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NASA Contractor Report 4294

Supersonic Wind Tunnel Nozzles

A Selected, Annotated Bibliography

To Aid in the Development of Quiet

Wind Tunnel Technology

Stephen W. D. Wolf

MCAT Institute

Moffett Field, California

Prepared for

Ames Research Center

under Cooperative Agreement NCC2-604

National Aeronautics and

Space Administration

Office of Management

Scientific and Technical

Information Division

1998

CONTENTS

Introduction ......................................................................... l

Ordering Information .................. ..................................... 3

Bibliography ....................................................................... 5

Author Index ....................................................................... 69

Subject Index ...................................................................... 73

Corporate Source Index ................................................. 77

Acknowledgements

The financial support of the Fluid Dynamics Research Branch at NASA Ames Research Center

under Cooperative Agreement NCC2-604 is hereby acknowledged. The assistance of the staff

at the NASA Ames main library in the locating of literature for this bibliography has been

exceptional. The compilation of this bibliography would not have been possible in just 10

months without the tutoring of Mrs. Marie Tuttle (A librarian at NASA Langley Research

Center) over many years.

...

1|1

PRECEDING PAGE BLANK NOT FILMED I_G|_INTENTIONALI:.Y BLP,_K
iv
INTRODUCTION

This publication contains 298 citations related to supersonic nozzles, in particular, those used

in wind tunnels. The main purpose of this bibliography is to list available publications that may

be helpful to persons engaged in the design and development of Quiet supersonic nozzles. The

term Quiet requires some explanation here and refers to the minimization of disturbances and

nonuniformity in supersonic flows within the confines of a wind tunnel.

We achieve this minimization of tunnel disturbances by striving for uniform free stream flow

and laminar boundary layers on the nozzle walls. Consequently, the design of Quiet supersonic

nozzles requires understanding of settling chamber/contraction design and high speed transition in

addition to the other well known aspects of nozzle design. We have used our interpretation of

modern nozzle design requirements to decide which publications to include in this bibliography.

We have included those papers concerned only with the attainment of supersonic Mach

numbers (1 < Moo < 5) at the nozzle exit. However, as we learn more about supersonic transition,

I am sure we will find that this range is too large and needs to be subdivided. We concentrate this

bibliography on the lower end of the supersonic range for two reasons. First, testing in this Mach

number range still holds many aerodynamic unknowns and secondly, the next generation of

supersonic transports will undoubtedly operate in the Mach 2 to 3 range.

We include some interesting historical material dating back to the early days of supersonic

research during the 1920s. Of course, many of the old reports are now unavailable and the

bibliography starts with a 1926 paper by Stanton from the National Physical Laboratory in

England. The Laval nozzles used in a steam turbine in about 1925 were the first supersonic

nozzles ever built. However, the Laval nozzle alone was not adequate for use in supersonic wind

tunnels, since the aerodynamicist requires uniform flow in the test section. It was not until after

Prandtl and Busemann applied the Method of Characteristics to nozzle design in 1929, that the

classical supersonic nozzles, we are familiar with to-day, began to appear. Initially the emphasis

on nozzle design was to achieve the desired Mach number at the test section entrance. Work by

Laufer in the 1950s and 1960s lead to a change in this initial emphasis. Now we require a

supersonic nozzle design to produce a low disturbance flow at the desired Mach number. The era

of Quiet supersonic nozzles had arrived and will remain with us.

The design of a Quiet supersonic nozzle is still the subject of considerable research. The

most notable work of recent times has come from Beckwith and his co-workers at NASA Langley

Research Center. Their approach seems successful for Mach numbers of 3.5 and above. However,

widespread acceptance of their approach has yet to occur. We hope to provide a complete

overview of supersonic nozzle research and development, past and present, by covering most

aspects in this bibliography.

Obviously we have references to Quiet supersonic nozzle design, but we also include

references to nozzle design studies for rocket engines and chemical lasers. All the many different

types of nozzles are considered although, of course, the axisymmetric and planar (two-dimensional)

types are the most popular for wind tunnels. Several computer programs are included in the

papers to allow readers to quickly design their own nozzles. We provide citations on engineering

studies of different nozzle types which discuss such topics as nozzle contour accuracy and

adjustments, and achievable wall smoothness.

We include citations on numerous nozzle flow analyses which consider the three flow regimes

within a supersonic nozzle and its contraction. These analyses have allowed numerous test

phenomena to be explored perhaps simpler than by experiment. The vast amount of experimental

data on supersonic nozzles is well documented in this bibliography. The associated experiments

involve advanced topics like nozzle wall cooling and heating as well as the essential calibration

procedures. Measurements in supersonic wind tunnels are covered in this bibliography to show

what can and has been learnt about a nozzle once it is constructed.
Finally, the design and operation of supersonic wind tunnels is included for both historical

and practical reasons. These citations give a feel for the experience gathered on supersonic nozzles

in the practical sense. These citations also show the obvious age of most of the supersonic tunnels

in operation to-day.

The bibliography arrangement throughout is chronological by date of publication. However

there are some exceptions. Firstly, papers presented at conferences or meetings are placed under

dates of presentation. Secondly, English translations of papers are placed with the original citation

regardless of publication date for clarity. These rules mean this bibliography also serves as a

history of the development of supersonic nozzles and wind tunnels. We have included author,

subject, and corporate source indexes at the end of the bibliography. In most cases, authors'

abstracts are used. However, in some instances we did take license to shorten existing abstracts or

write abstracts for those citations we found had no abstract.

We hope that the all the citations can be obtained through normal library services. If no

abstract accompanies a citation this should be taken as an indication that the associated paper has

not yet been located by the compiler. This does not mean that the paper is unavailable. For

example, some normally easy to locate NASA/NACA references are currently unavailable to the

compiler due to earthquake related library problems. Identifying information, including accession

and report numbers when known, is included in the citation in order to simplify library requests.

Please note, that some of the citations have restrictions on distribution. These restrictions are

stated with the relevant citations.

This bibliography is our first attempt at collating the vast number of citations related to

supersonic nozzles and wind tunnels. This bibliography has come about because of the huge

wealth of knowledge we have found in the literature. This bibliography reflects the major changes

in supersonic nozzle design and uses since the 1950s. Subsequent bibliography updates are planned

and we would be most grateful for any assistance with corrections or additions to this bibliography.

Please write in the first instance to:

Dr. Stephen Wolf

Mail Stop 260-1

NASA Ames Research Center

Moffett Field

CA 94035- 1000, USA
Ordering Information

To assist with locating the citations in this bibliography, ordering information for the different

types of materials is given below:

Acquisition Number Type of Material Where Obtained

A??-?????

(Example:

A88-12345)

AIAA papers and

worldwide published

literature from

conferences and

periodicals available from AIAA.

Technical Information Service

American Institute of Aeronautics

and Astronautics (AIAA)

555 West 57th Street, 12th Floor

New York, NY 10019

USA

N??-?????

(Example:

N77-12345)

Report literature

with no distribution

limitations.

National Technical Information

Service (NTIS)

5285 Royal Port Road

Springfield, VA 22161

USA

X??-?????

(Example:

X66-12345)

Report literature

with distribution

limitation of some

type.

NASA Scientific and Technical

Information Facility (STIF)

PO Box 8757

B.W.I. Airport, MD 21240

USA

AD-??????

ATI-??????

(Example:

AD-123456)

Report literature

which has been

declassified

Defense Technical Information

Center (DTIC)

Defense Logistics Agency

Cameron Station

Alexandria, VA 22304

USA

N-?????? Pre- 1962 reports

and papers.

NASA Libraries

(Example: Books Libraries

TL 123 C66)

Please note that an "#" after and acquisition number (for example A66-12345#) indicates that the

document is available in microfiche form for your convenience.

Bibliography

1. *Stanton, T.E.: On the Flow of Gases at

High Speeds. Proceedings of the Royal Society

- Series A, vol. 111, July 1926, pp. 306-339.

In a 1916 paper on the discharge of gases under

high pressures, the late Lord Rayleigh called

attention to the deficiencies in the present state

of knowledge of the characteristics of the flow

of gas, from a vessel in which it is compressed,

through an orifice into the atmosphere or into a

receiver at a lower pressure. This paper

describes some of the first documented

experiments on high speed jets formed by

convergent-divergent nozzles. It was concluded

that Prandtl's theory was inadequate to account

for, at any rate, all the wave characteristics

observed.

*Engineering Department, National Physical

Laboratory, UK.

6. Busemann, A.: Orifices, Nozzles and

Diffusers. In: Handbook of Experimental

Physics, vol. 4 - Gas Dynamics - Part 3, 1931,

pp. 383-407, 26 refs. In German. English

translation is RTP Translation no. 2209 by the

British Ministry of Aircraft Production.

5070 247

(Ames Research Center library no.)

This early work reviews the theory of nozzle

flows and compares results with experiment.

The effects of condensation are considered. Jet

impulse and Carnot shock losses using Laval

nozzles are evaluated.

7. Karner, L.; and Ackeret, J.: Aeronautical

Education and Research at the Swiss Institute

of Technology in Zurich. NACA TM-616,

1931.

2. *Stanton, T.E., High-Speed Wind Channel

for Tests on Airfoils. ARC R&M 1130, 1928.

*Engineering Department, National Physical

Laboratory, UK.

3. *Briggs, L.J., and Dryden, H.L.:

Aerodynamic Characteristics of Twenty-Four

Airfoils at High Speeds. NACA Report 319,

1929.

*Langley Memorial Aeronautical Laboratory,

Langley Field, Virginia, USA.

8. *Bailey, A.; and Wood, S.A.:

Induced Wind Tunnel. British

1468, May 1932.

High Speed

ARC R&M

*National Physical Laboratory, Teddington,

UK.

9. *Stack, J.: The NACA High-Speed Wind

Tunnel and Tests of Six Propeller Sections.

NACA Report 463, 1933.

*Langley Memorial Aeronautical Laboratory,

Langley Field, Virginia, USA.

4. Prandtl, L.; and Busemann, A.:

Approximate Method of Graphically Solving

Problems of Two-Dimensional Supersonic

Flows. Stodola Festschrift, 1929, pp. 499-509.

In German.

10. Frankl, F.I.: Supersonic Flows with Axial

Symmetry. Izvestia Art, Akademii RKKA,

vol. 1, 1934. In Russian.

5. *Stanton, T.E.: The Variation of Velocity

in the Neighbourhood of the Throat of a

Constriction in a Wind Tunnel. ARC Report

N1388, 1931.

*Engineering Department, National Physical

Laboratory, UK.

11. *Santon, L.: Experimental Contribution to

the Study of Supersonic Wind Tunnels.

Publication Scientifiques et Techniques du

Ministere de l'Air Publication no. 68, .1935. In

French. English translation is RTP Translation

no. 1942 by the British Ministry of Aircraft

Production, 60 pp, 15 refs.

5341 310

(Ames Research Center library no.)

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IBIL_.....INI[NIII)fl ALL_ B_NK
I have undertaken the task of achieving

systematicallyvelocities lying between1 and

2.5 times the velocity of sound, and of

determining the laws governing their

development.Oneof the main obstaclesto the

attainmentof supersonicstreamsof high order,

which are of great interest practically, is the

very high powerrequired;I havethereforepaid

particular attention to the energyside of the

question. I have determined by systematic

trials, the bestshapeof funnel (nozzle),I have

shown especially the case with which the

supersonic stream can diverge and the

impossibility of its converging at all rapidly.

Avoiding the useof the free stream,which is

extravagantin powerrequirementsand liable to

irregularities, I havedevisedpractical funnels

giving velocitiesbetween1.2and 2.5 timesthe

velocity of sound. I have then introduced

obstacles(both cylindrical and plane)into the

funnels, firstly for optical examinationof the

flow and then for measurementsof resistance.

I obtainedan important resultwith a hot-wire

anemometerthat when the velocity increases

beyond 0.8 times the velocity of sound, the

fluid heats the hot-wire further instead of

coolingit.

*Consultantto the Ministry of Air, France.

12. Crocco, L.: High SpeedWind Tunnels.

In: L'Aerotecnica, 1935. In Italian. English

translation is USAAC, Material Command,

AMC Translation no. 366, July 1943.

13. Idelchik, I.E.:

of Wind Tunnels.

In Russian.

Investigation of the Nozzle

TsAGI Report no. 80, 1935.

14. Ackeret, J.: High Speed Wind Tunnels.

Presented at the 5th Convention of the Volta

Congress, Italy, September 30 - October 6,

1935. In German. English translation is NACA

TM-808, November 1936, 47 pp.

High-speed wind tunnels are of practical as

well as theoretical value for the solution of

certain aerodynamic problems. The design of

high-speed wind tunnels is reviewed. Different

tunnel drive systems are discussed. The

supersonic wind tunnel in Zurich is described

as an example of current state of the art in

high-speed wind tunnel design.

25. Ferri, A.: Investigations and Experiments

in the Guidonia Supersonic Wind Tunnel.

NACA TM-901, 1939.

26. Kurzweg, H.H.: Report on the Supersonic

Wind Tunnels of the Army Research Station at

Peenemunde. Peenemunde Archives Report no.

66/11, June 1939, 52 pp. In German. English

translation is DTIC ATI- 1812.

17. *Kisenko, M.S.: Comparative Results of

Tests on Several Different Types of Nozzles.

TsAGI Report no. 478, 1940. In Russian.

English translation is NACA TM-1066, June

1944, 44 pp, 4 refs.

This paper presents the results of tests

conducted to determine the effect of the

constructional elements of a Laval nozzle on

the velocity and pressure distribution and the

magnitude of the reaction force of the jet. The

effect was studied of the shapes of the entrance

section of the nozzle and three types of

divergent sections: namely, straight cone,

conoidal with cylindrical end piece and diffuser

obtained computationaily by a graphical method

due to Professor F. I. Frankl. The effect of

divergence angle of the nozzle on the jet

reaction was also investigated. The results of

the investigation showed that the shape of the

generator of the inner surface of the entrance

part of the nozzle essentially has no effect on

the character of the flow and on the reaction.

The nozzle that was obtained by graphical

computation assured the possibility of obtaining

a flow for which the velocity of all the gas

particles is parallel to the axis of symmetry of

the nozzle, the reaction being on the average of

2 to 3 percent greater than for the usual conical

nozzle under the same conditions. For the

conical nozzle, the maximum reaction was

obtained for a cone angle of 25 ° to 27 ° . At

the end of this paper a sample computation is

given by the graphical method. The tests were

started at the beginning of 1936 and this paper

was written at the same time.

*Central Aero-Hydrodynamic Institute

(TsAGI), Khukovsky, USSR.

18. *Lehnert, R.: Report on Three Component

Measurements of a Model of A-4 in the

Supersonic Wind Tunnel of the Army Research

6
Station Peenemunde. Peenemunde Archives

Report no. 66/33, October 1940. 37 pp. In

German. English translation published by

Office of Naval Intelligence, Technical

Intelligence Center, 1947.

5375.5 A-4/1

(Ames Research Center library no.)

Model A-4 (V2 rocket) with tail assembly was

to be investigated concerning its aerodynamic

properties during flight within the region close

to the speed of sound. The investigations

within the velocity range of v=14 to 46 m/sec.

were conducted by the Zeppelin Aircraft

Construction Co. at Friedrichshafen. The

results are available in test report 600/164.

These investigations were continued from high

subsonic velocities to 2.5 times the speed of

sound in the Peenemunde supersonic wind

tunnel. The measurements provides the

aerodynamic coefficients Ca .and C w as basis

for the calculation of trajectories, as well as the

position of the center of pressure.

*Peenemunde Army Research Station, Germany

19. Hermann, R.: The Supersonic Wind

Tunnel of the Heerswaffenamt and Its

Application in External Ballistics.

Peenemunde Archives Report nos. 66/0 and

66/11, December 1940, 54 pp. In German.

English translation is DTIC ATI-1801, June

1945.

The supersonic tunnel of the Heerswaffenamt

was constructed to facilitate the development of

spin- and fin-stabalized projectiles. The use of

a supersonic tunnel for this purpose is a

relatively recent undertaking; how much such

work can contribute to this development is not

generally realized even now. This paper

describes the supersonic tunnel, the most

powerful and best equipped in Germany, and

gives some experimental results. The first part

includes a discussion of the various types of

supersonic tunnels, and the principles upon

which the present tunnel operates are

described. The fundamental considerations

governing the choice of methods of

measurement and the size of equipment are

given. There follows a detailed technical

description of the installation and the

measuring equipment. The second part of this

paper contains preliminary experimental results

which were obtained in the wind tunnel and

concern problems in external ballistics. Fin

stabilization, aerodynamic resonance

frequencies and aerodynamic damping all

problems that arise in connection with the

stabilization of non-rotating projectiles at

supersonic velocities - these are clarified by

means of Schlieren photographs, three

component force measurements, and oscillation

records obtained on a model of a fin grenade at

M -- 1.4 and 1.8. Finally, Schlieren

photographs, and the results of measurements

of the aerodynamic forces on a non-rotating

model of a 15cm Skoda grenade, are presented

for the same Mach numbers.

20. Busemann, A.: Laval Nozzles for

Uniform Supersonic Flow. Zeltschrift VDI,

vol. 84, no. 45, November 1940, pp. 857-862.

In German. English translations are RTP

Translation no. 2511, by the British Ministry of

Aircraft Production, and NACA TT-152, June

1941 (Langley Research Center library no. 6410

907).

On the basis of Schlieren (refraction) pictures

there are treated from the estimates of

experience of gas dynamics, those sections

which are applicable to the flow in steam

turbines. At the mid-point stands the flow in a

Laval nozzle. The behavior of supersonic flow

has the result that, in the widened part of the

Laval nozzle, a jet with curly velocity

distribution is ordinarily formed. Only by the

use of particular measures in the shaping of the

nozzle, for which a definite minimum length is

necessary, is there success, even for supersonic

flow, in flattening out the velocity distribution

to such a point that it becomes useful for highvelocity canals. The viewpoints which are

decisive in this are given. Moreover, the

nozzles with oblique sections and the

occurrence of compression shocks are treated

21. *Heybey, W.H.: The PrandtI-Busemann

Method for the Graphical Evaluation of 2-D

Super. Flow. Its Application to the Design of

Wind Tunnel Nozzles and the Appropriate

Corrections. Parts I, II, and III. Peenemunde

Archives Report no. 66/56, February 1941, 112

pp, 8 refs. In German. English translation by

Cornell Aeronautical Laboratories is DTIC

ATI-1855, August 1946. An English translation

of Part III only ( Peenemunde Archives Report
no. 66/36g) is North American Report AL1715, May 1953.

DTIC ATI- 1855

This is a three part paper. Part I consists of an

exhaustive treatment of the fundamentals of

two-dimensional inviscid supersonic flow

theory developed by Prandtl and Busemann.

Part II discusses the practical application of the

Method of Characteristics in two-dimensional

supersonic nozzle design and construction.

Since the graphical method is an approximate

method which, in addition, assumes inviscid

flow, the wind tunnel nozzles developed by

this method will not provide the required flow

pattern. The literature has nothing to say

concerning the corrections which are necessary

because of these errors. Part III shows how,

using the basic concepts of the PrandtlBusemann method and considering the effect of

the wall boundary layers, such a correction may

be carried out.

*Wasserbau-Versuchsanstalt, Kochel, Germany.

22. *Berthold: Research on the Design of a

Continuous-Operation Wind Tunnel for

Subsonic and Supersonic Velocities with

Maximum Possible Efficiency. Peenemunde

Archives Report no. 66/41, May 1941, 28 pp.

In German. English translation by Cornell

Aeronautical Laboratory is included with

original report in DTIC ATI-1841, April 1946.

DTIC ATI- 1841

Several types of supersonic nozzles, exit cones,

fixed and flexible diffusers were tested to find

the most efficient and versatile arrangement for

the continuous-operation wind tunnel. A

closed chamber would show the least losses, but

the models would be hard to reach. To prevent

the formation of perpendicular pressure waves,

the best exit cone would have to have the same

contour as the supersonic nozzle. In this way,

most of the speed energy would be recovered

and converted into pressure again.

*Wasserbau-Versuchsanstalt, Kochel, Germany.

23. Seippel, C.: Supersonic Wind Tunnels.

The Brown Boveri Review, voi. 30, no. 7/8,

August 1943, pp. 178-183, 1 ref.

The flow of air at speeds above sound is

essentially different from that below sound and

requires special supersonic wind tunnels for

investigation. Whereas the older installations

could be operated intermittently only, there are

to-day plants which can be operated

continuously, and which are bringing a valuable

contribution to the science of ballistics,

aeronautics and turbo-machinery design.

24. Green, J.R.; and Southwell, R.V.:

Relaxation Methods Applied to Engineering

Problems. Part IX. High-Speed Flow of

Compressible Fluid Through a TwoDimensional Nozzle. Philosophical Transactions

of the Royal Society of London - Series A.

Mathematical and Physical Sciences, vol. 239,

no. 808, April 1944, pp. 367-386, 8 refs.

Methods developed in Parts IlI and V of this

series are here extended to the more difficult

problem of compressible fluid moving at high

speed through a converging-diverging nozzle.

Solutions of sufficient accuracy for practical

purposes can be obtained for a nozzle of any

specified shape, provide that the velocity of the

fluid nowhere exceeds the local speed of sound.

Otherwise the computed velocities fail to

converge - a result similar to what was

obtained by Taylor and Sharman using an

electrical tank. The reason for this failure is

discussed, and an alternative method (not in

itself entailing the 'relaxation' technique) is

proposed to meet this difficulty. In a

subsequent paper this will be applied to

determine the supersonic regime.

25. *Freidrichs, K.O.: Theoretical Studies on

the Flow Through Nozzles and Related

Problems - Applied Mathematics Panel 82.1R.

New York University AMG-NYU report no.

43, April 1944.

*Institute for Mathematics and Mechanics, New

York University, New York, USA.

26. *Shapiro, A.H.: Nozzles for Supersonic

Flow Without Shock Fronts. Presented at the

ASME Annual Meeting, November 29 -

December 3, 1943. Journal of Applied

Mechanics, vol. 11, no. 2, June 1944, pp. A93-

A100, 7 refs.
Flow patterns for compressible fluids at

supersonicvelocities are discussed,and it is

shown that shock fronts form when

neighboring Mach lines (envelopes of wave

fronts originating from point disturbances)

intersect. A criterion for divergence of Mach

lines is developed for cases in which the

passage is symmetrical in two or three

dimensions and has a straight axis. This

criterion is used as the basis for designing

supersonic nozzles and diffusers. The analysis

indicates that only a nozzle of infinite length

can discharge a parallel stream into a tube of

constant cross section without the formation of

shock fronts. Methods are presented fro

designing nozzles of finite length, with the

intensity of shock fronts reduced to as small a

value as possible, and it is shown that nozzles

of reasonable length may be designed so that

shock fronts are insignificant. Experimental

observations indicate that the proposed method

of nozzle design is a practical one. With regard

to supersonic diffusers having a straight axis, it

is shown that shock fronts cannot be avoided,

even though the diffuser is of infinite length.

However, the methods of this paper may be

used as an aid in determining the best diffuser

design.

*Department of Mechanical Engineering,

Massachusetts Institute of Technology, USA.

27. *Puckett, A.E.: Final report on the Model

Supersonic Wind Tunnel Project. NDRC-AOA-269, July 1944, 120 pp, 17 refs.

5341 CIT/15

(Ames Research Center library no.)

A small-scale supersonic tunnel has been

designed, constructed and operated with a

working section of 2.50 x 2.56 in. Its

characteristics have been investigated

completely at Mach numbers of 2.0 and 3.2, at

which speeds the phenomena are representative

of the operating range. Preliminary tests have

been made with a nozzle designed for a Mach

number of 4.4, indicating that Mach numbers

of this order may be used for model testing.

Data necessary for the engineering design of a

large-scale supersonic tunnel have been

obtained and are given in detail. An optical

system has been developed with which highspeed schlieren photographs may be made of

the flow in the tunnel. A model support

system and balance system have been developed

which will permit force and pressure

measurements to be made on a model supported

in the tunnel at the same time that the flow is

being observed optically.

*California Institute of Technology, Pasadena,

California, USA.

28. Fox, L.; and Southwell, R.V.: On the

Flow of Gas Through a Nozzle with Velocities

Exceeding the Speed of Sound. Proceedings of

the Royal Society - Series A, vol. 183, no. 992,

August 1944, pp. 38-54, 5 refs.

An iterative method outlined by Green &

Southweil (1944), but not applied in their paper

for the reason that it makes no use of

'relaxation methods', is here applied to

determine the supersonic regime for gas

flowing irrotationally through a convergentdivergent nozzle, i.e. that (unique) regime in

which the pressure and density of the gas

decrease continuously in its passage from end

to end. Osbourne Reynolds's approximate

treatment of the problem (1886) assumed the

velocity to be distributed uniformly over each

cross-section, and in consequence found a

unique value for the limiting mass-flow,

whether the velocity be subsonic or supersonic

downstream of the 'throat' (upstream it is

always subsonic). Here, a more exact treatment

shows that the supersonic value is very slightly

(0.045%) greater than the subsonic value, which

Reynolds's theory overestimates by 0.083%. the

two regimes of course imply two different

values of the pressure at exit, and for

intermediate pressures (on the assumptions of

this paper) there is no solution of the problem.

Even in the subsonic regime (when the mass

flow is critical) velocities exceeding the local

speed of sound are attained in regions

adjoining the nozzle walls near the throat.

29. *Freidrichs, K.O.: On Supersonic

Compressors and Nozzles. Applied Mathematics

Panel report 82.2R. New York University

AMG-NYU Report no. 77, October 1944.

*Institute for Mathematics and Mechanics, New

York University, New York, USA.
30. *Stack, J." Compressible Flows in

Aeronautics. The 8th Wright Brothers Lecture,

December 1944. In: Journal of the

Aeronautical Sciences, vol. 12, no. 2, April

1945, pp. 127-148, 34 refs.

This lecture considers the position of

aerodynamics in the general aero-thermohydrodynamic field and briefly reviews some

of the early high speed research and wind

tunnels. Aeronautical engineering problems

and developments are discussed, in particular

the effect of compressibility on control surface

effectiveness. The lecture concludes, "Much

remains ahead as the problem of increasing

speed is solved to the achievement of clockstopping speeds in east-to-west flight."

*Langley Memorial Aeronautical Laboratory,

Langley Field, Virginia, USA.

3q. Lukasiewicz, J.: Design and Calibration

Tests of a 5.5 inch Square Supersonic Wind

Tunnel. ARC R&M 2745, 1945.

32. *Eber, G.R.: The Supersonic Wind Tunnel

of Wasserbau-Versuchsanstait Kochelsee.

Peenemunde Archives Report no. 66/182, June

1945, 57 pp. In German.

DTIC ATI- 1962

The report describes the planned construction

of a supersonic wind tunnel. Special attention

is given to the following subjects: layout of the

wind tunnel, arrangement of the installation

views of the models, of the range of

measurements, theoretical pump performance in

comparison to the theoretical tunnel

performance, distribution of blowers in the

exhaust installation, data of the airdry unit,

data for the engine, and assembly drawings of

the test room.

*Wasserbau-Versuchsanstalt

G.m.b.h., Kochel, Germany.

Kochelsee

33. *Hermann, R.: The Efficiency of the

Supersonic Wind Tunnel Installation of

Wasserbau- Versuchsanstalt Kochelsee.

Peenemunde Archives Report no. 66/183, June

1945, 18 pp. In German.

DTIC ATI- 1963

*Wasserbau-Versuchsanstalt

G.m.b.h., Kochel, Germany.

Kochelsee

34. *Atkin, A.O.L.: Two-Dimensional

Supersonic Channel Design - Part I. ARC

9194, Novembgr 1945, 12 pp, 3 refs. Also:

ARC R&M 2174, 1946.

534 ! 238a

(Ames Research Center library no.)

A method of designing channels to convert

uniform supersonic flow of any Mach number

into uniform supersonic flow of any other

Mach number is given. The theory is exact,

neglecting the boundary layer, and tables are

given enabling all parts of the channels to be

calculated quickly with high accuracy. Use is

made of construction of transforming divergent

radial flow into a uniform stream, first given

by Busemann in 1931; an exact analytic

expression has been found for this method.

The method of "analytical characteristics" used

in the present paper can be applied to any type

of supersonic flow and is not restricted to

purely radial flow. Finally in the Appendix

details of the calculations involved are given.

Symmetrical channels only have been

considered but any two walls which give the

same velocity along the axis can be used.

*Aerodynamics Division, National Physical

Laboratory, Teddington, UK.

35. *Eaton, A.R.; and Bradfield, W.S.: Report

on Calibration Methods for Supersonic Wind

Tunnel Nozzles M=1.25, 1.50, 1.75, 2.00, 2.25,

and 2.50. John Hopkins University APLJHU/CM-144, November 1945, 33 pp.

This paper describes the Daingerfield wind

tunnel facilities, including the design and

construction of eight nozzles. The test section

size is 15" by 20" for one-blower operation and

19" by 27 1/2" for two-blower operation. The

methods of calibrating the nozzles are

discussed.

*Lone Star Laboratory, Daingerfield, Texas,

USA.

10
36. *Pinkel, I.I.; and Shames, H.: Supersonic

Nozzle Design Procedure. Presented at

NACA/AERL Advanced Topics in Supersonic

Flow Seminar. Lecture no. 7, 194._____fi6, 7 pp.

5341.1 41

(Langley Research Center library no.)

This paper presents a solution to the problem

of transforming a parallel one-dimensional flow

of sonic velocity into a parallel onedimensional flow of supersonic velocity. The

method is applicable to two-dimensional

asymmetric nozzle designs.

*Flight Propulsion Research Laboratory,

Cleveland, Ohio, USA.

37. *Ferri, A.: Application of the Method of

Characteristics to Supersonic Rotational Flow.

NACA Report 841, 1946, 12 pp, 12 refs.

A system for calculating the physical properties

of supersonic rotational flow with axial

symmetry and supersonic rotational flow in

two-dimensional field was determined by use

of the characteristics method. The system was

applied to the study of external and internal

flow for supersonic inlets with axial symmetry.

For a circular conical inlet the shock that

occurred at the lip of the inlet and became a

normal shock at the axis. The region in which

strong shock occurred increased with the

increase of the angle of the internal cone at the

lip of the inlet. For an inlet with a central

body, the method of characteristics was applied

to the design of an internal-channel shape that

theoretically, results in a very efficient

recompression in the inlet; it was shown that if

an effuser is connected with the diffuser a

body of revolution with very small shock-wave

drag can be determined.

*Langley Memorial Aeronautical Laboratory,

Langley Field, Virginia, USA.

38. Frossel, W.: Experimental Investigation of

the Compressible Flow At and Near a

Cambered Wall Part IV Nozzle Flow.

January 1946, 33 pp. In German. English

translation is DTIC ATI- 102029.

DTIC ATI- 102029

39. *Fejer, A.A.: Report on Discussion with

German Engineers and Scientists - Supersonic

Air Flow Research. PMR-359-0-2, May 1946,

4 pp.

DTIC ATI-3734

On May 13, 1946, a group of Packard engineers

interviewed German scientists from

Peenemunde in regard to high speed flow

problems and problems associated with

experimental flow research. The problems

connected with the design and manufacture of

supersonic nozzles were discussed with Dr.

Hermann and other members of his old

research group. In addition effects of

condensation and the development of nonintrusive measurement techniques (in particular

X-ray and sonic wave techniques) were

discussed. Of immediate interest were for

instance, Dr. Hermann's statements concerning

the required accuracy limits of supersonic test

nozzles and Dr. Goethert's comments on the

significance of boundary layer removal in the

transonic range of flight.

*Packard Motor Car Company, Aircraft Engine

Division, Toledo, Ohio, USA.

40. *Foelsch, K.: A New Method of Designing

Two-Dimensional Lavai Nozzles for a Parallel

and Uniform Jet. NA-46-235-2, May 1946, 50

pp, 4 refs.

6410 1071

(Ames Research Center library no.)

