 and an inlet flow angle of 6° makes a full revolution before leaving the diffuser. This
will result in high friction loss due to viscous drag on the walls and accordingly its
pressure recovery is significantly lower than is found with vaned diffusers.

Generally the vaneless diffuser demonstrates lower pressure recovery by as much

as 20% and lower stage efficiency by 10% compared to a vaned diffuser.

1.3.2. Vaned Diffusers

The role of the vane in a vaned diffuser is to shorten the flow path by deswirling
the flow, allowing a smaller outlet diameter to be used. A vaneless space precedes the
vaned diffuser to help reduce flow unsteadiness and Mach number at the leading edge of
the vanes so as to avoid shock waves. Boundary layer develops and generates appreciable
blockage at the vane leading edge. In order to reduce this blockage, the vaneless space
should be minimized until it doesn’t give any unfavorable effects such as increase in
noise level or pressure fluctuations due to interaction of the impeller and diffuser. The
flow exiting the impeller follows an approximate logarithmic Spiral path to the vane
leading edge and is guided by the diffuser channels. The semi-vaneless space follows the
vaneless space, ending in a passage throat, which may limit the maximum flow rate in a
compressor. The number of diffuser vanes has a direct bearing on the efficiency. With
large number of vanes, the angle of divergence is smaller and the efficiency rises until
friction and blockage overcomes the advantage of more gradual diffusion.

Although the vaned diffuser typically exhibits higher pressure recovery, the flow
range is limited at low flow rate due to vane stall. At high flow rates, flow choking at the
throat may also limit flow range.

The major feature of the low solidity vaned diffuser is the absence of a geometric
throat which limits flow range of the centrifugal compressor with the vaned diffusers. The
low solidity vaned diffusers exhibit high efficiency comparable to conventional vaned
diffusers, while holding flow range levels approaching that of vaneless diffusers.

In order to show the variety of vaned diffusers with respect to vane shape,

different types of vaned diffuser are listed and described in Figure 1.5.

 

 

 

 

(a) Straight channel
diffuser

 

 

 

 

 

 

 

. . . (i) Low solidity vaned
(h) Pipe / conical diffuser diffuser

(9) Multiple cascade
diffuser

 

 

 

Figure 1.5 Types of vaned diffusers

 

0 Straight Channel / Wedge Diffuser

The simple geometry of this kind of diffuser enables an easy manufacturing

process; and, thus, it is one of the most popular types. Nevertheless, it is large in size.

. Vane Island Diffuser

The vane island diffuser is basically a refined straight channel diffuser used for
high pressure ratios and transonic inlet Mach numbers. It is also large in size, but the
number of vanes is very small. To improve the flow conditions, the inlet is curved at the

suction side. In total, this leads to a good pressure recovery.

0 Straight Plate Diffuser
Typically, the straight plate diffuser has a large number of vanes(Z>30), and the

pressure recovery is not very good. Its merit is rather cheap manufacturing process due to
the simple geometry. A chamfered pressure side leading edge might be used to improve

incidence matching in the severe initial diffusion rate.

0 Circular Arc Diffuser

Since the geometry is simple and the ends of the vanes are not profiled except a
sharpening, the circular arc diffuser can be manufactured easily. It doesnT Show any

outstanding aerodynamic characteristic.

. Cambered Airfoil Diffuser

The cambered airfoil diffuser, which is used for both transonic and subsonic flow,

is often designed on the base of data from axial cascades.

10

0 Twisted Diffuser

The peculiarity of the refined cambered vanes is their 3-dimensional twisted Shape
that matches to the flow. A good efficiency, a wide range and a high pressure recovery are

obtained.

0 Multiple Cascade Diffuser

As the manufacturing process grows with additional cascades, cambered vanes are
usually chosen to reduce the expenses. The advantages are a higher efficiency and a

reduced risk of separation due to the higher number of vanes at the increased radii.

. Pipe / Conical Diffuser

The pipe diffuser is used for higher pressure ratios and transonic applications. The
pressure recovery is good compared to the channel diffuser. The circular cross section of
the drillings is considered to allow these diffusers to swallow a highly non-uniform flow
much better than the 2-dimensioanl cascade type. Also it is economic because of Simple

geometry definition and easy manufacturing process required.

0 Low Solidity Vaned Diffuser

This diffuser is often used for low flow coefficient compressors and gains a good

pressure recovery in combination with a wide operation range.

1.4. Objective of the Present Work

One of the critical problems in the design of the centrifugal compressor is the

diffusion of a high level of kinetic energy entering the radial diffuser. An adverse pressure

11

gradient thickens the boundary layer at the wall resulting in flow separation if the

pressure gradient becomes excessive.
A centrifugal compressor stage can have an overall efficiency as high as 85i 2%

in the pressure ratio range of 2 to 6. For such a compressor, if operating at favorable
condition, the diffuser efficiency can be about 75 to 85%, While the impeller efficiency
can be above 90%, which is a remarkably high value in view of the large energy added. It
compares well with the best transonic and supersonic axial compressor rotors that add
much lower energy per stage. However, at off-design flows the diffuser efficiency drops
rapidly While the impeller efficiency remains almost constant.

The high impeller performance has been achieved within the confines of
mechanical limitations that permit very little variation in the blade or rotor design. Thus,
it can be said that improvement in radial impeller efficiency can only be incremental and
will require a very significant amount of development effort.

Therefore diffuser improvement offers a more promising approach to better
compressor performance than does the impeller. Moreover, a diffuser is much less
restricted by the mechanical limitations when compared to the impeller of a centrifugal
compressor. If the radial diffuser efficiency of 85 to 90% can be attained, an improvement
of 4 to 5 percentage points in overall efficiency of the centrifugal compressor can be
achieved.

It has been possible to obtain high diffuser efficiency (up to 85%) with the help of
specifically designed vaned diffusers. But the major disadvantage of the vaned diffusers
is that they limit the range of operation of the compressor. In this work the vaned diffuser

design has been studied in detail with a View to understand all the parameters that help in

12

attaining high efficiency. At the same time to identify the parameters, which restrict the
flow range of the compressor as wide flow, range is very important for most compressor
applications.

It is well known that the low solidity vaned diffusers have significant advantage
over both the vaneless and the conventional vaned diffusers because they are able to
attain efficiency competitive with vaned diffusers and an operating range approaching
that of vaneless diffusers. Interest has recently increased in the use of low solidity vaned
diffusers for industrial centrifugal compressors. The compressor industry has been
designing and testing the low solidity vaned diffusers over the last sixteen years.
Nonetheless, the important design parameters and their effects on performance are not
well established. For this reason, continued research is required to establish better design
procedures and to better define the range of applications.

In this work, the low solidity vaned diffusers were designed, manufactured,
experimentally tested and analyzed numerically using 3-D viscous Navier-Stokes code to
understand the influence of vital aerodynamic and geometric parameters on the flow
phenomena.

The four new low solidity vaned diffusers along with one conventional vaned
diffuser and two vaneless diffusers were tested downstream of the same impeller at
Michigan State University’s Turbomachinery Laboratory.

This work contains the results of those tests. The overall Steady performance of
the compressor with the different diffusers was compared with the results obtained by 3-

D viscous Navier-Stokes code simulation. The influence of the geometric design

13

parameters on the flow was investigated through numerical simulation. Besides steady

performance analysis, unsteady performance analysis has been carried out.

The main objective of this work is to contribute to the design methodology and

performance assessment of low solidity vaned diffuser by:

Designing and testing four LSVDS,

Understanding their steady and unsteady performance,

Numerically validating the experimental data,

Determining the influence and effect of both the geometric and aerodynamic
parameters of LSVD on its performance,

Numerically predicting the influence and effect of both the geometric and
aerodynamic parameters of the LSVD on its performance for configurations

where experimental testing was not performed.

14

2. THE CENTRIFUGAL COMPRESSOR

2.1. Steady Flow of a Centrifugal Compressor

2.1.1. Flow Between Impeller and Diffuser

Centrifugal compressor stage optimization requires a proper impeller/diffuser
matching, as this has considerable influence on the efficiency and stability of the stage.
For a good stage performance, the efficiency of the impeller and the diffuser are of equal
importance. However, the efficiencies of both these components are interdependent due
to the impeller/diffuser interaction.

The impeller flow is strongly affected by three-dimensional boundary layers,

 

A .g
I

Separated flow
(wake)

 

 

 

 

U

Figure 2.1 J et-Wake flow pattern of impeller discharging flow

 

 

15

 

secondary flows, and flow separation. Thus, the flow discharged from the impeller is
mostly often highly non-uniform with significant three-dimensional velocity components
exhibiting jet/wake flow pattern. Jet/wake flow patterns are generated by Coriolis force,
curvature, boundary layer, and tip clearance effects that separate the flow into high (jet)
and low (wake) velocity fluid. Turning of the flow from axial to radial direction generates
secondary flow, which drives low momentum fluid to the shroud. Once the flow has
separated on the suction side the separated flow region in the meridional plane rapidly
grows toward the hub surface. The pressure gradient from pressure Side to suction side
(blade-to-blade) also influences the secondary flow driving low momentum fluid toward
the suction side.

The diffuser pressure recovery is largely affected by the highly distorted, unsteady
impeller discharge flow. On the other hand, the diffuser vanes are believed to act on the
internal three-dimensional impeller flows. The non-uniform flow from the impeller is
sensed as an unsteady flow by the vaned diffuser vanes, while the presence of diffuser
vanes is seen as an unsteady disturbance by the impeller. Moreover, this interaction
between the impeller and diffuser vanes is a strong source of noise and vibrational
excitation.

The interaction between the impeller and diffuser flow is one of the critical
problems in design of highly loaded centrifugal compressors. The diffuser has to remove
these non-uniformities in velocity and flow direction so as to efficiently recover the static
pressure.

Many investigators have studied the jet/wake flow behavior at the impeller exit, in

order to understand the various effects contributing to this kind of flow. And also many

16

investigations have been carried out on the interaction of the impeller and the diffuser
vanes on the impeller discharge flow how jet and wake mix in the vaneless space or
diffuser downstream of the impeller.

Eckardt (1975) performed detailed measurements in the impeller discharge
mixing zone for a radial type impeller running at tip speed of 300m/s by high frequency
measuring system. From the measured relative velocity distribution behind the impeller
(Figure 2.2) he showed a region with high radial flow component near the pressure side
having relatively stable flow and low total pressure losses and a region near suction
side/shroud comer with low mass flow, high turbulence and losses. Thus, he showed the
jet-wake flow exiting the impeller. Similar measurements in the vaneless space following
the impeller up to a radius ratio of r/r2=1.089 showed that the jet and wake have not

mixed completely and the flow is not axisymmetric.

 

m ’ ‘«\
\\\li)

 

 

 

PS

 

 

 

 

 

Figure 2.2 An example of measured jet/wake flow at the exit of impeller (Eckardt,
1975)

17

Baghdadi (1977) studied the effect of impeller blade wakes on the performance of
the vaned diffuser by using a vortex rig. The vortex rig could produce only the axial
distortions in the flow at diffuser inlet. Thus, he could compare the results of vortex rig
with the results of an actual compressor to examine the effect of impeller blade wakes. He
found close agreement in the performance of the vaned diffusers used with the vortex rig
and the actual compressor. Therefore, he concluded that the impeller blade wakes do not
significantly affect diffuser performance. The reason for this could be that the blade
wakes mix very rapidly by energy transfer or due to the lack of response of the diffuser
vanes to the high frequency flow variations imposed by the rotating wakes.

Johnson and Moore (1980, 1982, 1983), using a ghost impeller Similar to the
Eckardt’s impeller, measured the three mutually perpendicular velocity components and
rotary stagnation pressure to study the wake formation and development. They found that
the wake flow was an accumulation of low rotary stagnation pressure fluid at the suction
side/shroud comer of the impeller blade passage and that the turbulent mixing associated
with the shroud boundary layer separation and the strength of the secondary flow strongly
influence the size and location of the wake, respectively. The major flow phenomena
contributing to the formation and development of the wake were:

(a) The adverse static pressure gradient between the inlet and the exit of the axial
to radial bend in the impeller near the shroud/suction side comer, which results in a
substantial increase in low stagnation pressure fluid at the inlet region of the bend, and

(b) The convection of low stagnation pressure fluid by the secondary flows, which
are generated in the boundary layer due to the curvature and rotation of the impeller

passage.

18

They also showed that the mass flow rate had an influence on the location of the
wake at the impeller outlet; the wake was located on the suction surface for below design
flows, near the suction surface/shroud comer at design flow and on the shroud at above
design flows. Since the secondary flows are a function of mass flow rate, they Showed
that the secondary flows in the impeller passage contribute to the formation of the wake
and that they also have strong influence on the position of the wake at the impeller exit
plane.

Krain (1981) performed L2F measurements both inside the impeller (near the exit)
and in the diffuser with a vaneless and a vaned diffuser downstream of the impeller. The
diffuser blades have a slight effect on the velocity profiles at the shroud, whereas the
velocity patterns at the hub region were Similar with both diffusers. The small effect of
the diffuser vanes on the impeller flow was presumed to be due to high vane leading edge
to impeller exit radius ratio of 1.1. However, the measurements in the vaneless space of
the vaned diffuser showed unsteady flow angle variations of up to 17°, and up to 13° in
the diffuser throat region. Thus, there does not exist any station ahead of the diffuser
throat where flow is fully mixed out.

Krain (1988) studied the flow behavior in three different types of centrifugal
impellers. The impellers tested were (a) radially ending Eckardt impeller, (b) radially
ending splitter blade impeller (14 + 14 blades) and (c) new backswept impeller. He
concluded that the secondary flows and distorted throughflows found in all three
impellers were caused by the swirling impeller flow inside the impeller. Moreover, he

found that the vortex flow had influence on the throughflow patterns, thus, it was

19

 

 

 

 

 

I I l
I
I l I
, . : i .
I! I i '
1 I l
M ’ i l I '
cm: I, ’l
l o o
.. i ' / /
' I T 0.5 m
0.3
o 7 7 0.1
0 0.1 0.3 0.5 0.7 0.. 1 .0
P.

(a) radially ending Eckardt impeller

 

 

 

 

 

 

leuz

 

 

 

 

0 vs
(C) backswept impeller

Figure 2.3 Comparison of impeller discharge velocity (Krain, 1988)

impossible to avoid distorted impeller discharge flow, unless the flow development is

guided in such a way that the vortex flow fully disappeared at the impeller discharge.

20

Fisher and Inoue (1981) found that the vaned diffuser played a major role in
establishing the circumferential variations in the mean flow conditions at the impeller
exit. They observed that by increasing the blade angle, the circumferential variations
increased. However, an increase in the number of diffuser vanes decreased the variation
of the flow conditions in the circumferential direction. They also found that the vane
setting radius had a major effect on the flow conditions. Figure 2.4 shows the velocity
variation in circumferential direction for two different radial clearances between impeller
tip and diffuser vanes (4% and 10% of r2).

Inoue and Cumpsty (1984) carried out hot-Wire measurements in the vaneless
space between the impeller and vaned diffuser at a range of flow coefficients for three
different diffusers with 10, 20, and 30 vanes set at each of three different radius ratios,
1.04, 1.1, and 1.2. It was found that the circumferential distortion of flow from the
impeller was very rapidly attenuated in the entrance region of the diffuser vanes and had
only minor effects on the flow inside the vaned diffuser passages. The effect of the
diffuser vanes on the flow discharge from the impeller was evident and reversal of the
flow back into the impeller was detected when the diffuser vanes were close to the
impeller and flow rate was low. The time mean total and static pressure at impeller outlet
were found to vary over the pitch of a diffuser vane, and a variation in the strength of
impeller wake was also observed. Inoue and Cumpsty (1984) in their work show that the
angular velocity profile did not vary as significantly as the radial velocity across the span
with radius. They also found that the circumferential distortions of the radial velocity in

vaneless diffuser did not disappear even at r/r2=1.3. However, the distortion patterns of

21

tangential velocity decreased rapidly with radius, which can be attributed to the energy

transfer between jet and wake regions.

 

 

 

 

 

 

 

 

 

 

 

9° 1
0
1.3
' __°_ EXPERWENTI
1 —PREDICTION " "2
o . 1.1
1 V
. .. 0.9
0.0
10 o 10 2° 3° ‘0
0
(a) r3/r2=1.04
90 J
|
304
“m2 707?“.77" O~ ._
I.» | ‘H\"“-\o A
: ~-EQ, __ ‘7‘” _.___.———- '7’.
m; 1.3
1 1r 0 EXPERIMENT .
l I I
1 y PREDICTION f ‘ "2
1 4. 1.1
O
* , O
i V o r 1
} o o o 0 ° V
i _ o 1° 0
F . 0.9
i
0.3
10 0 10 20 3° ‘0

e
(b) r3/r2=1.10

Figure 2.4 Traverse at diffuser inlet (Fisher et al., 1981)

22

Hathaway et al. (1993) studied flow field of the NASA low speed centrifugal
compressor impeller using laser anemometry and 3D Viscous code (Dawes code) in order
to understand a detailed primary and secondary flow development within an unshrouded
centrifugal compressor impeller. The results obtained by them were very similar to those
of the Krain and others. In addition to this they also showed that 3D viscous code results
were in good agreement with the experimental results. They also compared their results
with the results of the Krain’s impellers and found good agreement. They found that the
low-momentum fluid near the blade surfaces migrates outward toward the blade tip. The
fluid that moves up the blade pressure and suction surfaces is entrained into the tip
clearance jet and the fluid is transported toward the pressure side/Shroud corner of the
characteristic throughflow momentum wake that is found in unshrouded centrifugal
impellers. They also studied the impeller wake mixing phenomenon downstream of
centrifugal impeller. They measured absolute flow angles at four different locations up to
a r/rz of 1.065 and found that the throughflow momentum wake region generated as a
result of tip clearance flow mixes out more slowly than does the viscous blade wake as
the flow moves through the vaneless diffuser. This was concluded from the pitchwise
absolute flow angle distribution study at 50% span and 90% span as shown in Figure 2.5.
Thus, the flow field in the vaneless space near the shroud surface is composed of low
momentum regions of the viscous blade wake and the throughflow momentum wake.

