C.P. No. 943

MINISTRY OF TECHNOLOGY

AERONAUTICAL RESEARCH COUNCIL L,eRAR,

CURREN J PAPERS ROYAL AIRCRAFT ESTARLl’3.4~“~‘~

BEDFORD.

A Theoretical Investigation of the

Effect of Aspect Ratio on

Axial Flow Compressor Performance

BY

J. H. Hor/ock and G J. Fohmi

LONDON: HER MAJESTY’S STATIONERY OFFICE

1967

SIX SHILLINGS NET

C.P, N0.943~

Mw, 1966

A Theoretical Investigation of the Effeot of Aspeot Ratio on Axial Flow Compressor Performance

-By- J. H. Horlock and G. J. Fahmi

su?dJAARY

The performance of axial flow compressors is known to be affeoted by the ohoice of aspeot ratio (the ratio of blade height to axial ohord length). An analysis of the inviscid, inoompressible flow in axial oompressors of different aspeot ratios is given in this paper. The main analysis is based on actuator diso theory, but a oomparison is made between oaloulations based on this theory and the more recently developed streamline ourvature analysis. This oomparison shows close agreement between the oaloulations based on the two theories.

List of contents

1. Introduction

2. Analysis 2.1 General 2.2 The design problem 2.3 The off-design problem

2.3.1 The single-stage aompressor 2.3.1.1 High hub tip ratio (0.750) 2.3.1.2 LOW hub tip ratio (0.555) /

2.3.2 The two-stage oompressor (high hub/M ratio) 2.3.3 The multi-stage oompressor (high hub tip ratio) P

2.4 Numerioal solutions

3. Presentation and Disoussion of Results 3.1 Aspeot ratio effeots for stages of hub/tip ratio 0.750 3.2 Detailed study of single-stage performance

4. conolusions

Notation

References

Appendices

I./ __________________--------------------------

*Replaces A.R.C.28 187.

-2-

1. Introduotion

The performance of single-stage and multi-stage axial flow cnmpreasors has been observed to be adversely affected by an increase of aspect ratio (blade length to half stage length). This deterioration in perfarmanoe appears to be related to a reduotion in the operating range of individual blade rows which results in a lmer surge pressure ratio in multi-stage oompressors.

Suoh differences in performance of compressors with different aspect ratios have been known to exist for some time, but the published literature on this subject is limited. Some experiments which show the effect of aspeot ratio in two-d.imensicnal oasoade tests have been reported1#2, but these tests have mainly been carried out at design point incidence and have not been extended Into the stall region. Most of the multi-stage compressor tests on the effeot of aspeot ratio have been obtained by aircraft' engine companies and have not been published.

Several suggestions have been made to explain this "aspect ratio" effeot - differences in the three-dimensional axisymmetrio flow, variaticms in the.seoondary and tip clearance flows, the differing perfcrmance of the blade rows acting as diffusers of different aspect ratios. It has even been suggested that the effect is a simple Reynolds number one, since compressor tests with low aspect ratio are usually made at the same blade speed and blade height, but larger chord. However it appears that differences in performance exist even when the Reynolds number is ,maintained oonstant as the aspect ratio is changed. No firm conolusion on the dominant effect has yet been drawn.

In this paper an attempt is made to investigate the first of the effeots listed above - the ohange in the three-almensional axlsymmetrio flaws with variation of aspeot ratio, using aotuatar-diso theory. In the course of the investigation, oaloulations based on aotuator-diso thecry have been oompared with oaloulations based on "streamline, curvature" analysis, first suggested by Smith, Traugott and Wislioenus4 and developed by the research establishments and the engine ccmpanies (L. H. Smith, General Electric, W. Stubner, Pratt and Whitney, J. Ringrose, R. Hetherington, Rolls Royce Ltd.).

National Gas Turbine Establishment, A programme developed at Rolls Royce by

Hetherington and Silveater was used in the oomparison given in this paper.

Three different examples were calculated - a single-stage compressor (high and low hub/tip ratio), a two-stage ocmpresscr and a multi-stage compressor (both with high hub/tip ratio). The aspect ratio was varied in each of these three examples, but the blade design (of the "exponential" type) was similar.