A graphical method for the determination of

the contours of a two-dimensional nozzle for

effecting ideal expansion of gases to a uniform

parallel jet was developed by Prandtl and

Busemann. The present report develops an

analytical solution to the problem to eliminate

the labourious graphical construction and the

graphical error inherent in the former method.

Mathematical equations are developed which

permit the immediate determination of the

coordinates of any streamline in point source

flow. The equations are extended to permit

solution of the flow from the parallel throat

section of the Laval nozzle.

*Engineering Department, North American

Aviation, Inc., lnglewood, California, USA.

11
42. *Emmons, H.W.: The Theoretical Flow of

a Frictionless Adiabatic Perfect Gas Inside of a

Two Dimensional Hyperbolic Nozzle. NACA

TN-1003, May 1946, 54 pp, 10 refs.

A series of solutions for the two-dimensional

flow of a frictionless, adiabatic, perfect gas

inside of a hyperbolic nozzle have been

presented. These solutions show an almost

continuous transformation of known subsonic

solutions to the known subsonic-supersonic

solution. From this report it can be concluded

that for the corresponding two-dimensional

problem, a perfect fluid theory supplemented

with shock waves is still not enough. For

adequate check with experiment, a theory must

be based upon a fluid with friction (at least in

the regions near the walls; in other regions

friction would have no effect). Solutions with

this imperfect fluid involve a prohibitive

amount of labor with present computing

techniques.

*Harvard University,

Massachusetts, USA.

Cambridge,

42. Bibliography on German Supersonic

Research. USAF AMC Bibliography-l, June

1946, 118 pp, 784 refs (approx.).

DTIC AD-B953385

This Bibliography supersedes the preprint

published in March 1946, listing captured

German documents on supersonics and closely

related data which are available at the Air

Documents Division of Intelligence, T-2, at

Wright Field, Dayton, Ohio. Topics covered in

this extensive Bibliography include supersonic

aerodynamics (theory, experiments, heat

transfer, wind tunnels), transonic aerodynamics

(theory, experiments, testing techniques), power

plants (including Laval nozzles), development

of jet and rocket propelled planes and missiles,

and boundary layer theory and experiments.

No abstracts are given. Many of the titles are

in German.

43. *Smelt, R.: A Critical Review of German

Research on High-Speed Airflow. The 696th

Royal Aeronautical Society Lecture, October

1946. In: The Royal Aeronautical Society

Journal, vol. 50, 1946, pp. 899-934.

This lecture examines the German work on the

compressibility phenomena intensified by the

need to develop high-speed fighters and jet

propulsion. The appearance of the V2 in

England was evidence of a considerable

background of knowledge of supersonic

aerodynamics. This review concentrates on the

highlights of the German work, in particular

those aspects which have given strong

confirmation of our own ideas or have

modified greatly our line of attack on the

compressibility problem. German high-speed

wind tunnels are described. In supersonic

research, the German contribution to

sweepback and low aspect ratio wings is

discussed. It is concluded that German

progress was hampered by a lack of cooperation

between aircraft manufacturers and the

research organizations. Consequently, the

Germans have given the British research

worker a whole series of suggestions for highspeed aircraft which are almost entirely untried

or inadequately tried in flight.

*Gas Dynamics Department, Royal Aircraft

Establishment, UK.

44. *Puckett, A.E.: Supersonic Nozzle Design.

Journal of Applied Mechanics, vol. 13, no. 4,

December 1946, pp. A265-A270, 8 refs.

A two-dimensional flow field in which the

velocity is everywhere supersonic can always be

represented approximately by a number of

small adjacent quadrilateral flow fields in each

of which the velocity and pressure is constant.

These quadrilaterals must be separated by lines

representing waves in the flow; changes in

velocity and pressure through any wave can be

computed. By increasing the number of small

area into which the complete flowfield is

divided, the accuracy of this approximation

may be increased without limit. This

constitutes the "method of characteristics"

solution, which has been known for many

years. This method may be applied to the

graphical computation of flow in a supersonic

nozzle, with the particular aim of producing

uniform supersonic flow at the end of the

nozzle. It is pointed out that such a

computation is essentially simple and rapid, and

its essential features are presented in a form

which, it is hoped, may be easily applied to

engineering problems.

12
*California Institute of Technology, Pasadena,

California, USA.

45. *Heybey, W.H.: Nozzle Design and

Correction for Two Dimensional Supersonic

Flow. NOL Memo 9132, 1947.

*US Naval Ordnance Laboratory, White Oak,

Maryland, USA.

46. *Liepmann, H.W.; and Puckett, A.E.:

Introduction to Aerodynamics of a

Compressible Fluid. Chapter 13 - The Method

of Characteristics. Published by John Wiley

and Sons Inc., 1947, pp. 210-232.

TL 573 L5

(Ames Research Center library no.)

This chapter examines first compressible flow

along a single wall and then progresses to the

flow between two walls. A section on

supersonic nozzle design discusses the

application of the method of characteristics.

*Guggenheim Aeronautical Laboratory,

California Institute of Technology, Pasadena,

California, USA.

47. Sauer, R.: Method of Characteristics for

Three-Dimensional Axially Symmetric

Supersonic Flows. English translation of

unpublished August 1940 German paper.

NACA TM-II33, January 1947, 36 pp, 6 refs.

An approximate method for three-dimensional

axially symmetrical supersonic flows is

developed; it is based on the characteristics

theory (represented partly graphically, partly

analytically). Thereafter this method is applied

to the construction of rotationally symmetrical

nozzles.

48. *Stram, L.: Shock Free Supersonic Nozzle

Design. CAEC Memo Report no. 2004,

February 1947, 12 pp, 6 refs.

5391 14

(Langley Research Center library no.)

The object of this report is to review the

methods used in designing two-dimensional

shock free supersonic tunnels. The report

concentrates on the method of characteristics.

*Continental Aviation and Engineering Corp.,

Detroit, Michigan, USA.

49. *Shapiro, A.H.; and Edelman, G.M.:

Method of Characteristics for Two Dimensional

Supersonic Flow - Graphical and Numerical

Procedures. MIT Meteor Report no. 7,

February 1947.

*Department of Mechanical Engineering,

Massachusetts Institute of Technology, USA.

50, *Cronvich, L.L.: Numerical-Graphical

Methods of Characteristics for Plane Potential

Shock-Free Flow Problems. Journal of the

Aeronautical Sciences, vol. 14, no. 4, Aoril

1947, pp. 237-242, 6 refs.

Two numerical-graphical methods of solution

of supersonic flow problems are developed

from the basic theory of characteristics. Both

are restricted to plane potential shock-free

flow. The "lattice-point" method,

recommended for flows with given boundaries,

is applied to flow in a hyperbolic channel. The

"field" method, suitable for problems in which

flow boundaries are to be determined, as in the

case of supersonic nozzle design, is used for a

problem of parallel routing of an initially

expanded flow. Complete rules of procedure

are presented for each method.

*The John Hopkins University, Silver Springs,

Maryland, USA.

51. *Shapiro, A.H.; and Edeiman, G.M.:

Method of Characteristics for Two Dimensional

Supersonic Flow - Graphical and Numerical

Procedures. Journal of Applied Mechanics,

vol. 14, no. 2, June 1947, pp. A154-AI62,

6 refs.

The method of characteristics for twodimensional supersonic flow is reviewed and

summarized. A characteristics chart is

presented for use with the graphical procedure

of Prandtl and Busemann. A new numerical

procedure is described which eliminates

graphical operations and which allows more

accurate solutions. To facilitate the numerical

13
method, a table of useful functions is included.

*Department of Mechanical Engineering,

Massachusetts Institute of Technology, USA.

52. Sauer, R.: General Characteristics of the

Flow Through Nozzles at Near Critical Speeds.

English translation of German paper presented

in 1944. NACA TM-II47, June 1947, 20 pp,

5 refs.

Approximation formulas were developed for

the position and form of the critical curve for

transition through the critical velocity in the

neighborhood of the narrowest cross-section of

flat and rounded Laval nozzles. In comparison

with nozzle flows calculated by Oswatitsch and

Rothstein (1942), they showed satisfactory

agreement. In addition, corresponding

approximation formulas were deduced for the

flow over profiles with local supersonic regions.

53. *Nilson, E.N.: The Method of

Characteristics for Three-Dimensional Axially

Symmetric Supersonic Flow. UACRD

M-2101-1, September 1947.

*Research Dept., United Aircraft Corp., USA.

54. Royle, J.K.; Bowling, A.G.; and

Lukasiewicz, J.: Calibration of Two

Dimensional and Conical Supersonic MultiNozzles. RAE Aero 2221 SD 23, September

1947.

55. *Nilson, E.N.: Design of an Inlet for a

Two-Dimensional Supersonic Nozzle. Meteor

Report UAC-13, December 1947, 25 pp,

t 3 refs.

6410 1351

(Langley Research Center library no.)

An analytical method is presented for the

construction for an inlet of a two-dimensional

supersonic shock free nozzle. This construction

is an adaptation to two dimensions of the

method developed recently (Freidrichs - 1944)

for three-dimensional nozzles. It affords an

analytical description of the flow of a nonviscous fluid through a two-dimensional Laval

nozzle from the subsonic to the supersonic

regime, and in particular permits a study of the

transition through the speed of sound. The

construction is carried out for a nozzle

designed to produce exhaust flow of constant

speed and direction at Mach number 1.5.

Compensation for boundary layer is not

included in this construction, and subsequent

adjustment of the constructed contour for

boundary layer displacement thickness is

necessary.

*Research Dept., United Aircraft Corp., USA.

58. *Allen, H.J.: The Asymmetrical

Adjustable Supersonic Nozzle for Wind-Tunnel

Applications. NACA RM-A8EI7, 1948.

*Ames Aeronautical Laboratory, Moffett Field,

California, USA.

57. Hawthorne, W.R.; et al: Analysis of

Various Systems for Supersonic Wind Tunnels.

MIT Meteor R UAC-23, 1948.

58. Nilson, E.N.: Analytical Correction of a

Two-Dimensional Nozzle for Uniform Exhaust

Flow. MIT Meteor R UAC-15, 1948

*Research Dept., United Aircraft Corp., USA.

59. *Peterson, J.W.: Nozzle Design for the

Supersonic Wind Tunnel. University of

Michigan Report EMP-7, 1948.

*University of Michigan, Ann Arbor,

Michigan, USA.

60. *Bogdonoff, S.M." The Princeton Pilot

Variable Density Supersonic Wind Tunnel.

Project Squid. Princeton University TM PR-8,

1948.

*Princeton University, Princeton, New Jersey,

USA.

61. *Courant, R.; and Freidrichs, K.O.:

Supersonic Flow and Shock Waves. Chapter 5

- Flow in Nozzles and Jets. Published by

Interscience Publishers, New York, 1948, pp.

377-396, I I refs.

14
This chapter considers flow through different

nozzles including the De Laval nozzle. Shock

patterns in nozzles are considered. The

"perfect nozzle" is discussed.

*Institute for Mathematics and Mechanics, New

York University, New York, USA.

62. *Pinkel, I.I.: Equations for the Design of

Two-Dimensional Supersonic Nozzles. NACA

Report 907, 1948, 24 pp, 2 refs.

Equations are presented for obtaining the wall

coordinates of two-dimensional supersonic

nozzles. The equations are based on the

application of the method of characteristics to

irrotational flow of perfect gases in channels.

Curves and tables are included for obtaining

the parameters required by the equations for

the wall coordinates. A brief discussion of

characteristics as applied to nozzle design is

given to assist in understanding and using the

nozzle-design method of this report. A sample

design is shown.

*Flight Propulsion Research Laboratory,

Cleveland, Ohio, USA.

63. *Cronvich, L.L.: A Numerical-Graphical

Methods of Characteristics for Axially

Symmetric Isentropic Flow. Journal of the

Aeronautical Sciences, vol. 15, no. 3, March

1948, pp. 155-162, 11 refs.

A graphical-numerical method of

characteristics, based on the Tollmien method,

is developed for axially symmetric isentropic

flow problems. Complete rules of procedure

are presented for the application of the method.

Similar methods have been given by Ferrari

and Ferri. As an illustration, the flow around

a conical-nosed body is calculated. In this

problem a procedure is given for approximating

the curved shock wave, assuming constant

entropy behind the shock wave.

*The John Hopkins University, Silver Springs,

Maryland, USA.

64. Edelman, G.M.: The Design, Development

and Testing of Two-Dimensional Sharp

Cornered Supersonic Nozzles. MIT Meteor

Report 22, May 1948.

65. *Meyer, R.E.: The Method of

Characteristics for Problems of Compressible

Flow Involving Two Independent Variables.

Part 1 - The General Theory. Quarterly

Journal of Mechanics and Applied

Mathematics, vol. 1, no. 2, June 1948, pp. 196-

219, 14 refs.

The paper gives a review of present state of

development of the method of characteristics

for the solution of problems of compressible

flow. The theory applies when the flow

depends on two independent variables only (one

of which may be time); heat radiation, heat

conduction, and viscosity are neglected, and the

theory of this form appears to give a good

approximation in a large number of practical

applications. The flow, if steady, is taken to

be supersonic.

*Department of Mathematics, University of

Manchester, UK.

66. *Crown, J.C.: Supersonic Nozzle Design.

NACA TN-1651, June 1948, 34 pp, 10 refs.

The theory of supersonic flow in nozzles is

discussed, emphasis being placed on the

physical rather than the mathematical point of

view. Methods, both graphic and analytic, for

designing nozzles are described together with a

discussion of design factors. In addition, the

analysis of a given nozzle shapes to determine

velocity distribution and possible existence of

shock waves is considered. A description of a

supersonic protractor is included in conjunction

with a discussion of its application to nozzle

analysis and design.

*Ames Aeronautical Laboratory, Moffett Field,

California, USA.

67. *Kane, E.D.; Chambre, P.L.; and Schaaf,

S.A.: Supersonic Nozzle Designs for Low

Pressure Gas Flows. HE-150-48, July 1948, 15

PP.

5391/4

(Ames Research Center Library no.)

Following a discussion of difficulties in

connection with designing nozzles of

conventional type for use at low pressures, the

possibilities of two new designs, respectively

15
called a slip plate and a molecular plate, are

investigated. The theoretical behavior expected

of each is outlined and experimental data for

the slip plate nozzle are discussed.

*Department of Engineering, University of

California, Berkeley, California, USA.

68. *Puckett, A.E.: Design and Operation of a

12-Inch Supersonic Wind Tunnel. Presented at

the Annual Summer Meeting of Institute of the

Aeronautical Sciences, July 1948. Preprint

#160 published by IAS, 30 pp.

5341 CIT/14

(Ames Research Center library no.)

A small supersonic wind tunnel, with test

section approximately 12" square, has recently

been put into operation at the Jet propulsion

Laboratory, at the California Institute of

Technology. Some of the newer design and

performance features of this wind tunnel will

be discussed in the present paper. The tunnel

has been operated satisfactorily up to Mach

number 3.0, and preliminary calibration in this

range is in progress.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

69. *Kurzweg, H.H.:

Nozzles and Diffusers.

1948.

The Use of Grating

NOL Memo 9848, July

*US Naval Ordnance Laboratory, White Oak,

Maryland, USA.

70. *Holt, M.: The Behaviour of the Velocity

Along a Straight Characteristic in Steady

Irrotational lsentropie Flow with Axial

Symmetry. Quarterly Journal of Mechanics

and Applied Mathematics, vol. 1, part 3,

September 194_8., pp. 358-364, 1 ref.

In this paper attention is confined to the steady

irrotational isentropic flow of a perfect gas at

supersonic speeds, in particular, flow in which

one characteristic is straight. In two

dimensions any characteristic along which the

velocity is constant in magnitude and direction

is straight and, conversely, if a characteristic is

straight the velocity must be constant along it;

in three-dimensional flow with axial symmetry

the velocity long a straight characteristic is not

generally constant but varies according to a

definite relation with the radial distance. We

establish this relation and describe the types of

flow corresponding to it.

*Department of Mathematics, University of

Manchester, UK.

71. *Tsien, H.S.: Wind-Tunnel Testing

Problems in Superaerodynamics. Journal of the

Aeronautical Sciences, vol. 15, no. 10, October

1948, pp. 573-580, 9 refs.

The problems of experimentation of rarefied

gas are discussed. First, the extremely large

viscous effects in a wind-tunnel nozzle are

shown. Then the difficulties of flow

measurement are surveyed, pointing out

particularly the unconventional behavior of the

Pitot tube in rarefied gas. The performance of

a hot-wire anemometer is then studied in some

detail to show its feasibility. Finally, the rules

of achieving complete flow simulation of

rarefied gas flow are formulated.

*Massachusetts Institute of Technology,

Massachusetts, USA.

72. *Evvard, J.C.; and Wyatt, D.D.:

Investigation of a Variable Mach Number

Supersonic Tunnel with Nonintersecting

Characteristics. NACA RM-E8JI3, November

1948, 28 pp, 3 refs.

A method is presented for the design of

supersonic-wind-tunnel nozzles that produce

uniform flow over a continuously variable

Mach number range without the use of flexible

walls. Experimental results obtained from a

preliminary investigation of such a tunnel are

included. Overexpansion of the flow in the

neighborhood of the throat was observed at all

Mach numbers. Boundary-layer effects were

noticeable above the design Mach number of

2.0. Mach numbers were obtained in the range

of 1.76 to 2.65 with the limits imposed by

either tunnel choking or the structural design

of the tunnel. At any given flow-turning

angle, less than l-percent variation in Mach

number was observed in the test-section flow

downstream of the overexpansion region.

16
*Lewis Flight Propulsion Laboratory,

Cleveland, Ohio, USA.

73. *Meyer, R.E.: The Method of

Characteristics for Problems of Compressible

Flow Involving Two Independent Variables.

Part 2 - Integration Along a Mach Line. The

Radial Focusing Effect in Axially Symmetrical

Flow. Quarterly Journal of Mechanics and

Applied Mathematics, vol. 1, part 4, December

1948, pp. 451-469, 7 refs.

The paper deals with the growth and decay of

disturbances along Mach lines in isentropic,

irrotational, steady, two-dimensional or axially

symmetric, supersonic flow; in particular, the

distribution of disturbances is investigated

along a Mach line in axially symmetrical flow

on which the velocity is constant. As an

example, the field of flow in the entry of the

contractor of circular cross-section is calculated

from the focusing laws, and the analytical expressions are compared with the results of the

numerical methods of Massau and Tupper. The

disturbance generated by the diffuser entry

leads to a singularity of the flow pattern on the

axis, the nature of which is investigated within

the framework of the linear theory.

*Department of Mathematics, University of

Manchester, UK.

74. Boden, O.W.: Supersonic Wind Tunnel.

NA Report no. 14, C/49, 1949.

75, Hulbert, J.K.; Sutton, M.A.; and Von

Eschen, G.L: An Experimental and Analytical

Investigation of Critical Design Parameters for

High Mach Number Open-Jet Supersonic Wind

Tunnel. Ohio State University P-344 R-9,

1949.

76. Drougge, G.: A Method for Continuous

Variation of the Mach Number in a Supersonic

Wind Tunnel and Some Experimental Results

Obtained at Low Supersonic Speeds., Technical Research Institute of Sweden TRIS Report

29, 1949.

77. Kane, E.D.; and Emerson, D.E.:

Construction and Operation of a Small Low

Density Supersonic Wind Tunnel. University

of California Report HE- 150-57, 1949.

78. *Monroe, L.L.: Nozzle Contours for a

Flexible-Wall Supersonic Nozzle - Theoretical

and Experimental Investigation. CSAS Thesis,

1949, 86 pp.

5341.1 48

(Ames Research Center library no.)

*Case School of Applied Science, Cleveland,

Ohio, USA.

79. *Kurzweg, H.H.: A Few Aspects of Future

Supersonic Wind-Tunnel Design and Test

Techniques. NOL Report no. 1133, 1949, pp.

103-119.

This paper concentrates on a few interesting

points of future problems in aeronautics and

ballistics. The size of future supersonic windtunnels is discussed. The use of grating

diffusers is proposed to reduce costs in large

wind tunnel construction. Grating Nozzle

designs are also presented as a viable

alternative to conventional designs. Finally,

testing techniques for heat-transfer experiments

are discussed. It is concluded that temperature

control of the tunnel walls in a wide

temperature range must be provided for.

*US Naval Ordnance Laboratory, White Oak,

Maryland, USA.

80. *Ferri, A.: Elements of Aerodynamics of

Supersonic Flows. Chapter 8 - Two

Dimensional Effusers. Published by The

MacMillan Company, 1949, pp. 161-178,

74 refs.

QA 930 F4 (Ames Research Center library no.)

This book section considers the theoretical

design of the supersonic part of a twodimensional effuser. The case of supersonic

two-dimensional jets is analyzed in detail with

flow visualization.

*Langley Memorial Aeronautical Laboratory,

Langley Field, Virginia, USA.

17
81. *Gompf, G.F.: Supersonic Nozzle Design

for Viscous Fluids. GALCIT Thesis 10, 1949.

*Guggenheim Aeronautical Laboratory,

California Institute of Technology, Pasadena,

California, USA.

82. *Holder, D.W.; and North, R.J.: The 9 x 3

inch National Physical Laboratory Induced

Flow High Speed Wind Tunnel. ARC 12387,

1949.

*National Physical Laboratory, Teddington,

UK.

83. *Foelsch, K.: The Analytical Design of an

Axially Symmetric Lavai Nozzle for a Parallel

and Uniform Jet. Journal of the Aeronautical

Sciences, vol. 16, no. 3, March 1949, pp. 161-

166 and 188, 6 refs.

The equations for the nozzle's contours are

derived by integration of the characteristic

equation of the axially symmetric flow. Since

it is not possible to integrate these equations

mathematically in an exact form, it was

necessary to find a way to approximate the

calculations. The approximation offers itself

by considering and comparing the conditions of

the flow in a cone with those in a nozzle, as a

linearization of the characteristic equations.

The first part of the report deals with

equations for the transition curve by which the

conical source flow is converted into a parallel

stream of uniform velocity. The equations are

derived by integration along a Mach line of the

flow in the region where the conversion takes

place. A factor f is introduced expressing a

relation between the direction and the velocity

of the flow along a certain Mach line. f

remains undetermined and is not involved in

the final equations. In the second part of the

report, the spherical sonic flow section is

converted into a plane circular section of

the throat. The nozzle's contour adjacent to

the throat is formed by the arc of a circle

connected with the transition curve by a

straight line. The gas dynamic properties of

the boundary Mach line are calculated in Table

l, the use of which shortens the calculations

considerably.

*Engineering Department, North American

Aviation, Inc., Inglewood, California, USA.

84. Oswatitsch, K.; and Rothstein, W.: Flow

Pattern in a Converging-Diverging Nozzle.

English translation of unpublished 1942 paper.

NACA TM-1215, March 1949, 42 pp, 4 refs.

The present report describes a new method for

the prediction of the flow pattern of a gas in

the two-dimensional and axially symmetrical

case. It is assumed that the expansion of the

gas is adiabatic and the flow stationary. The

several assumptions necessary on the nozzle

shape effect, in general, no essential limitation

on the conventional nozzles. The method is

applicable throughout the entire speed range;

the velocity of sound itself plays no singular

part. The principle weight is placed on the

treatment of the flow near the throat of a

converging-diverging nozzle. For slender

nozzles, formulas are derived for the

calculation of the velocity components as

functions of the location.

85. *Bershader, D.: An Interferometric Study

of Supersonic Channel Flow. Review of

Scientific Instruments, vol. 20, no. 4, Aoril

194_.___99, pp. 260-275, 10 refs.

The Zehnder-Mach interferometer has been

applied to the study of supersonic flow of air

expanding from a pressure tank into the

atmosphere through two channels of rectangular

cross-section. Both channels were about l cm

in width. One was a divergent channel (half

angle = 4.0 °) and the other a Laval nozzle

constructed by the "characteristics" method for

M=l.7. It was found possible to measure the

density distribution with a rather small

estimated probable error (2%). Knowledge of

the _tagnation temperature and pressure made it

possible also to compute pressure, temperature,

and velocity. The report takes up, in some

detail, accuracy problems in supersonic nozzles.

Results obtained for the potential flow agree,

for the most part, within one percent with the

well-known theory of isentropic channel flow.

*Palmer Physical Laboratory, Princeton

University, Princeton, New Jersey, USA.

86. *Schaaf, S.A.: An Axially Symmetric

Nozzle with Boundary Layer Correction. UC

HE-150-58, June 1949, 13 pp, 7 refs.

5371 18 (Ames Research Center library no.)

18
In this report the ordinates are determined for

an axially-symmetric supersonic nozzle to be

used at pressures in the range 50-100 microns

Hg at the test section (nozzle exit). The nozzle

is designed on the basis of an isentropic core

corrected for boundary layer growth to produce

a parallel flow at Mach number of 4.17 at the

test section. Preliminary tests on a similar

nozzle which is not corrected for boundary

layer growth are discussed.

*Department of Engineering, University of

California, Berkeley, California, USA

87. *Henderson, H.W.: NOL 18 x 18cm

Supersonic Wind Tunnel - Design Criteria,

Description, Operating Technique. NOL Memo

10379, August 1949, 42 pp, l ref.

5341 NOL/3

(Ames Research Center library no.)

The 18 x 18 cm tunnel is a versatile research

tool designed to make possible detailed

experimental study of primary problems such

as; (l) how the design of the various parts of

supersonic wind tunnels can be improved (the

diffuser, for example) and (2) how such

instruments as the interferometer can be used

to obtain aerodynamic data. This report covers

in detail the mechanical features of the 18 x 18

cm tunnel and is intended as a guide for the

operation of the tunnel and the planning of the

experimental work with it. The design criteria

used in arriving at the present design and some

of the types of experimental work planned for

the tunnel are indicated.

*US Naval Ordnance Laboratory, White Oak,

Maryland, USA.

88. *Culbertson, P.E: Calibration Report on

the University of Michigan Supersonic Wind

Tunnel. University of Michigan UMM-36,

November 1949, 39 pp, 10 refs.

Part I of this report contains a description of

general tunnel characteristics and measuring

facilities available without regard to a specific

Mach number. The subsequent sections present

the aerodynamic flow calibration of the tunnel

at specific Mach numbers. At present this will

include only the Mach 1.90 configuration. As

additional nozzle blocks are calibrated,

supplementary sections will be added to this

basic report. A description and analysis of the

force measuring facilities available will be the

subject of a separate report.

*Engineering Research Institute, University of

Michigan, Ann Arbor, Michigan, USA.

89. *Bonney, E.A.: Engineering Supersonic

Aerodynamics. Chapter 2 - One-Dimensional

Flow - Nozzles and Diffusers. Published by

McGraw-Hill Book Company Inc., 1950, pp.

33-70, 4 refs.

TL 573 B58

(Ames Research Center library no.)

This chapter examines one-dimensional

compressible flow. The basics are reviewed

followed by discussion of the problems of

supersonic nozzle design. Some flow

visualization is presented to emphasis to show

the effect of back pressure on flows through a

De Laval nozzle

*Applied Physics Laboratory, The John

Hopkins University, Silver Springs, Maryland,

USA.

90. Emerson, D.E.; and Schaaf, S.A.:

Performance of a Supersonic Nozzle in the

Rarefied Gas Dynamics Regime. University of

California Report HE-150-72, 1950.

91. *Pope, A.: Aerodynamics of Supersonic

Flight. Chapter 6 - Supersonic Wind Tunnels.

Published by Pitman Publishing Corp., 1950,

pp. 104-137, 3 refs.

TL 573 P6

(Ames Research Center library no.)

This chapter provides an overview of the

current state of the art in supersonic wind

tunnels. The design of supersonic tunnels is

discussed and a list of operational supersonic

tunnels presented. Simple supersonic nozzle

design is considered. Also apparatus for flow

visualization in supersonic tunnels is considered

*Daniel Guggenheim School of Aeronautics,

Georgia Institute of Technology, Georgia, USA.

19
92. *Garby, L.C.; and Nelson, W.C.:

University of Michigan 8 x 13 inch

Intermittent Flow Supersonic Wind Tunnel.

University of Michigan UMM-59, 1950.

*University of Michigan, Ann Arbor,

Michigan, USA.

93. Miller, L.T.: The Supersonic Wind

Tunnel. John Hopkins University Report 44-

11-02, 1950.

94. *Frost,

Considerations.

WTM- 188, 1950.

R.C.: Nozzle Design

University of Michigan Report

*University of Michigan, Ann Arbor,

Michigan, USA.

95. *Harrop, R.; Bright, P.I.F.; and Caiger,

M.T.: The Design and Testing of Supersonic

Nozzles. ARC R&M 2712, May 1950, 40 pp,

l 0 refs.

The theory of the flow through a throat near

sonic velocity is developed, and is followed by

a discussion of the conventional method of

designing supersonic nozzles using the method

of characteristics. A method of improvifig the

Mach number distribution of the nozzle using

the experimental results is developed. The

nozzles designed were tested in a 3-in. square

wind tunnel in which the Mach number

distribution was obtained by shaping the top

wall of the working-section. Considerable

difficulty was found in improving the

distribution; this was considered to be due to

the discontinuity in curvature at the point of

inflexion and the influence on the boundary

layer of the sudden relaxation of the pressure

gradient along the wall. An alternative

method of design was developed which

avoided this discontinuity in curvature, and

considerably better results were obtained when

attempts were made to improve the

experimental Mach number distribution. The

flow through the throat of the liners was

determined experimentally and compared with

the theory. The agreement was good on the

whole, although there were differences in the

subsonic entry region because the bottom wall

only became flat a short distance before the

throat. In addition, tests were made which

showed that the assumption of twodimensional flow through the throat was

justified. The method developed to improve

the distribution in the nozzle was extended to

derive liner shapes for Mach numbers differing

by 0.10 from the design Mach number. It was

found that changes of this order could be made

fairly successfully but further modification was

necessary to reach the standard required for

tunnel use. The necessity for a smooth and

accurately constructed liner surface is stressed.

The limitations of the methods used for

designing supersonic nozzles are discussed and

several problems are mentioned which it is

thought will need further consideration.

*Royal Aircraft Establishment, UK.

96. *Johannesen, N.H; and Meyer, R.E.:

Axially Symmetrical Supersonic Flows Near the

Center of an Expansion. The Aeronautical

Quarterly, vol. 2, August 1950, pp. 127-142,

7 refs.

When a uniform, two-dimensional supersonic

flow expands suddenly round a corner in a wall

it forms a pattern known as a Prandtl-Meyer

expansion or centered simple wave. If the flow

is two-dimensional but not initially uniform, or

if it is axially-symmetrical, the expansion is

still centered, but is not a simple wave. An

approximate solution is given in this paper for

the isentropic, irrotational, steady twodimensional or axially-symmetrical flow of a

perfect gas in the neighbourhood of the center

of such an expansion. The solution is designed

to replace the conventional method of

characteristics in such a region. The main

application is to a jet issuing from a nozzle that

discharges into a container with pressure lower

than that in the nozzle; in particular, a formula

is derived for initial curvature, at the lip of the

nozzle, of the boundary of the jet. The

solution also applies to the flow near an edge in

a boundary wall, and a formula is derived for

the velocity gradient on the wall immediately

downstream of the edge.

*Mechanical Engineering Laboratory, The

Technical University of Denmark, Denmark.

97. *Beavan, J.A.; and Holder, D.W.: Recent

Developments in High Speed Research - In the

Aerodynamics Division of the National

20
Physical Laboratory. The 800th Royal

Aeronautical Society Lecture. In: The Journal

of the Royal Aeronautical Society, vol. 54,

September 1950, pp. 545-586, 63 refs.

This lecture reviews the vast amount of high

speed research carried out at NPL since 1935.

The lecture is divided into sections. First, the

NPL high speed tunnels are described including

the latest 18 x 14 inch transonic tunnel. Next,

the measuring instruments and experimental

techniques are reviewed in detail. Then recent

experiments are reviewed including

fundamental and applied research at supersonic

speeds. Finally, the scope of future work is

discussed.

*National Physical Lab., Teddington, UK.

