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Michigan State
University

 

 

 

This is to certify that the

thesis entitled

PERFORMANCE ASSESSMENT OF RADIAL VANELESS
DIFFUSERS FOR CENTRIFUGAL COMPRESSORS

presented by

Fahed A.N. AL-Awaidy

has been accepted towards fulﬁllment
of the requirements for

Ph.D. degree in Mechanical Engineering

 

 

Ala”

Major prlfessor

Date ““ 05" 58

 

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PERFORMANCE ASSESSNIENT OF RADIAL VANELESS
DIFFUSERS FOR CENTRIFUGAL COMPRESSORS

Fahed A. N. AL-Awaidy

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

PERFORMANCE ASSESSMENT OF RADIAL VANELESS
DIFFUSERS FOR CENTRIFUGAL COMPRESSORS

By

Fahed A. N. AL-Awaidy

Vaneless radial diffusers continue to be used widely with industrial centrifugal
compressors, and many experimental and analytical studies have investigated their steady
and unsteady effects on the compressor stage.

In vaneless diffusers of centrifugal compressors, many different flow phenomena
interfere with one another and different geometric parameters inﬂuence the flow field.
Variations of these parameters allow the designer to optimize the vaneless diffuser for
certain applications or to use a variable geometry to control the stage over a wide range.
Among the main geometrical parameters affecting the vaneless diffuser performance are
the ratio of vaneless diffuser inlet width to impeller radius (balrz) and the ratio of vaneless
diffuser outlet radius to impeller radius (rs/r2) which is also called radius ratio.

Two vaneless diffusers, VNLDl and VNLDZ, that differ in their passage widths
(VNLDZ wider than VNLDl) are tested experimentally downstream of the same
centrifugal impeller to investigate the effect of this variation on the overall compressor

stage performance. Each diffuser was tested at four different impeller speeds, which are

18800 rpm, 24000 rpm, 28000 rpm, and 32000 rpm respectively. These speeds
corresponds to impeller tip Mach numbers of M, = 0.7, 0.89, 1.04, and 1.19 respectively.
A theoretical analysis was carried out also from the diffuser inlet radius to the diffuser
outlet radius using different values of radius ratio. The results of this theoretical analysis
were compared to the measured performance curves of both vaneless diffusers.

The analysis and comparison of these two vaneless diffusers resulted in a detailed
description of the actual ﬂow mechanism in these diffusers. The inﬂuence of geometrical
and aerodynamical parameters of both vaneless diffusers on the compressor stage
performance was studied and investigated. Also the pressure recovery characteristics
were studied and compared for both vaneless diffusers. In addition to the steady
performance analysis, unsteady performance analyses of the compressor stage with both
vaneless diffusers have been carried out. The results showed that the centrifugal
compressor stage has better overall performance with VNLD2 than with VNLDl at
impeller speeds of 18800 rpm, 24000 rpm, and 28000 rpm. At impeller speed of 32000
rpm, VNLDl was better. In terms of ﬂow coefﬁcient, the centrifugal compressor with
VNLD2 showed wider range of flow operation than with VNLDl at all impeller

rotational speeds.

To my parents, my wife, my kids, and my teachers

iv

ACKNOWLEDGMENTS

In the beginning, I thank Allah (SWT) for the completion of this dissertation.
Then, I would like to express my deepest gratitude to Professor Abraham Engeda, the
chairperson of my committee, for his wise advice, understanding, encouragement, and
kind support throughout my study in the department of Mechanical Engineering at
Michigan State University. I am also grateful to the other members of my committee,
Professor John McGrath, Professor Craig Somerton, and Professor Patricia Lamm for
their encouragement, kindness, and valuable comments.

My appreciation also goes to the General Organization for Technical Education
and Vocational Training in Riyadh, Saudi Arabia, which granted me a scholarship to
pursue my graduate study in the USA. I would like to express my thanks to other
individuals who contributed, in some way, to the completion of this research especially
my colleagues in the Turbomachinery Lab., Michigan State University. I thank also Mr.
Craig Gunn for his help in preparing my dissertation.

Last but certainly not the least, my thanks and deep appreciation go to my parents
for their love and support at all times. Also I would like to express my indebtedness,
appreciation and gratitude to great companion, my wife Badriyah Al-Jmaiaah, the most
important person who stood by me and was a trusted friend and a compassionate partner
in all my life. Her emotional support, understanding, love and constant encouragement

made my life much happier and my work much easier. I am also grateful to my

daughters, Hessah and Lujain, and my sons, Abdullah and Mohamad, for the joy they

brought into our life and for their love which have been my source of motivation.

vi

TABLE OF CONTENTS

 

LIST OF TABLES ................................................................................. IX
LIST OF FIGURES ................................................................................ X
NOMENCLATURE ............................................................................ XIII
1. INTRODUCTION .................................................................................................. 1
1.1 TIIRBOMACHINES: DEFINITION AND CATEGORIZATION ........................................ 1
1.2 THE CENTRIFUGAL COMPRESSOR ........................................................................ 2
1.2.1 Steady ﬂow in centrifugal compressor ......................................................... 4
1.2.2 Centrifugal Compressor Stall ...................................................................... 6

1.3 OBIECTIVEOFTHECURRENTWORK .................................................................... 9
2. FLOW IN VANELESS DIFFUSERS - -- ..... ...... . - 13
2.1 TYPES OF RADIAL DIFFUSERS ............................................................................ 13
2.1.1 Vaned Diﬂuser ........................................................................................... 13
2.1.2 Vaneless Diﬁ‘user ....................................................................................... 16

2.2 VANELESS DIFFUSER ........................................................................................ 17
2.2.1 Mode of Operation .................................................................................... 17
2.2.2 Losses in Vaneless Diffuser ........................................................................ 20

2.3 RESEARCH STATUS ON VANELESS DIFFUSER ..................................................... 21
3. THEORY OF DIFFUSION .................................................................................. 34
3.1 DIFFUSION PHENOMENON ................................................................................. 34
3.2 PERFORMANCE PARAMETERS OF DIFFUSION ...................................................... 38
3.2.1 Geometric Performance Parameters .......................................................... 38
3.2.1.1 Passage Width/Radius ............................................................................ 39
3.2.1.2 Length to Width Ratio ............................................................................ 40
3.2.1.3 Divergence Angle ................................................................................... 42
3.2.1.4 Vane Leading Edge Shape ...................................................................... 45
3.2.1.5 Vane Shape ............................................................................................ 47
3.2.1.6 Area Ratio .............................................................................................. 48
3.2.1.7 Radius Ratio ........................................................................................... 49
3.2.1.8 Vane Number ......................................................................................... 51
3.2.1.9 Throat Blockage ..................................................................................... 53
3.2.1.10 Incidence ............................................................................................. 54

3.2.2 Aerodynamic Performance Parameters ...................................................... 55
3.2.2.1 Aerodynamic Blockage .......................................................................... 56
3.2.2.2 Reynolds Number ................................................................................... 57

vii

3.2.2.3 Mach Number ........................................................................................ 58

3.2.2.4 Inlet Velocity Proﬁle .............................................................................. 59

3.2.3 Overall Performance Parameters .............................................................. 60
3.2.3.1 Pressure Recovery Coefficient ................................................................ 60
3.2.3.2 Effectiveness .......................................................................................... 62
3.2.3.3 Total Pressure Loss ................................................................................ 62
3.2.3.4 Flow Range ............................................................................................ 62
3.2.3.5 Distortion ............................................................................................... 65

3.3 FLOW ANALYSIS IN VANELESS DIFFUSER .......................................................... 65
3.3.1 Incompressible and Inviscid Flow .............................................................. 68
3.3.2 Compressible and Inviscid Flow ................................................................ 74

4. EXPERIMENTAL SETUP .................................................................................. 75
4.1 THE CENTRIFUGAL COMPRESSOR TEST STAND .................................................. 75
4.2 INVESTIGATED VANELESS DIFFUSERS ................................................................ 77
4.3 MEASUREMENT POSITIONS AND MEASUREMENTS .............................................. 77
4.4 STEADY PERFORMANCE MEASUREMENT ............................................................ 82
4.4.1 Instrumentation ......................................................................................... 82
4.4.2 Data Collection and Reduction .................................................................. 83
4.4.3 Instrument Accuracy and Result Uncertainty ............................................. 91

4.5 UNSTEADY PERFORMANCE MEASUREMENT ....................................................... 93
4.5.1 Obtaining and Storing the Pressure Signal ................................................ 93
4.5.2 Signal Processing ...................................................................................... 95
4.5.3 Analysis of the Data ................................................................................... 97

5. RESULTS AND DISCUSSIONS ......................................................................... 99
5.1 OVERALL COMPRESSOR STAGE PERFORMANCE CHARACTERISTICS .................. 100
5.1.1 Stage Eﬂiciency and Head Coeﬁ‘icient ..................................................... 100
5.1.2 Flow Range ............................................................................................. 104
5.1.3 At Peak Efﬁciency ................................................................................... I 05

5.2 PRESSURE RISE IN THE COMPRESSOR STAGE .................................................... 107
5.3 OVERALL VANELESS DIFFUSER PERFORMANCE CHARACTERISTICS .................. 1 10
5.3.1 Vaneless Dijfuser Efficiency .................................................................... 1 10
5.3.2 Pressure Recovery of the Vaneless Diffusers ............................................ 114
5.3.2.1 Total Pressure Recovery Cp2-5 .............................................................. 114
5.3.2.2 Subdivided Pressure Recoveries ........................................................... 117

5.4 COMPARISON BETWEEN THE EXPERIMENTAL AND THEORETICAL RESULTS ....... 121
5.5 UNSTEADY PERFORMANCE OF THE COMPRESSOR STAGE .................................. 125
5.5.1 Unsteady Flow in the Inducer .................................................................. 126
5.5.2 Unsteady Flow in the Impeller ................................................................. 129
5.5.3 Unsteady Flow in the Diffuser ................................................................. I34

6. CONCLUSIONS AND RECOMMENDATIONS ............................................. 136
BIBLIOGRAPHY ................................................................................ 140

viii

LIST OF TABLES

Table 4-1 Design parameter of the tested vaneless diffusers .......................................... 77
Table 4-2 Measurement Locations And Measured Quantities ........................................ 81
Table 4-3 Instrument speciﬁcations ............................................................................... 93
Table 5-1 Surge Characteristics through the Compressor Stage with VNLDl and VNLD2

at all Impeller Speeds Using Transducer D ............................................................ 134

ix

LIST OF FIGURES

Figure 1.1 Turbomachines categorization according to ﬂow path: ................................... 3
Figure 1.2 Turbomachines categorization according to function: ..................................... 3
Figure 1.3 Typical centrifugal compressor ...................................................................... 5
Figure 1.4 Separation on a blade ..................................................................................... 6
Figure 1.5 Pattern of Rotating Stall (Parnpreen 1993) ...................................................... 8
Figure 2.1 Types of vaned diffusers .............................................................................. 15
Figure 2.2 Assembly of centrifugal impeller and radial vaneless diffuser ...................... 16
Figure 2.3 Pressure-recovery coefﬁcient versus range for vaned and vaneless Radial
Diffusers (Wilson 1991) ......................................................................................... 17
Figure 2.4 Flow through centrifugal compressor stage .................................................. 18
Figure 2.5 Velocity diagrams at impeller inlet and impeller exit .................................... 19
Figure 2.6 Enthalpy-Entropy diagram for the complete centrifugal compressor stage... 20
Figure 2.7 Flow path in vaneless diffuser (Elder and Forster 1987) ............................... 25
Figure 2.8 Critical Inlet Flow Angle vs. Diffuser Width (Frigne 1980) .......................... 29
Figure 2.9 Diffuser inlet shape ...................................................................................... 30
Figure 3.1 Diffusion mechanisms: (a) isolated airfoil; (b) duct diffuser ......................... 35
Figure 3.2 Diffuser types based on shape: a) conical, b) annular, c) square section, (1)
two-dimensional or rectangular (channel) ............................................................... 36
Figure 3.3 Diffusion in a constant-area bend ................................................................. 37
Figure 3.4 Simple schematic of the channel diffuser (Runstadler, et a1. 1975) ............... 39
Figure 3.5 Comparison of compressor maps (Stein and Rautenberg 1985) .................... 40
Figure 3.6 Pressure rise through the vaned diffuser (Clements and Am 1988) ............... 41
Figure 3.7 Representative locations of several optima of performance ........................... 43
Figure 3.8 Diffuser performance map, AS=0.25, M=0.6, B=0.08 .................................. 44
Figure 3.9 Compressor ﬂow range and compressor efficiency versus 20 (Clements and
Am 1987) ............................................................................................................... 45
Figure 3.10 Leading edge shapes (Yoshinaga et. a1. 1980) ............................................ 46
Figure 3.11 Effect of leading edge shapes on the stage efﬁciency (Yoshinaga et. al. 1980)
............................................................................................................................... 46
Figure 3.12 Diffuser recovery (Bammert et. al. 1983) ................................................... 48
Figure 3.13 Pressure recovery of vaneless and vaned diffusers versus area ratio ............ 49
Figure 3.14 Circumferential static pressure distribution (Jiang and Yang 1982) ............ 50
Figure 3.15 Effect of diffuser vane number (Rodgers 1982) .......................................... 51
Figure 3.16 Blade number effects for rin/r2=l.106 (Camatti et. a1. 1995) ........................ 52
Figure 3.17 Comparison of measured and boundary-layer predicted stall limit .............. 54
Figure 3.18 Effect of diffuser leading edge Mach number and incidence on range (Reeves
1977) ...................................................................................................................... 55
Figure 3.19 Aerodynamic blockage ............................................................................... 57
Figure 3.20 Choke and surge ......................................................................................... 63
Figure 3.21 Different kinds of surge (Cumpsty 1989) .................................................... 65
Figure 3.22 Elementary View of Flow in Vaneless Diffuser .......................................... 67

Figure 4.1 Centrifugal Compressor test rig .................................................................... 75

Figure 4.2 Impeller of the tested conﬁguration .............................................................. 76
Figure 4.3 Measurement planes in inlet pipe ................................................................. 78
Figure 4.4 Measurement Planes in the Compressor Stage .............................................. 79
Figure 4.5 Probe location in the diffuser ........................................................................ 80
Figure 4.6 Unsteady pressure signal ﬂow path .............................................................. 97
Figure 5.1 Performance characteristics of the compressor stage with VNLDl ............. 102
Figure 5.2 Performance characteristics of the compressor stage with VNLD2 ............. 103
Figure 5.3 Total Operating range of the compressor stage with VNLDl and VNLD2 vs.
impeller tip Mach number M. ............................................................................... 104
Figure 5.4 Compressor stage at peak efﬁciency vs. impeller tip Mach number Mt for
VNLDI and VNLD2 ............................................................................................ 105
Figure 5.5 Loss coefﬁcient at peak efﬁciency vs. Mt for VNLDl and VNLD2 ............ 106
Figure 5.6 Inﬂuence of diffuser type on the compressor stage pressure history with
VNLDl ................................................................................................................ 108
Figure 5.7 Inﬂuence of diffuser type on the compressor stage pressure history with
VNLD2 ................................................................................................................ 109
Figure 5.8 Vaneless diffuser performance characteristics: diffuser efﬁciency total-to-
static for VNLDl and VNLD2 .............................................................................. 111
Figure 5.9 Vaneless diffuser performance characteristics: diffuser efﬁciency static-to-
static for VNLDI and VNLD2 .............................................................................. 112
Figure 5.10 Variation of Total Diffuser Pressure Recovery Cp2-5 for VNLDl ............ 115
Figure 5.11 Variation of Total Diffuser Pressure Recovery Cp2-5 for VNLD2 ............ 115
Figure 5.12 Pressure Recovery Cp2-3 for VNLDl ...................................................... 116
Figure 5.13 Pressure Recovery Cp2-3 for VNLD2 ............. ' ......................................... 116
Figure 5.14 Pressure Recovery Cp3-4 for VNLDl ...................................................... 118
Figure 5.15 Pressure Recovery Cp3-4 for VNLD2 ...................................................... 118
Figure 5.16 Pressure Recovery Cp4-5 for VNLDl ...................................................... 119
Figure 5.17 Pressure Recovery Cp4-5 for VNLD2 ...................................................... 119
Figure 5.18 Variation in the Static Pressure Ratio with the Radius ratio for VNLDl and
VNLD2 ................................................................................................................ 122
Figure 5.19 Variation in the squared of Local Flow Mach Number with the Radius ratio
for VNLDl and VNLD2 ....................................................................................... 123
Figure 5.20 Power spectrum of the compressor stage with VNLDl at 32000 rpm
Transducer A ........................................................................................................ 127
Figure 5.21 Power spectrum of the compressor stage with VNLD2 at 32000 rpm
Transducer A ........................................................................................................ 128
Figure 5.22 Power spectrum of the compressor stage with VNLDl at 32000 rpm
Transducer C ........................................................................................................ 130
Figure 5.23 Power spectrum of the compressor stage with VNLD2 at 32000 rpm
Transducer C ........................................................................................................ 131
Figure 5.24 Power spectrum of the compressor stage with VNLDl at 32000 rpm
Transducer D ........................................................................................................ 132
Figure 5.25 Power spectrum of the compressor stage with VNLD2 at 32000 rpm
Transducer D ........................................................................................................ 133

xi

>1

CVND

Cp

d,D

NOMENCLATURE

area (m2)

area vector

speed of sound

diffuser width, width at the impeller exit (mm)
absolute velocity (m/s)
conventional vaned diffuser
pressure recovery coefﬁcient
speciﬁc heat (J/kg K)
diameter (mm)

Force (N)

acceleration of gravity (In/52)
enthalpy per unit mass (J/kg)
local ﬂow Mach number
impeller tip Mach number
mass (kg)

mass ﬂow rate (kg/s)
rotational speed (rpm)
pressure (N/mz)

gas constant (J/kg.K)

radial coordinate, radius (m)

temperature (°C), torque (N.m)

xii

U impeller or tip speed (m/s)

V velocity vector

~V volume (m3)

VNLD vaneless diffuser

W relative velocity (In/s)

w work done by a unit mass of ﬂowing ﬂuid (J/kg)
Z vane number

2 axial coordinate

Greek Symbols

0: ﬂow angle with respect to tangent (deg)
B vane angle with respect to tangent (deg)
4) ﬂow coefﬁcient

7 ratio of speciﬁc heats

1| efﬁciency

11am diffuser effectiveness

A radius ratio across the diffuser

p. dynamic viscosity (kg/(ms) = N s/mz), work coefﬁcient
v kinematic viscosity (m2/s)

1: pressure ratio

p density (kg/m3)

1: temperature ratio

xiii

Superscripts

Subscripts

loss coefﬁcient

head coefﬁcient

time rate of change

average or mean value

degree

stagnation or total condition

stage inlet, diffuser number

impeller exit, diffuser number
impeller exit - measurement station
diffuser inlet

diffuser middle - measurement station
diffuser exit

stage exit

compressor

radial component

isentropic, surface

circumferential or tangential component

axial component

xiv

1. INTRODUCTION

1.1 Turbomachines: Deﬁnition and Categorization

Turbomachines could be deﬁned as all devices in which energy is transferred
either to or from a continuously ﬂowing ﬂuid by dynamic action of one or more moving
blade rows. The rotation of these blade rows (rotor) changes the stagnation enthalpy of
the ﬂuid moving through it by either doing positive work (producing power) or negative
work (absorbing power), depending upon the effect required of the machine. These
enthalpy changes are linked with the pressure changes occurring simultaneously in the
ﬂuid. Machines that could be classiﬁed as turbomachines are fans, pumps, compressors,
and turbines. The term pump is used when referring to machines that increase the
pressure of a ﬂowing liquid. Fan is used for machines imparting only a small increase in
pressure to a ﬂowing gas. A compressor gives a substantial rise in pressure to a ﬂowing
gas. The boundary between fans and compressors is often taken as the area where the
pressure ratio across the machine is l.05-l.l. The subject matter usually included under
turbomachines is restricted moreover to the energy exchange process between the rotor of
a turbomachine and the ﬂuid passing through it. Topics such as turbine blade vibrations

are therefore excluded.