2. Analysis

2.1 General - The aotuatar-disc analysis Is developed here for single-, two- and multi-stage ocanpressors, excluding all loases due to annulus wall boundary layers ana associated. seocnaary flows. The problem is reduced to one of three-dimensions1 adsymmetric, incompressible, inviscid flow. The limitations of this approach are recognised, but alnoe it is knmn that "aspeot-ratio" effeots oocur in compressors in which there are relatively small ohanges in annulus area, it is oasidered that the present simplified approach, of studying the three-dimensional axdsymmetrio effects alone in an annulus with oylindrioal walls, is justifies.

solution/

-3-

s0kn0n 0f the fh7 Oquati~s, at and off design, involves setting up differential equaticas for the axial velocity that would exist far downstream of each blade row,,? radial equilibrium were attained. Essentially, the tangential vorticity, the radlel gradient of this "infinity" velocity distribution, is obtained.

The differential equation is obta3ned from the Brag@awthorne expression

5 = J-(qr + z) . , . ..(I)

If it is supposed that radial displacements are small, that the flcm deviates but little frcrm a free vortex and that the gradients in stagnation pressure are also small then the tangential vorticity remains unohanged at a given radius downstream of the ith disc (see Ref. 5). Hence

where Ci, ie, i refer to 1ocatioPls immediately downstream of the &LSO, at the trailing edge, and at the imaginary "far downstream" looation respeotively.

The tangential velocity is aontrolled at the trailing edge and also remains unohanged at a given radius between the discs 5 .

For the design problem Ce is speoified, and In this case for "exponential" blading,

b

%ie = a + i d-stream of rotor

b

‘e(i+i)e = a- ; downstream of statar

. . where a and b are oonstants.

. ..(3)

For the off-design case, oie and p(i+l)e are specified so that

%ie a ’ - 'tietan pie downstream of rotas

. ..(4)

%(i+l)e = 'x(i+l)etan '(i+l)e downstream of stator.

In the solution of both design and off-design problems, the BrageHawthorne equation (1) is linearised by writing d+ = Cxir dr.

SubstiMid

-4-

Substitution Of (2) and (3) or (2) and (4) into (I) then gives the differential equation for Cd,

%i %i -g-- +

%ie a(%*) *oie i -. r ar dr

2.2 The design problem

For the design problem, in which there are no gradients M stagnation enthalpy, equal work being done at all radii, the equation for axial velocity becomes

The "Infinity" axial velocities are then obtained analytioally (see Ref. 6) and the trailing-edge velocity distributicm fron interferenoe equations of the form

C xie = % - (

cti -2cxie, >y; + ( %+I; %A),“;

. ..(5)

. ..(6)

. ..(7)

allowing for interference effects frw adjacent aiscs only. (It is shown in Ref. 7 that if the first root only of the actuator disc equations for the perturbation in axial velocity is being taken, then it is justifiable to consider interference effects fran adjacent rows only.)

The design angles are then deduoed from

b a-- R tan (I i -

C xie

for a statar

u-t b, tanp =

a+E for a rotor.

'x.Le

. ..(a

This method of design was used for the single-stage and the two-stage ccaapressors (both with hub/tip ratio E 0.750). Fcr the multi-stage

design (U.S.F.) $e ith rotor exit air angle was as that for the second-stage rotor, and the i stator exit air angle was as that for the first-stage stator.

It was assumed that the angle distributions with radius were unchanged "off-design", at all flcm coefficients. These distribution8 are given in Appendix 4.

2.3/

-5-

2.3 The off-design problem

For the off-design case equation (5) has to be solved direotly at the trailing edge af a stationary row, say the ith row. 'The tangential components of the velooity "C," are given by equation (4), with the flm angles now known from the design calculations of Section 2.2.

Again the axial velocity is given by 8n equation such as (7), or,

C x3-e = ZC i xi + FzLcxi-l + 'i'*i+l . ..(9)

where a, F, 7 are constants and i i I, 2, 3 . . . . .

