Axial flow fans and compressors : aerodynamic design and performance 9780291398505, 0291398502

Citation preview

AXIAL FLOW FANS AND COMPRESSORS

To my grandson, Neil, without whose interest this book might never have been completed

Cranfield Series on Turbomachinery Technology Series Editor: Robin L. Elder

Axial Flow Fans and Compressors Aerodynamic Design and Performance

a. b.

McKe n z ie Visiting Professor School o f Mechanical Engineering Cranfield University Bedford

Ashgate Aldershot • Brookfield USA • Singapore • Sydney

O A. B. McKenzie 1997 All rights reserved. No pan of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. Published by Ashgate Publishing Limited Gower House Croft Road Aldershot Hants GU11 3HR England Ashgate Publishing Company Old Post Road Brookfield Vermont 05036 USA British Library Cataloguing in Publication Data McKenzie, A. B. Axial flow fans and compressors : aerodynamic design and performance. - (Cranfield series in turbomachinery) 1. Axial flow compressors 2. Axial flow compressors - Design 3. Aerodynamics I. Title 621.5' 1 Library of Congress Cataloging-in-Publkation Data McKenzie, A. B., 1926Axial flow fans and compressors : aerodynamic design and performance / A. B. McKenzie, p. cm. Includes bibliographical references. ISBN 0-291-39850-2 1. Fans (Machinery)*-Aerodynamics. 2. Axial flow compressors-Aerodynamics. I. Title TJ960.M35 1997 97-1249 621.6’ l-dc21 CIP ISBN 0 29139 850 2 Printed in Great Britain by The Ipswich Book Company, Suffolk

Contents

Preface 1

2

3

4

The axial fan Introduction The domestic ventilator Work done The diffusing blade passage Mass flow variation The fan characteristic

xi 1

2 3 4 7 9

Reaction Introduction Definition Choice of reaction Variation of reaction with radius

12 13 15 16

The work and flow coefficient diagram Introduction Additions to the diagram Reactions other than 50% The IGV/rotor fan The rotor/stator fan

17 18 22 24 24

Blade loading parameters Introduction Cascade data Total pressure losses Deviation Axial velocity ratio Compressor data Blade geometry selection

27 27 29 29 30 30 32

vi

5

6

7

8

9

Axialflow fans and compressors

Blade geometry Introduction The C series of aerofoils American practice Cascade geometry The double circular arc blade Modem trends

35 35 36 36 37 38

Aspect ratio Introduction Surge margin improvement Other benefits Technical considerations Equivalent cone angle End wall loss parameter Design criteria

41 41 42 43 45 45 47

Relative motion effects Introduction Blade design with secondary losses Wakes in relative motion Work and flow coefficient effects Radial flow shift through the rotor

49 50 52 53 54

Vortex flow Introduction Free vortex designs Constant reaction Arbitrary vortex Simple equilibrium Examples of simple equilibrium Constant ‘reaction* design Throughflow computations

56 56 57 60 60 61 63 65

Mach number effects Introduction High subsonic Mach number • Passage throat width Supersonic Mach number Blade forms for supersonic operation Passage shock waves S/C requirement Laser anemometry Effect of Mach number on overall pressure ratio

66 66 67 69 70 70 71 72 73

Contents

10

Reynolds number effects Introduction Performance variation WasselTs correlation Surface finish effects

11

Compressible flow relationships Introduction Notation Fundamental relationships Applications

12

The stage characteristic Introduction The work coefficient characteristic The efficiency characteristic The pressure rise coefficient Experimental stage characteristics

13

The repeating stage concept Introduction The linear repeating stage Stage of unity work coefficient

14

Spanwise matching of high diameter ratio stages Introduction Variable axial profile Variable work done design An alternative approach

15

Spanwise matching of low diameter ratio stages Introduction Example Increased diameter ratio Conclusions from the approximate method Alternative methods

16

Stall Introduction Criteria for progressive or abrupt stall Surge initiation Rotating stall Hysteresis

viii

17

18

19

20

21

22

Axialflow fans and compressors Vibration Passive stall control

119 120

Introduction An alternative criterion for surge More complex approaches Surge margin

124 126 129 129

Surge

Performance presentation Introduction Performance graphs Isentropic and polytropic efficiency Polytropic efficiency Efficiency assessment Efficiency with interstage bleed flows

132 133 136 138 140 142

Stage matching and surge control Introduction The stage matching problem Bleed off-take Variable stagger stator blades Industrial axial compressors Twin spool gas turbines Off-design operation of twin spool gas turbines Active surge control

144 144 147 149 150 151 153 156

Inlet flow maldistribution Introduction Compressors in parallel Distortion parameter Inlet Temperature distortion

157 158 161 162

Compressor rig testing Introduction Power requirements Facility layout Test procedure

164 164 168 171

Stage performance prediction Introduction A preferred method Other methods Off design efficiency

174 174 179 180

Contents 23

24

25

26

27

28

ix

Overall performance prediction Introduction Stage stacking Overall performance correlation High speed corrections Test comparison with prediction

181 181 183 188 190

Performance with altered gas properties Introduction The significance of density ratio Gases other than air Compression of helium Viscosity and Reynolds number

191 192 193 194 195

Design for a domestic ventilator Specification Overall parameters Blade speed and dimensions Blade selection Half speed operation

196 196 197 198 200

Design for an industrial fan Specification Preliminary considerations Choice of diameter ratio Rotor blade geometry The outlet stator The outlet diffuser

201 201 202 203 206 208

Design for a transonic wind tunnel fan Specification Preliminary considerations Selection of vector geometry The rotor blade The stator Annulus dimensions Design speed Fan efficiency Outlet diffuser Power requirement Operation at higher tunnel Mach numbers

209 209 210 212 216 218 220 220 223 224 224

Design for an industrial compressor Introduction Design specification

226 226

Axialflow fans and compressors

X

General considerations Design parameter selection Rotor blade geometry Stator blade geometry Annulus diagram Variation of stage numbers Additional front stages Scaled versions Volume flow 29

30

31

227 227 230 234 236 237 238 240 240

Outline design for a jet engine compressor Introduction Specification Overall parameters First stage Last stage Blading

241 241 242 243 245 247

HP compressor mid-stage Introduction Datum stage Blade end modifications Rotor design Stator blade Design method

248 248 249 251 253 255

The high bypass fan Introduction General arrangement Aerodynamic parameters Rotor blade geometry Fan blade integrity

256 256 257 260 260

Bibliography

262

Preface

My introduction to axial compressors was at Rolls Royce in 1947 when the technology was still in its infancy, so it was relatively easy to absorb existing knowledge and thereafter keep abreast as the technology developed. The task facing newcomers to the subject today must be vastly more formidable, faced with literally thousands of technical papers produced over the last five decades and growing at an ever greater pace. Despite the wealth of detailed publications available there have been only a few books which attempt a general introduction to the subject in sufficient depth to provide an adequate understanding on which to base further research, development and particularly aerodynamic design. It is my hope that this volume will go some way to serve this purpose, and if only a few readers become as fascinated by the subject as I have been for nearly fifty years, the effort will be well rewarded. A few novel concepts which may not be generally accepted have been introduced. I feel these have sufficient merit to justify inclusion, if only to stimulate further thought, which may confirm or reject them. Examples are to be found in Chapters 7, 14, 15 and 17. A method of overall performance prediction described in Chapter 23 also contains some features not previously published. As is to be expected I have drawn extensively on my thirty seven years experience with Rolls Royce, and I am grateful to the Company for permission to publish some of the subject matter. This is not to say that Rolls Royce endorse any of the material, the responsibility for which is entirely my own. I also wish to thank Mr D P Hope of Rolls Royce for many helpful suggestions and much of the material for Chapter 31. I am also indebted to Professor R.L.Elder and Dr.K.Ramsden at Cranfield University for their help and guidance in the preparation of the text.

1 The axial fan

Introduction The simplest form of axial compressor is the single stage fan. The distinction between a fan and a compressor has been defined by describing the fan as an air mover, whereas the purpose of a compressor is to increase the pressure and density of the air or other working gas. While this definition is substantially true, nevertheless the specification of a fan usually calls for a pressure rise, even if this is only a centimetre or two of water gauge. In turbofan aero-engines the fan may develop a pressure ratio in the region of 2 : 1, but is still an air mover in that the majority of the airflow passes directly to a propulsion nozzle where the pressure energy is converted directly to kinetic energy in the propulsive je t

Figure 1.1

Axial ventilator fan

2

Axialflow fans and compressors

The domestic ventilator A familiar form of axial flow fan is the domestic ventilator. This consists of a single row of blades driven by an electric motor. An example is shown diagrammatically in figure 1.1. Rotation of the blades induces a draft of air from the room to the exterior. Examination of the section of the blades will show a shape as in figure 1.2a or 1.2b. For the simplest designs the blade is of constant thickness (called “cambered plate") but more sophisticated designs have an aerofoil section i.e. similar to the cross section of an aircraft wing.

