79
mm#43 32:4 PURDUE RESEARCH FOUNDATION Peict Me. 3664 AN EXPERIMENTAL INVESTIGATION ON THE EFFECT OF SUBSONIC INLET MACH NUMBER ON THE PERFORMANCE "OF CONICAL DIFFUSERS Rowert V. Vu Deomat e Robert W. Fox SCHOOL OF MECHANICAL ENGINEERSIN FLUID MECHANICS GROUP PURDUE UNIVERSITY Teclmcal Report FM¶TR -66-1 February 1966 ARMY RESEARCH OFFICE (DURHAM) DA Project No. 200 1050 1B700 / ARO(D) Project No. 4332 Contract No. DA-31-124-ARO(D)-138 JUDUSAL SCIOIIFIC AMD 120MCA~L INPVRMATION SJ-21 -1 " , ... 7 e--r• /

-1 · Fluid Mechanics Group Technical Report FMTR - 66 - 1 AN EXPERIHENWTAL INVESTIGATION ON THE EFFECT OF SUBSONIC INLET MACH NUMBER ON THE PERFORMANCE OF CONICAL DIFFUSERS Contract

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Page 1: -1 · Fluid Mechanics Group Technical Report FMTR - 66 - 1 AN EXPERIHENWTAL INVESTIGATION ON THE EFFECT OF SUBSONIC INLET MACH NUMBER ON THE PERFORMANCE OF CONICAL DIFFUSERS Contract

mm#43 32:4

PURDUE RESEARCH FOUNDATION Peict Me. 3664

AN EXPERIMENTAL INVESTIGATIONON THE EFFECT OF SUBSONIC INLET

MACH NUMBER ON THE PERFORMANCE

"OF CONICAL DIFFUSERS

Rowert V. Vu Deomat e

Robert W. Fox

SCHOOL OF MECHANICAL ENGINEERSINFLUID MECHANICS GROUP

PURDUE UNIVERSITY

Teclmcal Report FM¶TR -66-1February 1966

ARMY RESEARCH OFFICE (DURHAM)

DA Project No. 200 1050 1B700 / ARO(D) Project No. 4332Contract No. DA-31-124-ARO(D)-138

JUDUSAL SCIOIIFIC AMD120MCA~L INPVRMATIONSJ-21 -1 "

, ... • 7 e--r• /

Page 2: -1 · Fluid Mechanics Group Technical Report FMTR - 66 - 1 AN EXPERIHENWTAL INVESTIGATION ON THE EFFECT OF SUBSONIC INLET MACH NUMBER ON THE PERFORMANCE OF CONICAL DIFFUSERS Contract

Purdue Research Foundation

Lafayette, Indiana

DA Project No. 200 1050 1B700 / ARO(D) Project No. 4332

School of Mechanical Engineering

Fluid Mechanics Group

Technical Report FMTR - 66 - 1

AN EXPERIHENWTAL INVESTIGATION ON THE EFFECT OF SUBSONICINLET MACH NUMBER ON THE PERFORMANCE OF CONICAL DIFFUSERS

Contract No. DA-31-124-ARO(D)-138

by

Robert V. Van Dewoestine

Robert W. Fox

December 1966I

Requests for additional copies by Agencies of the Departmentof Defense, their contractors, and other Government agenciesshould be directed to:

Armed Services Technical Information AgencyArlington Hall StationArlington 12, Virginia

Department of Defense contractors must be established for ASTIAservices or have their "need-to-know" certified by the cogni-zant military agency of their project or contract.

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ii

ACKNOWLEDGEMENTS

This research was sponsored by the United States Army

through the Army Research Office (Durham), under contract

number DA-31-124-ARO(D)-138. Their financial support is

gratefully acknowledged.

The work reported herein formed the basis of an MS

thesis in Mechanical Engineering at Purdue University.

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CONTENTS

Page

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . iv

LIST OF FIGURES . . . . . . . . . . . . . . . . . . v

ABSTRACT * e a . a * . . . . . .1 a a . a . . viii

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . 1

EXPERIMENTAL FACILITY . .. .. .. .. .. . . .. 5

CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . 32

REFERENCES . . . . . . .... . . . . . . . . o 34

APPENDICES

Appendix A. Data and Calculated Performance.Parameters for Current Investi-gation . . . . a . . . 0 . . . 0 6 0 . 35

Appendix B. Tabulation of Diffuser Perfor-mance at Selected Mach Numbersand cross-plots of Data Usedin Plotting Performance Maps . . . . . 55

Appendix C. Method of Obtaining PerformanceMaps . * o * . a a e * o * o o o e a o 66