Three oases are oonsiaered below, a single-stage, a two-stage and a multi-stage aschine.

2.3.1 The single-stage compressor

2.3.1.1 High hub/tip ratio (0*7501

The first example oonsidered is that of a single-stage @..a1 flow ompressor - en inlet guide vane row followed by a rotor row followed by a etator row - of hub/tip ratio 0.750.

Each row of blades is replaced by an actuator disc placed at mid-chord of the blades, and the tangential velocity is controlled at a trailin~edge looation midway between the actuator discs, i.e., it is assumed that the blade rows have the same axial chord and the axial clearance is zero.

For the three rows the three equations to be solved beoome:

for the .&de vane

dC C

3 + wxo + vxi + y7. L) tan a, e xi ar sr

% bGiCxo + FiCxi +Y,Cx )ta aie) = 0 a

for the rotor

dC C

xa [U - (j7aCx + Y,Cxa + K~c~3)tanP2e1 -+

x, dr r

5 [u - (&cxi + %Cxa + GCCx3)tan 19~~ ar

- (&cxo + BICx, + &1)t*n aleI

. ..(I01

. ..(I11

for/

-6-

for the atator

where

In non-dimensional form these equations beoome

.&Vi + cy,v, + DL EL 0

az*y + as2V2 + a2,vs + Da 1 0

a3%v+ + a,,v, + a v + D = 0 333 3

. ..(I31

d c Vi ii - 2%

( > aR c X0

d c

v =- Aa 1

( > aR c

X0

ana aij3 Di am functions of non-dimensional radius R = $-,C t Xi'

fi = tan(a& Fi = and aspect ratio A.R.

A cmplete statement of the equations is given in Appendix 1.

2.3.1.2 LOW hub/tip ratio (0.555)

The problem of a low hub/tip ratio single-stage axial flow compressor was also considered. Solutions of the equations were carried out in a similar fashion to that in the previous section. Flow angles at exit from s mw were obtained from the design of the high hub/tip ratio stage by means of extrapolation,

2.3.2 The twc-stage oompressor

The next example consiaered is that of a two-stage, five row ompressor-inlet guide vanes, first rotor, fFrst stator, second rotor, second stator. Again all rum are replaced by actuator discs located at mid-chord of the blades and interference effeots due to adjacent discs only are considered. Five equations are derived for the "infinity" distributions of axial veloaity.

The/

The general form of

LVi + eiav2

-7-

these equations is

+Di E 0

a V +a,,V,+a V +D' = 0 ai 2 as 3 a

asiVi + asaVa + as,V, + a V +D E 0 34 4 9

adzVa + a,,Vs + a,,V, + a4sVs + D = 0 4

. ..(I41

asaVa + as,V, + as4V, + as5Vs + D = 0. II

A oomplete statement of these equations is given in Appendix 2.

2.3.3 Tha multi-stage oompressor (ultimate steady flow1

Finally, actuato~&i.so theory is applied to obtain the flow through a stage in a multi-stage machine Fn which the stage is deeply embedded, i.e., there are many similar stages both upstream and. downstream. In the aotuatorcdiso enelysis this stage is replaoed by ho actuator dlsos, ana the flow entering the stage is identical to that 1eavFng the stags.

The equation for the axial velocity that would exist in radial equilibrium upstream of the rotor diso is

dC C x9 + - -5 (r Cese) = 35 , '0se x8 ar r dr al.-

.,.(15)

The equation for the equilibrium axial velocity that would exist downstream of the rotor disc is

'eRe d St -+--(rCeRe) = -.

r dr ar . ..(I@

Downstream crf the stator diso and upstream of the rotor diso of the next stage

dC c d C XB be

X8 ar +-- (rCese)

r dr I ; (has + AW)

since the velooity distributions are the same at entry to and exit from the stage

and

Frm (15) .=d (17)

hoR = has + AW.