Fig. 1.2a

Cambered plate blades

Fig. 1.2b

Figure 13

Rotor inlet and outlet vectors

The axial fan

3

When the fan is running the air flows towards the blades with an axial velocity Va. Due to the blade motion, U, the velocity of the air relative to the moving blade at its leading edge is V|, as shown in figure 1.3. The angle, ot|, of the relative velocity from the axial direction is similar to the angle of the blade at its leading edge, so that the flow passes smoothly along both blade surfaces. Due to the curvature of the blade section, and the influence of neighbouring blades, the flow relative to the blade is turned towards the axial direction as it passes through the blade passage. The resulting vector diagram at the trailing edge is also shown in figure 1.3. Due to the flow turning produced within the blade passage the outlet flow has a circumferential velocity component, Vw3, in the same direction as the blade movement It is assumed for the present that the axial velocity does not change in passing through the blades. Work done Work is done when a force moves its point of application. The motor produces a circumferential force on the blades and the work done by the movement of this force is transmitted to the airflow. m The work done per second = Ft.U, and so x.co = F,.U where Ft = tangential force on the blade U = blade velocity = co.r co = angular velocity of blades r = radius of rotation x = torque = F,.r The torque acting on the rotor blades is reacted by the rate of change of angular momentum of the air. Hence torque can be written: t = MrVw3 where M is the rate of mass flow and Vw3 is the tangential velocity at rotor exit. Hence:

T od =

MUVw3

The energy transfer to the airflow per unit mass flow is: AH = tcd/M = UVw3 In more general terms this can be written as: AH = U3VW3 - UqVwq

4

Axialflow fans and compressors

In this form allowance is made for the situation where the flow may leave the rotor at a different radius from which it enters, and the blade speed changes from Uo to U3. There may also be a whirl velocity ahead of the rotor, Vw0. In accurate analysis and design work it is necessary to take account of radial changes across the blade row. For immediate purposes it will be sufficient to write: AH = U.AVw where AVw is the change of whirl velocity across the rotor. It is convenient to superimpose the inlet and outlet vector diagrams on a base of the common blade speed as in fig. 1.4. This form of the velocity triangle diagram is fundamental to an understanding of the design and performance of axial fans and compressors.

Fig. 1.4

Inlet and outlet vector diagrams superimposed

The diffusing blade passage The relative inlet velocity, Vt, is reduced to V2 in passing through the blade row. The inlet flow area of the relative flow is given by: n s h cos a t where n is the number of blades, s is the circumferential distance between blades (the pitch or space) and h is the span or radial height of the blade. At blade outlet the relative flow area becomes n.s.h.cos CX2. Continuity of mass flow gives: M = p 1A] V1 = piAiVi where p is the density of the air and A is the cross sectional flow area. For low speeds compared to the speed of sound the density change can be assumed negligible and hence: V2/V 1 = Ai/A2 = cos 0.5*105,the power n = - 0.2 For Re < OJMC^.the power n = - 0.5 Bullock (1964) quotes a similar equation: (l-T l,)/(l-il 2) = a + b(Re1/Re2)c He points out however that in the literature the values of ‘a’ vary from 0 to 0.5, of *b* from 0.5 to 1 and of *c’ from 0.1 to 0.2. He concludes a detailed discussion with the observation that c = - 0.2 is satisfactory for Reynolds numbers greater than 4*10* provided the blade surfaces are aerodynamically smooth. He also indicates that the unsteady pressure and velocity fields produced in compressors by blades passing through the wakes of preceding blade rows are probably responsible for the comparatively low Reynolds number at which the effect of turbulent flow is evident in the behaviour with varying Reynolds number as compared to cascade tests. WassePs correlation Wassell (1967) uses the same equation as Carter et al, but puts the index n = p*q, where p is determined by the level of mean Mach number through the compressor, and q is determined by the ratio of the ’effective’ length to the mean annulus height He develops an impressive correlation of data from twenty different compressors which includes the effects on surge pressure ratio and mass flow as well as efficiency. The correlation is limited to Reynolds numbers greater than the critical, but this is indicated to be as low as 0.25* 105 for single stage fans and multi-stage compressors, compared to 1.0*10* for cascades. Because it is one of the most practically useful methods for Reynolds number corrections the essentials of Wassell’s correlation are given in figures 10.1 through 10.3. In figure 10.1 for the parameter p the base has been changed from V/VT to mean Mach number in order to avoid any confusion over units. The mean Mach number can be taken as the value at the design speed relative to the inlet of the mid-stage rotor, or the average of first and last stage values. All other parameters are explained on the diagrams.

Reynolds number effects

77

Application of the correlation Use of the correlation is best illustrated by an example. Say a compressor has been tested at an inlet pressure of 60 kPa and the results are to be corrected to an inlet pressure of 101.3 kPa. The inlet temperature is 288 K and the rpm constant for both cases.

ha

h.

Mmui Mach No.

Figure 10.1

OGV

Mean annul us h t ■ ‘/j [hi+h?l U , - UN/(N - 7x) N * No. of stages

Efftctlv* length I iman annulus height

Wassel efficiency correction parameters Adaptedfrom Wassel (1967) with permission of ASME

Efficiency correction For the efficiency correlation Wassel defines a Reynolds Number Rei based on the mean relative inlet velocity to the first stage rotor, the first stage rotor chord and the inlet density and viscosity. If this Reynolds number is 0.7* 105 at 60 kPa inlet pressure it will be 0.7(101.3/60)* 103 = 1.18*105 at the higher pressure, since density is proportional to pressure at constant temperature. For the efficiency correlation let the mean Mach number be 0.7, which gives p = 0.85. Also let the length of the rotor ( L r ) be 400 mm and the mean annulus height 109 mm. The effective length (1^) is given by: = 400*6/(6 - 0.5) = 436 for the 6 stages. The correction is to allow for the additional length of a typical stator as compared to the long chord or double row outlet guide vanes used at the outlet of some compressors. The mean annulus height is 109 mm, which results in a value

78

Axialflow fans and compressors

of 4 for the ratio of effective length to mean annulus height, and from figure 10.1(b) the value of q is 0.14, and hence n = p*q = 0.119. For the lower Reynolds number 1 - Tio.7 = W.TMO5)"0119 For the higher one:

1 - Hu* = k( 1.18* 10s)]*0119

Hence we can write:

1 - n u i = (1 - tjXO.7/1.18)0'119

Thus, if Ho.7 = 85%, then: 1 - n,.,t = 0.15(0J93)°119, and n,.„ = 85.9%

Mass flow correction For the mass flow correction the linear dimension of the Reynolds number, Re2, is defined as the distance x from the first rotor leading edge to the point where the throat width of the passage intersects the suction surface of the blade, as shown on figure 10.2.

Re* * piVj„*x/Hi Reynold** No. R** 10*4

Figure 10J

Wassel mass flow correction Adaptedfrom Wassel (1967) with permission cfASME

If x/C = 0.5, then Re2 = 0.5Rei and so Re2 = 0.35* 105. From figure 10.2, if Olx = 0.9 then: (0/*XQa/Qa* - 1 ) 52-0.05 Hence

Qa/Qa* = 1 - (0.05/0.9) = 0.944

At standard atmospheric inlet pressure the Reynolds number Re2 will be : Rej = OJRe, = 0.5* 1.18* 105= 0.59'K)3 Hence:

(O/xXQa/Qa*- 1) = -0.025

Reynolds number effects

and: Hence

79

Qa/Qa* = 1 - (0.025/0.9) = 0.972 Qs*/Q«o = 0.972/0.944 = 1.03

Thus the mass flow is estimated to be 3% greater at standard atmospheric inlet pressure compared with the test pressure. Surge pressure ratio correction For the surge pressure ratio correlation another Reynolds number Re3 is defined as:

Re3 = piVah/^i

where Va is the axial velocity at inlet to the first stage rotor and h is the first stage rotor height For typical geometry this results in Re3 = U Rei

Reynold's No. Re»* 10**

Figure 103

Wassel surge pressure ratio correction Adaptedfrom Wassel(1967) with permission of ASME

For Re, = 0.7* 105, Rej = 1.05M05 and for Re, = 1.18*10*. Re3 = 1.77M05 At Rej = 1.05M03figure 10.3 gives (Rs - Rs*)/Rs* = 0.01 and at Re3 = J.77‘ 105: Hence

(Rs - Rs*)/Rs* = 0.05 RsWRsw = 1.05/1.01 = 1.04

which results in a corrected surge pressure ratio of 5.2, for a test value of 5.