The categorization of turbomachines varies depending on the purpose of each.
They could be categorized by ﬂow path as indicated by the simple diagram in Figure 1.1.
As indicated by this Figure, the machine could be termed an axial ﬂow turbomachine
when the path of the through-ﬂow is parallel to the axis of rotation. On the other hand,
the machine could be termed a radial (centrifugal) ﬂow turbomachine when the path of
the through-ﬂow is in a plane perpendicular to the axis of rotation. The mixed ﬂow term
refers to the direction of the through-ﬂow at rotor outlet when both radial and axial
velocity components are present in signiﬁcant amounts.

Turbomachines could be categorized also by function. Referring to Figure 1.2,
they could be categorized as those absorbing power to increase the ﬂuid pressure or head
(fans, compressors, and pumps) and those that produce power by expanding ﬂuid to a
lower pressure or head (hydraulic, steam, and gas turbines). Analysis and discussion

throughout this work are limited to the diffusion process in the centrifugal compressors.

1.2 The Centrifugal Compressor

In the 1940s and early 19503 most of the gas turbine engines designed and/or built
in the United States used centrifugal-ﬂow compressors. Today, gas turbine engines are
built with axial-ﬂow compressors, centrifugal-ﬂow compressors, and combinations of
one or more axial-ﬂow stages followed by a centrifugal-ﬂow compressors. Interest in the
centrifugal compressors rises because of the wide ﬁeld of their applications, e.g., in small
gas turbines for road vehicles and commercial and military helicopters as well as for
diesel engine turbochargers, chemical plant processes, factory workshop air supplies, and
large-scale air-conditioning plants, etc. The centrifugal compressor has more than one

advantage over the axial unit. The construction of the centrifugal compressor is simple

and rugged, which results in a lower drop in performance with adherence of dust to
blades. It has higher stage pressure ratio than the axial compressor. It has a shorter
length for the same pressure ratio, wider range of stable operation between surging and
choking limits at a given rotational speed, and a ﬂow direction of discharge air that is

convenient for the installation of an intercooler and/or heat exchanger.

(a) Radial (b) Mixed Flow (c) Axial
(Centrifugal)

 

Figure 1.1 Turbomachines categorization according to flow path:

(a) Radial (or centrifugal); (b) Mixed flow; (c) Axial

 

(a) Power Producers
Water Turbines Steam and Gas Turbines
Pelton Francis Axial
W WE; %
i
i i
\
(b) Power Absorbers
Pumps Compressors
Centrifugal Axial Centrifugal Axial

 

. . t-E‘A
i ’

Figure 1.2 Turbomachines categorization according to function:

(a) Power producers; (b) Power absorbers

1.2.1 Steady flow in centrifugal compressor

Figure 1.3 shows a common type of centrifugal compressor. It consists
essentially of a rotating impeller followed by diffuser. Fluid enters the impeller through
the eye or inducer, whose function is to turn the relative ﬂow as it enters the impeller
passages. If there are no prewhirl vanes in front of the impeller, the ﬂuid ﬂow into the
impeller will be in the axial direction. For this case the impeller blades should be curved
in the direction of rotation for smooth entry. The amount of curvature (twist) varying
from hub to tip at the inlet and depending on the axial velocity and the impeller rotational
speed.

The function of the impeller is to increase the energy level of the ﬂuid by whirling
it outwards, thereby increasing the angular momentum of the ﬂuid. Both the static
pressure and the velocity are increased within the impeller. At the impeller exit, the
blades shown in Figure 1.3 are straight and in the radial direction. The velocity of the air
leaving this impeller, in contrast to that of the air leaving the axial impeller or rotor, has
no axial component. After leaving the impeller, the air passes through a radial diffuser,
consisting of vaned or vaneless ﬂow passages in which momentum is exchange for
pressure. Radial diffusers may consist of a vaneless portion, as shown, followed by a
series of stator vanes. The purpose of the diffuser is to convert the kinetic energy, which
is as high as 50% of the total energy added by the impeller, of the ﬂuid leaving the
impeller into pressure energy. This shows the signiﬁcance that a well-designed diffuser
can have on the stage efﬁciency.

In the case of vaneless diffusers (VNLD), the ﬂow is further deceleratcd
downstream of the jet-wake mixing process. However, the radial component is reduced

by the increase of the ﬂow area, which is determined by the conservation of mass; while

the tangential component is reduced with increase in radius, which is determined by the
conservation of angular momentum. The VNLD provides a wide operating range with a
reasonable efﬁciency.

In the case of a conventional vaned diffuser (CVND), the vanes are separated
from the impeller by a short vaneless space in which the jet and wake mix and the ﬂow is
deceleratcd to subsonic velocities. In the semivaneless space, the region between the
leading edge and throat of the diffuser changes the pattern of the isobar from nearly
parallel to perpendicular to the flow direction. In the divergent channel, a further decrease
of the velocity is realized with a subsequent increase of static pressure, which leads to an
excellent performance. The throat of the CVND limits the maximum massﬂow that can
ﬂow through the compressor stage. If the massﬂow is reduced, the boundary layers in the
diffuser channel can be so weak that separation occurs.

The air leaving the diffuser is then directed either to a return channel (if the Stage
is followed by additional stages) or to the collector. The function of the collector, which

is also called scroll or volute, is to collect the ﬂow from the diffuser and deliver it to the

outlet pipe.

Radial bladed

  
  

 

 

 

I: Diffuser vanes - ' Outlet
Collecror Diffuser vanes

 

Figure 1.3 Typical centrifugal compressor

1.2.2 Centrifugal Compressor Stall

Stall can be regarded as the cessation of continued rise in lift on an airfoil to the
former or in Static pressure recovery in a diffuser or cascade to the latter. In the either
case, stall is the result of boundary layer separation. In cascade aerodynamics, stall refers
to a drop in the turning angle and lift (C1). The lift achieves a maximum just before the
stall occurs as angle of attack increases from low values to high values. At a certain angle
of incidence the ﬂow separates on the suction side like shown in Figure 1.4. Similarly,
stall can occur if the diffusion is too high. The ﬂow will separate, if the kinetic energy in
the ﬂow is too low to sustain the ﬂow against the forces caused by the adverse pressure

gradient.

 

 

 

 

 

Figure 1.4 Separation on a blade
Stall can be deﬁned as the response of a component on a local separation of the

boundary layer. The corresponding perturbation can propagate upstream and downstream
but is triggered by impeller or diffuser ﬂow. It limits the pressure rise that can be
achieved in one component of the compressor and can occur at positive and negative
values of the pressure rise curve of the whole system. After Jansen (1964) investigated

rotating pressure ﬂuctuations in a vaneless radial diffuser both theoretically and

experimentally, it was necessary to extend the deﬁnition for Stall. Jansen reported
pressure ﬂuctuations due to instability in the main ﬂow. This is also called stall in the
ongoing work. In contrast to stall, surge affects the whole system and not only certain
components. The pressure ﬂuctuations at a surged operating point are present in the
compressor as well as in the inlet pipe and discharge pipe. Stall can appear in all
components of the compressor stage, but this distortion disappears in the inlet and
discharge pipe.

Rotating stall is a ﬂow phenomenon characterized by rotating circumferential
distortions in the ﬂow ﬁeld. Such distortions may be described by equidistant rotating
zones of low ﬂow surrounded by zones of relatively high ﬂow, as Shown in Figure 1.5.
The zones of low ﬂow are called stall cells and may rotate relative to the impeller. In
rotating stall, impeller passages take turns stalling, then recovering. Rotating stall can
occur as an intermittent series of local static pressure oscillations or as a continuous
ﬂuctuation of local static pressure. In both cases, large pressure oscillations indicate the
presence of zones of retarded ﬂow that rotate circumferentially either in the same or in
the opposite sense as the rotor rotation.

Rodgers (1977a) showed that both impeller and diffuser can trigger rotating stall.
The former is called impeller rotating stall; the latter is called diffuser rotating stall.
Kaemmer (1984) reported that both impeller and diffuser inﬂuence the stall behavior of
the other part. Despite this, most publications take only the impeller or diffuser in

consideration by itself. This leads to non-comparable results in their stall investigations.

Region of
normal ﬂow

" " Region of low
(stalled) ﬂow

 

Figure 1.5 Pattern of Rotating Stall (Parnpreen 1993)

Stall in the impeller can be due to unsteady phenomena in the inducer or in the
radial part of the impeller. Both kinds of stall are of a different nature, so they will be
treated here separately. Inducer stall can be observed only in compressors without inlet
guide vanes. The ﬂow separates if the incidence angle at the inducer is too high.
Therefore, inducer stall is due to ﬂow separation because of incidence.

For impeller rotating Stall, pressure ﬂuctuations occur throughout the entire
meridional extent of blade channels. 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 towards the passage entry. Here ﬂuid moves out of the passage into the
inducer. If, due to the rotation, the passage ﬂow conditions becomes more favorable, the
passage ﬂow can recover and the motion is repeated. However, in the case of stall the
ﬂow is separating at the pressure side, while the ﬂow at a stable operation point separates

at the suction side, due to the jet-wake pattern.

For diffuser stall, Jansen (1964) performed one of the ﬁrst experimental and
theoretical investigations in self-excited rotating pressure ﬂuctuations. He showed in his
calculations that even potential ﬂow in a radial diffuser can become unstable. This
instability causes rotating pressure perturbations. This has been called rotating stall based
on patterns observed in axial cascades. Jansen suggested the separation of the three-
dimensional wall boundary layer as a trigger for rotating stall. Diffuser stall resulted in a
degradation of diffuser static pressure recovery. Overall stage efﬁciency and range are
limited by this effect. Both amplitude and the rotational speed of the pressure pattern
gradually increase as the mass ﬂow rate in the machine is gradually decreased beyond the

critically stable operating conditions.

1.3 Objective of the Current Work

The demand for improved diffuser performance becomes increasingly insistent
with reﬁnement in impeller design and emphasis on high compressor efﬁciency. The
energy size of a single stage centrifugal compressor can vary from few kilowatts to
megawatts. The centrifugal compressor consists of three basic components: inducer,
impeller, and diffuser. The heart of the compressor is the impeller, where all the energy
transfer takes place; it would therefore be the likely suspect for any shortcomings that
could occur. Surprisingly, the designer has had more success with the impeller than with
the inducer or the diffusing system. In most centrifugal compressors both the rotor and
the radial diffuser are limited by the diffusing capabilities of the ﬂow channels.

At the inducer, the ﬂuid comes from the pippins on board into the impeller, which
could be rotating from 1000 to 100,000 rpm making it a challenging spot where the

designer must apply all his knowledge and experience. The diffuser system is a

stationary part of the machine that accepts the ﬂuid from the high speed impeller and
slows it down; a high proportion of the ﬂuid energy (50% sometimes) can be kinetic
energy. The design of an appropriate diffusing system to slow down the ﬂuid efficiently
has been for a long time, and still is, one of the main difﬁculties in compressor design.

The diffuser system of a centrifugal compressor comes basically in two general
categories either as a vaneless or vaned diffuser, each followed by a collector, a volute,
or the next stage. Vaned diffusers can generally be further subdivided into two types
depending on channel geometry as straight channel or curved channel, or depending on
solidity as conventional or low solidity. In the vaneless diffuser, basically, diffusion
occurs in a radial space bounded by two plane walls. The vaneless diffuser, the most
common diffuser, employed for centrifugal compressors and pumps, is similar in ﬂow
physics to the channel, conical, and annular diffusers. It may be said to represent the
most complex diffusion of these family of diffusers. Through the years a wide range of
experimental research has been carried on conical, channel, and annular diffusers as
discrete elements, as opposed to the vaneless diffuser, which has always been handled as
part of a turbomachinery system.

Actual ﬂow in the vaneless space is where the ﬂow scrubs the side walls at high
velocities, which results in a boundary layer growth from the initial conditions at the tip
of the impeller. In order for boundary layer calculations to be made, these initial
conditions must be known; but they are only vaguely understood today. Under the
adverse pressure gradients in the vaneless space, the boundary layer grows. If it grows
thick, signiﬁcant secondary ﬂows will develop.

The vaneless diffuser is the most popular diffuser because of its characteristics:

10

0 simple and inexpensive construction

0 wide operating range and

0 the ability to reduce sonic absolute velocity to a subsonic one without the

formation of shock waves

The ﬂow in the vaneless diffuser is basically governed by the continuity, energy,
and momentum equations. In practice, the compressor designer is often interested only in
how certain aerodynamic parameters vary radially as the ﬂow diffuses in the vaneless

diffuser. The most important of these being:

0 P, static pressure 0 P0, total pressure

0 a, ﬂow angle 0 p, density

0 C, absolute velocity 0 M, the Mach number.
0 T, static temperature 0 To, total temperature

0 rCu, unit angular momentum

The fundamental part of any compressor, whether centrifugal or axial, is the
impeller where the energy increase of the air passing through occurs. However, the
impeller development is restricted by the mechanical limitations that permit very little
variation in the blade or rotor design. However, no matter how good the impeller design
from an aerodynamic point of view, the ﬂow at the impeller exit needs to be modiﬁed for
several reasons. For air delivery to a pipe system or to a second stage in a multistage
machine, it is necessary to concentrate the ﬂow in a given direction. Also, a considerable
portion of the energy of the ﬂow at the exit of the impeller is in the form of kinetic
energy. This kinetic energy in the absence of guide vanes or a spiral casing is entirely

lost, which results in lower stage efﬁciency. For these reasons, it is generally found

11

desirable to increase the static pressure at the expense of a reduced velocity of the air
stream exiting from the impeller. This could be done in the stationary elements of the
compressor. Therefore, diffuser design and development is the area that can provide
further improvement in centrifugal compressor performance. Additionally, a diffuser is
much less restricted by the mechanical limitations when compared to the impeller of a
centrifugal compressor.

Due to the wide range of its operating conditions, vaneless diffusers have been
used in SAUDI ARAMCO (Saudi ARAMCO Oil Company), SABIC (Saudi Basic
Industries Corporation) and other companies in Saudi Arabia. Therefore, in Saudi Arabia
research and development are needed on the vaneless diffuser.

This current work is based on a theoretical and experimental ﬂow analysis of two
vaneless diffusers. One of these vaneless diffusers is a typical industrial vaneless diffuser
and the second one was designed by the MSU Turbomachinery Lab for high performance
and good pressure recovery. The comparative theoretical and experimental study and
analysis of these two vaneless diffusers is expected to give detailed information on:

0 the actual ﬂow mechanism in these diffusers

- the inﬂuence of geometrical parameters on the diffuser performance

0 the inﬂuence of aerodynamic parameters on the diffuser performance

0 the pressure recovery characteristics and

° performing unsteady performance analysis of the compressor

These two vaneless diffusers will be tested downstream of the same impeller at
the MSU Turbomachinery Lab. The theoretical and experimental results will be

compared.

12

2. FLOW IN VANELESS DIFFUSERS

2.1 Types of Radial Diffusers

Different types of radial diffusers have been used and developed. This is a result
of the wide applications of the centrifugal compressors to increase the pressure ratio and
efﬁciency. Radial diffusers could be divided into two types: vaned diffusers and vaneless

diffusers.

2.1.1 Vaned Diffuser

The concept of the vaned diffuser is to Shorten the ﬂow path compared to the long
ﬂow path in the vaneless diffuser. Also, vanes can be used to direct the ﬂow more in the
radial direction, to increase the rate of diffusion, and to decrease the losses. The
efﬁciency is related directly to the number of vanes in the diffuser. As the number of
vanes increases, the angle of divergence is smaller; and the efﬁciency increases until
friction and blockage overcome the advantage of more gradual diffusion. With this
advantage of higher efﬁciency (higher pressure recovery), the ﬂow range is limited at low
ﬂow rate due to vane stall and due to throat choke.

Vaned diffusers may be of many forms, some of which are illustrated as follows

(Figure 2.1):

13

Straight Channel/Wedge Diffuser: It has a simple geometry; and due to this
simplicity, it is easy to manufacture and very popular. The disadvantage is its large size.

Straight Plate Diffuser: It has a large number of vanes, Z>30, but the pressure
recovery is not good. Like the Straight Channel/Wedge diffuser, it has simple geometry
and is easy and inexpensive to manufacture.

Vaned Island Diffuser: This is a reﬁned straight channel, which is used for a
high pressure ratio and transonic inlet Mach number M3>1. Again, it is large in size, but
the number of vanes is small.

Circular Arc Diffuser: It has a simple geometry, so it is easy to manufacture; but
it doesnt have any outstanding aerodynamic characteristic.

CamberedlAerofoil Diffuser: This type of diffusers is used for transonic and
subsonic ﬂow applications. Small in size with a good pressure recovery, it has been
designed based on axial cascade data.

Twisted Diffuser: It is a reﬁned cambered vane, which has a 3-D twisted shape
to produce good efﬁciency. It has a wide range and high pressure ratio.

Multiple Cascade Diffuser: Again, it is a cambered vane in cascade to produce
higher efﬁciency. Due to the high number of vanes at the increased radii, the risk of
separation is reduced.

PipelConical Diffuser: It is used for a higher pressure ratio and transonic ﬂow
applications. It is large in size but with good pressure recovery.

Low Solidity Vaned Diffuser: It is used for low ﬂow angles or coefﬁcients but

with good pressure recovery and wide operating range. Nowadays, it is of great interest.

14

 

(a) Straight Channel Diffuser (b) Straight Plate Diffuser (c) Varied Island Diffuser

re A% a

((1) Circular Arc Diffuser (e) Cambered/Aerofoil Diffuser (1) Twisted Diffuser

   

(g) Multiple Cascade Diffuser (h) Pipe I Conical Diffuser (i) Low Solidity Vane Diffuser

Figure 2.1 Types of vaned diffusers

15

2.1.2 Vaneless Diffuser
Diffusion in vaneless diffuser occurs in a radial space bounded by two plane walls

as shown in Figure 2.2. Thus, a vaneless diffuser requires a considerable radial space,

which results in the long path of the Spiral ﬂow that is the opposite of the vaned diffuser.

 

Figure 2.2 Assembly of centrifugal impeller and radial vaneless diffuser

The vaneless diffuser has certain inherent advantages over the vaned diffuser.
The vaneless diffuser has a wide range of air ﬂows and tip speeds over the vaned diffuser
as shown in Figure 2.3. The distribution of velocities at the impeller outlet, both in
magnitude and direction, precludes the possibility of introducing ﬁxed vanes that will
provide the optimum angle of attack for all incident air at any operating condition.
Changes in this angle with volume ﬂow and tip speed reduce still further the probability
of satisfactory incidence. In addition to that, the presence of diffuser vanes near the
impeller outlet may result in relative velocities equal to that of sound, with consequent
Shock losses. On the other hand, continuous diffusion of supersonic circumferential-
velocity components apparently can be accomplished in the vaneless diffuser and

changes in the ﬂow angle, in the absence of vanes, apparently will produce no serious

16

increase in diffuser losses. Moreover, the vaneless diffuser is inexpensive to manufacture
and more tolerant to erosion and fouling than vaned diffusers. However, the vaneless
diffuser needs a large diameter because of its low diffusion ratio. The vaneless diffuser

could be used widely in automotive turbochargers because of the wide range it offers.

{N r r

 

/VANEO
VANE 1. [SS

 
 

pnessuns-thovtnr COEFFICIENT, c,.

 

best «thorny pomt, be:

 

 

 

 

LIV—1 I
0.8 to 1.2
RELATIVE FLOW cocrnutm (we...)

Figure 2.3 Pressure-recovery coefﬁcient versus range for vaned and vaneless Radial
Diffusers (Wilson 1991)

2.2 Vaneless Diffuser

2.2.1 Mode of Operation
The ﬂow in a vaneless diffuser is similar in ﬂow physics to the channel, conical,

and annular diffusers. These types of diffusers will be discussed in the next chapter from
the geometric point of view. It could be said that the ﬂow in the vaneless diffuser
represents the most complex diffusion of this family of diffusers. In the past, a wide
range of experimental research has been conducted on conical, channel, and annular

diffusers as discrete elements; while the vaneless diffuser has been handled as a

turbomachine element.

17

To analyze the ﬂow in vaneless diffuser, a brief description of the ﬂow through
the centrifugal compressor is needed. The ﬂow through a centrifugal compressor stage is
shown on Figure 2.4. As described earlier in Section 1.2, the ﬂuid is drawn into the
impeller (where the energy transfer occurs) through the inlet casing. Within the impeller,
both the static pressure and velocity are increased. The curved surface of revolution of
the impeller is called the hub, and the curved surface forming the outer boundary to the

ﬂow of ﬂuid is called the shroud.