Pinarbasi and Johnson (1994) also showed very similar results through hot Wire
anemometer measurements at numerous radius locations in the vaneless diffuser

downstream of a backswept impeller.

23

    

. was-911"-” "'

fi‘fimim deg'

 

 

 

a. .. - .. - I .019 , L
0 I‘ 'I
‘O 20 II .......... 1.037 2" t
5;: i; — i .065 IE .
“£- 15 II'. it: ’
$- .1! ~ “I. PS ..\ l’
10 i 9: ' °‘. 58 I i (I. ..“~ it
I If” '..\\ l I ’ \

a. I ". . . r
. '.. ° 0” 0.. ..'\
I ’ .' ‘0 ,° 0
P‘ ' , 0 \ . a‘. 0’ o. ‘ 5
0 IF'}°I"°' \\ a" "'2 'I". ‘
o A ‘ ‘ '

 

 

T . - ‘ '0 ICC
«.100 -—50 o 5
(b) At 90% span .- -
Figure 2.5 Pitchwise distribution of absolute flow angle difference at impeller exit
(Hathaway et al., 1993)

24

Thus, the flow received by any diffuser downstream of a centrifugal compressor is
very non-uniform and contains jet and wake flow patterns caused by the secondary flows
inside the impeller blade passage. In the vaneless space downstream of the impeller, the
dynamic variations and the flow distortions in the circumferential direction tend to mix
out in Short radial distance. However, the passage wakes and the flow variations in the

axial direction across the Span tend to persist through out the vaneless diffuser.

2.1.2. Diffuser Design Parameters

The performance of turbomachinery is dominated by diffusion. In most centrifugal
compressors both the impeller and the diffuser are limited by the diffusion capabilities of
the flow channels. The kinetic energy at the diffuser inlet easily amounts to 50 % of the
total energy added by the impeller. An efficient transformation of this energy into
pressure is therefore an important part of compressor design. A large part of aerodynamic
losses in turbomachines is due to local or general areas of boundary layer separation
resulting from local or general degree of diffusion that is too large for the boundary layer
to overcome the unfavorable pressure gradient.

There are different groups of diffusers one can use to achieve an appropriate

pressure rise.

2.1.2.1. 2-Dimensional Simple Diffusers

Kline et a]. (1959) have identified the significant flow regimes in straight-wall

two-dimensional diffusers with thin turbulent inlet boundary layers and completed

25

stability map. They found that maximum pressure recovery occurred when a condition of
transitory stall exists. From dimensional analysis, area ratio, divergence angle, inlet
Reynolds number, inlet Mach Number, aspect ratio, and inlet blockage are the parameters
affecting the diffuser performance (Figure 2.6).

Runstadler et a1. (1969) performed the similar experiments as Kline et a1. (1958)
and showed the diffuser performance as a function of inlet Mach number, aspect ratio and
blockage. They demonstrated that the Single most important parameter governing the

performance is the boundary layer blockage in the throat.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

: : Lll'léClF
W 29 ‘i’ W2
‘- XI
7|
1.5
1 2 3 4 6 810 20 4O 60
UVVI

 

Figure 2.6 Flow regime in straight wall 2 dimensional diffusers (Kline et al., 1959)

Figure 2.7 shows the losses in a typical diffusing element versus the pressure
recovery, which was developed using measured data for certain conical diffusers. The
impacts of aerodynamic blockage as well as area ratio on diffuser performance are Shown.

High diffuser effectiveness requires attention to many geometric parameters and a limited

26

level of aerodynamic blockage. If a diffuser effectiveness of 90% is to be achieved, the
inlet aerodynamic blockage should be under 3%. Pressure recoveries in actual

turbomachinery are frequently on the order of 0.5 to 0.7 at the best efficiency point.

 

 

 

 

lung:
1
K=C 1/ 1
08‘ p( 11' )
06* \\
3‘ 18°. —‘ "
04 15°. "“
2% """"" ~
I {'30 ’ "’ ..
,0 -s 9%
q,
02 - , 6%' ..
I? «of: 1 as ,
0336 =3
0 a . E
O 02 Q4 06 08 1

Q:

Figure 2.7 Loss map of a diffuser (J apikse, 1984)

27

2.1.2.2. Vaneless Diffusers

In the vaneless diffuser diffusion is caused by an increasing radius by two radial
walls. For an incompressible, inviscid fluid, the process of pressure recovery is described
by the following equations. This forms the well-known logarithmic spiral flow path

through the vaneless diffuser of constant depth (Ot=constant).

p-c,-2nrb=p-cu-2nrbtana=m (2-1)

cu - r = const (2-2)

However, for air, density varies with pressure and temperature and viscosity

exists. Considering these effects, the governing equations are as follow:

p-c, -27zrb=p-cu o27zrbtana=m (2-3)
d 2
E(rC,)(p2C,,2nr2b2) = 470‘ In (2-4)
p 2 dC, dP z,
_ __ _______ 2-
rC" pC’dr dr b (5)
I, =—c, 3CC,

2

where,

r, = -c, Rec,

2

The broader implications of the basic differential equations have been
summarized in several characteristic plots by Johnson et a1. (1965) as shown in Figure 2.8

and Figure 2.9. The primary independent parameters are inlet swirl ratio ( 11,. = Cu2 /C,2)

28

 

 

 

    

 

 

 

 

 

 

 

 

 

 

 

I T I I I I T T—T—I and 0' I ' ' ' :.::-
o: \ "v 1° 0.09 _ ’9 ‘l ‘0'. mean
D 0 CWnNT ' T v I
§ : 0.36 .. ill : ..
a 0.2 ..
S : I
E 1 m ‘ 3.0%- d
.5 0.1 _ I as
(’4‘- - a
- 9 o to I to
« ’ '3 \
Fl“. I
x, was «In. Pm ’0 an o c con—w“ I4 III
"7 m m.“
FIgure 2-3 Contours of total pressure Figure 2.9 Contours of loss of stage

loss coefficient efficiency per unit work coefficient

A A

and width parameter (A 2 Cf r2 / b2 ), where the wall friction coefficient is adjusted so that

the prediction agrees with the experimental results.

2.1.2.3. Vaned Diffusers

Semivaneless space between the leading edge and the diffuser vane throat is the
most important part of vaned diffusers because the inlet blockage factor is decided by it.

Yoshinaga et a1. (1980) tested 16 different vaned diffusers in a compressor rig and
compared with the data on the two-dimensional diffuser with the inlet blockage of 0.05.
These test results showed that the pressure recovery increases up to a critical diffusion
limit of 0.5 where diffusion ratio is defined as C4/C3.

Aungier (1988,1990) showed the systematic procedure for the design of vaned
diffuser from an evaluation of experimental data for 18 different diffuser design. He made
full use of blade loading to achieve maximum pressure recovery within the available
Space. Also he suggested a new linearized blade-to-blade flow analysis yielding accurate

predictions for so simple a method.

29

1.0

 

 

Cpi (INCOMPRESSIBLE)

 

 

 

 

 

 

 

 

 

a.
U
E A
g R
E
III A
K .
III R
E A
3 T
III I
E 0 '
_ VANELESS DIFFUSER
0.0 J A L
1.0 1.5 2.0 2-5 3.0

AREA RATIO W4NV3 LENGTH I WIDTH LIW

Figure 2.10 Performance of the vaned diffusers (Y oshinaga et al., 1980)

2.2. Instability of a Compressor Stage

Stability is defined with respect to the equilibrium operating condition in a
system, where it tends to return to its equilibrium operating condition, if the system
disturbed slightly. Beyond this point instability might happen locally with a component
called “stall” or totally in a system called “surge”.

Figure 2.11 is the numerically calculated flow in a 2—D channel diffuser which
shows separated flow region due to excessive diffusion. The streaklines from the diffuser
inlet are drawn in the upper part and the pressure contours lines and velocities are shown
in the lower part. Boundary layer develops rapidly and separates at both walls due to

excessive adverse pressure gradient. This condition is called as “diffuser stall”.

30

 

Figure 2.11 An example of the separated flow in a 2-D diffuser

2.2.1. Stall in a Compressor Component

In a diffusing flow, resulting from area change or flow curvature as in an airfoil,
there is a possibility that the flow at the wall is retarded so severely that it can no longer
follow the wall surface. The necessary energy to overcome this gradient is transmitted
from the main inviscid stream to the boundary layer by Viscous or turbulent stresses.
When the momentum in the boundary layer is insufficient to overcome this pressure
gradient, the flow will separate and local return flow will occur. From a macroscopic
point of View, this reorientation of the flow can have a steady characteristic (steady stall)
or can be an unsteady phenomenon in which separated and attached flow are alternating
(rotating stall). This last phenomenon is due to the fact that local flow separation

influences the surrounding flow field in such a way that other zones of separated flow are

31

created which in turn are influencing the initial separated zone. Stall can occur in the
inducer (due to incidence), impeller (jet and wake flow), vaneless diffuser (negative radial
velocity), vaned diffuser channels, and return channels.

The effect of secondary flow can cause flow separation leading to flow instability.
The instabilities in the compressor can be classified as the component stall, stage stall,

and system instability described as surge.

 

 

 

 

 

 

Figure 2.12 Inducer stall due to high incidence

2.2.1.1. Inducer Stall

Stall in the impeller can be due to unsteady phenomena in the inducer or in the
radial part of the impeller. When the inducer stalls, high energy fluid emerges from the
impeller to the inlet region. The reversed flow discharged from the impeller during
inducer stall has a significant impact on the velocity distribution at the inlet.

Mizuki et al. (1976) observed flow at a low flow rate in the inlet duct, the inducer,
the impeller channels, and along the shroud casing. This backflow was attributed to a

separated flow at the inducer inlet leading edge. Furthermore, they observed a three

32

dimensional eddy in the inducer channel that became Stronger toward the suction side as
well as at the shroud casing.

Senoo et al. (1979) investigated a supersonic centrifugal impeller. He was able to
associate all necessary phenomena to the impeller, because the compressor had no
diffuser so that the flow range was not limited by the diffuser. He suggested that the stall
point in the inducer be correlated to the incidence at the tip of inducer and to the
relationship between the relative velocity in front of the inducer and the relative velocity
in the inducer throat.

Kammer et al. (1982) reported that pressure fluctuations are non-periodic though

unsteady in nature in case of inducer stall.

 

 

ONE-DIMENSION AL OUASI-THREE DIMENSIONAL ANALYSIS

 

   
 

 

 

 

 

 

 

ANALYSIS 0 “9 9'93”"
preswiri angle '
9 0 ° 0 909 O

1.2 1 .. .10 m 0.8

'. A33 609

'3 n 45 dog

.. ‘
1 ‘ 0.6 A
g A | I: A A 0 on :
a; g n o a to o
.2. 3 o o
0.8 ~ 0.4. o 0
ONE DIMENSIONAL ANALYSIS
prsswiri angle
0 a 4 OUASI-THREE, a 02 g 22:29
' DIMENSIONAL 3.
ANALYSIS “3"”
0 deg preswirl n 45 deg
0.4 v . o e ,
0 s 10 15 20 0 0.2 0.4 0.0 0.0 I 1.2 1.4 1.0
I" “.11

Figure 2.13 Critical conditions of inducer stall (Senoo et al., 1979)

Karnmer et al. (1985) measured the subsequent backflow in terms of temperature,

pressure, and flow angle. When the inducer stalls, high energy flow moves back from the

33

impeller. This backflow has a large tangential flow component. The centrifugal force due
to this tangential flow component supports the separation of backflow and the main flow.
This causes an increase in temperature and pressure in the inducer. As stall is initiated,
the reversed flow at the tip blocks the inlet annulus; and the main flow is accelerated. In
addition, a tangential velocity is generated, and it produces prewhirl at the inlet. As mass
flow continues to be reduced, the axial velocity distribution becomes more distorted; and

the prewhirl affects the main flow.

2.2.1.2. Impeller Stall

During impeller rotating stall, pressure fluctuations occur throughout the entire
meridional extent of the blade channels.

Visual evidence of rotating stall in a centrifugal impeller passage was given by
Lennemann et al. (1970). They visualized the phenomena of rotating stall in the impeller
using hydrogen bubble technique.

Figure 2.14 shows the sequence of the unsteady motion triggered by pressure Side
separation in an unshrouded impeller, which is significantly different from that of the
shrouded impeller. The boundary layer separates on the blade pressure Side, and the
subsequent backflow is supported strongly by the relative eddy effect. The fluid is first
driven back along the blade pressure side and further upstream along the blade suction
side toward the passage entry. Here fluid moves out of the passage into the inducer. If,
due to the rotation, the passage flow conditions become more favorable, the passage flow

can recover and the motion is repeated. However, in the case of stall the flow is

34

separating at the pressure side, while the flow at a stable operation point separates at the

suction Side due to the jet/wake pattern.

 

 

 

 

 

Figure 2.14 Sequence of passage stall in a single passage, unshrouded impeller
(Lennemann et al., 1970)

Rodgers (1977) considered the relationship between the relative velocity at the
impeller exit and the relative velocity at the impeller inlet as a criterion for impeller stall.
He investigated stall criteria using twelve different backswept impellers and suggested a
modified diffusion factor taking the effect of meridoinal curvature into consideration. The

revised diffusion factor for an impeller with no prewhirl is defined as follows:

 

D,=1— +7t-r23u-u2+0.l.b 1+£1 (2-6)
z-s-wlm r WI

5 M

I

This factor is based on the diffusion factor for the axial compressor and extended
for centrifugal impellers. The third term takes the load for one single blade in
consideration and the fourth term accounts for the influence of curvature of the mean

streamline curvature.

35

Senoo et al. (1979) reported that the stall point of the impeller is determined by
the ratio between the relative velocity at the impeller exit to the relative velocity at the
impeller inlet, as Rodgers did. Such a correlation is only possible, if no backflow occurs
in the inducer.

Kiimmer et al. (1982) observed that the rotating stall in their configuration did not
always appear in a quasi-steady state. At high speeds, the compressor periodically ran into
rotating stall and recovered afterwards.

Fringe et a1. (1983) found that three operating modes that they called mild, abrupt,
and progressive stall. The propagation velocity of the patterns increased with reduction of
the flow rate for mild and abrupt stall. In their tests, the propagation velocity relative to
the impeller rotation speed was 25 — 35 %. Progressive impeller rotating stall due to flow
separation in the impeller shows typical propagation speed (50~80%) and moderate

velocity oscillation of 10%, where the stall cell number seems to remain constant.

2.2.1.3. Vaneless Diffuser Stall

Flow becomes more and more distorted axially in a vaneless diffuser with a small
flow rate and the distorted flow patterns rotate in the direction of the impeller rotation. It
is not like as the rotating stall in an impeller or a vaned diffuser.

One of the first studies on self-excited rotating pressure fluctuation was done by
Jansen (1964). He concluded that diffuser rotating stall will occur when there is local
return flow in the diffuser.

From momentum and continuity equations, he derived the linear form of

governing equation:

36

_1__8_V2¢+cota a

. 1 a
___V2 __V2 = -
war r 8r ¢+ ° ° (27)

r2 36

where 0 is a streamfunction and its simplest solution can be expressed as

¢ = W(r)ei(w,,t+ma) (2-8)
where \y(r) is the local amplitude. He showed in his calculation that even a potential flow

in a radial diffuser can become unstable and that the unsteady response of the vaneless
diffuser flow is triggered by viscous flow effects but is governed by the inviscid flow. He
suggested that the separation of the three-dimensional wall boundary layer trigger rotating
stall. This instability causes rotating pressure perturbations.

Senoo (1978,1979) calculated the flows in various vaneless diffusers including
boundary layer effects and more complex and likely boundary conditions. He related the
reverse flow to the inlet flow angle and diffuser width.

Van den Braembussche et a]. (1980) showed that Senoo’s prediction of critical
diffuser inlet flow angle agrees well with experimental data if a Reynolds number
correction is applied as shown in Figure 2.15.

Fringe et al. (1983) performed experimental investigation of the sub synchronous
rotating flow patterns in a centrifugal compressor with vaneless diffuser. He found
diffuser rotating stall due to a strong interaction between boundary layer and inviscid core
flow in the vaneless diffuser. Typical for this rotating stall is the low relative propagation

speed (c0,/Q<=0.2) and the moderate amplitude of the velocity fluctuations around 10%.

Abdelhamid (1980) proposed stability criterion based on linearized equation for
two-dimensional incompressible and frictionless flow assuming that the perturbations are

harmonic functions.