Appendix D. Discussion of Diffuser Choking . 0 . 0 67

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iv

LIST OF TABLES

Table Page

1. Thread Movements and Their Interpretation . . . . 10

Al. Data Summary for 2# = 2.0 and N/R 1 = 8.0 . .0. . 36

A2. Data Summary for 2# = 2.0 and N/R 1 = 16.0 . . . . 37

A3. Data Summary for 2# = 2.0 and N/R 1 = 32.0 . .0. . 38

A4. Data Summary for 2# = 4.0 and N/R 1 = 4.0 .a. . . 39

A5. Data Summary for 2# = 4.0 and N/R1 = 8.0 . .0. . 40

A6. Data Summary for 2# - 4.0 and N/R, - 16.0 .e. . . 41

A7. Data Summary for 2# = 4.0 and N/R 1 = 32.0 . . . . 42

A8. Data Summary for 2# - 8.0 and Y/R = 2.0 o . e 9 43

A9. Data Summary for 2# = 8.0 and N/R 1 = 4.0 9 & e 9 44

A10. Data Summary for 20 = 8.0 and N/R = 8.0 9 . a e 45

All. Data Summary for 2* = 8.0 ane N/R 1 = 16..0 . . . . 46

A12. Data Summary for 2ý = 8.0 and N/R = 26.8 9 . .*. 47

A13. Data Summary for 20 = 15.8 and /R1 = 2.0 . . . 48

A14. Data Summary for 2# = 15.8 and N/R 1 = 4.0 * . .e. 49

A15. Data Summary for 2# = 15.8 and N/R1 = 8.0 . . . . 50

A16. Data Summary for 2# = 15.8 and N/R 1 = 13.4 . . . 51

A17. Data Summary for 2# = 31.2 and N/R 1 = 2.0 . . .. 52

A18. Data Summary for 2# = 31.2 and N/R 1 = 4.0 . . . 53

A19. Data Summary for 2# = 31.2 and N/R 1 = 6.7 . .e. . 54

Bl. Diffuser Performance at Selected Mach t!umbers . . 65

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V

LIST OF FIGURES

Figure Page

1. Lines of First Appreciable Stall and Lines ofMaximum CpR at Constant Length Ratio for Conicaland Plane-Palled Diffusers (Taken from Reference 2). 3

2. Experimental Facility. . . . . . . . . . . . . . . . 6

3. Detail of Nozzle and Straight Section. . . . . . . . 7

4. Effect of Inlet Mach number on Flow Regimes in 1?Conical Diffusers.. .. ....... . . . . .

5. Diffuser Performance vs. Inlet Mach Number forAR = 1.30. * o ..... . .e. . .a. 16

6. Diffuser Performance vs. Inlet Mach Number forAR = 1.64* ... . . . . . . . . . . .. . . 0.. . . . 17

7. Diffuser Performance vs. Inlet Mach Number forAR = 2.43. .*. . . . e .. . . % .e . .* e * # . .. *. 18

8. Diffuser Performance vs. Inlet Mach Number forAR m 4.48% .. . . . . . ..e .. ..e a 0 0 0 a.. . . . . 19

9. Diffuser Perfolmance vs. Inlet Mach Number forAR = 8.27 . . . . . . . . . . . . . . . . . . .* . 20

10. Diffuser Performance vs. Inlet Mach Number for2# = 20 .D.u. .P . vs. . n.e. . Mah. N r ... . 22

12. Diffuser Performance vs. Inlet Mach Number for21 = 4D .f.u. .P . vs. . I.e. t M.acN.u r .. 23

12. Diffuser Performance vs. Inlet Mach Number for2+ = 80 . . . . . . . . . . . . . . . . . . . . . . . 24

13. Diffuser Performance vs. Inlet Mach Number for241 = 15.80 .. . . . . . . .a a.. . 0. .. 0. . .. . . . 25

14. Diffuser Performance vs. Inlet Mach Number for2# = 31.20 . . . . . . . . . .. . 0. .. . . . . . . 26

15. Performance Map for Conical Diffusers withM 1 =0.25. . . . . . . . ... 28

o-.. .. . .

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v

Figure Page

16. Performance Map for Conical Diffusers withM1 = 0.55, .6 . . . . . * . . . 0 .. .. . 1 0. . 29

17. Performance Map for Conical Diffusers withM1 = 0.70 . . & o . *. .. . . . . . o. . . . * e 30

18. Diffuser Performance vs. AR-1 for ConstantN/R 1 at M- 0.70.. .e . . . . .* . . * . . . .. 31

Appendix B

B1. CPR vs N/R 1 at constant AR for M1 = 0.25. .0. .. 56

D2. CPR vs AR at constant 2# for M1 = 0.25. . . .a. . 57

B3. CPR vs 2# at constant N/R 1 for M1 0.25. . .a. . 58

B4. CPR vs N/R 1 at constant AR for It M 0.55. 0 . . . 59

B5. CPR vs AR at constant 2+ for M1 = 0.55. . . .. . 60

B6. CPR vs 2# at constant N/R 1 for M1 = 0.55. .*. . . 61

D7. C PR vs N/R 1 at constant AR for M1 = 0.70. .o. . . 62

B8. CPR vs AR at constant 2# for M1 = 0.70. . * .... 63

B9. Cpil vs 2# at constant N/R 1 for = 0.70. .*. . . 64

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vii

NOENCLATURE

A Area

AR Area ratio - (outlet area)/(inlet area)

CPR Performance = (P2 -P 1 )/ql

CPRi Ideal performance - (P2-P1}i/ql

M Mach Number

N Diffuser length along centerline

P Static pressure

q Mean dynamic pressure - 1pU

R Diffuser radius

U Free stream velocity

u Velocit at any point

W Diffuser width - two-dimensional, plane-walled

X Distance along centerline from diffuser inlet

6* Displacement thickness of boundary layer

Effectiveness = (P2-PI)/(P2-PI)i

0 Momentum thickness of boundary layer

p Density

2# Total divergence angle

Subscripts

i Ideal

0 Stagnation

1 Diffuser inlet plane

2 Diffuser outlet plane

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viii

ABSTRACT

Experiments have been performed to determine the

effect of subsonic inlet Mach number on diffuser performance

and flow regimes for a wide range of conical diffuser geome-

tries.