98. *Lindsey, W.F.; and Chew, W.L.: The

Development and Performance of Two Small

Tunnels Capable of Intermittent Operation at

Mach Numbers Between 0.4 and 4.0. NACA

TN-2189, September 1950, 90 pp, 27 refs.

The design, development, and performance of

equipment suitable for use by educational

institutions for student training and basic

compressible-flow research are described. The

equipment consists of an induction tunnel

having a 4- by 16-inch test section and capable

of operating at Mach numbers ranging from

about 0.4 to 1.4 and a blowdown tunnel having

a 4- by 4-inch test section for supersonic Mach

numbers up to about 4.0. Nozzle pressure

distribution tests made in the induction tunnel

showed satisfactory performance at subsonic

speeds. At low supersonic speeds (Mach

numbers 1.2 and 1.4), however, adverse

condensation effects were encountered when

test were made under high-humidity

conditions. The supersonic nozzles of the

blowdown tunnel produced average Mach

numbers close to the design values and

sufficient uniform velocity distributions for

most of the intended uses of this equipment.

* Langley Aeronautical Laboratory, Langley

Field, Virginia, USA.

99. *Brinich, P.F.: Boundary Layer

Measurements in 3.84-by-10 inch Supersonic

Channel. NACA TN-2203, October 1950, 51

pp, 10 refs.

Boundary-layer measurements were made in

the transonic and supersonic regions of a

channel having maximum cross-sectional

dimensions 3.84 by 10 inches and designed by

potential-flow methods for a uniform Mach

number of 2.08 in the test section. At inlet

pressures from 37 to 13 inches of mercury

absolute, turbulent boundary layers were

observed throughout the channel; at an inlet

pressure of 5 inches, laminar boundary layers

were observed near the channel entrance with

turbulent layers downstream. A comparison of

the experimental and theoretically computed

boundary layers at the high inlet pressures

showed good agreement when empirical friction

coefficients were evaluated from Reynolds

numbers based on the kinematic viscosity of

the air at the wall. Despite this agreement

between experiment and theory, local

differences in rates of boundary-layer growth

still existed that are attributed to secondary

flows in the boundary layer. At low inlet

pressures, substantial increases in the

boundary-layer rates of growth with an uneven

development of the boundary layer along the

bottom wall of the channel were observed.

Experimental and empirical skin-friction

coefficients were in poor agreement at all inlet

pressures. Secondary flows in the boundary

layer caused by static-pressure gradients

transverse to the upstream direction are

believed to be the reasons for the poor

agreement.

*Lewis Flight Propulsion Laboratory,

Cleveland, Ohio, USA.

100. *Meyer, R.E.; and Holt, M.: The

Correction of Wind Tunnel Nozzles for TwoDimensional, Supersonic Flow. The

Aeronautical Quarterly, vol. 2, November 1950,

pp. 195-208, 6 refs.

The paper is concerned with the twodimensional, steady, irrotational, iscentropic

flow of a perfect gas in a wind tunnel nozzle

which is found to produce a flow in the test

rhombus deviating slightly from the desired

uniform flow. The minimum corrections are

derived that must be applied to the liners in

order to produce a uniform flow in the test

rhombus. If the uncorrected nozzle produces a

flow of uniform direction, measurement of the

pressure on the axis, in the test rhombus,

suffices to determine these corrections. If not,

21
further pressuremeasurementsare required. A

simple test is indicated for checking whether

the flow stream direction is uniform. The

method cannot be used to correct for deviations

from a two-dimensional flow.

*Department of Mathematics, University of

Manchester, UK.

101. *Cohen, C.B.; and Valerino, A.S.:

Investigation of Operating Pressure Ratio of a

Supersonic Wind Tunnel Utilizing Distributed

Boundary-Layer Suction in Test Section.

NACA RM E50H04, November 1950, 39 pp,

l ref.

An investigation to determine the effect of

distributed boundary layer suction on the

pressure recovery of a supersonic wind tunnel

has been conducted in a 3.84- by 10-inch

tunnel operating at a Mach number of 2.0.

With suction applied to two walls of a constant

area section in the vicinity of the normal

shock, a reduction of 4 percent of the

operating pressure ratio was obtained. This

reduction was attributed to an improvement

(reduction in Mach number) in the flow

characteristics at the subsonic-diffuser inlet.

The normal shock predicted by onedimensional theory was, in practice, replaced

by a multiple-branch shock configuration. The

change in static pressure, total pressure, and

Mach number occurred gradually in the

streamwise direction and finally approached the

predicted Rankine-Hugoniot values.

*Lewis Flight Propulsion Laboratory,

Cleveland, Ohio, USA.

102. *Hilton, W.F.: High Speed

Aerodynamics: Part III - Wind Tunnels.

Published by Longmans, Green and Co.,

London, 1951, pp. 359-477, 2 refs.

TL 570 H55

(Ames Research Center library no.)

Part III of this book is split into two sections.

The first deals with high-speed wind tunnels

including discussion of design, effects of

humidity, and the physical principles

underlying the operation of supersonic tunnels.

The second section deals with high-speed

tunnel apparatus and techniques. This section

covers such topics as measurements in highspeed wind tunnels and flow visualization.

*National Physical Laboratory, Teddington, UK

103. *McKenney, J.D.: An Investigation of

Flow Separation in a Two-Dimensional

Transparent Nozzle. JPL PR 20-129, 1951.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

104. *Bogdonoff, S.M.: Design, Construction

and Operation of the Princeton 4 x 8 inch

Variable Density Supersonic Tunnel. Project

Squid. Princeton University PS TR-34, 1951.

*Princeton University, Princeton, New Jersey,

USA.

105. *Dhawan, S.; and Roshko, A.: A Flexible

Nozzle for a Small Supersonic Wind Tunnel.

Journal of the Aeronautical Sciences, vol. 18,

no. 4, April 1951, pp. 253-258, 1 ref.

The design of a small supersonic wind-tunnel

test section (4 by 10 in.) incorporating a

flexible nozzle is outlined. The flexible nozzle

consists of a high strength stepped steel plate.

Two screw jacks provide an easy means of

continuously changing the nozzle's shape

according to the aerodynamic requirements.

The boundary-layer compensation can also be

varied during operation. Pressure surveys,

together with schlieren and interferometric

analysis of the test section, show the flow to be

uniform over the operating range (M = 1.1 to

1.5).

*Guggenheim Aeronautical Laboratory,

California Institute of Technology, Pasadena,

California, USA.

106. Cunsolo, D.: Calculation of the Shape of

a Two-Dimensional Supersonic Nozzle in

Closed Form. L'Aerotecnica, vol. 31, no. 4,

August 1951. In Italian. English translation is

NACA TM-1358, January 1953, 29 pp.

22
The idea is advanced of making a supersonic

nozzle by producing one, two, or three

successive turns of the whole flow; with the

result that the wall contour can be calculated

exactly by means of the Prandtl-Meyer "Lost

Solution."

107. *Armstrong, A.H.; and Smith, M.G.:

Two-Dimensional Supersonic Nozzle Design

Part I: Theory. Armament Research

Establishment Report 5/51, October 1951, 36

pp.

N-12619

(Langley Research Center library no.)

In this report certain aspects of the design of a

nozzle for a supersonic wind tunnel are

examined. Modifications to the standard

Prandtl-Busemann method are suggested which

should improve the agreement between

theoretical flow patterns and that actually

achieved in practice. Consideration is given to

the questions of the subsonic and transonic

portions of the nozzle, the continuity of

curvature on the boundary of the supersonic

part, the taking of the mean values on the

characteristics and the boundary layer

correction. It is believed that the suggestions

here made constitute an improvement on the

Prandtl-Busemann method in its simplest form,

without unduly complicating the actual

computation. Part II of the report, to be

published shortly (Unfortunately, Part II

appears never to have been published - SW),

will deal with the numerical application of the

theory.

*Physical Research Division, Armament

Research Establishment, Ministry of Supply,

UK.

108. *Temple, E.B.: The Effect of Small

Variations in the Nozzle Contour on the Flow

in the Test Section of a Supersonic Nozzle.

NSLM A&R 100-81, December 1951.

*Naval Supersonic Laboratory, Massachusetts

Institute of Technology, Massachusetts, USA.

109. *Clippinger, R.F.:

Symmetric Nozzles.

December 195 I.

Supersonic Axially

BRL Report 794,

*Ballistic Research Laboratory, Aberdeen

Proving Ground, Maryland, USA.

110. Drougge, G.: Some Measurements at

Low Supersonic Speeds by a Method for

Continuous Variation of the Mach Number.

Aeronautical Research Institute of Sweden

ARIS Report 42, 1952.

111. Serruys, M.: General Study of the Flow

of Gas Through a Supersonic Nozzle (In the

Steady or Unsteady State) with Possible Heat

Addition. Ministere de i'Air Publications

Scientifiques et Techniques (PST) no. 272,

1952, 60 pp. In French.

N-21010

(Ames Research Center library no.)

112. *Evvard, J.C.; and Marcus, L.R.:

Achievement of Continuous Wall Curvature in

Design of Two-Dimensional Symmetrical

Supersonic Nozzles. NACA TN-2616, January

1952, 8 pp, 5 refs.

Auxiliary boundary conditions are derived to

assure continuity of wall curvature in applying

the method of characteristics to the design of

two-dimensional symmetrical supersonic

nozzles. An illustrative example is included.

*Lewis Flight Propulsion Laboratory,

Cleveland, Ohio.

113. *Corrsin, S.: Effect of Wind Tunnel

Nozzle on Steady-Flow Nonuniformities.

Readers' Forum. Journal of the Aeronautical

Sciences, vol. 19, no. 2, February 1952, pp.

135-136, 1 ref.

Since Prandtl's 1932 discussion on the

attainment of uniform flow in a low-speed

constant density, wind tunnel, designers have

been acutely conscious of the benefits of high

contraction ratio as a means of reducing the

dimensionless measure of steady-flow

irregularity in the working section. Two simple

generalizations are of interest: (a r) the effect of

upstream density (-temperature-') irregularities

on the working section velocity irregularities in

23
a low-speed tunnel; and (b) extension to

compressible flow of Prandtl's rough estimate

for the effect of upstream irregularities, now in

both mean velocity and stagnation temperature.

*Aeronautics Department, The John Hopkins

University, Baltimore, Maryland, USA.

114. *Evvard, J.C.; and Maslen, S.H.: ThreeDimensional Supersonic Nozzles and Inlets of

Arbitrary Exit Cross Section. NACA TN2688, April 19;52, 12 pp, 6 refs.

A method is presented for obtaining threedimensional unsymmetric supersonic nozzles

and inlets from known axisymmetric flows.

Streamlines bounding the desired exit shape are

traced through the known basic flow solution to

give the required unsymmetrical wall contours.

Several examples are given.

*Lewis Flight Propulsion Laboratory,

Cleveland, Ohio, USA.

115. *Crown, J.C.: Design of Nozzles Having

Continuous Wall Curvature. Readers' Forum.

Journal of the Aeronautical Sciences, vol. 19,

no. 5, May 1952, pp. 358-359, 2 refs.

Many nozzles for supersonic wind tunnels are

now designed using the Foelsch method with a

cubic initial curve. Nozzle contours obtained

from the Foelsch method have inherently a

discontinuity in curvature at the "inflexion"

point. Since a flexible plate cannot be bent to

follow a nozzle contour having a discontinuity

in curvature, it seems desirable to develop a

method for designing nozzles having continuous

wall curvature at all points. The basic formulas

for designing such a nozzle are presented

herein.

*Naval Ordnance Laboratory, White Oak,

Maryland, USA.

116. *Ruptash, J.: Supersonic Wind Tunnels -

Theory, Design and Performance. UTIA

Review 5, June 1952, 190 pp, 122 refs.

AD-001377

N-51372

The purpose of this review, which was started

in January 1951, in conjunction with the

author's work on the design of the UTIA 5- by

7-inch supersonic wind tunnel, is to present a

treatment of some of the fundamental

supersonic wind tunnel design and performance

problems. Unfortunately, due to the limited

time available, many important details have

been only briefly mentioned. However, the

author feels that the selected topics which have

been reviewed in detail are at least among the

important fundamentals of supersonic wind

tunnel design and performance.

*Institute of Aerophysics, University of

Tennessee, USA.

117. *Haefeli, R.C.: Use of Fences to

Increase Uniformity of Boundary Layer on

Side Walls of Supersonic Wind Tunnels.

NACA RM-E52E19, July 1952, 15 pp, 8 refs.

An investigation of the use of solid fences

installed on the side walls of a supersonic wind

tunnel to retard the development of transverse

flow and to increase the uniformity of the

side-wall boundary layer is reported.

Beneficial results were obtained with fences

which had depths of the order of the

boundary-layer displacement thickness and

which followed potential-flow streamlines

through the nozzle. Reduction of the number

of fences on each side wall from four to two

eliminated their effectiveness.

*Lewis Flt. Prop. Lab., Cleveland, Ohio, USA.

118. *Frost, R.C.; and Liepman, H.P.:

Supersonic Nozzles with Continuous Wall

Curvature. Readers' Forum. Journal of the

Aeronautical Sciences, vol. 19, no. 10, October

1952, pp. 716, 4 refs.

This note discusses an alternative to the Crown

method for the design of supersonic nozzles

with continuous wall curvature. The

alternative method uses a physically desirable

Mach number distribution along the centerline

of the nozzle. In this case, the point of

inflection must be upstream of the end point of

the patching Mach line. This patching Mach

line divides the region of curved intersecting

characteristics from the simple wave region

with straight nonintersecting characteristics.

24
*Consolidated Vultee Aircraft Corp., Fort

Worth,Texas,USA.

119. *Reshotko, E.; and Haefeli, R.C.:

Investigation of Axially Symmetric and TwoDimensional Multi-Nozzles for Producing

Supersonic Streams. NACA RM-E52H28,

October 1952, 35 pp, 4 refs.

The flow characteristics of three axially

symmetric multi-nozzles of nominal design

Mach numbers 2.46, 3.07, and 7.01 and a twodimensional multi-nozzle of nominal design

Mach number 3.07 were investigated. Three

types of disturbance, classified as oblique shock

waves, corner shock waves, and wakes, were

observed in the flow fields. The effect of the

geometry of the multi-nozzles on these

disturbances and on the actual Mach number

and pressure recovery obtained with the multinozzle is discussed herein. The magnitude of

the disturbances was found to depend on the

exit turning angle of the individual nozzles.

Generally, Mach number variations of 4.5

percent or less existed in a region which could

be used as a test section. The use of multinozzles, however, appears to be restricted to

experiments in which nonuniformity of flow

and large pressure losses can be tolerated and

for which simple fabrication and quick

interchange of nozzles are desired.

*Lewis Flight Propulsion Laboratory,

Cleveland, Ohio, USA.

120. LaBerge, J.G.: Design, Calibration and

Correction of a 1.6 Mach Number Nozzle.

NAE LR-41, November 1952.

121. British Development of Variable Mach

Number Supersonic Wind Tunnels. RAE Aero

344, 1953.

122. Fallis, W.B.; Johnson, G.W.; et al: Design

and Calibration of the Institute of Aerophysics

16 x 16 inch Supersonic Wind Tunnel. UTIA

Report 15, 1953

123. *Shapiro, A.H.: The Dynamics and

Thermodynamics of Compressible Fluid Flow.

Volume 1. Chapter 15 - Method of

Characteristics for Two-Dimensional

Supersonic Flow. Published by Ronald Press

Company, 1953, pp. 462-524, 10 refs.

QA 9 ! 3 $497

(Ames Research Center library no.)

The method of characteristics is described.

Then the method is developed in two ways:

first by an extension of the linearized theory,

in which physical concepts are emphasized; and

second, by formal mathematical methods. The

latter development is more rigorous and leads

to a better appreciation of the concept of

characteristic curves, an appreciation which

will be useful in attacking other types of

problems involving the method of

characteristics. A section is devoted to nozzle

design which considers amongst other types,

sharp-corner nozzles.

*Department of Mechanical Engineering,

Massachusetts Institute of Technology, USA.

124. Intermittent Supersonic Wind Tunnels:

Notes on British Experience. RAE TM Aero

345, 1953.

125. Cunsolo, D.: Calculation of the Shape of

a Two-Dimensional Supersonic Nozzle in

Closed Form. English translation of 1951

Italian paper. NACA TM-1358, January 1953,

29 pp.

The idea is advanced of making a supersonic

nozzle by producing one, two, or three

successive turns of the whole flow; with the

result that the wall contour can be calculated

exactly by means of the Prandtl-Meyer "Lost

Solution."

126. LaBerge, J.G.: Design and Calibration of

Supersonic Wind Tunnel Nozzles. In:

Proceedings of Symposium on High Speed

Aerodynamics, NAE Ottawa, January 1953, 35

pp.

127. *Orlin, W.J.; Heins, A.; and Douglas, B.:

A New Type Symmetrical Two-Dimensional

Variable Mach Number Nozzle. ARO Inc.,

RJA Branch, NP Report 2, January 1953.

25
*ARO Inc., Arnold AFS, Tullahoma,

Tennessee,USA.

*Jet Propulsion Laboratory, Pasadena,

California,USA.

128. Syvertson, C.A.; and Savin, R.C.: The

Design of Variable Mach Number Asymmetric

Supersonic Nozzles by Two Procedures

Employing Inclined and Curved Sonic Lines.

NACA TN-2922, March 1953.

129. *Heybey, W.H.: The Prandti-Busemann

Method for the Graphical Evaluation of 2-D

Super. Flow. Its Application to the Design of

Wind Tunnel Nozzles and the Appropriate Corrections. Part III Principles and

Accomplishments of the Correction of Wind

Tunnel Nozzles. English translation of

Peenemunde Archives Report no. 66/36g,

February 1941. North American Report AL1715, May 1953, 63 pp.

DTIC ATI- 1836

To obtain a test section which will be free of

structure wave and have a constant velocity

along its axis, corrections have to be made on

the initial design of the contour of windtunnel

nozzles. The first correction deals with failures

which are caused by small errors in design and

manufacture only. The second correction

considers the fact that air is not an ideal gas

but, owing friction on the enclosed walls,

produces a boundary layer. To illustrate the

described methods, the correction of a nozzle

designed for Ma = 1.57 is calculated.

*Wasserbau-Versuchsanstalt, Kochel, Germany.

130. *Riise, H.N.; and Serreli, P.V.H.:

Flexible Nozzles for Supersonic Wind Tunnels.

Presented at AGARD Wind Tunnel and Model

Testing Panel Meeting, May 1953, 26 pp.

N-24357 (Ames Research Center library no.)

This paper briefly describes common methods

for establishing supersonic flow for wind

tunnels, and shows the range of requirements

best met by flexible nozzles. A method of

designing nozzle shapes well adapted to use in

conjunction with flexible nozzles is presented

along with some experimental results.

Mechanical and structural design problems are

discussed, and some recommendations made.

131. *Orlin, W.J.: The Semi-Flexible

Supersonic Nozzle. Presented at AGARD Wind

Tunnel and Model Testing Panel Meeting, May

1953, 12 pp.

N-24360

(Ames Research Center library no.)

A new type variable supersonic nozzle is

described. This nozzle has rigid upstream walls

which are joined by flexible plates at or

downstream of the inflection point. Cancellation boundaries are obtained by controlling the

flexible plate and conditions only (i.e., without

intermediate jacks). Variation of Mach number

is achieved solely by symmetrical rotation of

the rigid walls about fixed centers.

*ARO Inc, Arnold AFS, Tullahoma, Tennessee,

USA.

132. *Riise, H.N.: Functions of PrandtlMeyer Angle for Supersonic Nozzle Design.

JPL Publication no. 26, December 1953, 47 pp,

1 ref.

N-32079

(Ames Research Center library no.)

This report is a tabulation of Mach number,

Mach angle, and area ratio vs Prandtl-Meyer

angle. The tabulation was made to facilitate

design of supersonic nozzles up to Mach

number = 10 and was computed in increments

of O.Oi ° in Prandtl-Meyer angle through the

range _b=0 to _b=102.34.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

133. *MacDermott, W.N.: Correction of

Flexible Plate Supersonic Nozzle Contours by

Influence Methods. AEDC-TN-53-8,

December 1953, 21 pp, 11 refs.

N-31301

(Langley Research Center library no.)

Method of obtaining the contour corrections

necessary for the production of a satisfactory

26
flow uniformity at the exit of a flexible plate

supersonic nozzle are reviewed. Basic

requirementsof the methodsare considered,

and in particular it is found that contour

corrections, small in comparison with the

boundary-layer thickness, produce flow

changeswhich cannot be described by the

simple theory of characteristics. A procedure

involving use of experimentally determined

jack influences was successfully applied to

correction of nozzle profiles in a 12-in.

supersonic wind tunnel. Considerations of

further application of this method are

discussed.

*ARO Inc, Arnold AFS,Tullahoma,Tennessee,

USA.

134. *Shapiro, A.H.: The Dynamics and

Thermodynamics of Compressible Fluid Flow.

Volume 2. Section 21.4 - Flow in Throat of

Converging-Diverging Nozzle and Section 21.5

- relaxation Method. Published by Ronald

Press Company, 1954, pp. 826-840, 7 refs.

QA 913 $497

(Ames Research Center library no.)

These sections review the methods available for

studying mixed subsonic and supersonic flow.

First the solution by power series is considered

for the flow in a supersonic nozzle throat. The

shape of the sonic line is discussed for twodimensional and axisymmetric nozzles. Finally,

the relaxation method is applied to twodimensional nozzle with hyperbolic walls.

*Department of Mechanical Engineering,

Massachusetts Institute of Technology, USA.

135. *LaBerge, J.G.; and Conlin, L.T.: A

Technique of Manufacture of Supersonic

Nozzles. In: Proceedings of 2nd Canadian

Symposium on Aerodynamics. Paper no. 5,

February 1954, pp 264-279, 1 ref.

N-32646

(Ames Research Center library no.)

A manufacturing method is described that

eliminates the tedious and time-consuming

process of correcting tunnel liners during the

calibration process. It is found that, since no

error is introduced in machining the liner

profile from a master template, a satisfactory

flow is obtained provided a suitably smooth

template is used. The manufacturing technique

described has become the standard method for

producing nozzles for both the NAE 10-inch

and 30-inch tunnels. Experiments in the NAE

tunnels demonstrate a flow non-uniformity of

not more than _+1% about the mean measured

Mach number. To-date the work has been

confined to two-dimensional nozzles but is now

being extended to axi-symmetric nozzles.

*National Aeronautical Establishment, Ottawa,

Canada.

136. *Ferri, A.; and Bogdonoff, S.M.: Design

and Operation of Intermittent Supersonic Wind

Tunnels. AGARDograph-l, May 1954, 113 pp,

72 refs.

TL 500 N6 (Ames Research Center library no.)

A study has been made of the operating

characteristics of intermittent wind tunnels,

particularly of the blow-down type. For the

same test Mach and Reynolds numbers, the

blow-down tunnel is considerably cheaper to

build and to operate than the comparable

continuous tunnel. For tests of many different

set-ups, as required for research and preliminary development, the flexibility of the blowdown jet may be more important than long

running time. Moderate size equipment of the

blow-down type can reach full scale Reynolds

numbers with full scale airplane deflections

simulated in the model tests. The detailed

performance of the components of such

equipment have been obtained from

calculations and experience. Typical

construction, test set-up, instrumentation, and

extensions to the transonic and hypersonic

region have been discussed. Some examples of

operating intermittent tunnels are also given.

*Polytechnic Institute of Brooklyn, New York,

New York, USA.

137. *Baron, J.R.: Analytic Design of a

Family of Supersonic Nozzles by the

Freidrichs' Method, Including Computation

Tables and a Summary of Calibration Data.

WADC TR-54-279, June 1954, 432 pp, 48 refs.

AD-55902

27
The design procedure for the family of

supersonic nozzles in use at the Naval

Supersonic Laboratory of the Massachusetts

Institute of Technology is herein presented.

The basis for the potential-flow design is the

analytical method first outlined by Freidrichs,

to which has been added some results which

furnish a higher order of approximation to the

nozzle contours. The implied mathematical

convergence in the method is discussed and

reference is made to continuous curvature

streamlines. The accumulated computations of

the Laboratory are tabulated for the

convenience of those wishing to avail

themselves of the family of contours successfully used. Experimental results from

calibrations conducted within the uniform flow

regime and at the nozzle boundaries are

presented, and interpretations are given in

terms of the design, fabrication, measurement

accuracy, and model requirements.

*Naval Supersonic Laboratory, Massachusetts

Institute of Technology, USA.

138. *Riise, H.N.: Flexible-Plate Nozzle

Design for Two-Dimensional Supersonic Wind

Tunnels. JPL Report no. 20-74, June 1954. 46

pp, 5 refs.

A semi-analytical method for the design of

flexible-plate, potential-flow supersonic nozzle

contours is presented. The method consists

essentially of a fairly rigid control of the

second and third derivatives of the nozzle

displacement curve, both upstream and

downstream from the inflection point. Using

the method of characteristics as a tool, the

technique of designing a completely flexible or

combination of solid- and flexible-plate nozzle

is illustrated. The presentation includes a table

and graphs that have proved helpful in the

design of supersonic nozzles at the Jet

Propulsion Laboratory of the California

Institute of Technology.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

139. *Laufer, J.: Factors Affecting Transition

Reynolds Numbers on Models in Supersonic

Wind Tunnels. Readers' Forum. Journal of

the Aeronautical Sciences, vol. 21, no. 7, J_0__/y_

1954, pp. 497-498, 5 refs.

The great scatter in transition Reynolds

numbers measured in different supersonic wind

tunnels is believed to be caused by disturbances

of various degrees present in the tunnels. In

general, these disturbances found in supersonic

wind tunnel nozzle flows may be of three

different types: (a) vorticity fluctuations (or

transverse waves); (b) sound, or longitudinal

waves - including weak compression waves

emanating from the imperfect nozzle walls; and

(c) temperature fluctuations. The JPL research

into this problem will attempt to successively

eliminate the above mentioned three

contributions to the perturbation field in the

supersonic tunnel. Data is presented from the

JPL 18 in. by 20 in. supersonic tunnel on a 5°

included angle cone. The first set of

experiments indicate that in low Mach number

flows (M<2.5) the turbulence level of the

settling chamber had a strong effect on the

boundary layer transition Reynolds number.

However, no such effect could be detected for

higher Mach number flows.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

140. *Baron, J.R.; and Durgin, F.H.: An

Experimental Investigation of Heat Transfer to

the Cooled Sidewall of M = 2.5, 3.0, and 3.5

Supersonic Nozzles. NSLM Wind Tunnel

Report 65, July 1954, 82 pp, 27 refs.

AD-74144

Heat-transfer rates have been measured at the

plane boundary of the flow through twodimensional supersonic nozzles in the variable

density, continuous-type wind tunnel at the

Naval Supersonic Laboratory. A range of

Mach number, Reynolds number, and pressure

gradient was obtained by the use of fixedblock nozzles designed for exhaust flow at

Mach numbers of 2.5, 3.0, and 3.5. Heat

transfer was induced by cooling the outer

surface of the channel wall to ice and to dryice temperatures which produced a ratio of

surface-to-stagnation temperatures as low as

0.7. Despite the presence of pressure gradients,

the turbulent recovery factor of 0.89 was found

to be independent of Mach and Reynolds

number. Local heat-transfer coefficients were

in reasonable agreement with the flat-plate

constant-surface-temperature theory of Van

Driest after correcting for the varying

28
temperature potential history. Pressuregradient influences were not apparent

downstream of the nozzle throat but were

distinguishable in the subsonic region. The

results are in qualitative agreement with an

analysis presented for the turbulent boundary

layer with constant pressure gradient.

*Naval Supersonic Laboratory, Massachusetts

Institute of Technology, Massachusetts, USA.

141. *Westkaemper, J: The Design of a Mach

Number 2.75 Nozzle and Variable Throat

Diffuser for the OAL Supersonic Wind Tunnel.

OAL Memo 80, September 1954.

*Ordnance Aerophysics

Daingerfield, Texas, USA.

Laboratory,

142. *Morris, D.E.; and Winter, K.G.:

Requirements for Uniformity of Flow in

Supersonic Wind Tunnels. RAE TN no.

Aero.2342, September 1954, 9 pp.

N-48101

AD-48625

An analysis is made of the effects of nonuniformity of flow on the pressure

measurements on the surface of the model and

also on the force and moment measurements

and the following standards of flow uniformity

are derived - variations in flow direction to be

less than +0.1 ° in the range M = 1.4 to 3;

variation in Mach number to be less than

+0.003 at M = 1.4 increasing to +0.01 at M = 3.

A brief analysis is made of the errors in model

manufacture and their effects on force and

pressure measurements. Using the same

standards as were used in deducing the

requirements for flow uniformity quoted above

it is concluded that present standards of model

manufacture are satisfactory overall, though for

accurate pressure plotting tests at low

supersonic Mach numbers (M _ 1.4) a higher

standard is desirable.

*National Aeronautical Establishment, Ottawa,

Canada.

143. *Kenney, J.T.; and Webb, L.M.: A

Summary of the Techniques of Variable Mach

Number Supersonic Wind Tunnel Nozzle

Design. AGARDograph-3, October 1954, 142

pp, 47 refs.

AD-56640

This report is a survey of the techniques of

two-dimensional wind tunnel nozzle design. A

procedure for the aerodynamic design of

flexible nozzles capable of continuous Mach

number variation is developed in detail. The

special structural, mechanical, calibration and

cost estimation problems involved in flexible

nozzle construction are discussed.

*Sandberg-Serrell Corp., Pasadena, California,

USA.

144. *Smelt, R.: Factors Influencing Precision

in Supersonic Wind Tunnels. AEDC-TN-54-

25, November 1954, 21 pp, 2 refs.

N-33527

(Ames Research Center library no.)

During the design of the supersonic wind

tunnel of the Gas Dynamics Facility at AEDC,

a considerable effort has been expended in

developing methods of prediction of precision,

largely because the intended use of this tunnel

places unusually high demands on the precision

of test data. In this report, some of the

concepts which have been utilized in this

prediction are summarized. The influence of

nozzle shape errors and condensation on test

data is reviewed.

*ARO Inc., Arnold AFS, Tullahoma,

Tennessee, USA.

145. *Baron, J.R.; and Durgin, F.H.: An

Experimental Investigation of Heat Transfer at

the Boundaries of Supersonic Nozzles. WADCTR-54-541, December 1954, 81 pp, 27 refs.

AD-074144

Heat transfer rates have been measured at the

plane boundary of the flow through twodimensional supersonic nozzles in the variable

density, continuous-type wind tunnel at the

Naval Supersonic Laboratory. A range of

Mach number, Reynolds number, and pressure

29
gradientwasobtainedby the use of fixed block

nozzles designed for exhaust flow at Mach

numbers of 2.5, 3.0, and 3.5. Heat transfer was

induced by cooling the outer surface of the

channel wall to ice and to dry-ice temperatures

which produced a ratio of surface-to-stagnation

temperature as low as 0.7. Despite the presence

of pressure gradients, the turbulent recovery

factor of 0.89 was found to be independent of

Mach and Reynolds numbers. Local heattransfer coefficients were in reasonable

agreement with flat-plate constant-surfacetemperature theory of Van Driest after

correcting for the varying temperature potential

history. Reynolds-number bases (extending to

3.5 x 10 7 ) were free-stream conditions and the

effective lengths of boundary layer growth.

Pressure-gradient influences were no apparent

downstream of the nozzle throat but were

distinguishable in the subsonic region. The

results are in qualitative agreement with an

analysis presented for the turbulent boundary

layer with constant pressure gradient.

*Naval Supersonic Laboratory, Massachusetts

Institute of Technology, USA.

146. *Beckwith, I.E.; and Moore, J.A.: An

Accurate and Rapid Method for the Design of

Supersonic Nozzles. NACA TN-3322,

February 1955. 57 pp, 10 refs.