37

20

 

 

 

 

18 1
16 ‘ O
14 . . I- H
“fr/ff“-
o . , ’/
12 « 7' o '
O"/°
E I ,,.’//
ac 21° ,3
,"V' .
8 I O
o 0,... .
o
4 .
2 -1
o , - 7 . .
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
b2”:

Figure 2.15 Critical inlet flow angle with diffuser width (Van den Braembussche et
al., 1980)

2.2.1.4. Vaned Diffuser Stall

Stall in a vaned diffuser may be initiated in the semi-vaneless space at the diffuser
inlet. The static pressure recovery in this region and incidence angle at the vane leading
edge both increase as mass flow is reduced. The combinations of these effects contribute
to the initiation of stall. Stalls with l to 7 stall cells have been observed in centrifugal
compressors with vaned diffusers. Generally, the propagation velocity is much lower for
these modes of rotating stall than for those encountered in compressors with vaneless
diffusers. Furthermore, lobe number generally decreases as operational speed increases

according to Haupt et al. (1988) and Seidel et al. (1991).

38

Haupt et al. (1988) found a higher number of instances of rotating stall occurring
at relatively higher flow rates when their compressor was fitted with a straight channel
diffuser than with a cambered vane diffuser. On the other hand, flow oscillation

amplitudes for the cambered vaned diffuser exceeded those of the straight channel.

2.2.2. Surge

On the contrary to the rotating stall, where annulus averaged mass flowrate
remains roughly constant, surge produces a fluctuation in the system flowrate leading to
violent changes of inlet and exit conditions. Surge is a system phenomenon, whereas stall
is considered as a local phenomenon. The onset of surge occurs when the operating point
lies near the maximum pressure ratio associated with the operating speed. Whereas most
axial compressors manifest rotating stall behavior before surge occurs, the centrifugal
compressors start surging with or without preliminary rotating stall. Surge causes the
compressor system to vibrate and can result in mechanical failure especially to high
pressure ratio compressors.

Generally, surge intensity increases with increase in stage pressure ratio and the
frequency of flow fluctuation associated with surge is very low in the order of less than

lOHz.

2.3. Research Status on Low Solidity Vaned Diffuser

The first reference to a LSVD was in a Japanese patent by Senoo (1978) who
characterized the vanes by a solidity of less than 0.9 and introduced both single and

tandem row LSVDS. It also suggests that the centrifugal stage had better performance

39

with LSVD than with the vaneless diffuser without any loss of flow range. Since then
Senoo has presented a series of papers that give the details of LSVD performance.

Senoo et al. (1981,1983) presented and discussed the results for both single and
tandem row LSVDS installed in a centrifugal blower. They used USA 358 airfoil shape
for the vanes conformally mapped into a circular cascade. The single row LSVD tested
had 11 blades with 0.69 solidity. The tests with this LSVD were performed with two
different stagger angles of 70° and 68°. In addition, another single row LSVD with 13
vanes and 0.82 solidity was also tested. In the case of the two-row tandem cascade LSVD,
the first row had a solidity of 0.345 with 11 blades, and the second row had a solidity of
0.63. The tests were performed for various combinations of vane setting or stagger angles
and radius ratios between the two rows to arrive at the peak recovery in the diffuser
(Figure 2.16).

The results of LSVD tests showed dramatic improvements in pressure recovery
with respect to a vaneless diffuser, especially near surge flow. Most importantly, they
found almost no reduction in flow range with LSVDS. Near surge, the tandem cascade
configurations offered a much smaller additional increase in Cp, but the improvement at
high flows was nearly double that of the single row LSVDS. Further they observed that
the variation in stagger angle and solidity had a small effect on the performance with
relatively minor changes in surge location. The oil film patterns of the single row cascade
showed strong secondary flows along the sidewalls indicating the vane suction surface
boundary layers were sucked and moved toward the pressure surface of the adjacent vane.
This delays the boundary layer separation on the suction surface. From the oil film

patterns of two row tandem cascade it was found that the accumulated boundary layer on

40

the first row pressure surface is redirected to the main flow via the slit, allowing new
boundary layers to form on the rear row. Thus, 3-D boundary layer effects along the

sidewalls delay stall onset leading to a higher pressure rise.

0.8

 

 

 

 

 

With Cascade
(Prediction)
0.7 I CasACade . * -l _. $0.12
_,I..-" " '-
0.6
a. a 0:024
D . __
0.5 .. .- — ...°
, 0
Q n
O 0.4 0' ° 1
l
0.3 y . Vaneless Diffuser
(prediction)
0.2
0.1
0
1 1.5 2

Figure 2.16 Comparison of pressure distributions (Senoo et al., 1983)

Senoo (1984) summarized the effect of solidity, vane number, and stagger angle
on the performance of the LSVD and emphasized the need to positively use secondary
flow to obtain enhanced diffuser performance. In addition to the data presented in his
1983 paper, new data for a 22 vane LSVD with the same solidin and stagger angle as for
the 11 vane configuration as well as a ll vane design with 0.82 solidity was included.

The peak Cp values were nearly same for 11 and 22 vane configurations, but the
peak efficiency point was at about 20% to 25% higher flow for 22 vanes and there was no
noticeable change in surge line location with the vane number. However, the Cp drop
from peak to surge was more rapid in case of 22 vane LSVD. With the increase in solidin

ratio, the peak Cp attained was lowered and moved to higher flow rate. Moreover the

41

surge occurred at about 20% higher flow rate for LSVD with solidity of 0.82. The surge
point moves about 10% lower as the stagger angle increased.

Osborne and Sorokes (1988) used single row LSVDS with single and multistage
compressors having radial and mixed flow impellers, along with a wide range of specific
speeds and various sizes and gases. From their tests it was concluded that LSVDS were
successful with respect to efficiency and flow range even at high and medium specific
speeds. They also showed that attractive performance gains resulted with simple flat plate
vanes and for geometric parameters (such as vane number and vane setting radius ratios)
which were beyond Senoo’s study. However the solidity of 0.69 was retained for almost
all configurations tested, and the stagger angles were maintained relatively high.

Hayami et al. (1990) showed the LSVD with 0.69 solidity performed better than
the vaneless diffuser of a transonic centrifugal compressor. The vanes were conformally
transformed from linear cascade of double circular arc vanes. The LSVD also
demonstrated good pressure recovery over a wide range of inflow angles, and the pressure
recovery improved with increase in the inlet Mach number of up to 1.1. They also found
that the LSVD had maximum pressure recovery at an incidence angle of -2° to -3°.

Sorokes and Welch (1991, 1992) developed a rotatable LSVD system, which was
used to study the effect of stagger angle. In addition to stagger angle they also studied the
effect of vane leading edge radius ratio (by placing the vanes at both 1.08 and 1.15 radius
ratio) and the effect of chord length of the vanes by using small and many (SIM) and large
and few (UF) arrangements of the LSVD. All LSVD arrangements tested had 0.735

sohdfiy.

42

They observed that the best efficiency point, head rise to surge, stability range,
and choke margin all exhibit strong sensitivity to stagger angle. The overload capacity
displayed a marked decrease as the stagger angle was increased. The factors contributing
to this effects were, flow separation from the pressure surface of the vanes, and at high
stagger angles the distance between two vanes at the trailing edge decreased tended to
form a throat. On the other hand, when the stagger angle was decreased, the LSVD vanes
stalled, reducing the surge margin. It was also observed that the decrease in surge margin
was significant even for small decrease in stagger angle.

In a comparative study of the vane leading edge radius ratio and the SIM and UP
arrangements, they found that the 1.08 IJF build had the highest pressure recovery. While
the 1.15 UF build exhibited advantage over the 1.08 UF build in terms of surge margin,
both the 1.08 and 1.15 SIM arrangements had better stall margin than their respective UF
counterparts. Thus, the 1.08 IJF build had greater sensitivity to off design incidence,
even though its pressure recovery was better than the other builds. They also observed
that the length and/or exit angle of the LSVD vanes had influence on the downstream
components.

Hohlweg et a1. (1993) performed experiments on a process compressor and an air
compressor with LSVDS. The LSVD used with the process compressor had 10 vanes with
0.7 solidity, while three LSVDS were tested with an air compressor, all having 16 vanes
and 0.7 solidity but different design incidence of —4. 1°, -1.9° and +0.3°.

In their results they found that the LSVD with highest negative incidence provided
maximum flow range, while the LSVD with +0.3° incidence had small flow range and the

stage efficiency was less than the other two LSVDS. However, the LSVD with -1.9°

43

incidence had better stage peak efficiency than the one with -4.1°. Thus, they concluded
that negative design incidence in general was good for LSVD performance and there
should be an optimum negative incidence based on the impeller tip Mach number that
would provide both good flow range and efficiency.

From the results of low Mach number process compressor testing, they observed
that the LSVD had almost the same peak efficiency as the conventional vaned diffuser,
but the flow range of LSVD was considerably lower than the conventional vaned diffuser.
They speculated from this observation that the low vane number might have allowed
large stall cells to develop due to low flow angles at the vane leading edge, even though
the design incidence of the LSVD was -3. 1°.

Amineni(l996) performed experiments on four different LSVDS having solidity
of 0.6 and 0.7 and vane number of 14 and 16 to understand the effects of turning angle
and solidity on the performance of the diffusers, and compared these results with
numerical analysis. The experiments were performed at three different impeller tip Mach
numbers to study the effect of rotational speed on the performance of the diffusers. He
showed that the peak efficiency of the compressor increased with an increase in blade
turning angle of the low solidity vaned diffuser while the flow range suffered. He also
found that the effect of the solidity on the peak efficiency of the compressor stage was
very small while lower solidity diffusers were able to provide better flow range. He found
that the low solidity vaned diffusers stalled when the vane suction surface separation was
accompanied by the end wall separation. He found that nearly 75% of the total pressure
recovery in the low solidity vaned diffusers occurred between the impeller exit and the

vane trailing edge radius and that the pressure recovery between impeller exit and vane

leading edge was much higher in the case of low solidity vaned diffusers than the
conventional vaned or vaneless diffusers.

Thus, there is no clear understanding of the effect of the vane number and solidity
of the LSVD, which seem to be two major parameters in the LSVD design. Moreover, the
effect of vane number and vane leading edge radius ratio on the impeller discharge flow
is not clearly understood in the case of the LSVD, as some of the reports indicate that the
LSVDS with small vane leading edge radius ratios performed better, which is not the case

in conventional vaned diffusers.

2.4. Low Solidity Vaned Diffuser Design

Since there is no clear performance method available for LSVDS, a simple
approach for design was chosen concluded from numerical and experimental results with
comparable LSVDS carried out by earlier engineers. All four LSVDS were designed with
simple flat plate similar to the approach taken by Sorokes et al. (1991,1992) and Hohlweg
et al. (1993) because of their reported success and low manufacturing costs. Amineni
(1996) investigated LSVDS with 14 vanes and 16 vanes and showed that any increase in
vane number manifests into a more stable flow through the diffuser due to blade loading
reduction. In this work vane number and solidity was fixed with 18 vanes and 0.9
respectively initially(LSVD5). By trimming the vane trailing edge solidity of 0.8, 0.7, and
0.6 were obtained in turn.

Since the vane inlet angle is regarded to be an important design parameter, the test
results of many investigators have been used. The vane inlet angle is determined by first

calculating the flow angle at the design point and then adding the required incidence

45

angle to it. The design flow angle (a2) at the impeller exit was evaluated from a quasi one

dimensional flow calculation through the impeller. From the reports of Hohlweg et al.
(1993) and Sorokes et al. (1992) it has become very clear that the design incidence angle
has a major impact on the flow range and the pressure recovery of the LSVD. Figure 2-5
represents the incidence effect on flow range and it can be seen that in general the flow
range tends to increase as the design incidence angle becomes negative up to a certain
negative incidence; thus, indicating that there is an optimum incidence angle at which
highest flow range can be attained. Figure 2-6 shows the insensibility of the peak
efficiency at a design incidence of around -2°. Hohlweg et al. (1993), also obtained
highest efficiency for the LSVD with -1.9° design incidence. Thus, for all four LSVDS
designed for experimental testing had -2° design incidence.

On the basis of four existing LSVDS a new LSVD with 18 vanes was designed for
the highest solidity that still avoids a throat leading to an initial solidity of 0.9. By cutting
back the vane tips, solidities of 0.8, 0.7, and 0.6 were also generated. To determine
maximum solidity for a vane that has an outer diameter just at the throat, the following
simple calculation was carried out.

The geometrical parameters of LSVD are shown in . With given inlet radius (r3),

vane inlet angle (B3), vane number (Z), and blade thickness (tbl), pitch (3) is

. 180
S = 2 - r3 - Sln(—2—) (2-9)

Since the blade contour does not form a single line, the blade length has to be

corrected

46

t
l . =l+ ”’ 2-10
“0" 2tan fl3 ( )

 

The solidity is defined as the ratio of adjusted blade length to pitch

1 .
a=fl (2-11)

With 18 vanes for a given compressor, the maximum solidity came to 0.936.
For convenience, solidity of 0.9 was chosen for a starting solidity and the trailing
edges of the diffuser vanes were trimmed to vary the solidity with -0.1 solidity step.

Once the solidity were determined, vane exit angle ([34) and vane trailing edge

radius (r4) would be:

20sin(18%) tbl
cos fl, _ 2r3 sin ,85

 

tanfl, = tanflj + (2-12)

 

r4 = r3 COSA (2-13)

 

 

 

 

 

Figure 2.17 Maximum solidity

47

3. EXPERIMENTAL SETUP

3.1. Test Compressor

The present investigations of performance of different diffusion systems for a
centrifugal compressor were carried out on the first stage of a plant air package
compressor. The schematic outline of the test rig is shown in Figure 3.1. The centrifugal
compressor was driven by a variable speed motor with a maximum power output of 225
kW. The impeller and the motor were coupled through a gearbox of 9.054 gear ratio. The

speed of the motor was accurately controlled by a frequency controller capable of

 

Settling Chamber

 

 

 

 

 

 

 

 

 

 

 

 

 

otor 8: Filter
I T
Throttling Valves
Gearbox
1 Discharge Pipe
l
o ‘0
O {3: o
\ rifice

 

 

 

 

 

 

 

 

 

 

 

 

 

_ _ \ \

Inlet Pi e
Compressor p

 

 

 

Figure 3.1 Compressor test stand

48

adjusting the power supplied to the motor in accordance with the load on compressor.

The impeller is unshrouded and has 19 blades with backward leaning angle
BZb=70.7°, as shown in Figure 3.2. The blade camberline has ellipsoidal shape in
cylindrical section. The inlet hub and shroud diameters are 47.09 mm and 147.67 mm
respectively. The impeller tip diameter is 244 mm, with exit blade width of 13.33 mm.

The compressor was tested in an open air loop. The air entered the compressor
through an air filter, a settling chamber, and an inlet pipe. The settling chamber provides
the compressor with an air supply free of the temperature stratification, thus enabling the
compressor inlet temperature to be measured accurately. After being compressed in the

impeller, the air is discharged to the outlet pipe after passing through the diffuser and the

 

Figure 3.2 Centrifugal compressor impeller

49

volute of the compressor. The air in the outlet pipe is muffled with the aid of silencer
before it is discharged. The mass flow rate through the compressor could be controlled by
either of the throttle valves located in the inlet or the outlet pipes. However, for the results

presented here the mass flow rate was controlled by the throttle valve located in the outlet

pipe-

3.2. Investigated Low Solidity Vaned Diffusers

Four low solidity vaned diffusers (LSVD5 through LSVD8) were tested
downstream of the same impeller. The vanes of all the low solidity vaned diffusers were
machined on to an aluminum plate. Figure 3.3 shows the notation of a low solidity vaned
diffuser. The low solidity vaned diffusers have constant width from inlet to exit, and the
width of the diffusers was equal to that of the conventional vaned diffuser. Similarly, the
radius ratio of the vaneless space between the impeller exit and the leading edge of the
vanes was the same in all the low solidity vaned diffusers and the conventional vaned
diffuser. All diffusers were tested at three different speeds corresponding to the impeller
tip Mach number (Mu) of 0.69, 0.88 and 1.02. Amineni (1996) designed and performed
tests on the vaneless diffusers, conventional vaned diffuser and LSVD] through LSVD4

with the same configuration. The principle specifications of the diffusers are given in

 

 

 

 

 

Table 3-1.
Table 3-1 Diffuser Geometric Parameters
bad/b, r3/r2 r/rz rs/rz Z 6 i 0 Designed by
VNL1 0.70 - - 1.53 - - - - Elliott Co.
VNL2 0.83 - - 1.53 - - - - Elliott Co.
CVND 1.0 1.09 - 1.53 15 - 0 1.15 Elliott Co.