For incompressible flow the line of first appreciable

stall, line a-a, is essentially that found by McDonald and

Fox (Reference 2). As the Mach number is increased, the flow

tends more toward separation in all cases.

Diffuser performance maps are presented for three dif-

ferent inlet Mach numbers (M1 = 0.25, 0.55, 0.70). There is

no significant variation in the location of the line of max-

imum performance at constant length to inlet radius ratio,

line a-a, with inlet Mach number. For M1 - 0.25 line a-a

of the present study is virtually identical to that found in

the earlier water flow studies of McDonald and Fox (Reference

2).

. . . . .. . . . . . . . W.

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1

INTRODUCTION

Performance of conical diffusers is dependent on

both flow and geometric variables. Previous work has

indicated that the geometric variables of importance are

total divergence angle, 2#, length to inlet radius ratio,

N/R1P and area ratio, AR. The flow variables are more

numerous and often somewhat more difficult to identify. In

part they are inlet boundary layer thickness, Mach number,

turbulence inten3ity, and Reynolds number. The large number

of variables makes a generalized theory of diffusers dif-

ficult; considerable data are required to determine the effect

of a single variables over a range of the other variables.

In the past many investigators have been more interested

in improving the performance of a single diffuser rather than

formulating any relationships for a wide range of geometries

and flow conditions. A summary of previous investigations of

two-dimensional, plane-walled diffusers is given by Kline, et

all* for the case of steady, incompressible flow with a thin

inlet boundary layer (compared to the inlet wieth of the dif-

fuser). The summary includes observations of flow regime

(degree of separation) and measurements of performance over

a wide range of diffuser divergence angles and length ratios.

* Superscript numbers will be used to denote items in theLie% of References.

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2

The results showed that flow reaime was primarily dependent

on the qeowtetr. of the diffuser, but that the performance

depended on other variables as well. The results of Refer-

ence 1 were presented on coordinates of divergence angle versus

length ratio. The location of "first appreciable stall*

was designated as lina a-a; the line of maximum pressure

recovery for fixed V/W1 was designated as line a-a. The

location of these lines for two-dimensional, plane-walled

diffusers is shown in rigure 1. McDonald and Fox 2 performed

a systematic investigation of flow regimes and diffuser

performance over a wide range of conical diffuser geometries.

The location of lines a-a and a-a as presented in Reference

2 are also shown in Figure 1. Poth of these studies were for

incompressible flow and were primarily concerned with the

effect of geometric variables on flow rimes and diffuser

performance.

The purpose of this work is to extend the investigations

of McDonald to regions of compressible flow; i.e., to de-

termine the effect of subsonic inlet !.ach number on flow regime

and performance in conical diffusers. Several investigators

(Ackeret3 ; Copp4 ; Little and Wilbur 5; b'aumann6 ; Scherrer and

Anderson 7) have taken data on the effects of Mach number on

diffuser performance; however, these data are only for a small

number of geometries grouped around the line of optimum

performance; the values of the geometrical parameters em-

ployed in these earlier investigations are shown in Figure 1.

It should he noted that in all cases the exit of the diffusers

was joined to a tailpipe. This limited data indicated that

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Pi=•"I"- V

3

-I I

Plane-Valled

Conical32 CL CL Line of Maximum C_

at Constant Length'Ratio

04 i-tl Line of First*Appreciable Stall

4M -%C.Q

% %C

Conical Diffuser Ge eries41Investigated by .. ,

Little & Wilbur 5

Scop 4Scherrer & Anderson

7

2 A Ackeret 3

*Naumannf6

4 8 S

N/W, N/R 1

Figure I. Lines of First Appreciable Stall and Lines ofMaximum CPR at Constant Length Ratio for Conicaland Plane-b.alled Diffusers (Taken from Reference2)

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4

there is little effect of Mach number on diffuser performance

or flow regime until the flow becomes choked. In view of the

limited data available, a systematic investigation was wider-

taken to determine the effect of subsonic inlet Mach number

on diffuser performance and flow regime over a wide range of

conical diffuser geometries.

In the present study the dependonce of flow regime and

performance on inlet Mach number was determined experiment-

ally for the nineteen conical diffuser geometries employed in

the work of McDonald and Fox2 . The results were then cor-

related with the geometric variables in an attempt to find

useful relationships for predicting diffuser behavior ander

a given set of inlet conditions.