Collector scroll

   

\ _______
\

_ _ _
_.l |‘— Inducer Pressure, Abe. Velocity

 

 

7 ________
Increasing

Figure 2.4 Flow through centrifugal compressor stage

At the entry to the impeller the ﬂow has a relative velocity W1 at an angle Bl to

the axis of rotation as shown in Figure 2.5. The inducer section or rotating guide vanes as
they are sometimes called turns this relative ﬂow into the axial direction. The inducer

starts at the inlet casing and ﬁnishes in the region where the ﬂow is beginning to turn into

the radial direction.

18

 

 

 

 

 

CFC”

 

 

 

Impeller inlet Impeller Exit

Figure 2.5 Velocity diagrams at impeller inlet and impeller exit

As mentioned before, the energy transfer takes place in the impeller, which results
in work done on the ﬂuid. This work is equal to the stagnation enthalpy rise (see

Figure2.6) in the impeller, which could be expressed by the Euler equation as

W=U2Cu2 -UICUI =h02 -h01 (21)
c2
where the stagnation enthalpy is h, = h + -2— (2.2)

The energy transformation takes place in the vaneless diffuser, which is indicated
by path 3-5 on Figure 2.6. The vaneless diffuser consists of two parallel planes that the
air from the impeller ﬂows between them (See Figure 2.2). So the diffusion occurs in a
radial space bounded by the two parallel planes. According to this, actual ﬂow in the
vaneless space is where the ﬂow rubs the sidewalls at high velocities, which results in a
boundary layer growth from the initial conditions at the tip of the impeller. Since the ﬂow
at the impeller outlet is nonuniform, the conditions at the impeller tip have been assumed
to be steady with a uniform velocity proﬁle. With this assumption, the diffusion may be
efficiently accomplished and could be controlled by the diffusion rate and the wall

boundary layer.

19

2.2.2 Losses in Vaneless Diffuser
The losses in the vaneless diffuser could be divided into losses due to impact and

losses due to friction. The impact losses arise when the impeller width is less than the
diffuser width and/or if the active ﬂow doesn’t ﬁll the impeller cross-sectional width at
the exit. For such cases, the impact losses at the entrance to the diffuser must be added to
the frictional losses. This is the general case, but it should be noted that the equality of
the velocities at the impeller outlet and diffuser inlet is a result of the ﬁlling of the outlet
width of the impeller and the equality of the widths of the impeller and diffuser for the
given compressor, which is the condition always obtained. This condition causes a
considerable deviation between the theoretical and experimental results.

P
02 P05 1C:

h A 02 051/

 

 

 

 

 

 

 

 

 

Figure 2.6 Enthalpy-Entropy diagram for the complete centrifugal compressor stage

20

The frictional losses occur at the diffuser wall during the passage of the gas
through the vaneless diffuser where the conversion of kinetic energy into pressure rise
takes place. These losses are usually expressed in terms of a friction coefﬁcient that is a
measure of the loss in total pressure through the diffuser. The available data on friction
coefﬁcients in vaneless diffusers are meager and Show a rather wide scatter, partly
because of the difﬁculties inherent in the determination of such coefﬁcients and partly
because of diversity in their deﬁnition. Accordingly, for certain applications (for
example in design of diffusers) it is recommended that each designer check appropriate
values of the friction coefﬁcient based on similar machines when contemplating a new

design.

2.3 Research Status on Vaneless Diffuser

During the last years, the research in the vaneless diffuser area has been active.
Part of the previous research work related to vaneless diffusers will be surveyed in this
section as well as the next chapter.

One of the earliest efforts to predict the performance of the vaneless diffuser was
done by Polikovsky. and Nevelson (1943). A theoretical and experimental investigation
was initiated on the vaneless diffuser of a centrifugal fan. The method of computation is
based on the principles developed by Pﬂeiderer. Polikovosky and Nevelson worked over
and developed this principle so as to provide a practical method for the computation of
vaneless diffusers. Their method was based on one-dimensional analysis. The
comparison of the computations with experimental data shows sufﬁciently good

agreement and permits the determination of the limits within which the friction

21

coefficient lies. They generalized their conclusion, which they were found applicable to
the centrifugal fan, to that for axial fans.

Brown and Bradshaw (1947) presented a method of designing vaneless diffusers
using data given for Simple conical diffusers. They designed and studied experimentally
a family of diffusers with different cone angles having the same throat height. They then
studied them for different throat height with the same diffuser. This method was
investigated with ﬁve vaneless diffusers in combination with a mixed-ﬂow impeller in a
variable component test rig. They found that this method resulted in compressor
efﬁciencies equal to those shown by the vaned diffuser designed for the same impeller
and retained the characteristically wide operating range of vaned diffuser.

Barina (1947) develops a paper similar to the previous one in which an
experimental investigation has been conducted in a variable component rig of two
vaneless diffusers. These two vaneless diffusers are of different passage curvature and
are designed for similar mixed-ﬂow impellers. The result of this paper showed that the
large difference in passage curvature of these diffusers made no appreciable differences
in diffuser performance at the peak compressor efﬁciency for the range of speeds
investigated.

Brown (1947) investigated friction coefficients for three constant-area vaneless
diffusers. These coefficients have been calculated from total- and static- pressure surveys
in conjunction with a centrifugal impeller. These surveys have been taken at several radii
and from the usual over-all measurements of temperature, pressure and air ﬂow. Brown
found that the average value of the friction coefficient through the entire diffuser was

approximately 50 percent higher than that for fully developed turbulent ﬂow in smooth

22

pipes while at the diffuser entrance was about three times the pipe values and in the
middle of the diffuser agreed well with the smooth-pipe values. He also found that the
friction coefﬁcients computed from total pressures were signiﬁcantly larger than smooth-
pipe values only at the diffuser entrance. Average values of the static-pressure friction
coefficient over the entire ﬂow path in the diffuser were about 50 percent higher than
those found from von Karman’s equation for turbulent, smooth-pipe ﬂow. Finally, he
found that the over-all friction coefﬁcient increased with decreasing diameter.

Bradshaw and Laskin (1948) did an experimental study in a variable-component
rig of four vaneless diffusers of different diameters over a range of tip speeds from 500 to
1300 feet per second and air ﬂows from open throat to surge. They found that the
important losses in efficiency occurred in the vicinity of the diffuser entrance and diffuser
exit regions, internal losses being comparatively negligible. Diffuser-entrance losses
were approximately constant at about 6% for all diameters. Diffuser-exit losses increased
from 3 to 15 points as diffuser diameter decreased, the losses being approximately
inversely proportional to the square of the diffuser diameter. The overall efﬁciency of
the compressor is therefore reduced as the diffuser diameter is reduced. Also, they found
that the effect of diameter on diffuser-entrance losses, internal losses in the diffuser, and
impeller efﬁciency was slight. In addition, variation in load coefﬁcient and impeller tip
speed produce comparatively small changes in diffuser efﬁciency and the changes are, in
general, similar for diffusers of different diameters.

Stanitz (1952) introduced a comprehensive treatment of the vaneless diffuser and
published a correct set of one-dimensional equations for the radial momentum, tangential

momentum, conservation of mass, conservation of energy, and the equation of state. In

23

this paper, the analysis method and the design method have been developed for one-
dimensional, compressible ﬂow with friction, heat transfer, and arbitrary area change in
vaneless diffusers with arbitrary proﬁles in the axial-radial plane. The effects of mixing
losses due to nonuniform ﬂow conditions at the impeller discharge were not included.
He presented three groups of numerical examples in which the effects of friction, heat
transfer, and diffuser wall spacing are investigated. As a result of these examples, he
found that heat transfer from the ﬂuid has the opposite effect of friction on pressure rise
in vaneless diffusers and is therefore to be desired.

Stanitz (1952) showed that a typical static pressure rise coefﬁcient for a vaneless
diffuser is lower than for a vaned diffuser because the radial distance over which a
sufﬁcient reduction is achieved corresponds to a very long ﬂow path especially at small
ﬂow angles a2. Refering to Elder and Forster (1987), the ﬂow in a vaneless diffuser with
a radius ratio of 2 and an inlet ﬂow angle of 5° will rotate 400° before leaving the diffuser
as shown in Figure 2.7. High friction losses result, and the real pressure rise is much
lower than the ideal one. On the other hand the vaneless diffusers are well suited for off-
design operation because they are compatible with a wide range of absolute ﬂow angles
a2, and they can only choke if the radial component of the Mach number exceeds unity
(VKI 1965). Dean (1976) states that backﬂow into the impeller is less frequent with

vaneless diffusers than with vaned diffusers caused by vane pressure loading.

24

 

 

 

Figure 2.7 Flow path in vaneless diffuser (Elder and Forster 1987)

Stanitz (1952) found also that even with relatively low friction coefﬁcients and a
neglect mixing losses at the impeller tip, the friction losses in most vaneless diffuser
designs are considerable, where the computed diffuser efﬁciencies in the low 80’s; and
these losses result from the usually large ratio of wetted surface to ﬂow area in vaneless
diffusers. Finally, Stanitz suggests that the diffuser efﬁciency can be improved as the

compressor ﬂow coefﬁcient decreased so that the diffuser walls can be spaced farther

25

apart (thus, reducing the ratio of wetted surface to ﬂow area) without increasing the
length of the ﬂow path in the diffuser.

Through their paper, Dean and Senoo, (1960) have developed a new and more
realistic theory for approximating real ﬂows in vaneless diffusers. The theory is not
complete, since it doesn’t include compressibility and the blockage effect of diffuser
sidewall, boundary layer growth. However, it does introduce the important unsteady
ﬂow phenomena of re-distorted ﬂow leaving a centrifugal impeller and entering a
vaneless diffuser. The following particular results were obtained:

1. Inlet-ﬂow distortions can have signiﬁcant inﬂuences on vaneless-diffuser ﬂow
behavior. The magnitude of the inﬂuence depends upon the impeller discharge angle, the
degree of distortion, the diffuser wall friction and geometry, and on other variables in the
theory such as impeller ﬂow and work coefﬁcients.

2. It is impossible to predict the behavior of a diffuser receiving a distorted inlet
ﬂow from information on axisymmetric ﬂow.

3. A rotating distorted ﬂow in a vaneless diffuser leads to a signiﬁcant pressure
work transfer between high and low relative velocity regions.

4. The mixing shear stresses between jet and wake regions are shown to be less
important than wall shear Stresses in governing the ﬂow behavior.

5. The total pressure loss in the diffuser as a fraction of inlet dynamic pressure
may be less for distorted than for undistorted ﬂow. However, with backward-leaning
blades, the impeller work input is always larger for undistorted ﬂow.

6. These results point out the need for a realistic prediction of the ﬂow pattern

discharged from a centrifugal impeller if the diffuser ﬂow is to be predicted.

26

With Jansen (1964), the ﬂow in radial diffusers in the absence of unsteady ﬂow is
isolated, and an extensive analytical and experimental study concerning this has been
undertaken. In the absence of wakes from the impeller or other unsteady ﬂow
phenomena, the formation of a boundary layer on the sidewalls of the diffuser is the main
cause of a loss in diffuser efﬁciency. The boundary layers, which are three dimensional
in character, are investigated for several inlet conditions; and the theoretical results are
compared with those of the experiments. Jansen (1964) eliminated the discrepancies
between theory and experiment by adjusting the friction factor f so that it varied along the
radius and so that its magnitude resulted in the experimentally found pressure loss. He
pointed that when the ﬂuid passes a stationary section prior to entering the diffuser the
ﬂow may enter the diffuser with a fully developed boundary layer. On the other hand,
the boundary-layer growth in a diffuser could develop so rapidly that at a certain point
the boundary layers of the two sidewalls would meet at the center. Accordingly, he said
that some of the relations stated in his paper concerning the free-stream ﬂow are no
longer applicable. Jansen (1964) also pointed that the Mach number associated with the
total velocity is often close to 1.3. At these Mach numbers compressibility effects
inﬂuence the behavior of the boundary layer to a large extent, and this in turn affects the
pressure rise in the diffuser. In his study, Jansen (1964) extended the compressible
turbulent boundary-layer transformation to the axisymmetric case. This transformation
changes the physical geometry of the diffuser in such a fashion that one obtains an
equivalent shape for which the incompressible ﬂow equations are valid. He found that
the present transformation is applicable to the fully developed boundary layer without

modiﬁcation if one takes the diverging wall into account.

27

Johnston and Dean (1966) developed two simple analyses to predict losses in
centrifugal compressor (or pump) vaneless diffusers. These two simple analyses are one-
dimensional, axisymmetric friction loss and sudden-expansion mixing to account for
losses in the diffuser caused by wakes of separated impeller blades. They restricted their
analyses to incompressible ﬂow so that no shocks will exist and one can obtain a good
approximation for the actual losses. In their analyses, they determined total pressure
losses (and hence the diffuser efﬁciency) by the use of an apparent friction factor or wall
friction coefﬁcient. It was account for the actual wall shear stress and for changes of
momentum ﬂux due to alteration in velocity-proﬁle shape along the diffuser ﬂow path.
They showed that these theories of friction loss and sudden-expansion might be used to
replace the more exact, but more difﬁcult, method of Dean and Senoo (1960) over a very
wide range of compressor parameters. Johnston and Dean (1966) also found that their
analyses are consistent with available experimental data.

Senoo (197 8) pursued a different route and calculated the incompressible,
circumferentially symmetrical, Stationary ﬂow in VNLD including boundary layer
effects. This calculation showed that the streamlines at the wall ﬂow inward at certain
radial positions. Senoo (1979) veriﬁed his theoretical results experimentally. In his
model, he states that rotating stall occurs if the boundary layer of the diffuser hub and
shroud wall grow together. Senoo (1979) investigated ﬂow parameters at the diffuser
inlet affecting rotating stall by using his model. He showed that the axial inhomogenety
in the ﬂow has large inﬂuence on the rotating stall. Furthermore, he showed that rotrating
stall occurs in diffuser with smaller diffuser width ratio can be operated Stable at lower

massﬂows as a diffuser with a larger diffuser width ratio. The radius ratio only has

28

inﬂuence on the critical diffuser inlet angle on diffuser with a large diffuser width ratio.
Additionally, he showed that the critical ﬂow angle at diffuser inlet is higher at higher

Mach numbers.

 

16 — + ...
stable

    

12—

Critical Diffuser Inlet Angle [Degress]

 

 

 

O l l l l l l l l l I l l l l

0 .02 .04 .06 .08 .10 .12 .14
Diffuser Width -;:-
Figure 2.8 Critical Inlet Flow Angle vs. Diffuser Width (Frigne 1980)

Ligrani (1982) shows that the Reynolds number has an inﬂuence on rotating stall
in the VNLD. The model of Senoo showed a good agreement with the experiments if the
critical impeller exit angle is corrected with the Reynolds number. The corrected ﬂow
angle at the diffuser inlet , diffuser width, and stable operation range is shown in Figure
2.8.

Nishida (1995) observed in a two-process compressor that the critical ﬂowangle
also depends on contraction ratio b3/b2 and inlet curvature radius II as shown on Figure

2.9. He developed a correlation for the critical ﬂow angle at the impeller inlet, which is

based on the correlation of Senoo. On the other hand, he showed again that the stall

29

pattern depended on the diffuser and the impeller. The same diffuser with different

impellers had different stall pattern just as the same impeller with different diffusers.

b3 Diffuser '

r
g
g
/

\\\\\\\\\\‘

 

Figure 2.9 Diffuser inlet shape
Through their paper, the Whitﬁeld and Roberts (1983) compared the performance

of a turbocharger compressor with two prototype diffuser-volute systems to the
performance with the standard turbocharger volute system. The two prototype volutes
are substantial modiﬁcations to the standard design with a signiﬁcant reduction in
vaneless diffuser radius ratio. Although no improvements in performance in terms of
pressure ratio and surge margin are Shown, the comparison is encouraging in terms of the
changes in volute design. Also, the prototype volutes were designed with tongues, which
prevented any recirculating ﬂows in the volute passage. They found that the effect of the
tongues upon the pressure variation with azimuth angle has been demonstrated, and it is
intended to further test these volutes with the tongues cut back.

Inoue and Cumpsty (1984) investigated the discharged ﬂow from centrifugal
impellers, which is highly distorted. Its behavior in the diffuser could be expected to
have a determining effect on the performance of the compressor. A limited number of

experiments were carried out, and extensive measurements were made in building a

30

vaneless diffuser. Also, a number of experiments were carried out on vaned diffusers.
The performance of the vaneless diffuser can be predicted with reasonable accuracy at
the design point, provided the ﬂow proﬁle entering the diffuser is either known or can be
estimated. Inoue and Cumpsty (1984) found that although the unsteady part of the
pattern at inlet to the vaned diffuser was generally similar to the vaneless diffuser, it was
affected to some extent by the diffuser vanes. Also, they found that the circumferential
mean radial velocity proﬁle in the axial direction at the vaned diffuser inlet was almost
identical with that for vaneless diffuser. Reversed ﬂow, on the other hand, appeared in
the low radial velocity region near the diffuser vane leading edge when the ﬂow rate was
small, and this led to an increase of loss near the sidewalls.

Yingkang and Sjolander (1987) in this paper present measurements of the Steady
aerodynamic characteristics of a series of ﬁve vaneless diffusers with walls varying from
mildly divergent to strongly convergent. They determined that the static pressure
recovery and the ﬂow were traversed at the inlet and the outlet of the diffuser for a broad
range of ﬂow rates in each case. They also found that the wall convergence results in a
negative (stabilizing) slope in the pressure rise curve for the diffuser. In the middle of the
ﬂow range the highest pressure recovery was obtained with the 5.5 degree diffuser
(maximum convergent). They also found that at a high ﬂow rate, convergence was
observed to reduce the pressure recovery far less than one would expect and at
intermediate ﬂow rates convergence actually improved the pressure recovery. They also
found that when convergent walls are used, the ﬂow uniformity at the diffuser outlet was
improved. They found also that the convergent diffusers had the useful characteristic of

suppressing ﬂow reversal towards the outlet of the diffuser. This could delay the

31

appearance of rotating stall in wide diffusers where the stall appears to be triggered by
the onset of ﬂow reversal near the outlet. Finally, they suggested a useful rule of thumb
for choosing the convergence angle for different values of inlet height to radius.

Through his paper, Aungier (1988) presented a fast and accurate analysis to
predict the overall performance of stationary vaneless diffuser passages in
turbomachines. This method employs a three-dimensional boundary layer analysis,
supplemented by simple but effective models to account for ﬂow separation and merged
boundary layers. He presented a practical engineering method to predict the overall
aerodynamic performance of vaneless annular passages, speciﬁcally aimed at the
vaneless diffuser and return bend of centrifugal compressors. His method employs a
simple inviscid ﬂow analysis based on the assumptions that the ﬂow is axisymmetric and
time steady. Also, he assumed that the total pressure, total enthalpy, and angular
momentum vary linearly with mass-ﬂow function. He found that this method is
computationally very fast and convergence problems are extremely rare. He compares
the predicted and experimental overall vaneless diffuser performance, which are the total
pressure loss coefﬁcient and the static pressure recovery coefﬁcient. He found that the
agreement between predictions and experiment is very satisfactory. He suggested that
this method should be applicable to other vaneless, annular passage ﬂows such as inlets
and exhaust diffusers. Engeda (1995]) discusses and develops simple analytical
procedures to account for the diffusion process. In his method, he applies the
conservation laws on the ﬂuid as it leaves the impeller. He restricted his analysis to two-
dimensional, inviscid and incompressible ﬂow. He compared the experimental and the

predicted values to Show the variation of the mean pressure, ﬂow angle, and tangential

32

velocity radially in the diffuser. He found that the general trends are similar, but more
similarity can be obtained by accounting for compressibility and viscous effects. He
pointed out that this comparison is a comparison of the mean values at design point, so
any deviation from design point becomes difﬁcult to predict even for the advanced
theoretical analysis.

Through this paper, Engeda (1995-2) analyzes the ﬂow in a vaneless radial
diffuser using a viscous code. This code is VANDUCT (Viscous Annular Duct), which
was modiﬁed for this work. With this code, Engeda examines the validity of using 2D or
3D viscid and inviscid solution methods on the basic of ﬂow prediction in a radial
vaneless diffuser. He applied this code to predict both the pinched and unpinched
diffuser conﬁguration; which are the tangential velocity, pressure ratio, and ﬂow angle in
this work. He obtained fair, general trends for both pinched and unpinched versions.
However, the pinching effect on ﬂow angle was accurately predicted. He suggested that
numerical codes have come a great way and should be classiﬁed as design tools in

turbomachinery.