" (AW) = 0. ar

. ..(I81

But/

But

then

-a-

. ..(I91

or

ana

‘(%Re - %se ) = rOJ - CxRe+- Pe - Cxseb ae)

= Constant,

From equation (15) and (16)

. ..(20)

%JRe a + - - (rCeRe). . ..(a)

r dr

Frcm equation (19) and (21)

nac %s %iR 2-c -= c %Re - %se

ar *al- r J i (r&J ,..(22)

Equations (19) and (22) now form the required two differential equations for the unknowns CxR and Cxs. They sre re-written in a non-dimensional form In Appendix lc.

2.4 NumerIcal solution

This section outlines the general method of solution that has been adopted thra@out. Each of the three cases considered in the previous asotions yielded a set uf simultaneam linear first-order differential equations.

The Runge-Kutta numerical teohnique for the integration of a set of first-order differential equations was oh-en.

The/

-9-

The equations to be solved must be written in the fcmu

i ( >) = g%(R, > , > , . . . 2 , other factors)

X0

-L(i) = qR,g, . . .

X0

,c-, (

X0

X3 C Xi - "'g It,- , . . . 3 C

x0 =0

n 11 I

> . ..(23)

- - - where other factors include such quantities as #, f, F, CL, p, y and K. n represents the number d rows in the machine.

Numerioal solutions of these equations requires an initial assumption of the values of the rlepandent variables at scme radial station R. (usually the gemetrio mean section), and a knowledge of the values of the fluid angles at exit from each blade row as a fYmction of radius. These are known fran the earlier design analysis, and are assumed to remain unchanged with flow coefficient. With the blading design chosen and the dimensions of the machine fixed, the values cf the constants (K, Z, p, 7) are known.

As a first approximation, values of unity for the dependent variables are assumed at radial station (Ro). When this and the values of exit fluid angles and other constants corresponding to the radial station are substituted into the set cf equation (Zj), eaoh of the equations will yield new values af c c C =i xa xn

O'C , ..L - C at R. + ML This process is continued and. new values of

x0 X0 X0 C C xi - . . . . .

C 2 are then calculated at R. + 2AR and R. + 31Ul and so on until C

XC xc the cuter diameter is reached. Similarly for the inner diameter.

The final axial velocity profile behind esoh row of blades is thus produced. A check on the initial values that were assigned to the dependent variables is oontained in the continuity condition whioh must be satisfied at the trailing edge of each row. Thus at any flew coefficient ($J ), the maSS fluiv at entry to the stage is

MO = Ki( ' ;') where K, = 2?rp<Cxo

th and ahadd be equal to the mass flow behind the n rm.

- 10 -

if ' - ' s X0, ahd the inte@d 2

= 1, 2, 3 . ..I

then a new Mtialvalue uf 3 at the mean section is taken as C

X0

C

( > xi A

2nd = -22 C

=o approx .

Ai

whilst the initial values of the p&files that satisfied continuity wi.l.l remain as they were for the first apprmdmation.

With new initial values, the whole oaloulation is carried out again, and the profiles obtained re-cheoked for oontinuity. This proaess, for the oases investigated, was found to be rapidly convergent and only two apprudmations were necessary.

t

By speoifylng the spaoe ohord ratio at all radii in the design ses Appendix 4) it w&s possible to obtain the nominal values of deflection E*) and inlet-air angle (a* or p*) for each blade se&ion. Fran the

off-design calculations, it was possible to calculate the inlet angle (a or p) to eaoh row at the inter-blade looations and the oorresponaing values M (i - I.*) z (a - a*) or (p - p*). The off-design perfwmanoe

could then be plotted on the Howell ohart of (s/s*) against the local blade section.

.+$-for

The oomputer program devised for the numerical. solution of the set of differential equations thus has the special feature of prediating the design and off-design performance of the compressor stage over a wide range of flus up to stall and for different aspect ratios, by the mere change uf value of two quantities, namely, aspect ratio and flow ooeffioient.

The solution for the single stage was oheoked against stre amgi, curvature caloulations of the performance provided by Rolls Royce Ltd. .

3. Presentation and Discussion of Results

The oaloulations are presented in the folldng way:-

A - Single-stags compressor.

B - Two-stage compressor.

c - Multi-stage oompressw (ultimate steady flow).