 

 

 

 

 

 

 

 

 

 

 

50

 

LSVD1 1.0 1.09 1.23 1.53 14 14.6 -2 0.7 Amineni

 

LSVDZ 1.0 1.09 1.21 1.53 16 12.9 -2 0.6 Amineni

 

LSVD3 1.0 1.09 1.20 1.53 14 12.6 -2 0.7 Amineni

 

LSVD4 1.0 1.09 1.19 1.53 16 11.1 -2 0.6 Amineni

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LSVD5 1.0 1.09 1.23 1.53 18 14.6 -2 0.9 Kim
LSVD6 1.0 1.09 1.21 1.53 18 13.1 -2 0.8 Kim
LSVD7 1.0 1.09 1.19 1.53 18 11.5 -2 0.7 Kim
LSVDB 1.0 1.09 1.17 1.53 18 9.9 -2 0.6 Kim

 

 

 

 

Figure 3.3 LSVD geometry notation

3.3. Measurement

The contents of this report present both steady and unsteady results of the
experiments performed with the centrifugal compressor test stand having different
diffuser configurations described in previous sections. Several static and total
temperatures along with static and total pressures and pressure fluctuations at different
planes of the compressor stage were measured in order to determine the mass flow rate

through the stage, overall performance, and the performance and interaction of various

51

components of the compressor stage. This section presents the details of all the
measurement locations and the measured quantities at these locations.

The mass flow rate was measured with an ASME standard orifice plate. Two total
and two static temperatures were measured at different circumferential positions located
opposite to each other at the same plane of the inlet pipe, upstream of the orifice. The
differential pressure across the orifice plate was measured by two sets of static taps
located 76.2 mm downstream and 152.4 mm upstream of the plate. The static pressure at
the orifice was also measured at two locations in the same plane, 152.4 mm upstream of
the plate.

The stage inlet static and total pressures were measured at two 90° apart
circumferential positions each. Similarly, the inlet static and total temperatures are also
measured at two different circumferential positions. The pressures are measured at a
plane mid way between the orifice plate and the inducer, while the temperatures are
measured at a plane located at 330.2 mm from the inducer. Figure 3.4 shows all the

measurement planes in the inlet pipe.

 

 

 

 

 

 

 

 

Total -
Pressure Orifice
Settling
Ch I r 4— 11' b Inducer
Total \Prg Total_& Total &
Temperature Differential Static Temperatures

Pressures

Figure 3.4 Measurement planes in inlet pipe

52

The inducer behavior is studied by measuring the static temperature just upstream
of the inducer and the static pressures at two different axial positions in the inducer.
Moreover the pressure fluctuations at the inlet of the inducer are also measured. Figure
3.5 shows the location of the different measurement probes in the compressor stage. The
pressure fluctuations and the static pressure in the impeller are measured at a rimp/rz ratio
of 0.77. All measurements in the impeller are done at the same circumferential plane, and
both the dynamic transducers measuring pressure fluctuations and the static pressure taps
were located at an angle of 425° with respect to each other. All the static taps and the
dynamic transducers in the inducer and the impeller were located on the casing of the

compressor.

 

     
 

/

Inducer Dom (lindZ)

/ 1ndueer Upstream“

 

 

 

 

Figure 3.5 Measurement locations

The pressures at the exit of the impeller and at various locations in the diffuser
were measured through the taps drilled on the back plate of the compressor. All these taps
were located 150° away from the volute tongue in order to minimize any flow asymmetry

caused by the presence of volute. Figure 3.5 shows the location of the taps and different

53

probes on the back plate of the compressor. In all, eight static taps were used to measure
the pressure recovery from the impeller exit to the diffuser exit. A set of static taps was
located at a radius ratio (ma/r2) of 1.04 to measure the static pressure at the impeller exit.
One pair was located at the leading edge radius (r3) of all vaned diffusers, a pair was
located at the trailing edge radius (r4) of the LSVDS or the mid channel of the CVND, and
the last pair was located at the diffuser exit radius (r5). In addition to these static pressures
the total pressure at the impeller exit was measured at the vane leading edge radius and
the pressure fluctuations in the diffuser were measured at the LSVD1 trailing edge radius.

The leading edge radius was chosen for total pressure probe location, since it is
assumed that the jet and wake pattern flow coming out of the impeller is mixed out and
the flow pattern becomes quasi uniform at this radius. The static taps, the total pressure
probe, and the dynamic pressure transducer were placed between the two vanes of the
CVND in an attempt to minimize the flow distortion effects caused by the presence of the
vanes.

The stage exit pressures and temperatures are measured in the pipe connected to
the volute. The exit total and static pressures are measured at four circumferential
locations 90° apart in the pipe at the same plane. Similarly the exit total and static
temperatures are also measured at four locations at a plane, which is 76.2 mm
downstream of the plane where pressures are measured. In order to avoid the heat transfer
effects on the temperature measurements the casing of the compressor was covered with
insulating material. Table 3-2 summarizes all measurement locations and the quantities

measured.

54

Table 3-2. Summary of Measurements and Measurement Locations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Location Position Static Notation Other probes Unsteady
pressure pressure
taps transducers
Orifice as per ASME 2 p0,;
standards
Inlet Pipe 21 _ 2 pr 2 total pressure
r— T 5 2 total temperature
1:
Inducer zinc“ 1 pm,
Upstream r = 0'74
ls
Inducer 2- d2 1 pm; 1 temperature Transducer A
Downstream m = 0'40
’is
Impeller r. 2 p, Transducer
LP = 0.77 mp B & C
’2 M = 42.5°
Im ller Exit 2
°° ’2—“=1.04 pi
r 2
Diffuser Inlet r3 _ 1 1 2 p; 1 Kiel probe
r2 .
Diffuser r4 _ 2 p4 Transducer D
Middle ,— 1-21
2
Diffuser Exit r5 _ 2 ps 1 total pressure
7 _ 1'53 1 total temperature
2
Discharge pipe 2 p6 2 total pressure
2 total temperature
3.4. Steady Performance Data Acquisition

3.4.1. Instrumentation

The steady static and total pressures were measured with three different types of

pressure measuring devices:

- Validyne - variable reluctance pressure transducers

55

 

- Omega - hand held manometers/high stability pressure transducer using
molecular bonded strain gage

- Water / mercury manometers

The water and mercury manometers have a resolution of 2.54 mm. One of the
water manometers is used to measure the differential pressure across the orifice plate and
the other is used to measure the stage inlet static pressure. The only mercury manometer
is used to measure the stage exit static pressure. The application of the water and mercury
manometers at these locations is considered necessary to validate the proper functioning
of the Validyne and Omega pressure transducers.

The static pressures were measured with 3.175 mm taps and the total pressures
were measured with Kiel probes. Flexible tubing was routed from the static pressure taps
and the Kiel probes to the Validyne and Omega transducers. The Validyne transducers are
connected to the Validyne digital transducer indicators with Belden type 8434 cable,
while the Omega transducers have digital display integrated to the transducer. The
Validyne transducers were calibrated with an Omega pressure calibrator in conjunction
with the water and mercury manometers, which provide an additional check during the
calibration. On the other hand, the Omega pressure transducers were factory calibrated
and they were checked for proper function with the water and mercury manometers
before use. All pressures were read to the second decimal digit, either in inches of water
or mercury. The Validyne pressure transducers are able to measure with an accuracy of
10.25% of full scale, which includes the effects of linearity, hysteresis and repeatability at
an operating temperature range of -17°C to 72°C. Detailed specifications of the

instruments are shown in APPENDD( B.

56

Total temperature probes that were half shielded with bleed slots measured the
total temperatures. All temperature measurements were done by copper-constantan (T-
type) thermocouples connected to the Omega digital temperature indicators (DP460). The
digital displays were calibrated by switching the display to a built—in calibration setting
and applying 0.00 mV at the thermocouple input to adjust zero reading and similarly
applying 39.00 mV for full scale display reading of 560.0. Once calibrated, the digital
displays were capable of indicating temperatures in either °C or °F. For the present study
°C display was chosen with 0.1 °C resolution. The accuracy of the Omega digital
temperature indicators was 10.5 °C at 01°C resolution setting under the operating

temperatures of 5 to 45°C for T-type thermocouples.

3.4.2. Data Collection and Reduction

The compressor was tested at three different impeller tip Mach numbers (Mu =
0.69, 0.88, 1.02) for each diffuser configuration. At each speed the temperature and
pressure measurements were collected from all probe locations for approximately 9 to 13
different mass flow rates, ranging from compressor choke to surge in order to obtain a
complete speed line. The mass flow rate through the compressor was controlled with the
throttle valve located at the stage exit.

At each flow point, the data were collected when the compressor stage reached
steady state condition in terms of the temperature. The stability criterion was the
temperatures at the stage inlet and exit oscillated within i0.1°C . Once the stage was
considered stable, all the pressures and temperatures were recorded and transferred on to

a PowerPC for further data reduction and processing.

57

The data reduction and processing were done by an EXCEL program. The
program first converts the recorded pressures and temperatures into N/m2 and K. At this

stage the temperatures and pressures at each measurement plane are compared with each
other and with downstream and upstream measurement planes. In this way any faulty or
malfunctioning transducers are detected, and the data from them are eliminated before
obtaining average pressures and temperatures at each measurement plane. The program
uses the averaged pressures and temperatures at various planes to calculate the stage
overall performance and the component performance parameters. The program is also
capable of plotting these performance parameters with the mass flow rate or the impeller
exit flow angles. This on-line plotting capability of the program acts as a good tool to
monitor the behavior of the stage and the whole system; moreover, it also provides
greater flexibility in control and operation.

The overall performance parameters calculated were the stage static and total
pressure ratios, the total temperature ratio, the total-to-total isentropic efficiency of the
stage, the head coefficient, the work coefficient, and the stage pressure recovery. In
addition to the above mentioned overall performance parameters, individual component
performance was determined by calculating the impeller pressure ratio, the impeller total-
to-total efficiency, the pressure recovery of the impeller, the diffuser, and the volute.

In order to understand the pressure recovery phenomenon in all three types of
diffusers, the diffusers were subdivided into three regions; and the pressure recovery in
each of these regions was calculated. The subdivision was based on the low solidity

vaned diffusers: (1) the vaneless space from impeller exit to the vane leading edge, (2) the

58

vaned region, from vane leading edge to trailing edge, and (3) the downstream vaneless
space from vane trailing edge to the diffuser exit.
The stage and impeller total pressure ratio compares the total pressures at the

stage exit and rotor exit, with the stage inlet total pressure. As such, they are

P03
7Z' = — _1
0.roror P01 (3 )
and
P06
Ir . =— (3'2)
°‘ 8 P01
Similarly, the rotor and stage static pressure ratios are given as
P
”IDIOT = A (3-3)
P.
P 6
fl" = - 3-4
stage R ( )

The isentropic efficiency can likewise be calculated for both the rotor and the
stage. Efficiency is the ratio of work done in an ideal process to the actual work. For
compression process between two states 1 and 2, this can be expressed as a ratio of the
isentropic work (representing the ideal process) and the real work. In terms of enthalpy

this becomes (Figure 1-2)

w h -h
77:: s=—£2-S——Ol— (3'5)

W hoz - hon

 

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

equation (3-5) in terms of temperatures

59

W' 7025 _ T01

’ (3-6)
762 - 731

n.=—=

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

are related according to

(3'7)

Thus, substituting into equation (3-6), the isentropic efficiency for a compression

process between state 1 and 2 can be written as

0",)
ii] / -‘
1’01 (3'8)

.12.}
To:

77.:

It is also known as total-to-total isentropic efficiency as the total conditions at the
state 1 and 2 are used to for calculation.

In the present investigation equation (3-8) was used to find the isentropic total to
total efficiency of the rotor and the stage. However, the heat transfer through the casing is
considered to be negligible and the stage exit total temperature is used for calculating the
rotor efficiency too, i.e. T06 = T03. The ratio of stage exit to inlet total temperature is also

given as

To. T...
T = _ : _'_ 3'9
0 T31 701 ( )

Thus, the appropriate expressions for rotor and stage efficiency are

60

 

_ (flommr Y4”) "‘1
To —1

"r -r , rotor _

(3-10)

and

 

(3-11)

III—Lung: _

_ (IrOJIage yrx) _ 1
To —1

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

nondimensional form is given as

Ah .

W=751f (3'12)
2 2

and is known as isentropic head coefficient. Using equation (3-7) the head
coefficient can be written in terms of measured quantities and gas properties as

___ Cme kjromge YX) _ 1J
i” av:

 

(3-1 3)

The work coefficient relates the isentropic head coefficient and the isentropic
efficiency. It is a nondimensional value of the actual head produced by the compressor
and is given as

_cP(T06—Tm)
#122

 

(3-14)

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

61

'l’
77
The static pressure recovery between any two stations 1 and 2 was calculated as
the percentage of impeller peripheral dynamic (or velocity) pressure.

PZ—Pl
MAUi

 

Cp = (3-16)

Thus the pressure recovery of all the compressor components and the static
pressure rise between various stations in the diffuser were calculated using equation (3-
16). In addition to the static pressure recovery of the diffuser calculated as mentioned
above, the static pressure rise from the vane leading edge station to the diffuser exit was

also calculated as percentage of the dynamic pressure at the vane leading edge station.

 

(3-17)

The total pressure loss from the vane leading edge station to the volute exit was

determined in terms of total pressure loss coefficient, which is expressed as

_P03_P06

f-
%AU§

94m

The mass flow rate through the compressor was calculated from the differential
pressure measured across the orifice as per the ASME standards. The equations used for
the calculation are given in Miller (1992). In this report the mass flow rate is presented in

nondimensional form known as flow coefficient which is given by

¢=——%;7 @4m
,0le 42

 

62

The flow angles at the impeller exit were calculated at the vane leading edge
station as the static and total pressures at this station were measured. From the measured

total and static pressures, the Mach number was determined

(’71)
M3: 2 [fa] -1 (3-20)

 

7-1 P3.

Assuming that there was negligible heat transfer through the casing, i.e. T03=T06
and the Mach number obtained above, the static temperature at the vane leading edge

station was calculated

T06

—l
1+—72 M32

 

T. = (3-21)

Now the absolute flow velocity was calculated from the' basic relation that relates

the total and static temperature at any point

C3 = \[2cpT06[1-[I3—]] (3-22)
T06

On the other hand, the radial component of the velocity at vane leading edge

 

station was calculated from the continuity

7h

 

= 3-23
r3 2703b3 ( )
The flow angle then was obtained from equations (3-22) and (3-23)
a, = sin”1 (£1) (3-24)
C3

63

However, in this calculation of flow angle, no blockage caused by the boundary
layer growth was considered. Thus, the flow angles calculated were invariably higher than

the actual flow angles.

3.5. Unsteady Performance Data Acquisition

3.5.1. Obtaining and Storing the Pressure Signal

The pressure fluctuations were measured by PCB pressure transducers. The
transducers in the inducer and in the impeller were mounted on the shroud wall, whereas
the transducer in the diffuser was mounted on the compressor back plate. All pressure
transducers were flush mounted because this eliminated any gap between the transducer
diaphragm and the measurement location. Thus, no usable frequency range of the
transducer was lost.

The PCB transducer uses a stack of thin piezoelectric quartz crystal wafers to
convert the applied pressure on the transducer diaphragm into electric charge. The charge
produced is proportional to the applied pressure. The transducer has a built-in
accelerometer that compensates for any acceleration and reduces distortion and resonance
in high vibration environments. The transducer also has a built-in temperature
compensation that allows it to operate in a temperature range of — 240° C ~ +205°C . The
transducer can measure pressure fluctuations in a range of 0 ~ 6.89x105 N/m2 with 13.8

N/m2 resolution. It has a natural frequency of 250 kHz with a usable frequency of up to

80 kHz.

When a constant pressure is applied to the PCB transducers for a long time (> 100
sec), the output charge does not remain constant and decreases with time. For the
transducers used for experiments described in this report the output charge would be
constant for about 30~60 seconds. This makes it impossible to measure the steady
absolute pressure with these transducers, and they can only measure pressure fluctuations.
Thus, the averaged static pressure was measured through the static taps and Validyne
transducers at every plane where unsteady transducers were mounted.

The signal from the PCB pressure transducer was conducted to an inline amplifier
through a lO-feet of low-noise coaxial cable. The inline amplifier conditions the
transducer output signal. This amplifier has high input impedance (1011 Q) and a range
capacitor in order to avoid any distortions in the signal through input capacitance
shunting.

The signal was then passed on to the signal conditioner through a 50-feet low-
noise coaxial cable. Even though one inline amplifier was used for each transducer, one
signal conditioner was used for all four signals. The signal conditioner powered both the
inline amplifier and the PCB transducer and could also amplify the signal with fixed gain
of l, 10, 100. During the system evaluation tests, it was found that the gain had no effect
on the signal to noise ratio, indicating that the noise was being added to the signal before
it reached the signal conditioner. Since the signal to noise ratio was unchanged with
signal gain and the amplitude of the signal was small, a gain of 100 was used to obtain
better resolution of the signal.

The amplified signals from the signal conditioner were transferred to a 4-channel

digital tape recorder and stored on to a tape. The stored data on to a tape were transferred

65

to a PC for further processing and analysis through the signal analyzer and the signal
processing software. The output connectors can develop the input signals or the tape
reproduction signals. The real time signals are monitored through two-channel HP signal
analyzer. The HP signal analyzer also provided the capability for on-line signal analysis
through the various features available with it. It was possible to obtain the power
spectrum, phase and cross-correlation between two signals for on-line monitoring of the

compressor. The complete signal flow path is shown in Figure 3.6.

3.5.2. Signal Processing

Since the signal analyzer had only two channels, the signal capture through the
signal analyzer was done in pairs of two transducers. Transducer B located in impeller
was used as reference for all captures, i.e. signal from transducer B was captured through
channel 1 and the signal from transducers A, C, and D was captured through channel 2 of
the signal analyzer alternately at each flow point. Thus, at each flow point for a given
capture frequency, three captures were made with BA, BC, and BD transducer
combinations at the two channels of the signal analyzer.