80

Axialflow fans and compressors

Surface finish effects It is well known that the fhction factor for pipe flow becomes constant above a value of the Reynolds number which varies with the surface roughness of the pipe. The value of the friction factor falls as the roughness is reduced and the Reynolds number at which it becomes constant increases, as described by Moody (1944), and adapted by Shepherd (1956). Similar effects are to be expected in compressors with variation of the blading surface finish. Schaffler (1979) presents the results of a series of compressor tests which agree reasonably well with Wassell's correlation but indicate a constant efficiency above an upper critical Reynolds number which is a function of the surface finish of the blades.

Velocity

'Laminar sublayer

Turbulent boundary layer Roughness within laminar sublayer * hydraulically smooth

Roughness protrudes Into turbulent layer * hydraulically rough Figure 10.4

Aerodynamic roughness

Approx. Reynolds number Figure 10.5

Roughness effect on efficiency

Reynolds number effects

81

The mechanism, which is shown diagrammatically in figure 10.4, is that when the roughness is such that the peaks of the surface irregularities do not protrude through the laminar sub-boundary layer the turbulent boundary layer is unaffected and the flow behaves as if the surface is aerodynamically smooth. At some higher Reynolds number, implying a relatively thinner boundary layer, the peaks of the surface irregularities will protrude into the turbulent boundary layer and cause the flow to behave as if the surface is aerodynamically rough, producing a constant efficiency with further increase of Reynolds number. Hence the increase of efficiency with increasing Reynolds number is dependent on the quality of the blade surface finish. Schaffler's results illustrate clearly that polished blade surfaces, particularly on the rear stages of a compressor, will delay performance deterioration due to falling Reynolds number at increased altitude. Miller (1977) quotes the upper critical Reynolds number as: R„c =16C/kd, where C is the blade chord and kd» is the surface roughness measured by the Centre Line Average method, which is quoted in micro-inches i.e. inches* 1C* = 25.4 nm For forged blading a CLA value of 32 is representative, and if polished this can be reduced to 16, with the effect shown in figure 10.5. Care should be taken to ensure that the Reynolds number is high enough to exceed the upper critical before incurring the cost of polishing blading. This may lead to polishing only a number of rear stages and ignoring forward stages where the Reynolds number is less than the upper critical over the operating range. For small compressors it may be found that polishing to a CLA value below 32 is ineffective in producing any improvement, whereas for large turbofans it can produce worthwhile improvements, but not requiring polishing of the front half of the core compressor stages. It has been suggested that polished blade surfaces may reduce the amount of dirt which is accumulated on the blades over a period in service and that this effect may justify polishing of blades where the above arguments would not necessarily justify the cost involved. It could also be that polishing to a smoother surface finish is justified for this reason.

11 Compressible flow relationships

Introduction It is convenient both for the calculation of flow properties in ducts and for the non-dimensional presentation of compressor performance characteristics to use a number of nondimensional and quasi-nondimensional groups. These can be developed from a few fundamental relationships. Notation a = local speed of sound = CyGt)1/2 A = local cross sectional flow area Cp = specific heat at constant pressure Cy = specific heat at constant volume Y= Cp/Cv G = gas constant = 0.287 for air M = mass flow rate Mn= Mach Number = V/a p = static pressure P = total pressure t = static temperature T = total temperature V = local velocity p * density

m/s m2 kJ/kgK kJ/kgK kJ/kgK kg/s kPa kPa K K m/s kg/m3

Fundamental Relationships Gas Law

p/p = Gt

d)

Compressible flow relationships Continuity of mass flow

83 M = pAV........ ..........................(2)

Energy

T « t + V2/2Cp................................. (3)

Isentropic relation

Ftp = (TA)y(T“!)...............................(4) G = Cp-C*........................................(5)

From (3) and (5) we can obtain: and from (4) Rearranging (3) hence From (1) and (2)

TA a 1 + 0.5(y- 1)Mh2.........................(6) P/jp = {1 + 0.5(y - OMn2}**"0................... (7) V2/2Cp = T -t; V/V(CpT) = {2(1 - 1fT))in.......................(8) M/A = pV/Gt

hence:

Q = MVT/AP = (1/GXV/VTXTAXp/P).............. .(9)

and

q = MVT/Ap = (1/GXV/VTXTA)..................... (10)

From equation (8) it is apparent that V/>/(CpT) is non dimensional and hence Q and q are only quasi-nondimensional The true nondimensional forms are: (MVT/APXGWC,) = [VMCpT)](TAXp/P) and

(MVT/ApXG/VC,) = [V/V(CpT)](TA)

When written in this form any self consistent set of units will give the same values. It is common practice, however, to use the quasi-nondimensional forms given by equations (9) and (10). Since the value of Cp varies appreciably for the range of temperatures encountered for air compressors, different tables or curves are required for various ranges of temperature. Gases other than air will also require their own values for the relationships. Since: G = Cp - C*; and y = Cp/Cy. we have: Cp = G{*y/(Y - 1)}. While G is constant at 287 kJ/kgK for air in the range of temperature of interest to compressors, the value of Cp rises with increasing temperature and it is usual to specify the data by the value of y which falls from about 1.4 at 250K to 1.35 at 850K. A typical set of graphs are shown on figure 11.1 plotted to a base of Mach number. The most notable feature of these curves is that Q reaches a maximum when the Mach number = 1.0, while all the other parameters increase continuously. An excellent resume of the theory of gas dynamics which explains the background to this and other transonic phenomena is given in an appendix to

84

Axialflow fans and compressors

‘Gas turbine theory' by Cohen et al (1972). A comprehensive set of tables for isentropic compressible flow and related topics are given by Palmer et al (1987). Applications Airflow measurement By means of a well flared entry to a ducting system the mass flow rate may be measured by means of total and static pressures as indicated in figure 11.2. By measuring the dynamic pressure, i.e. total - static, and the total as a difference to atmospheric, which should be very small if the flow is drawn directly from atmosphere, the ratio of the absolute values of total and static pressures are derived. The value of Q is then obtained from tables or graphs. Provided an effective flow area for the duct cross section at the measuring plane is known and the atmospheric temperature has been measured the actual mass flow rate may be calculated: M = (MVT/AP) (AP/VT) The effective flow area divided by the geometric area is known as the discharge coefficient, Q , and can be determined by measurements of total pressure across the duct boundary layer in the plane of measurement For a well designed inlet flare the value of C/T/P)/(M>/T/AP) = 5.276/16.8 = 0.314m2 To find the mass average velocity in the duct. From flow data V/VT = 5.

V = 5.0V457 = 106.9 m/s

To find the static pressure: P/p = 1.044 at MN= 0.25 p = P/(P/p) = 405.2/1.044 = 388.1kPa To find the dynamic pressure in mm Hg. Dynamic pressure = P - p = 405.2 - 388.1 = 17.1kPa To convert this dynamic pressure to the equivalent of Mercury column: 101.3kPa = 760 mm Hg, hence:-

17.1kPa = 760*17.1/101.3 = 128.3 mm Hg

12 The stage characteristic

Introduction The performance of an individual stage can be represented approximately as a unique set of curves for all rotational speeds, in terms of AH/U2, and AP/(pU2) plotted to a base of Va/U, as previously shown on figure 1.7. This is usually called the stage characteristic. It is only genuinely unique with variation of rotational speed for a limited range of Reynolds number and when the blade inlet relative Mach numbers are low, say less than 0.3. As Mach number increases some variation appears in the curves obtained due to falling efficiency and to varying axial velocity ratio across the blading, resulting from increasing density ratio as speed increases. These variations are sufficiently small that the concept of the unique stage characteristic is an extremely useful one. By measurement of casing static pressures between blade rows individual stage or blade row characteristics can be derived from multistage tests and provide a useful analysis tool for performance development Prediction of individual stage characteristics provides the basis for stage stacking performance prediction methods as discussed in Chapter 22.

The work coefficient characteristic The basic parameters of the stage characteristic are the work coefficient AH/U2, and the flow coefficient Va/U. As discussed previously, if the air oudet angle from the blades were to be constant independent of the incidence, AH/U2 would vary linearly with Va/U. Although the outlet angle is nearly constant at incidences well away from stall, it rises significantly near stall and as indicated by Howell (1945), the deflection may reach a maximum at stall. At that point the outlet angle must rise at the same rate as the incidence. Despite this, most stage characteristics tend to indicate a work v flow coefficient curve which is approximately a straight line above the peak efficiency flow coefficient although of a lower negative gradient than corresponding to constant outlet angles. Howell and Bonham (1951) gave graphical data for the slope of the curve at the design

Axialflow fans and compressors

88

point. This indicated that the gradient of the curve diminished as the work coefficient increased. Data derived from the experiments reported in McKenzie (1980) tended to show that Howell and Bonham's correlation could be improved if the S/C was introduced as a parameter. Intuitively it can be readily appreciated that the greater the spacing of the blades the greater will be the tendency for the outlet angle to increase with incidence.