Id

- II -

In the main body of oaloulation (Section 3.1) a canparisan between the performance of compressors of di'fferent aspect ratios (A R = 1 2, 3) but Of constant high hub/tip ratio (0.750) is given for eaoh of the thre: ex~~lea A, B, C.

These comparisons are shown on two main plots:-

(i) (Trailing-edge axial velocity)/blade speed vs. non-dimensional radius, at exit fran Inlet guide vanes, rotor and stator, for two flea ooeffioients (0.662 - higher then design, 0.475 - off design).

(ii) (Incidence - nominal incidenoe)/nominal defleotion vs. (deflection/nomind defleotion), (Howell's curve), for rotor and stator, at root, mean and tip diameters, and for three flow coefficients (0.662, O-527 - at design, 0.475).

A more detailed study is then made (in Section 3.2) of example A, the single ntage:-

(a) The calculated performance of the high hub/tip ratio stage is oanpared with calculations based on streamline curvature analysis.

(b) Aotuatediso calculations are given for .a lower hub/tip ratio stage (0.555) and for a wider range of aspeot ratios (AR 1,2,3,4,5). /

3.1 Aspect-ratio effects for stages of hub/tip ratio 0.750

A- Sin.de-Stage Comnressor

The "off-design" axial velocity profiles at the trailing edge of the blade rows show noticeable differences for the three aspeot ratios (Fig, 4). The stator blade row receives the flow at inoidences that differ with the aspeot ratio (Fig. 5B). The first stall in the stage appears at the stator tip, occurring earlier for A R = 1 tkanfar AR = 3. This later stator root stall for A R = 3 is achieved at the expense af an earlier rotor tip stall (Fig. 5A) although rotor root stall, occurring first, appears little affected by ohnnge of aspect ratio.

The differenoe in axial velocity profile at the trailing edge of the stator for the three aspect ratios suggests that the performanoe of following blade rows wcxlld be affeoted substantially.

B- Two-Stage Compressor

The axial velocity profiles at the trailing-edge locations of the two-stage cbmpressor are shown in Fig. 6. The operating points on the Howell curve for each blade row (Fig. 7) show substantial aspeot-ratio effeots.

Stall in the two-stage machine appears to ooour

(i) for low aspect ratio, at the first-stage stator tip,

(ii) for high aspeot ratio, simultaneously at second statar root and all along the first stator.

There/

-12 -

There are two other interesting features of the calculations:

(a) The oalaulations for the two-stage oompressor show a definite trend for the pattern of axial velocity at blade row trailing edges to repeat in the second stage.

(b) The presence of a second stage hastens the stall of the first-stags stator and magtiies differences between the performance of compressors of different aspect ratios.

C - Multi-Stage Compressor

The "ultimate steady flow" analysis developed for the multi-stage canpressor strictly applies only to deeply embedded stages of identical geometry, through which the flow pattern repeats. However the solutions obtained (Figs. 8 and 9) are similar to those for the second stage of the tnwstags design. This suggests that the "ultimate steady flow" profiles are established after the stator of the first stage.

These "ultimate steady flow" profiles are different for different aspect-ratio blades. Again it appears that for the low-aspect-ratio maohine, rotor tip stall is delayed at the expense of early stator tip stall.

3.2 Detailed study of single-stage performance

(i) Predictions of the axial velocities at the trailing edges of blade rows, based on actuator-disa and streamline ourvature calculations, have been compared for the three aspect ratios. The maximum difference between these velocities is some I$, and to all intents and purposes the two analyses give identical results.

(ii) For a loser hub/tip ratio (0*555), calculations were made of single-stage performance, using a wider range of aspect ratios

(A R = I, 2, 3, 4, 5). These results are presented in Fig. 10.

These results show the larger aspect-ratio effeots expected in a low hub/tip ratio mrrohine, but it is signifioant that the greatest differenoes in velooity profiles oocur between A R = 1 and 2, and that the differenoes, diminish with increasing aspect ratio.

4. Conclusions

An actuator-disc analysis for predioting the performance of single-, two- and multi-stage axial-flow compressors of varying aspeot ratio is described. Calculations based on this analysis have been compared with streamline curvature calculations. The comparison shows exaellent agreement between the two sets of calculations.