Even though the captures could be made at any sampling frequency of up to
261.12 kHz per channel, but most captures were made at 12 kHz and 4096 Hz sampling
frequencies. The high frequency was used to observe the blade to blade pressure
fluctuations and small captures of 64 records were taken. Each record has 1024 sample
points. The captures at 2048 Hz were taken to study the unsteady flow patterns in
different components of the compressors. The record lengths at this frequency ranged

anywhere between 8 to 64 records. The choice of either 2048 Hz or 4096 Hz was based

66

on the available memory of the signal analyzer and the required resolution of the capture.
Moreover, literature survey has shown that in most cases the rotating stall frequency was
lower than the impeller rotational frequency. The maximum rotational frequency in the
present experiments was 460 Hz and with 2048 Hz sampling frequency the usable
frequency range was 800 Hz and with 4096 Hz sampling frequency the usable frequency
range was 1600 Hz. Unsteady signals were also recorded on digital tape so that the data
can be retrieved later with various frequency ranges and give better confirmation of what
happens during transients.

Once the capture was taken and stored on the PC, the signal data is processed
using in-house signal processing software (UDACS). The software has various data
preparation tools such as windowing, filtering, removal of mean, removal of linear trend
etc. It also provides options to choose different kinds of filters and windowing methods.
From the prepared data power spectrum, cross spectrum, amplitude spectrum, phase, and
coherence are calculated. In addition to these features the software was also capable of
graphical display of the raw data in time domain and the results or processed data in
frequency domain. Following parameters were used for the computation of the spectral
functions:

0 64 records from each transducer were captured

0 the sampling frequency was 4096 Hz

0 each record contained 1024 discrete points, which corresponds to 0.25 seconds

0 all records were detrended

o a Hanning window was applied

0 50% overlapping was used

67

o the power spectrum, the cross spectrum, the coherence, and the phase shift
were calculated
0 the output is represented in terms of decibels, the reference being 1 kPa.

The details of the software and the procedures used to accomplish the results can

be found in Wilmsen (1996).

3.5.3. Analysis of the Data

After performing all the spectral analysis, one should determine whether any

 

 

 

 

 

 

 

 

 

 

 

Figure 3.6 Unsteady flow signal path

68

peaks could be found in the power spectra. If no single peaks are present, a periodic

signal can be excluded; and consequently no rotating stall can be expected. If the power

spectrum increases for one operating point at all frequencies, this is a sign for a general

increase of unsteadiness. But if one peak is detected, one should look at the cross

spectrum of B and C, as well as at the coherence of B and C. If all graphs show the

existence of a peak, the analysis described below should follow.

0 If a peak is not present at all transducer - locations, a surge can be excluded. If
a surge occurs, the peak should be visible in all transducers.

o A peak that is present at all operating points is not due to flow phenomena.
This may have its causes in vibrations or electrical distortions.

o If peaks occur that are not common in transducer B and C, a rotating stall in
the impeller can be with good uncertainty excluded.

0 If a peak appears that is common in all transducer and the phase shift between
B and C is close to zero, this could be a surge. Ideally, the phase shift between B and
C should be zero, but the setup with a volute could possibly make the flow uneven up
to the impeller and cause a small phase shift between B and C.

If a peak occurs only in the diffuser or in the inducer, a local periodic instability
would be detected. It could be rotating or intermittent. This can be examined by
examining the time domain. If the stall is rotating, no information about rotational speed
and number of cells can be achieved, therefore a second transducer at the same radial
position is necessary. But if the signal is strong enough it might be also visible in the

signals from the two transducers in the impeller. A peak that is common in B and C and

69

where the phase shift is not close to zero could be a rotating stall. The following analysis

should be performed to determine the numbers of cells.

3.5.3.1. Determination of the Number of Rotating Cells

The pressure fluctuations in the case of rotating stall are a function of time and
circumferential position. With the simplification of a constant amplitude the pressure

becomes as shown as

p(t.¢) = p- sin(w..t - m¢> (3-25)
where cost is the rotational speed of the stall and m is the number of lobes. For a negative

number of lobes the rotational direction of the stall cells is the opposite of the direction of
the rotation of the impeller.
In the casing there are the two transducers B and C at the same radial position.

The signal at transducer B will reach at transducer C with a time shift of At.

p(:,¢,) = 120 + Awe) (3-26)

in terms of fluctuation this becomes

p- sin(a)5,t — m¢B) = p- sin(a),, (t + At) — m¢C) (3-27)
and the number of lobes becomes

_a)fl-Atik-2n

¢c —¢B

 

(3-28)

The product of the rotational speed of the stall cell and the time shift can be

interpreted as the phase shift between the signals of the transducer signals. The

70

geometrical angle between the transducer is 42.5 degrees. With the phase shift

information, the number of cells can be determined as shown in Table 3-3.
Table 3-3 Number of rotating stall cells.

Number of cells: in Phaseshift [degree]

105.0
147.5
-170.0
-127.5
-85.0
-42.5
0.0
42.5
85.0
127. 5
170.0
-147.5
-105.0

1
1
O
0
0
l 0
0
0
0
0
0

I
.—a p—a

 

ONLII-bWN—‘O

A negative number of cells means that the rotating direction of the stall cells is the
opposite to that of the impeller. If the number of cells is positive, the cells rotate in the

same direction as the impeller.

a) I
‘0 ell : :3 (3'29)

C

The rotational frequency of the cells can be found by dividing the frequency of the

pattern by the number of cells.

71

4. EXPERIMENTAL RESULTS OF STEADY PERFORMANCE

Four low solidity vaned diffusers (LSVD5 through LSVD8) were tested
downstream of the same impeller. Testing was conducted at three rotating speeds
(Mu=0.69, 0.88, and 1.02), each from maximum flow rate to surge flow with a minimum
of 9 operating points per speed line. The results of this testing are presented here.
Amineni (1996) designed and performed tests on the vaneless diffusers, conventional
vaned diffuser and LSVD1 through LSVD4 with the same configuration.

The overall performances of each of these diffusers are compared with each other
in order to understand the advantages and disadvantages of three types of diffusers used
in centrifugal compressor stages. In addition, the flow range of operation, peak efficiency
obtained by the low solidity vaned diffusers is compared with the vaneless and
conventional vaned diffusers. Moreover, the effects of the LSVD vane number, the
solidity, and the turning angle on the overall performance of the compressor stage are also
discussed. All the performance curves are normalized with respect to the design flow of

VNL1 running at Mu = 1.02.

72

4.1. Overall Performance Characteristics

In this work four low solidity vaned diffusers (LSVD5 through LSVD8) were
experimentally tested downstream of the same impeller at three different speeds
corresponding to the impeller tip Mach number (M..) of 0.69, 0.88 and 1.02.

The overall performance of each of these four diffusers is compared with each
other in order to enumerate the advantages and disadvantages of the three types of
diffusers used in centrifugal compressor stages. In addition, the range of operation, peak
efficiency and the pressure rise obtained by the low solidity vaned diffusers were
compared with the vaneless and conventional vaned diffusers.

The performance characteristics of the compressor stage with LSVDS along with
both vaneless and vaned diffusers at three different speeds are shown in Figure 4.1,
Figure 4.2, and Figure 4.3 at the impeller tip Mach number of 1.02, 0.88, and 0.69
respectively.

At Mu = 1.02 in Figure 4.1, the characteristic curves of the VNLs and all the
LSVDS are vertical at the right end, with the mass flow rate being approximately constant
for all these diffusers. On the other hand, the maximum flow rate attained by the stage
with CVND was about 14% less than the other diffusers. This clearly indicates that the
maximum flow through the compressor was controlled by the vaned diffuser throat choke
in case of the CVND while the inducer choke, which will be discussed in the next
chapter, in case of both the vaneless and the low solidity vaned diffusers. However, at
lower speeds (Mu = 0.88 and 0.69) than designed it can be noticed that their overload
capacity decreased with the speed even though the LSVDS lack a true diffuser throat. This

decrease in overload capacity of the compressor with LSVDS resulted from the high

73

negative incidence flow on the vanes at lower than design speed. The high negative
incidence causes the pressure side stall of the LSVD vanes, which can be shown from the
numerically simulated results in Chapter 6. The vanes along with the stalled flow form a
virtual throat which limits the maximum possible flow through the compressor, similar to
the CVND.

The VNL1 shows better stall margin than did VNL2 at all speeds. This is because
the flow is more radial than VNL2 at a given flow rate. VNL1 is narrower in terms of
width by 18% than VNL2, which makes the flow more radial leading to shorter fluid
path. The LSVDS didnt exhibit surge flow rate equivalent to VNL1, contrary to the

observations of Hayami et al. (1990) and Senoo et al. (1983) (6 = 10°). The reason for this
difference could be that the LSVD vanes in the present test had higher turning angle (0)

up to 14.6 ° and were made of thin flat plates which are more sensitive to incidence.

The efficiency of the compressor with LSVDS was better than the vaneless
diffusers for a wide range of flow at all speeds. Among LSVDS, LSVD5 achieved highest
peak efficiency at all speeds at the cost of flow range. At Mu = 0.69 the LSVD5 achieved
slightly better peak efficiency than the CVND. However, LSVD8 (0.6 solidity) didn’t
show any advantage over the vaneless diffuser in terms of both the efficiency and the
flow range at Mu = 0.69. LSVD8 has the lowest turning angle (9.9°) among the tested
diffusers and it has high negative incidence at high flow and Mn = 0.69. It might be
predicted that the low solidity vaned diffuser with higher vane setting angle would
achieve both better efficiency and the overload capacity at lower speed than design while
the stall margin would suffer. LSVD5 has a solidity of 0.9, which is the maximum

solidity for being a low solidity vaned diffuser. Moreover, it can also be seen that the

74

peak efficiency of the LSVDS at all speeds was attained at higher mass flow than the
CVND. Thus LSVD provides greater stable operating range between peak efficiency flow
point and surge flow.

In general at all speeds the efficiency and the pressure ratio of the compressor
with LSVDS were superior to the best performing vaneless diffuser over a wide flow
range. The flow range obtained by the LSVD was also comparable to the vaneless
diffusers. Thus LSVD gives greater flexibility in design as they can be adjusted to peak in

performance over a wide range of impeller flow conditions.

4.1.1. Effect of Solidity

Figure 4.4(a) to (c) show the effect of solidity on the performance at three
different rotational speeds. It is shown in Figure 4.4(a) that the flow range increases as the
solidity decreases and the vaneless diffusers have the widest flow range. If the flat plate
vane of LSVDs were replaced by streamlined airfoil, the LSVDS would achieve the better
flow range. The flow range decreases with the impeller tip Mach number. In the present
work a reduction in solidity caused a reduction in blade turning angle as the number of
vanes was kept constant at 18. This can be attributed to the decrease in blade turning
angle. However, it seems that the peak efficiency rises with the solidity in Figure 4.4(b).
Also it can be known that the stage with LSVD having the flat plate vane offers good

performance at lower speed.

75

 

0.9 0

0.8 *

0.6 **

0.5 ->

0.4 ..

0'3 .4»

 

0.2

 

 

0.5

 

0.9 4*

0.8 **

0.6 ‘t

0.5 ->

0.4 ..

 

 

 

 

 

0.3
0.5

0.7 0.9 1.1 1.3

it.

Figure 4.1 Performance characteristics of the stage at M..=1.02

76

 

—O—CVND—l
--O--VN1.1 I
--¢--VNL2

+LSVDl
—o—st02
—o—st03
+st04
+st05
+LSVD6‘
+st07!
+stoe__§

 

 

 

0.6 ..
0.5 l»

0.4 0

 

 

0.2

 

row?
- -o - -VNL1

- no - -v~.2

+stm
—o—st02
—+—st03
—O—LSV04
+st05
+18%
+st07

 

 

-o—str>§~

 

 

0.5 0. 7

1.1

 

0.9 4

0.8 ~

0.6 i

0.5 -

0.4 1'

 

 

0.3

  

.Me I
00- '0 "fl‘l.*'.".

°-

I
‘...’..O....

'--~—-——-s

 

 

0.5 0.7 0.9 l. 1

$-

Figure 4.2 Performance characteristics of the stage at M.,=0.88

77

-a—CVND ‘
"OHVMJ
"*"VNJ
—-rr—LSVDI
—°—LSVDQ
—t—LSVD3
—O—LSVDA
+LSVD5
—O-—LSVD(>
+LSVD7
l+_L_S_Y23l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2 4
1.1 «~
1 ..
0.9 «» "—01—— 'cvrTo l
--o--VNL1 _
--fi-°VNL2 '
0.3 «» l
—x—stoi
—o—LSVD2‘
§ 0.7 —i—stoa
+LSVD4I
—e—stosl
0-6 '* —o—stooI
+st07,
0.5 ~» __+L1VB§-
0.4 «»
0.3 <»
0.2 Y T 7 O .
0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7
$-
1.1
1 a.
0'9 ” Fri—CTN?
"envnu ,
0.8 «» --t--VNL2 '
+st01
07 _ —0-LSVD2
:2 ' —o—st03
—o-stoa
0.6 .. +stos
—0—st06
05 «~ +st07'
' IP_+L§Y082
0.4 ..
0.3 «»
0.2 . . 2 , .
0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7

tit:

Figure 4.3 Performance characteristics of the stage at M..=0.69

78

This is because of lower density increase at lower speed. At higher speed, the flow
angle tends to decrease faster as the flow diffuses within the diffuser. The higher speed
compressor, the less turning angle vane should be used or the vane should be curved. At
Mu=0.69, there is small difference both in peak efficiency and pressure recovery (Figure
4.4(c)). As impeller speed increases, the differences become higher. One interesting thing
in Figure 4.4(c) is that the trendlines of pressure recovery at the different speeds
encountered around the solidity of 0.35 and showed the lowest pressure recovery. The
diffuser with higher solidity than 0.35 would achieve better pressure recovery with the
impeller tip speed and vice versa one with lower than 0.35.

In general, the higher solidity diffuser shows the better pressure recovery and this

can be a cause of a stall at a higher flow rate.

 

 

x Mu=0.69 ‘l
1.5 ~.....,___ . l o Mira-0.88 l
T" ”M «My a Mir-1.02 ,
1'4 .. X "'-..-....hh‘“‘ ...... PO'Y- (Mugofig) l
--------- X .' - - — -Po|y. (Mu=0.88) l

"-- * Poly. (Mu-1.02)

 

 

0.9

0.8 -

0.7 4

 

 

 

0.6

 

0 0.2 0.4 0.6 0.8 1 1.2
0'

(a) flow range versus solidity

79

1.12

 

 

 

    

 

 

 

 

 

 

 

 

 

X
x .. ..... "'
1.1 « ...... ‘
0",
("O-‘- .' ’ t
i ..od’...' ”
1.08 "
1.06 § ........................
IlN mafia-v"-
a.-. .........
1.04
102 ‘ ‘ x M02069
A O Mu=0.88
A M03102
4 l Poly. (Mu-1.02) l
1 ~ A - - - -Poly. (1410:0110)
""" 3°9- WP?&§9).
0.98
0 0.2 0.4 0.6 0.8 1 1.2
O
(b) peak efficrency versus solidity
0.6
x' 'Mu=0.69” "j
055 0 MU=O.88
A Mu=1.02
Poly. (Mm-1.02) .
------ Poly. (Mu-0.69) l .-
- - - - Poly. (Mu=0.88) . l."
0.5 ‘ .A” W*: '
ch-e
0.45
0.4
0.35
A
0.3
0 0.2 0.4 0.6 0.8 1 1.2

O'

(c) diffuser pressure recovery versus solidity

Figure 4.4 Effect of solidity on the performance

80

4.1.2. Effect of Vane Number

Figure 4.5(a) to (c) show the effect of vane number on the performance of the
stage with the low solidity vaned diffusers of 14-vane, 16-vane, and 18-vane having the
same solidity of 0.7 at three different speeds. It is shown in Figure 4.5(a) that the overload
capacities of the stage with vaneless diffusers and LSVDS are the same and 14% less for
that with the vaned diffuser due to the choke at the diffuser throat.

The overload capacities of the stage with VNLs and LSVDS at Mu=1.02
correspond to the inducer choke. However, the stage with the LSVD with less number of
vanes has slightly better overload capacity and this becomes more clear at lower speed.
However, when it comes to the stall margin the stage with fewer vane number of LSVD is
better. For a fixed solidity and blade inlet angle, reduction in blade number causes an
increase in blade turning angle and accordingly in blade loading. The surge margin was
improved by increasing the number of vanes at a fixed solidity. It can be explained that
the shorter vane allows the higher positive incidence angle because of smaller turning
angle.

At all speeds, the LSVD with less vanes attain the best peak efficiency. This
might be due to the higher blade turning angle which results in a shorter flow path to

reduce friction losses and causes more flow diffusion which reduces losses in the volute.