Figure 12.1

The work characteristic slope. Based on Howell and Bonham (1951)

Writing y for AH/U2 and yd for the design value and referring to figure 12.1 where

0

90

180

270

360

Circumferential station - dagraaa

Figure 202

Circumferential variation of stage static pressures with 90®sector inlet spoiler

The first point can be explained by considering a compressor operating on a vertical part of a pressure ratio v mass flow characteristic with inlet distortion of the total pressure. If two parallel compressors are considered, they must both operate with the same mass flow function, since this is the only value possible at this particular speed. The unique mass flow function corresponds to a unique velocity since the total temperature is constant. The second point can be demonstrated by considering the static pressures through the stages of the compressor when operating with uniform inlet flow at two pressure ratios corresponding to the operating points with a distorted flow. In figure 20.3 the maximum and minimum pressures at each stage from figure

160

Axialflow fans and compressors

Out

3

3.5

4

4.5

5

Outlet static / Intel total p rw u f

Figure 203 Design speed stage static pressures with uniform inlet flow 20.2 arc represented by lines 'A' and ’B\ which correspond to the overall pressure ratios with maximum and minimum inlet total pressures respectively. In figure 20.4 the difference between the maximum and minimum stage pressures derived from figure 20.3 are compared to the values given by test from figure 20.2. The good agreement suggests that the assumptions of the compressors in parallel theory give a good approximation to the flow behaviour. The third point indicates that the effective proportion of the annulus area occupied by the low pressure inlet flow increases through the stages. This is inconsistent with the theory, but would tend to cause a greater pressure ratio for the low pressure inlet flow as the axial velocity would fall more rapidly, giving more pressure rise from the rear stages. The corresponding reduction of annulus area occupied by the high pressure inlet flow would reduce its pressure ratio.

Stag* inlet

Figure 20.4 Comparison of test and deduced pressure differences The test performance with uniform flow and distorted flow are compared with the performance predicted by the theory in figure 20.5. The prediction is

Inlet flow maldistribution

161

% Design mass flow

Figure 20.5 Test and predicted performance with distorted inlet flow pessimistic and does not give the increased range of mass flow at a constant speed observed on test. Despite these deficiencies the effect on the surge line is at least a first approximation to the experimental results. Distortion parameter More extensive research on the subject was reported by Reid (1969). In particular Reid examined the effect of varying the extent of the flow distortion, and derived the parameter DQo which has proved valuable to define the severity of the flow pattern, however complex it may be. The parameter is determined by the 60° sector of the compressor inlet annulus which has the lowest average total pressure, which is denoted by Pm. The average total pressure of the complete annulus is PAv, and the mean inlet dynamic pressure is P av - Pav. Since the static pressure may vary over the annulus the dynamic pressure is calculated from a knowledge of the total mass flow and the average total pressure, PAv. Thus we can write: Dc« = (P av -

P«o)/(Pav - P av)

This has proved a practical means of defining the severity of an inlet distortion and has been used as a basis for contractual agreement between aeroengine and airframe manufacturers. Care has to be taken if intake suction tests are used to determine a value for Dc«) as these would normally have a uniform static pressure across the inlet/engine interface plane, whereas the compressor or fan can induce a variable static pressure as demonstrated in figure 20.2. This means that the static pressure gradients along the surface of the intake may differ in the

162

Axialflow fans and compressors

two cases and in consequence boundary layer separation may not be the same. The resulting DQo in the engine may therefore be different from that measured on an intake suction rig test. The only totally satisfactory method is to conduct the intake tests with a representative compressor in position when measuring the intake/engine interface conditions. Unfortunately this is not always practical at an early stage in the development programme. The value of DQo which can be tolerated for an acceptable loss of surge pressure ratio tends to increase as the overall pressure ratio increases. This is obvious from the consideration that in the compressors in parallel theory the deficit in pressure has to be restored within the blading. Thus a given deficit of pressure may be impossible to restore in a single stage fan, but could be a minor matter for a multi-stage compressor with a design speed pressure ratio of 10. It is also important that there should be no point within the blading where the static pressure has free circumferential communication, other than inter-blade row gaps which typically do not exceed 25% of blade chords. For example, if an inter­ stage bleed off-take has a manifold close to the annulus and no circumferential partitions, the static pressure may become circumferentially uniform and the pressure deficit has to be restored in only half the total number of stages. This would cause a more serious loss of surge pressure ratio, which could be reduced by placing partitions at a number of points around the manifold so as to prevent free communication of the static pressure. Inlet temperature distortion The compressors in parallel theory can readily be applied to the case of temperature variation over the inlet face of the compressor. For the case where the total pressure is uniform it indicates that equal pressure ratios have to be

Common rpm = 288K N/VT, = 100%

; I Average performance with temperature maldistribution

Inlet mass flow Figure 20.6

—►

Inlet temperature maldistribution

Inlet flaw maldistribution

163

generated by the various sectors of the compressor which are operating at different values of N/VT( as indicated in figure 20.6. Obviously the sector operating with the highest Ti will have the lowest surge pressure ratio, and will be the critical one. If inlet pressure and temperature both vary this can also be assessed by applying the varying pressure ratios at the appropriate nondimensional speeds. It will be apparent that the theory will indicate a variation of outlet temperature even when the inlet temperature is uniform. For a two shaft compressor system this implies a variation of inlet temperature to the second compressor. Whether this will diminish significantly due to mixing will depend on the design of the connecting duct. It is common for such ducts to be relatively short in comparison to their circumference, and also to have between four and eight struts which will prevent complete circumferential mixing.

21 Compressor rig testing

Introduction It is a feature of the gas turbine that the major components can be tested separately. This has major advantages for the compressor as it is inconvenient to assess the full range of the performance characteristics in an engine, e.g. the margin of pressure ratio from the equilibrium running line to the surge line is critical to satisfactory transient operation but difficult to assess at all speeds in an engine. Any rig test, however, is only an approximation to the performance in the engine, albeit often a very close one. The high levels of power required to test compressors at sea level inlet pressure are often not available, and inlet throttling is required to reduce power and therefore the Reynolds number is also reduced. Inlet total pressure may not be uniform over the compressor inlet face on the engine due to intake flow separation caused by cross wind effects during ground running, or aircraft manoeuvres during flight. Intake simulators may have to be used on rig tests to reproduce the appropriate conditions. Blade tip clearances may differ between rig and engine due to differences of temperature and rotational speed. All these and other factors must be accounted for and corrections applied to rig test data before the best possible representation of performance in the engine is obtained. Despite these problems rig testing provides a very useful development tool, and is used by most organisations involved in axial compressor manufacture. Power requirements The power required to drive an axial compressor is given by: W = MCpAT

Compressor rig testing

165

where W is the shaft power, M is the mass flow rate, Cp is the specific heat of air at constant pressure, and AT is the temperature rise across the compressor. For a mass flow of lOOkg/s and a temperature rise of 100°C this gives a power of approximately 10,000kW. Test facilities of this size and greater exist at the major manufacturers plants, but it will be appreciated that there is a considerable incentive to reduce power requirements where possible. Considering the factors concerned, the mass flow can be reduced in two possible ways. If the inlet pressure is reduced by a throttle valve upstream of the compressor the mass flow will be reduced in proportion to the pressure for a constant value of the flow function MVT/P. Thus if the machine has a design speed pressure ratio of 5, the inlet pressure may be reduced to say one third of atmospheric pressure. This will allow pressure ratios from about 3.5 upwards to be tested at the design speed. Allowance has to be made for outlet ducting pressure losses so a pressure ratio of 3 would not be available. The throttle pressure drop would be reduced when testing at lower speeds to allow the lower pressure ratios to be obtained. The power requirement falls rapidly with speed reduction, in fact approximately as speed cubed for constant inlet pressure and temperature. A more extreme method of reducing the mass flow is to manufacture a scale model of the compressor. If this is made to 1/2 linear scale the mass flow will be 1/4 of full scale and the power required will also be 1/4 of full scale. Further power reduction by inlet throttling of the model is possible. Although great care is necessary to produce scale models which are in all respects aerodynamically accurate the use of models for very large components such as high bypass ratio fans has proved satisfactory. Both in throttling and in scaling down, the major aerodynamic parameter of concern is the Reynolds number. Unless the test value is close to the operating value significant corrections will be necessary to account for this effect, as described in Chapter 10. In aero-engine practice the lower Reynolds numbers due to reduced pressure at high altitude are often of most concern. In this case a throttled inlet rig test may give a more appropriate value of Reynolds number than one at sea level atmospheric inlet pressure. Another method of reducing power is to run the rig tests at a lower inlet temperature than appropriate to the normal engine operating value. This occurs naturally if the high pressure component of a two or three shaft engine is tested at atmospheric inlet temperature. For example, if the high pressure component of a three shaft engine has an inlet temperature in the engine at sea level of 500K and is rig tested at 288K the temperature rise will be reduced in the ratio of the inlet temperatures. This is because we have the relationship: AT/T, = (R'HVtir. 1( where Ti is the inlet temperature, R is the pressure ratio, y is the isentropic index, and T} is the polytropic efficiency. Thus if the design pressure ratio of the