Results of these theoretical investigations oonfirm the existenoe of differenoes, small but significant, between ,the performance of machines of different aspect ratios. They SUg@St that in Si,l&Wd.ag@3, twC-Stage Slid

multi-stage machines of low aspect ratio, local stall first occurs at the stator tip. For higher aspect ratios, a complete stator stall (root to tip), usually oocurs, although in the two-stage machine there is a tendency towards

stall/

-13 -

stall of the second stator root. In general rotor stall follows stat= atdl, with little difference between aspeot ratio, at the hub and mean regions of the blade. The rotor tip tends to stall earlier when the aspect ratio is high. These results suggest severe stator stall and e&Q,- rotor tip stall In high-aspect-ratio maohines and appear to be consistent with the experimental results that show the range of performance of high-aspect-ratio machines is narrower than that for low aspect ratio.

These general conclusions are emphasised in the oalaulations of performance of the low hub/tip ratio compressor stage.

An extension of the analysis is at present being carried out, introducing losses into the flew equations. Detailed experimental traverses on a single-stage atidal-flow compressor (A R = 1 and 2) are planned in the near future.

Notation

rp 0, x

'r

%l

%

RP; t

oylindrioal co-ordinates (Fig, 1)

velocity in direation r

wlooity in direation 0

velocity in direction x

non-aimensional radius (= radius/tip radius)

fluid an le at entry or exit from a stator row (absolute) (Fig. 2 f

fluid an le at entry or exit from a rotor row (relative) (Fig. 2 7

blade speed (n, angular velocity! r, radius)

stagnation enthalpy

stream function

flow ooefficient (= Cxo/Um)

aspeot ratio (= blade height/da1 chord length)

constant (= tip radius/mean radius)

non-dimensional gradient of axial Yelooity in r direction

tangent of air angle at exit from a blade row

F = af/aR

AW work done on the fluid by the moving blade r(xT

M/

- 14 -

M mass flow af- the air

P mean density of the air - - "Is P, 7, F, m interference ooefficf.ents

x distance fran aotuator d.I.50 (always positive)

c blade height

'1 vortioity component in tangential dlreotion 8 r.Ce

Subsoriuts (see Fig.d

0

1, 2, 3, 4, 5

o-i, 02, 03, 04, 05

1.3, 2~9, 30, b, 59

s, R

OS, OR

Se, Be

t, m, h

entry oonditions

radial equilibrium conditions (that would be attained far downstream of a blade row)

positions of the aotuator discs replaoing blade row

positions of the tmlling edges of blade rows

raaial equilibrium oonaitions (oaae of ultimate steady flow)

positions of the aotuatar disoe (ease of ultimate steady flow)

position8 of the trailing eclgsa (case of ultimate steady flov)

tip, mean, hub

Appendices/

- 15 -

Appendices

l- The Sin&-Stage ComPressor

Equ8tims (IO), (Ill 8nd (12) w be expressed n0dimenSi0naw by dividing each of these equations through by CxoI the inlet axial velmity,

and replacing I-, the radius, by .R(= $ ), the non-dimensional radius. t

After sorme remangement, the equations beoomer-

for the guide vane,

for the atator,

where K = rt/Q 9 #J = "xo&' Z- The Two-Stage Ccmnpmss~/

- 46 -

2- The Two-Stage Ccmpressor

Equations similar to those for the single-stage compressor am farmed for the inlet guide vanes, first rotor, first stator, second rotor, seaoti stator. Expressed non-dimensionally and with sane rearrangement, the equations beoamer-

for the guide vane,

for the second rotor,

for the second stator,

3 - The Multi-Stage Canpressor

The two differential equations in their final non-dimensional form arez

Equation (22)

e --- I Equation (IYY

- 10 -

where P =+-ae, f, =tanp e

a a %

F, = -f,, F, = -f:, , K p _ aR art 5

ana C XSe

= QCxs + PC XR

C FRe

= QC- + pcxs

where --R 2E P 8

=e , Q = I-P.