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5

EXPERIMENTAL FACILITY

The arrangement and dimensions of the wind tunnel used

in the present study are shown in Figure 2. The tunnel was

of the blow through type. Air from a Spencer turbo-blower

came through a 24 inch diameter pipe and into a transition

section, the transition section changed the passage from the

round pipe to a 20 inch x 20 inch square channel which served

as an upstream plenum. This plenum section, containing flow

straighteners and screens, was 32 inches in length. Flow

entered the diffuser test sections through a converging

8nozzle designed according to Smith and Wang (The nozzle

was designed from curve (a) of Reference 8; the nozzle

contour was taken from a chart given by the authors and

scaled up to the desired size.) The nozzle was bolted

through the downstream face of the plenum and extended a dis-

tance of 7.86 inches upstream into the plenum. For ease of

construction, the nozzle was fabricated in two pieces as

shown in Figure 3. The constant area section extended for

5 inches beyond the plenum wall. The inside of the straight

section was machined and polished to insure close matching

with both the end of the nozzle and the diffuser. The dif-

fuser was then bolted to the straight section with the align-

ment maintained by two pins. The exit of the diffuser was

fastened to a plexiglass plate which was in turn bolted to

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41 0

41W

14 V4 0U.F 41

S4I

C,41r44V-4

044'Aac"4

4j r-I '=

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7

41 4

KA 1

.44

p4

V 0M 41

riS

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8

the downstream section of the tunnel. The attachment was

made so that the exit plane of the diffuser was flush with

the plate. The downstream part of the tunnel was clamped

to the plywood sheet upon which it rested in such a manner

that it could be moved back and forth to allow for different

diffuser lengths. The downstream plenum was 42 inches long;

the flow exhausted to the room.

Wall pressure measurements were taken along the diffuser

length; the pressure tap locations are given in Appendix A.

Tygon tubing was run from the pressure taps to a bank of

mercury manometers. The manometers had a least count of 0.05

inches and this was used as the basic module of the readings

taken. Since there was usually a fluctuation in the readings

of the manometers of 0.025 inches, it was felt that it would

be unrealistic to take readings closer than the least count.

During the early runs a great deal of trouble was en-

countered with separation and irregular flow in diffusers

which should have run smoothly. This was traced to distur-

bances in the air at the exit of the blower. To correct

this condition, a set of flow straighteners and 4 screens

were installed in the upstream plenum. The straighteners

consisted of a 1½ inch square grid of sheet metal 4 inches

long. This broke up the large disturbances and the screens

following the straighteners further reduced the scale of the

disturbances. Three other steps were also taken which helped

even more than the straighteners and screens. The butterfly

valve on the blower outlet, which was at first used to control

the air flow, was left wide open; the air flow was controlled

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9

by a butterfly valve on the blower inlet. This eliminated

the large vortex which was being shed off of the partially

opened outlet valve. Through use of the bypass the blower

power level was maintained above 150 kw. This put the blower

above its surge point. Extraneous piping was removed from

the blower inlet so that the blower inlet flow was reasonably

uniform. With these precautions taken, the output of the

blower became quite regular and at low speed the diffusers

2behaved as they had for McDonald and Fox

The diffusers employed in the present work were those

used by McDonald and Fox2 The range of divergence angles

and length ratios cover a wide range of diffuser geometries

including the region of maximum diffuser performance. A des-

cription of the diffuser design and construction can be found

in Reference 2 (page 37.).

The degree of separation (flow regime) in the diffusers

was determined by observations of cotton threads taped to the

diffuser walls. Threads were equally spaced around the

circumference of the diffuser at several axial positions

along the diffuser length. Each of the threads was rein-

forced with a slight amount of glue on the free end. Without

the glue the threads tended to ravel in the high velocity

air stream. To obtain the maximum sensitivity, the amount of

glue used was kept to an absolute minimum. The degree of

separation was determined according to the criteria of Table 1.

The cases where separation was localized in one part of the

diffuser (such as the downstream end) are noted in the data

presentation.

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10

Table 1. Flow Regime Criteria

Movement and orientation of thread Type of flow Symbol

Thread held near wall, pointing Steady flow with -downstream, occasionally wiggling occasional

disturbance

Major part of time thread points Intermittent Idownstream, wiggling; random transitoryflickering (thread quickly points stallupstream, then downstream again)indicating temporary and localseparation

Thread whips continually Local transitory Tupstream and downstream, indicating stallrapid and chaotic occurence anddisappearance of separation

Thread whips upstream and Local transito.y TIFdownstream major part of time; stall withthread held in upstream position intermittentwiggling at random intervals fixed stall

Thread held upstream major part Local fixed FITof time; temporary whipping at stall withrandom intervals intermittent

transitory stall

Thread held upstream with Local fixed stall Fend wiggling

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11

RESULTS

The flow regime was determined in a given diffuser as a

fumction of inlet Mach number. The flow regimes are indicatee

vm Figure 4. The first symbol indicates the low speed flow

regime; the second symbol indicates the flow regime at the

UEghest inlet Mach number tested. The low speed results

differed little from those of McDonald and Fox. However,

wIth increasing inlet Mach number the flow tended more toward

separation in all cases. In instances where this does not

show on Figure 4, it is because the worsening of the flow

was not enough to push it into the next flow regime category.

Amother item worthy of note is that as length was added to

the diffusers, the flow tended to worsen only in the added

section. In other words, the flow in the first 4 inches of

am 8 degree, 4 inch diffuser tended to be the same as the

flow in the first 4 inches of an 8 degree, 8 inch diffuser.