166

Axialflow fans and compressors

high pressure compressor is 5, and the efficiency 85%, taking y = 1.4 gives AT/Ti = 0.687. Hence the temperature rise at the design point in the engine would be 0.687*500 = 343.5°C, but on rig test it would be 0.687*288 = 197.9°C. However for a given non dimensional speed parameter N/VT] the quasinondimensional mass flow function mVTj/Pj would be constant and therefore mass flow would rise inversely as VT falls and would reduce in proportion to Pi. These effects can be more readily appreciated if the expression for power is written with non dimensional groups for mass flow and temperature: W = (M'/Ti/P1XCpAT/Ti)Pi/'/T, Hence:

W/(P,VT,) = (MVT,/P,XCp AT/Ti)

The group on the L.H.S. is a quasi-nondimensional and indicates that the power is proportional to the inlet pressure and to the square root of the inlet temperature. Reduced inlet temperature also has the advantage of reducing the required rotational speed. Similar Mach numbers are achieved in the compressor when N/VTi is held constant If an engine has an upper limit to its mechanical speed it may not be possible to simulate altitude performance at sea level temperatures because the altitude value of N/VTj may require the maximum N to be exceeded. Supplying a rig test compressor with cooled inlet air is a means of simulating altitude conditions without overspeeding mechanically. A cold air supply of the necessary size requires a major engineering facility but is conveniently available where a compressor rig test facility is allied to an engine altitude test plant

Variation of specific heat The specific heat at constant pressure ,Cpt is a function of temperature. For air it rises from a value of approximately lkJ/kgK at 200K to l.lkJ/kgK at 800K as shown on figure 18.5. The effect of Cp variation is therefore secondary, but must be taken into account in accurate analysis of performance data. Some research testing has been conducted using the FREON refrigerant gases. The advantage of these is that their low sonic velocity allows high Mach numbers to be developed at low velocities and rotational speeds. Mechanical stresses are thus reduced, which eases design problems and reduces the risk of mechanical failure. On the other hand the gas has to be cooled and recirculated, which leads to a considerable increase of complexity of the test facility.

Power measurement Compressor efficiency can be derived from pressure and temperature measurements alone. While there is no alternative to pressure measurements this is no real problem as these can be made with high accuracy at all levels of

Compressor rig testing

167

pressure. Temperature measurement is more difficult and accuracy of temperature rise assessment becomes progressively less acceptable as the rise falls below 100°C corresponding to pressure ratios less than 2.5 for 288K inlet temperature. For this reason it is desirable to have an alternative means of deriving the temperature rise. From the basic equation for power it is obvious that this can be done if the mass flow and power are measured. Since the mass flow and rotational speed must be measured for their own sake, torque is the necessary additional measurement On small low speed research rigs this is commonly done by mounting the driving motor on trunnion bearings and measuring the torque reaction directly. For larger test facilities this is not practical, and a torque meter is required. One type of torque meter consists of a short length of highly stressed shaft to which an accurate straingauge is attached. The straingauge gives a measure of the torsional deflection of the shaft which is calibrated against torque. Another form of torque meter consists of a calibrated torque shaft with a toothed wheel at one end. The other end carries an outer quill shaft which has another toothed wheel at its free end, adjacent to the first toothed wheel. Torque in the calibrated shaft causes a phase displacement of the teeth in the two wheels. This is measured electronically in modem versions of the instrument but in early types the measurement was made optically. Both these types of torque meter can give an accuracy of ± XU% of full scale deflection. It is desirable to arrange the test facility drive train such that the torque shaft can be easily replaced. A number of torque shafts suitable for a range of maximum torques should be provided so that the most suitable can be used for each test

Power sources Three types of power source are conventionally used for compressor rig test facilities - electric motor, steam turbine, or gas turbine. Electric drive is commonly used for powers below lOOOkW and has been used up to 4000kW. Above this size special supply arrangements may be necessary which are unlikely to be economic for the relatively low utilisation of the facility, which is unlikely to exceed some hundreds of running hours per year. Steam turbines provide a very suitable type of drive provided a steam supply is readily available. If boilers have to be fired specially for the test facility the low utilisation may be further reduced by the time necessary to raise steam. A gas turbine is a convenient form of drive in that start up is only a matter of a few minutes and no large scale associated equipment such as boilers is required. They are available in a suitable range of sizes. Rolls Royce first installed a gas turbine powered test facility in 1951 and chose a similar source for a much larger new plant in 1980. It is not uncommon for compressor test facilities to be part of a group of facilities providing test arrangements for combustors, turbines, and engine altitude testing. These facilities require large air supplies and it can be convenient to use the compressed air supply through a turbine to drive a

168

Axialflow fans and compressors

compressor test facility. The air supply may be heated in a combustor to increase the turbine power if desired. Facility layout

Inlet arrangements The general arrangement of a typical test facility is shown diagrammatically in figure 21.1. Atmospheric air is drawn in through filters to a plenum. The filter banks should be arranged symmetrically to the downstream flow in order to avoid creating whirling flow in the ducting. A well flared bellmouth takes the flow smoothly from the plenum to the intake ducting system. Suitable dimensions for the flare are shown in figure 21.2. These are important as the mass flow measurement is made a short way downstream of the throat of the flare. A well proportioned flare will give a thin boundary layer at the measurement station and a discharge coefficient in excess 0.99. The exact value of the discharge coefficient can be determined by pitot tube traverses across the boundary layer.

Mass flow measurement The mass flow is measured by the mean of a number of static taps on the duct wall as indicated in figure 21.2. The pressure drop across the filters or the absolute pressure in the plenum must also be measured. Alternatively a fixed pitot tube Beading outside the duct boundary layer will give the same result. Inlet throttl

Return bleed

/ distributor

J .—

'Airmeter 1Air filter

/

__ .__ .

r~ \

Bleed control throttle Metering

— Outlet throttle

/ “f

/unit

Smoothing screens

1!

_

/Torquemeter

\ .

.

\ Outlet plenum

box

““

orifice

Figure 21.1

Test facility arrangement

The size of the airmeter measuring plane should be chosen so that the Mach number does not exceed 0.4. This results in a maximum static depression of 1500 mm water gauge (110 mm of mercury or 15 kPa). The lower limit of the

Compressor rig testing

169

measuring depression is dependent on the accuracy of the measuring system but should be such as to maintain an accuracy of at least

Figure 21.2

Airmeter flare dimensions Adaptedfrom Rolls Royce internal report

Downstream of the airmeter the duct is of increasing diameter to suit the inlet throttle valve. The length from the flow measuring plane to the throttle must be sufficient to prevent any upstream influence on the flow in the measuring plane whatever the throttle setting. A length equal to at least three diameters of the measuring plane should be provided.

The inlet throttle The throttle may take a number of forms two of which are illustrated in figure 21.3. Note that these are such as to avoid creating whirl in the downstream duct or to deflect the flow to one side of the duct as would a butterfly type throttle. The throttle would normally be driven by electric motor, except for very small facilities where it may be hand operated.

The inlet plenum It is necessary to allow the flow to settle downstream of the throttle, and for this purpose the ducting is further enlarged downstream to give a mass average velocity in the region of 15m/s. A number of baffle plates are fitted in the large diameter pipe and possibly a honeycomb straightener if there is a possibility of whirl being present At design speed the axial velocity at entry to the compressor blading will be in the range 100 to 200m/s so there will be a large acceleration from the inlet pipe to the blading. This will help to maintain a uniform total pressure across the inlet face of the compressor for normal testing. If testing with non-uniform inlet total pressure is required provision should be made to fit distortion producing screens some way ahead of the blading but after most of the acceleration has taken place. If placed where the velocity is too low the screens

170

Axialflow fans and compressors

will not be effective. Inlet total pressure and temperature must be measured ahead of the blading. In the absence of distortion screens the inlet ducting arrangements described should provide a sufficiently uniform total pressure such that only 3 or 4 total pressure probes are necessary. With distortion screens an extensive array of probes is required. Alternatively an area traverse may be

Jen \

\ /

- r r r r r t :

4

* i± i,

*:

Multi vane type

Figure 21.3

Two types of inlet throttle

made, but this is inconvenient and time consuming for routine testing.

Inlet temperature Total temperature is normally constant from atmosphere to the compressor inlet face. Where this is the case thermometers are often placed in the plenum behind the filters, which has the advantage of being a region of very low velocity. In some test arrangements it is necessary to return some compressor bleed flows to the inlet pipe. These add heat to the inlet flow, therefore the compressor inlet temperature must be measured downstream of the bleed flow re-injection point. It is important that the bleed flow should be completely mixed with the main inlet flow before the temperature measuring plane, and to ensure this a distributor pipe as indicated in figure 21.4 can be used. Apart from measurement problems, a non-uniform inlet temperature will adversely influence the compressor performance similarly to a non-uniform total pressure.