4 - Air Andes at Exit from the Blade Rows - The design values are presented as fknotions of radius (R) and space-chord (S/C). These values are also used off design in the high hub/tip ratio oaloulations.

Air angle at exit franl

R VC I.G.V. Rotor 1 Stator 1 Rotor 2 Statm 2

0.750 0~7% 25*6O 12.1" 24*Y0 12*00 25.20

0.800 04k3l+ 2704~ l9*3o 27.00 19'2Q 27'20

0.850 O*S& 29*20 26-4" 29.0~ 26*4" 29do

0*900 0*904 30*9O 33.3" 31.00 33*3O X*9"

0*950 04955 32.5' 39*8O 33*1° 39'9O 32*8'

i*coO I*005 34.20 45-9O 3502~ J&o0 3JP7"

These values were extrapolated for the low hub/tip ratio stage.

- 19 -

References

Title. etc.

Reynolds number effects in cascades and axial flow qmpressors. Journal of Engineering for Power, Vo1.86, Series A, pp.236-242, July, 1964..

1 J. H. Horlook, R. shim, D. Pollard

and A. Lewkowics

2 J. C. Emery, L. J. Herrig and

J. R. Em%

3, w. c. swan

4

8

Systematic twc-dimensional tests of NACA 65-Series oompressor blades at low speeds. NACA TN-3916, 1957.

An experiment with aspeot ratio as a meens af extending the useful range of a transonio inlet stage of an axial flow oompressor. Journal of Engineering for Power, Vo1.86, Fm.-ies A, pp.243-246, July, 1964..

L. H. Smith, Jr., S. C. Traugott and

G. F. Wislicenus

A practical eolution of a three-dimensional flow problem of axial turbomachinery. Tram AShE - 75, PP.789403, 1953.

W. R. Hawthorne and

J. H. Horlock

J. H. Horlook

Actuator diso theory of the incompressible flow in axial compressors. Proc. I. Mech. E., 176, No.30, 789, 1962.

Axial flow oompreesors. Butterworths Scientific Publications 1958.

J. H. Horlook Ccmmuniaation relating to the paper "Three-Dimensional Design of Multi-Stage Axial Flow Canpreseors" by J. W. Rd.lly. J. Mech. Eng. Soi. 3, No.3, 286, 1961.

R. Hetherington end

M. E. Sllvester

Computation of cmpressor performnoe inoluding the effeots of bade and streamline ourvature. T.G.R. No.90002, Internal Report, Rolls Royce Ltd., Derby.

FIG 1 COORDINATE SYSTEM

k I -J-Q I

- fhc

-

lSt STATOR

2nd STATOR

noron

STATOR

FIG 2 AIR ANGLE NOTATION

FIG. 3 ACTUATOR 01% AN0 TRAILING EOGE STATIONS FOR THE SVSTEMS ANALYSE0 .

lEAR..l 2: A.R = 2 3SA.R=3

,60

c&=- 662 w

u .60

75 .60 05 .90 .95 1.00

Radlur Ratio R

PREDICTED VELOCITY PROFILES FOR FIG.4 SINGLE-STAGE COMPRESSOR

I \ \ \

I e \ i \ \ \ ,\ \ A \ c \ ,” \ \ ;I U \ \ \ G \

-c - \ 4 \ \ \ \ \ \ \ \ \ \ \ J z \ \ \ . \ \ \ 2 ,Gi \ d: J- \: \- d: (P

‘ 0

00; 9 ? 0 w s=&.

& h

d: d:

PREDICTED OPERAJlNd POINTS FOR SIWGLE-STAGE COMPRESSOR, PLOTTED ON HOWELLk CURVES

1~00

I J f 3,

1 :A.R.= 1 l~A.R.=l 3-‘A.R.= 3

1.