To determine performance the data were taken for each

diffuser as the Mach number was increased incrementally up to

a maximum. For about half the diffusers this maximum was

at the point of local choking and for the others it was at

the limit of the blower. In either case, the maximum inlet

Mach number was always greater than 0.65. Data were taken for

at least 10 values of the Mach number between low speed flow

and the limit points. The data taken were the plenum (stag-

nation) pressure, diffuser inlet static pressure (in the

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12

a-a Line of First Appreciable StallI forI ncompressible Flow (From Reference 2)

?T+Tlr TIF+? TIF+F__ ________

First symbol indicates low speed flow regime: seconsymbol indicates flow regime at highest subsonicinlet Mach nuber,

24 S3S 2

Figure 4. Ef fact of Inlet Mach Number an flow begimes InConical Diffusers

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13

constant area portion of the nozzle), the static pressures

pt stations alonq the diffusers and the downstream plenum

pressure. From these the diffuser performance and the pressure

profile along the diffuser could be obtained. All the data

taken are summarized in Appendix A.

The tunnel system was checked to determine the inlet

turbulence intensity and inlet boundary-layer thickness. A

hot wire anemometer was used for both of these measurements.

The equipment used was a constant current Flow Corporation

model HWB 3. A single wire was mounted, calibrated and then

used for all measurements, For an inlet free stream velocity

of 160 fps the turbulence intensity Ias found to be at a

rather high level of 10%. There was evideontally a high

turbulence level created in the blower that was only parti-

ally corrected by the screens and large contraction ratio.

The velocity profile was integrated to give the momentum

and displacement thicknesses. For an inlet free stream

velocity of 160 fps the ratio of momentum thickness and dis-

placement thickness to inlet radius were 0.011 and 0.017

respectively. The actual boundary layer thickness was on

the order of 0.06 inches.

In calculating the performance from the pressure data

the following assumptions were made-

1. Friction in the nozzle is negligible and the nozzle

flow is one-dimensional. This is reasonable becau.-e of the

short distance involved. Thus, the one-dimensional itentropic

relations can be used to calculate the Mach number at the

diffuser entrance.

"w.-...-w.~. . . . .. w-. . . . . . . . . . . . . . . .

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14

2. Stagnation conditions occur in the upstream section

of the wind tunnel. Calculations showed a better than 100:1

velocity ratio between the test section and the upstream

plenum. Thus, the upstream air is essentially stagnant with

respect to the test section.

3. The static pressure at the exit of the diffuser is

the same as that read by a static pressure tap located in the

plane of the diffuser exit and 6 inches from its centerline.

Diffuser performance as a function of inlet Mach number

was originally plotted on nineteen separate graphs, one for

each diffuser. In general, the performance showed little

variation over the range of Mach numbers tested. Close to

choking, however, there is sudden, sharp decrease in per-

formance.* This is very similar to the results obtained by

previous investigators. Any systematic variation of diffuser

performance with inlet Mach number seemed to be dependent on

the line of first appreciable stall. Below the line of first

appreciable stall the smaller angle diffusers with relatively

smooth flow exhibited a slight upward trend in performance as

the inlet Mach number was increased. This trend was not

present in the diffusers close to the first appreciable stall

line; in diffusers close to the first appreciable stall

line performance is essentially constant until choking is

reached. Above the line of first appreciable stall, the per-

formance decreased with increasing Mach number. In general

as the location above the line increased, the drop off in per-

formance, with increasing inlet Mach number, increased.

* See Appendix D.

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15

The separate performance curves were combined into sets

for either constant area ratio, constant length ratio, or

constant divergence angle. The results plotted for constant

area ratio are presented in Figures 5-9. In Figure 5, all

of the curves essentially fall on the same line. Examination

of the flow regime chart shows that all three of the dif-

fusers in the figure lie well inside the unseparated region.

In Figure 6, all but one of the curves fall together. Examin-

ation of the flow regime chart shows that the diffuser with

the lowest performance for all Mach numbers has a geomtry

which lies above the line of first appreciable stall. In

Figure 7, the two geometries with the lower performance are

located above the line of first appreciable stalli the dif-

fuser showing the lowest performance lies at the greatest

distance above the line. This same trend in diffuser per-

formance is observed at increased area ratio as shown in

Figures 8 and 9.

For a given area ratio, diffuser performance, at a given

Mach number, is independent of diffuser angle (or length ratio)

for diffuser geometries lying below the line of first appreci-

able stall. For a given area ratio, diffuser performance

will drop off at all Mach numbers as one proceeds to geo-

metries lying above line a-a. The drop off in performance

increases with increasing distance above line a-a (increased

flow separation). The consistancy of these results can be taken

an further substantiation of the location of the line of

first appreciable stall in conical diffusers as presented by

McDonald and Fox2 .

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16

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17

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19

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20

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21

No systematic variation in diffuser performance as a

function of Mach number was observed when the curves were

plotted for constant length ratios. Consequently these plots

are not reproduced here.