33

3. THEORY OF DIFFUSION

Through this work, a diffuser is deﬁned as any passage in which the ﬂow
decelerates between the inlet and outlet. A nozzle is then the functional inverse - any
passage in which the ﬂow accelerates between the inlet the outlet. It is common
experience that nozzles tend to work and that diffusers tend to give trouble. Any
reasonable approach to nozzle design will sufﬁce to give a low ﬂuctuation level at the

outlet.

3.] Diffusion Phenomenon

The design of a turbomachine is dominated by diffusion, the conversion of
velocity into static pressure rise. In most centrifugal compressors both the impeller and
the radial diffuser are limited by the diffusion capabilities of the ﬂow channel. A large
proportion of the aerodynamic losses (apart from kinetic energy leaving losses) in
turbomachines is due to local or general areas of boundary layer separation resulting from
a local or general degree of diffusion that is too large for the boundary layer to overcome.
Accordingly, the understanding of diffusion will result in an efﬁcient compressors and
pumps.

Diffusion can occur on an isolated surface or in a duct as shown in Figure 3.1. It

can occur because of area change or of ﬂow curvature. In both cases, the boundary layer

34

must remain attached in order to reduce the velocity from W1 to W2. When separation

occurs. the main ﬂow forms a jet that dissipates into turbulence.

/ DIFFUSION \
pom, O/ WMWWZ
mrmrrum pres sure ..__. \

and maxrmum velocity

wt

10) Isolated o-rloul

lb) Duct differed

Figure 3.1 Diffusion mechanisms: (a) isolated airfoil; (b) duct diffuser

Some symmetrical, straight-axis diffusers of area change type are Shown in Figure
3.2. These diffusers are of increasing area type (diverging), which is good for subsonic
inlet conditions. For supersonic inlet conditions, a converging supersonic diffuser should
be used. Diffusion in a constant area bend is also shown in Figure 3.3. In this Figure,
diffusion occurs locally when ﬂow approaches a bend in a constant-area duct. Therefore,
diffusion occurs when approaching the outside of a bend and leaving the inside of a bend.
These are locations where boundary layers are less Stable and where separation is

possible.

 

 

TO)

(0) Conical (b) Annular

 

 

 

(:1 Square section (It) Lug-dimensional ct

Figure 3.2 Diffuser types based on shape: a) conical, b) annular, c) square section, d)
two-dimensional or rectangular (channel)

The inlet boundary-layer condition has a very significant inﬂuence on the
performance of any diffuser. In laminar boundary layers the drag forces between layers
is small, and this is why laminar ﬂows cannot diffuse for without separation. In turbulent
ﬂows, the inner strata of the boundary-layers are given energy by exchange of “packets”
of ﬂuid from the higher energy regions. Accordingly, ﬂows with laminar boundary
layers at inlet will not withstand as much diffusion without separation as will turbulent

layers.

36

DIFFUSION

  

DIFFUSION

j/

Figure 3.3 Diffusion in a constant-area bend

The term separation is short for separation of the ﬂow from the guiding surface,
which occurs when the main flow is encountering a pressure rise (or rate of diffusion)
severe enough to bring the boundary layer to rest. Separation is a steady-ﬂow
phenomenon. However, frequently it is unsteady. The type of unsteadiness is where a jet
oscillates from one wall of a rectangular diffusing passage to another. This will give high
losses in the diffuser. Such a ﬂow can also produce losses in downstream blade row
designed to accept a fully attached ﬂow. Radial ﬂow compressors of high pressure ratio
generally experience a region of separation near the impeller circumference on the
suction side of the blades. In the cases where a diffuser is used downstream of the
impeller it is appear desirable to allow a relatively short distance, of about 5 percent of
the impeller radius, for the jets and wakes to mix out sufficiently for the diffuser to be
capable efﬁciently.

Accordingly, diffusion could be done by one, or both, of two principal conversion

techniques:
1- The conservation of mass principle pC,A = const. (3.1)
2- The conservation of angular momentum principle rCu = const. (3.2)

The radial velocity in the law of conservation of mass (3.1) determines the
dimensions of the downstream cross-sections, but since its amount is low compared to the
tangential component, the main part of the pressure rise is gained by reducing the
circumferential velocity with increasing radius. This context is explained by the

conservation of angular momentum in equation (3.2).

3.2 Performance Parameters of Diffusion

As indicated in the previous chapter, large gains in efﬁciency and pressure ratio
could be made in a centrifugal compressor design by increasing the diffusion of kinetic
energy to pressure energy. The speciﬁcation of a wide variety of geometric and
aerodynamic parameters is essential before the performance of a diffuser is uniquely
given. In this section, the geometric, aerodynamic, and overall performance parameters

of diffusion will be discussed.

3.2.1 Geometric Performance Parameters

For all classes of diffusers, various geometric parameters are used. In the
following sections the most important geometric parameters and their inﬂuence on the
performance parameters are described brieﬂy. As these investigations are very time and
cost extensive, several papers of different investigators are consulted. For illustration

purposes, a simple schematic of the channel diffuser is shown in Figure 3.4.

38

.E‘E'qi‘." 1n; ' ‘-. '.__

 

Aspect ratio AS=bl/wl, Area ratio AR=A2JA1
Non-dimensional length L/Wl
W = throat width, b =throat depth

L = centerlinc length. 29 = divergence angle

 

 

Ar: throat area=bW1,Ae=cxitarea= bW2

 

Figure 3.4 Simple schematic of the channel diffuser (Runstadler, et al. 1975)

3.2.1.1 Passage Width/Radius

The efﬁciency of the compressor stage can be improved by reducing the passage
width of the vaned diffuser. Stein and Rautenberg (1985) achieved an increase in overall
pressure rise and efﬁciency by reducing the passage width of a vaned diffuser by 10%.
Strictly Speaking for the narrow diffuser (b3/r2 = 0.108), the maximum efﬁciency is 2%
higher and the efﬁciency near surge exceeds the wide version (b3/r2 = 0.12) by 4%. This
effect loses importance at lower speeds. Figure 3.5 shows that reducing the passage
width/radius causes the shift in the choke lines to the left (lower mass ﬂow rate) in a
higher extent than the surge lines. Thus, the overall ﬂow range of the compressor is
decreased. The passage width reduction equalizes the difference in the ﬂow angles at hub
and shroud from 30° to 10°, which has a positive inﬂuence on the ﬂow conditions at the
diffuser inlet; and thereby it provides a good component matching. By reducing the
passage width/radius, one can push the surge point of a compressor with vaned diffuser to

be same as that with a vaneless diffuser.

39

P
to

wide diffuser
3.8 narrow diffuser
'6
K.
3.4
_O
E
a, 3.0
a
8 2.6
a
S 2.2
a
g 1.8
on

b.

 

5::

=8.59 kg / s

5
o

8888

 

isentropic efﬁciency Tl . 1%]

n

O
I\)

3 4 5 o 7 8 9 10 ll

mass flow rate In [kg I s]

Figure 3.5 Comparison of compressor maps (Stein and Rautenberg 1985)

3.2.1.2 Length to Width Ratio

In order to ﬁnd the optimum length to width ratio, the opening angle always has
to be taken into consideration. One can thus obtain maximum diffusion in a straight
channel diffuser either with a high length to width ratio in combination with a small
opening angle or a small length to width ratio in combination with a high opening angle.
Clements and Am (1988) tested different channel length to width ratios of straight wedge

diffusers in a turbocharger compressor, and they found an optimum value of 3.7. The

40

existence of an optimum value can be explained by several effects. The ﬁrst half of the
channel has the highest inﬂuence concerning the pressure rise whereas the latter part
contributes only a small amount of pressure recovery. This is caused by the boundary
layer growth over the channel length. Reaching a certain thickness, the boundary layers
may become unstable and the resulting increase of blockage causes the point of
separation to move towards the diffuser throat. Therefore, the optimum length to width
ratio will decrease. This hypothesis is proved by Figure 3.6 where the pressure gradient in
the latter half of the diffuser channel is signiﬁcantly lower at the higher throat blockage

condition.

 

Local pressure ratio PtocclP or

 

‘02 .._.. n-nooomntn m-‘O.520ko/s
24 - o—o n-72000r/rrin m-‘OAN Ito/s -

 

 

I I I I I I
0 l 2 3 4 5

Non-dimenslonol length X/W‘

 

Figure 3.6 Pressure rise through the vaned diffuser (Clements and Artt 1988)

41

Moreover, Clements and Ant found that a reduction of the diffuser diameter does
not necessarily lead into a loss of stage performance. Furthermore, the minor loss in the
channel pressure recovery can be compensated in the downstream vaneless part and in
the volute, which can be explained by a higher exit dynamic head and a less distorted exit
velocity proﬁle in the shorter channel. Falling short of a minimum diffuser diameter,
stage efficiency losses occur because the downstream vaneless part and the volute cannot
compensate for the loss of the high pressure gradients anymore, which are typical for the

vaned part.

3.2.1.3 Divergence Angle

Taking a simple pipe with 26 = 0° , the static pressure decreases due to losses.
This results in Cm < 0 and 77,. = —oo. On the other hand, a raising divergence angle up to
about 2° will lead to an equilibrium between momentum conversion and frictional static
pressure loss leading into zero values both for CPR and 1),. With a further lifting of the
divergence angle the additional losses increase resulting into optimum values for the
pressure recovery and efﬁciency.

Kline et al. (1959) have shown that for 2-dimensional diffusers that the maximum
C M cannot occur at the same angle as the maximum 7), , but it will be reached later at a
divergence angle of about 8°. This is qualitatively illustrated in Figure 3.7.

A value of 6° < 26 < 8° was determined by Reneau et al. (1967) for the
maximum effectiveness, maximum pressure recovery and minimum head loss, but the

optimum pressure recovery exists over a wide range of geometries.

42

 

 

 

——MINIMUM HEAD LOSS

MAXIMUM EFFECTIVESS

    

PEAK RECOVERY, co.
Cpr

 

uwI CONSTANT

 

 

 

AREA RATIO 0R INCLUDED ANGLE 28

Figure 3.7 Representative locations of several optima of performance

at constant L / W1 (Reneau et. al. 1967)

In order to ﬁnd the best suited divergence angle, Runstadler and Dean (1969)
show in various performance maps like Figure 3.8 the interaction with the length to width
ratio and the area ratio. A long diffuser should have a relatively small divergence angle
because the boundary layers grow over the length and result into separation, but they still
provide a high pressure recovery. Contrary to this, a short diffuser allows a higher
divergence angle; but as separation takes place near the diffuser channel inlet, at small

area ratio, only a lower pressure recovery can be obtained.

43

 

5.0

 

O
'u
l

4.0

 

 

\.
\R .
\\\k

\I \\‘i\\‘

892382813391

 

 

‘k \\\

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/ 2 .
:25 / g?’// /
(206233 ' ’57/ l
messy/x
/Z
2/ /
/6
4 I 6 8 10 1214 161820

Length I Width Ratio - L / W 1

Figure 3.8 Diffuser performance map, AS=0.25, M=0.6, B=0.08

(Runstadler and Dean 1969)

In Figure 3.9 Clements and Artt (1987) prove for a straight wedge diffuser a

stagnating peak efficiency for 26 > 12° associated with a loss in ﬂow range due to a

decrease of the throat blockage.

 

 

 

 

 

 

 

 

., 81 x No sidewall divergence 81 X No sldewol divergence
5;: n Sidewdl divergence 5* II Sldewol diveroence
3 ‘ 5 v P I
2 E N x O
i x s3 "
s . i
a X §§ x
a m
77 ' £77 -
I
I . ”i 2 .
D. G
g x
75 " x a n 75 - x
2 4 6 8 10 12 I4 16 18 2 4 6 8 10 12 14 16 18
2 9,,“ 2 am

Figure 3.9 Compressor ﬂow range and compressor efﬁciency versus 29 (Clements
and Artt 1987)

3.2.1.4 Vane Leading Edge Shape

While trying to improve the stage efﬁciency of a centrifugal compressor,
Yoshinaga et. al. (1980) concluded from their experimental investigations with sixteen
camber vaned diffusers that the leading edge shape of vanes have considerable inﬂuence
on the performance of the diffuser and the attendant centrifugal compressor. The validity
of this statement becomes obvious if one considers that the impeller exit ﬂow is
extremely distorted across the vane height. To analyze this problem the leading edges

were cut out to the conﬁgurations shown in Figure 3.10.

45

 

h h/ba=I/8 h h/bsgI/B
——L_‘
b: . b

D.'/D.,=-'l.l Dr/D:=I-06 D.'/o,=I.I o,/D,-=I.os
\ \
(a) vo-w' (s) VD-ll'

Figure 3.10 Leading edge shapes (Yoshinaga et. al. 1980)

Whereas the rectangular cutting resulted into a loss of efﬁciency the triangular
cutting provided a rise in efﬁciency of more than 0.5% compared with its original stage at

the design point as shown in Figure 3.11.

 

 

 

 

 

 

 

 

 

 

 

 

 

“O ‘0
g.“ -o- VD-IO 3;“ _ -o— VD-II
> —e— VD-IO' > —e— VD-ll’
g 0.9 - 8 0-9 '
.92 .9
Q Q .
e e

0.8 0.8 -
S 4' § ‘>
3 ’ é '

e
E 1.0 'E 1.0 r
.92 52
o 0 ..
s s
o o
O 0.8 U 0.8 l-
72? i '
I 0.6 l l I I l I 0.6 I I l l 1
0.8 l .0 1 .2 0.8 1.0 1.2
Flow Coefﬁcient III/o dos Flow Coefficient (II/(l) dos

Figure 3.1] Effect of leading edge shapes on the stage efﬁciency (Yoshinaga et. al.
1980)

46

3.2.1.5 Vane Shape

Bammert et al. (1983) used three different kinds of diffusers to investigate the
inﬂuence of the vane shape on the performance of a centrifugal compressor stage. The
tested vane shapes are cambered vanes, straight channel vanes, and twisted vanes.

By analyzing the essential compressor components they found out that the
diffuser has only a weak effect on the impeller but a high inﬂuence on the collecting
chamber. The diffuser blades do not affect the ﬂow in the impeller very much because a
possible retroaction of the heavy ﬂow disturbances in the diffuser channel on the impeller
ﬂow is blocked upstream by the simultaneous supersonic phenomena taking place in the
diffuser throat.

In the low speed range the performance map of the twisted diffuser was especially
shifted towards higher mass ﬂow in comparison to the cambered vane and the straight
channel diffuser. Besides, the twisted diffuser shows its best efﬁciency at lower ﬂow
range. In detail its efﬁciency is 4% higher than for the compressor with the cambered
vane diffuser and 3% higher than for the conﬁguration with the straight channel diffuser.
Another point of interest is the operation range, which is up to twice as high for the
compressor with the twisted diffuser compared with the two other variants. Figure 3.12
shows the superiority of the twisted diffuser, which has a vane shape that matches with

the incoming ﬂow distribution.

47

" .n‘t'ljn-

_ -‘V‘I' h. I‘V.

 

— cambered vane diffuser e n- 14000 rpm
— — —- straimt channel diffuser II n - 14 600 rpm

 

 

 

 

 

—.—.— twisteddiffuser 0 n-18000tpm
0.8 “...-w

.. ¥
’1 . t

3 0.6 _'k

2‘ ° *

o T

> a

o 0.5 .

s I

g 0.4 7

:I

E

'0

 

0.3

 

 

 

 

 

 

 

 

0.2
6 7 8 9

mass flow rate In [kg/ 5]

Figure 3.12 Diffuser recovery (Bammert et. al. 1983)

3.2.1.6 Area Ratio

Yoshinaga et al. (1980) investigated 16 different vaned diffusers on a model
compressor rig in order to improve the efficiency of a centrifugal compressor stage. The
pressure recoveries were compared with those of two-dimensional channel diffusers. This
comparison showed that the vaned diffusers reach their peak pressure recovery at smaller
area ratios and smaller length to width ratios. This peak pressure recovery was attained
for a combination of the length to width ratio around 5.5 and an area ratio around 2,
which is illustrated in Figure 3.13. The value for the given vaneless diffuser is lower
because of its smaller area ratio. The obvious existence of an optimum area ratio is
coupled with the values for the divergence angle and the length to width ratio because a

change of the area ratio can be obtained by varying these parameters. If the divergence

48

 

angle exceeds a certain limit, separation may occur due to a high vane loading. In the
case of increasing the length to width ratio the boundary layers grow and reduce the
effective area ratio. Both effects lead to a drop in pressure recovery and Show the

usefulness of a well adjusted area ratio.

 

1.0

Cpi (INCOMPRESSIBLE)

08’
'

0.6-

0.4-

 

PRESSURE RECOVERY Cp

0. 2 -
VANELESS DIFFUSER

 

 

.40 L r L - -
1.0 1.5 2.0 2.5 3.0

AREA RATIO Vl/Vl.

 

Figure 3.13 Pressure recovery of vaneless and vaned diffusers versus area ratio

(Yoshinaga et. al. 1980)

3.2.1.7 Radius Ratio

The radius ratio is a very important geometric parameter since it determines the
extent of mixing the jet and wake ﬂow leaving the impeller. Eckardt (1976), who
investigated the ﬂow in a high speed centrifugal compressor impeller in detail, pointed
out that "the ﬂow equalization process takes place mainly across the channel width due to

decreasing meridional curvature turbulence stabilization, whereas the Coriolis forces

49

maintain a remarkable circumferential ﬂow distortion along the shroud wall up to
r/ r; 7-1.2 The same value for the radius ratio was found by Jiang and Yang (1982)
who tried to improve the pressure recovery of a vane island diffuser. Applying the vane
island tip at four different radius ratios, they found that the pressure variation over the
circumferential locations was about 20% at r/ r, z 1.05 and 1.10. In order to provide a
satisfactory mixing in the vaneless space the authors suggest a radius ratio from 1.15 to
1.20. This range provides a minimum of losses in combination with an optimum pressure

recovery as it can be seen in Figure 3.14. Besides a rise in efﬁciency of 4% was obtained

by lifting the radius ratio from 1.10 to 1.20.

 

 

 

 

6-6.0 -

3:

8-50 -

.C

8

0-4.0 "

9 30

3- . h

a

93

(3.-20 ' or/rr=l-05 v=ll°

U A III FLIO

1194.0 . ur/IFHS °‘°"

‘” Of/fFIZO n=23700rpm
0 l l l l l J I J

 

0 l 2 3 4 5 6 7 8
circumferential positions

Figure 3.14 Circumferential static pressure distribution (Jiang and Yang 1982)

50

3.2.1.8 Vane Number

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

Dean (1974) indicates that the number of vanes employed in vane island diffusers
may vary in a range of 8 to 60. Came and Herbert (1980) could not ﬁnd any signiﬁcant
difference in the compressor ﬂow range with a vane number variation. Rodgers (1982)
achieved similar results by comparing the stage performance of a high efﬁciency, low
pressure ratio stage with both a 13 and a 21 vane channel diffuser at the same throat area.

Figure 3.15 shows the obtained minor changes in ﬂow ranges and pressure recovery.

 

 

O 13 vanes
O 21 vanes
0.9 throat area 22.8 sq m.
.2 = e:
3 o
c "" 0 8 I-
3 g (I Q)
'- o
O
0 7 — % O
1‘: Q %
qIo °.
1.0 —
'0 Q)
8 E
5 o
.9 Q T)
E; :1: 0.8 -
Q Q
g 8 M32 = 0.7 }
0.6 I l l

 

 

0.04 0.06 0.08 0.10 0.12
stage flow coefficient

Figure 3.15 Effect of diffuser vane number (Rodgers 1982)

51

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

In this context Elder and Forster (1987 ) mention that a reduction of the number of
diffuser vanes permits the mixing of jets and wakes in the vaneless space, which prevents
the region being blocked by low momentum ﬂow.

This argument is unimportant for low solidity vaned diffuser since the throat is
missing. Nevertheless Camatti et. al. (1995) found an inﬂuence of the blade number on
the performance of Low solidity vaned diffuser’s. Figure 3.16 shows that an increase
from Z=6 to 2:12 leads to higher efﬁciency but in a narrower range of volume ﬂow

coefﬁcients.