81

L]

0.8 L

TIN 0.7 *r

0.6 **

 

 

 

 

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1.1
1 ..
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0.9 4
0.8 .. 0:0.7 tor LSVD:
3: --<>- -VN.l
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g —o-—st02(z-1o)j
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82

l
i
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l "o.
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0 8 0:0.7 tor 15W:
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0.3 «»
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0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7
¢N
(c) M..=0.69

Figure 4.5 Effect of vane number on the performance

4.1.3. Effect of Turning Angle

Figure 4.6(a) and (b) show the influence of the turning angle of eight different
LSVDS on flow range and the peak efficiency, respectively at different rotational impeller
speeds regardless of vane number, solidity.

From Figure 4.6(a), the overload capacities of the stage running at Mu=1.02 with
LSVDS (marked by circles) lie in almost horizontal straight line indicating the inducer
choke. All LSVDs have almost the same overload capacity except LSVD5 which has the
highest turning angle of 14.64° and the highest solidity of 0.9. LSVD1 has turning angle

of 146° similar to LSVD5 with solidity of 0.7. Thus decrease in overload capacity of

83

LSVD5 resulted from virtual throat choke caused by high solidity for a low solidity vaned
diffuser. The virtual throat was generated by the pressure side stall. This can be seen from
the numerical simulation results. As rotational impeller speed decreases, the stage with
LSVDS having the lower turning angle show better overload capacity. The decrease in
overload capacity results from negative incidence flow to the vane leading edge at lower
than design speed. It can be seen from Figure 4.6(a) by filled circle, triangle, and square
that the stage with LSVD having higher turning angle exhibits the higher surge flow rate
due to excessive diffusion. At all speeds, the flow range gets narrower as the turning
angle increases.

The data are somewhat scattered in Figure 4.6(b), the higher the turning angle, the

 

 

 

 

 

 

higher the peak efficiency.
1.0
----------------- r1 ............ a
14 a ------------- I- - b ...................... 5',
A ‘—‘_ "— — ‘— M-A— _____ _. ‘— ~_‘__~_A _ _ -"€
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oMax. FlowOMu=1.02
0'2 .,. OM10. HOWOMUBIIQ
AMin. FIowOMu=0.88
lMin. FlowCMu=0.69
0 . A 1
9 10 11 12 13 14 15
Turning Angle(Degree)

(a)

84

 

 

 

 

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:1
’ 9
1.1 W ’ I I
o n ,r”’ A
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.. —— Linear (1411:0130)
° — Linear (Mu=1.02)
1 . . .
9 10 11 12 13 14 15
Turning Angle (Degree)

(b)

Figure 4.6 Effect of turning angle

4.2. Pressure Rise in the Stage with the Low Solidity Vaned Diffusers

In an attempt to understand the pressure rise in the stage with the low solidity
vaned diffusers, the static pressure from stage inlet to exit measured at eight different
locations are shown and discussed regarding to the factor limiting the flow. There is no
significant observed difference in terms of pressure rises among all four low solidity
vaned diffuser configurations at the different rotational speeds. Thus the data of LSVD5
and LSVD8 are shown only for the rotational speed of Mn = 1.02 and discussed. In Figure
4.7 the ratio of the static pressure to the stage inlet total pressure is plotted, with respect
to the different locations at which the pressure measurements were made for different

operating flow points.

85

stus @4511!

 

86

 

 

Total Pressure Ratio

stm alumna

 

31:12 A “8

s06

 

 

Firm Hrr2 Him P2 P3 F“ 5 F6 R5
Hwemaim
(b) LSVD8

Figure 4.7 Pressure rise in the stage with the low solidity vaned diffuser

87

Total Pressure Ratio

From the static pressure characteristics of LSVD5 (Figure 4.7(a)), the pressures
from stage inlet to the diffuser inlet are constant for the first two operating points.
However from diffuser inlet to stage exit the pressure rise is different each other, thus
indicating that neither the inducer nor the impeller is responsible for limiting the
maximum flow through the compressor. It can be seen that there is a sudden pressure
drop in the diffuser at high mass flow rates. The pressure drop is due to the negative
incidence loss.

In Figure 4.7(b) the sudden pressure drop can be seen in the impeller at high mass
flows (Op#1 to Op#3), which can not be seen in LSVD5 (Figure 4.7(a)) and in the
diffuser, which is common for both LSVD5 and LSVD8. The pressure drop in the
impeller is caused by the inducer choke and one in the diffuser is due to the high negative
incidence loss but its rate is less steep even a high mass flow rate for the LSVD8. The
LSVD8 is not the limiting component for maximum flow through the compressor. In
chapter 2, a solidity of 0.936 is determined to be the maximum value for being a low
solidity vaned diffuser. However, the LSVD5 having a solidity of 0.9 is responsible for
limiting the maximum flow. At high mass flow rates the flow has a high negative
incidence on the vanes due to which the flow separates on the pressure side and forms a
large stalled region. This large stalled flow blocks a major area between two vanes
forming a virtual throat and causing the flow to accelerate.

The pressure rise characteristics of LSVD8 is a mixture of the characteristics of
VNLs and CVND, which are not shown here. It can be seen that the sudden pressure drop

occurs both in the impeller and in the LSVD8 at high mass flow rate. However the

88

maximum flow rate attained by the stage with LSVD8 was equivalent to that of the VNLs

as seen in performance characteristics (Figure 4.1).

4.3. Pressure Recoveries in the Diffusers

Figure 4.8 through Figure 4.10 show the pressure recovery (Cp2-5) in the various
diffusers at all speeds. At all speeds it can be seen that the pressure recoveries of VNLs
remains almost constant with respect to the flow rate and the CVND has the highest peak
pressure recovery. The pressure recovery of the LSVDS at all speeds is in between the
VNLs and the CVND. It can also be observed that the LSVDS have the pressure recovery
trend similar to the CVND, which is because of the negative incidence loss at high mass
flow rates. The LSVD with higher solidity or turning angle tends to yield higher Cp2-5 at
high mass flow rates at all speeds. This can be expected because of lower losses and
blockage by the stall on the pressure surface of each vane. On the other hand at low mass
flow rates, the LSVD with lower solidity seems to offer better Cp2-5. At the left ends of
the figures, the irregular trends came from erroneous pressure at the diffuser inlet (P2).
This reading was affected by the suction side of the vane leading edge where the pressure
changes drastically along the vane leading edge radius. At Mu = 0.88 the irregular trends
are clearly observed for all LSVDS and CVND in Figure 4.9. The next subsection
attempts to explain such observations by breaking the pressure recovery of the diffuser

Cp2-5 into the pressure recovery of two different regions.

89

 

054»

Cp(2-5)
{3

01-1»

 

 

 

 

 

 

 

07 09 1.1 1.3
q)!
Figure 4.8 Diffuser pressure recovery (C925) at M..=1.02

90

 

 

 

Cp(2-5)

 

 

 

 

 

 

05 07 09 1.1 1.3 1.5

it)!
Figure 4.9 Diffuser pressure recovery (szg) at M..=0.88

91

 

 

 

 

 

054) '

cash
8

02..

 

Oi "

 

 

 

 

03 05 07 09 ll 13 l.5 1.7
4"
Figure 4.10 Diffuser pressure recovery (C925) at M..=0.69

92

 

 

4.3.1. Subdivided Pressure Recoveries

In an attempt to understand the detailed pressure recovery in the low solidity
vaned diffuser the diffuser was subdivided. Generally the vaned diffuser can be divided
into three parts: upstream vaneless space, vaned region, and downstream vaneless space.
As can be seen from the numerical calculation, the pressure around the leading edge
changes drastically at the same radius. So the diffusers are subdivided into two parts: (1)
upstream vaneless space and vaned region and (2) downstream vaneless space. In this
Figure 4.11 through Figure 4.13 show the subdivided pressure recoveries in the different
diffusers at three different impeller speed. At the top (a)s represent the pressure recoveries
of upstream vaneless space and vaned region, and (b)s for downstream vaneless space. It
can be seen that the pressure is recovered in the downstream vaneless space of CVND
and LSVDS at high mass flow rate, while the pressure is lost. However, as the flow rate
decreases, Cp24 increase rapidly for a short flow rate decrement and then gradually up to
optimum point. It can be known by comparing Cp24 and Cp45 One interesting can be
found for VNLs, which is almost zero pressure recovery between upstream vaneless space
and vaned region at high mass flow rate. The radius ratio of P4 probes are 1.21 and the
corresponding flow angles for VNL1 are between 456° ~ 55 .7°. The pressure recovery of
the vaneless diffusers at high mass flow rate is a contribution of the diffusion from a
certain radius ratio. As the flow decreases, Cp45 decreases slowly and Cp24 increases for a

short flow rate decrement and remains almost constant. However,

93

 

 

 

 

 

 

 

 

 

 

 

 

 

0.5
04 <>
0,. \
i . \
5 \ . e
A. v
0.2.. 6...“; . u
A: ................ A':.::.° .......... .9
"-4 ______ ,.
0.1 .
0 , #
0.5 0.7 0.9 H "3
¢I
(a) C1324 at Mu=1,02
0.5 2 ‘
I n CVND1
"°"VNL1 I
"*"VNL2 I
0.4“ II LSVD]
+st02
+st05
0.3~ LSVD6:
.7, '+L$VD7.
“ ‘+st03
‘6 ————__-.
U
0.2“ . °-
0. .
0.1 i:
0 5 A
0.5 0.7 0.9 1.1 1.3

4,-
0» CP4-5 at Mu=1,02

Figure 4.11 Subdivided pressure recovery in the diffusers at M..=1.02

94

Cp(2-4)

Cp(4-5)

0.5

 

0.4 "
_\
0.31, \ _ _
o , > ‘ I
i ..
0.2” '

 

 

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6.? A
3
o . ~ . - :
0.5 0.7 0.9 1.] 1.3 1.5
q,-
(a) Cp24 at M..=O.88
0.6
‘-°-CVND f
"°"VNL1
0.5*' '°*”VN|_2
+LSVD1
+LSVD2|
0.4 4* +LSVDS
+LSVD6
+LSVD7
0.3 4’ :LSVDBJ v.0.
0.2 "
0.] ‘ "
o a 4, . :
0.5 0.7 0.9 H 1.3 1.5

4,.
(b) Cp4.5 at M..=O.88

Figure 4.12 Subdivided pressure recovery in the diffusers at M..=0.88

95

Cp(2-4)

Cp(4-5)

 

 

 

 

 

 

 

 

 

 

 

0.5 _ _
+CVND
"°"VNL1
on ""“VNLZ
' l-r-stm
!-°—st02
_ . 1+LSVD5
0.3" . ;-°-st06
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:“stoa
0.2“
0.1 ".A.
o - r ~ '4
0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7
¢l
(a) Cp2-4 at M..=O.69
0.7
i-O-CVND i
(w f"°"VNL1
'T f"*“VNL2 '
{+stmi
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|+LSVDS‘
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L_+_____L__s_ypa; MM,» "
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0.2”
0.1 '*
o .
0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7

¢l
(c) Cp4.5 at M..=O.69
Figure 4.13 Subdivided pressure recovery in the diffusers at M..=0.69

96

5. EXPERIMENTAL RESULTS ON INSTABILITY IN A
CENTRIFUGAL COMPRESSOR STAGE

The causes of the instability in the centrifugal compressor stage with the different
diffusers were determined with the aid of four dynamic pressure probes installed in the
inducer (probe A), the impeller (probe B and C), and the diffuser (probe D) based on
phase angle correlation. The results for Mu=1.02 are shown here because of the similar
patterns with the impeller tip speed. Both transducer B and transducer C were located in
the impeller at the same radius but different circumferential position.

Since most rotating stall signals reported in the literature were below the

rotational speed of the impeller, the data between 0-500 Hz are plotted here.

5.1. Instabilities of the Centrifugal Compressor Stage

5.1.1. Unsteady Behavior of the Stage with the Vaneless Diffusers

Figure 5.1(a) to (c) illustrate the power spectra of the signal from the inducer, the
impeller, and the diffuser respectively of the compressor with the VNL2 at M“ = 1.02.
The rotational frequency of 460 Hz is clearly seen along with a weak peak at 360 Hz.
This weak peak was common to all configurations and constant in its level and occurred

at M“ = 1.02 only. Thus, it is presumed that 360 Hz peak is an electrical noise.

97

From Figure 5.1(a), no significant pressure fluctuations are found in the inducer at
high mass flow rates. However the pressure fluctuations grow at Op#10 for VNL2. These
fluctuations indicate the onset of inducer stall. This corresponds to the abrupt temperature
increases at the inducer in Figure 5.8. The fluctuations are non-periodic.

From Figure 5.1(b) it can be seen that the energy level of the signals from the
impeller is generally higher than in the inducer since transducer B is located in the
impeller. The pressure fluctuations have medium level of energy over the whole
frequency range at the first four operating points of the VNL2 configuration. The high
energy in the fluctuations is due to the inducer choke and the associated losses. The level
of energy decreases between Op#S and Op#9 indicating that the flow in the impeller is
stable yielding the best performance. At Op#10 the fluctuations begin to increase and at
Op#12, two peaks, one at 488 Hz and the other at 6 Hz are clearly seen. There is weak
periodic instability at 294 Hz. This could be possible impeller stall. The peak at 6 Hz
corresponds to the stage surge and the peak at 488 Hz was found to be due to a rotating
stall in the impeller. As the peak at 488 Hz can not be seen at inducer inlet and is stronger
in its energy level than one in the diffuser, this instability seems to be attributed to a
destabilization of the impeller flow. Detailed analysis will be given later in this chapter.

From the power spectra of transducer D for VNL2 in Figure 5.1(c), it can be seen
that the pressure fluctuations have very low energy for the first nine operating points.
Thus, the diffuser operates very stable in the operating range and has no negative effects
on the stage stability. Between the Op#10 and Op#12 the fluctuations increase over the
whole frequency range. A strong peak at 6 Hz is found in all transducers of VNL2

configuration. The energy at this peak is between 32 and 46 dB, which is much higher

98

than at any other peaks. Since the peaks occurred at the same frequency in all transducer
signals, it can be classified as surge peak. The peak at 6 Hz has the highest energy level at
transducer D than at any other transducer. This is expected as stage surge where 488 Hz
rotating impeller stall was aggravated by diffuser rotating stall. The flow angle out of
impeller is l 1.5 degrees and this corresponds to the critical flow angle suggested by Van
den Braembusche (1980).

Figure 5.2(a) to (c) are the power spectra of the signal from the inducer, the
impeller, and the diffuser respectively of the compressor with the VNL1 at M“ = 1.02.
The energy levels of the impeller at the last point (Op#l3) are slightly lower than those of
VNL2 at the last point (Op#l 1). The relative velocity leaving the impeller tip with VNL1
is bigger than with VNL2 at the same flow rate because the VNL1 has smaller inlet flow
area. So this flow rate is the critical flow rate causing the impeller passage stall due to the

excessive diffusion ratio (W2/W1).

5.1.2. Unsteady Behavior of the Stage with the Vaned Diffuser

Figure 5.3 (a) to (c) are the power spectra of the signal from the inducer, the
impeller, and the diffuser respectively of the compressor with the vaned diffuser at M.I =
1.02. The rotational frequency of 460 Hz is clearly seen along with a weak peak at 360
Hz. The rotational frequency of 460 Hz is seen in all configurations with higher energy
than in the inducer.

As shown in Figure 5.3(a), the inducer seems to be stable because of the diffuser
throat choke limiting the throughflow, hence avoiding critical incidence at inducer

leading edge. It is presumed that the stage surge was caused due to the diffuser stall at a

99

higher flow rate than the flow rate causing critical incidence at the inducer. It is clear in
Figure 5.8 that there is no sudden temperature rise with CVND configuration.

Only small fluctuations are seen in the power spectra of transducer B for the
CVND (Figure 5.3(b)) configuration, except at the last operating point. Thus, the impeller
is not the critical component causing the instability for this configuration and the 8 Hz
peak seen at the last operating point is mild surge and its fluctuation level is lower than
those of both diffuser and inducer are. Detailed analysis revealed that two-cell rotating
stall running opposite to the impeller at 80Hz at flow rate just below Op#10. Its relative
speed to the impeller is 0.17 and it has weak fluctuation level with no harmonics.

In the case of CVND configuration in Figure 5.3(c), from Op#l to Op#4 flow
fluctuation can be detected in the low frequency range (O~100Hz), as the diffuser is
choked. The pressure fluctuations increase between Op#S and Op#8. The pressure side
stall causes these increased fluctuations. However, Op#9 and Op#10 seem to have much

less fluctuations than at Op#8. The stage attained highest head (WN) at these operating

points. The surge peak at Op#ll can be seen with 8 Hz frequency.
The peak in CVND configuration is weaker in energy than in LSVDS or VNLs
configurations indicating the stage with CVND might have been operated just up to the

onset of the surge.

5.1.3. Unsteady Behavior of the Stage with the Low Solidity Vaned Diffusers

Figure 5.4 through Figure 5.7 are the power spectra of the signal from the inducer,
the impeller, and the diffuser, respectively of the compressor with low solidity vaned

diffusers at Mu = 1.02.

100

From the figures of power spectra at inducer with LSVDS (Figure 5.4(a) through
Figure 5.7(a)), no significant pressure fluctuations are found in the inducer at high mass
flow rates. However, the pressure fluctuations grow at the last operating points except for
LSVD6. These fluctuations indicate the onset of inducer stall. The fluctuations are non-
periodic. For LSVD6, there was no inducer stall because flow fluctuations at 294 Hz,
which appear in all the configurations of both LSVDS and VNLs, were abnormally
developed into the surge and limited the throughflow.