Figures 10-14 show diffuser performance versus inlet

Mach number at constant divergence angle. On these plots

the results are not as clear as those plotted for constant

area ratio; however a systematic variation is evident. For

a given divergence angle, the performance at any Mach number

is a maximu, for diffusers with the maximum area ratio. The

spread of pez ormance as a function of the area ratio for a

given divergent;s angle decreases as the divergence angle is

increased. At a divergence angle of 31.2 degrees, diffuser

performance is uniformly low and essmtially Mt of

area ratio at all Mach numbers.

Figures 15, 16, and 17 present performance maps for

conical diffusers at Mach number of 0.25, 0.55 and 0.70

respectively. Lines of constant porformance are presented on

plots of area ratio versus length ratio. For a given value

of M1 , these constant performance contours were obtained from

three different cross plots of the data*; the data were plot-

ted as CPR vs N/R1 at constant AR, CPR vs AR at constant 2#

and CPR vs 2# at constant N/Ri. A summary of the data employed

and the actual cross plots are given in Appendix B.

The location of the line of maximum performance at con-

stant diffuser length to inlet radius ratio, line *-a is

shown on each of the performance maps. On Figure 15 the

dashed line shows the location of line a-a as determined in

SeeA .Kpendik C-.

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05 0 0 (4

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23

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25

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26

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27

the water flow studies of McDonald and Fox2 . The agreement

with the present air flow studies for incompressible flow is

excellent. A comparisc of Figures 15 and 16 shows that

there is a slight upward shift in the location of the line

a-a as the inlet Mach number is increased from 0.25 to 0.55.

However the shift is within the uncertainty in the data.

When the inlet Mach number is increased to 0.70, line a-a

is slightly lower than that for N1 = 0.25 (Compare Figures

15 and 17)1 again the shift is within the uncertainty in the

data.

From the performance maps it can be seen that for a

given inlet Mach number and diffuser area ratio, there is an

optimum diffuser length which will result in maximum pressure

recovery. This point is illustrated further in Figure 18.

Figure 18 shows diffuser performance as a function of area

ratic for various values of the length ratio and an inlet

Mach number of 0.70. It can be seen that at low values of

area ratio the curves coincide. As the area ratio increases,

the curves for the lower values of length ratio drop off.

From this plot, one can readily determine the optimum length

ratio for maximum performance at a given area ratio. For

example, for an area ratio = 1.70 and Mach number = 0.70,

Figure 18 indicates that no increase in performance is to be

gained by going to an NIR1 above 8.0.

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28

aa

FigUe IS- Performance NaP for Conical DiffUsers with M1-0.25

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29

So-

202

10•

S4 a 16 32N/RC

Figure 16. Performance Map for Conical Diffusers with NI,,O.55

.................................................-. .-..... r.,... . •.

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30

vI

S• 0.70

0.251

2-2

N/R0

Figure 17. Performance Map for Conical Diffusers with N1 -0.70

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31

0Q

64

In %4'4

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32

CONCLUSIONS

From a consideration of the foregoing experimental re-

sults, the following conclusions can be drawn:

1. For incompressible flow thle line of first appreciable

stall, line a-a, is essentially that found by McDonald

and Fox2 . As the Mach number is increased, however,

the flow tends more toward separation in all cases.

2. The variation of the diffuser pexformance with

inlet Mach number appears to corzelate on the

location of line a-a for incomprooible flow.

- For diffuser geometries lying bee-ow line a-a

there Js a slight increase in diftasr pewfozmem

with increasing Mach number.

- For diffuser geometries lying close to line a-a

diffuser performance is essentially constant up

to the point of local choking.

- For diffuser geometries lying above the line a-a

diffuser performance decreases with increasing

Mach number.

3. At a given area ratio, diffuser performance, for a

given Mach num.'er, is independent of diffuser diver-

gence angle (or length ratio) for diffuser geometries

lying below the line of first appr-ciable stall. For

a given area ratio, diffuser performance will drop

off at all Mach numbers as one proceeds to geosetries

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33

lying above line a-a. The drop off in performance

increases with increasing distance above the line

a-a.

4. For a given divergence angle, diffuser performance

at any Mach number is maximum for the maxirnm area

ratio. The spread in performance as a function of

area ratio for a given divergence angle decreases

as the divergence angle is increased. At a diver-

gence angle of 31.2 degrees, diffuser performance

is uniformly low and independent of area ratio at

all Mach numbers.

5. There is no significant variation in the location

of the line of maximum performance at constant

length to inlet radius ratio, line a-a, with inlet

Mach number. For M1 - 0.25 line a-a of the present

study is virtually identical to that found in the

earlier water flow studies of McDonald and Fox2 .

6. For a given area ratio and inlet Mach number there

is an optimum length beyond which no increase in

diffuser performance is obtained.

S-~~~............... -v .- -. .. ...

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34

REFERENCES

1. Kline, -. J., Abbott, D.E., and Fox, R.W., "Opti-OnDesign of Straight Wall Diffusers," Transactionq ofASME, Journal of Basic Engineering, vol. 81, September1959.

2. McDonald, A.T., and Fox, R'.o, 'Incompressible Flow inConical Diffusers," Purdue Research Foundation, Reportno. 1, September 1964.