Compressor rig testing

171

Outlet measurements At the compressor outlet the essential measurements are again total pressure and temperature. The total pressure generally has significant radial variation, usually being highest near the blade mid-height. The total temperature on the other hand tends to be highest near the blade ends. Radial rakes of 5 or 6 limbs are therefore desirable to obtain a reasonably representative average value for both pressure and temperature. About 5 rakes spaced circumferentially around the annulus insure against any lack of axisymmetric flow and allow a good overall average from the 25 or 30 readings for each parameter. Area averages of the measurements are commonly used but mass or momentum averages are preferred by some engineers. The differences are generally small but can be significant for single stage fans where the dynamic pressures are a high proportion of the overall pressure rise. An alternative and very simple means of obtaining the outlet total pressure is to have a short duct of constant annulus dimensions behind the blading. This should preferably be at least two annulus heights in length with five static taps circumferentially spaced on each of the annulus walls half way along its length. The total pressure is calculated from the average of the static pressures as described in Chapter 11.

Discharge arrangements Downstream of the outlet measuring plane it may be desirable to reproduce the flow path of the intended installation e.g. the diffuser and combustion chamber head in the case of a gas turbine. This is desirable in so far as these features may influence the flow upstream in the final blade rows of the compressor. Beyond this it is usual to discharge the flow into an outlet plenum and from there through one or more throttle valves to atmosphere. A silencing muffler may be fitted to the final discharge pipe, if required for environmental reasons. The positioning of the outlet throttles relative to the compressor can influence the frequency of the surge cycle and the ease of recovery from surge. If the throttles are fitted at the exit of a large outlet plenum the surge cycle frequency will be low. As the plenum volume is reduced the frequency increases and at some limiting plenum size the compressor may appear to stabilise in a deep stall condition. This can be a dangerous condition where large amounts of energy are absorbed by recirculation of air within the blade rows of the compressor, leading to large and rapid increases of temperature which have been known to melt even steel blading. Test procedure It is convenient to conduct the testing at predetermined values of the nondimensional speed parameter NWT|. Having brought the compressor close to the

172

Axialflow fans and compressors

required speed, it is necessary to measure the inlet temperature and calculate the exact rpm for the chosen value of N/VlV It is usual to carry out the acceleration with the throttles set to operate well clear of surge. A preliminary calculation of the required inlet pressure versus speed to keep within the power available should be made, and the inlet throttles adjusted to follow this pressure/speed relationship as the plant is slowly accelerated. The permissible inlet pressure should make allowance for the increase of power towards surge, since it is generally more convenient to conduct each constant speed curve at a constant inlet pressure. If bleed valves or variable stagger stators are fitted it is necessary to specify a schedule for their settings against speed. For a new design on initial test these may have to be decided on past experience of similar compressors, or possibly on the output of performance predictions where these are available. For subsequent development tests the analysis of the initial performance will provide further guidance for the bleed valve and blade settings. The outlet throttles are set simultaneously during the acceleration to follow a pressure ratio v speed relationship estimated to be well clear of surge. If necessary this pressure ratio v speed relationship should also be set so as to be greater than may encounter any choked flutter vibration of the blading. In running each constant speed curve it is best to start at the lowest pressure ratio required and take a full set of measurements. The outlet throttles are then closed to take the pressure ratio to surge. Again a previous estimate of the probable surge conditions should be made. The outlet throttles should be closed more slowly as the expected surge point is approached. Surge may be detected audibly, but microphones may be necessary in the test cell if the control room is remote or well sound proofed. A sensitive test for surge is the oscillation of a manometer or pressure gauge attached to an outlet pressure tapping or to an airmeter pressure tapping. A snap measurement of both of these pressures is desirable to locate the surge pressure ratio and mass flow. At high speeds the pressure ratio measurement is often the more important as the mass flow variation may be small. At low speeds the mass flow measurement may be the more important as the curve of pressure ratio against mass flow often tends to be relatively flat towards surge. Having located the surge point, suitable intervals of pressure ratio or mass flow can be determined for making full sets of measurements, including a set as close as possible to the surge point. The outlet throttles will have been opened as rapidly as possible after locating the surge point, and it is convenient to commence with the lowest pressure ratio required. At least six points are desirable to define the characteristic fully. It is necessary to allow time at each point for temperatures to stabilise. There is no particular order in which the different speed curves must be run, but it may be convenient to run them in either ascending or descending order. If there are known or suspected regions where dangerous blade vibration may occur these may be left until last. On the other hand, if strain gauges are fitted to some blades, it may be best to carry out a survey for areas of high stress initially,

Compressor rig testing

173

as the gauges may be prone to failure after prolonged running, particularly if the compressor is surged frequently. Regions of high stress may then be avoided for extensive running during the full performance calibration. The number of speed curves required to fully define the performance will vary depending on the particular requirements of the test, and the application of the compressor. Typically curves may be run at intervals of 10% of the design speed from 30% to 80% and then 5% intervals to 110% if this is mechanically safe.

Measurements and analysis Manual recording of manometers, thermocouples and other gauges has given way over the last several decades to automatic data recording using scani-valves, transducers etc. linked to a digital computer which is programmed to record and analyse the data to give any desired output. This has introduced the possibility of recording and analysing much more data than was practical previously. For example with manual recording it took a skilled team of five or six testers about one hour to run one speed curve. Using a slide rule and tables or graphs it took one engineer about the same time to analyse the measured data and plot the overall performance curves for one speed. The analysis of interstage static pressures to obtain individual stage characteristics took much longer, typically two or three man weeks depending on the number of stages and the number of test speeds analysed, with the result that these characteristics were not analysed for all tests. With automatic data recording and computerised analysis this situation has been revolutionised, and where it is justified the analysed performance can be available in real time. The same is true for detailed traverse measurements where the traverse probe is computer controlled to move from one position to another, recording and plotting the measurements of total and static pressure and airflow angle automatically. Further information on compressor testing is to be found in Dimmock (1961) and the ASME power test codes for compressors and exhausters.

22 Stage performance prediction

Introduction Many methods are available for the prediction of stage performance on a two dimensional basis. They all depend on two basic requirements; the first is a knowledge of the variation of the air outlet angle as a function of the inlet angle, and the second is the variation of the losses or efficiency, again as a function of the inlet angle. The first requirement determines the work characteristic, while the second gives the pressure rise. The method described by Howell (1945) is typical of the application of correlated cascade data to produce stage performance predictions. By introducing secondary losses and a work factor, the data was corrected to give an approximation to three dimensional stage performance, based on the mid-span blade geometry for moderate to high diameter ratios. For low diameter ratios (less than, say, 0.6) Howell’s method can be used for the various radial blade sections as described in Chapter 15. A preferred method Another method, also originally described by Howell and Bonham (1951), has been modified by the author to produce a very simple and direct method for the prediction of stage performance in terms of work, pressure rise and flow coefficients.. The optimum (maximum efficiency) air angles are determined for rotor and stator by the methods of McKenzie (1980) as summarised in Chapter 4. The outlet angle of the preceding stator is also determined. The vector diagram quantities for the maximum efficiency conditions are thus known and the work and flow coefficients can be calculated. If the optimum angles for rotor and stator are not consistent with a common flow coefficient an average value should be used. If they are far from consistency it indicates some radical mismatch in the design, and the performance prediction is unlikely to be valid. A difference

Stage performance prediction

175

of 5% in the optimum flow coefficients is the maximum to be tolerated. The rotor and stator optimum flow coefficients are given by the relationships: For the rotor

Va/U = l/(tanao + tanaO

and for the stator

VaAJ = l/{ tan a 2 + tan a 3}

where cto is the outlet angle of the preceding stator, i)1'2 For a known inlet temperature the temperature rise can now be found. At the match point all stages can be assumed to operate at their optimum efficiencies.

Axialflow fans and compressors

186

The optimum value of AH/U2 is therefore calculated for the mid span of each stage from the blade geometry. These are expressed as values of AT/N2 and summed to give the value of overall AT/N2 . Since a value for overall AT has already been obtained, a value for N* the speed at the match point, can be derived. For most aero engine type compressors the match point speed lies between 90% and 95% of the design speed. This results from the tendency to place the front stages on the choke side of maximum efficiency at the design point in order to improve the low speed surge line shape, and also from designers choosing to operate at above critical Mach numbers on early stages. For industrial compressors the situation could be different and the designer may seek to design at the match point to maximise the efficiency. Having determined an approximate value for the match speed and temperature rise the inlet and outlet velocities are calculable. This allows the axial Mach number at both inlet and outlet to be determined and the ratio of stagnation densities across the compressor to be calculated. A second approximation to the temperature rise can then be obtained, and this also requires a better approximation to the optimum efficiency. This is obtained by applying the methods described in Chapter 22 to each stage. Individual stage pressure ratios are obtained using the stage temperature ratio and the optimum efficiency with the appropriate value for the ratio of specific heats. The overall pressure ratio and temperature ratio give the optimum value of efficiency assuming a mean value for the ratio of specific heats.