A Procedure is given for designing twodimensional nozzles in which the streamline

coordinates are computed directly from

tabulated flow parameters and appropriate

equations. The method of characteristics is

used to obtain the first part of the flow, which

consists of a continuous expansion from a

uniform sonic flow to a radial flow. The

Foelsch equation's are then used for the

transition from radial flow to the final uniform

flow. Information is presented which enables

the designer to select and compute rapidly the

wall contour for any nozzle or series of nozzles

for a wide range of length-to-height ratio,

Mach number, and wall angle at the inflection

point. In general, a nozzle is determined by

specifying any two of these three parameters.

*Langley Aeronautical Laboratory, Langley

Field, Virginia, USA.

147. *MacDermott, W.N.: The Correction of

Flexible Plate Supersonic Nozzle Contours by

Influence Methods. Journal of the

Aeronautical Sciences, vol. 22, no. 5, May

1955, pp. 289-296, 10 refs.

Methods of obtaining the contour corrections

necessary for the production of a satisfactory

flow uniformity at the exit of a flexible plate

supersonic nozzle are reviewed. Basic

requirements of the methods are considered,

and in particular it is found that contour

corrections, small in comparison with the

boundary-layer thickness, produce flow

changes which cannot be adequately

described by the simple theory of

characteristics. A procedure involving use of

experimentally determined jack influences

was successfully applied to correction of nozzle

profiles in a 12-in. supersonic wind tunnel.

Considerations of further application of this

method are discussed.

*ARO Inc, Arnold AFS, Tullahoma, Tennessee,

USA.

148. *Hill, J.A.F.: On the Calibration of

Supersonic Wind-Tunnels. Readers' Forum.

Journal of the Aeronautical Sciences, vol. 22,

no. 6, June 1955, pp. 441-443, 2 refs.

Some difficulties encountered in the calibration

of a supersonic wind-tunnel nozzle have

recently been reported by Murphy (1953). We

have found that the expansions in supersonic

wind-tunnel nozzles are generally isentropic (in

the absence of condensation) and that the most

reliable method of calibration is to determine

Mach number from the ratio of pitot pressure

Pp to PT" A duplication of this work in a

hypersonic nozzle seems desirable.

*Naval Supersonic Laboratory, Massachusetts

Institute of Technology, USA.

149. *Rosen, J.: The Design and Calibration

of a Variable Mach Number Nozzle. Journal

of the Aeronautical Sciences, vol. 22, no. 7,

July 1955, pp. 484-490.

A method of designing a symmetric Mach

number nozzle with adjustable flexible walls

has been developed. The continuous variation

of the Mach number is controlled by one single

3O
screw mechanism, which in a defined manner

simultaneously affects the coordinates and

derivatives of the inlet and throat curvatures

up to the inflection point. The flexible part of

the curvature between the inflection point and

the test section consists of a spring, with linear

thickness distribution, rigidly clampedat the

level of the test section (150 x 150 mm z = 5.9

in. x 5.9 in.). Due to small curvatures and a

suitable choice of the linear thickness

distribution of the flexible part of the wall, a

good Mach number distribution (_+0.015 or less)

has been realized within the whole Mach

number range from 1.5 to 2.5.

*Division of Steam Engineering, The Royal

Institute of Technology, Stockholm, Sweden.

150. *Liepman, H.P.: An Analytic Method for

the Design of Two-Dimensional Asymmetric

Nozzles. Journal of the Aeronautical Sciences,

vol. 22, no. 10, October 1955, pp. 701-709, 17

refs.

An analytic method is presented for the design

of two-dimensional asymmetric curved nozzles.

Such nozzles may be used to continuously vary

the Mach number by relative translation of

one contour with respect to the other. The

continuity equation and the condition of

irrotationality for steady compressible flow are

given in curvilinear coordinates with stream

function and velocity potential as independent

variables. Using Bernoulli's equation for

isentropic gas and a suitable chosen analytic

velocity distribution along the initial

expansion contour, which is specified in terms

of its curvature, a set of partial differential

equations is obtained. These equations are

solved by expanding the dependent variables -

velocity q, flow direction 0, and curvilinear

coordinates (x. y) of a streamline - in powers

of the stream function. This solution

determines the nozzle contours for any constant

value of the stream function as well as all flow

characteristics in the subsonic region and the

supersonic expansion region of the nozzle.

From the general solution and the boundary

conditions at the sonic line it follows that the

curvature of the contour must be zero at the

throat. After the patching Mach line is

calculated numerically the recompression

contour can be determined to complete the

nozzle calculations. These equations show that

the Mach number gradient must go to zero at

the design Mach wave. This requirement

implies continuous wall curvature at the

corners of the recompression region. The

variation of Mach number by relative

translation of fixed contours of the asymmetric

type is then discussed. An iterative method is

derived for this purpose which should converge

very rapidly as compared to the iteration

required by the characteristics method of

design.

*Engineering Research Institute, University of

Michigan, Ann Arbor, Michigan, USA.

151. *Sivells, J.C.: Design of TwoDimensional Continuous-Curvature Supersonic

Nozzles. Journal of the Aeronautical Sciences,

vol. 22, no. 10, October 1955, pp. 685-692 and

732, 6 refs.

In order to cover continuously a rather wide

range of Mach numbers, several supersonic

wind tunnels have flexible-plate nozzles

incorporated in their design. The elastic curve

of a flexible plate supported at discrete points

must have continuous curvature. It is,

therefore, desirable that the curvature of the

aerodynamic contour also be continuous to

enable the flexible plate to conform to the

desired contour. A method is presented herein

for designing two-dimensional supersonic

nozzles having continuous curvature.

Approximations are made for determining

the length of the nozzle and for correcting the

perfect-fluid profile for the effect of the

boundary-layer growth. Computing terms are

included for making the successive

approximations that are necessary to establish

the angles of the inflection and characteristic

points that will satisfy the desired

requirements of nozzle length, throat radius,

and continuous third derivative at the

inflection point. After these angles are

established, the coordinates of the perfect-fluid

profile, downstream of the inflection point, can

be obtained by the characteristics method.

*ARO Inc, Arnold AFS, Tullahoma, Tennessee,

USA.

152. *Carafoli, E.: High Speed Aerodynamics

(Compressible Flow). Chapter 20 -

31
Application of Characteristics to the Design of

Plane Effusors, Diffusers and Jets. English

version published by Editura Tehnica, 1956,

pp. 425-444.

TL 573 C313

(Ames Research Center library no.)

This chapter describes the calculation of a twodimensional effuser. Both graphical and

analytic methods are used to determine the

contour of the effuser.

*Institute of Applied Mechanics, Bucharest,

Rumania.

153. *Meyer, R.E.: Perturbations of

Supersonic Nozzle Flows. The Aeronautical

Quarterly, February 1956, pp. 71-84, 8 refs.

Small, steady perturbations of general twodimensional steady, shock-free, supersonic

flows are studied and the perturbation fields of

symmetrical nozzle flows are described in

detail. The relation between errors in the

shape of the supersonic part of the nozzle liners

and the deviations from uniformity of the flow

of the test section is given to an approximation

sufficient for the treatment of a number of

problems arising from experiment and in the

design of nozzles.

*Department of Aeronautics, University of

Sydney, Australia.

154. *Morkovin, M.V.: Critical Review no

1223 of MacDermott paper in Journal of the

Aeronautical Sciences, vol. 22, no. 5, May

1955. In: Mechanics of Fluids Section of

Applied Mechanics Review, vol. 9, no. 4, Aoril

1956, pp. 172.

*Aeronautics Department, The John Hopkins

University, Baltimore, Maryland, USA.

155. *Kennedy, E.C.: Design of an Axially

Symmetric Contraction-Expansion Nozzle For

Exit Mach Number 2.7203. OAL Memo 89,

July 1956.

*Ordnance Aerophysics

Daingerfield, Texas, USA.

Laboratory,

156. *Sivells, J.C.: Analytic Determination of

Two-Dimensional Supersonic Nozzle Contours

having Continuous Curvature. AEDC-TR-56-

11, July 1956, 29 pp, 5 refs.

AD-88606

An analytical method is presented for

determining the contours of two-dimensional

supersonic nozzles having continuous curvature.

The continuity of curvature is necessary for

flexible-plate type nozzles inasmuch as the

aerodynamic contour must be such that it can

be closely simulated by the elastic curve of the

flexible plate. The method described is more

accurate and less time consuming than the

characteristics method of obtaining contours.

The assumption is made that radial flow can be

obtained at the inflection point through the use

of a simple polynomial for the initial part of

the contour. This radial flow is converted to

parallel flow at the test section Mach number

as described herein.

*ARO Inc., Arnold AFS, Tullahoma,

Tennessee, USA.

157. Leavy, L.E.: A Supersonic Wind Tunnel

for Mach Numbers up to 3.5. AGARD Report

no. 70, August 1956.

158. *Hall, M.G.: The Accuracy of the

Method of Characteristics for Plane Supersonic

Flow. The Quarterly Journal of Mechanics and

Applied Mathematics, vol. 9, part 3, September

1956, pp. 320-333, 7 refs.

The mechanism by which errors are propagated

through a computation is analyzed, and the

resultant effect of various types of errors

determined. A procedure is outlined for

planning computations to achieve specified

accuracy with minimum labour.

*Department of Aeronautical Engineering, The

University of Sydney, Australia.

159. *Hill, J.A.F.; Baron, J.R.; et al: Mach

Number Measurements in High Speed Wind

Tunnels. AGARDograph-22, October 1956,

125 pp, 81 refs.

32
TL 500 N6 no.22

(Ames Research Center library no.)

Measurements of subsonic and supersonic Mach

numbers in air are discussed from the point of

view of calibration measurements of an empty

wind tunnel, of measurements of local Mach

numbers at points in the flow field around a

model, and of simulating free flight Mach

number in the presence of wind tunnel wall

interference. Errors in deducing Mach number

from particular measurements are discussed and

certain measuring procedures recommended.

*Naval Supersonic Laboratory, Massachusetts

Institute of Technology, USA.

160. *Squires, R.K.; Roberts, R.C.; and Fisher,

E.R.: A Method for Designing Supersonic

Nozzles using the Centerline Mach Number

Distribution. Aeroballistic Report 285,

NAVORD-3995, October 1956, 31 pp, 12 refs.

AD-121412

N-51372

This report describes a new method for

computing supersonic nozzle potential flow

contours which is based on a combination of

three existing theories. The contour is

determined by specifying the nozzle exit

dimension and by choosing a Mach number

distribution function for the centerline of the

entire nozzle. The new method can be used to

design fixed block, semi-flexible, flexible

nozzles by choosing a suitable centerline Mach

number distribution. The new method is also

adaptable to high-speed computing machines;

therefore, the contours can be computed

sufficiently accurately to obtain maximum

utilization of present fabrication methods.

*US Naval Ordnance Laboratory, White Oak,

Maryland, USA.

161. *Kurzweg, H.H.: The Aerodynamic

Development of the V-2. In: History of

German Guided Missiles. AGARDograph-20,

1957, pp. 50-69, 15 refs.

This paper reviews the systematic studies of

drag, stability, control, and aerodynamic

heating of supersonic bodies which had to be

initiated before long range rockets like the A-4

could be successfully launched. Supersonic

wind tunnel tests are discussed together with

the facilities used. It is concluded that this

pioneering work did indeed help the V-2 to

fly, and it prepared the ground for the future

investigations in which we are still involved.

*Aeroballistic Research Department, US Naval

Ordnance Laboratory, White Oak, Maryland,

USA.

162. *Cole, D.: The Laminar Boundary Layer

Near a Sonic Throat. In: Proceedings of the

Heat Transfer and Fluid Mechanics Institute,

June 1957, pp. 119-137, 7 refs.

QC 145 H35 (Ames Research Center library

no.)

Two-dimensional laminar boundary-layer flow

is considered for a perfect gas with Prandtl

number unity and viscosity proportional to

temperature. The physical situation represented

by these equations is flow through a

convergent-divergent channel with constant

surface temperature and with sonic velocity at

the throat. It is shown that flows with large

Falkner-Skan parameters may be investigated

analytically by means of series expansions

provided that there is no heat transfer at the

walls. If there is heat transfer, however, it

becomes necessary to use a singular expansion

procedure in two space variables.

*Consultant to California Institute of

Technology, Pasadena, California, USA.

163. *Goranson, G.G.; Barnett, R.M.; et al: A

Method for the Calibration of Flexible-Plate

Supersonic Wind Tunnels and Calibration

Results for the 12-inch Wind Tunnel at the

Jet Propulsion Laboratory. JPL Report 20-

110, June 1957, 78 pp, 2 refs.

N-57799

(Ames Research Center library no.)

An iterative technique for rapid and accurate

calibration of a flexible-plate supersonic-windtunnel nozzle is described. The technique

depends mainly on an automatic pressure-ratio

or difference-plotting apparatus and a

knowledge of the jack influence curves.

Calibration results are presented for a family of

33
continuous-third-derivativenozzlesat 10Mach

numbersbetween2.20 and 4.04 in the 12-in.

wind tunnel at the Jet PropulsionLaboratory.

The design of continuous-third-derivative

supersonic-wind-tunnelnozzleswasdescribed

in Reportno.20-74by Riise(1954).

*Jet Propulsion Laboratory, Pasadena,

California, USA.

164. Ryzhov, O.S.: On Flows in the Region of

the Transition Surface. English translation of

Prik. Matematika i Mexahika (Journal of

Applied Mathematics and Mechanics) published

by Pergaman Press, vol. 22, no. 4, 195.____88, pp.

608-621, 5 refs.

The peculiarity of transition through the

velocity of sound in a plane nozzle, i.e., in the

case when the tangent to the sonic line

coincides with the direction of the

characteristics which pass through the axis of

the channel, was pointed out by Khristianovich.

Later Frankl, on the basis of hodograph

transformation, investigated in detail the

character of a plane stream in the vicinity of

the sonic line. Applying a direct method

Falkovich obtained the main term of the

solution in the form of a third degree

polynomial which considerably simplified all

the calculations of the transition region of the

nozzle. In the present work on the basis of this

solution, some properties of flow with axial

symmetry are investigated, the investigation is

based on the method of Falkovich, since, in

this case, it is not necessary to make use of the

hodograph transformation.

165. *Hoilingdale, S.; and Barritt, M.M.: An

Application of a Computer to Wind Tunnel

Design. The Computer Journal, vol. 1, April

1958, pp. 42-48 (Part 1), pp. 64-68 (Part 2), 10

refs.

This article describes an application of a

computer to the aerodynamic design and

automatic control of a large wind tunnel. A

new mathematical approach was used to avoid

singularities in the partial differential equations

governing the flow. The work was started in

1953 on the ACE Pilot model at the N.P.L.,

Teddington, and completed on one of the

DEUCE computers at the RAE Farnborough.

*Royal Aircraft Establishment, Farnborough,

UK

166. *Rap, G.V.R.: Exhaust Nozzle Contour

for Optimum Thrust. Journal of the American

Rocket Society (Jet Propulsion), vol. 28, no. 6,

June 1958, pp. 377-382, 6 refs.

A method for designing the wall contour of an

exhaust nozzle to yield optimum thrust is

established. The nozzle length, ambient

pressure and flow conditions in the immediate

vicinity of the throat appear as governing

conditions under which the thrust on the nozzle

is maximized. Isentropic flow is assumed and

the variational integral of this maximizing

problem is formulated by considering a suitable

chosen control surface. The solution of the

variational problem yields certain flow

properties on the control surface, and the

nozzle contour is constructed by the method of

characteristics to give this flow. An example is

carried out and typical nozzle contours given.

*Marquardt Aircraft Co., Van Nuys, California,

USA.

167. *Frazer, R.P.; Eisenklam, P.; and Wilkie,

D.: Investigation of Supersonic Flow

Separation in Nozzles. Journal of Mechanical

Engineering Science, vol. 1, no. 3, 195_____._99, pp.

267-279, 13 refs.

The investigation reported in this paper

constitutes a study of flow separation in nozzles

within a large experimental universe. The

results of these investigations show that, for

flow through conical nozzles pressure expansion

along the wall is almost one-dimensional and

iscentropic and the wall pressure depends on

the area ratio only. For flow through curved

nozzles, the expansion depends on the radius of

curvature as well as the throat area. For the

three types of nozzles tested (Axi-symmetric

and slit-nozzles with curved and straight

divergence), there is one separation pressure

for each ambient discharge pressure, and is a

function of nozzle divergence angle only. It

has been observed that the jet separates

asymmetrically at a low reservoir pressure and,

on lowering the pressure still further, the

separation becomes unstable, with the jet

oscillating rapidly from one side of the nozzle

wall to the other.

34
*Department of Chemical Engineering, Imperial

College of Science and Technology, London,

UK.

168. *Barritt, M.M.: Calculation of Flexible

Wall Shapes and Preparation of Control Tapes

for the Bedford 8-ft x 8-ft Wind Tunnel.

ARC R&M 3187, February 1959, 33 pp, 13

refs.

N73-25041

This report describes an application of a digital

computer to the aerodynamic design and

automatic control of a large wind tunnel with

flexible walls. The computational problem was

threefold: first, calculation of the wall shapes

for a set of 'pivotal' operating speeds between

M = l and 2.8; second, computation of the

necessary movements of the set of screw jacks

which flex the walls; and finally, preparation

of the set of digitally punched control tapes. A

new mathematical approach was used for the

first part in order to avoid singularities in the

partial differential equations governing the

flow in the convergent-divergent nozzle of the

tunnel. The work was started in 1953 on the

ACE Pilot Model at the National Physical

Laboratory and completed on one of the Royal

Aircraft Establishment DEUCE computers.

*Royal Aircraft Establishment Bedford, UK.

169. *Morkovin, M.V.: On Supersonic Wind

Tunnels with Low Free-Stream Turbulence.

Journal of Applied Mechanics, vol. 26, no. 9,

September 1959, pp. 319-323, 24 refs.

Measurements in supersonic wind tunnels have

become almost routine in the last decade and

yet little is known about the free-stream

disturbances, which are present, and about the

means of minimizing them. The present note

outlines the problems of minimizing the mean

as well as the unsteady variations of velocity

and temperature and gives guidance where the

trends are clear. It is found that in many wind

tunnels the free-stream fluctuations are likely

to be dominated by aerodynamic sound in the

sense of Lighthill and by shivering Mach waves

and wall vibrations. Only conjectures can be

offered on the means of minimizing the

resulting sound intensity at the present time.

*Aeronautics Department, The John Hopkins

University, Baltimore, Maryland, USA.

170. *Lord, W.T.: A Theoretical Study of

Annular Supersonic Nozzles. ARC R&M 3227,

October 1959, 28 pp, 37 refs.

N73-25035

This paper is concerned with the design of

annular supersonic nozzles to produce uniform

flow in supersonic wind tunnels which are axisymmetrical and which have an internal coaxial

circular cylinder throughout. Symmetrical twodimensional and conventional axi-symmetrical

nozzles are special cases of annular design.

Proposals are made for design criteria sufficient

to ensure that the flow inside a nozzle is free

from limit lines and shock waves; the criteria

for (symmetrical) two-dimensional and

(conventional) axi-symmetrical nozzles are new.

The two outstanding procedures for designing

two-dimensional and axi-symmetrical nozzles

are generalized to apply to annular nozzles.

One of the design procedures is mainly

analytical and the other is mainly numerical;

the analytical expressions in both procedures

are made much more complicated by the

presence of the internal cylinder but the

numerical process (the method of

characteristics) is not. The design criteria and

the mainly numerical design procedure are

successfully applied to the design of a

particular annular nozzle.

*Royal Aircraft Establishment, UK.

171. *Schueler, C.J.; and Strike, W.T.:

Calibration of a 40-Inch Continuous Flow

Tunnel at Mach Numbers 1.5 to 6.

AEDC-TN-59-136, November 1959, 41 pp, 9

refs.

A test program was conducted to calibrate the

von Karman Gas Dynamics Facility's 40- by

40-in., continuous, supersonic wind tunnel

(Tunnel A). Theoretical nozzle contours were

adjusted, and local Mach numbers and flow

angles were measured within a region of the

test section. Results of the calibration at Mach

numbers from 1.5 to 6 in half Mach number

increments are presented. Included in the

nozzle calibration program were tests of two

typical models, AGARD Calibration Model B

35
and a 15-deg cone cylinder. Along the axis of

the test section the total variation in Mach

number was less than _+0.5 percent at all Mach

numbers and slightly larger variations were

measured off axis within a 12-in. diameter core.

The average flow angles on the test section axis

were less than 0.1 deg in both the horizontal

and vertical planes. Significant changes in

average Mach numbers were observed for

decreases in free-stream Reynolds number at

the high Mach numbers. The pressure

distribution measurements on the cone-cylinder

model were in reasonable agreement with

theory, and the force characteristics of

AGARD Calibration Model B agreed well with

results from another wind tunnel.

*ARO Inc, Arnold AFS, Tullahoma, Tennessee,

USA.

172. *Landsbaum, E.M.: Contour Nozzles.

American Rocket Society Journal, vol. 30, no.

3, March 1960, pp. 244-250, 20 refs.

A number of contour nozzles for an ideal gas

with "t = 1.22 are presented. The variation of

gamma is considered. The design is based upon

the assumption of a radial flow section in the

initial divergent section which is turned to

uniform axially directed flow at the exit. For

each specified exit Mach number, about 95 per

cent of the maximum expansion angles are

used. The contours obtained were cut back in

order to yield nozzles of various exit areas.

The surface area of the divergent section,

thrust coefficient and length of these cutback

nozzles are compared with those properties of

15-deg half-angle conical nozzles with the same

exit area. Simple heat flux calculations for

some of the designs are also presented. These

designs result in moderate savings in length,

surface area and heat flux over a 15-deg nozzle

with the same thrust coefficient. Greater

savings are possible at the expense of reducing

the thrust coefficient.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

173. *Rao, G.V.R.: Approximation of

Optimum Thrust Nozzle Contour. Journal of

the American Rocket Society (Jet Propulsion),

vol. 30, no. 6, June 1960, pp. 561, 3 refs.

Besides the nozzle thrust, a design engineer

would like to know a nozzle's weight and

cooling requirements to enable him to make the

proper choice. For this purpose an approximation to the optimum thrust contour is

enough, and a simple geometric method is

described here.

*Rocketdyne Division, North American

Aviation Inc., Canoga Park, California, USA.

174. *Vrebalovich, T.: On Supersonic Wind

Tunnels with Low Free-Stream Turbulence.

(Discussion of the Morkovin report of same

title with an Author's Closure.) Discussion.

Journal of Applied Mechanics, vol. 27, no. 6,

June 1960, pp. 362-364, 6 refs.

This response discusses some of the results

from the JPL 12 in. by 20 in. supersonic wind

tunnels which add proof to the ideas presented

in Morkovin's paper. Other results indicate

that our understanding is not complete.

Obviously it is difficult to reduce any

fluctuations originating from the turbulent wall

boundary layers; but the large amplitude of

these fluctuations at the higher Mach numbers

may have significant effects on supersonic

wind tunnel model testing and should be

investigated. The author's suggestions for

reducing disturbance levels and their effects in

wind tunnels should be considered as part of

good supersonic wind tunnel design.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

175. *Goddard, F.E.: Supersonic Tunnels. In:

High Speed Problems of Aircraft and

Experimental Methods, Volume VIII of High

Speed Aerodynamics and Jet Propulsion, Published by Princeton University Press, 1961, pp.

491-532, 21 refs.

TL 573 H52

(Ames Research Center library no.)

This book section reviews the design of all

major components of supersonic wind tunnels

including a study of supersonic nozzle design.

Operational requirements, performance calculations and measurement techniques are

discussed.

36
*Jet Propulsion Laboratory, Pasadena,

California, USA.

176. *Irani, P.A.; and Satyanarayana, B.:

Aerodynamic Design of Two-Dimensional

Supersonic Nozzle Contours with Boundary

Layer Corrections. NAL TN-AE-7-61,

February 1961, 62 pp.

N64-80779

*National Aeronautical Laboratory, Bangalore,

India.

177. *Pope, A.: Wind Tunnel Calibration

Techniques. Section 5 - Calibration of

Supersonic Wind Tunnels. AGARDograph-54,

April 1961, pp. 27-42, 104 refs.

N63-80505

TL 500 N6 no.54

(Ames Research Center library no.)

This paper discusses air-flow measuring

instruments, their use, and the manner of

working up and presenting the data obtained

when calibrating low-speed, nearsonic,

transonic, supersonic, and hypersonic wind

tunnels.

*Sandia Corp., New Mexico, USA.

178. *Ahlberg, J.H.; Hamilton, S.; et al:

Truncated Perfect Nozzles in Optimum Nozzle

Design. American Rocket Society Journal, vol.

31, no. 5, May 1961, pp. 614-620, 16 refs.

A graphical technique for selecting optimum

nozzle contours from a family of truncated

perfect nozzles is presented which permits

simultaneous consideration of various types of

optima. This procedure includes the effects of

friction, as well as the thermodynamic

properties of the reacting gas. Results are

given of hot and cold flow tests, showing the

effect of wall contour and wall cooling upon

oblique shock separation.

*United Aircraft Corp., East Hartford,

Connecticut, USA.

179. *MacDermott, W.N.: Preliminary

Experimental Results of the Reduction of

Viscous Effects in a Low-Density Supersonic

Nozzle by Wall Cryopumping. AEDC-TN-61-

71, October 1961, 46 pp, 8 refs.

AD-264656

N66-87627

A low-density supersonic nozzle was operated

with carbon dioxide over a range of supply

pressures from l0 microns to 600 microns and

the transition from a boundary layer-inviscid

core flow to a fully developed viscous flow was

observed. A liquid-nitrogen cryogenic pump

was used to pump the flow through this nozzle.

Sizable reductions of viscous effects in the

nozzle flow were observed when the cryogenic

pump was extended to the wall of the nozzle.

*ARO Inc., Arnold AFS, Tullahoma,

Tennessee, USA.

180. *Maxwell, H.; and Jacocks, J.L.:

Nondimensional Calculation of Turbulent

Boundary-Layer Development in TwoDimensional Nozzles of Supersonic Wind

Tunnels. AEDC-TN-61-153, January 1962, 25

pp, 3 refs.

N62-11832

The method developed by Maurice Tucker for

calculating the growth of turbulent boundary

layers in two-dimensional compressible flow

has been adapted to the computation of a

dimensionless boundary layer parameter.

Equations and calculational procedures are

presented for correcting two-dimensional

supersonic nozzles for boundary layer growth

using only one or two tables, depending on the

geometry. The tables are supplied for the

Mach number range from 1.5 to 8.0

Agreement of calculated data with measured

data and effect of Mach number distribution

are shown.

*ARO Inc., Arnold AFS, Tullahoma,

Tennessee, USA.

181. *Holt, M.: The Design of Plane and

Axisymmetric Nozzles by the Method of

Integral Relations. AFOSR-3140. In:

37
Proceedings of IUATM Symposium

Transsonicum,September 1962, pp. 310-324, 12

refs.

A65-12340

Applications to the nozzle problem of the

method of integral relations, which is very

effective in solving problems governed by

nonlinear partial differential equations with the

aid of electronic computers. The method is so

presented that it can be applied with equal

facility either to the design or flow problem.

In the application of the method to the problem

of hypersonic flow past a blunt body, the

numerical integration scheme is started on the

axis, where symmetry conditions must be

satisfied, and proceeds towards the saddle

points, the positions of which are not known in

advance. An alternative scheme is proposed for

the nozzle problem. In this case there is no

need to satisfy symmetry conditions at the start

of the integration.

*University of California, Berkeley, California,

USA.

182. *Hail, I.M.: Transonic Flow in TwoDimensional and Axially-Symmetric Nozzles.

The Quarterly Journal of Mechanics and

Applied Mathematics, vol. 15, part 4,

November 1962, pp. 487-508, 10 refs.

By means of suitable expansions in inverse

powers of R, the radius of curvature of the

nozzle profile at the throat measured in throat

half-heights, the velocity components in the

throat region of a convergent-divergent nozzle

can be calculated. The first three terms of the

series solution have been obtained both for

two-dimensional and for axially-symmetric

nozzles. The numerical accuracy of the

solution is confirmed by comparison with the

known exact solution along the branchline.

*Mechanics of Fluids Department, University

of Manchester, UK.

183. *Migdal, D.; and Landis, F.:

Characteristics of Conical Supersonic Nozzles.

American Rocket Society Journal, vol. 32, no.

12, December 1962, pp. 1898-1901, 8 refs.

Conical supersonic nozzles were analyzed by

the method of characteristics to show the

effects of wall angle, throat-to-cone fairing,

area ratio, and the thermodynamic properties as

characterized by the iscentropic expansion

coefficient. A detailed analysis indicated that

the results differ from those obtained with the

usual source flow assumptions and that both the

vacuum thrust efficiency and the wall pressure

distribution are functions of the aforementioned variables.

*Pratt and Whitney Aircraft, East Hartford,

Connecticut. USA.

184. *Anderson, A.: Flow Characteristics of a

12-inch Intermittent Supersonic Tunnel.

AEDC-TDR-63-203, 1963, 44 pp, 5 refs.

AD-418578

N63-22438

Test section flow characteristics are presented

for the nominal Mach number range from 1.5

to 5 over the available Reynolds number range.

Along the axis of the test section for all

contours, the maximum variation in Mach

Number is +0.01, and the average flow angles

in pitch and yaw are less than 0.2 deg.

Somewhat larger variations in Mach number

and flow angularity are found off-axis. At the

higher Mach numbers, significant changes in

the average test section Mach number with

decreasing Reynolds number are accompanied

by corresponding changes in the tunnel

boundary layer.

*ARO Inc., Arnold AFS, Tuilahoma,

Tennessee, USA.

185. Alikhashkin, Y.; Favorskii, A.P.; and

Chushkin, P.I.: On the Calculation of the Flow

in a Plane Laval Nozzle. Zhurnai

Vychisletel'noy Matematika i atematicheskoi

Fiziki (Journal of Computer Mathematics and

Physics), vol. 3, 1963, pp 1130-1134, 4 refs. In

Russian. English translation is NASA TT F10494, December 1966, 9 pp. N67-13834#.

A method of calculation is presented for a

potential uniform flow of a perfect gas in the

subsonic and transonic part of a plane

symmetrical Laval nozzle with a given form of

contour.

38
186. *Williams, J.C.: Viscous Compressible

and Incompressible Flow in Slender Channels.

AIAA Journal, vol. 1, no. 1, January 1963, pp.

185-195, 13 refs.

An analytical study is made of the viscous flow

in slender channels. Similar solutions to the

approximate equations of motion, valid for

flow at moderate or high Reynolds numbers in

slender channels, are found for incompressible

two-dimensional and axisymmetric flows and

for compressible flows through twodimensional channels with adiabatic walls. A

study of compressible flows in convergentdivergent channels yields results regarding the

effect of viscosity on the location of the sonic

line, on the pressure ratio at the geometric

throat and on the discharge coefficient for such

channels.

*Department of Mechanical Engineering, North

Carolina State College, North Carolina, USA.

187. *Pasqua, P.F.; Stevens, P.N.; et al:

Analytical Studies of Nozzle Throat Cooling.

AEDC-TDR-63-58, April 1963, 163 pp, 20

refs.

AD-400746

N63-14607

Analytical studies have been made concerning

many of the problems associated with the

expansion of extremely high temperature and

pressure plasmas through the converging section

of a hypersonic wind tunnel nozzle. The

problems in this study relate to the

establishment of heat fluxes to the nozzle wail;

methods of removing the heat load or

protecting the nozzle wall; determining the

stress levels in the nozzle liner; analyzing

various materials for strength and thermal

properties. In all cases parametric studies have

been made resulting in design criteria which

can be used for specific conditions. The

conditions are established from the

performance envelope for a typical low density

hypersonic wind tunnel. Throughout the report

the performance envelope is plotted on

stagnation pressure and temperature coordinates

which correspond to free stream velocities and

altitudes up to 25 kilofeet/sec and 350 kilofeet

respectively. Ultimate use of the information

will depend upon the reliability of the

assumptions made which in many cases must be

determined by new experiments. The

appendices contain listings of FORTRAN

programs for nozzle and rib stress calculations,

and backside cooling calculations.