3. Ackeret, J., "High Speed Wind Tunnels," NACA TM 808f 1936.

4. Copp, M.R., "Fffects of Inlet Wall Contour on the Pres-sure Recovery of a 10 Degree, 10 Inch Inlet-DiameterConical Diffuser," NACA RM L51FIla, 1951.

S. Little, r.P. and Vilbur, J.S., "Performance and Boundary-Layer Data from 12 and 23 Degree Diffusers of Area Ratio2.0 at Mach numbers up to Choking and Reynolds numbersto 7.5 x 106," 11ACA Report 1201, 1954.

6. Naumann, A., "Diffuser Ffficiencies at High SubsonicVelocities," Technical Institute for Aeronautics,Aachen, Rep. no. FB 1705, March 30, 1943. (DeutscheLuftfahrtforschung, Lerlinrldershof, 1942).

7. Scherrer, R. and Anderson, F.E., "Preliminary Investi-gation of a Family of Diffusers Designed for near SonicInlet Velocities," 1IACA TN 3668, 1956.

8. Smith, R.H. and Wang, Chi-Teh, "Contracting Cones GivingUniform Throat Speeds," Journal of the PeronauticalSciences, vol. 11, no. 4, October 1944.

~- -m4.

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35

APPENDIX A

Data and Calculated Performance Paramters for

Current Investigation

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48

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49

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50

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51

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52

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53

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45

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55

APPENDIX P

Tabulation of Diffuser Performance at Selected Mach Numbers

and Cross Plots of Data Used in Plotting Performance Maps

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56

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S7

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58

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59

-' 2

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60

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61

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62

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63

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64

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k

65

Table B.1 Diffuser Performance at Selected Mach Numbers.Ta',ulated data taken from plots of CPR vs M.

Cp

N/R ARCPR2 1 M1 - 0.25 M1 - 0.55 1 - 0.70degrees

2.0 8.0 1.30 .32 .37 .43

2.0 16.0 1.64 .50 .55 .59

2.0 32.0 2.43 .68 .71 .73

4.0 4.0 1.30 .38 .40 .42

4.0 8.0 1.64 .55 .59

4.0 16.0 2.43 .71 .74

4.0 32.0 4.48 .85 .83 .84

8.0 2,.0 1.30 .38 .40 .43

8.0 4.0 1.64 .52 .54 .55

8.0 8.0 2.43 .70 .69 .69

8.0 16.0 4.48 .81 .79 .79

8.0 26.8 8.27 .86 .83 .83

15.8 2.0 1.64 .46 .41 .39

15.8 4.0 2.43 .48 .48 46

15.8 8.0 4.48 .52 .53 .51

15.8 13.4 8.27 .60 .58 .56

31.2 2.0 Z,43 .32 .22

31.2 4.0 4.48 .31 .27 .21

31.2 6.7 8.27 .32 .28 .23

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66

APPENDIX C. Method of Obtaining Performance Naps

The diffuser performance maps (contours of constant CpR

on coordinates of AR-1 vs N/R 1 ) of Figures 16, 17, and 18 have

been drawn from the cross-plots given in Appendix B; the data

used in the cross-plots is tabulated in Tables B.1.

For a given inlet Mach number the data of Table B-1 has

been plotted as CPR vs 2# at constant N/Rl. (For M1 - 0.25

these plots are shown in Figure Bl, B2 and B3 respectively.)

From each of these plots one can then obtain a series of

diffuser geometries which will yield a given value of CPR.

Consider the case of M1 - 0.25; suppose further that we are

interested in obtaining diffuser geometries for which C -

0.5. From Figure B1 we see that there are five conical

diffuser geometries for which we would expect CPR - 0.5;

from Figure 12 we obtain three additional geometries; Figure

B3 yields another five geometries. Thus the contour of CpR -

0.5 on the performance map of Figure 15 is based on a total

of thirteen points.

'By following this procedure sufficient points were

obtained to enable smooth contours of constant CPR to be

established on the performance maps.

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67

"APPENDIX D. Discussion of Diffuser Choking

The results of the present study indicate that for a

given inlet Mach number, diffuser performance may be multi-

valued, i.e. there may be a value of the inlet Mach number

for which the slope of the C vs M1 curve becomes infinite.

This is not surprising. In fact it can be shown that the-

oretically this occurs for an inlet Mach number of unity.

The diffuser performance is given by

P2S(•a- 1)

P2-P1ICPR 0T7.1l - P2P7

Treating air as an ideal gas, then P1 - IRT," and the

sonic velocity is given by c 7

Thus we can writeP 2-1•-1

C PR 2

where k is the specific heat ratic (1=1.4 for air).

In the present study the diffuser is nreceOeO by a con-

verging section (fig. 3); the flo- fror the diffuser din-

charges to the atmosphere. Thus for a given diffuser there

is a wide range of upstream staoraticn pressures which %.ill

give a throat Mach number of unity. rince, P 2 = constant,

then with M1 = 1, tbP diffuser inlet pressure, P,, can be

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68

increast-d arbitrarily by increasing the upstream stagnation

pressure; thus the slope of the CpR vs M1 curve becomes in-

finite at a value of P = 1.