From the figures of power spectra at impeller with LSVDS (Figure 5.4(b) through
Figure 5.7(b)), the energy level over the whole frequency range is slightly higher at first
three operating points and then decreases between Op#4 and Op#6. The higher energy at
the first three operating points is due to the inducer choke. However, between Op#7 and
Op#10 the fluctuations at lower frequencies increase to be very high at Op#10 and
Op#l 1. Such patterns were not seen either in VNLs or CVND configurations. Thus, this
high energy fluctuation at low frequency is possibly due to the vanes of the LSVD. At last
operating points, flow fluctuations at 294 Hz can be detected both upstream and
downstream of impeller and its energy level is higher in the impeller than in the inducer
or in the diffuser. These fluctuations seem to be attributed to a destabilization of the
impeller. For LSVD5 configuration, this 294 Hz fluctuation in the impeller is higher than
any other configuration leading to surge.

From the figures of power spectra at diffuser with LSVDS (Figure 5.4(c) through
Figure 5.7(c)), very high fluctuations are seen in the first two operating points due to the

pressure side stall of the diffuser vanes. The fluctuations between Op#4 and Op#10 are

101

small indicating that the diffuser does not cause any instability in this operating range.

However at operating point 11 fluctuations increase and the surge peaks are seen at 8 Hz.

102

 

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103

 

 

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105

 

 

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Figure 5.4 Power spectrum of the stage with the LSVD5

106

 

 

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107

 

 

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108

 

 

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Figure 5.7 Power spectrum of the stage with the LSVD8

109

 

5.2. Inducer Stall

Figure 5.8 represents the dimensionless temperature at all speeds and total
pressure ratio at Mu=1.02. This figure shows that at a certain mass flow the temperature
in the inducer rises suddenly. The noise during the operation increases according to the
inducer temperature rise. This is caused by highly energized fluid that flows back from
the impeller to the inducer. This backflow at the shroud causes the main flow to
accelerate. From Figure 5.8 the diffuser has no influence on the mass flow at which the

inducer stalls.

 

 

 

 

 

 

 

 

 

1.12
1.1 +

.2

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n:

1.08 - 2

§

1.06 1 E

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1.04 1
1.02 1

1 . v . . . . . 0.5
0.3 0.4 0.5 0.6 0.7 as 0.9 1 1.1 12

Figure 5.8 Temperature: in the diffuser

110

5.3. Rotating Stall

A rotating stall was found only with the vaneless diffuser configurations. It is
presumed the progressive impeller stall due to the destabilization of the impeller flow. It
was found that four or five rotating cells running opposite to the impeller appears and its
relative speed is constant irrespective of impeller speed. Flow fluctuation at 488 Hz is
stronger in the impeller than in the diffuser and the inducer for VNL1 at Mu=1.02. This
fluctuation of 488 Hz in the impeller is even stronger than that of 6 Hz which is the surge
frequency. This fluctuation was added to the destabilization of the vaneless diffuser and
triggered the stage surge with high fluctuation.

Another fluctuation occurred at 294 Hz with VNLs and LSVDS in the impeller but

those fluctuations were not clear.

Table 5-1 Summary of the impeller rotating stall

 

 

 

 

 

 

 

 

 

 

 

 

 

Mu 0.69 0.88 1.02 1.17
VNL1 m -5 -4 -4 —5
60/ 0.23 0.275 0.24 0.2
m9 366Hz 440Hz 488Hz 564Hz
VNL2 m -5/-2 -4/+3 +4 -5
01/ 0296/0555 0.266/0.5 0.26 0.208
m!) 464/348 422/602Hz 490Hz 554Hz
5.4. Surge

Deep surges of VNLs were triggered by the diffuser stall which added already
existing rotating impeller stall. Flow fluctuation at Mu=1.02 is stronger in the diffuser
than in any components. This surge might be triggered by a destabilization of the diffuser.

This means that the diffuser is the critical component.

111

Deep surge was never reached in vaned diffuser because there was only single
component stall. Flow fluctuation at Mu=1.02 is much stronger in the diffuser than in any
components. This surge might be triggered by a destabilization of the diffuser also. Table

5-2 summarized the surge characteristics.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5-2 Summary of surge
Mu=l .02 fSURGE(Hz) INDUCER IMP__B IMP_C DIFFUSER
VNL2 6 46 32 46
CVND 8 30 28 25 41
LSVD3 6 34 35 44
LSVD5 8 35 37 30 46
LSVD6 8 31 28 25 41
LSVD7 8 42 35 34 46
LSVD8 6 42 34 34 44
M..=0.88 fSURGE(Hz) INDUCER IMP_B IMP_C DIFFUSER
VNL2 4 35 21 25 34
CVND 6 15 18 23
LSVD5 8 36 33 31 40
LSVD6 8 35 30 28 36
LSVD7 6 36 30 28 37
LSVD8 6 37 29 32 13
M..=0.69 fSURGE(Hz) INDUCER IMP_B IMP_C DIFFUSER
VNL2 6 46 44 45 47
CVND
LSVD5 6 22 20 18 22
LSVD6 6 24 24 22 30
LSVD7 6 25 25 22 30
LSVD8 6 27 27 30 30

 

 

 

 

 

 

 

112

6. NUMERICAL CALCULATION OF LOW SOLIDITY VANED
DIFFUSERS

It is essential for a fluid engineer to understand a detailed flow behavior of the
diffuser in order to develop and predict the performance of turbomachinery. The flow
field in the low solidity vaned diffuser was numerically simulated to understand the flow
behavior in the diffuser and thus to define the design parameters affecting the
performance using 3-D viscous Navier-Stokes code. The LSVD5 and the LSVD8 were
modeled for numerical simulation at the design flow, near surge flow, and near choke
flow and compared with the experimental results. The effect of solidity or the turning
angle on the diffuser flow was studied.

This chapter explains 3-D viscous Navier-Stokes code, grid generation, and

boundary conditions used for numerical simulation and its results.

6.1. 3-D Viscous Flow Solver

The code employed for this work is TASCflow, which solves the 3-D Reynolds
Stress averaged Navier-Stokes (N-S) equations and the time averaged mass and energy
equations in stationary or rotating frames of reference. The viscous effects are simulated

by the standard k-e turbulence model and log-law wall functions for a hydraulically

smooth surface. The primitive variables are found directly with the methods such as the

113

streamfunction-vorticity approach, which, by differentiation of the basic N-S equations,

eliminates the pressure term and reduces the number of equations to be solved.

In partial differential equation form, the governing equations for a general scalar,

momentum and mass are

and

where

300+; ——_(pu¢)= 9%[1‘ [a—‘bnw.

a a 8P 3 512514,. 1
_ —__ _ 1_ s
&(Wt) ax} (pujul) &j+&j [flefi'[&j $1. ]/+ u,-
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p_RT

”cf = ”dynamic + #turbulent

k +k

turbulent

(17' = kdynamic

(5'1)

(5'2)

(53)

(5'4)

The partial differential equations are discretized by means of an implicit

formulation at each node, so that each algebraic equation contains unknown values from

its neighboring nodes. The second order accurate discretization scheme uses skewed-

upwind differencing combined with physical advection correction. This fully implicit

formulation avoids stability limits that occur with explicit methods. A finite volume

114

approach is used, which insures conservation of mass, momentum, and energy over any
region of the computational domain.

Amineni (1996) used BTOB3D code for his numerical analysis of the low solidity
vaned diffusers. He chose BTOB3D code encouraged by many researchers’ reports
showing the capability of predicting the flow inside the turbomachinery components.
Dalbert et al. (1995) carried out two sets of flow field calculation using both BTOB3D
and TASCflow, which are commercially available 3-D Navier—Stokes codes, and showed
those current computational fluid dynamics (CFD) codes can achieve reasonable level of
accuracy when used with about 100,000 nodes. He concluded that the turbulence model

of TASCflow is superior if detailed flow is important.

6.2. Grid Generation and Boundary Conditions

A single blade passage was modeled with body-fitted, H-grid structured mesh.
The blade is located in the center of the domain and nodes are buried in the width of the
blade to improve resolution of the leading and trailing edges, and to reduce grid skewness
in these regions. The computational mesh, shown in Figure 5-1, consists of 105 x 50 x 17
gridlines in the streamwise (I), pitchwise (J) and spanwise (K) direction resulting in
89,250 nodes.

The adjacent regions of the full diffuser were modeled by periodic boundary
condition. At the inlet, total pressure, total temperature, and velocity direction were
specified. In every case, the inlet endwall boundary layer thickness was assumed to be

zero, and a uniform flow condition across both the span and pitch was assumed.

115

The inlet boundary condition can be taken from (1) the measurement data of the
impeller exit, (2) CPD results of impeller simulation, or (3) one-dimensional flow
analysis. A simulation using measurement data at an impeller exit is ideal and highly
relevant for code validation. But it is known that the traverse data obtained near the surge
and stall flows are unstable and not reliable. And this measurement is not possible unless
a test rig has the appropriate measuring equipment including space for it. Casey et a1
(1995) carried out numerical calculations of the vaned diffuser of a pump using three
different inlet boundary conditions and compared those calculation results with each
other. He found out that more complicated inlet boundary conditions do not yield
significantly better results than simple (uniform) inlet boundary condition. Thus, using
uniform inlet condition seemed appropriate for this work.

The inlet total pressure, total temperature, and velocity direction were determined
based on velocity triangles and checked against measured temperature rise.

At the outlet, the mass flow rate was specified. The walls were modeled as an
adiabatic smooth wall and the logarithmic law of the wall was used as a wall boundary
condition. The wall function was used to prescribe the shear stress on solid surfaces.

The flow was assumed steady, compressible, and turbulent. The working fluid
was dry air governed by the equation of perfect gas. The turbulence model used was a

standard k-e model.

The total pressure ratio curves of the stage with the VNL1, the CVND, the
LSVD5, and the LSVD8 and the three selected flows used for the numerical calculation
on the constant speed line of Mu=0.69 are shown Figure 6.2. The ratios of mass flow rates

of the near surge and the near choke to the design flow are 0.73 and 1.41 respectively. In

116

Figure 6.3 the measured pressures divided by the stage inlet total pressures at different
locations of the stage with LSVD5 are shown.
The calculation was carried out on a Sun Ultra] Workstation until the maximum

residual was less than 104. The whole diffuser geometry is shown in Figure 6.4.

 

 

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Figure 6.1 Computational mesh of LSVD5 (105 x 50 x 17)

117

 

 

 

 

 

 

 

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4).:

Figure 6.2 Pressure ratio curves of the stage with the flows used for the numerical
calculation

118

LSVDS @Mu=0.69

 

 

 

NEAR CHOKE

 

 

Pind1 Pind2 Pimp P2 P3 P4 P5 P6 P06
Probe Location

Figure 6.3 Pressure rise in the stage with the LSVD5

 

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Figure 6.4 Geometry of the LSVD5

119

Pressure Ratlo

6.3. Calculation Results

This section will discuss the result from the numerical calculation of the LSVD5
and the LSVD8 at the design flow, near surge, and near choke flow. From this result, the
low solidity vaned diffuser was modified for better performance and will be discussed in

the next section.

6.3.1. Pressure Distributions in the Diffusers

Figure 6.5 through Figure 6.7 show the calculated static pressure distributions of
the LSVD5 and the LSVD8 for the flows of design, near surge, and near choke
respectively and at Mu=0.69.

From Figure 6.5(a), the pressure rises steeply and the contour lines are aligned for
the design flow between the adjacent vanes of LSVD5 with an incidence angle of —1.9°.
Most of the pressure recovery is achieved up to the trailing edge of the diffuser vane. The
pressure rise becomes less steep in the area from the trailing edge of the diffuser vane and
more and more uniform circumferentially as the diffuser radius increases. In tests of this
operating speed, the peak efficiency of the LSVD5 is even higher than that of the CVND
designed with the cambered airfoil type vane. Compared to the LSVD5, the pressure rise
of the LSVD8 is similar but due to a less flow guidance on turning from shorter vane the
pressure recovery of the LSVD8 is lower as shown in Figure 6.5(b). This agrees with the
experimental data and the calculated efficiency differences of the diffusers between the
LSVD5 and LSVD8 are 1.5% and 4.2% based on total-to-total and total-to-static

calculation respectively.

120

Figure 6.6(a) and Figure 6.6(b) represent the calculated static pressure
distributions of the LSVD5 and the LSVD8 respectively at near surge flow and M..=0.69.
The incidence angle of these is +5.0°. It is apparent for the LSVD5 as shown in Figure
6.6(a) that the pressure gradient of the diffuser vane suction side is steep up to half of the
diffuser length and then the flow is separated from the suction side of the rest half of the
diffuser vane. This is due to excessive blade loading from the thin flat plate vane, which
is sensitive to the incidence angle. Compared to the LSVD5, the flow of the LSVD8 has
less separated region with the same incidence angle and the pressure distribution at
downstream of the vane trailing edge is more uniform circumferentially at a radius as
shown in Figure 6.6(b). The chord length difference, which is directly related to the
solidity and the turning angle with this configuration, makes a big difference in the flow
field and pressure recovery at off-design flow condition. The calculated efficiency
differences of the diffusers between the LSVD5 and LSVD8 are -2.3% and -1.3% based
on total-to-total and total-to-static calculation respectively.

Figure 6.7(a) and Figure 6.7(b) represent the calculated static pressure
distributions of the LSVD5 and the LSVD8 respectively at near choke flow and M..=0.69.
The incidence angle of these is —9.7°. There is a hole at the leading edge of the vane
suction side indicating the stagnation point. The pressure drops steeply along the vane
suction side (lower surface) but starts to gain near trailing edge. However, the flow
moving along the vane pressure side (upper surface) starting from the stagnation point
accelerates while turning around the leading edge causing sudden pressure dr0p. From
then the diffusion starts. There is additional pressure rise after the trailing edge and this

agrees with the experimental data. The calculated efficiency differences of the diffusers

121

between LSVD5 and LSVD8 are -0.7% and -4.0% based on total-to-total and total-to-

static calculation respectively. This difference at off-design comes from the chord length.

6.3.2. Flow Field in the Diffusers

Figure 6.8 through Figure 6.10 represent the flow pattern including velocity
vectors and streaklines from the diffuser inlet of LSVD5 and LSVD8 for the flows of
design, near surge, and near choke respectively and at M..=0.69. Each section represents
near the wall (2% from the wall), 25% from the wall, and the mid-span of the low solidity
vaned diffuser from left to right, respectively. The solid lines are the streaklines from the
diffuser inlet and the arrows for the velocity vectors at corresponding grids.

In Figure 6.8(a) the fluid of the LSVD5 with incidence angle of —1.9° tends to
flow more tangentially as we look at the flow close to the wall. Due to the viscous effect
the boundary layer is developing and thus, retarding the radial component velocity. The
main flow is well guided within the vane but the flow after the trailing edge turns
tangentially. This seems to be attributed to the shape of trailing edge as well as the
viscous effect. Compared to LSVD5, the flow in LSVD8 is guided by shorter blade
resulting higher friction loss due to longer flow path. This agrees with the experimental
data and the calculated differences of the diffuser efficiencies are 1.5% and 4.2% based
on total-to-static and static-to-static calculation, respectively.

In Figure 6.9(a), the LSVD5 stalls at the near wall of the suction side and large
recirculation area is shown near the trailing edge of suction side. However, the main flow
of mid-span seems to be well guided yet. The secondary flow can be found at this flow.

Figure 6.9(b) shows the flow pattern of LSVD8 at near surge flow. When compared to

122

LSVD5 (longer vane) with the same boundary conditions, the flow of LSVD8 seems
much healthier than that of LSVD5. This is because LSVD5 is much more loaded than
LSVD8. Therefore, the surge of LSVD5 is expected to happen earlier if the cause of the
surge is due to the diffuser stall.

Figure 6.10(a) shows the flow of the LSVD5 with the incidence angle -9.7°. The
flow near the leading edge is complex. The flow after the stagnation point accelerates and
especially for the flow turning around the leading edge along the pressure side. The
stalled area of the vane pressure side and furthermore the backflow from the trailing edge
to leading edge can be seen. The flow stalled in the pressure side of the diffuser vane
from the leading edge due to high negative incidence forming a virtual throat. The virtual
throat limited the flow rate and made the different overload capacity from that of the

vaneless diffuser (see Figure 3). The flow of LSVD8 is similar to the LSVD5.

6.3.3. Separation at the Diffuser Vane

Figure 6.11 through Figure 6.13 show the streaklines starting from the leading
edge of the LSVD5 and the LSVD8 for the flows of design, near surge, and near choke
respectively and at M..=0.69. Here the near wall (2% from the wall), 25% from the wall,
and the mid-span of the low solidity vaned diffuser are represented by the gray density.

Figure 6.1 1(a) and (b) show the streaklines starting from the leading edge of
LSVD5 and LSVD8 at the design flow. It is shown that the flow is nicely guided by the
vane and the flow of LSVD5 is more guided passing shorter path than LSVD8.

Figure 6.12(a) and (b) streaklines starting from the leading edge of LSVD5 and

LSVD8 at the near surge flow. The flow of the LSVD5 near the wall is separated and

123

recirculating at the vane suction side. However, the flow of the LSVD8 is much healthier
than the LSVD5 achieving better performance with the same incidence angle.