*Nuclear Engineering Department, University

of Tennessee, Knoxville, Tennessee, USA.

188. *Darwell, H.M.; and Badham, H.: Shock

Formation in Conical Nozzles. Technical Note.

AIAA Journal, vol. l, no. 8, August 1963, pp.

1932-1934, 4 refs.

Evaluation of axially symmetric gas flow in

conventional conical nozzles by the method of

characteristics has revealed the possibility of

shock formation within the nozzle. Negative

Mach lines, originating at or just downstream

of the junction of the throat profile and the

cone, intersect near the axis. Modified

computer programs have been run to determine

the nature of this phenomenon, and it is

concluded that the effect is real. It is shown

that the shock formation can be removed by

changes in the wall contour near the junction.

*Imperial Metal Industries Ltd., Summerfield

Research Station, Kidderminster,

Worcestershire, UK.

189. Carriere, P.: Calculation of Supersonic

Nozzle Shapes using the Method of

Characteristics. Ecole Nationale Superior

Aero ENSA Report, 1964. In French.

190. *Hall, I.M.; and Sutton, E.P.: Transonic

Flow in Ducts and Nozzles, a Survey. In:

Symposium Transsonicum published by

Springer Verlag, 1964, pp. 325-344.

*Mechanics of Fluids Department, University

of Manchester, UK.

191. Handbook of Supersonic Aerodynamics:

Section 17 - Ducts, Nozzles and Diffusers.

Produced by The John Hopkins University.

NAVWEPS-1488, January 1964, 450 pp, 413

refs.

N66-13589

39
This handbook section presents the basic

techniques and related information needed for

the control of duct flow in high-speed

propulsion devices and in supersonic and

hypersonic wind tunnels. The general

mechanical and thermodynamic theory of

steady flow in a duct is simplified as much as

possible and is concisely reviewed. Nonsteady, one-dimensional flows are discussed

and methods of solution for a great number of

practical problems are outlined. Generalized

techniques are presented for the inclusion of

viscous and heat-transfer effects by means of

which boundary-layer correction may be made

to profiles designed for potential flow. The

general solutions of duct flow are applied to

specific problems and are amply supplemented

by experimental data. Also presented are many

practical geometric modifications and design

techniques. An included Bibliography directs

the reader to related research past and present.

192. *McCabe, A.: Design of Supersonic

Nozzles. ARC R&M 3440, March 1964, 36 pp,

25 refs.

N67-34665#

This paper presents a method of design of a

supersonic nozzle which incorporates recent

developments in compressible flow theory.

Continuous curvature of the contour is ensured

by defining a continuous gradient of PrandtlMeyer angle along the nozzle axis. The flow in

the throat was calculated from results given by

Hall (1962). A matching technique was used to

determine a triplet of values for the throat

radius of curvature, the flow deflection at the

inflection point and the Prandtl-Meyer angle at

the point on the nozzle axis where the left

running characteristic through the inflection

point intersects the nozzle axis. The majority

of the new work is to be found in the Appendices. Appendix B presents a method of

determining the co-ordinates along a particular

characteristic by inverting the results given by

Hall (1962). Appendix C reviews the accuracy

of the method of characteristics and, Appendix

D suggests a method by which it may be

possible to increase the accuracy without

resorting to calculations made at very small step

sizes.

*The Mechanics of Fluids Department,

University of Manchester, UK.

193. *Back, L.H.; Massier, P.F.; and Gier,

H.L.: Convective Heat Transfer in

Convergent-Divergent Nozzles. International

Journal of Heat and Mass Transfer, vol. 7, no.

5, May 1964, pp. 549-568, 24 refs.

The results of an experimental investigation of

convective heat transfer from turbulent

boundary layers accelerated under the influence

of large pressure gradients in a cooled

convergent-divergent nozzle are presented.

The most significant unexpected trend in the

results is the reduction in the heat-transfer

coefficient, below that typical of a turbulent

boundary layer, at stagnation pressures less

than 75 psia. Heat transfer predictions with

which the data were compared either

incorporate a prediction of the boundary-layer

characteristics or are related to pipe flow. At

the higher stagnation pressures, predicted

values from a modification of Bartz's

turbulent-boundary-layer analysis are in fair

agreement with the data. As a possible

explanation of the low heat transfer at the

lower stagnation pressures, a parameter is

found which is a measure of the importance of

flow acceleration in reducing the turbulent

transport below that typical of a fully turbulent

boundary layer.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

194. *Lieu, B.H.:

Supersonic Nozzle.

1964, 35 pp, 15 refs.

Air Film Cooling of a

NOLTR-64-65, August

N64- 31672#

An experimental study was made of the

internal air-film cooling of a Mach 2.4,

nonadiabatic wall, axially symmetric nozzle.

The main stream air was heated to supply

temperatures from 672 to 1212°R at supply

pressures from l l5 to 465 psia. The film

coolant air was injected through a single

peripheral slot at an angle of l0 ° from the

nozzle wall. The coolant-to-main stream mass

flow ratios were varied up to 20 percent.

Steady-state nozzle wall temperatures were

measured in both the subsonic and supersonic

flow regimes. The turbulent pipe flow

equations of Dittus and Boelter was found to be

applicable in predicting the heat transfer rates

in the absence of film cooling. A modified

40
version of the semi-empirical equation of

Hatch and Papell was found applicable in

estimating the film cooled nozzle wall temperatures.

*US Naval Ordnance Laboratory, White Oak,

Maryland, USA.

195. *Pope, A.; and Goin, K.L.: High-Speed

Wind Tunnel Testing. Chapter 1 HighSpeed Wind Tunnel Theory and Chapter 10 -

Calibration and Use of Supersonic Tunnels

Published by John Wiley and Sons Inc., 1965,

pp 1-65 and pp 349-401, 33 refs.

Chapter l gives an extensive overview of

supersonic wind tunnel design. Both theoretical

and practical aspects are covered in

considerable depth. Chapter l0 considers the

calibration of supersonic nozzles and the

operation of supersonic tunnels. This book is

to be considered essential reading for any

supersonic wind tunnel designer.

*Sandia Corp., Albuquerque, New Mexico,

USA.

196. *O'Brien, R.L.: Laminarization of Nozzle

Wall Boundary Layers as a Means of Reducing

Heat Flux. Report AFRPL-TR-65-40,

February 1965, 156 pp, 31 refs.

X65-13236 (Available to US Government

Agencies and US Government Contractors

Only)

A program was conducted to determine the

effects of favorable pressure gradients,

mainstream turbulence, wall cooling, and

turbulent boundary layer removal in the

convergent section on the heat flux and

boundary layer characteristics at the throat of a

supersonic nozzle. The objective of this

investigation was to determine whether a

laminar boundary layer could be maintained in

the throat region of such a nozzle for the

purpose of reducing the throat heat flux. The

effort under this program was divided into

both theoretical and experimental

investigations. The theoretical investigation

consisted of analysis of the laminar and

turbulent heat-transfer rates for a range of

nozzle conditions. The experimental

investigation consisted of the measurement of

the heat transfer rates for both laminar and

turbulent flow in the throat of a asymmetric

nozzle installed in a continuous-flow wind

tunnel. It was found that up to some lower

limit on Reynolds number, both the boundary

layer profiles and heat flux at the throat were

laminar in the high pressure gradient nozzle

both with and without suction removal of the

turbulent boundary layer upstream of the

convergent section. This indicates that natural

reverse transition (laminarization) was

occurring in the nozzle for these conditions. It

was also found that high favorable (i.e.

negative) pressure gradients and increased wall

cooling tend to promote the occurrence of

reverse transition. It was also found that flush

suction slots with sharp downstream corners

which are located upstream of the convergent

section of the nozzle are not an effective means

of initiating a laminar boundary layer in the

convergent section of a nozzle.

*United Aircraft Research Laboratory, East

Hartford, Connecticut, USA.

197. *Gibbings, J.C.: A Note on the

Combination of a Contraction with a

Supersonic Nozzle for a Wind Tunnel. RAE

TR no. 65066, March 1965, 19 pp, 4 refs.

N66-18405

AD-464401

The effect of fairing a contraction, starting

from a square cross section, into a twodimensional supersonic nozzle is considered

with particular emphasis upon the avoidance of

pressure gradients along the contraction walls

that would be unfavourable to the development

of the boundary layer flow. A contraction wall

profile, derived from two-dimensional

irrotational incompressible flow, was found

from model tests to give satisfactory results.

*Royal Aircraft Establishment, UK.

198. *Hail, M.G.: Experimental Measurements

in a Three-Dimensional Turbulent Boundary

Layer in Supersonic Flow. In: Recent

Developments in Boundary Layer Research,

AGARDograph-97, May 1965, pp. 829-853,

11 refs.

41
Measurements of mean values in time of pitot

pressure and flow direction have been made in

the boundary layer over the insulated side-wall

of a specially-constructed supersonic nozzle.

The external flow first accelerated and then

decelerated, and the cross-wise pressure

gradients were such that the boundary layer

cross-flow was first in one direction and then

in the opposite, as happens over wings with

swept leading-edges. The external Mach

number ranged between 1.6 and 2.0. Boundary

layer traverses were made at intervals along

external streamlines; from each traverse,

profiles of Mach number and streamwise and

cross-wise components of velocity were

derived. The results were supplemented by

measurements of skin friction using surfacetubes. A preliminary analysis reveals serious

limitations in the assumed forms for the crossflow profiles, but there is evidence that the

streamwise component behaves as it would in

an equivalent two-dimensional boundary layer.

*Royal Aircraft Establishment, Farnborough,

UK.

199. *Jeffries, N.P.; and Cumbers, L.L.:

Computer Program for Calculation of Laminar

Boundary Layer in a Supersonic Nozzle. GER65SD3007, June 196_5, 48 pp, 5 refs.

N66-24647#

A computer program is described which is

capable of computing the laminar boundary

layer in an axisymmetric supersonic nozzle.

The program also determines the nozzle contour

which will maximize the thrust obtained under

a specified set of operating conditions, taking

into account the effects of the boundary layer.

The boundary layer thickness is computed by

using a correlation suggested by Howarth; and

the optimum nozzle contour is found by the

approximate method of Rap. The program was

originally developed to determine the design

and performance of electrothermal thrusters,

but it has also been applied to supersonic

nozzles for other applications such as chemical

rockets and wind tunnel facilities.

*Space Power and Propulsion Section, General

Electric Company, Evendale, Ohio, USA.

200. *Migdal, D.: Study on Pressure

Distributions in Conical Nozzles. Grumman

Aircraft Engineering Corp. paper, ADR-01-10-

65.1, September 1965, 25 pp.

N66-87191

*Grumman Aircraft Engineering Corp.,

Bethpage, New York, USA.

201. *Back, L.H.; Massier, P.F.; and Gier,

H.L.: Comparison of Measured and Predicted

Flows Through Conical Supersonic Nozzles

with Emphasis on the Transonic Regime.

AIAA Journal, vol. 3, no. 9, September 1965,

pp. 1606-1614, 18 refs.

To understand better equilibrium flows through

supersonic nozzles, wall static pressures have

been measured in nozzles with circular-arc

throats having different ratios of throat radius

of curvature to throat radius rc/rth, circulararc or conical convergent sections, and conical

divergent sections. These measurements were

made with air at stagnation temperatures of

530 ° and 1500°R and over a stagnation

pressure range from 45 to 250 psia. The flow

through the transonic regime was found to

depend essentially on local configuration, i.e.,

on the ratio rc/rth; two-dimensional isentropic

flow predictions agreed with the data in this

region for the nozzles with r_/rtt = 2.0, but

were inadequate for the nozz_:e w_th rc/rth =

0.625. By comparison, the simple onedimensional isentropic flow prediction was as

much as 45% high in the throat region for one

nozzle; in the conical sections, deviations of a

smaller magnitude were found. The effects of

wall cooling and variation in the boundarylayer thickness at the nozzle inlet were

investigated, as were differences in pressure

readings with taps of various sizes. Some

separation pressure data are presented to show

the effect of wall cooling. Other flow features

that indicate the extent of deviations from onedimensional flow include flow coefficients,

thrust ratios, and local mass fluxes. It is hoped

that these comparisons between measurements

and predictions will be useful in studying

nozzle flows with the additional complexity of

chemical reactions.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

42
202. Favorskii, A.P.: Design of Laval Nozzles.

Zhurnal Vychisletel'noy Matematika i

Matematicheskoi Fiziki (Journal of Computer

Mathematics and Physics), October 1965, pp.

955-959, 4 refs. In Russian.

A66-11015#

Consideration of the problem of steady-state

irrotational flow of a perfect gas in plane and

axisymmetric Laval nozzles. Solutions are

obtained for both the direct problem of

calculating the flow in nozzles of a certain

form and for the inverse problem of

constructing a nozzle wall according to a given

velocity distribution on the axis of symmetry.

The solutions are carried out numerically

according to a variant of the method of integral

relations.

203. Demetriades, A.; and Von Seggern, L.:

Design, Performance and Operation of the

Mach 3 Wind Tunnel. Aeronautics Division of

Philco Corp., Newport Beach, CA, PC Report

U-3390, November 1965.

204. *Carden, W.H.: Local Heat-Transfer

Coefficients in a Nozzle with High Speed

Laminar Flow. Also AEDC-TDR-64-61, April

1964. AIAA Journal, vol. 3, no. 12, December

1965, pp. 2183-2188, 17 refs.

An experimental investigation of the local heattransfer coefficient in the throat region of a

nozzle operating under conditions of cold wall,

low-density, high-speed flow has been

conducted. Results are presented for nitrogen

gas for reservoir temperatures from 5200 ° to

6500°R and reservoir pressures from 0.9 to 1.5

atm. The experimental results have been

compared with several analytic procedures for

predicting the heat-transfer coefficient in

laminar flow. The simple flat-plate equation is

shown to underestimate the heat-transfer

coefficient. The method of Cohen and

Reshotko predicts coefficients that are in

agreement with the experimental results. The

incremental flat-plate method of Pasqua and

Stevens and a modification of a solution of

Beckwith and Cohen exhibit good results when

referenced to the value calculated by the simple

flat-plate equation at the nozzle exit. The

effects of thermal radiation upstream of the

nozzle throat are indicated.

*ARO Inc., Arnold AFS, Tullahoma,

Tennessee, USA.

205. *Sichel, M.: The Effect of Longitudinal

Viscosity on the Flow at a Nozzle Throat.

Journal of Fluid Mechanics, vol. 25, part 4,

August 1966, pp. 769-786, 28 refs.

An inviscid transonic theory appears to be

inadequate to describe the flow near the throat

of a converging-diverging nozzle during the

transition from the symmetrical Taylor (1930)

type of flow to the subsonic-supersonic Meyer

(1908) flow. A viscous transonic equation

taking account of heat conduction and

longitudinal viscosity has been developed

previously (Cole 1949; Sichel 1963; Szaniawski

1963) An exact, nozzle-type of similarity

solution of the viscous transonic equation,

similar to the inviscid solution of Tomotika &

Tamada (1950), has been found. This solution

does provide a description of the gradual

transition from the Taylor to the Meyer flow

and shows the initial stages in the development

of a shock wave downstream of the nozzle

throat. The solution provides a viscous, shocklike transition from an inviscid, supersonic,

accelerating flow to an inviscid, subsonic,

decelerating flow.

*Department of Aerospace Engineering,

University of Michigan, Ann Arbor, Michigan,

USA.

206. *Hopkins, D.F.; and Hill, D.E.: Effect of

Small Radius of Curvature on Transonic Flow

in Axisymmetric Nozzles. AIAA Journal, vol.

4, no. 8, August 1966, pp. 1337-1343, 8 refs.

An analysis was made of the transonic flow in

axisymmetric nozzles having wall radii between

one-quarter and three times the throat radius.

Entrance angles were varied from 30 ° to 750 .

The analysis is based on Freidrichs' equations,

by which the flowfield is developed for a

prescribed velocity distribution along the nozzle

axis. Each variable is expressed as a series in

terms of the stream function, and fourth order

terms are retained to give an accurate solution

for a small throat radius of curvature. The

usual assumption of steady, isentropic,

irrotational flow is made, and the specific heat

ratio is constant. In the throat region, the

solution has been found to compare favorably

with available experimental data for both small

43
and large throat curvatures. With a large wall

radius of curvature, the solution is comparable

to those of Sauer, Oswatitsch, and Hall. With a

small radius of curvature, the sonic line is

found to differ appreciably from the parabolic

sonic line of Sauer's solution. For the wall

radii equal to or less than the throat radius, an

inflection point occurs in the sonic line near

the nozzle wall. The entrance angle influences

the flow in the transonic region only when the

wall radius is less than 1 1/2 time the throat

radius.

*Douglas Aircraft Company, Santa Monica,

California, USA.

207. *Lee, R.E.; Yanta, W.J.; et al: The NOL

Boundary Layer Channel. NOLTR 66-185,

November 1966, 39 pp, 13 refs.

AD-646748

N67-25477#

A Mach 3 to 7 blow-down wind tunnel facility

for investigating boundary layer phenomena in

the transitional and turbulent range is

described. The facility, referred to as the

Boundary Layer Channel, utilizes a flexible

plate and a flat plate to form the two opposite

walls of a two-dimensional supersonic nozzle.

The plate is 8 feet long. The channel operates

at supply temperatures up to 1000°F and

supply pressures from 0.1 to 10 atmospheres.

The Reynolds number j_er foot capability is

from 3 x 104 to 2.4 x 10/.

*US Naval Ordnance Laboratory, White Oak,

Maryland, USA.

208. *Back, L.H.; and Cuffel, R.F.: Detection

of Oblique Shocks in a Conical Nozzle with a

Circular-Arc Throat. Technical Note. AIAA

Journal, vol. 4, no. 12, December 1966, pp.

2219-2221, 9 refs.

Method of characteristics predictions of

supersonic flow through conical nozzles reveal

shock formation where characteristics

originating just downstream of the tangent

between the conical divergent section and

throat curvature section approach the nozzle

axis. This note presents some measurements

that confirm the predicted shock formation.

To eliminate this shock formation, Darwell

(1963) and Migdal (1965) suggest attaching the

conical divergent section at the inflection point

of a conventionally designed contour nozzle.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

209. *Back, L.H.; Massier, P.F.; and Cuff el,

R.F.: Flow Phenomena and Convective Heat

Transfer in a Conical Supersonic Nozzle.

Journal of Spacecraft and Rockets, vol. 4, no.

8, August 1967, pp. 1040-1047, 30 refs.

An experimental investigation of gasdynamics

and convective heat transfer in a cooled

conical nozzle with a 45-deg convergent and

15-deg divergent half-angle and a small

circular-arc throat has revealed a variety of

flow phenomena that can occur and,

consequently, influence the convective heat

transfer significantly. The investigation with

air spanned a range of stagnation pressures

from 30 to 250 psia and stagnation

temperatures from 1000 ° to 2000°R. With the

inlet boundary layer turbulent, a reduction in

heat transfer below that typical of a turbulent"

boundary-layer occurred along the convergent

section, so that at the throat at the lower

Reynolds numbers apparently reverse transition

to a laminar bouadary layer had occurred. The

largest reduction in heat transfer amounted to

about 50%. Wall static pressure measurements

indicate, in addition to large deviations from

one-dimensional flow in the transonic region,

adverse pressure gradients in the nozzle inlet

curvature section and just downstream of the

tangency between the circular-arc throat and

conical divergent section. In the nozzle inlet

region, the heat transfer is typical of that

found in separated flow regions; whereas just

downstream of the tangency, apparently

retransition from a laminar or partially laminar

boundary layer to a turbulent layer occurred

for those tests where reverse or partial reverse

transition had taken place along the convergent

section. Heat-transfer predictions are in fair

agreement with the data, providing that the

boundary layer is either turbulent or essentially

laminar.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

44
210. *Williams, J.C.: Conical Nozzle Flow

with Velocity Slip and Temperature Jump.

AIAA Journal, vol. 5, no. 12, December 1967,

pp. 2128-2134, 7 refs.

A study is made of source-type viscous

compressible flow in a conical nozzle. For such

a flow an exact solution to the Navier-Stokes

equations together with the first-order velocity-slip and temperature-jump boundary

condition is possible. It is found that solutions

of this type are possible only for certain

combinations of centerline Mach number,

Reynolds number, wall angle and ratio of wall

temperature to centerline temperature.

Solutions of this type are obtained for Reynolds

numbers from 5 to 500 and are used to estimate

the magnitude of velocity slip and temperature

jump in this Reynolds number range, and to

assess the effect of slip on the wall skin

friction, on the mass flow through the nozzle,

and on the pressure difference between the

nozzle centerline and the wall.

*North Carolina State University, Raleigh,

North Carolina, USA.

211. *Back, L.H.; Massier, P.F.; and Cuffel,

R.F.: Effect of Inlet Boundary-Layer

Thickness and Structure on Heat Transfer in a

Supersonic Nozzle. Engineering Notes. AIAA

Journal of Spacecraft and Rockets, vol. 5, no.

1, January 1968, pp. 121-123, 3 refs.

The purpose of this note is to present the

results obtained with relatively thin inlet

velocity and temperature boundary layers and

compare them to the thicker turbulent inlet

layer results recently published. Heat-transfer

coefficients were generally higher along a

supersonic nozzle with relatively thin inlet

velocity and temperature boundary layers than

with thicker, turbulent inlet layers.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

212. *Vanco, M.R.; and Goldman, L.J.:

Computer Program for Design of TwoDimensional Supersonic Nozzle with Sharp

Edged Throat. NASA TM-X-1502, January

1968, 19 pp.

N68-14747#

The FORTRAN IV computer program for the

design of a two-dimensional supersonic nozzle

with sharp-edged throat i.s presented along with

the equations used. The nozzle, which has

uniform parallel flow at the exit, is designed on

the basis of two-dimensional isentropic flow of

a perfect gas. The program requires as input

the exit Mach number and the specific-heat

ratio. The output yields the nozzle contour for

the supersonic portion. Input and output for a

sample case are included.

*NASA Lewis Research Center, Cleveland,

Ohio, USA.

213, *Hopkins, D.F.; and Hill, D.E.:

Transonic Flow in Unconventional Nozzles.

AIAA Journal, vol. 6, no. 5, May 1968, pp.

838-842, 4 refs.

The description of the compressible gas flow in

the throat region of unconventional rocket

nozzles must be known in order to optimize

the wall contours and to predict the

performance. The existence of both subsonic

and supersonic flow in close proximity does not

permit the use of conventional analytical

techniques to obtain a mathematical description

of the flow. The analysis presented in this

paper can treat annular flow passages that are

either parallel to the nozzle axis or inclined to

it at some arbitrary angle. The solution is not

limited to nozzles with moderate wall radii of

curvature; sufficient terms have been retained

in the series solution to treat nearly sharp wall

curvatures in the throat region. The usual

assumption of steady, isentropic, irrotational

flow with constant specific heats is made. The

shape of the sonic line is not symmetrical about

the geometric center of the annular throat as in

the case of bell nozzles. The flow reaches

sonic velocity further upstream of the

geometric throat on the inner wall than on the

outer wall curvatures being equal.

*Douglas Aircraft Company, Santa Monica,

California, USA.

214. *Boldman, D.R.; Schmidt, J.F.; and

Gallagher, A.K.: Laminarization of a

Turbulent Boundary Layer as Observed from

Heat Transfer and Boundary Layer

45
Measurements in Conical Nozzles. NASA TND-4788, September 1968, 34 pp.

N68-33642#

Heat transfer measurements were obtained in

30 ° and 60 ° half-angle of convergence nozzles

at a nominal stagnation temperature of 970°R

(539 K) and over a range of stagnation

pressures of 2.0to 20.4 atmospheres (2.03 x 103

to 20.67 x 10 3 N/m2). These conditions

provided nozzle throat Reynoldsnumbers based

on diameter of about 6.0 x 103 to 5.0 x I0 t_.

Boundary layer time-mean velocity and

temperature measurements were obtained at one

station in a water cooled pipe inlet and at a

subsonic (Mach number _<0.08) station in each

nozzle at the stagnation pressures of 3.1 and

20.4 _atmospheres (3.14 x 10 ) and 20.67 x 103

N/re'-). The heat transfer and boundary layer

surveys suggested the occurrence of

laminarization of an initially turbulent

boundary layer.

*NASA Lewis R.C., Cleveland, Ohio, USA.

215. *Kliegel, J,R.; and Quan, V.:

Convergent-Divergent Nozzle Flows. AIAA

Journal, vol. 6, no. 9, September 1968, pp.

1728- 1734, 9 refs.

Utilizing normalized coordinates, the equations

governing inviscid, isentropic expansions of

perfect gases through convergent-divergent

nozzles can be solved as inverse power

expansions in the normalized throat wall radius

of curvature. The solution for the complete

nozzle flowfield is obtained in the form of a

perturbation about the one-dimensional

flowfield. The corrections are found to be

polynomial in the perpendicular coordinate.

Both the first- and second-order corrections to

the one-dimensional flowfield have been

worked out. Solutions are obtained for both

choked and unchoked nozzle flows as well as

for multistream nozzle expansion such as

characteristically occurs in a barrier cooled

rocket engine. Comparison with Hall's

transonic analysis reveals that the transonic

solution is obtained from the full nozzle

solution through a coordinate transformation

and reordering of the complete solution.

*Propulsion Analysis Department, TRW

Systems, Redondo Beach, California, USA.

216. *Nelms, L.T.: Design of Minimum

Length Supersonic Nozzle Contours and

Associated Sub-Contours. AEDC-TR-68-212,

November 1968, 96 pp.

AD-843755

X69-11596 (Available to US Government

Agency and US Government Contractors Only)

A method for designing the minimum length,

supersonic, inviscid nozzle contour based on a

uniform starting line will be presented. A

family of subcontours, all of which have the

same exit flow, can also be calculated. The

method applies to both axisymmetric and two

dimensional nozzles and utilizes either perfect

or real gas. A computer program utilizing this

method has been developed and is also given.

*ARO Inc., Arnold AFS, Tullahoma,

Tennessee, USA.

217. *Back, L.H.; Massier, P.F.; and Cuff el,

R.F.: Flow and Heat Transfer Measurements

in Subsonic Air Flow Through a Contraction

Section. International Journal of Heat and

Mass Transfer, vol. 12, no. l, January 1969, pp.

1-13.

Flow and heat-transfer measurements are

presented for heated air flowing subsonically

through a contraction section smoothly

connecting a tube to a conical section. These

measurements spanned a range of cooled wallto-stagnation temperature ratios,Tw/T ! o from

1/3 to 2/3, Reynolds numbers from 2 x l04 to

2 x l03, with data obtained for both laminar

and turbulent boundary layers. Flow

visualization results indicated that the flow

separated just upstream of the curved contraction section and reattached near its end, As a

consequence of the curved section and the

associated separated flow effects, the heat

transfer in the separation region under certain

operating conditions was reduced below values

measured upstream in the tube. Values of the

heat-transfer coefficient were higher with thin

boundary layers produced by a short, cooled

upstream length, and the distribution of the

heat-transfer coefficient in the redeveloped

region depended on whether the boundarylayer was turbulent or laminar. Effects of wall

cooling in terms of Tw/Tto that were found

upstream in the tube were not observable in the

separation and reattachment regions.

46
*Jet Propulsion Laboratory, Pasadena,

California, USA.

218. *Migdal, D.; Klein, K.; and Moretti, G.:

Time-Dependent Calculations for Transonic

Nozzle Flow. Technical Note. AIAA Journal,

vol. 7, no. 2, February 1969, pp. 372-374, 11

refs.

Wall pressure measurements in the transonic

regime of supersonic nozzles indicate that there

are no satisfactory theoretical predictions

methods when wall curvature effects are large.

In this note we examine the use of a

nonconservative form of the basic equations in

the analysis of axisymmetric, transonic nozzle

flows and compare the results with experimental data. In addition, the technique of

coordinate stretching in time-dependent

calculations is introduced to account properly

for subsonic boundary conditions.

*Grumman Aircraft Engineering Corp.,

Bethpage, New York, USA.

219. *Back, L.H.; Cuffel, R.F.; and Massier,

P.F.: Laminarization of a Turbulent Boundary

Layer in Nozzle Flow. Technical Note. AIAA

Journal, vol. 7, no. 4, April 1969, pp. 730-733,

12 refs.

the effect of

coefficient, an

the boundary

axisymmetric

measurements

are presented

Previous investigations of turbulent boundarylayer heat transfer from heated air flowing

through cooled supersonic nozzles have lead to

the observation of a reduction in turbulent

transport of heat under certain operating conditions, and effect also apparent in rocket engine

tests. In order to better understand the

conditions for which laminarization occurs and

laminarization on the friction

investigation of the structure of

layer was undertaken in an

nozzle. Boundary layer

upstream and within the nozzle

and this data reveal a strong

effect of flow acceleration on the structure of

an originally turbulent boundary layer.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

220. *Kliegel, J.R.; and Levine, J.N.:

Transonic Flow in Small Throat Radius of

Curvature Nozzles. AIAA Journal, vol. 7, no.

7, July 1969, pp. 1375-1378, 7 refs.

For most rocket nozzles of current interest, the

normalized wall radius of curvature R is less

than or equal to i, and it is generally believed

that expansion methods are inapplicable to the

study of the transonic flow region in a

convergent-divergent nozzle. It is shown,

however, that this limitation is due to the

coordinate syste m employed in the analysis

rather than to a fundamental limitation of the

expansion method itself.

*Dynamic Science, Monrovia, California, USA.

221. *Cuff el, R.F.; Back, L.H.; and Massier,

P.F.: Transonic Flowfield in a Supersonic

Nozzle with Small Throat Radius of Curvature.

Technical Note. AIAA Journal, vol. 7, no. 7,

July 1969, pp. 1364-1366, 15 refs.

This note presents some internal flow

measurements in the transonic regime of a

nozzle with a small ratio of throat radius of

curvature to throat radius (rc/rth = 0.625) and

compares some recently developed prediction

methods of other investigators with the data.

The measurements revealed radial variations in

the flow, At the physical throat, the Mach

number was 0.8 at the axis and 1.4 near the

wall. The three methods considered predicted

the transonic flowfieid reasonably well in

nozzles which have a small throat radius of

curvature (r /r <1.0), such as that for the

.c t

nozzle investlgate_.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

222. *Morden, D.B.; and Farquhar, B.W.:

Comment on Transonic Flow in Unconventional

Nozzles. Technical Comment. AIAA Journal,

vol. 7, no. 8, August 1969, pp. 1661-1662,

l ref.

This comment concerns discrepancies in the

published analysis by Hopkins and Hill (AIAA

Journal, May 1968). The "corrected" equations

are presented.

*The Boeing Company, Seattle, Washington,

USA.

47
223. *Massier, P.F.; Back, L.H.; et al: Viscous

Effects on the Flow Coefficient for a

Supersonic Nozzle. Technical Note. AIAA

Journal, vol. 8, no. 3, March 1970, pp. 605-

607, 7 refs.

Experimental values of adiabatic flow

coefficient are presented for choked flow in a

supersonic nozzle. The adiabatic flow

coefficient is influenced by the nozzle contour,

particularly in the throat region which

establishes the inviscid core flow distribution,

and by the viscous (boundary-layer) effects. In

the experiments, which were conducted with

argon, nitrogen, and helium, the boundary

layers in the throat region of the nozzle are

believed to have been laminar even at the

higher throat Reynolds number (350,000),

because of the high values of the acceleration

factor K. The experimental trend of an

increasing flow coefficient with Reynolds

number is in agreement with a laminar boundary-layer prediction, although most of the data

points at the intermediate and higher Reynolds

numbers were somewhat lower than the

predicted values of C D.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

224. *Back, L.H.: Acceleration and Cooling

Effects in Laminar Boundary Layers -

Subsonic, Transonic, and Supersonic Speeds.

AIAA Journal, vol. 8, no. 4, April 1970, pp.

794-802.