1.3 1 L
. T - - - 6 blades
1 .2_ — I —_ 12 blades

Ideal * ’

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.4 ' 0.6 ' C.8 ' 1.0 ' 1'.2 ' 1..4\ 1.6
¢l¢des

Figure 3.16 Blade number effects for rm/r2=1.106 (Camatti et. al. 1995)

52

Another point of view is to determine the number of vanes with view to the
optimum incidence angle that leads to the best ﬂow range. Moreover, the rotor dynamics
might be important for a stable operation, i.e. the number of the impeller and diffuser

vanes have to be harmonized.

3.2.1.9 Throat Blockage

The blockage in the throat area is to be mentioned since it might amount up to one
third of the physical throat area as stated by Rodgers (1982). The general aerodynamic
blockage will be introduced in section 3.2.2.1.

Stall and choke occurring in the vaned diffuser limit the ﬂow range of a
centrifugal compressor. The conditions for choking are not only the mass ﬂow itself but
also the stagnating pressure and temperature and the effective cross sectional throat, for
which even the blockage factor has to be taken into consideration.

Kenny (1970) concludes from his experiments with cambered and pipe diffusers a
strong inﬂuence of the end wall boundary layer development on the Static pressure rise
ineffectiveness and total pressure loss. Later Kenny (1972) presented a method to predict
the blockage by the use of a boundary layer analysis, which reﬂects the experimental data
very well. Despite the analytical curve is 12% above the test curve, Figure 3.17 shows a
good agreement for the measured and boundary-layer predicted stall limit. He further
shows that the level of blockage is a function of the diffuser blade angle and/or the vane
number whereas the inﬂuence of speed is negligible.

Conrad et. a1 (1980) points out that a decrease of the stagger angle increases the
blockage factor. This is due to the lengthening of the ﬂow path, which produces thick

boundary layers despite the reduction in pressure gradient.

53

 

 

 

 

 

 

 

0.6
Boundary Lyer medic
0.5
fl Stall /‘/
LE /'
0.4 70‘ WV .
measured
Jaws-r1
0.3
0 2

 

 

 

 

 

 

 

 

'0.6 0.7 0.8 0.9 1.0

 

Figure 3.17 Comparison of measured and boundary-layer predicted stall limit
for pipe diffuser of a 6:1 pressure ratio (Kenny 1972)

3.2.1.10 Incidence

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

incidences, the ﬂow range is limited by choke effects.

54

Reeves (1976) carried out experiments with pipe diffusers and found a correlation
between the ﬂow range and both the Mach number and the incidence angle. At any
leading edge incidence a lower leading edge Mach number corresponds to a greater
range, and the range at a constant Mach number changes with the incidence. Reeves
found an incidence angle for optimum matching that was somewhat negative, and located

near the middle of the ﬂow range as shown in Figure 3.18.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

028° Mach NUmber
. O 0.85
0.24 - - D 0.95
. o t 0 It”
020 ' r - - , 3‘. - ‘ "°°
'/ o . ..--w 0 1.10
_AIIL 016—”. 2‘ ‘o“---¢:
w e ' r '—'_"‘ ‘ .
.. . -’ n. .
012 ’ 4 . E ‘x ‘2 __
'°‘ . are.
OOBT— I ‘L, _
O O .
004 v 3". 3
| | | ° °
C . o .
-8 -7 -6 -s -4 -3 -2 -1 0 1 2 3
choke Leading edge maximum flow incidence stall

Figure 3.18 Effect of diffuser leading edge Mach number and incidence on range
(Reeves 1977)

3.2.2 Aerodynamic Performance Parameters

The Aerodynamic parameters are found at the inlet to the diffuser. It was found
that the aerodynamic parameters became important in order to specify the performance of

the diffuser.

55

3.2.2.1 Aerodynamic Blockage

The blockage is the fraction, or percentage, of the inlet passage area that is
occluded by the boundary layer displacement thickness on all walls.

Japikse (1984) mentions that the displacement thickness is frequently taken as
equal on all surfaces, which show the following relationships for the blockage factor with
regard to Figure 3.2:

for channel diffusers with high aspect ratio, i.e. neglecting the end walls

B = (3.3)

 

for conical diffusers with uniform inlet boundary layers

45'
B = — 3.4
d, ( )

for annular diffuser with inlet passage height of h;

B = (3.5)

 

As the velocity in the boundary layer is decreased, the total volume ﬂow is
obviously smaller than in the frictionless case. Therefore, the main stream is pushed away
from the wall. The same displacement thickness would be caused by an imaginary layer

of the thickness 8‘ where the velocity would be zero. Traupel deﬁnes 5’ in the following

way (Figure 3.19):
5°~U=I(U-u)-dy (3.6)
0

Schlichting (1987) concludes from this formula the displacement thickness of any

ﬂow without pressure gradient as

56

6‘ = 0.01738 - Re°'°°’- 1 (3.7)
C

The displacement thickness along the vanes can be calculated like the

semivaneless space in a regular channel diffuser done for example by Hintelrnann (1994).

B = 61m +h63hroud + 6:1” (3.8)

ub

 

8
vane
hub wall ,5
111/1111112111111/1/11 I
I I

 

 

    

 

 

 

 

 

 

/
/ f—
l L--- —— -----
/
E; h
>/ J
x I. ...... _ --.“..- y
j l v
Aff/l/i7/l/I/l/l/l/l/l/l/ II
shroudwall ‘5
w .3?

 

 

Figure 3.19 Aerodynamic blockage

3.2.2.2 Reynolds Number

This dimensionless number describes the relation of inertia forces to viscous

forces and it is deﬁned as

p-C-D
p

Re = (3.9)

 

where for any kind of diffuser a hydraulic diameter is typically introduced that is
related to the special geometry. In other applications D is replaced by another

characteristic length.

57

The Reynolds number is also used to distinguish laminar from turbulent ﬂow,
which depends on other factors like the hydraulic diameter or the surface roughness. If its
value converges against inﬁnity, the viscous forces can be neglected and the equations of
conversation are called Euler-equations. In this case the ﬂow is highly turbulent. If Re is
very small, the inertia forces play a minor role; and the ﬂow is called creeping ﬂow,
which is of the laminar type.

Rhoden (1956) and Stuart (1955) investigated the inﬂuence of the Reynolds
number on the pressure distribution for 2-dimensional cascades. From these results it can
be concluded that the pressure distributions on the suction side are about equal for Re-

numbers larger than 1.5 .10‘ referred to the inlet velocity and the blade chord. According
to Vavra (1960) slight deviations occur if the Reynolds number is decreased to 10° and

entirely changed pressure patterns exist for values below 105 .

3.2.2.3 Mach Number

The Mach number, named after the Austrian physicist Ernst Mach, is deﬁned as

the ﬂow speed to the speed of sound at a point in a ﬂuid.

M = =——— (3.10)

E C
a ‘17- R - T

For smaller values than 0.3 the ﬂuid can be assumed as incompressible, but for
numbers larger than 0.3 compressibility effects have to be considered. If the Mach
number of the inlet velocity exceeds certain values, the losses increase radically because

of shock patterns that occur in the ﬂow, which inﬂuence the behaviour of the boundary

layers. Compressibility effects may also change the pressure distributions along the

58

blades, so that the blade loading may increase rapidly. Because shock patterns can be
produced only if the velocities at stations on the proﬁle become supersonic, it is
frequently stated that the local speed of sound must not be exceeded at any point (V avra
1960). Though the Mach number in the subsonic range does not have any overwhelming
inﬂuence on diffuser performance, its variation is important for achieving higher

performance.

3.2.2.4 Inlet Velocity Proﬁle

At the impeller exit, the ﬂow is often being considered as being made of two jets:
one with a high velocity relative to the impeller, the other with a small or even zero
velocity which is often referred as wake ﬂow. Depending on the size of the vaneless
space the two jets are mixed, and a smoother proﬁle can be achieved so that the blockage

of the region by low momentum ﬂow can be prevented.

59

 

3.2.3 Overall Performance Parameters

3.2.3.1 Pressure Recovery Coefﬁcient

The fundamental purpose of a diffuser is to convert dynamic pressure at inlet to
static pressure rise at outlet. The pressure recovery coefﬁcient is deﬁned as the ratio of

these two parameters; in other words

Cp 5 (3.11)

 

Ideally, the value of Cp could reach unity. In practice, only in very favorable
circumstances can a pressure recovery coefﬁcient of over 0.8 be obtained.
An ideal or theoretical pressure recovery can be set if the ﬂow is assumed to be

compressible and isentropic. From the isentropic relations

('5

P

P T T
P -H (....

0 0

 

where the total and static values are related as

2

Substitute into (3.12), then

 

T __
P 0 2c C2 R

 

 

60

By using the ﬁrst two terms of the binomial expansion, an approximate solution

could be obtained as

 

 

i~1 C2 -1 p°C2 (315)

P0 " 2R7, ' 2P0 '
or

c2

P=Po — p°2 (3.16)

Substitute from (3.16) into (3.11) then
2
szﬂa—_I:ol+ 1-3% 2?. (3.17)
[pact] p01 C1
2

In an adiabatic diffuser, the total temperature does not change, which implies for

perfect— gas that

 

p02 P02
— = (3.18)
pol Pol
And for frictionless ﬂow, P02 = P0,
Then
C 2
Cpi=1— 4] (3.19)
C, /

This is the ideal pressure recovery coefﬁcient. It is simply a design guide and

could be used to deduce some very important functional relationships.

61

3.2.3.2 Effectiveness

The ratio between the actual and the ideal pressure recovery coefﬁcients is known

as the diffuser effectiveness

c
my, = 3;: (3.20)

It is an excellent parameter to use to judge the probable level of performance

when it is required to estimate expected performance under unknown conditions, relative

to the available data.

3.2.3.3 Total Pressure Loss

The losses of total pressure are expressed in the total pressure loss coefﬁcient

_APo
6‘1

._ U2
2P

(3.21)

 

This parameter must refer to the entire ﬂow ﬁeld; and, therefore, one must
consider integrated total pressure loss values including all stream tubes through the
diffuser. In the most common deﬁnition of loss coefﬁcient that is given above, integrated
mass average parameters are used across the diffuser inlet and outlet. At these points a
detailed measurement with suitable numerical averaging across the entire ﬂow ﬁeld is

required.

3.2.3.4 Flow Range

An important variable for determining the overall performance of a compressor is
the mass ﬂow rate. Its upper and lower limit deﬁne the ﬂow range, which is illustrated in

Figure 3.20.

62

The highest achievable mass ﬂow rate appears at choke conditions when the
velocity through the cross-sectional area at any of the compressor components appears to

be sonic. At this state the density has to be evaluated at the sonic conditions, which leads

to equation (3.22).

mam = A - p‘ ~ a‘ (3.22)
Typically, a convenient nondimensional group is formed as the ratio of the actual

mass ﬂow rate a to the choking mass ﬂow rate mew.

 

 

 

 

 

 

 

I Lines of
I constant
/ fﬁciency
100% speed /
Maximum

0 / efﬁciency
3 /

E

2

:I

In

In

2

a

E

o

[-

Surge lige.”
,,-r” oke line
Mass flow rate
Figure 3.20 Choke and surge

63

On the other side, the minimum mass ﬂow rate is limited by the effects called stall
and surge. A brief description of the surge and stall phenomena will be given here in
addition to the previous discussion of the in the previous chapters. These phenomena are
very complex and regardless of the type of change occurring in the ﬂow pattern, the
conventional terminology for the point of instability is ’Surge point’ and the line marking
the locus of these points for different rotational speeds is known as the ’surge line’.

Cumpsty (1989) distinguishes three different types of ﬂow change shown in
Figure 3.21. The ﬁrst case (a) is called progressive stall characterized by a small drop in
overall performance and it is indicated only by a change of noise or by high frequency
instrumentation. Figure 3.21 (b) shows an abrupt stall leading into a large drop in
pressure rise and ﬂow rate. In both cases, a and b, the ﬂow looses its axisymmetric
characteristics, turning into a circumferential nonuniform pattern that rotates around the
annulus. This phenomenon is often referred as a rotating stall and goes along with a
constant time-mean mass ﬂow despite a variable local mass ﬂow. In the third case
depicted in Figure 3.21 (c) the annulus averaged mass ﬂow varies with the time, which
causes the entire compressor to change from being stalled to unstalled and back again. In

deep surge the ﬂow distortion can even be reversed.

unstolled
Ap Ap characteristic Ap

throttle I

line \/

 

 

 

 

 

 

 

stalled
characteristic
mass ﬂow mass flow mass ﬂow
(a) ‘pro gressive' stall (b) ‘abrupt’ stall (c) surge

Figure 3.21 Different kinds of surge (Cumpsty 1989)

3.2.3.5 Distortion

The distortion level leaving a diffuser is an additional performance parameter that
gains importance if the ﬂow into a combustor is to be well understood or the ﬂow into
other critical elements such as a heat exchanger core or regenerator are points of interest.
Unfortunately, the industry has not established a common standard and some techniques
used have not even been documented as mentioned by Japikse (1983). The usual way to
deﬁne the distortion is to Show how the velocity ﬁeld or the total pressure distribution

departs from some type of norm at the diffuser exit.

3.3 Flow Analysis in Vaneless Diffuser

The ﬂow in a vaneless diffuser could be analyzed by defining ﬁrst the application
area as indicated in Figure 3.22. As shown on this Figure, path o-t is the path of the ﬂow
leaving the impeller to a straight channel vaned diffuser. This means ideally that

diffusion occurs by increasing the area. This path represents the upper limit of possible

65

paths. Path o-q is the path of the ﬂow leaving the impeller to a cambered/curved vaned
diffuser.

This means ideally that diffusion occurs by increasing area and ﬂow around a
curve. Path o-s is the path of the ﬂow leaving the impeller to a vaneless diffuser. Ideally,
it is a logarithmic spiral path, and it is the lower limit in these paths. According to this
path, the ﬂow in a vaneless diffuser with a radius ratio of 2 and an inlet angle of 6°
rotates one round before leaving the diffuser. This will result in high friction losses due
to viscous drag on the walls; and accordingly, its pressure recovery is signiﬁcantly lower
than that with vaned diffuser.

As illustrated earlier, the function of the diffuser is to convert the dynamic energy
of the advancing ﬂow into pressure as rapidly as possible without incurring ﬂow
separation at the most adverse operating condition. Because diffusion of the tangential
component is essentially a function of radial distance only, any acceleration of the
diffusion process must be affected by increasing the rate of diffusion of the radial and
axial components of velocity, that is, by increasing the rate of expansion of the ﬂow area.
In other words, the radial component of the ﬂow diffuses due to the area increase
(conservation of mass), and the tangential component diffuses as it is inversely

proportional to the radius (conservation of angular momentum).

 

Diffuser

Impeller r

_l/2

 

 

 

Figure 3.22 Elementary View of Flow in Vaneless Diffuser

The ﬂow in the vaneless diffuser could be analyzed by estimating the radial
change in the different parameters involved, which are:

Static Pressure, P; Total Pressure, Po; Flow Angle, 0t; Absolute Velocity, c; Density, p;
Static Temperature, T; Total Temperature, To; and Mach Number, M.

Analysis in this section will be applied on a two-dimensional model in cylindrical
coordinates. This analysis could be achieved by applying the conservation equations on
this two-dimensional simple case from the diffuser inlet to the diffuser outlet. Begin with
Navier-Stokes (N-S) equations in the r-0-z coordinate system. The conservation
equations in general forms are as follows:

(C,, C... and C2 are the velocities in the r, 0, and 2 directions respectively)

Conservation of mass (continuity):

3p 1 8 1 a 8
_ __ __(p(' —fp(,' = 3.23
at +r3r(prC')+r86 ")+az z) 0 ( )

67

Conservation of linear momentum in r-direction

 

 

 

2
+ +C 8C, a]

ac,+Cac, c,ac, __
p8: 'ar rae ‘az r

/

 

 

 

(3.24)

r

—F—i+ azc,+lac,+132c,+azc, C, 2%]
3r # dr2 rdr r2 362 322 r2 r239j

Conservation of linear momentum in O-direction

 

 

 

dCu+C dCU+CudCU+C dCU+C,Cu‘
,0 3t ' dr r 076 2 dz r 1
23C]
- —-—L 3.25
drz rdr+r2 362 + 0'22 r2+r236 ( )

/

 

 

_ ldp+ [32c,+rac, 132C, 32c, c,

 

Conservation of angular momentum

Fxﬁ,+jcvrxgpd¥+iw =§;JCVFprd¥+JCSFXVpV-dA (3.26)

This analysis is restricted to a radial vaneless diffuser with constant width
downstream of a centrifugal impeller. This analysis will be applied to two cases: 1)

lncompressible and Inviscid ﬂow and 2) Compressible and Inviscid ﬂow.

3.3.1 lncompressible and Invide Flow

Assumptions:

3 . .
Steady state (3 = 0); Two-Dimensron (r - 6) ; Neglect body forces;
Neglect surface forces; Inviscid ﬂow (a = 0); lncompressible (p = const.)

68

d
Axi—symmetric [35 = ); Adiabatic ﬂow (q=0); The z-axis aligned with the

axes of rotation of the impeller

Governing equations: The governing equations after simpliﬁcation will be:

Continuity equation
1.3.“, )._— 0 (3.27)
r Br
or rC, = const. (3.28)
Momentum in the r-direction
c 3C, _C3 =__1_£ (3.29)

 

 

Momentum in the (’9-direction

ac, c

 

 

 

 

C, + C, “ = 0 (3.30)
8r r
reduces to
C“ = -aC“ (3.31)
r 8r

Substitute (3.31) into (3.29)

3C 8C 1 OF
C -—' C —"—=——— 3.32
' 3r + " 3r p 3r ( )

which becomes

fir-ear; +c,ac, =0 (3.33)

p

the ﬂow is assumed to be adiabatic and frictionless (isentropic) then

69

ﬂ = (i), (3.34)

From the equation of state

 

1
p2 .. E;— P2 (3.35)
From (3.35) into (3.34)
1
—1- — RT? (P2 )7 3 36
p - P2 P ( . >

Substitute into (3.33) to obtain

(3.37)

 

From the velocity triangle
C2 = c} + C: :5 C,2 = of, + cf, (3.38)
then
1 1
sac, + Cuac. = 3d(Cf + c: ) = 3d(C’) = CdC (3,39)

Substitute (3.39) into (3.37) and integrate from P/P2=l to P/Pz, and from C2 to C

I

P

?[£J7d(_l’_)__deC (3.40)
12.,P2 P. .,RT.

P,

 

evaluate at the end points

70

 

 

7 P 7 1 2 2 (3.41)
_ ._ _1 =___ _
7-1181 2RT2(C C2)
Further reduced
7-! 2 2
L ’ = 7‘1C2 "C (3.42)
P. 7 2R7.
f
with
C
M=—— (3.43)
)RT
1:1
ﬁnally becomes

_g_
_P_ _ 7-1 2 _C_2 7-] (3.44)
[1311”? Ml! ell

Recall from velocity triangle at the impeller exit or diffuser inlet, equation (3.38) and
C,2 = CZSt'not2 and Cu2 = CzCosa2 (3.45)

For analysis of turbomachines, and the rotating machines in general, the
conservation of angular momentum equation (3.26), is often used in scalar form by
considering only the component directed along the axis of rotation which is the z-axes as

assumed before. Accordingly, equation (3.26) will be

72 = j“ (7x91609071) (3.46)

where ('r‘xi7) = rcu, —rc,, (3.47)

71

pV -dA = pc,A (3.48)
then

Tz = Ir2cu2p2cr2M2 -_[rlCulplCrldAl (3‘49)
42 41

Since the ﬂow enter the impeller in the axial direction, then Cu1=0. Also, from continuity

m = plAlC,1 = pzAQC,2 = const. (3.50)
then Tz = rit(r2Cu2 — neg, )= mac“, = const. (3.51)
or rCu = const. (3.52)

which indicates that the tangential velocity component diffuses. It is unaffected by area
change. This is because in axisymmetric ﬂow, and in the absence of turning vanes and

wall friction, the tangential velocity is inversely proportional to the radius.