Constant speed characteristics All the necessary values for the match point and the work characteristic gradient are now known. A number of speeds are selected such as 1.2, 1.1, 1.0, 0.9, 0.8 etc. times the match speed, to as low a value as desired. Intermediate speeds at 1.15, 1.05, etc. may be desirable in the upper speed range. The procedure has been applied successfully to very low speeds such as 0.2 times the match speed, which are not always suitable to test without special instrumentation, but are useful for engine start-up studies. For each constant speed curve: a v r ,) ' = i + (a t /n 2x n / Vt ,)2 A first approximation assumes po/pi = (Tq/Ti) which is equivalent to assuming T| = 86% approximately.

Hence :

(Vaj/Van)* = (Tn/Ti)*2(An/AO (Vai/VanXd = (VaI/Van)’/(VaI/Van)** = /(Vai/Van)rei

from figure 23.2

Overall performance prediction and

187

71* = tT ( ti7 0 R = (T n /T |)* p

where (3 = x\V(Y-1)

(Va/Van) = R ( T |/T n X A n /A |) (Vai/Van)«i = (Va^VaD)V(Va^VaD)“

Hence another value of tTAi ~ is read from figure 23.2. If this differs from the previous value by more than 0.5% further iterations should be made until agreement is obtained. At each speed a series of arbitrary values of Mret are chosen. Values from 0.7 to 1.2 usually cover the required range, and intervals of either 0.1 or 0.05 are satisfactory depending on the detail of characteristic definition required. For each value of $Mni the calculation proceeds as follows: 4'ld = l+ ta n © 0. ( l -,**)

Hence CP/M)iei is evaluated, and iyr|* is obtained from figure 23.3 and so r\ is derived from: = oi/n V AT/N2 = MVKAT/N5)’ Th/Ti = 1 + (AT/N2XN/n/T,)2 r

1st Approximation :

= a v r i ) 'n'(’M)

Vaj /Van = R(Ti / T nXAn/A|)

(Va,/Va„ )W/N = Mrd{(Va,.VaII)'/3/N |‘ Va,/N = {(Val.Van),n /N)(Va^Va0)l/1 V a^Ti = (Va^N)(N/VT,) MVTj/A|P| = /(Va^/TD MVTB/Ab Po = 1(MVTi/A|P, )IK)(TiJT{)mAJAa Va0 /VTn = /(MVTd/Aq Pn ) 2nd. approximation: Vai/Va„ = {(Va^/T,)/(Va0/VTn))(T1/TB)1'2

188

Axialflow fans and compressors Vai/VT, = ((VaiVaB)l/I/N)(Vai/Vao)in(N/VT|) MVTi/A, P, =/(Vai/VT|)

MViyP, = Ai(MVT^A|Pi) Hu = (RT"l'1r- D/AT/T, When the values of Vai/Vag for a constant speed curve are examined it is found that they give a maximum value at a greater mass flow than corresponds to maximum pressure ratio. This is markedly so at high speeds, but maximum pressure ratio and maximum velocity ratio tend to converge as speed is reduced. Maximum velocity ratio corresponds to maximum density ratio and as discussed in Chapter 17 this is an indication of surge. High speed corrections At the upper end of the speed range the predicted constant speed characteristics may give a maximum mass flow, the flow reducing at lower pressure ratios as indicated in figure 23.4. This indicates choking in the final stage, and the real characteristic is taken as having the maximum flow constant as pressure ratio is further reduced. The temperature rise is also taken as constant as pressure ratio falls below the value corresponding to maximum flow, (figure 23.5) and efficiency values can be calculated from this temperature rise and arbitrary pressure ratios. The explanation for this is that when the rear stage chokes further reduction of the overall pressure ratio is due only to increasing losses in the outlet stator, and the operation of the compressor proper, in front of the choked plane, is unaffected by downstream changes such as opening of the outlet throttle. A further correction is necessary to adjust for choking of the front stage at high speeds. From a knowledge of the first rotor throat width at its mid span the relative inlet Mach number and inlet flow angle to just choke the rotor passage can be calculated and hence an estimate of the choking mass flow for each speed can be made. Where this mass flow is less than given by the procedure of the preceding paragraph it is accepted as the predicted value. As indicated on figure 23.4 the pressure ratio v mass flow curve is blended into the basic predicted curve if the latter falls to less than the choking flow before reaching surge. Otherwise the characteristic is completely vertical and surge is determined by the maximum velocity ratio Vai/Van in the same way as previously discussed. The efficiency values on the choked part of the characteristic are obtained from the assumption that the temperature ratio Tq/Ti will be the same as for the non-inlet choked characteristic at the same value of the outlet flow function.

Overall performance prediction

189

m V T b /P b = (M /V T i/P ,X P i/P n X T n A 'i)1/l = ( M V T ^ > [)d .(P i/P n )d ,(T 0/ T I) ' /3

Hence: (Pn/Pi)d, = ((MVTyPO/CMVTi/POd,)(Pn/Pi)

It is apparent from this relationship that the line joining corresponding points on the original and choked pressure ratio characteristics is a straight line through the origin; Pq/Pi = 0; MVTj/Pi = 0. The efficiency at a choked pressure ratio can now be calculated from he choked pressure ratio and the unchanged temperature ratio.

260

90

240

80

c Si

£ 220

70

2

60

|

200

cUi

50

3 180

40

I 160

30

20

140 2

2.5

3

3.5

4

4.5

Pressure ratio

Figure 23.4

Choke corrections to mass flow and efficiency

Pressure ratio

Figure 23.5

Choke corrections to temperature ratio

190

Axialflow fans and compressors

Test comparison with prediction The predicted and test characteristics of a six stage compressor are shown on figures 23.5 and 23.6. This is the same compressor as used to demonstrate the linear relationship between 4/ibj and Mni in figure 23.1. At the higher speeds it is clear that the maximum pressure ratio occurs at a significantly lower flow than maximum density ratio and the latter is the closer prediction of surge.

% Design (low

Figure 23.6

Predicted and test pressure ratio characteristics

70 r

30

>

»

40

>

i

50

t

i

>

60

i

70

»

i

*

80

% Design flow

Figure 23.7

Predicted and test efficiencies

i— i

90

i

100

»— i

110

24 Performance with altered gas properties

Introduction To this point air has been assumed as the working gas, however, it is necessary to consider the effect of the variation of the properties of air on the design and operation of compressors, and also, for industrial compressors, the use of gases other than air. Air has a fixed gas constant of 287 J/kgK but the specific heat at constant pressure increases with temperature. When designing at specified conditions the appropriate values of Cp and y (= Cp/Cv) can be chosen, and varied from stage to stage through the machine as necessary. However, an aero engine compressor might be designed for a subsonic aircraft speed at high altitude using an inlet total temperature of 250K, but could be operated supersonically at low altitude with an inlet total temperature of 430K. The corresponding value of Cp at the compressor inlet would increase by a little less than 1.5% in the latter case, and this would have some small but measurable effect on the performance. For the high pressure compressor of a three shaft turbofan the mean value of Cp at altitude cruise conditions might be 1076 J/kgK. At sea level take off this value would change by less than 0.2%. However, if this compressor is rig tested with normal room temperature at inlet, then the mean Cp for the temperature range of the compression would fall to 1012 J/kgK, i.e. a drop of almost 6%, which should certainly be accounted for in test analysis. Clearly, for an industrial compressor operating with entirely different gases the change of Cp could be much greater and there will also be a change of the gas constant It is obviously desirable to be able to estimate the performance of a compressor operating with a gas of different properties to the one for which it was designed, or with which it was tested. This chapter gives an outline of methods by which approximate corrections can be made and indicates some of the problems involved in the compression of different gases.

192

Axialflow fans and compressors

The significance of density ratio Moyes (1956) investigated the case of a change of specific heat of air. He assumed that the polytropic efficiency of the compressor would be the same when it was operated so that the incidence to all blade rows was the same with both values of Cp This requires that the flow coefficient onto each stage remains the same when the gas properties change. The continuity equation then shows that the density ratio will be the same with the two sets of properties: M =piA|Vaj = p2A2Va2 P2/P 1= (A.yA.XVaj/Vas) = Constant * (Va,/U,)/(Va2/U2) This implies that if a set of performance characteristics are plotted in the form of density ratio and polytropic efficiency against first stage flow coefficient they will apply whatever the gas properties. This leaves the question of the equivalent rotational speeds for the two gases and this requires that Mach numbers should 4 r

100*

Efficiency

80

60 2

Ui

-

0.3

0.4

0.5

0.6

Flow coeff. Va, / U

Figure 24.