The structure of laminar boundary layers is

investigated analytically over a large range of

flow acceleration, surface cooling, and flow

speeds. For flow of a perfect gas over an

isothermal surface, the transformed boundarylayer equations with the similarity assumption

were solved numerically for values of an

acceleration parameter _ up to 20, a value not

uncommon to transonic flow in supersonic

nozzles, and for flat-faced bodies placed in

supersonic flow, as well as for values of the

surface-to-total-gas enthalpy gw ranging from

0 (severely cooled surface) to I. the solutions

were inverted and shown in the physical plane

where the velocity and total enthalpy profiles

depend upon the flow speed or compressibility

parameter S in addition to /_ and gw" Friction

and heat transfer parameters, as well as

thicknesses associated with the boundary layer,

are also shown. In general, the effects of

acceleration, cooling, and flow speed are

significant, but the dependence of the heattransfer parameter on fl and g)v is weak when

gw is small. Application otthe similarity

solutions to accelerated flow of real gases for

which viscosity is not proportional to

temperature and for which Prandtl number is

not unity is discussed.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

225. *Back, L.H.; Cuffel, R.F.; and Massier,

P.F.: Laminarization of a Turbulent Boundary

Layer in Nozzle Flow - Boundary Layer and

Heat Transfer Measurements with Wall Cool.

ASME Journal of Heat Transfer, vol. 92, no. 3,

August 1970, pp. 333-344, 33 refs.

Boundary layer and heat transfer measurements

are presented for flow through a cooled conical

nozzle with a convergent and divergent halfangle of 10 deg for a wall-to-total-gas

temperature ratio of 0.5. A reduction in heat

transfer below values typical of a turbulent

boundary layer was found when values of the

parameter K exceeded about 2 to 3 x 10- .

o

The boundary layer measurements, when

viewed in conjunction with the heat transfer

measurements, reveal the complicated nature of

the flow and thermal behavior and their

interrelationship when laminarization occurs.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

226. *Levine, J.N.; and Coats, D.E.;

Transonic Flow in a Converging-Diverging

Nozzle. NASA CR-IIII04, September 1970,

125 pp.

N71 - 10444#

The transonic equations of motion for a

converging diverging nozzle, including the

effect of variable gamma, were solved in

toroidal coordinates using a combination of an

asymptotic small parameter expansion and a

double coordinate expansion. The analysis was

kept general so that high order solutions could

be recursively calculated. It was found that the

use of toroidal coordinates and different

expansion parameters did not significantly

48
extend the range of normalized throat wall

radii of curvature for which expansion

solutions could be accuratelycalculated. An

explanationof why expansionmethodsfail for

small R is given. Calculationsmade,including

the effect of variable gamma (for a

homogeneousunstriatedflow), indicatethat its

effect is negligible in the transonicregion. A

new techniquefor solvingthe subsonicportion

of the nozzleflow is alsodescribed.

*DynamicScience,Irvine, California,USA.

227. *Back, L.H.; and Cuffel, R.F.: Flow

Coefficients for Supersonic Nozzles with

Comparatively Small Radius of Curvature

Throats. Journal of Spacecraft and Rockets,

vol. 8, no. 2, February 1971, pp. 196-198, 20

refs.

This note is concerned with the determination

of the mass flow rate through choked nozzles

with emphasis on comparatively small radius of

curvature throats. In the flow regime

investigj_ted (throat Reynolds numbers larger

v V than 10 ) iscous (boundary layer) effects are

not believed to be significant, so that the flow

field can be regarded as essentially isentropic.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

228. *Back, L.H.: Laminar Boundary Layers

with Large Wall Heating and Flow

Acceleration. Technical Note. AIAA Journal,

vol. 9, no. 5, May 1971, pp. 966-969, 13 refs.

The effect of large wall heating and flow

acceleration on the structure of laminar

boundary layers was analyzed over a range of

flow speeds. The heat-transfer parameter was

found to increase significantly with the amount

of wall heating in flow acceleration regions

provided that frictional effects are not

important and that the laminar boundary layer

is not on the verge of transition to a turbulent

boundary layer before the flow is accelerated.

Because of flow acceleration, the velocity

profiles with wall heating do not have an

inflection point in the region near the wall

where the velocity increases and therefore

would appear to be more stable to small

disturbances.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

229. *Rothe, D.E.: Electron-Beam Studies of

Viscous Flow in Supersonic Nozzle. AIAA

Journal, vol. 9, no. 5, May 1971, pp. 804-811,

19 refs.

Performance predictions for attitude control

jets of satellites and manned spacecraft suffer

from the lack of well-substantiated theoretical

and experimental data in the fully viscous

nozzle-flow regime. This paper presents an

experimental investigation of the internal and

external flow for nozzle Rey/_oids nu_nbers

in the general range between 10" and 10-' with

nitrogen as the test gas. Electron-beam

techniques are used for measuring gas density

and rotational temperatures at selected points

throughout the flow. Discharge coefficients are

also measured. In addition, some effects of

ambient pressure on the external flow structure

are studied by flow visualization experiments.

At the lower Reynolds numbers studied,

experimentally determined temperatures

indicate the existence of a supersonic bubble

inside the nozzle expansion cone, with a

subsequent shock-free viscous transition to

subsonic flow. These results substantiate the

theoretical prediction of this phenomenon, first

made by Pae in an earlier phase of this

program.

*Cornell Aeronautical Laboratory Inc., Buffalo,

New York, USA.

230. *Wagner, J.L.: A Cold Flow Field

Experimental Study Associated with a 2-D

Multiple Nozzle. NOLTR 71-78, July 1971, 89

pp, 13 refs.

N72-18306#

AD-731677

A cold flow-field study of a rapid expansion,

Mach 4.73, two-dimensional multiple nozzle

array has been carried out in the Hypersonic

Research Tunnel No.4 at the Naval Ordnance

Laboratory. The nozzles are of the type used

in a gas dynamics laser where the quality of the

downstream flow is important. Consequently,

this report examines the uniformity of the

flowfield in such a multiple nozzle array. Tests

were conducted at supply conditions of 45 psia

49
and 540°R. Pitot pressure, static pressure, and

total pressure were measured along the axial,

vertical, and horizontal centerlines within the

nozzle and to 21 exit heights downstream.

Shadowgraph pictures provided quantitative

flow field observations. The shock structure

consisted of sidewall shocks, nozzle trailing

edge shocks, and nozzle throat shocks. Viscous

phenomena consisted of the boundary layers on

the sidewalls and contoured wails, as well as

the turbulent wake caused by the trailing edges

of the center nozzle blades. Mach number,

static temperature, static density, and velocity

profiles are presented. This flowfield

information is useful to the prediction of the

degradation of beam quality resulting from the

non-homogeneity of a gas-dynamic-laser

flowfield.

*US Naval Ordnance Laboratory, White Oak,

Maryland, USA.

231. *Wortman, A.; and Mills, A.F.: Highly

Accelerated Compressible Laminar Boundary

Layer Flows with Mass Transfer. ASME

Journal of Heat Transfer, vol. 93, no. 3, August

1971, pp. 281-289, 13 refs.

Exact numerical solutions have been obtained

for highly accelerated self-similar laminar

boundary layer flows with and without mass

transfer. Values of the acceleration parameter

fl in the range 0 to 20 were considered.

Variable gas properties were realistically

modeled by assuming pcx h-1, # cx h _°, and Pr

= constant. The results presented show the

dependence of wall shear stress, heat transfer

rate, and displacement thickness on the

problem parameters which include _, Mach

number, wall enthalpy ratio, mass transfer rate,

w and Pr. The inadequacy of solutions

obtained under the simplifying assumptions of

Pr = 1.0 and w = 1.0 is clearly displayed. The

numerical solution procedure employed proved

quite adequate for a class of problem which has

presented serious difficulties to previous

investigators.

*Aerodynamics Research Branch, Northrop

Corp., Hawthorne, California, USA.

232. *Back, L.H.; Cuff el, R.F.; and Massier,

P.F.: Influence of Contraction Section Shape

and Inlet Flow Direction on Supersonic Nozzle

Flow Performance. Journal of Spacecraft and

Rockets, vol. 9, no. 6, June 1972, pp. 420-427,

16 refs.

Wall static pressure measurements and

performance parameters are presented for

axisymmetric supersonic nozzles with relatively

steep convergent sections and comparatively

small radius-of-curvature throats. The nozzle

walls were essentially adiabatic. These results

are compared with those obtained in other

nozzles tested previously to appraise the

influence of contraction shape on performance.

Both the flow coefficient and the thrust were

less than the corresponding values for onedimensional, isentropic, plane flow for both the

axial and radial inflow nozzles considered, but

the specific impulse, the most important

performance parameter, was found to be

relatively unchanged. The thrust decrement for

the axial inflow nozzles was established

primarily by the shape of the contraction

section, and could be estimated reasonably well

from a conical sink flow consideration. The

radial inflow nozzle has a potential advantage

from a cooling point of view if used in a

rocket engine.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

233. *Beckwith, I.E.; and Bertram, M.H.: A

Survey of NASA Langley Studies on HighSpeed Transition and the Quiet Tunnel. NASA

TM-X-2566, July 1972, 67 pp, 41 refs.

N72-26239

The present studies include a quantitative

experimental and theoretical assessment of the

role of wind-tunnel disturbances in the

boundary-layer transition process at hypersonic

speeds. The various approaches and recent

results for the development of a low-noiselevel tunnel are presented. A statistical

parametric study of transition data with a large

computer is shown for cones in free flight,

ballistic ranges, and wind tunnels at essentially

zero angle of attack. New transition results for

slender cones at small angle of attack are also

given, as are studies of transition at high angle

of attack, which are compared with various

correlation attempts. Included are results

which indicate that hypersonic transition in the

50
outer part of the boundary layer precedes the

manifestation of transition at the wall

("precursor" transition).

*NASA Langley Research Center, Hampton,

Virginia, USA.

234. *Back, L.H.; and Massier, P.F.: Viscous

Non-Adiabatic Laminar Flow Through a

Supersonic Nozzle: Experimental Results and

Numerical Calculations. ASME Journal of

Heat Transfer, vol. 94, no. 4, November 1972,

pp. 437-445, 29 refs.

Flow and thermal regimes found in relatively

low Reynolds-number flows of hightemperature gases in cooled convergentdivergent nozzles used in propulsion systems

and in research facilities are investigated by a

combined experimental and numerical

approach. The experiments were conducted

with argon at temperatures up to 14,200 deg R,

and the throat Reynolds number ranged from

2200 to 2800. The numerical calculations

involved the laminar-flow equations in differential form. Taken together, the experiments

and the numerical calculations provide

information on the pressure, heat-flux, and

shear-stress distributions along internal flows

with heat transfer, and on the velocity and

enthalpy distributions across the flow as well as

along the flow. The influence of heat

conduction and of viscous shear extended to

the centerline all along the nozzle.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

235. *Nash-Webber, J.; and Oates, G.C.: An

Engineering Approach to the Design of

Laminarizing Nozzle Flows. Journal of Basic

Engineering, December 1972, pp. 897-904, 18

refs.

Despite intensive research into laminarization

over the past twenty years, there has resulted

hitherto no prediction method suitable for ab

intio engineering design applications.

Following a critical survey of currently

proposed prediction criteria, this paper presents

experimental evidence for a new prediction

scheme applicable for the first time to

compressible adiabatic flows. It is shown that

this scheme is readily applicable for

engineering design purposes. Extension to

nonadiabatic flows is discussed.

*Northern Research and Engineering Corp.,

Cambridge, Massachusetts, USA.

236. *Joly, M.: CARACATH Program for the

Computation of Two-Dimensional Nozzle Flow

Using the Method of Characteristics. Research

Institute of St Louis ISL-12/73, May 1973, 49

pp, 5 refs. In French.

N74-17981 #

The computation of ideal non-viscous gas flow

in a two-dimensional supersonic nozzle is

presented. The transonic flow was computed

using an approximate method and the supersonic flow was computed using the method of

characteristics. The program written for an

IBM 360-40 computer is described and

numerical examples, including the evolution of

Mach number in the nozzle plane of symmetry,

at the nozzle wall, and along a line parallel to

the plane of symmetry of the nozzle are given.

*Institut Franco-Allemand de Recherches, Saint

Louis, France.

237. *Beckwith, I.E.; Harvey, W.D.; et al:

Control of Supersonic Wind-Tunnel Noise by

Laminarization of Nozzle-Wall Boundary

Layers. NASA TM-X-2879, December 1973,

57 pp, 64 refs.

N74-11119

One of the principal design requirements for a

"quiet" supersonic or hypersonic wind tunnel is

to maintain laminar boundary layers on the

nozzle walls and thereby reduce disturbance

levels in the test flow. The purpose of this

report is to review the conditions and apparent

reasons for laminar boundary layers which have

been observed during previous investigations on

the walls of several nozzles for exit Mach

numbers from 2 to 20. Based on these results,

an analysis and an assessment of nozzle design

requirements for laminar boundary layers

including low Reynolds numbers, high

acceleration, suction slots, wall temperature

control, wall roughness, and area suction are

presented.

51
*NASA Langley Research Center, Hampton,

Virginia, USA.

238. *Barger, R.L.: Streamline Curvature

Design Procedure for Subsonic and Transonic

Ducts. NASA TN-D-7368, December 1973, 16

pp, 11 refs.

N74-11818

A procedure for designing ducts for subsonic

and transonic speeds is described. Examples

discussed are a wind-tunnel contraction cone, a

supersonic nozzle, and a diffuser. A listing of

the computer program is included.

*NASA Langley Research Center, Hampton,

Virginia, USA.

239. *Cline, M.C.: Computation of Steady

Nozzle Flow by a Time-Dependent Method.

AIAA Journal, vol. 12, no. 4, April 1974, pp.

419-420, 11 refs. Also: NASA TM-X-71918.

The equations of motion governing steady,

inviscid flow are of a mixed type, that is,

hyperbolic in the supersonic region and elliptic

in the subsonic region. These mathematical

difficulties may be removed by using the so

called time-dependent method, where the

governing equations become hyperbolic

everywhere. The steady-state solution may be

obtained as the asymptotic solution for large

time. This technique has been used to

compute converging-diverging nozzle flows

by Prozan (as reported by Saunders and

Cuffel et al.), Migdal et al., Wehofer and

Moger, Laval, and Serra. This technique has

also been used to compute converging nozzle

flows by Wehofer and Moger and Brown and

Ozcan. While the results of the preceding

calculations are for the most part good, the

computational times are rather large. In

addition, although the computer program of

Serra included a centerbody and those of

Wehofer and Brown included the exhaust jet,

none of the preceding codes is able to calculate

both, that is, plug nozzles. Therefore, the

object of this research was to develop a

production type computer program capable of

solving converging, converging-diverging, and

plug two-dimensional nozzle flows in

computational times of ! minute or less on a

CDC 6600 computer.

*University of California, Los Alamos

Scientific Laboratory, Los Alamos, New

Mexico, USA.

240. *Swallow, R.J.; and Aiello, R.A.: NASA

Lewis 8 by 6 Foot Supersonic Wind Tunnel.

NASA TM-X-71542, May 1974, 24 pp, 4 refs.

N74-25789#

Performance data are presented for the tunnel,

which has a model support system, auxiliary

systems, instrumentation, control room

equipment, and automatic recording and

computing equipment are also described.

Information is presented on criteria for

designing models and on shop facilities

available to prospective users.

*NASA Lewis Research Center, Cleveland,

Ohio, USA.

241. Kreskovsky, J.P.; Shamroth, S.J.; and

McDonald, H.: Parametric Study of

Relaminarization of Turbulent Boundary

Layers on Nozzle Walls. NASA CR-2370, June

1974.

N74-28758

By means of comparisons between theoretical

predictions and experimental data, the accuracy

of a boundary procedure to predict the

simultaneous solution of the boundary layer

partial differential equations present

investigation show the ability of the procedure

to accurately predict properties of the boundary

layers subjected to large streamwise

accelerations, the procedure is used to conduct

a parametric study of the effect of free stream

turbulence, heat transfer, Reynolds number,

acceleration, and Mach number on boundary

layers in supersonic nozzles to assist in the

design of a quiet tunnel. Results of the

investigation show that, even in the presence of

moderate free-stream turbulence levels, the

boundary layer in the approach section of the

quiet tunnel nozzle relaminarizes and becomes

thin enough to be removed by a small slot.

242. *Aielio, R.A.: NASA Lewis 10 by 10

Foot Supersonic Wind Tunnel. NASA TM-X71625, November 1974, 47 pp.

52
N75-14780#

Performancedataare presentedfor this tunnel,

which hasa Mach number rangefrom 2.0 to

3.5. Also described are the tunnel circuit,

model support systems, auxiliary systems,

instrumentation, control roomequipment,and

automaticrecordingand computingequipment.

Information is presented on criteria for

designing models and on shop facilities

availableto users.

*NASA Lewis ResearchCenter, Cleveland,

Ohio,USA.

243. *Pfenninger, W.; and Syberg, J.:

Reduction of Acoustic Disturbances in the Test

Section of Supersonic Wind Tunnels by

Laminarizing their Nozzle and Test Section

Wall Boundary Layers by Means of Suction.

NASA CR-2436, November 1974, 305 pp, 80

refs.

N75-12977#

The feasibility of quiet, suction laminarized,

high Reynolds number (Re) supersonic wind

tunnel nozzles was studied. According to nozzle

wall boundary layer development and stability

studies, relatively weak area suction can

prevent amplified nozzle wall TS (TollmienSchlichting) boundary layer oscillations.

Stronger suction is needed in and shortly

upstream of the supersonic concave curvature

nozzle area to avoid transition due to amplified

TG (Taylor-Goertler) vortices. To control TG

instability, moderately rapid and slow

expansion nozzles require smaller total suction

rates than rapid expansion nozzles, at the cost

of larger nozzle length Re and increased TS

disturbances. The total suction mass flow ratios

for the laminarization of high Re supersonic air

nozzles increase from 0.005 at Mach 3 (test

section) to 0.0105 at Mach 9. Nozzle wall

cooling decreases TS oscillations; TG instability

in the concave curvature region, though, may

be worse. Due to smaller nozzle length Re and

Goertler parameters, Mach 9 helium nozzles

require half as much suction for their

laminarization as Mach 9 air nozzles of the

same U*D*/u* (test section). Boundary layer

crossflow instability on the side walls of twodimensional high Re supersonic nozzles due to

streamline curvature requires strong local

suction to avoid transition. Nozzle wall surface

roughness is critical in the throat area,

especially at high Mach numbers, but not in

the downstream nozzle region. Allowable

surface roughness in the throat area of a Mach

9 helium nozzle is five times larger than for a

comparable Mach 9 air nozzle. Test section

mean flow irregularities can be minimized with

suction through longitudinal or highly swept

slots (swept behind local Mach cone) as well as

finely perforated surfaces (hole spacing _<

subsonic nozzle wall boundary layer thickness).

Longitudinal slot suction is optimized when the

suction-induced crossflow velocity increases

linearly with surface distance from the slot

"attachment line" toward the slot (through

suitable slot geometry). Suction in supersonic

blowdown tunnels may be operated by one or

several individual vacuum spheres.

*Boeing Commercial Airplane Co., Seattle,

Washington, USA.

244. *Beckwith, I.E.: Development of a High

Reynolds Number Quiet Tunnel for Transition

Research. AIAA Journal, vol. 13, no. 3, March

1975, pp. 300-306, 33 refs.

High noise levels in conventional supersonic

and hypersonic wind tunnels modify or

dominate transition on test models. Transition

research and predictions for flight conditions

then require at least a partial simulation in

wind tunnels of the much lower disturbance

levels usually present in flight. The minimum

operational limit for Reynolds numbers is a

"quiet" wind tunnel will depend on unit

Reynolds number and are established by

transition Reynolds number correlations of

free-flight data. High facility noise levels also

dominate fluctuating pressure loads under

fully turbulent boundary layers. Reliable

measurements of these loads are required for

panel vibration and flutter research. By analogy

with recent data on the effects of stream

turbulence and noise on low-speed turbulent

shear layers, the basic structure of supersonic

turbulent shear layers may be modified by

high facility noise levels. Required research

in these areas determines the maximum

design Reynolds numbers for a quiet tunnel.

Experimental data for current techniques to

control and reduce noise levels in supersonic

and hypersonic wind tunnels by laminarization

of nozzle wall boundary layers and by noise

radiation shields are presented. These results

53
and possible effects of Taylor-Goertler

vortices observed in a nozzle wall boundary

layer are used to predict the limits of quiet

performance for a proposed 20 in. quiet tunnel.

*NASA Langley Research Center, Hampton,

Virginia, USA.

245. *Dumitrescu, L.Z.: Minimum Length

Axisymmetric Laval Nozzle. AIAA Journal,

vol. 13, no. 4, April 1975, pp. 520-521, 5 refs.

This paper deals with determination of a class

of minimum-length axisymmetric Laval

nozzles, which are compared to the simple

conical type, emphasizing the extra length

needed to ensure uniform flow conditions.

Submission of the paper has been prompted by

the publication of Reddall; in fact, most of the

following results have been obtained (and

applied) over ten years ago, including the

derivation of the hodograph equation for

axisymmetric source flow, but were left

dormant in a journal of limited circulation.

*Institute of Fluid Mechanics and Aerospace

Technology, Bucharest, Rumania.

246. *Jaeggy, B.C.: A FORTRAN Program for

the Computation of Two-Dimensional or

Axisymmetric Nozzles. Anglo-German

Research Institute of St Louis ISL-R-I10/75,

April 1975, 58 pp, 6 refs. In French.

N77-11012#

This program, minimizing operator

interventions, provides the necessary codes for

the manufacturing of the nozzle using the

following data: ratio of heat mass of gas, Mach

number required at the nozzle exit, ratio of

throat curvature radius to height or to throat

radius, and height or diameter of exit section.

The program and numerical methods used are

described in this paper.

*Institut Franco-Allemand de Recherches, Saint

Louis, France.

247. *Brown, E.F.; and Hamilton, G.L.:

Survey of Exhaust-Nozzle Flow Analysis.

AIAA Paper 75-60. AIAA Journal of Aircraft,

vol. 13, no. 1, January 1976, pp. 4-11, 82 refs.

This paper reviews methods capable of solving

the problems of two-dimensional (planar or

axisymmetric) isentropic (inviscid and shockfree) flow of a perfect gas. The methods cited

are divided into two groups: indirect methods

and direct methods. Indirect methods (or

inverse methods) involve the specification of a

velocity (or pressure) distribution along some

reference line in the flowfield (usually the

centerline). These methods compute the

boundary geometry and are sometimes called

design methods. In direct methods, the

boundary geometry (nozzle wail) is specified

and the resulting solution then represents a

complete description of the nozzle flowfield. It

is the authors' hope that the classification and

discussion of relative merits of the methods

cited in this paper will bring to the attention of

the nozzle designer the vast number of

analytical methods available to him and will

enable him to select the method that possess the

appropriate combination of accuracy, speed,

and computational flexibility.

*Virginia Polytechnic Institute and State

University, Blacksburg, Virginia, USA.

248. *Cline, M.C.: Computation of TwoDimensional, Viscous Nozzle Flows. AIAA

Journal, vol. 14, no. 3, March 1976, pp. 295-

296, 4 refs.

The calculation of viscous nozzle flows can be

accomplished by either solving the inviscidcore and viscous-boundary-layer equations

separately or by solving the viscous equations

for the entire flowfield. In the inviscid-core,

boundary-layer approach, the assumption is

made that the boundary layer is thin when

compared to the nozzle diameter. However, for

Reynolds numbers on the order of 103 based

on the throat diameter, this assumption is

questionable. On the other hand, while the

viscous equation approach is physically

desirable, the computations tend to be rather

lengthy. Therefore, the object of this research

was to modify an efficient inviscid code to

solve the viscous equations. This new code,

called VNAP (Viscous Nozzle Analysis

Program), is then used to calculate the flow in

a chemical laser nozzle. This numerical

solution is compared with both the inviscidcore, boundary-layer solution and experimental

data presented by Hyde.

54
*Theoretical Division, University of California,

Los Alamos, New Mexico, USA.

249. *Back, L.H.; and Cuff el, R.F.:

Compressible Laminar Boundary Layers with

Large Acceleration and Cooling. Technical

Note. AIAA Joarnal, vol. 14, no. 7, July 1976,

pp. 968-971, 13 refs.

This note extends an approximate prediction

method involving the integral form of the

momentum equation to deduce the flow

qualities of interest when compressible effects

become important and heat transfer may occur.

the approximate method is applicable to a twodimensional laminar boundary layer on an

impermeable surface of negligible curvature for

a specified integral momentum equation. The

proposed approximate method involves the use

of similar solutions in conjunction with the

integral momentum equation for isentropic

freestream flow of a perfect gas by assuming

that viscosity is proportional to stagnation

condition and Prandtl number is unity. The

study pertain to larger values of acceleration

(acceleration parameter to 20 rather than 2)

than previously considered to account for

rapidly accelerating flows such as in a

supersonic nozzle. A discussion of some

applications confirms the advantages of the

method in establishing better confidence in the

predictions.

*Jet Propulsion Laboratory, Pasadena,

California, USA.

250. *Mclntosh, A.C.; and Pike, J.: The 1-4-

1 System of Jack Movements for the Flexible

Liners of Supersonic Wind Tunnels. RAE TM

Aero.1684, August 1976, 20 pp, 4 refs.

In a wind tunnel with flexible liners the

movement of a single supporting jack causes

ripples along the plate, and consequently

complicated changes in the flow pattern. A

method is proposed for containing these ripples

by moving the adjacent jacks. A system called

the 1-4-1 system is derived and test data is

shown to verify the smoothing and shortening

effect it has on the resulting flow disturbances.

*Royal Aircraft Establishment, UK.

251. *Brown, E.F.; Brecht, T.J.; and Walsh,

K.E.: A Relaxation Solution of Transonic

Nozzle Flows Including Rotational Effects.

AIAA Journal of Aircraft, vol. 14, no. 10,

October 1977, pp. 944-951, 12 refs.

A computational procedure is described for

rotational transonic flows. The effects of

rotationality were introduced by a rotation

function, and the resulting "potential-like"

equations were solved by type-dependent

relaxation. The method has been used to

predict the flowfield in propulsion-type nozzles

using both arbitrarily specified and

experimentally measured entrance conditions.

In these runs, good agreement with analysis and

available experimental results was obtained, and

a significant influence due to the rotationality

of the flow was observed.

*Mechanical Engineering Department, Virginia

Polytechnic Institute and State University,

Blacksburg, Virginia, USA.

252. *Reed, T.D.; Pope, T.C.; and Cooksey,

J.M.: Calibration of Transonic and Supersonic

Wind Tunnels. NASA CR-2920, November

1977, 287 pp, 123 refs.

N78-15058#

State-of-the art instrumentation and

procedures for calibrating transonic (0.6 < M <

1.4) and supersonic (M < 3.5) wind tunnels are

reviewed and evaluated. Major emphasis is

given to transonic tunnels. Background

information was obtained via a literature

search, personal contacts, and a questionnaire

which was sent to 106 domestic and foreign

facilities. Completed questionnaires were

received for 88 tunnels and included

government, industry and university-owned

facilities. Continuous, blowdown and

intermittent tunnels are considered. The

required measurements of pressure,

temperature, flow angularity, noise and

humidity are discussed, and the effects of

measurement uncertainties are summarized,

Included is a comprehensive review of

instrumentation currently used to calibrate

empty-tunnel flow conditions. The recent

results of relevant research are noted and

recommendations for achieving improved data

accuracy are made where appropriate. It is

55
concluded, for general testing purposes, that

satisfactory calibration measurements can be

achieved in both transonic and supersonic

tunnels. The goal of calibrating transonic

tunnels to within 0.001 in centerline Math

number appears to be feasible with existing

instrumentation, provided correct calibration

procedures are carefully followed. A

comparable accuracy can be achieved offcenterline with carefully designed, conventional

probes, except near Mach 1. In the range 0.95

< M < 1.05, the laser doppler velocimeter

appears to offer the most promise for improved

calibration accuracy off-centerline. With

regard to procedures, tunnel operators are

cautioned to: (1) verify by measurements that

expansions from a settling chamber to a test

section are indeed isentropic, and (2) obtain

calibrations over the entire range of Reynolds

number and humidity levels. Also, it is

suggested that calibration data should include

off-centerline measurements of Mach number

and flow angularity. Finally, three problem

areas for transonic tunnels are identified and

discussed, viz. (1) the lack of standard criteria

for flow uniformity and unsteadiness, (2) the

undesirable noise generated by ventilated walls,

and (3) wall interference.

*Vought Corporation, Dallas, Texas, USA.

253. *Anders, J.B.; Stainback, P.C.; and

Beckwith, I.E.: A New Technique for Reducing

Test Section Noise in Supersonic Wind

Tunnels. AIAA Paper 78-817. In: Proceedings

of AIAA 10th Aerodynamic Testing

Conference, April 1978, pp. 354-364, 25 refs.

A78-32371#

A new technique is presented for obtaining a

low-noise test environment in a high-speed

wind tunnel. This technique utilizes the fact

that the primary noise source for high

supersonic/hypersonic wind tunnels is radiated

noise from the turbulent, tunnel-wall boundary

layer. Because of the high directionality of

sound in supersonic flows this test section noise

originates far upstream on the walls of the

nozzle at the "acoustic origin." It is shown

that tailoring the nozzle contour to reduce the

acoustic origin Mach number significantly

reduces the noise level in the upstream half of

the nozzle test rhombus. Experimental noise

measurements are presented from a

conventional, Mach 5 nozzle and are compared

with measurements from a rapid-expansion,

Mach 5 nozzle.

*NASA Langley Research Center, Hampton,

Virginia, USA.

254. *Hoffman, J.D.; and Allman, J.G.:

Design of Maximum Thrust Nozzle Contours by

Direct Optimization Methods. AIAA Paper 78-

1048. Presented at AIAA/SAE 14th Joint Propulsion Conference, July 1978, 8 pp, 17 refs.

A78-43573#

A procedure is presented for the design of

maximum thrust nozzle contours by direct

optimization methods. The nozzle contour is

modeled as a second-degree polynomial having

a fixed initial expansion contour. The

coefficients of the polynomial are varied by

direct optimization methods to determine the

maximum thrust contour. Three direct optimization methods are considered: multidimensional line search, the method of steepest

decent, and Newton's method. Results are

presented to illustrate the behavior of the three

direct optimization methods, and to

demonstrate that second-degree polynomial

contours yield thrusts substantially identical to

the thrusts developed by nozzle contours

determined by calculus of variations methods.

*Mechanical Engineering Department, Purdue

University, West Lafayette, Indiana, USA.

255. *Mitra, N.K.; and Fiebig, M.: Supersonic

Nozzle Flowfieids: A Comparison of Fully

Viscous and Navier-Stokes Solutions. In:

Theoretical and Experimental Fluid Mechanics,

Chapter 3 - Nozzle Flow, published by

Springer-Verlag, 1979, pp. 157-165, 8 refs.

This paper describes the process of selecting a

suitable scheme for the numerical solution of

the full Navier-Stokes and energy equations in

a Laval nozzle with different initial conditions

and boundary conditions. A comparison is

made between the computed flowfields and

corresponding fully viscous channel flow

solutions. The present work shows that nozzle

flows with larger Reynolds numbers can also be

handled with Crocco's scheme. In addition,

56
fully viscous channel flow solutions, when

available, are an ideal choice as an initial field.

*DLR, West Germany.

256. *Anders, J.B.; Stainback, P.C.; and

Beckwith, I.E.: New Technique for Reducing

Test Section Noise in Supersonic Wind

Tunnels. AIAA Journal, vol. 18, no. 1,

January 1980, pp. 5-6, 11 refs.

The major problem in the design of a lownoise supersonic wind tunnel is to reduce the

noise radiated from the turbulent, nozzle-wall

boundary layer. This broadband noise is

generally the dominant disturbance mode in

wind tunnels at Mach numbers greater than

about 2.5. These acoustic disturbances are

propagated along Mach lines in supersonic

flow; hence, their sources are located far

upstream of the test section at so-called

"acoustic origins" near the nozzle wall. It is

shown that tailoring the nozzle contour to

reduce the Mach number and boundary-layer

thickness at the acoustic origins significantly

reduces the noise levels in the upstream part of

the test rhombus.