 

Accordingly
Cu r2 1
C12 — r — it (3.53)

,1 = — (3.54)

Again from the continuity equation (3.50) it is known that across the diffuser and for

compressible ﬂow

p27tbrC, = p, anrzCrz (3.55)

72

then

Cr =p2 r2=p2 I
Cr2 pr pl

 

 

(3.56)

Substituting from (3.53), (3.56), and the velocity triangle relations, (3.38) and (3.45) into

equation (3.44) we get, considering the vaneless space between r2 and r with constant

width b

This is for the general case, i.e. compressible and incompressible cases and both for

inviscid ﬂow. For incompressible ﬂow p = constant, then from (3.57) we will have

..7_
..1 2 -1
T}: = {1 +—2 M22[1 712]}, (3.58)
2

From the velocity triangle, the flow angle for incompressible case could be

expressed as

 

C
_ -1 r
a — tan ( CuZ A] (3.59)

for variable angle across the diffuser. The local formula is deﬁned as

a=tan" 9-): an" 9—2) (3.60)
Cu / Caz

/

73

3.3.2 Compressible and Inviscid Flow
For Inviscid and Compressible case, substitute from (3.34) into (3.57) for

isentropic ﬂow

2 7-]

 

P __ 7—1 2 1 P 7 , 2 I 2
P2 — 1+ 2 M2 1 [12(sz Sm 0:2 ’12 Cos a, (3.61)
Or solve for Mach number
.. -1
3
r_-1
P 7 1
P, '
M2 = __Z (3.62)
t]. J... i ’ .2 .1. 2
2 1 12(13] Sm a2 12 Cos a,

 

 

The ﬂow angle for compressible ﬂow could be expressed as

 

_ C p ]
a=tan‘ ' — (3.63)
[C142 P2

for variable angle across the diffuser. The local formula is deﬁned as

a = tan" 25]: tan” 9’4]
C C

U} "2)

which the same as that for incompressible ﬂow equation (3.60).

74

4. EXPERIMENTAL SETUP

4.1 The Centrifugal Compressor Test Stand

The present investigations of performance of different diffusion systems for a

centrifugal compressor were canied out on the ﬁrst stage of a plant air-package

compressor. The schematic outline of the test rig is shown in Figure 4.1. A variable

speed motor with a maximum power input of 225 kW drove the centrifugal compressor.

The impeller and the motor were coupled through a gearbox of 9.06 gear ratio. The

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

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

 

 

 

 

 

 

Throttling Valves

Settling Chamber & Filter

 
 
 

 

 

 

 

 

otor
Gearbox
Discharge Pipe
l
-_4~, '—
IEIE I " " °
|_ I [—7’ C.—
”ﬁlo-{1' .
fl II | .F‘..]I IE‘IIJI
lg" :II ."J‘:__ L'i_-;::I <
5“.— — IﬁﬁT—J‘m.

 

 

 

 

 

 

 

 

Compressor Inlet Pipe

   

 

Figure 4.1 Centrifugal Compressor test rig
The unshrouded cast impeller has 19 blades with 19.30 backsweep. The blade

camberlines have ellipsoidal shapes in cylindrical sections. The inlet hub and shroud

75

 

diameters were rlh/rz = 0.193 and rig/r2 = 0.605 respectively. The exit blade width at the
tip was bz/rz = 0.0546. The compressor was tested in an open air loop. The air entered the
compressor through an air ﬁlter, settling chamber, and inlet pipe. The settling chamber
provided the compressor with an air supply free of the temperature stratiﬁcation and thus
enabled 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 volute of the compressor. The air in the outlet pipe is mufﬂed before
it is discharged. The mass ﬂow rate through the compressor could be controlled by
throttle valves located in the inlet and the outlet pipes. However, for the results presented

here, the mass ﬂow rate was controlled by the throttle valve located in the outlet pipe.

 

Figure 4.2 Impeller of the tested conﬁguration

76

 

4.2 Investigated Vaneless Diffusers

Two vaneless diffusers were tested in this work Both diffusers were tested
downstream of the same impeller and were ﬁxed to the casing of the compressor with
three ﬂat head screws. They had the same diffuser inlet radius to impeller tip radius ratio
(rs/r2) of 1.09 and the same diffuser exit radius to impeller tip radius ratio (rs/r2) of 1.53.
In order to investigate and understand the effect of diffuser width on the centrifugal
compressor performance and the matching of the diffuser with the upstream impeller and
the downstream volute, the two vaneless diffusers had different b3/r2 ratio. The b3/r2 ratio
for VNLD] and VNLD2 were 0.077 and 0.092, respectively. Both VNLD] and VNLD2
were pinched from b2/r2 (0.109) to mm in a radial distance of 0.44 mm. The major

geometric parameters of the two diffusers are given below in Table 4-1.

Table 4-1 Design parameter of the tested vaneless diffusers

 

 

 

 

 

 

 

 

 

 

 

 

 

r2(mm) ru/rz nJrz b7/f2 bslrz I'3/f2 rs/rz
Impeller 122 0.193 0.605 0.109 - - —
VNLDl — - - - 0.077 1.09 1.53
VNLD2 - - - - 0.092 1.09 1.53

 

 

4.3 Measurement Positions and Measurements

The contents of this work involve both steady and unsteady experimental results
taken from a centrifugal compressor having different vaneless diffuser conﬁgurations
described in the previous section. Several static and total temperatures, static and total
pressures, and unsteady pressure ﬂuctuations were measured at different planes of the
compressor stage in order to determine the mass ﬂow rate through the stage, the overall

performance, and the performance and interaction of various components of the

77

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 down and upstream of the plate. The total
pressure at the oriﬁce was also measured at two locations in the same plane, 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 4.2 shows all the

measurement planes in the inlet pipe.

Tom] Orifice
Pressure
4 l

 

Settling
Chamber ‘—

Total V Total & Total & Static

Temperature Dli'frfessmga] Static Temperatures
er en Pressures

_. Inducer

 

 

 

 

 

 

 

Figure 4.3 Measurement planes in inlet pipe
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

4.3 shows the location of the different planes, where measurement probes are installed.

78

 

I?

The pressure ﬂuctuations and the static pressure in the impeller are measured at rtmp/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. The pressures at the exit of the impeller and at various
locations in the diffuser were measured by the taps drilled on the backplate of the
compressor. All these taps were located 150° - 210° away from the volute tongue in order
to avoid any ﬂow asymmetry caused by the presence of volute. Figure 4.4 shows the
location of the different probes on the backplate 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 of (errz) 1.04 to measure the static

pressure at the impeller exit.

 

§ Diﬂuser exit (3)
§ Diffuser middle (a)
\ Dimtser inlet (1’3)
Impeller exit (er
Inducer downstream (2m)
Inducer upstream (It-u)

////////////x

%

 

 

 

L..- .
Figure 4.4 Measurement Planes in the Compressor Stage

79

 
 
 
   
  

diffuser exit
unsteady presmre probe
Kielsche pobe

static tap

0-00

/ ﬂ...— diffuser un'ddle
__ diffuser inlet

impeller exit

impeller

 

 

 

Figure 4.5 Probe location in the diffuser

The stage exit pressures and temperatures are measured in the pipe connected to
the volute. The exit total and static pressures as well as the exit total and static
temperatures are measured at four circumferential locations 90° apart in the pipe. The
exit total and static temperatures are measured at a 76.2 mm downstream of the plane
where pressures measured. In order to avoid the heat transfer effects on the temperature
measurements, the casing of the compressor was covered with the insulating material.

Table 4-2 summarizes all measurement locations and the quantities measured.

80

 

Table 4-2 Measurement Locations And Measured Quantities

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Location Position Static Name Other probes Unsteady
pressure pressure
taps transducers
Oriﬁce as described in 2 pm
ASME
regulations
Inlet Pipe 3; _ 5 2 pl 2 total pressure
r - 2 total temperature
I:
Inducer z ind! _ 1 pindl
Upstream — 0.74
r1:
Inducer 1 mt; _ 0 396 1 pm; 1 temperature Transducer A
Downstream r - '
ls
Impeller I'm _ 2 pm Transducer B
— - 0.77 & C
r: M: = 42.5 °
Impeller Exit In =1 04 2 p;
r 2
Diffuser Inlet j; =1 1 2 pg 1 total pressure
1'2
Diffuser Middle r4 =1 21 2 p4 Transducer D
rz
Diffuser Exit 5 =1 53 2 ps 1 total pressure
r2 ' 1 total temperature
Discharge pipe 2 pa 2 total pressure
2 total temperature

 

 

 

 

 

 

81

 

 

4.4 Steady Performance Measurement

This section enumerates the details of the instrumentation used to obtain the
steady data, along with the data reduction procedure and the uncertainties in the
performance parameters. Amineni (1996) and Kim (1998) designed and performed tests

on the low solidity vaned diffusers with the same conﬁguration.

4.4.1 Instrumentation

The steady static and total pressures were measured with three different types of
pressure measuring devices:

1) Validyne - variable reluctance pressure transducers
2) Omega - hand held manometers
3) water/mercury manometers

The water and mercury manometers had 1/10 of an inch resolution. One of the
water manometers was used to measure the differential pressure across the oriﬁce plate
and the other was used for measuring the stage inlet static pressure; while the only
mercury manometer was used to measure the stage exit static pressure. The usage of the
water and mercury manometers at these locations was considered necessary to validate
the proper functioning of the Validyne and Omega pressure transducers.

The static pressures were measured with 1/8-inch (3.18 mm) taps and the total
pressures were measured with Kielsche type pressure probes. Flexible tubing was routed
from the static pressure taps and the Kiel probes to the Validyne and Omega transducers.
The Validyne transducers were connected to the Validyne digital transducer indicators

with Belden type 8434 cable, while the Omega transducers had digital display integrated

82

 

to the transducer. The Validyne transducers were calibrated with an Omega pressure
calibrator in conjunction with the water and mercury manometers. The water and
mercury manometers used during the calibration process provided an additional check.
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 total temperatures were measured by half shielded with bleed-slot, total
temperature probes. All temperature measurements were done by copper-constantan (T-
type) thermocouples connected to the Omega digital temperature indicators. 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 0F or 0C. For the present study oC

display was chosen with 0.1 0C resolution.

4.4.2 Data Collection and Reduction
The compressor was tested at four different impeller speeds of 18800 rpm, 24000

rpm, 28000 rpm, and 32000 rpm for each vaneless diffuser conﬁguration. The
corresponding impeller tip Mach numbers are M. = 0.7, 0.89, 1.04, and 1.19. At each
speed the temperature and pressure measurements were collected from all probe locations
for approximately 9 to 11 different mass ﬂow rates, ranging from compressor choke to
surge in order to obtain a complete speed line. As mentioned earlier, the mass ﬂow rate

through the compressor was controlled with the throttle valve located at the stage exit.

83

 

At each ﬂow point, the data were collected when the compressor stage reached
stability in terms of the temperatures. Stability was reached if the temperatures at the
stage inlet and exit stayed steady within 101°C. Thus, the stage inlet and exit
temperatures were continuously monitored and recorded every 2 minutes until stability
was attained. When the stage was considered stable, all the pressures and temperatures
were recorded and transferred to a PowerPC for further data reduction and processing.

An Excel program was used for the data reduction and processing. The program
ﬁrst converts the recorded pressures and temperatures into N/m2 and °K from either
inches of mercury or inches of water and °C respectively. 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 overall performance of the
stage is calculated by using the averaged pressures and temperatures at various planes.
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.

There are too many parameters for the whole ﬁeld to have been more than spotted
with experiment. These parameters which will be calculated are 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

84

 

Ir ’7‘ n:- ....L

performance was determined by calculating the impeller pressure ratio; the impeller total-
to-total efﬁciency; and the pressure recovery of the impeller, the diffuser, and the volute.
The stage and impeller total pressure ratio compares the total pressures at the
stage exit and rotor exit with the stage inlet total pressure. Because of the existence of a
jet and wake system at the impeller exit, it was not possible to measure the total pressure
at this location. Therefore, the closest available pressure probe placed downstream was
used to obtain the necessary information. In other words, state three in equation (4.1)

replaced state two. As such, they are

”armor = fa. (4° 1)
P01
and
P06
7: = — 4.2
0.51113: P01 ( )
Similarly, the rotor and stage static pressure ratios are given as
rotor = & (4‘3)
P1
P6
7: = — 4.4
stage PI ( )

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 in a real
process. 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 2.6)

77, = ‘ =— (4.5)

 

85

 

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

(4.5) in terms of temperatures

w T -T
773 = __s_ = 023 01
w To2

(4.6)
- T01

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

are related according to

(4.7)

p = (rm—11%)

.22.
P01 T01 /
Thus, substituting into equation (4.6), the isentropic efficiency for a compression

process between state 1 and 2 can be written as

PO!

775 = T02 (4.8)

Tm

[P02 '77:]4

 

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

In the present investigation, equation (4.8) was used to ﬁnd the isentropic total to
total efﬁciency of the rotor and the stage. However, the heat transfer through the casing is
assumed to be negligible; and, therefore, 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

T06

To = —
T01

=53— (4.9)
T0]

Thus, the appropriate expressions for rotor and stage efﬁciency are

 

Z1)
_ (”O,rotor 7 ‘1
nt-t,rotor —

 

(4. 10)

and

__ (”mange 1.7;!) '1

7
"barrage - l

 

(4.11)

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. The
circumferential speed at state 2 is used to obtain a nondimensional form of the head

coefﬁcient according to equation (4.12)

 

l}! = Ah” (4.12)
-1122

MN

and is known as isentropic head coefﬁcient. Using equation (4.7) the head coefﬁcient can
be written in terms of measured quantities and gas properties as
_7-_I
cpnl[(jr0.stagei 7 ) — I]
2

 

(4.13)
U:
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

 

# = care—T0,)

I 2
_U2
2

(4. 14)

87

The relation between the head coefﬁcient, work coefﬁcient and the efﬁciency is
n = 1’- (4.15)
77

The static pressure recovery between any two stations 1 and 2 was calculated as

the percentage of impeller peripheral dynamic (or velocity) pressure.

(4. 16)

 

'z'poUz2

Thus the pressure recovery of all the compressor components and the static
pressure rise between various stations in the diffuser were calculated using equation
(4.16). In addition to the static pressure recovery of the diffuser calculated as mentioned
above, the static pressure rise from the diffuser inlet to the diffuser exit was also

calculated as percentage of the dynamic pressure at the diffuser inlet.

(4.17)

 

The total pressure loss from the diffuser inlet to the volute exit was determined in
terms of total pressure loss coefﬁcient, which is expressed as
5 = M (4.18)
5.001722
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 that is given by

88

 

¢ =-—— (4.19)

M 2
pol/2 42

 

The ﬂow angles at the impeller exit were calculated at the diffuser inlet as the
static and total pressures at this station were measured. From the measured total and static

pressures, the Mach number was determined

 

:1)
M3: ._2_ [523. ’ -1 (4.20)

‘7‘] 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 diffuser inlet was calculated

T, = T06 (4.21)

1+7’TC'1M,2

 

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

total and static temperature at any point

C, = chprw[1-[£]] (4.22)
To.

On the other hand, the radial component of the velocity at diffuser inlet was

 

calculated from the continuity

til
27D‘3b3p3

r3

(4.23)

 

The ﬂow angle then was obtained from equations (4.22) and (4.23), with referring to

Figure 2.5

 

a, =Sin"[C’3] (4.24)
C
3 /

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

The diffuser efﬁciency, 1113, measures the diffuser performance between the

diffuser inlet at r; and the diffuser outlet at r5. Referring to Figure 2.6, it is deﬁned as the
ratio of the ideal to the actual enthalpy rise required to accomplish the actual pressure rise
between the radii r3 and r5. It dose not involve any work transfer because h02=h05.
Depending on the outlet point, the diffuser efficiency could be deﬁned either as diffuser
static-to-static efﬁciency if the enthalpy rise taken from inlet static to outlet static. On the
other hand, it could be deﬁned as diffuser total-to-static efﬁciency if the enthalpy rise

taken from inlet static to outlet total.

 

h5 'h2
= ‘ 4.25
"D’s—3 h5 - hz ( )
has Th2
"DJ ho -h2 ( )

Assume that the ﬂuid behaves as a perfect gas and using equation (4.7), then

 

 

7;!
3..-, 5]? _,
r P
no.-. = ,3 = 2T (4.27)
_5_1 4-1
T2 T2
7;!
no.-. = T’ = 3. (4.28)
_05_..1 L5_1
T2 T2

90

All the quantities are measured except T2, so the ratios Tsfl‘z and T05sz should be

replaced using equation (4.21) and that T02=T05, then
7-]

[52-], —1[1+-’1:1M§]
P, 2

n = — (4.29)
D "I (M3 —M5 )

 

r ~<
'7‘ N

K_—\
‘3 I
l
N

(4.30)

 

"DJ-3 =

T

N
3
Nu

N I

Equations (4.29) and (4.30) give the diffuser efﬁciencies in terms of measured
and computed values of total and static pressures and mach numbers at the diffuser inlet

and diffuser outlet.

4.4.3 Instrument Accuracy and Result Uncertainty
Errors could present when experimental measurements are made. These errors

could be due to instrument accuracy, competence of the people using the instruments, etc.
The interest is in knowing the uncertainty in the ﬁnal result due to the uncertainties in the
primary measurements. Experimental error may be of two types. Fixed or systematic
error causes repeated measurements to be in error by the same amount for each trial.
Fixed error is the same for each reading and can be removed by proper calibration or
correction. Random error or nonrepeatapility is different for every reading and hence
cannot be removed. The factors that introduce random error are uncertain by their nature.
To eliminate the effects of ﬁxed errors, it is assume that the equipment has been

constructed correctly and calibrated properly. It is assume also that instrumentation has

91

 

adequate resolution and that ﬂuctuations in readings are not excessive. Also, it is assume
that care is used in making and recording observations so that only random errors remain.
The estimation in the probable random errors in experimental results could be taken care
of by performing uncertainty analysis. Through this section, the accuracy of the
instrument used and the stage efﬁciency uncertainty will be presented.

The Validyne pressure transducers were able to measure with an accuracy of

i0.25% of full scale; which includes the effects of linearity, hysteresis, and repeatability

at an operating temperature range of 0 0F (-17.78 0C) to 160 0F (71.1 0C). The accuracy

of the Omega digital temperature indicators was 310.5 0C at 0.1 0C resolution setting under

the operating temperatures of 5 to 45°C for T-type thermocouples. Equation (4.11)

indicates that the stage efficiency is a function of P01, P06, To], and T06.

7-1
_ -— I
772-: stage = (”0mg 1 ) = ”(P01 ' P06 ’70] ’TO6 )
’ 1,—1

 

Let un be the uncertainty in the stage efficiency and um, um, um, and ums be the

uncertainties in the independent variables or the primary measurements. Holman (1994)

showed that the uncertainty in the result is

2 2 2 2 0'5
an an an an
= ——— ———- 431

In this work, data reduction is performed which results in rather complicated

 

 

affairs. Accordingly, a small adaptation is provided for direct calculation of uncertainties
without resorting to analytical determination of the partial derivatives in equation (4.31).
For enough changes in the independent values which assigned as x here, the partial

derivatives can be determined by

92

92 z ﬁ(x+Ax)‘77(x) (432)
(ix Ax

These values could be inserted in equation (4.31) to calculate the uncertainty in
the compressor stage efﬁciency as shown in Table 4—3.

Table 4-3 Instrument speciﬁcations

 

 

 

 

P01 P06 T01 T06 11mg,
Company Validyne + Validyne-l- Omega + u. Omega + u. -
u. sensor 11. sensor sensor sensor
Range 20 psi 50 psi -99.9-401.4°C -99.9-401.4°C -
Accuracy 11.25% 11.25% 11.1% 11.1% 12.35%

 

 

 

 

 

 

 

 

4.5 Unsteady Performance Measurement

4.5.1 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, as where
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 used
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

93

compensation that allows it to operate in a temperature range of 1 205° C(1 401° F). 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 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 10 feet of low-noise coaxial cable. The inline ampliﬁer conditions the transducer
output signal. This ampliﬁer has high input impedance (1011 ohms ) 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 foot 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 1, 10, or 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.

94

The amplified signals from the signal conditioner were transferred to a two-
channel HP signal analyzer. The signals were stored and transferred to a PC for further
processing and analysis through the signal analyzer and the signal processing software.
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 4.5.

4.5.2 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, most captures were made at 12 kHz and 4096 Hz sampling
frequency. The high frequency was used to observe the blade to blade pressure
ﬂuctuations, and small captures of 5 to 10 records were taken. Each record had 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

on the available memory of the signal analyzer and the required resolution of the capture.