Figure 6.l3(a) and (b) streaklines starting from the leading edge of the LSVD5
and the LSVD8 at the near choke flow. The stalled area along the pressure side (upper

surface of the vane) is shown.

6.3.4. Vane Setting Angle Effect

In an attempt to. understand the effect of the vane setting angle on the diffuser
performance, two degrees of vane setting angle was added and subtracted from the
LSVD5. The rest of parameters remain the same. The same boundary conditions were
employed. Figure 6.14 through Figure 6.17 show the calculated results of these LSVDS
where the pressure contours, the flow pattern, and the streaklines from the leading edge
are combined in one figure in the counterclockwise direction.

First, in an attempt to develop the overload capacity the vane setting angle was
increased by two degrees (called LSVD5”). Figure 6.14 represents the calculation with
near choke conditions at Mu=0.69. Compared to the LSVD5 the flow near leading edge is
much healthier and yields much better diffuser efficiencies as shown in Figure 6.18 and
Figure 6.19. The definitions of diffuser efficiency are explained in Appendix B. However,
as shown from Figure 6.15, the flow with near surge conditions became much worse. The
whole area of the vane suction side stalls and the diffuser efficiencies are dropping about
5% by setting the vane angle two degrees radially for the same flow conditions of near
surge. It seems the flow rate corresponding to the peak efficiency moves at a higher flow

rate .

124

Secondly, in an attempt to increase surge margin capacity the vane setting angle
was reduced by two degrees (called LSVD5'2). Figure 6.17 represents the calculation with
near surge flow conditions at Mu=0.69. Compared to LSVD5 the flow at the vane suction
side stalls only near end wall area offering better diffuser efficiencies about 5%. The
pressure recovery between the vane channel is steeper than the LSVD5. It is apparent that
the trailing edge/suction side has less separated flow zone than the LSVD5. Here at this
flow condition, two-degree vane setting angle corresponds to 5% difference of the
diffuser efficiencies. However, the peak efficiency seems to be lower than LSVD5. As
presumed before, it seems that the optimum incidence angle for the maximum efficiency
is near —2 degrees. The pressure recovery of LSVD5“2 at near choke flow is very poor.
Due to high negative incidence angle the separated flow at the vane pressure side
generates a thick flow blockage (Figure 6.16). The flow accelerates from the vane leading
edge. The first diffuser efficiency is the lowest among all the calculated diffuser including
LSVD8, which offers 2 to 4 % higher than LSVD5. Furthermore, the second efficiency of
LSVDS’2 is really poor close to zero.

The LSVD8 has the lowest peak efficiency at the design flow due to the small
turning angle. This implies the sensitivity of the turning angle (or the solidity) to the
maximum diffuser efficiency. However, as the flow more away than the design flow the
efficiencies of LSVD8 become higher than LSVD5. This implies the sensitivity of the
flow incidence (vane setting angle) to the diffuser performance including operating range.

The diffuser efficiencies are shown in Figure 6.18 and Figure 6.19 based on total-
to-static and static-to-static respectively. The effect of vane setting angle on the pressure

recovery and flow range agrees well with Sorokes et a1. (1992).

125

 

(a) LSVD5

 

(b) LSVD8
Figure 6.5 Pressure distribution at design flow & M..=0.69

126

 

 

 

 

 

 

 

 

 

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(b) LSVD8
Figure 6.6 Pressure distribution at near surge flow & M.=0.69

127

 

 

 

 

 

 

 

 

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128

 

(a) LSVD5

 

 

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I
I

I7EE*IZ

.7I1E0I2
.IIIE’I!
.594E’I2
.SIIE’II
.HIIE‘I2
.312E’I2
.21.!‘02
.125E’I2
.IS1E’I2
.87IE0I1

HQIEOI1

.IIII.I1
.5IflE’I1
.IZIE’I1
.IIIE’I1
.751E*I1
.I1II‘I1
.I7SEOI1
.97IE0II
.IIIE+II

 

(b) LSVD8
Figure 6.8 Flow pattern at design flow & M..=0.69

129

 

 

 

(a) LSVD5

 

(b) LSVD8
Figure 6.9 Flow pattern at near surge flow & M..=0.69

130

 

SPEED
2.HHIE*I2

.DZEE'II
.2I3!¢I2
.II1E‘I2
.ISIE’IZ
.DIIE‘I2
.713E*I2
.SI1E’I2
.HIIE*I2
.396E‘I2
.22QE¢IZ
.1I1E'IZ
.7III‘I1
.5IIE’I1
.3H4E*I1
.12IE'I1
.DIIE‘I1
.I'ZI‘I1
.HMIE‘I1
.22HE‘I1

 

 

.IIIE’II

 

 

 

 

SPEED
2.5255‘I2

.SIDE*I2
.2728’I2
.198E’I2
.I2IE'I2
.DISE'IZ
.757E’I2
.IQ1E'I2
.S1SE*02
.IIDEOIZ
.ZIZEOIZ

PPPPPPPNNNN

.136E‘I2
1.I1II‘I2
I.IIIE¢I1
7.575E’I1
6.313E*I1
5.I§IE*I1
I.7I7I*I1
2.525E*I1
1.262E’I1
I.IIIE°II

 

 

 

 

(a) LSVD5

 

(b) LSVD8
Figure 6.10 Flow pattern at near choke flow & M..=0.69

131

 

SPEED

1- r-

IIOVIPPPO-l-Pv-

 

 

.P N. I

2.
2.

2.

238E*I2
126E9I2

D1HE'IZ

.902E'I2
.79IE*I2
.670E’I2
.556E’I2
.QSHE'IZ
.IQZE*I2
.231E’I2
.119E’IZ
.II’E’IZ
.ISII‘I1
.ISSE‘I1
.71HE’I1
.595E'I1
.M’EE'I1
.I!7I*I1
.230E0I1
.11DE’I1
.IIIE’II

 

 

SPEED

 

 

I P N I t a V O o r r r P r v r P N u N

2.

391E‘I2

.271E*I2
.152E'I2
.IIZE'IZ
.D18EOI2
.7DSE’IZ
.D’HE'IZ
.SSHE'IZ
.flIHE’IZ
.315E‘I2
.195E‘I2
.I’DE’IZ
.IIII‘I1
.37IE*I1
.17HE'I1
.D7IE0I1
.7IDIOI1
.II?I‘I1
.391E0I1
.1ISE’I1
.IIIE'II

 

 

 

 

 

 

(a) LSVD5

 

 

 

(b) LSVD8
Figure 6.11 Flow from leading edge pattern at defign flow & M¢=0.69

132

 

(a) LSVD5

 

(b) LSVD8
Figure 6.12 Flow from leading edge at near surge flow & M..=0.69

133

 

 

(a) LSVD5

 

 

 

 

 

(b) LSVD8
Figure 6.13 Flow from leading edge at near choke flow & M..=0.69

134

 

 

 

13

12

11

1.

P
1.HIDE*I3

1.375E*05

1.350E*IS

1.325E‘IS

1.300E'IS

1.275E*DS

1.25IE*I5

1.225E’I5

1.2.DE*05

1.173E‘I5

1.1SIE0IS

1.125E*03

 

1.1IIE‘IS

 

Figure 6.14 LSVD5+2 for near choke flow at Mu=0.69

135

 

 

 

 

 

000000000

SSSSSSSSS

555555555

111111111

111111111

000000000

111111111

ZZZZZZZZZ

000000000

 

Figure 6.15 LSVD5+2 for near surge flow at M..=o.69

136

 

 

 

 

 

P
1.HIIE0IS

1.375E'I5

1.380E903

1.328E‘IE

1.3.IE’IS

1.275E‘DE

1.2EIE*IE

1.225E'I5

1.2IIEPIE

1.175E’IE

1.1SIE*IS

1.125E*DE

 

1.1..E‘IE

 

Figure 6.16 LSVDS‘2 for near choke flow at M..=0.69

137

 

 

 

 

 

000000000

555555555

SSSSSSSSS

111111111

555555555

111111111

000000000

111111111

SSSSSSSS

888888888

 

Figure 6.17 LSVDS‘2 for near surge now at M..=o.69

138

 

 

 

 

 

 

 

 

 

   

 

 

 

     

 

 

 

 

0.9
0.85 4
0.8
g 0.75 ~
, ,/- 1 — \\
0-7 g : -*- st05-2 1 \
l \
'1 2 -e- stos+2 ; \\
0.65 1 - +st05 ‘ \.
--°--stoa
0.6 . . . . . 1
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
00
Figure 6.18 The first diffuser efficiency
0.9
0.85 ~ x”‘~ __________
0.8 ~
0.75 .
"I
,3: 0.7 .,
0.65 ~
-*- LSVDS-2 1. \
0-6 * " .1 -----st05+2 1 \\
| +st05 ‘ ‘1
0.55 - \
-*-- stoa \
\\
0.5 =
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
00

Figure 6.19 The second diffuser efficiency

139

7. CONCLUSIONS AND RECOMMENDATIONS

Experimental testing of a centrifugal compressor with the low solidity vaned
diffusers along with two vaneless diffusers and one vaned diffuser has been carried out to
understand the effect of design parameters on performance and the results were compared
with those from numerical simulation. The design parameters include solidity, turning
angle, incidence angle, and the number of vanes. The testing was performed at three
different rotational speeds (Mu=0.69, 0.88, 1.02). The LSVD fulfilled the high
expectations since they seemed to combine the advantages of the vaned diffuser systems
by providing a good pressure recovery over a wide flow range. Besides steady
performance analysis, pressure fluctuations were measured to understand the instability of
a compressor stage such as stall and surge using fast response dynamic pressure
transducers.

From the results of experimental test and numerical simulation, it is found that
solidity is the major parameter affecting the centrifugal compressor along with blade
turning angle. The high flow limits for the LSVDS and VNLDs tend to overlap at the
designed rotational speed. However, the LSVDS lose their equivalent overload capacity at
lower than the designed rotational speed. This effect is due to higher sensitivity of the flat
plate vane to the incidence angle, which turns to lower negative value (more incidence

angle) at lower than the designed rotational speed. The entailed stall on the pressure

140

surface is suspected to form an artificial throat limiting the maximum flow through the
compressor. This pressure side stall is supported by numerical simulation along with the
effects of solidity, blade turning angle and vane setting angle. On the other hand, the real
throat of the CVND causes the loss of overload capacity as well. This throat choke allows
only a mass flow rate that is approximately 14% less than that achieved by the LSVDS
and VNLs at the designed rotational speed. Concerning efficiency, the LSVDS achieve
slightly lower than the vaned diffuser but their behavior is similar to the VNL since they
obtain higher values over a wide flow range. The efficiency of LSVD5 (0.9 solidity and
146° turning angle) is even higher than that of CVND at M..=0.69. Moreover, the peak
efficiency of the LSVDS at all speeds was attained at higher mass flow than the CVND.
Thus, LSVD provides greater stable operating range between peak efficiency flow point
and surge flow.

The solidity should be considered as a major design parameter. It gives significant
effect on the peak efficiency and flow range; thus, it can be used as an initial design
parameter to correlate other parameters like blade length, vane setting angle, radius ratio
of vane leading edge, and vane number. In general, the higher solidity diffuser shows the
better pressure recovery and this can be a cause of stall at the higher flow rate.

The number of vanes does not have significant effect on the overall performance.
At a fixed solidity a LSVD with fewer number of vanes provides better overload capacity
and peak efficiency at all speeds even though the difference is small. Better efficiency is
due to the higher blade turning angle which shortens the flow path through the diffuser.
This means less friction loss despite of the longer vane. On the other hand, a LSVD with

more vanes at constant solidity seems to move the surge point to lower mass flow, which

141

might be due to the shorter vanes allowing a higher positive incidence angle. The low
surge flow of the vaneless diffuser obviously cannot be reached by any vaned diffuser
configuration.

The vane setting angle effect on the performance has been studied by means of
CFD. It shows significant effect on the flow range and rather less on peak efficiency.
Flow range will widen with a negative incidence angle, which will suffer peak efficiency
due to higher friction loss caused by longer flow path. An incidence of —2 degrees seems
to be an optimal incidence angle yielding the best peak efficiency. However, the flow
exiting impeller is not uniform in terms of velocity. Profiled leading edge based on
measured data in detail from the impeller exit should be considered together for
optimization.

A rotating stall was found only with the vaneless diffuser configurations. It is
presumed the progressive impeller stall due to the destabilization of the impeller passage
flow. This fluctuation was added to the destabilization of the vaneless diffuser and
triggered the stage surge with high fluctuation. Deep surge was never reached in vaned
diffuser because there was only single component stall. Flow fluctuation at M..=l.02 is
much stronger in the diffuser than in any components. This surge might be triggered by a
destabilization of the diffuser also.

By comparing its results to the experimental data the CFD could be validated. The
CFD is very helpful tool to design and develop the turbomachinery. It is believed that
more profiled vane will develop the performance of centrifugal compressor. This will be

carried out by means of CFD.

142

APPENDICES

APPENDIX A

APPENDIX A

Diffuser Efficiencies
The diffuser does not involve work transfer. The efficiency of the diffuser can be
defined by the ratio of a rise in enthalpy along an isentropic process to actual enthalpy rise

from the diffuser inlet to diffuser outlet.

 

h 3.—h

"DJ—S = iii—’1‘? (A'1 )
h .-h

"0.5—s = I: _ h: (A’Z)

The rise in pressure taken from inlet static to outlet total pressure is used for the
efficiency, 11 13.1.5, while the rise in pressure from inlet static to outlet static pressure for
the efficiency, 1] 9,5,5. The process is shown in Figure A-l. Assuming a perfect gas, n 9.13
can be related to inlet static and out total pressure and to the inlet Mach number.

.

"A
[as] -1
_(T053'-T2)/T2= P2

 

77 _ - (A-3)
DJ 5 (Tos-T2)/T2 1%-]
T2
Combining Eq.3-21 with Eq.A-3 reduces to
“A
Eu _1
P
”DJ-S = 7:1 (A'4)
__ M22

By a similar procedure, 11 115-5 can be related to pressure and Mach number.

143

"'4
] —1](1+7T—]M52]

72103—143)

1%:

The polytropic efficiency is defined by

”0.3-s =

7—1
=__?_’_
n-l

n

770.?

P
where —— = Const.

pn

n generally varies from diffuser inlet to outlet.

1%)"

55.-
P2

01'

(A-5)

(A-G)

An overall value can be determined from

(A-7)

 

 

 

 

 

S

 

 

Figure A.1 h-s diagram in a diffuser

APPENDIX B

Smifications of Instruments

APPENDIX B

 

 

 

 

 

 

 

 

 

 

 

 

SPECIFICATION Pressure transducer
Company Validyne
DP15-32-N3S4A (PLndl) 2.0psid
DP15-34-N3S4A (FindlAPOl-f) 3.2psid
Pressure DP15-36-N3S4A (Pimp) 5.0psid
Range DP15-42-N384A (P2,P3,Po3) 20psid
DP15—44-N3S4A (P4,P5) 32psid
DP15-46-N3S4A (P06) 50psid
Excitation 5Vrms, 3kHz to 5kHz
Output :35mVN
Accuracy 10.25% FS includes non-linearity and

hysteris, and non-repeatability

 

Temperature range

Oto 160°F

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Inductance 20 mH, each coil
Sensor material 410 Stainless steel
Pressure ports 1/8”-27 N171“ — Bleed screws
SPECIFICATION Pressure transducer (2xP06)
Company/Model No. Omega/PX425-O30AV
Excitation lOVdc
Output 30mV :1: 0.3mV
Pressure Range 0. to 50 psia
Accuracy 10.2% span includes linearity and hysteris
Temperature range -54 to 120°C
Gages Diffused semiconductor
SPECIFICATION Pressure transducer (P4,Po3,P05)
Company/Model No. Omega/HHP-201E
Pressure Range 0. to 30 psi
Display 41/2 digit LCD display
Accuracy 10.2% span includes linearity and hysteris
Temperature range 0 to 40°C
*REMARKS

 

HHP-lOOC/lOlB/lOlC/IOID were used
for others, which are similar to HHP-201E.

 

145

 

 

 

 

SPECIFICATION

Temperature reading

 

 

 

 

 

 

 

 

Company/Model No. Omega/Type T+DP460
Temperature range —99.9 to 401.4 °C
Accuracy :1: 0.5 °C

Temperature coefficient 0.03°/°C; 5 to 45 °C
Rgxatability :1 count

Time stability 1 °C per year
Input impedance 20 MO
Reading rate 1 per second

 

 

Ambient temperature range

 

5 to 45 °C; 80%RH non-condensing

 

 

 

 

 

 

 

 

 

 

 

SPECIFICATION Dynamic transducer
Company/Model No. PCB/1 12A02
Sensitivity 1.0 pC/psi
Resolution 0.002 psi
Resonant Frequengy 250 kHz
Rise Time 2 us
Pressure Range 0.01 to 100 psi
Capacitance 1 8pF
Temperature range :t400°F

 

 

 

 

 

 

 

 

 

 

SPECIFICATION Inline amplifier
Company/Model No. PCB/402A02
Gain 2.5 mV/psi
Input Resistance 1011 ohm
Input Capacitance 100 pF
Noise 15 uV rms

 

146

 

 

 

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BIBLIOGRAPHY

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150

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