!a! u

.75 80 85 .90 95 1.00

Radius Ratlo R

FIG.6a PREDICTED VELOCITY PROFILES FOR STAGE 1 OF TWO-STAGE COMPRESSOR

3 I

I

.75 ,a0 ,a5 .90

-95 100

Radius Rat10 A

FIG.Gb PREDICTED VELOCITY PROFILES FOR STAGE 2 OF TWO-STAGE COMPRESSOR

-?= N m 9 Lp

f ;y

cr 4 4 ‘PI - a

ww r 8;

FIGS. 7o.b.=PREOICTEO OPERATING POINTS FOR STAGE; OF TWO-STAGE COMPRESSOR.PLOTTEO ON HOWELL’S CURVES

E 3

12

R=lllO

10

4

6

12

VI

R* 750

0

6

/’ / n:100

/

-\

/’ / /’ / / /

‘L /’ / / /

l'AR*l 2rAR=2

3sAR=3

R = 750 / FIG. d 7

-. 6 -b -2 0 2 I-i* -4

E*

l-00 \

.80

Cx,ae

u

.60

.Lll

1.00

.a0

C&t u

.60

lrAR=l 2:AR=2 3sAR=3

I 75 60 85 90 .95 1.00

Radius Rot10 R

FIG.6 PREDICTED VELOCITY PROFILES FOR EMBEDDED STAGE OF MULTI-STAGE COMPRESSOR

z \ z

\ \ .‘\

,” \ \ ,; \

\ \ \ \ \

\ \ g \ -3 - \ ; ,\

” \ \ 6s: \. 1”:

N

FIGS.9 a,b. PREDICTED OPERATING POINTS FOR EMBEOOEO STAGE OF MULTI-STAGE COMPRESSOR, PLOTTEO ON HOWELL’S CURVES

: _.

.

:

--.

i

--:

,: ‘

N

FIG.10 PREOICTEO VELOCITY PROFILES FOR LOW HUB-TIP RATIO SINGLE- STAGE COMPRESSOR

D 9177~/1/129520 Kl+ a/67 XL & CL

C.P.943 May, 1966 Horlock, J.H. and F&ml, G.J.

A THEORETICAL INVESTIGATION OF THE EFFECT OF ASPECT RATIO ON AXIAL FLOW COMPRESSOR PERFORMANCE

The performance of axial flow compressors 1s known to be affected by the choxce of aspect ratlo (the ratlo of blade height to axial chord length). An analysis of the ~nnscd, uunnpresslble flow m anal compressors of different aspect rat203 1s even In this paper. The mu analysis 1s based on actuator &SC theory, but a comparison 1s made between calculations based on this theory and the mere recently developed streamline curvature analysu. This ccmparlson shcws close agreement between the calculations based on the two

C.P.943 May, 1966 Horlock, J.H. and Fahmi, G.J.

A TiBORETICAL INVESTIGATION OF TI52 EFFECT OF ASPECT RATIO ON AXIAL FLCW COMPRESSCR PERFORMANCE

The performance cf axial flow compressors 1s known to be affected by the choxe cf xpect ratlo (the rat.10 of blade height to anal chord length). An analysis of the ~nvwxd, inccmpresslble flow in axial compressors of dlfferent aspect ratios 1s @"en U-I this paper. The man analysis 1s based on actuator disc theory, but a ccmparlscn 1s made between calculations based on this theory and the mere recently developed streamlue curvature analysu. Ths ccmparlscn shows close agreement between the calculations based on the two

I theories. theones.

C-P.943 May, 1966 Horlock, J.H. and Fahml, G.J.

A T'BORETICAL INVESTIGATICN GF THE EFFECT OF ASPECT RATIO ON AXIAL FLOif COWRESSOR PERFORWNCE

The performance of anal flarv compressors 1s known to be affected by the choxce of aspect ratlo (the ratlo of blade heqht to anal chcrd length). An analysis of the ~nnscld, uxccmpresslble flow in anal compressors of different aspect ratios 1s given in this paper. The mm analysu 1s based on actuator disc theory, but a comparlscn 1s made between calculations based on this theory and the mare recently developed streamlIne curvature analys~5. Tnls ccmparxcn shows close wreement between the calculations based on the two

. _

C.P. No. 943

0 Crown copyright 1967

Prrnted and published by HER MAJESTY~S STATIONERY OFFICE

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C.P. No. 943 S 0 Code No 23-9017-43