Performance plot suitable for any gas

also be the same. This is not possible throughout the compressor because the Mach number will fall at a different rate through the stages due to the different temperature rises required for the same density ratio. Since the first stage Mach number is the greatest, and therefore the most critical, the closest approximation to the performance with another gas will be obtained when the first stage Mach numbers are the same. This will be achieved by running at the same values of N/V(tG0 or U/V(*yGt), where U is the first stage tip speed, if the compressor is scaled. The static temperature is necessary in this parameter for strict equality of the Mach numbers as the ratio T/t for the same Mach number will differ for gases with different values of Y- For characteristics run at constant values of UhlT the value of t will vary somewhat over the mass flow range. The value at

Performance with altered gas properties

193

the maximum efficiency flow will be suitable to define the whole characteristic with acceptable accuracy. Gases other than air When gases other than air are considered the change of molecular weight, and therefore of gas constant as well as specific heat have to be taken into consideration. Table 24.1 illustrates the property variations for a number of common gases. Table 24.1 Properties of common gases Gas Air Argon CO2 Helium Hydrogen Methane Freon 11

MW 28.97 39.94 44.01 4.00 2.02 16.04 137.4

G 287 208 189 2079 4116 518 60.5

1005 518 652 5277 14155 2368 666

y 1.4

1.67 1.29 1.66 1.41 1.28 1.1

a 340 316 275 994 1293 436 138

a/a* 1.0 0.93 0.81 2.92 3.8 1.28 0.41

M.W. is the molecular weight G is the gas constant in J/kg K Cp is the specific heat at constant pressure in J/kg K at a temperature of 288 K y is the ratio of specific heats = Cp/Cv at 288 K a is the speed of sound at 288 K static temperature. Note that in all cases G*(MW) = 8314 J/kg mole K which is the universal gas constant

Saturated gases When operating near to saturation, as in steam and refrigeration plant, gases tend to depart significantly from the perfect gas law. In these circumstances the constants given in the table, other than the molecular weight vary considerably and it is necessary to use a Mollier diagram to determine the changes of state. A series of these diagrams are given by Gresh (1991) for the gases most commonly used in industrial processes.

The speed of sound According to the kinetic theory of gases the value of y is 1.67 for a monatomic gas, e.g. helium, and 1.4 for a diatomic gas, e.g. oxygen and nitrogen. For

194

Axialflow fans and compressors

polyatomic gases such as carbon dioxide, methane, and Freon 11 the value of y is lower, as shown in the table. The speed of sound, a, is given by: a « VCjfGt) Since y varies only from 1.1 to 1.67 it has less influence on the sonic velocity than the gas constant or molecular weight, which varies by a ratio of 68:1 for the gases listed. Thus the speed of sound in hydrogen is more than 9 times what it is in Freon 11. It can be shown that the pressure ratio achieved by a stage of given blading is a function of the efficiency, the Mach number and the value of y and Cp or the gas constant. Thus very high blade speeds and gas velocities are required to produce the same pressure ratio with hydrogen compared to air. On the other hand quite low blade speeds and gas velocities can produce the same pressure ratio and Mach number with Freon 11. Advantage has been taken of this to allow high Mach number research units to be run at modest speeds and stresses by using Freon instead of air. Compression of helium The effect of using helium instead of air in a conventional stage illustrates the problems which arise. Assume a stage designed for air to run at a blade speed of 300 m/s with a flow coefficient Va/U = 0.6 and a work coefficient AH/U2 = 0.4 and inlet whirl angle of 20°, at 288 K inlet total temperature. The temperature rise across the stage would be 35.8°C and the total pressure ratio 1.45 for a polytropic efficiency of 90%. The relative Mach number at inlet to the rotor is 0.9. If the stage is run at the same blade speed using helium the temperature rise is only 6.82°C and the pressure ratio 1.055. The Mach number relative to the rotor at inlet is only 0.3. While the stage efficiency might be somewhat higher at this greatly reduced Mach number, further stages would be grossly mismatched unless the annulus areas were suitably modified. If, on the other hand, the stage were to be run with helium at the same Mach number as for air the blade speed would require to be 860 m/s. This would be impractical on account of the extreme mechanical stresses, but would produce a pressure ratio of 1.5 compared with the ratio of 1.45 for air at the same Mach number. Looked at the other way round, if a compressor were designed to use helium it would be possible to obtain useful test data by running with air at a suitably reduced blade speed. The problem encountered when designing for a gas such as helium is that for mechanically viable blade speeds the pressure ratio obtainable per stage is low relative to that obtainable with air and other gases of greater molecular weight. This has lead to experiments on designs featuring high values of AH/U2 and tandem rotor blades such as in figure 24.2. Bammert and Staude (1979) have shown successful results from a compressor having three stages of tandem rotors

Performance with altered gas properties

195

Tni]’"0 outk Leading rotor, outlet ,

Figure 2AJ2

Section of two row rotor and vector diagram Adaptedfrom Bammert and Staude (1979) with permission ofASME with an inlet and outlet stage having conventional rotors. The basic vector diagram was for 100% reaction and AH/U2 = 1.0 and Va/U = 0.75 approximately. The combined tandem rotors had a very low overall aspect ratio, and it would be interesting to know whether single rotors of the same aspect ratio would produce as good a performance. Viscosity and Reynolds number Another parameter which may affect the performance with different gases is the Reynolds number. A table of kinematic viscosities for industrial gases is given by Gresh and this shows air to have almost the highest value, while hydrogen is one of the lowest with a value about half that for air. This means that the Reynolds number will be two times greater in hydrogen for a blade of given dimensions operating at the same velocity as in air.

25 Design for a domestic ventilator i i

Specification A domestic ventilator fan, suitable for a typical kitchen, requires a volume flow of 0.2 m3/s. This would provide for about fifteen changes of air per hour in a large domestic kitchen. The pressure difference from the room to the outside would be negligible, and an acceptable velocity through the fan blade annulus is 10 m/s. The driving motor will be in the fan hub, and the discharge will be directly from the annulus without any diffusion. The inner annulus diameter must be large enough to accommodate the motor. Overall parameters The inlet total pressure, Pi, and the outlet static pressure, p2, will both be equal to the atmospheric pressure, hence the total pressure rise will be: AP = P j-P ,= p j + '/2pV2-P, But P2 = Pi and so:

AP = V: pVa2/cos2a

where P2 is the outlet total pressure, V is the outlet velocity, Va is the axial velocity and a is the swirl angle of the exit flow. It is assumed that no outlet guide vanes are required and the mean value of a is not more than 15°. AP = 0.5* 1.225* 102/cos215° = 65.65 Pa The work input per unit mass flow is given by: AH = AP/pr] = 69 rrf/s2

Design for a domestic ventilator

197

A modest value of 80% is assumed for the blading efficiency to allow for losses associated with motor support struts, relatively large tip clearance, low Reynolds number and discharge losses. The volume flow, Q = AVa, and hence the power requirement will be: W = MAH = QpAH = QAP/n = 0.1*65.65/0.8 = 8.2 watts At this minimal level of power the motor and fan efficiency are obviously of little concern and an induction motor would probably be of sufficiently excess power to run close to its synchronous speed which may be chosen as 3000 rpm. Blade speed and dimensions Referring to figure 3.9 the constant radial value of AH/Va2 is 0.67, and in order to avoid excessive outlet whirl angles which would make a row of outlet guide vanes desirable, a hub value of Va/U of 0.6 is indicated as a maximum. The hub blade speed is therefore: Uhub = Va/(Va/U) = 10/0.6 = 16.7 m/s For the selected rpm of 3000 we have: Uhub = 3000nd/60 =157d = 16.7 m/s Hence the hub diameter,

d = 16.7/157 = 0.106 m

and the annulus areaA = Q/Va = 0.2/10= 0.02 m2 = ji(D2 - d2)/4 Hence the tip diameter,

D = 0.192 m

and the diameter ratio,d/D = 0.106/0.192 = 0.552 These appear suitable dimensions which will accommodate the motor within the hub diameter and also result in a suitable hub to tip diameter ratio. A value much less than 0.5 for the diameter ratio could result in difficulties in blade twist and radial matching of the design parameters. A diameter ratio greater than, say, 0.7 would lead to an excessive overall diameter and an unnecessary loss of efficiency due to additional annulus surface area and a greater ratio of tip clearance to blade height for the same radial clearance.

198

Axialflow fans and compressors

Blade selection The rotor inlet and outlet angles for hub, mean and tip diameters are calculated in table 25.1. Table 25.1 Diam.mm Um/s Va/U 0tj0 AH/UVa a 2° tanOa c°

106 16.7 0.6 59 0.402 51.7 1.465 52.7

149 23.5 0.427 66.9 0.286 64.1 2.202 64.0

192 30.2 0.331 71.7 0.222 70.34 2.91 70.1