*NASA Langley Research Center, Hampton,

Virginia, USA.

257. *Erickson, L.L.; Kassner, D.L.; et ah

Single-Mode Panel Flutter of a Wind Tunnel

Flex-Wall. AIAA Journal of Aircraft, voi. 17,

no. 7, July 1980, pp. 521-527, 11 refs.

Twice during the spring of 1978, the two steelplate "flex-walls" that form the variablegeometry nozzle of the 11- x ll-foot transonic

wind tunnel at Ames Research Center experienced a severe dynamic instability. Both

walls fluttered in the fundamental beambending mode and experienced stresses

approaching the yield strength of the material.

Both flutter incidents occurred at Mach

numbers of about 1.15. The tunnel, operational

for 24 years, had no history of such an

instability. The cause of these flutter

incidents, the steps taken to prevent a

recurrence, and the requalification of the

facility are described.

*NASA Ames Research Center, Moffett Field,

California, USA.

258. *Drummond, D.; Rogers, B.; and

Demetriades, A.: Design and Operating

Characteristics of the Supersonic Wind Tunnel.

Montana State University SWT-TR-81-01,

January 1981.

*Department of Mechanical Engineering,

Montana State University, Bozeman, Montana,

USA.

259. *Baker, T.J.: Numerical Computation of

Transonic Potential Flow Through Nozzles.

The Aeronautical Quarterly, vol. 32, part 1,

February 1981, pp. 31-42, 14 refs.

A numerical method for computing potential

flow through either a planar or axisymmetric

nozzle is described. Some results obtained from

a computer program based on this method are

presented and compared with experimental

data.

*Aircraft Research Association Ltd., Bedford,

UK.

260. *Beckwith, I.E.: Comments on Settling

Chamber Design for Quiet Blowdown Wind

Tunnels. NASA TM-81948, March 1981, 39

pp, 22 refs.

N81-20085#

Recently developed methods indicate that the

total turbulence levels, which include both the

acoustic and vorticity modes, can be reduced to

1 percent or less in the settling chamber of a

typical blowdown tunnel. Based on recent data

and the present analysis of two different

blowdown facilities at Langley, methods to

achieve these low levels of acoustic and

vorticity distributions are recommended.

Included are pertinent design details of the

damping screens and honeycomb and also the

recommended minimum pressure drop across

the porous components which will provide the

required two orders of magnitude attenuation

of the acoustic noise levels.

*NASA Langley Research Center, Hampton,

Virginia, USA.

57
261. *Demetriades, A.: Roughness Effect on

Boundary-Layer Transition in a Nozzle Throat.

AIAA Paper 81-4057. AIAA Journal, vol. 19,

no. 3, March 1981, pp. 282-289, 16 refs.

A81-4057

A boundary-layer transition study was carried

out in the throat region of the DeLaval nozzle

of a supersonic wind tunnel. The study was

motivated equally by the need to find

thresholds for laminar boundary-layer flow in

the tunnel walls when roughness is present and

by the desire to simulate transition on

roughened blunt bodies in supersonic and

hypersonic flow. Detailed inviscid and viscous

flow measurements were done from the low

subsonic to the supersonic regions of the nozzle

throat. The roughness was caused by attaching

distributed roughness overlays on the nozzle

surface. Transition, detected by hot-film

anemometers, was found to move upstream as

the flow Reynolds number and/or the

roughness height increased. Cast in the

coordinates of some of the empirical bluntbody transition correlations currently in use,

the present transition data agree with the

available blunt-body data when the

nondimensionai roughness exceeds unity and

support the concept of a constant roughness

Reynolds number for transition in that regime.

At the lower roughness heights, the results

show that the transition Reynolds number

departs from the aforementioned correlations

and approaches a limit insensitive to roughness

but characteristic of the experimental facility.

*Mechanical Engineering Department, Montana

State University, Bozeman, Montana, USA.

262. *Dutton, J.C.; and Addy, A.L.:

Transonic Flow in the Throat Region of

Axisymmetric Nozzles. AIAA Paper 81-4136.

Technical Note. AIAA Journal, vol. 19, no. 6,

June 1981, pp. 801-804, 6 refs.

The purpose of this Note is to present the

series solution for axisymmetric nozzles which

satisfies the governing differential equations in

cylindrical coordinates. The expansion variable

employed is • = (Rc+rl) -1, where the value of

the parameter rl is arbitrary. The results of this

solution are compared to two data sets for

which the nozzle wall radius of curvature is

relatively small.

*Department of Mechanical Engineering, Texas

A&M University, College Station, Texas, USA.

263. *Allman, J.G.; and Hoffman, J.D.:

Design of Maximum Thrust Nozzle Contours by

Direct Optimization Methods. AIAA Paper 78-

1048R. AIAA Journal, vol. 19, no. 6, June

1981, pp. 750-751, 4 refs.

A procedure for the design of maximum thrust

nozzle contours by direct optimization methods

is presented. The nozzle contour is a seconddegree polynomial having a fixed initial

expansion contour. The coefficients of the

polynomial are varied by direct

optimization methods to determine the

maximum thrust contour. Three direct

optimization methods are considered:

multidimensional line search, the method of

steepest descent, and Newton's method. Results

are presented to illustrate the behavior of the

direct optimization methods, and to

demonstrate that second-degree polynomial

contours yield thrusts comparable to the thrusts

developed by nozzle contours determined

by calculus of variations methods.

*Purdue University, West Lafayette, Indiana,

USA.

264. *Demetriades, A.: Boundary Layer

Transition in a Supersonic Nozzle Throat in

the Presence of Cooling and Surface

Roughness. Montana State University

MSU/SWT TR-82-01, August 1981, 181 pp, 18

refs.

Observations of boundary-layer transition in a

supersonic wind-tunnel nozzle throat were

made in the region where the local Mach

number increased from 0.4 to 2. The wall

temperature ranged from adiabatic to 0.66

times the stagnation temperature, and its

surface configuration varied from random

sand-grain to waffle-type and wire-screen

roughness. The roughness height was changed

from a fraction to a multiple of the local

momentum thickness. It was found that wall

cooling accelerates transition markedly, and

that for a given average peak-to-valley

roughness height, the random sand-type

roughness is the most efficient trigger of

transition, followed by the waffle-type

roughness and then by the wire-screen

58
roughness. Weaveorientation had a weak

effect on transition, but on the other handthe

transition Reynolds number decreased

drastically when the weave wavelength

increased.Transition tripping by loweringthe

wall temperature would be even more

pronounced were it not for local relaminarization phenomenaobservedat these

lower temperatures. Such isolated relaminarization or restabilization regions were

seen only when the roughness heights were

relatively small. A substantial portion of these

data cannot be a counted for by existing bluntbody boundary-layer transition correlations.

*Mechanical Engineering Department, Montana

State University, Bozeman, Montana, USA.

265. *Campbell, R.L.: Computer Analysis of

Flow Perturbations Generated by Placement of

Choke Bumps in a Wind Tunnel. NASA TP1892, August 1981, 42 pp, 7 refs.

N81-30088

An inviscid analytical study has been conducted

to determine the upstream flow perturbations

caused by placing choke bumps in a wind

tunnel. A computer program based on the

stream-tube curvature method was used to

calculate the resulting flow fields for a nominal

free-stream Mach number range of 0.6 to 0.9.

The choke bump geometry was also varied to

investigate the effect of bump shape on the

disturbance produced. Results from the study

indicate that a region of significant variation

from the free-stream conditions exists upstream

of the throat of the tunnel. The greatest

upstream disturbance distance generally

occurred along the tunnel center line and

extended from a minimum of about 0.25 tunnel

height ahead of the throat to a maximum of

about 2.0 tunnel heights for the cases

considered. The extent of the disturbance

region was, as a rule, dependent on Mach

number and the geometry of the choke bump.

In general, the upstream disturbance distance

decreased for increasing nominal free-stream

Mach number and for decreasing length-toheight ratio of the bump. A polynomial-curve

choke bump usually produced less of a

disturbance than did a circular-arc bump, and

going to an axisymmetric configuration

(modeling choke bumps on all the tunnel walls)

generally resulted in a lower upstream

disturbance distance than with the

corresponding two-dimensional case. Finally,

for some of the circular-arc configurations,

certain flow parameters could be estimated by

using the throat geometry.

*NASA Langley Research Center, Hampton,

Virginia, USA.

266. Hermann, R.: The Supersonic Wind

Tunnel Installations at Peenemunde and Kochel

and Their Contributions to the Aerodynamics

of Rockets. In: Proceedings of the 32nd

International Astrological Conference,

September 1981, pp. 435-446.

A83-11285

The goal in 1937 was to build an aerodynamicballistic research institute to provide for all

aerodynamic, stability and heat transfer

research needs. The construction of the

supersonic tunnel, with a 40 cmx 40 cm testsection, is described, which was operational at

Peenemunde in 1939 and moved to Kochel in

1943. Seven wind tunnel Laval nozzles,

ranging up to Mach number 5, were in use.

Their theory, design and construction is

outlined and their wave patterns are illustrated.

Detailed measurements of delta wings such as

the 'Glider A9' or the 'Wasserfall' are

presented. The influence of exhaust jet on

drag and stability is discussed.

267. *Lin, C.Q.; and Shen, S.F.: Analysis of

Transonic Flow with Shocks in Slender

Hyperbolic Nozzles. AIAA Paper 82-0160.

Presented at AIAA 20th Aerospace Sciences

Meeting, January 1982, 9 pp, 4 refs.

A82-17813#

Analytical solutions of lwo-dimensionai and

axisymmetric transonic potential flow with

shock in slender hyperbolic nozzles are

obtained by using asymptotic expansions. A

measure of the slenderness of the nozzle is

defined by a parameter delta, with only the

case of fully developed transonic shock with

strength of order delta considered; however,

alternative expansions based on either the

velocity potential of the stream function

formulation, are included. In either case, the

entropy increase across the shock is of the

59
order delta to the 3rd power, while the

vorticity for the flow behind the shock is of

order delta to the 4th power. The present

theory is, in principle, more accurate than

transonicdiscretizationschemeswhichsolvethe

governingequationswith jump conditions. In

a two-dimensional example, the comparison

with a state-of-the-art finite-difference

computationshowsexcellentagreementin the

predictedshockshape.

*CornellUniversity, Ithaca,NewYork, USA.

268. *Beckwith, I.E.; Creel, T.R.; et al: Free

Stream Noise and Transition Measurements in

a Mach 3.5 Pilot Quiet Tunnel. AIAA Paper

83-0042. Presented at AIAA 21st Aerospace

Sciences Meeting, January 1983, 24 pp, 30 refs.

A small scale, Mach 3.5 low disturbance tunnel

for boundary-layer transition research has been

designed, built, and tested. Free stream noise

levels and transition Reynolds numbers on a 5°

half-angle cone have been measured over a unit

Reynolds number range from 10 to 60 million

per meter. A two-dimensional nozzle used in

the facility incorporates unusual design features

of a rapid expansion contour, boundary-layer

bleed slots upstream of the throat, and an exit

width to height ratio of 1.7 to provide noise

levels in the upstream regions of the test

rhombus that are substantially lower than in

conventional nozzles. The normalized rms

levels or fluctuating static pressures obtained

from hot-wire measurements vary from

extremely low values of less than 0.03 percent

(essentially with in the instrument noise range)

up to about 0.8 percent depending on the unit

Reynolds number, the axial location in the test

rhombus, and the bleed slot flow. As is well

known, the higher noise levels are caused by

eddy Mach wave radiation from the turbulent

boundary layers on the nozzle walls. When the

valve which controls the boundary-layer bleed

flow is open, the wall boundary layers over

upstream regions of the nozzle are laminar at

the lower unit Reynolds numbers and the

absence of high frequency radiated noise then

results in cone transition Reynolds numbers

that are in the range of free-flight data. As

the unit Reynolds numbers are increased, the

nozzle wall boundary layers become transitional

and turbulent. The noise then increases to

peak levels of about 0.5 percent with

significant energy up to 150 KHz. The cone

transition Reynolds number then decrease

considerably to values that are in the range of

those measured in conventional wind tunnels.

*NASA Langley Research Center, Hampton,

Virginia, USA.

269. *Nachshon, Y.: Simple and Accurate

Calculation of Supersonic Nozzle Contour.

Technical Note. AIAA Journal, voi. 21, no. 5,

May 1983, pp. 783-784, 4 refs.

The method of characteristics is commonly used

to design a supersonic nozzle. This method is

widely applied to large nozzles where the

boundary-layer displacement thickness is

small compared to the nonviscous flow. As the

nozzle becomes larger and the Mach

number higher, one should use more

characteristics lines in order to achieve an

accurate supersonic profile. Such a profile is

necessary to obtain a uniform flowfieid at the

exit of the nozzle in the supersonic test

chamber. A simple method that considerably

increases the accuracy of the solution for a

given number of characteristics lines is

described in this paper.

*Armament Development Authority, Haifa,

Israel.

270. *Beckwith, I.E.; Creel, T.R.; et al: FreeStream Noise and Transition Measurements on

a Cone in a Mach 3.5 Pilot Low Disturbance

Tunnel. NASA TP-2180, September 1983, 68

pp, 34 refs.

N83-34229#

This paper describes experiments with a 10 x 6

in. Mach 3.5 two-dimensional nozzle to

demonstrate a reduction in free stream

disturbance levels over conventional nozzle

designs and to observe the subsequent effects

upon transition on a slender cone. Three

notable features of the nozzle design are: first,

the use of a rapid-expansion contour; second,

the selection of a wide separation of the two

planar sidewalls in order that noise generated

by the sidewalls reaches the tunnel centerline

downstream of the model location; and third,

the provision for boundary layer bleed slots

shortly upstream of the nozzle throat for

removal of the turbulent boundary layer on the

60
contractionwalls. For unit Re),noldsnumbers

from 2.5 x 105up to 15 x 10" per inch, the

observed root-mean-square values of the

fluctuating static pressures were found to vary

from extremely low values of less than 0.03

percent up to 0.8 percent of the mean static

pressure. When the boundary-layer bleed valve

was open, the upstream regions of the nozzle

wall boundary layers were laminar, which

resulted in the cone transition Reynolds number

approaching those reported for free flight.

*NASA Langley Research Center, Hampton,

Virginia, USA.

271. *Malik, M.R.: Instability and Transition

in Supersonic Boundary Layers. Presented at

the Energy Sources Technology Conference,

February 1984. In: Laminar Turbulent

Boundary Layers published by ASME, pp. 139-

147, 23 refs.

TL 357 E54

(Ames Research Center library no.)

Linear compressibility stability theory is used

to analyze the recently available flight

transition data (Moo=l.2, 1.35, 1.6, 1.92) and

"'quiet" tunnel data (Moo=3.5) for a 5 degree

half angle cone. The results show that, for

these, low supersonic Mach numbers, the

exponent N in the e N type transition

correlation ranges between 9 and 11. These

values of N are within the range of values

previously determined for subsonic flows (both

flight and ground, two- and three-dimensional

mean flows). Computations show that the

transition in both the flight and quiet tunnel

experiment was caused by oblique first mode

disturbances. The paper contains detailed

results of the calculations including disturbance

wave number, wave angle, and group velocity.

*High Technology Corp., Hampton, Virginia,

USA.

272. *Beckwith, I.E.; Malik, M.R.; and Chen,

F.-J.: Nozzle Optimization Study for Quiet

Supersonic Wind Tunnels. AIAA Paper 84-

1628, Presented at AIAA 17th Fluid Dynamics,

Plasma Dynamics, and Lasers Conference, June

1984, 23 pp, 25 refs.

Recent results from a Mach 3.5 pilot quiet

tunnel at the NASA Langley Research Center

have shown that very low stream noise levels

can be achieved only when the nozzle wall

boundary layers are laminar r. For the key part

of the present study an e '_ method transition

criteria was applied to several nozzles with a

range of expansion rates and wall curvatures.

The design Mach number, exit dimensions, and

unit Reynolds numbers were the same as for

the pilot nozzle. The effect of nozzle design

parameters on the extent of laminar wall

boundary-layer flow and the corresponding

lengths of the quiet test regions depend on the

rate of change of the concave curvature and on

the wall angle at the inflection point. By

manipulation of these parameters, the

calculations indicate that it maybe possible to

increase significantly the size of the quiet test

regions compared with those observed in the

pilot nozzle. Some limited experimental results

from the pilot nozzle on the influence of nozzle

finish and flow contaminants on maintaining

and increasing the extent of laminar wall

boundary layers are also presented.

*NASA Langley Research Center, Hampton,

Virginia, USA.

273. *Beckwith, I.E.; Malik, M.R.; et al:

Effects of Nozzle Design Parameters on the

Extent of Quiet Test Flow at Mach 3.5.

Presented at IUTAM Symposium on LaminarTurbulent Transition, .July 1984 In: LaminarTurbulent Transition published by SpringerVerlag, 1985, pp. 589-600, 17 refs.

TA 357 L35

(Ames Research Center library no.)

To advance boundary-layer stability and

transition research and to ultimately provide

reliable predictions of transition for supersonic

flight vehicles, a wind tunnel is required with

much lower stream disturbance levels than in

conventional supersonic tunnels. Recent results

from a Mach 3.5 pilot quiet tunnel at the

NASA Langley Research Center have shown

that very low stream noise levels can be

achieved only when the nozzle wall boundary

layers are laminar. Transition Reynolds

numbers measured on a slender cone were then

in the same range as flight data. The linear

amplification of both Tollmein-Schlichting (TS)

and Goertler type instabilities was calculated

61
for the wall boundary layers in this Mach 3.5

pilot nozzle. By using an e N method, it was

determined that amplified Goertler vortices

were involved in the transition process. The

resulting transition criteria were then applied to

several nozzles with different expansion rates

and wall curvatures. By manipulation of these

parameters, the calculations indicate that it may

be possible to increase significantly the size of

the quiet test regions compared with those

observed in the pilot nozzle.

*NASA Langley Research Center, Hampton,

Virginia, USA.

274. *Penaranda, F.E.; and Freda, M.S.:

Supersonic Wind Tunnels. In: Aeronautical

Facilities Catalogue - Volume l, Wind Tunnels,

NASA RP-l132, January 1985, pp. 187-236.

N85-18991

This catalog updates and supplements previous

surveys conducted on aeronautical facilities.

NASA undertook this survey primarily to form

a database from which to assess its own

capabilities and that of the United States in

aeronautical research and development,

particularly in relation to that of the western

world. No information on Russian wind

tunnels is presented. Thirty-nine supersonic

wind tunnels are identified in this catalogue.

*Office of Aeronautics and Space Technology,

NASA HQ, Washington, DC, USA.

275. *Chen, F.-J.; Malik, M.R.; and Beckwith,

I.E.: Instabilities and Transition in the Wall

Boundary Layers of Low-Disturbance

Supersonic Nozzles. AIAA Paper 85-1573,

June 1985, 14 pp, 29 refs.

To advance boundary-layer stability and

transition research at supersonic speeds, a wind

tunnel with very low stream disturbance levels

is required. Recent work at NASA Langley has

shown that the required low noise levels can be

obtained only when the boundary layers are

laminar over the upstream regions of the nozzle

w qlls where the radiated noise originates. The

e'" method based on data from four test nozzles

was used to predict transition in four study

nozzles. The results indicate that even larger

quiet test length Reynolds numbers are possible

than observed in the test nozzles may be

obtained in longer nozzles designed with the

wall inflection point located far downstream.

*High Technology Corp., Hampton, Virginia,

USA.

276. *Bazin, M.: The New Controllable Mach

Supersonic Nozzle for the S3MA Wind Tunnel.

Presented at the 64th STA Meeting, October

1985, 16 pp.

The $3 blowdown tunnel of the ONERA

Modane test center has been in operation since

1960. Removable nozzles or test sections are

used: transonic inserts, 2D insert, supersonic

nozzles at M = 2 - 3.4 - 4.5. A supersonic

nozzle with controllable Mach number in the

range 1.65 to 3.8 has just been made, mainly

for missile and launcher tests. The design of

this nozzle is described along with its operating

range and main characteristics. This nozzle

consists of two symmetrical rigid blocks rotated

by an original single actuator system (a single

actuator for each half nozzle) which changes

the throat by rotating the rigid blocks and

adapting the divergent part, made of a flexible

plate.

*ONERA, Chatillon-Cedex, France.

277. *Varner, M.O.: Application of

Optimization Principles to Flexible Wall Nozzle

Design - A Case Study. AIAA Paper 86-0775,

March 1986, 15 pp, 5 refs.

A86-24755#

A flexible wall nozzle design approach is

presented that couples optimization concepts

and current design methodologies. The

optimization process provides for a tuned

nozzle design which meets specific performance

and operating environment requirements. A

case study involving a generic transonic flexible

nozzle wall design is utilized to focus on the

important steps in the nozzle design

optimization process. The integrated nozzle

design is based on the definition of the

optimum plate thickness, number of actuators,

actuator distribution and contour shape

covering the Mach number and Reynolds

number range of the nozzle. Use of this

technique provides the designer with the

62
capability to totally integrate geometric,

operation and performancerequirementsinto

the nozzledesign,yielding design simplicity

and controllability and minimizing

constructioncosts.

*Sverdrup Technology Inc., Tullahoma,

Tennessee,USA.

278. *Beckwith, I.E.; Chen, F.-J.; and Creel,

T.R.: Design Requirements for the NASA

Langley Supersonic Low-Disturbance Wind

Tunnel. AIAA Paper 86-0763. Presented at

AIAA 14th Aerodynamic Testing Conference,

March 1986, 15 pp, 22 refs.

Recent results from a research program at

NASA Langley to develop a quiet supersonic

tunnel have shown that limited upstream

regions of the nozzle-wall boundary layer in a

small Mach 3.5 pilot tunnel can be maintained

laminar at high unit Reynolds numbers. The

high level acoustic disturbances are then

eliminated and transition Reynolds numbers

measured on cones approach those for

atmospheric flight. Critical design

requirements for a large facility (which will be

a blow-down tunnel) are presented in this

paper. These requirements are based on studies

completed or underway in the pilot quiet

tunnels at Mach numbers of 3, 3.5, and 5. In

particular, the design requirements for high

quality supply air filters, noise attenuation

devices in the settling chamber, and nozzle

coordinate accuracy and surface finish are

illustrated and quantified with data from the

pilot tunnels.

*NASA Langley Research Center, Hampton,

Virginia, USA.

279. *Dillon, J.L.; Trimpi, R.L.; and Schultz,

A.E.: The NASA-Langley 20-inch Supersonic

Wind Tunnel. AIAA Paper 86-0765.

Presented at the AIAA 14th Aerodynamic

Testing Conference, March 1986, l0 pp, 8 refs.

The renewed emphasis on fundamental

aerodynamic research in high-speed flows at

the NASA Langley Research Center has

resulted in the acquisition of a new wind

tunnel. The new 20-in. Supersonic Wind

Tunnel) (SWT), formerly located at the Jet

Propulsion Laboratory (JPL), is in the process

of being assembled following extensive

modifications. Several unique features have

been incorporated into the new tunnel. Some

of these features are a "quiet" flow control

valve, thick sintered screens with very large

pressure drops, special fairings in the

contraction section, an "'instantaneous" relief

hatch in the test section, and a switching

exhaust system to permit flow into a vacuum

sphere during startup and shutdown and to

atmosphere during data acquisition. This paper

will describe the modifications, unique

features, and expected operating map of the

new tunnel.

*NASA Langley Research Center, Hampton,

Virginia, USA.

280. *Bushnell, D.M.; and Trimpi, R.L.:

Supersonic Wind Tunnel Optimization. AIAA

Paper 86-0773. In: Proceedings of the AIAA

14th Aerodynamic Testing Conference, June

1986, pp. 282-300, 90 refs.

An optimum supersonic facility is defined by

identifying (a) major shortfalls in current

supersonic facility capability, and (b) advanced

technology capable of addressing these

deficiencies. Major problem areas include (1)

large amplitude stream disturbances caused by

acoustic radiation from nozzle wall boundary

layers, of particular importance to the

boundary layer transition problem on models,

(2) flow field and model shape distortion

caused by sting supports and their installation,

(3) lack of sufficient three-dimensional flow

visualization and flow diagnostic capability to

identify "Reynolds number effects," (4) lack of

aerodynamic/propulsion facilities to investigate

the necessary range of vehicle attitudes and

transient propulsion behavior, and (5)

inordinately large energy usage, caused

primarily by inefficient diffusers. Remedies

proffered for these shortfalls include (a)

development of a quiet supersonic wind tunnel

with laminar wall boundary layers, (b) further

development/usage of magnetic balances, (c)

scanning "stimulated Raman spectroscopy" to

measure time-average, three-dimensional flow

field details, the data base to serve as both

diagnostics and, through computer graphics,

visualization, (d) an "effectively flexible" wall

free-jet wind tunnel capable of transient

attitude and speed changes, and (e) improved

diffusers. The optimum wind tunnel, which is

63
both technically and economically justifiable

(especially in view or the emerging CFD

capability),is not a singlefacility and not even

a new one. The major emphasisshould be

placeduponretrofit of existingtunnels.

*NASA Langley Research Center, Hampton,

Virginia, USA.

281. *Park, M.; and Caughey, D.A.:

Transonic Potential Flow in Hyperbolic

Nozzles. AIAA Journal, vol. 24, no. 6, June

1986, pp. 1037-1039, 7 refs.

The classical problem of transonic flow through

a hyperbolic nozzle with or without a shock

wave, has been revisited by applying recently

developed numerical methods. Both planar and

axisymmetrical cases have been considered.

The full potential equation is solved in

conservation form using the finite volume

method of Jameson and Caughey. To treat the

mixed nature of the equation, either a first- or

a second-order numerical viscosity in the

direction of the flow is added explicitly in

conservation form. A multigrid, alternating

direction implicit (ADI) method is used to solve

the difference equations and the results are

compared with analytical and numerical results

of earlier researchers. The scheme converges

rapidly, and results are in good agreement with

those of earlier workers, including analytical

results for flows containing shock waves.

*Cornell University, Ithaca, New York, USA.

282. Marks' Standard Handbook for

Mechanical Engineers. Supersonic and

Hypersonic Aerodynamics. Ninth Edition,

published by McGraw-Hill Book Co., 1987, pp.

1181-1192, 9 refs.

This section gives a very brief overview of

supersonic and hypersonic aerodynamics.

Comments about nozzle design are included.

This presentation covers such topics as a

proposed supersonic low-disturbance tunnel,

quiet test core lengths, effects of surface

damage on transition asymmetry in a supersonic

nozzle, allowable surface roughness, and the

influence of Goertler vortices on nozzle design.

The conclusions drawn are that large width

two-dimensional rapid expansion nozzles

guarantee wide quiet test cores that are well

suited for testing models at large angle of

attack and for swept wings. Also test results

indicate that the surface finish of the pilot

nozzle is critical. Experimental data and

calculations for Mach 3.0, 3.5 and 5.0 nozzles

give N-factors from 6 to 10 for transition

caused by Goertler vortices. The use of N -_

9.0 for the Goertler instability predicts quiet

cores in the new Mach 3.5 and Mach 6.0

axisymmetric-long pilot nozzles that are 3 to 4

times longer than observed in the test nozzles

to date. The new nozzles utilize a region of

radial flow which moves the inflection point

far downstream and delays the onset and

amplification of Goertler vortices.

*NASA Langley Research Center, Hampton,

Virginia, USA.

284. Tsybizov, Y.I.; and Zagvozdkin, V.V:

Flows in Laval Nozzles of Gas Turbine Engines

in Steady and Unsteady Operation. Aviatsion.

Tekhnika, vol. 31, no. 3, 198.__.__.88, pp. 85-87, 3

refs. In Russian. English translation in

Soviet Aeronautics published by Allerton Press,

pp. 97-100.

The paper describes the results of nozzle model

tests used in steady and unsteady gas turbine

engine operating states at low available

expansion degrees. It is concluded that the

shape of the subsonic part of the nozzle and

the different operation intensity variation rates

have a significant influence on the flow

pattern, pulsations, vibrations, and the noise

level.

283. *Beckwith, I.E.; Chen, F.-J.; and Malik,

M.R.: Design and Fabrication Requirements

for Low Noise Supersonic/Hypersonic Wind

Tunnels. In: Proceedings of Research in

Natural Laminar Flow and Laminar-Flow

Research Symposium, NASA CP-2487, _March

1987, pp. 947-964, 13 refs.

285. *Beckwith, I.E.; Chen, F.-J.; and Malik,

M.R.: Design and Fabrication Requirements

for Low-Noise Supersonic/Hypersonic Wind

Tunnels. AIAA Paper 88-0143. Presented at

AIAA 26th Aerospace Sciences Meeting,

January 1988, I I pp, 22 refs.

64
The experimental and theoretical program at

NASA Langley to develop a low-disturbance

wind tunnel is described. Theoretical analysis

of the experimental test results by means of a

linear stability theory has shown that

amplification of Goertler vortices on the

concave walls of nozzles at Mach numbers from

3 to 5 are the cause of transition. The downstream boundaries of the quiet test region are

determined by Mach lines extended

downstream from the transition locations on the

nozzle walls. The theory was then used to

design advanced nozzles for Mach numbers 3.5

and 6 that will provide much longer quiet test

regions. Transition on the nozzle walls is

extremely sensitive to nozzle wall roughness.

Allowable roughness on the two advanced

nozzles and the new proposed large-scale

facility were then calculated from a roughness

Reynolds number criterion based on the test

results.

*NASA Langley Research Center, Hampton,

Virginia, USA.

286. *Charpin, F.; and Hugouvieux, P.: Start

and Unstart in S2 Supersonic Wind Tunnel in

ONERA Modane-Avrieux Center. Presented at

69th STA Meeting, Los Angeles, May 1988.

ONERA TP 1988/9, 31 pp, 1 ref.

A89-29244#

To investigate the mechanism of flow

breakdown in the $2 wind tunnel at the

ONERA Modane-Avrieux center, a measurement system was designed, which makes it

possible to visualize in real time the variations

of the Mach number distributions along the

walls of the first throat, the test section, the

second throat, and the diffuser. The

measurement system consists of a set of

pressure multi-transducers producing the

instantaneous Mach number distributions.

Several cases are presented which clearly show

the effectiveness of the device, and the

monitoring and surveillance possibilities.

*ONERA, Modane-Avrieux, France.

287. *Ehrenfried, K.: Dynamics of Laval

Nozzle Flow Under Different Boundary

Conditions. Thesis from Max Planck Institute,

May 1988, 74 pp. In German.

N89-22083

A numerical one-dimensional calculation of the

transonic Laval nozzle flow was performed. A

computer program was developed and tested on

a steady example. Flow separation was taken

into account using a simplified model. In

calculations with separation, it is shown that

separated flow behind a shock wave, with a

periodic pressure excitation at a certain

frequency allows excitation and eigenfrequency

to be observed, providing a possible

explanation of the experimentally observed

irregular shock oscillations.

*Max Planck Institute, Stuttgart, West

Germany.

288. Guoyao, F.: Prediction of TwoDimensional Supersonic Nozzle Flow Field.

Journal of Propulsion Technology, no. 3, June

1988, pp. 6-11, 2 refs. In Chinese.

A89-47410#

This paper presents a method for ascertaining

two-dimensional characteristics which can be

applied to the calculation and design of a

rocket supersonic nozzle. Some useful

conclusions are drawn from the analysis of

computational results. The results brought

about by the method are so good that the

method can be suggested as a reference for

nozzle design and heat transfer analysis of

rocket nozzles.

289. *Beckwith, I.E.; and Bushnell, D.M.:

Wind-Tunnel Simulation of High-Speed Flight

Transition. Presented at the USSR Academy of

Sciences International Seminar on Problems of

Simulations in Wind Tunnels, July 1988. In:

Proceedings, vol. 1, pp. 33-46, 29 refs.