The data indicate that this sudeen sharp decrease in

diffuser performance occurred at a measured inlet Mach number

less than unity (but greater than M = 0.90). This may be

expected if one considers the location of the inlet pressure

tap. For ease of construction the inlet pressure tap (for

measurement of P1) was located in the straight section of

the inlet nozzle a distance of 1.12 inches upstream of the

diffuser throat. If one considers the flow between the

pressure tap and the diffuser throat as Fanno line flow,

small frictional effects will cause relatively large in-

creases in the Mach number for a measured Mach number M 1 0.90.

That the throat velocity is sonic for M130.90 can also be

demonstrated from consideration of the one-dimensional

isentropic flow tables. For M1 - 0.90, AI/A* - 1.0088 where

A* is the flow area at which the Mach number is unity. Thus

a very small increase in the boundary layer displacement thick-

ness between the measuring station and the diffuser throat is

sufficient to give a throat Mach number of unity.

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UnclassifiedSecuulty Claafication

DOCUMINT CONTROL DATA - R&D(ftew.6ir leldNGSene*I one. be* eoif abe a hubo IK Oaidm enmo swa be enteed VAGn MW overall report #a clawudied)

I. ORIOINATIN 6 ACTIVITY (Ceni.U "OW.) I20. REPORT SECURITy C LASSIFICATION

Purdue Research FoundationJ Unclassified

Purdue University 26 GROUPNA

S. REPORT TITLE

An Experimental Investigation on the Effect of Subsonic Inlet Mach Number onthe Performance of Conical Diffusers

.DESCRIPTIVE NOTES (7." ef a ndo mW.hehe I *Technical Report - Febru=r 19

S, AUTHOR(8) (Let e. iRmee W e,

Van Dewoestine, Robert V.Fox, Robert W.

41 *PORT DATE 7a. TOTAL NO. OOF@ PAgeas 7k. NO. Or maps

February 1966 68 1 8S8. CONTRACT OR SaANtmT Smt. ORIOiNATOR'S REPORT NUMER•M5)DA-31-1?.4-AHO-D-10B

IPA, M. Technical Report IHTR-66-12ii50I3330_

9& Sb. = QM OMM (Adip ee. mnwm gWaey bev s. eedje

_.__332.4I.& A VAN ILUUTLIUTATION WqTICKS

Ib~SliIid it tldI olInea II unllu5Lte(.

I I - uPPL,. 61 IM I ,, sPOSON14 MILITARY ACTIVITYS S. Amu Research Office-Durham.

e Box CM, Duke Stationso• IDurham, N. C. 2TT06IS. A IIrlaCT

Experiments have been performed to determine the effect of subsonic inlet Machnumber on diffuser performance and flow regimes for a wide range of conicaldiffuser geometries. For incompressible flow the line of first appreciablestall is essentially that found by McDonald and Fox. As the Mach number isincreased, the flow tends more toward separation in all cases. Diffuser

rformance maps are presented for three different inlet Mach numbersI- = 0.25 0.55, 0.70). There is no significant variation in the location of

the line of rAximum performnce at constant length to inlet radius ratio withinlet Mach number.

nM1~~FRM17

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Un( Ia ..: lt.Li

KEY WORDS LINK.;A OLi*t P 1LN

Conical fliffuzersIncompressible FlowCompressible FlowFlow Regimes

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the r*Port.*=o2e. EPOR SZCNTYCLASSFICATION: Water the over (1) OOQofltiad requawst many obtain copies a( this

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7.. OTALNUERC7 PGER he ~inla for) the reseach end development. Includ"eaddreas.shouldl follow as~aal Paginatlee Procedures, Le., enter the 13. ABSTRACT: Eter" an abstract giving a buief and (actual

numer f pgescona~nng nfomaton.summary of the document indicottive, if the report. oenti th-oughnumbr o paes cntanin infrmaiomit may also appear elsewhere An the body of the techistC. re-'Ii. NUMBER OF REFEZREMCZ Enter the total nI.mbir f port. If addititonal space is required, a continuation sheetreferences cited in the report. shall be attach"d.4a. CONTRACT Of GRANT NUMBER: If appropriate, . ter It is highly detirable that the abstract af clossllld rv-the fVplicable nmbcr of the contract or Von( under wbich parts bo %aclaaaified. Each paragraph of the abstiect shallthe report Was Written, end with an indication of thet military *&curlyr classuiflcotion8b, ft. & Od. PROJECT HUM80L Enter the appropricoo of the Information in the, paroshraih. ireprosonteo tor f S), (S).mlitary doeprtabent idsentificatio.s such as project nmbei~r. (C). o4. (U)).ettbp-njoci numrbo-, systes numbers, taok number. tcI. The.-e is ro limitatio.on imt"e length of the abstract. H-ow-f e. ORIGItNATOR'S REPORT NIVWBER(S): Enteir the o~fj. ever, the suggesteA length is frocm ISO) to 22S worda.dcis report isusplvi by which the document will be Identified 14. K1YV WORD)S: Key words are technically meatningful teriý,%sand controllen I-. !ha originating &ctivity. This nujmber ;auxl or short l&hrsss that characeterize a reiwitl and may be used asbe undque to this rejiot. index entries (ov csamD'optin the report. Key words must be

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