95

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 540 Hz, and with a 2048 Hz sampling frequency the usable
frequency range was 800 Hz and with 4096 Hz sampling frequency the usable frequency
range was 1600 Hz.

Once the capture was taken and stored on the PC, the signal data are 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 and the results or processed data in time or
frequency domain. The following parameters were used for the computation of the
spectral functions:

- 64 records from each transducer were captured

- the sampling frequency was 4096 Hz

- each record contained 1024 discrete points, which corresponds to 0.5 seconds

- all records were detrended

- a Hanning window was applied

- 50% overlapping was used

- the power spectrum, the cross spectrum, and the phase shift were calculated

- the output is represented in terms of decibels, the reference being 1 kPa.

96

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

be found in Wilmsen (1996).

 

 

 

 

 

 

 

 

 

Figure 4.6 Unsteady pressure signal flow path

4.5.3 Analysis of the Data
After performing all the spectral analysis, one should determine whether any

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

97

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 be followed:

- 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.

- 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.

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

- 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

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

98

5. RESULTS AND DISCUSSIONS

Two vaneless diffusers (VNLDl and VNLD2) were tested experimentally
downstream of the same impeller. Each vaneless diffuser was tested at four different
impeller speeds, 18800 rpm, 24000 rpm, 28000 rpm, and 32000 rpm. These speeds
correspond to impeller tip Mach numbers of Mt: 0.7, 0.89, 1.04, and 1.19. At each
speed, the compressor with each VNLD was investigated in terms of overall steady stage
performance, component-wise detailed steady local performance, and unsteady
performance. These investigations of each diffuser are compared in order to understand
the advantages and disadvantages of both vaneless diffusers used in centrifugal
compressor stage. That includes the operating range, the performance parameters at peak
efﬁciency, the inﬂuence of diffuser type on pressure history, pressure recovery in both
the vaneless diffusers, and the centrifugal compressor stage in addition to other
performance parameters.

The effect of the vaneless diffuser type on the unsteady flow regimes in the
inducer, the impeller, and the vaneless diffuser through the compressor stage is also
investigated. Investigations also include a comparison between the experimental and
theoretical results through the diffuser in terms of the pressure ratio.

Through this work, all the presented performance curves are normalized with
respect to the design point ﬂow and the performance parameters of VNLDl at impeller
speed of 28000 rpm (MF1.04). A typical test at any speed consisted of nine to eleven

operating points and ranging from choke (maximum ﬂow) to stall/surge.

5.1 Overall Compressor Stage Performance Characteristics

5.1.1 Stage Efﬁciency and Head Coefﬁcient
As mentioned before, two vaneless diffusers (VNLDI and VNLD2) were tested

experimentally downstream of the same impeller at four different impeller speeds: 18800
rpm, 24000 rpm, 28000 rpm, and 32000 rpm. It is noted that VNLD2 is wider than
VNLD] by nearly 17%. Through this section, the overall performance characteristics of
each of these two vaneless diffusers are compared with each other in order to investigate
the effect of both vaneless diffusers on the centrifugal compressor stage. Also, the results
obtained from both vaneless diffusers will be compared in terms of operating range, the
performance parameters at peak efﬁciency, and the inﬂuence of diffuser type on the
pressure history.

The performance characteristics of the centrifugal compressor stage with VNLD]
and VNLD2 at four different impeller speeds are shown in Figure 5.1 and Figure 5.2.
These performance characteristics consisting of the normalized head coefﬁcient (um) and
the normalized stage efﬁciency (TIN) both versus the normalized ﬂow coefﬁcient (on). All
curves in Figure 5.1 and Figure 5.2 have the same characteristic shape. Starting with a
high mass ﬂow at the choke condition, the values of um and The rise rapidly to a certain
extent and decrease much slower until the diffuser stalls and gives rise to compressor
surge. That condition is clearer as the impeller speed increased.

It should be noted in the beginning that the normalized head coefﬁcient, which is
a measure of the energy transferred by the compressor to the ﬂuid passing through it, is
decreased as the impeller speed increased. By comparing the head coefﬁcients plots for

both vaneless diffusers and at all speeds, it could be seen that generally VNLD2 showed a

100

better head coefﬁcient than VNLD] at low to medium impeller speeds (18800 rpm,
24000 rpm, and 28000 rpm). At 32000 rpm, VNLDl has a better head coefﬁcient over
the whole ﬂow range. Note that as the impeller speed increased, the difference in the
head coefﬁcient between VNLDl and VNLD2 decreased.

The normalized stage efﬁciency curves showed a similar manner in which they
decrease as the impeller speed increases. The centrifugal compressor with VNLD2
showed a better efﬁciency than with VNLD] at impeller speed of 18800 rpm, 24000 rpm,
and 28000 rpm. At 32000 rpm, VNLDl has a better efﬁciency than VNLD2 over the
whole ﬂow range.

In addition to having better head coefﬁcient and stage efﬁciency, the centrifugal
compressor with VNLD2 had a wider ﬂow range than with VNLDl at each impeller
speed. This could be noted from the performance curves on Figure 5.1 and Figure 5.2,
which show that the choke and surge ﬂow conditions for both vaneless diffusers are
different. VNLD2 choked at a higher mass ﬂow rate at all impeller speeds. Also

VNLD2 has the lowest surge mass ﬂow rate, indicating more stability than VNLDl.

101

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2
1.1 4 :
”——
1
0.9 4
z —4
a 0.0
0 7 q +1eaoo ‘
' +24000 l
+32000
0.5 3 i
0.4 - . . , . 4
0.2 0.4 0.8 0.8 1 1.2 1 4
¢N
(a) Head coefﬁcient WN vs. ﬂow coefﬁcient 9N
1.2
1.1 4
1
0.9 4
2
g 0.8 ~
0.7 4
+18800
0.5 _ +24000
+28000 i
0.5 4 +32000
0.4 . 4 . . . .
0.2 0.4 0.6 0.0 1 1.2 1.4
¢N

 

 

 

(b) Stage efﬁciency nN vs. ﬂow coefﬁcient ¢N

Figure 5.1 Performance characteristics of the compressor stage with VNLDI

102

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2
1.1 4
1 .4
0.9 4
Z
3' 0 8 4
0.7 4
l +18800 .
0.0 4 1 +24000 l
‘ +28000 '
0'5 ‘ Let—32000 I
X
0.4 . . . .
0.2 0.4 0.0 0.8 l 1.2 1.4
$01
(a) Head coefﬁcient \uN vs. ﬂow coefﬁcient ¢N
1.2
1.1 4
1 a
0.9 4
g 0.94
0.7 4
—o—laeoo
0.0 4 +24000
+28000
05 4 x
' +32ooo
0.4 . . . . .
0.2 0.4 0.6 0.8 1 1.2 1.4
On

 

 

(b) Stage efﬁciency up; vs. ﬂow coefﬁcient ¢N

Figure 5.2 Performance characteristics of the compressor stage with VNLD2

103

 

 

 

5.1.2 Flow Range
The total operating range of the centrifugal compressor stage (choke to surge) is

shown in Figure 5.3 as a function of the impeller tip Mach number. As expected,
VNLD2 has the higher operating range at impeller tip Mach number of 0.89, 1.04, and
1.19 by an average of 3%. At Mt=0.7, VNLD] has slightly a higher operating range than
VNLD2 due to the compressor stall at low ﬂow rate. It could be noted that at each speed,
the total operating range attained by each vaneless diffuser was limited by their surge
mass ﬂow rates. An interesting observation from Figure 5.3 is that VNLD] and VNLD2
have a similar trend in decrease of operating range as the impeller speed increases. Their

behavior is similar in that they show a linear decrease in the operating range.

 

 

 

 

 

 

 

 

mi
154 "-3'.
....-
70- .....
Q ...Q.
a Q ......
E ..‘. ........
5 65‘ "“IL
g 60" ..'. ‘~\
Q. Q
C ' ‘
$9 \
554 °.. “.
.0 .\
nonvxwl '~. ‘4
... \.\
50‘ --.--VNLD2 .. ~.
.~Q.‘\
...
Q
‘5 f V ‘

 

0.70 0.89 1.04 1.19

Mt

 

 

 

Figure 5.3 Total operating range of the compressor stage with VNLD] and VNLD2
vs. impeller tip Mach number M.

104

5.1.3 At Peak Efﬁciency
The variation of the peak efﬁciency of the compressor stage at each impeller

speed is shown in Figure 5.4. At impeller tip mach number of 0.7, 0.89, and 1.04;
VNLD2 has 2 to 3 percent higher normalized peak efﬁciency than VNLD]. This
difference in the normalized peak efﬁciency is almost constant at all three speeds. At
Mt=l.19, VNLD] has a higher normalized peak efﬁciency by approximately 2 percent,
which indicates that VNLD] has a better performance at higher impeller speeds while

VNLD2 have better results at lower to medium speeds.

 

 

 

 

 

 

 

 

 

1.15
1.10. .....
0 ........
1.05 4 ...... ."
'9. , .
E ........ ....
g 1.00 ‘ ‘ ........
Q . ;“-
\ .....
0.95 0
- - O - -VNLD1 "-
- - i - ~14an
0.90 . .
0.70 0.89 1.04 1.19

 

 

 

Figure 5.4 Compressor stage at peak efficiency vs. impeller tip Mach number Mt for
VNLD] and VNLD2

105

 

 

 

 

 

 

 

 

 

0.26
...‘.ooo--o.--.....-..
0.224 ,-' ,.
' ‘0
o ' , '.
0' '
0" o '
U 018- .." ...v'
C' .. . .
...... I"
...-'1 .......
0.14 ,4' "*"VNLDI
"unvmm
0.10 t r
0.70 0.89 1.04 1.19

 

 

 

Figure 5.5 Loss coefﬁcient at peak efﬁciency vs. Mt for VNLD] and VNLD2

With respect to Figure 5.5 the normalized loss coefﬁcient at peak efﬁciency for
both VNLD] and VNLD2 along with the downstream volute is shown at each impeller
speed. As expected, the loss coefﬁcient increases as the impeller speed increases.
VNLDl has higher losses at medium to high speeds, which are at an impeller tip Mach
number of 089,104, and 1.19. VNLD2 has higher losses at Mt=0.7, which is due to
compressor stall at a higher ﬂow rate. Also the total pressure measurements at station 3
is not reliable, which could cause that VNLD2 has higher losses at Mtwl From these
results, it could be noted that the centrifugal compressor stage with VNLD2 (the wider

vaneless diffuser) has slightly a better stage efficiency and lower losses than VNLDl (the

106

narrow one). But a very wide spacing of the vaneless diffuser walls should not be
recommended and this conclusion should be limited by an optimum value of the vaneless
diffuser width because of only a small gain in stage efﬁciency and a great risk of

boundary layer separation.

5.2 Pressure Rise in the Compressor Stage

The static pressure from the compressor stage inlet to the compressor stage exit
was measured at eight different locations as indicated in chapter four. This is an attempt
to understand the effect of changing the vaneless diffuser width on the static pressure rise
in the compressor stage. In Figure 5.6 and Figure 5.7, the ratio of the static pressure to
the static inlet total pressure has been plotted against the different locations at which the
static and total pressures were made. The curves on these ﬁgures are for all the different
operating points, which range from choked condition (maximum ﬂow) to near
compressor stall (minimum ﬂow). The observed differences in terms of pressure ratios
for both VNLD] and VNLD2 were similar for every tested speed. Moreover, the static
pressure rise characteristics of each vaneless diffuser were also similar. Thus, the data of
impeller speeds 28000 rpm and 32000 rpm for both vaneless diffusers are shown and
discussed.

By comparing Figures 5.6 and 5.7, it could be noted that there is no signiﬁcant
differences between them which indicates that by increasing the vaneless diffuser width
from that with VNLDl to that with VNLD2 the static pressure rise in the compressor

stage is almost the same and not affected. Thus, by increasing the vaneless diffuser width,

107

 

 

 

 

 

0 . . . . . .
Plndt Plnd2 Pimp P2 P3 P4 P5 P06

 

Probe Location

 

 

 

(a) At impeller speed 28000 rpm (Mt=l.04)

 

 

 

+099. It
+099. 02
.~ 4 099. 03

 

 

 

 

 

 

 

 

 

 

Pindl Pind2 Pimp P2 P3 P4 P5 P06
Probelocaﬁon

 

 

 

(b) At impeller speed 32000 rpm (Mt=1. 19)

Figure 5.6 Influence of diffuser type on the compressor stage pressure history with
VNLD]

108

 

2.5

 

  
 
 
 
 
 
 
 

:OPP..I-_1
;—.—0pp..2 l
‘ 099.3
F l—ie—OppJA

|+OppJS f
§+Opp.06 :
1.5 , l—O—Opp.l7 I

. l

-—.—Opp..8 1
+Opp..9 5
—-o—~—Opp. .10

.-....“ ~41»:

 

 
 

 

 

0.5 4

 

 

 

Pindl Pind2 Pimp P2 P3 P4 P5 P06

Probe location

 

 

 

(a) At impeller speed 28000 rpm (Mt=l.04)

 

 

 

 

 

 

 

 

 

 

 

T

Pindl Pind2 Pimp 1>2 93 P4 P5 P06
Probe location

 

 

 

(b) At impeller speed 32000 rpm (Mt=l.19)

Figure 5.7 Influence of diffuser type on the compressor stage pressure history with
VNLDZ

109

a better efficiency and a lower loss coefficient could be attained without affecting the
pressure rise in the compressor stage. Again that is a restricted conclusion by an
optimum width value.

From the static pressure rise in the compressor stage with VNLDl and VNLD2,
the ﬂow in both vaneless diffusers is stable. Moreover, the highest-pressure gain in both
VNLDl and VNLD2 seems to occur at maximum mass flow rates. This could be
because at high mass ﬂow rates the flow leaves the impeller more radially than at low
mass ﬂow rates. Since the ﬂow angles are higher at high mass ﬂow rates, the ﬂow path
in the diffuser is shorter leading to lower ﬂow losses. On the other hand, the volute
contributes in the compressor pressure rise at all mass ﬂow rates.

Figure 5.6(b) and Figure 5.7(b) clearly show that the limiting component for
maximum ﬂow through the compressor stage is the inducer not the vaneless diffuser.
This could be seen from the sudden pressure drop in the impeller at high mass ﬂow rate
(Op#l). The inducer choking causes the pressure drop. However, as the mass ﬂow rate

is decreased, this phenomenon vanishes.

5.3 Overall Vaneless Diffuser Performance Characteristics

5.3.1 Vaneless Diffuser Efficiency

The diffuser efﬁciency deﬁned earlier as a measure of the diffuser performance
between the diffuser inlet at r3 and the diffuser outlet at r5. The total-to-static efﬁciency
and static-to-static efﬁciency for VNLD] and VNLD2 are shown in Figure 5.8 and

Figure 5.9.

110

 

 

11

 

1.6 - + VNLD]

93-444 + ....
1'4“ 2400019111 ‘\V

13‘

:3 V?"

09~

 

 

TlD.t-s.N

 

 

 

0.8 I I I T I I
02 04 06 03 l 12 14

 

 

 

Figure 5.8 Vaneless diffuser performance characteristics: diffuser efﬁciency total-
to-static for VNLD] and VNLD2

111

 

 

 

‘ +VNID1

$000“ -I- m

 

 

1.8 .

 

 

 

zt .
9.0 1.4001111]
3 l"
S: 1.4 -
1 .‘H . '1
1.2 \ \
1 4“ '1)’
“ 3‘34-
0-8 I I T I' I I
0.2 0.4 0.6 0.8 1 1.2 1.4

 

 

 

Figure 5.9 Vaneless diffuser performance characteristics: diffuser efﬁciency static-
to-static for VNLD] and VNLD2

112

Both ﬁgures showed that the diffuser efﬁciency increased as the ﬂow coefﬁcient
decreased. Stanitz (1952) has also got this ﬁnding. This could be explained by the
relationship between the mass ﬂow rate and the velocity. As the ﬂow coefﬁcient
decreased, the velocity vectors becomes more tangential so that the ﬂow path in the
vaneless diffuser will be longer. This will make the ﬂow diffuses more, and the pressure
will rise more in which gives a better performance.

Also, it could be noted from Figure 5.8 and Figure 5.9 that the increase in diffuser
efﬁciency is smooth as the impeller speed low and becomes rapid and sharp as the
impeller speed increased. Both cases will be as the ﬂow coefﬁcient decreased. This
could be explained by knowing that the diffuser efﬁciency generally is a ratio of the
pressure ratio to the Mach number square of the ﬂow. Generally what is happen is a
combination of the numerator increase (pressure ratio) and the denominator decrease
(Mach number or velocity), which results in an efﬁciency increase; and this becomes
rapid and sharp as the impeller speed increases.

Regarding increasing the diffuser width, as expected that the diffuser efﬁciency
improved by spacing the diffuser walls farther apart. Both ﬁgures show that the diffuser
efﬁciency for VNLD2 is better than that of VNLDl at all impeller speeds. Until now the
wider diffuser (VNLD2) showed a better performance in terms of stage and diffuser

efﬁciencies, and the next step is to check the pressure recoveries.

113

5.3.2 Pressure Recovery of the Vaneless Diffusers
Through this section, the pressure recovery through VNLD] and VNLD2 will be

discussed in details to get more information regarding the differences between the two

vaneless diffusers.

5.3.2.1 Total Pressure Recovery Cp2.5

Figure 5. 10 and Figure 5. 11 show the total pressure recovery Cp2-5,from diffuser
inlet to diffuser exit, for VNLDl and VNLD2 at all impeller speeds. As shown on these
two ﬁgures, there are two peaks with each curve. One of these peaks is near choked
condition (maximum ﬂow) and the other near stall (minimum ﬂow). Also it could be
noted that all curves have the same trend in which the total pressure recovery decreased
as the ﬂow coefﬁcient decreased and increased as the impeller speed increased. At low
impeller speed, the Cp2-5 curves are smooth and become more disturbed as the impeller
speed increased.

By comparing Figure 5. 10 and Figure 5. ll , it can be seen that VNLD2 has a
better Cp2-5 than VNLDl at high ﬂow coefﬁcient and at impeller speeds of 18800 rpm,
24000 rpm, and 28000 rpm. As the ﬂow coefﬁcient decreased, both vaneless diffusers
show the same Cp2-5 except at high impeller speed where VNLDl leading VNLD2. Also
as the impeller speed increased, Cp2-5 becomes more stable with VNLD2 than with
VNLDl. Accordingly, increasing the width of the vaneless diffuser from VNLDl to
VNLD2 will improve slightly the pressure recovery Cp2-5 in general. This needs to be
investigated more by breaking the pressure recovery of the diffuser Cp2.5 into the
pressure recovery of three different regimes across the diffuser, which will be discussed

in the next section.

114

 

 

0.44

 

 

 

 

 

 

 

 

+18800
0.42 4
+24000
0.4 , +28000
+32000
0.38
E
U ‘
0.36 /
0.3. ﬂ
4" \ v
0.32 4 /
/
0.3 . . .
0.2 0.4 0.6 0 s l 1.2 l 4
9N

 

Figure 5.10 Variation of Total Diffuser Pressure Recovery Cp2-5 for VNLD]

 

 

 

0.44

0.42 -

0.4 -

0.38 -

0.36 -

0.34 4

0.32 4

0.3 d

0.28 -«

 

0.26

 

 

+18000
+24000
+28000
+32000

 

 

  
  
  

 

 

0.2

0.4

0.6

 

Figure 5.11 Variation of Total Diffuser Pressure Recovery Cp2-5 for VNLD2

115

 

 

 

 

Cp2r3

 

0.1
0091
0.08 -
0.07 ~
0.06 -
0.05 4
0.04 -
0.03 4

0.02 4

 

 

+18800
+24000
+2MOO

 

 

 

 

 

0.01

0.

2 0.4 0.6 0.8 1 1.2

PM

1.4

 

Figure 5.12 Pressure Recovery Cp2-3 for VNLD]

 

 

0.02

0.01

 

 

+18800
+24000
+28000
+32000

   
  
 

q

 

 

 

 

.t

 

 

 

 

0.2 0.4 0.6 0.8 1 1.2 1.4

9N

 

Figure 5.13 Pressure Recovery Cp2-3 for VNLD2

116

 

 

5.3.2.2 Subdivided Pressure Recoveries

Through this section, three different pressure recoveries across the vaneless
diffuser will be discussed. They are as follows:

- the pressure recovery in the vaneless space between the impeller
exit and the vaneless diffuser inlet (Cp2-3)

- the pressure recovery between the inlet and the middle of the
vaneless diffuser (Cp3.4)

- the pressure recovery from the middle to the exit of the vaneless
diffuser (Cp4.5)

Figure 5.12 and Figure 5.13 show the pressure recovery in the vaneless space
between the impeller exit and the diffuser inlet Cp2-3 at all impeller speeds for VNLDl
and VNLD2. As it is shown in these two ﬁgures, Cp2.3 has a general trend in which it
increases smoothly to a peak then it decreased as the ﬂow coefﬁcient decreased. This
shows the effect of the width reduction from impeller width to the vaneless diffusers
width. The width at the impeller exit is reduced to the vaneless diffuser width in this
region due to which there is a ﬂow acceleration in addition to the diffusion by area
decrease. The narrower the diffuser, the greater is the ﬂow acceleration and the lower the
area decrease. By comparing these two ﬁgures, Figure 5.12 and Figure 5.13, it could be
seen that Cp2-3 increases as the impeller rotational speed increases for both vaneless
diffusers. VNLD2 leading VNLDl at impeller speeds of 18800 RPM, 24000 RPM, and
28000 RPM while VNLDl leading at 32000 RPM. For both vaneless diffusers and at all
impeller speeds, Cp2-3 increases again as the ﬂow moving through toward the vaneless

diffuser.

117

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.21 1 +1ssoo
+24000
0.19 1
+20000
0.17 +32000
0.15 4
0.13 4
0.11 < d
If ‘—
0.09 4 ‘v/l
0.07 4
0.05 4 l
0.03 . . . . . .
02 0.4 0.6 0.3 1 12 m
9a
Figure 5.14 Pressure Recovery Cp3-4 for VNLD]
0.10
+1uoo
+24000
°"° 1 +20000
+32000
0.14
0.12 4
0.1
0.08 4
0.06 4
0.04 . .
0.2 0 4 0.6 0 s 1 1 2 1.4
PM

 

Figure 5.15 Pressure Recovery Cp3-4 for VNLD2

118

 

 

 

 

 

 

 

 

 

0.26 -

024 4 ’I

022 4 /

02 . l‘
°-"* \ 44",

0.16 .

 

+ 18800
+24000
+28000
+32000

0.14 -*

 

 

0.12 -1

 

 

 

 

0.1 V V T T T P
0.2 0.4 0.6 0.8 1 1.2 1.4

 

Figure 5.16 Pressure Recovery Cp4-5 for VNLD]

 

 

0.29

 

 

0.27 -1

0.25 -1

0.23 -1 i

0.21 - /

 

 

 

 

 

 

 

0'15 4 +1ssoo

0.13 4 +24000

+28000

°'” +32000
0.09 . T . . . 4
0.2 0.4 0.6 0.8 1 1.2 1.4

 

Figure 5.17 Pressure Recovery Cp4-5 for VNLD2

119

 

The pressure recovery between the vaneless diffuser inlet radius and the radius of
the middle of the vaneless diffuser Cp3-4 is given in Figure 5.14 and Figure 5.15 for both
vaneless diffusers and at all impeller rotational speed. For both vaneless diffusers, the
Cp3-4 increases as the impeller speed increases. Also the Cp3-4 increases as the ﬂow
coefﬁcient decreases, which is expected because as the velocity decreases the pressure
increases as the flow move toward the middle of the vaneless diffuser. The amount of
pressure recovery gained through Cp3-4 is higher than that by Cp2-3 that indicates the
effect of the diffuser on pressure recovery as the ﬂow entering the vaneless diffuser. As
in Cp2-3, the Cp3-4 for VNLD2 is higher than that of VNLDl for impeller speeds 18800
RPM, 24000 RPM, and 28000 RPM. By comparing the plots for Cp2-3 and Cp3-4, it
could be noted that these two pressure recoveries are exchanging between each other
depending on the ﬂow coefﬁcient. At high ﬂow coefﬁcient, Cp2-3 is maximum while
Cp3-4 is minimum and at low ﬂow coefﬁcient Cp2-3 is minimum while Cp3-4 is
maximum.

As the ﬂow passes the middle of both vaneless diffusers, it gains higher pressure
recovery. This could be seen through the plots for the pressure recovery from the middle
to the exit of the vaneless diffuser Cp44-5. Figure 5.16 and Figure 5.17 show that the
Cp4-5 is higher than Cp3-4 over the whole range. As shown on these ﬁgures that the
Cp4-5 for both vaneless diffusers is higher at high ﬂow coefﬁcient and decreases as the
ﬂow coefﬁcient decreased. This is at all impeller rotational speeds. This could be
explained as that at high ﬂow coefﬁcient the ﬂow angles are higher and thus the ﬂow
path is small and losses are lower. For both vaneless diffusers, the change in this

pressure recovery Cp4-5 with impeller rotational speed depends on the ﬂow coefﬁcient.

120

At high flow coefﬁcient the Cp4-5 increases as the impeller speed increased, and at low
ﬂow coefﬁcient the Cp4-5 decreased as the impeller speed increased. Both vaneless
diffusers, VNLD] and VNLD2, achieved nearly the same Cp4-5 at all speeds except at

the highest speed of 32000 RPM where VNLDl is better.

5.4 Comparison Between the Experimental and Theoretical Results

A comparison between the experimental and the theoretical results in terms of
static pressure ratio and the squared of the local flow Mach number M2 across both
vaneless diffusers is presented. The theoretical results presented conclude the
assumptions of compressible and incompressible ﬂuid ﬂow. This is to investigate more,
experimentally and theoretically, the effects of increasing the diffuser width on the ﬂow
in a vaneless diffuser. Because of the similar patterns at all impeller rotational speeds for
both vaneless diffusers, only the results for impeller rotational speed of 32000 RPM are
presented here.

Figure 5.18 shows the variation in static pressure ratio with the vaneless diffuser
radius ratio while Figure 5.19 shows the variation in the squared of the local ﬂow Mach
number with the vaneless diffuser radius ratio for both VNLDl and VNLD2. As shown
in both ﬁgures that in general the static pressure ratio increased across both vaneless

diffusers, while the squared local ﬂow Mach number decreased as expected.

121

 

1.3

 

 

1.25-

1.2 ~

 

 

1.15 1

 

I: 1.14

 

115 4

 

0%4

 

 

0.9

 

1.04 1.1 1.21 1.53

 

 

 

Figure 5.18 Variation in the Static Pressure Ratio with the Radius ratio for VNLD]
and VNLD2

122

 

 

 

 

 

 

 

 

 

 

 

 

4
3 5 -4 ‘\ +exp. VNLD]
—O—comp. VNLD]
\ —-—incomp. VNLD]
3* “ ---¢---exp.VNLD2
\ ---A4-- comp. VNLD2
2.5 4 - - 4x4 - - ineomp. VNLD2
N
2 2
1.5 1
1 .
0.5 4
0 . . .
1.04 1.1 1.21 1.53

 

 

 

Figure 5.19 Variation in the squared of Local Flow Mach Number with the Radius
ratio for VNLDl and VNLD2

123

The effect of increasing the vaneless diffuser width is to decrease M2 as shown in
Figure 5.19 where the VNLD2 curve is lower than that of VNLDl. This decrease in M2
results primarily from the decrease in the radial velocity component as a result from the
increase ﬂow area that occurs when the diffuser width increased. This decrease in M2
resulted in an increase in the static pressure ratio as shown in Figure 5.18 where the
VNLD2 curves are higher than that of VNLD]. In both ﬁgures and for both diffusers, the
theoretical results show higher values than the experimental one, which is expected
because the theoretical ones are more ideal than the experimental ones, which are the
actual. According to these results, increasing the vaneless diffuser width will slightly

improve the static pressure rise across the vaneless diffuser.

124

5.5 Unsteady Performance of the Compressor Stage

Through this section, the unsteady performance of the centrifugal compressor
stage with VNLDl and VNLD2 will be presented and discussed in an attempt to
investigate the'causes of instability through the compressor stage. This could be done
through the four dynamic pressure probes installed in the inducer (Transducer A), the
impeller (Transducers B and C), and the diffuser (Transducer D) to measure the pressure
ﬂuctuations through the compressor stage.

This unsteady performance analysis has been determined for both vaneless
diffusers at each operating point and for every speed. Because of the similar patterns at
all impeller rotational speeds, the data of the maximum impeller speed which is 32000
RPM are presented here for VNLDl and VNLD2. The outputs from transducer B are left
out because its signals are almost the same as transducer C. Both transducer B and
transducer C were located in the impeller at the same radius but different circumferential
position for the purpose of relative effects.

Most rotating stall signals reported in the literature were below the rotational
speed of the impeller. For this reason, the data in the range 0-540 Hz are plotted here.
Through the centrifugal compressor stage and with both vaneless diffuser and at each

transducer, a three-dimensional plot of the power spectrum is presented.

125

5.5.1 Unsteady Flow in the Inducer
Figure 5.20 and Figure 5.21 show the power spectra of the signal from transducer

A at the maximum impeller speed (32000 RPM) for VNLDl and VNLD2. As shown on
this ﬁgure and the following ﬁgures, the energy level of the unsteady signals at low
frequencies is generally larger than at high frequencies. This tendency is common with
both vaneless diffusers, at every operating point, at all transducers, and at every impeller
rotational speed.

Figure 5.20 shows a rotational frequency of 408 Hz in all four transducers through
the compressor stage. The energy level for this peak keeps constant through all the
Operation points. Also by comparing the two ﬁgures (Figure 5.20 and Figure 5.21) it
could be seen that one weak peak is present with both vaneless diffusers conﬁguration at
a rotational frequency of 60 Hz. This peak is common in all transducers and occurs only
at an impeller speed of 32000 RPM. The energy level for this peak is constant for all
operating points. Therefore, the 408 Hz with VNLD] and 60 Hz with both vaneless
diffusers are suspected of being caused by either electrical distortions or mechanical
vibrations and not in ﬂow phenomena.

No signiﬁcant pressure ﬂuctuations are found in the inducer at high mass ﬂow
rates. However, at low mass ﬂow rates the pressure ﬂuctuations grow at approximately
operating point number nine for VNLDl and VNLD2. These pressure ﬂuctuations
indicate the onset of inducer stall. The energy level of these pressure ﬂuctuations with
VNLD] is higher than that with VNLD2, which indicates that the inducer is more stable

with VNLD2. The surge phenomena will be discussed through the next section.

126

 

VNLDi [32,000 RPM
111 Transducer A

// /*

/

I , //
at

 

 

 

 

Figure 5.20 Power spectrum of the compressor stage with VNLDl at 32000 rpm
Transducer A

127

 

VNLDZIazoOORPM
WTWMA

W14!)
1'3 3
9 §

  

 

 

10.00— _ //
[l 72/ /// 1‘ '1 /
I 4 / s /1 » / , . ./
5.00— I / "// A/ﬂ // /’”1///‘0// 1’4///4
... ’“g "’1' 9
' - 4 4 | 7
" 5 09.0
4 4 ..... ‘ a
450' ' 50° ‘

 

 

Figure 5.21 Power spectrum of the compressor stage with VNLD2 at 32000 rpm
Transducer A

128

 

 

5.5.2 Unsteady Flow in the Impeller
Figure 5.22 and Figure 5.23 shows the power spectra from transducer C at

impeller rotational speed of 32000 RPM for VNLDl and VNLD2. The transducer C is
located in the impeller. The energy of the unsteady signals in the impeller is generally
higher than in the inducer. For both vaneless diffusers the peak at a frequency of
approximately 533 Hz, which corresponds to the impeller rotational speed, is much
higher in the impeller than in the inducer.

Figure 5.22 shows that at the ﬁrst three operating points, VNLD] is stable in the
whole frequency range. The level of energy in the unsteady signals begins to increase
after point three to a medium level and constant over approximately the frequency range.
On the other hand, VNLD2 in Figure 5.23 shows high energy level at low frequencies in
the whole frequency range and through all the operating points. This could be due to the
inducer choke and the associated losses. At operation number nine for VNLD] and
number seven for VNLD2 the ﬂuctuations begin to increase. At the last operation for
both vaneless diffusers one peak has been found. A strong peak is present with both
VNLDl and VNLD2 at frequency of 12 Hz but with slightly different energy level. The
energy in this peak is between 29 and 36 dB. It is much higher than all other signals.
Since the peak occurred at the same frequency in all transducer signals, it can be
classiﬁed as stage surge.

Table 5.1 summaries the characteristic data of the surge phenomena detected with
both VNLDl and VNLD2. Surge is always the responsible phenomena for the operating

range limit at low mass ﬂow.

129

 

VNLD1/32WORPM

////
//// .4
9‘

///////¢////

 

 

 

 

Figure 5.22 Power spectrum of the compressor stage with VNLD] at 32000 rpm
Transducer C

130

 

VNLDZ I 32000 RPM

Pmm [‘8]

7/l loll/)4 ”(K

I

 

 

 

 

Figure 5.23 Power spectrum of the compressor stage with VNLD2 at 32000 rpm
Transducer C

131

 

VNLDi I 32,000 RPM
171 Transducer D

//’ /

/l

///
/////a//4 ///////’

 

 

 

 

Figure 5.24 Power spectrum of the compressor stage with VNLD] at 32000 rpm
Transducer D

132

 

[a]

1500-

10.00—

5.”—

 

 

7

.427] if“
”(I 7’

'4

 

x77, (4

100

d

f

1.;

2, we. ~

///

WM 350

VNL02I32000RPM
WTWD

W11
41'- 4°"

,, /',/I//,// ’
///// l/yl/ ’71.,J‘ /I//
(”Q/9 ”MU/”x" W .

///

1"
400

   
 
  
 
 
   

_l

”1 I Eli! '
/ ,. 1' (4 llai/ 41/ ’ ' , (I
(1’; ///////)’ ”1" "4,1451%”? /,

450

 

. , ,
ff”!!! 1

7

.1" 6 °"

1

 

Figure 5.25 Power spectrum of the compressor stage with VNLD2 at 32000 rpm

Transducer D

133

 

5.5.3 Unsteady Flow in the Diffuser
In Figure 5.5 and 5.6 the power spectra from transducer D at impeller rotational

speed of 32000 RPM for VNLDl and VNLD2 are presented. The transducer D is located
in the diffuser.

For VNLDl in Figure 5.5, the pressure ﬂuctuations are low in the ﬁrst ﬁve
operating points. The VNLDl operates stable in this region, and the ﬂuctuations increase
from operation ﬁve and on over the whole frequency range. At operation point number
eleven, a peak of frequency 12 Hz is found with the highest energy level. This is
expected because transducer D is located in the diffuser, and the static pressure is highest
in the diffuser.

In Figure 5.6, VNLD2 show a similar trend but with more stability with no

pressure ﬂuctuations was detected until operation number seven. After this point, the

pressure ﬂuctuations increased and a peak was found at a frequency of 12 Hz.

Table 5-1 Surge Characteristics through the Compressor Stage with VNLDl and
VNLD2 at all Impeller speeds Using Transducer D

 

 

 

 

 

 

 

 

 

 

 

Diffuser type 18800 24000 28000 32000
RPM RPM RPM RPM

Surge freq. 6 Hz 6 Hz 8 Hz 12 Hz

VNLD] Energy level 26 dB 23 dB 15 dB 35 dB
Flow coeff. 0.292 0.428 0.494 0.586

Surge freq. 6 Hz 6 Hz 8 Hz 12 Hz

VNLD2 Energy level 17 dB 16 dB 17 dB 31 dB
Flow coeff. 0.333 0.414 0.430 0.575

 

 

 

134

 

As shown in Table 5-1, the surge frequency increases from 6 Hz to 12 Hz as the
impeller rotational speed increased. As shown in this table that the diffuser width has no
inﬂuence on the surge frequencies while there is a difference in the energy level of the
unsteady signals and the surge ﬂow coefﬁcient. VNLD2 show a better stability in which
the energy level of the unsteady signals is lower than for VNLDl. Also, the occurrence
of surge has been shifted to a lower ﬂow rate with VNLD2 in which it has a wider ﬂow

range than VNLDl.

135

6. CONCLUSIONS AND RECOMMENDATIONS

Two vaneless diffusers, VNLD] and VNLD2, that differ in their passage widths
are tested experimentally downstream of the same centrifugal impeller to investigate the
effect of this variation on the overall stage performance. Each diffuser was tested at four
different impeller speeds: 18800 rpm, 24000 rpm, 28000 rpm, and 32000 rpm. These
speeds corresponds to impeller tip Mach numbers of M: 0.7, 0.89, 1.04, and 1.19. A
theoretical analysis was also carried out from the diffuser inlet radius to the diffuser
outlet radius using different values of radius ratio. The results of this theoretical analysis
were compared to the measured performance curves of both vaneless diffusers. In
addition to that, unsteady analysis was carried out by measuring the pressure ﬂuctuations
through the centrifugal compressor components with both vaneless diffusers.

The overall performance of the compressor stage with VNLD2 showed a better
performance than with VNLD] at impeller tip speeds of 18800 RPM, 24000 RPM, and
28000 RPM. It has been found also that the centrifugal compressor stage with VNLD2
had a wider ﬂow range than with VNLD] at each impeller speed. This has been attained
as the choke ﬂow shifted to a higher ﬂow coefﬁcient and the surge point to a lower ﬂow
coefﬁcient for the compressor stage with VNLD2. In addition to stage efﬁciency, the
diffuser efﬁciencies, total-to-static and static-to-static, have been compared for both
vaneless diffusers. For both VNLDl and VNLD2 the efﬁciencies increased as the ﬂow
coefﬁcient decreased. It has been found that the diffuser efﬁciency slightly improved by

spacing the diffuser walls farther apart.

136

 

In addition to studying the overall performance of the compressor stage and the
vaneless diffuser, the pressure recovery of VNLD] and VNLD2 was studied from the
diffuser inlet radius to the diffuser exit through the total pressure recovery and the
subdivided pressure recoveries. For both vaneless diffusers, it was found that the major
part of the pressure recovery through the vaneless diffuser occurred between the middle
to the exit radii. It was also found that the pressure recovery between the impeller exit
and the diffuser inlet contributes in the total pressure recovery Cp2—5. Similar ﬁndings to
the stage performance have been found with the pressure recovery in which VNLD2
gives better pressure recovery at impeller speeds of 18800 RPM, 24000 RPM, and 28000
RPM. The variation in the static pressure ratio and the square of the local Mach number
has been carried out with the radius ratio from the diffuser inlet to the diffuser outlet radii
for both vaneless diffusers. The experimental and theoretical results were similar. As
expected it has been found that across the diffuser, the pressure ratio increased and the
velocity decreased. Also, it has been found that increasing the diffuser wall spacing will
result in a decreased the velocity and, as a result an increased pressure ratio.

The unsteady results showed that with increasing the diffuser width the impeller
rotating stall was shifted to lower ﬂow rates at all impeller rotating speeds. At the same
time, the frequencies of the rotating stalls decreased as the diffuser width increased.

According to these results, it could be concluded that increasing the vaneless
diffuser width would improve the compressor stage efﬁciency, attain wider operating
range, and give more stable operation at low to medium impeller speeds. At the same
time, as the vaneless diffuser width increased, the length of the ﬂow path increased,

which should result in increased losses. A very wide spacing of the diffuser walls should

137

 

not be recommended because of a small gain in efﬁciency and a great risk of separation.
The overall performance results for the stage, which have been found through this work,
may show that the difference between these two vaneless diffusers, which is
approximately 17 %, is within the optimum width. However, according to these results,
increasing the diffuser width is not recommended at high impeller rotating speeds (more
than 28000 RPM). Therefore the effects at high impeller speeds should be the subjects of
further investigation. Through this work the results were related to the ﬂow coefﬁcient
through the compressor stage. For future investigations, it will also be helpful to
investigate the results not only to the ﬂow coefﬁcient but also to the ﬂow angle at the
vaneless diffuser inlet. During these experiments, the total pressure P03, which has been
used to calculate the ﬂow angle at the diffuser inlet, was measured by Kiel type probe
located in the middle of the ﬂow channel. This probe is suspected to be too large relative

to the channel height, resulting in incorrect values at lower mass ﬂow rates.

138

 

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139

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144