The problem of, and a particular solution for,

the simulation of free-flight supersonic

boundary-layer transition in ground facilities

are discussed. Fundamental problems addressed

include: (a) technology requirements for

blowdown low-disturbance wind-tunnels from

upstream piping through to the diffuser with

emphasis on maintenance of laminar nozzle wall

flows, (b) characteristics and operational

aspects of the NASA-LaRC Pilot Supersonic

Quiet Tunnel, and (c) comparisons of high65
speed quiet facility transition studies with

results from free flight, stability theory, and

conventional ground facilities. Maintenance of

laminar nozzle wall flow is shown to be a

necessary condition for accurate simulation of

high-speed flight transition behavior in ground

facilities.

*NASA Langley Research Center, Hampton,

Virginia, USA.

configurations. It is shown that the one

investigated actually possesses the shortest

length as well as the smallest initial wall turn

angle at the throat. It also has an inflection

point on the wall contour, in contrast to the

other configurations.

*School of Aerospace and

Engineering, The University

Norman, Oklahoma, USA.

Mechanical

of Oklahoma,

290. *Van Every, D.; Raimondo, S.; and

Elfstrom, G.M.: Impact of Nozzle Design

Constraint on Test Section Flow Quality. In:

AGARD Aerodynamic Data Accuracy and

Quality: Requirements and Capabilities in Wind

Tunnel Testing, FDP Meeting, July 1988, I I

pp, l l refs.

N89- 16860#

A procedure is described which allows the

design of relatively short adjustable nozzles

without resorting to the assumption of radial

flow upstream of the nozzle inflection point.

This design procedure is used to generate a

number of fully flexible nozzle designs for a

design Mach number of 1.4. Flexible nozzle

parameters such as pressure load, number of

actuators and nozzle length are varied in order

that the influence of these parameters on test

section flow quality may be evaluated. The

influence of nozzle actuator setting accuracy is

also estimated. The parametric study shows

that high flow quality can be achieved for the

shortest nozzle considered. The examination of

jack setting errors shows that for well designed

nozzles, jack setting error will be a significant

source of test section flow nonuniformities.

*DSMA International Inc., Toronto, Canada.

291. *Argrow, B.M.; and Emanuel, G.:

Comparison of Minimum Length Nozzles.

Journal of Fluids Engineering, vol. l l0, no. 3,

September 1988, pp. 283-288, I I refs.

A second-order accurate method-ofcharacteristics algorithm is used to determine

the flow field and wall contour for a

supersonic, axisymmetric, minimum length

nozzle with a straight sonic line. Results are

presented for this nozzle and compared with

three other minimum length nozzle

292. Yamanaka, S.: Transonic Flow in Throat

Region of Supersonic Nozzles. Japanese

Society for Aeronautical and Space Sciences

Journal, vol. 37, no. 428, 198____99, pp. 451-455, 8

refs. In Japanese.

A90- 16799#

The transonic potential flows in the throat

region of two-dimensional and axisymmetric

nozzles were calculated using a biquadratic

equation for the velocity potential in case of

R/h = 3, 4 and 5, where R is the radius of the

throat wall and h is the half-width of throat.

In addition, the effects of the radius of

curvature of the wall were calculated; the flow

was also visualized using a schlieren technique.

293. *Schnerr, G.; and Dohrmann, U.:

Theoretical and Experimental Investigation of

2-D Diabatic Transonic and Supersonic Flow

Fields. In: Proceedings of IUTAM Symposium

Transonicum 3 published by Springer, 1989, 10

pp, 18 refs.

Inviscid, stationary 2-D flows of moist air

with nonequilibrium phase transition are

calculated numerically using the Euler equation

coupled with the classical nucleation theory.

In Laval nozzles with supercritical heat addition

the apparent normal shocks with local subsonic

regions in the surrounding supersonic flow

field are computed. Homogeneous

condensation in local supersonic regions around

profiles is calculated for the first time with

detailed analysis of the 2-D structure for

continuous change of state as well as for

stationary double shock systems. For nozzles

and profiles, all numerical results are well

verified by experiments.

*Institute fur Stromungslehre und St-maschinen

Universitat (TH) Karlsruhe, West Germany.

66
294. *Bushnell, D.M.: Notes on Initial

Disturbance Fields for the Transition Problem.

NASP TM-1051, March 1989, 27 pp, 115 refs.

This note describes the transition process as a

6-stage affair which is initiated by the ambient

disturbance environment. The importance of

stream turbulence, particulates, electrostatics,

and roughness are discussed. The overall

disturbance levels in flight are compared with

those disturbances found in wind tunnels.

*NASA Langley Research Center, Hampton,

Virginia, USA.

295. *Chen, F.-J.; Malik, M.R.; and Beckwith,

I.E.: Boundary-Layer Transition on a Cone

and Flat Plate at Mach 3.5. AIAA Journal,

vol. 27, no. 6, June 1989, pp. 687-693, 33 refs.

A89-36904#

Boundary-layer transition data on a cone and

flat plate obtained in the Mach 3.5 Pilot LowDisturbance Tunnel at NASA Langley are

presented. Measured flat plate transition

Reynolds numbers in this tunnel are an order

of magnitude higher than previous results

obtained in conventional noisy supersonic wind

tunnels. Transition predictions based on

compressible linear stability theory and the e N

method with N=I0 are in excellent agreement

with the measured locations of transition onset

for both the cone and flat plate under lownoise conditions in this tunnel. This

investigation has resolved the discrepancies

between the results of linear stability theory

and the data from conventional supersonic wind

tunnels regarding the ratio of cone to flat plate

transition Reynolds numbers.

*High Technology Corp., Hampton, Virginia,

USA.

296. *Argrow, B.M.; and Emanuel, G.: A

Computational Analysis of the Transonic Flow

Field of Two-Dimensional Minimum Length

Nozzles. AIAA Paper 89-1822. Presented at

the AIAA 20th Fluid Dynamics, Plasma

Dynamics and Lasers Conference, June 1989,

21 pp, 44 refs.

A89-42052#

The method of characteristics is used to

generate supersonic wall contours for twodimensional, straight sonic line (SSL) and

curved sonic line (CSL) minimum length

nozzles for exit Mach numbers of 2, 4, and 6.

These contours are combined with subsonic

inlets to determine the influence of the inlet

geometry on the sonic-line shape and location

and on the supersonic flow field. A modified

version of the code VNAP2 is used to compute

the inviscid and laminar flow fields for

Reynolds numbers of 1170, 11700, and 23400.

Results indicate that the inlet geometry directly

determines the sonic-line shape and location.

Supersonic flow field phenomena, including

boundary-layer separation and oblique shock

waves, are observed to be a direct result of the

inlet geometry, the sonic-line assumptions

made for SSL prove to be superior to those of

the CSL.

*University of Oklahoma, Norman, Oklahoma,

USA.

297. *Lee, C.Y.; McCool, R.C.; and Chitwood,

N.M.: Actively Cooled Panel Characteristics

Study. AIAA Paper 89-1726. Presented at

AIAA 24th Thermophysics Conference, June

1989, 12 pp, 2 refs.

A89-43241 #

A computer program was developed to study

the characteristics of an actively cooled panel

designed for autoheating flux on the order of

200 Btu/sq ft/sec. At this high heat flux, the

panel experiences very high thermal stress that

must be considered in addition to bending

stress due to internal pressure. This forces the

structural and thermal analyses to depend on

each other. The methodology used in the

computer program was developed to generate

trends of how design parameters affect the

panel structure and thermal performance. The

analytical results can then be used to identify a

design path leading to a panel design that is

optimized with respect to the vehicle as a

whole. Discussions of interactions between

structural and thermal design parameters are

provided.

*Space Systems Division, General Dynamics

Corp., San Diego, California, USA.

67
298. *Chen, F.-J.; Malik, M.R.; and Beckwith,

I.E.: Advanced Mach 3.5 Axisymmetric Quiet

Nozzle. High Technology Report no. HTC8903, August 1989, 29 pp, 23 refs.

To advance boundary-layer stability and

transition research and to ultimately provide

reliable predictions of transition for supersonic

flight vehicles, a wind tunnel is required with

very low stream disturbance levels comparable

to free flight conditions. Experimental and

theoretical research to develop a lowdisturbance supersonic wind tunnel has

achieved a breakthrough. A new concept for

nozzle design is presented which promises a

large increase in the length of the quiet test

core. The Advanced Mach 3.5 Axisymmetric

Quiet Nozzle is the first prototype built to

prove the new design concept. Experimental

results from this new nozzle on the extent of

laminar wall boundary layers are compared

with data from other nozzles and with

theoretical predictions based on linear stability

theory. The Reynolds numbers based on the

measured length of the quiet test core for this

new nozzle are in excellent agreement with the

theoretical predictions. The effect of surface

finish on the nozzle performance is also

discussed.

*High Technology Corp., Hampton, Virginia,

USA.

68
Author Index

A

Ackeret, J., 7, 14

Addy, A.L., 262

Ahlberg, J.H., 178

Aiello, R.A., 240, 242

Alikhashkin, Y., 185

Allen, H.J., 56

Allman, J.G., 254, 263

Anders, J.B., 253, 256

Anderson, A., 184

Argrow, B.M., 291, 296

Armstrong, A.H., 107

Atkin, A.O.L., 34

B

Back, L.H., 193, 201, 208, 209, 211, 217,

219, 221, 223, 224, 225, 227, 228, 232,

234, 249

Badham, H., 188

Bailey, A., 8

Baker, T.J., 259

Barger, R.L., 238

Barnett, R.M., 163

Baron, J.R., 137, 140, 145, 159

Barritt, M.M., 165, 168

Bazin, M., 276

Beavan, J.A., 97

Beckwith, I.E., 146, 233, 237, 244, 253, 256,

260, 268, 270, 272, 273, 275, 278, 283,

285, 289, 295, 298

Bershader, D., 85

Berthold, 22

Bertram, M.H., 233

Boden, O.W., 74

Bogdonoff, S.M., 60, 104, 136

Boldman, D.R., 214

Bonney, E.A., 89

Bowling, A.G., 54

Bradfield, W.S., 35

Brecht, T.J., 251

Briggs, L.J., 3

Bright, P.I.F., 95

Brinich, P.F., 99

Brown, E.F., 247, 251

Busemann, A., 4, 6, 20

Bushnell, D.M., 280, 289, 294

C

Caiger, M.T., 95

Campbell, R.L., 265

Carafoli, E., 152

Carden, W.H., 204

Carriere, P., 189

Caughey, D.A., 281

Chambre, P.L., 67

Charpin, F., 286

Chen, F.-J., 272, 275, 278, 283, 285, 295, 298

Chew, W.L., 98

China, 288

Chitwood, N.M., 297

Chushkin, P.I., 185

Cline, M.C., 239, 248

Clippinger, R.F., 109

Coats, D.E., 226

Cohen, C.B., 101

Cole, D., 162

Conlin, L.T., 135

Cooksey, J.M., 252

Corrsin, S., 113

Courant, R., 61

Creel, T.R., 268, 270, 278

Crocco, L., 12

Cronvich, L.L., 50, 63

Crown, J.C., 66, 115

Cuffel, R.F., 208, 209, 211, 217, 219, 221,

225, 227, 232, 249

Culbertson, P.E, 88

Cumbers, L.L., 199

Cunsolo, D., 106, 125

I)

Darwell, H.M., 188

Demetriades, A., 203, 258, 261, 264

Dhawan, S., 105

Dillon, J.L., 279

Dohrmann, U., 293

Douglas, B., 127

Drougge, G., 76, 110

Drummond, D., 258

Dryden, H.L., 3

Dumitrescu, L.Z., 245

Durgin, F.H., 140, 145

Dutton, J.C., 262

E

Eaton, A.R., 35

Eber, G.R., 32

Edelman, G.M., 49, 51, 64

Ehrenfried, K., 287

Eisenklam, P., 167

Elfstrom, G.M., 290

Emanuei, G., 291, 296

Emerson, D.E., 77, 90

Emmons, H.W., 41

Erickson, L.L., 257

Evvard, J.C., 72, 112, 114

69
F

Failis, W.B., 122

Farcluhar, B.W., 222

Favorskii, A.P., 185, 202

Fejer, A.A., 39

Ferri, A., 15, 37, 80, 136

Fiebig, M., 255

Fisher, E.R., 160

Foelsch, K., 40, 83

Fox, L., 28

Frankl, F.I., l0

Frazer, R.P., 167

Freda, M.S., 274

Freidrichs, K.O., 25, 29, 61

Frossel, W., 38

Frost, R.C., 94, 118

G

Gallagher, A.K., 214

Garby, L.C., 92

Gibbings, J.C., 197

Gier, H.L., 193, 201

Goddard, F.E., 175

Goin, K.L., 195

Goldman, L.J., 212

Gompf, G.F., 81

Goranson, G.G., 163

Green, J.R., 24

Guoyao, F., 288

H

Haefeli, R.C., 117, 119

Hall, I.M., 182, 190

Hall, M.G., 158, 198

Hamilton, G.L., 247

Hamilton, S., 178

Harrop, R., 95

Harvey, W.D., 237

Hawthorne, W.R., 57

Heins, A., 127

Henderson, H.W., 87

Hermann, R., 19, 33, 266

Heybey, W.H., 21, 45, 129

Hill, D.E., 206, 213

Hill, J.A.F., 148, 159

Hilton, W.F., 102

Hoffman, J.D., 254, 263

Holder, D.W., 82, 97

Hollingdale, S., 165

Holt, M., 70, 100, 181

Hopkins, D.F., 206, 213

Hugouvieux, P., 286

Hulbert, J.K., 75

70

I

Idelchik, I.E., 13

Irani, P.A., 176

J

Jacocks, J.L., 180

Jaeggy, B.C., 246

Jeffries, N.P., 199

Johannesen, N.H, 96

Johnson, G.W., 122

Joly, M., 236

K

Kane, E.D., 67, 77

Karner, L., 7

Kassner, D.L., 257

Kennedy, E.C., 155

Kenney, J.T., 143

Kisenko, M.S., 17

Klein, K., 218

Kiiegel, J.R., 215, 220

Kreskovsky, J.P., 241

Kurzweg, H.H., 16, 69, 79, 161

L

LaBerge, J.G., 120, 126, 135

Landis, F., 183

Landsbaum, E.M., 172

Laufer, J., 139

Leavy, L.E., 157

Lee, C.Y., 297

Lee, R.E., 207

Lehnert, R., 18

Levine, J.N., 220, 226

Liepman, H.P., 118, 150

Liepmann, H.W., 46

Lieu, B.H., 194

Lin, C.Q., 267

Lindsey, W.F., 98

Lord, W.T., 170

Lukasiewicz, J., 31, 54

M

MacDermott, W.N, 133, 147, 179

Malik, M.R., 271, 272, 273, 275, 283, 285,

295, 298

Marcus, L.R., i 12

Maslen, S.H., 114

Massier, P.F., 193, 201, 209, 211, 217, 219,

221, 223, 225, 232, 234

Maxwell, H., 180

McCabe, A., 192

McCool, R.C., 297

McDonald, H., 241
M

Mclntosh,A.C., 250

McKenney,J.D., 103

Meyer,R.E.,65, 73, 96, 100,153

Migdal, D., 183,200,218

Miller, L.T., 93

Mills, A.F., 231

Mitra, N.K., 255

Monroe, L.L., 78

Moore, J.A., 146

Morden, D.B., 222

Moretti, G., 218

Morkovin, M.V., 154, 169

Morris, D.E., 142 N

Nachshon, Y., 269

Nash-Webber, J., 235

Nelms, L.T., 216

Nelson, W.C., 92

Nilson, E.N., 53, 55, 58

North, R.J., 82 O

Oates, G.C., 235

Orlin, W.J., 127, 131

Oswatitsch, K., 84

O'Brien, R.L., 196 P

Park, M., 281

Pasqua, P.F., 187

Penaranda, F.E., 274

Peterson, J.W., 59

Pfenninger, W., 243

Pike, J., 250

Pinkel, I.l., 36, 62

Pope, A., 91, 177, 195

Pope, T.C., 252

Prandtl, L.,4

Puckett, A.E., 27, 44, 46, 68 Q

Quan, V., 215 R

Raimondo, S., 290

Rao, G.V.R., 166, 173

Reed, T.D., 252

Reshotko, E., 119

Riise, H.N., 130, 132, 138

Roberts, R.C., 160

Rogers, B., 258

Rosen, J., 149

Roshko, A., 105

Rothe, D.E., 229

R

Rothstein, W., 84

Royle, J.K., 54

Ruptash, J., 116

Ryzhov, O.S., 164 S

Santon, L., 11

Satyanarayana, B., 176

Sauer, R., 47, 52

Savin, R.C., 128

Schaaf, S.A., 67, 86, 90

Schmidt, J.F., 214

Schnerr, G., 293

Schueler, C.J., 171

Schultz, A.E., 279

Seippel, C., 23

Serrell, P.V.H., 130

Serruys, M., 111

Shames, H., 36

Shamroth, S.J., 241

Shapiro, A.H., 26, 49, 51, 123, 134

Shen, S.F., 267

Sichel, M., 205

Sivells, J.C., 151, 156

Smelt, R., 43, 144

Smith, M.G., 107

Southwell, R.V., 24, 28

Squires, R.K., 160

Stack, J., 9, 30

Stainback, P.C., 253, 256

Stanton, T.E., 1, 2,5

Stevens, P.N., 187

Stram, L., 48

Strike, W.T., 171

Sutton, E.P., 190

Sutton, M.A., 75

Swallow, R.J., 240

Syberg, J., 243

Syvertson, C.A., 128 T

Temple, E.B., 108

Trimpi, R.L., 279, 280

Tsien, H.S., 71

Tsybizov, Y.I., 284 V

Valerino, A.S., 101

Van Every, D., 290

Vanco, M.R., 212

Varner, M.O., 277

Von Eschen, G.L, 75

Von Seggern, L., 203

Vrebalovich, T., 174

71
W

Wagner,J.L., 230

Walsh,K.E., 251

Webb,L.M., 143

Westkaemper, J, 141

Wiikie, D., 167

Williams,J.C.,186,210

Winter, K.G., 142

Wood, S.A., 8

Wortman, A., 231

Wyatt, D.D., 72

Y

Yamanaka, S., 292

Yanta, W.J., 207

Z

Zagvozdkin, V.V, 284

72
Subject Index

Please Note: The following index, although in no way complete, is still useful in giving an

indication of where some material on definite subject areas may be found.

Bibliography: 42, 80, 97, 136, 143, 159, 191,

237, 243, 247, 252, 280, 294

Boundary layer suction:

Nozzle, 196, 231, 243, 244, 253, 260,

270, 272, 273, 275, 279, 283, 285,

289, 294, 295, 298

Measurements (Continued):

Review, 30, 252

Nozzle calibration:

General, 54, 88, 95,

148, 149, 171

120, 126, 135,

Review, 237 Review, 159, 195, 252

Test section, 101, 243

Comparison of nozzle theory and experiment:

6, 41, 84, 99, 140, 194, 201, 204, 206,

223, 233, 234, 241, 248, 251, 259,

262, 271, 289, 293, 294

Computer program included: 187, 199, 212,

216, 236, 238, 246

Nozzle contour correction strategies: 45, 58,

68, 95, 100, 108, 129, 133, 147, 153,

154, 163, 250

Nozzle design accuracy: 39, 85, 129, 137, 138,

142, 144, 153, 158, 192, 237, 265,

269, 283, 285, 290, 298

Nozzle design, Analytical:

Condensation considerations: 6, 61, 144, 293 Atkins method, 34, 116, 143, 152, 245

Contraction considerations: Crown method, 66, 115, 118

Experiment, 197, 217

General, 55, 113, 232, 238, 291

Flow uniformity considerations: 113, 139,

142, 153, 169, 174, 184, 188, 197,

208, 232, 260, 268

Flow visualization: 11, 18, 27, 80, 85, 91,

102, 103, 229, 292

Foelsch method, 40, 66, 83, 88, 116,

143, 146, 172

Freidrichs method, 25, 29, 137

General, 49, 50, 51, 55, 63, 114, 150,

165, 168, 170, 202, 212, 236, 238,

246, 263, 288

Integral method, 181

Historical: 2, 3, 7, 8, 9, 12, 14, 15, 16, 18,

19, 23, 30, 32, 33, 42, 43, 57, 60, 71,

161, 266

Nilson method, 53, 118, 143

Pinkel method, 36, 62

Inlet flow condition considerations, 17, 113,

169, 197, 232, 260, 291, 296

Measurements:

Experiment, 20 !

General, 11, 35, 38, 39, 85, 97, 102,

159, 161, 184, 195, 200, 207, 286

Puckett method, 44, 66

Review, 123

Sauer method, 47, 52, 188

Siveils method, 151, 156

Squires method, 160

Probes, 71, 88, 148, 177, 230, 252

73
Nozzle Design, Characteristics:

General, 4, 10, 20, 21, 44, 46, 48, 49,

51, 53, 59, 63, 95, 158, 236

Asymmetric, 123

Axisymmetric, 166, 170

Field method, 50

Lattice point method, 50

Three-dimensional, 114

Two-dimensional, 66, 91, 107, 112,

123, 129, 138, 143, 146, 151, 170,

189, 192, 216, 269, 291

Nozzle design, Cross-section types:

Asymmetric, 36, 56, 72, 105, 106,

ll4, 125, 128, 150, 191, 199

Axisymmetric, 10, 17, 26, 29, 47, 53,

63, 83, 86, 109, 155, 166, 172, 173,

178, 181, 199, 202, 208, 216, 245,

246, 254, 263, 288

Two-dimensional, 4, 20, 21, 26, 34

36, 40, 44, 45, 48, 49, 50, 51, 55, 61

62, 68, 78, 81, 89, 92, 93, 97, 101

104, 106, l l5, l l6, 120, 122, 125

126, 128, 131, 132, 141, 146, 160

168, 176, 181, 189, 191, 199, 202

212, 216, 236, 238, 242, 246, 250

258, 263, 269, 276, 288, 291

Nozzle design, Boundary laver correction:

21, 81, 86, 107, ll6, 129, 151, 176,

180, 186, 199

Nozzle design, Wall cooling: 297

Nozzle design, Engineering:

Flexible plate, 44, 55, 62, 66, 68, 76,

78, 95, 105, 107, 108, 110, ll2, ll5,

ll8, 121, 127, 130, 133, 137, 138,

143, 147, 149, 150, 151, 154, 156,

160, 163, 165, 168, 169, 171, 192,

199, 207, 238, 240, 242, 250, 257,

277, 290, 297

Flexible plate/Solid, 138, 160, 276

Nozzle

Nozzle

Nozzle

Nozzle

Nozzle

Nozzle

Nozzle

Nozzle

design, Engineering (Continued):

General, 39, 58, 68, 87, 98, 100, 105,

108, 130, 131, 133, 135, 143, 144,

147, 153, 154, 163, 165, 187, 191,

235, 250, 257, 265, 266, 276, 277,

290, 297, 298

Semi-flexible type, 131

Sharp-throat, 64, 123, 212

Sliding block, 56

design, Low pressure operation:

67, 77, 86, 90, 179, 229

design, Maximum thrust: 166, 173,

199, 254, 263

design, Minimum length: 20, 119, 216,

245, 291, 296

design, Multi-nozzle type: 54, 67, 69,

79, 119

design, Ouiet ooeration:

Axisymmetric, 283, 285, 298

Requirements, 244

Review, 235, 237, 243, 256

Two-dimensional, 233, 253, 270, 272,

273, 275, 278, 279, 280, 283, 289

design, .Review: 6, 39, 48, 78, 80, 89,

94, 116, 118, 123, 143, 152, 175, 191,

266, 274, 282

engineering:

General, 39, 58, 68, 87, 98, 100, 105,

108, 130, 131, 133, 135, 143, 144,

147, 153, 154, 163, 165, 187, 191,

235, 250, 257, 265, 266, 276, 277,

290, 297, 298

Roughness, 237, 243

Nozzle Experiments:

Asymmetric, 72, 95,

286

196, 198, 207,

74
Nozzle

Nozzle

Experiments (Continued):

Axisymmetric, 1, 13, 17, 86, 167, 179,

193, 194, 200, 201, 204, 208, 209,

214, 219, 221, 223, 225, 227, 229,

232, 234, 284

Boundary layers, 99, 117, 174, 179,

198, 204, 207, 211, 219, 223, 225,

256, 261, 264

Cooling walls, 140, 178, 179, 193,

194, 196, 201, 204, 207, 209, 211,

217, 223, 225, 234, 264

Flow uniformity, 139, 196, 285, 289,

294, 295

Heat transfer, 79, 140, 145, 194, 196,

204, 209, 211, 214, 225, 234

Laminarization, 193, 196, 209, 211,

214, 219, 223, 225

Multi-nozzle, 54, 67, 69, 230

Quiet Technology, 272,298

Review, 11, 42, 71, 75, 90, 110, 191

Roughness, 261, 264, 272, 283, 294

Separated flow, 167, 201

Sharp-throat, 64, 201, 221, 227, 229,

292

Side wall flows, 117, 198

Transition, 261, 264, 273

Two-dimensional, 8, 11, 20, 21, 22,

26, 27, 38, 39, 72, 76, 78, 85, 88, 95,

98, 99, 103, 127, 130, 131, 133, 137,

140, 145, 147, 149, 174, 192, 197,

198, 207, 253, 256, 257, 260, 261,

264, 268, 285, 286, 292

Unsteady flows, 167, 284

Wall vibrations, 169, 284

optimization: 22, 33, 66, 166, 172,

178, 183, 187, 213, 216, 245, 254, 263

273, 277, 280, 290

Nozzle

Nozzle

Nozzle

Theory, Boundary layers: 162, 199,

224, 228, 231, 249

Theory, Different shapes:

Annular, 170

Asymmetric, 125, 128, 205, 213, 251

Axisymmetric, 26, 70, 73, 75, 83, 84,

96, 109, 134, 164, 181, 182, 188, 206,

210, 213, 216, 218, 220, 224, 254,

255, 259, 262, 267, 281, 292

Multi-nozzle, 67, 119

Sharp-throat, 206, 213, 220, 262, 292

Theory, Flow Solutions:

Biquadratic solution, 292

Characteristics, 70, 73

Axisymmetric, 37, 47, 183

Two-dimensional, 37, 65, 80

Euler, 293

Expansion method, 162, 220, 226

Finite volume method, 281

Full potential solution, 281

Fully viscous solution, 255

Integral relations method, 185, 202

Navier-Stokes solution, 210, 248, 255

Relaxation type, 24, 28, 41, 247, 251

Review, 42, 61, 65, 66, 190, 191, 195,

235, 247, 259

Series expansion, 52, 96, 182, 213,

215, 247, 267

Stream-tube curvature method, 265

Strip integration, 28

Subsonic, 24

Temperature jump, 210

75
Nozzle Theory, Flow Solutions/Continued):

Throat, 5, 28, 84, 96, 134, 162, 164,

182, 186, 190, 205, 206, 262, 293, 296

Time dependent, 218, 239, 247, 248,

255

Transonic, 134, 164, 182, 185, 190,

205, 206, 213, 218, 220, 222, 226,

251, 259, 265, 267, 281, 287, 292,

293, 296

Two-dimensional, 5, 24, 26, 28, 46,

52, 73, 84, 96, 100, 106, 130, 134,

137, 150, 153, 164, 180, 181, 182,

185, 186, 192, 205, 213, 215, 216,

222, 226, 238, 239, 248, 251, 255,

257, 259, 265, 267, 277, 281, 292, 296

Velocity slip, 210

Viscous transonic solution, 205

Nozzle Theory, Test Phenomena:

Boundary layer suction, 231

Cooling walls, 187, 224, 249

Flow separation, 287

Flow uniformity effect, 241

Heat transfer, 187, 196, 231, 288

Heating walls, 111, 228

Laminarization, 224, 228, 241

Roughness, 285

Unsteady flows, 111, 287

Quiet technology:

Design, 253, 256, 260

Experiment, 139, 219, 268, 270, 272,

273, 279, 283, 295

Review, 169, 174, 233, 237, 243, 244,

278, 280, 285, 289, 294

Theory, 113, 142, 235, 271, 272, 275

Quiet technology (Continued):

Settling chamber considerations, 139,

260, 278, 289

Transition data from quiet tunnels,

cones, 139, 233, 268, 270, 271,

278, 295

flat plates, 295

Supersonic Tunne.l, Calibration:

General, 27, 31, 35, 79, 87, 98, 148,

163, 171, 177, 184

Review, 159, 252

Supersonic Tunnel, Design:

General, 8, 9, 19, 22, 27, 31, 32, 33,

35, 74, 75, 82, 87, 88, 98, 101, 104,

141, 203, 240, 242, 258, 266

Quiet requirements, 278, 279, 285

Review, 12, 23, 30, 42, 43, 79, 91, 97,

102, 136, 157, 195, 274, 282

Supersonic Tunnel, Experiment:

General, 9, 18, 19, 75, 233

Review, 14, 15, 23, 43, 97, 102, 124,

161

Supersonic Tunnel, Operation:

General, 2, 3, 7, 8, 9, 15, 16, 19, 57,

60, 68, 74, 77, 82, 87, 92, 93, 97, 101,

104, 121, 122, 171, 175, 195, 203,

240, 242, 258, 266, 286

Quiet, 279, 295

Review, 124, 136

76
Corporate Source Index

(Affiliation of First Authors)

Australia

University of Sydney, 153, 158

Canada

DSMA International Inc., 290

National Aeronautical Establishment,

120, 126, 135, 142

China - 288

Denmark

The Technical

Denmark, 96

England - 24, 28, 31

France

University of

Aircraft Research Association Ltd.,

259

Armament Research Establishment,

107

Imperial College of Science and

Technology, 167

Imperial Metal Industries Ltd., 188

National Physical Laboratory, 1, 2, 5,

8, 34, 82, 97, 102

Royal Aircraft Establishment, 43, 54,

95, 121, 124, 165, 168, 170, 197, 198,

250

University of Manchester, 65, 70, 73,

100, 182, 190, 192

- 11, 111, 189

Institut Franco-Allemand

Recherches, 236, 246

de

ONERA, 276, 286

Germany -4, 6, 14, 16, 18, 19, 20, 22, 38,

42, 43, 47, 52, 84, 129, 161

DLR, 255

ISSU Karlsruhe, 293

Kochel, 21, 32, 33, 39

Max Planck Institute, 287

Peenemunde/Kochel, 266

India

National Aeronautical Laboratory, 176

Israel

Armament Development Authority,

269

Itai 2 - 12, 15, 106, 125

Japan - 292

Rumania

Institute of Applied Mechanics, 152

Institute of Fluid Mechanics and

Aerospace, 245

Russia- 10, 13, 17, 164, 185, 202, 284

Sweden

Aeronautical Research Institute of

Sweden, 110

Technical Research Institute of

Sweden, 76

The Royal Institute of Technology,

149

Switzerland - 23

Swiss Institute of Technology, 7

77
United States

ARO Inc., 127, 131, 133, 144, 147,

151, 156, 171, 179, 180, 184, 204, 216

Ballistic Research Laboratory, 109

Boeing Commercial Airplane Co., 243

Boeing Co., 222

CalTech, 27, 44, 162

Case School of Applied Science, 78

Consolidated Vultee Aircraft Corp.,

118

Continental Aviation and Engineering

Corp., 48

Cornell Aeronautical Laboratory Inc.,

229

Cornell University, 267, 281

Douglas Aircraft Company, 206, 213

Dynamic Science, 220, 226

General Dynamics Corp., 297

General Electric Co., 199

Georgia Institute of Technology, 91

Grumman Aircraft Engineering Corp.,

200, 218

Guggenheim Aeronautical Laboratory,

CalTech, 46, 81, 105

Harvard University, 41

High Technology Corp., 271, 275,

295, 298

Jet Propulsion Laboratory, 68, 103,

130, 132, 138, 139, 163, 172, 174,

175, 193, 201, 208, 209, 211, 219,

221, 223, 224, 225, 227, 228, 232,

234, 249

John Hopkins University, 50, 63, 89,

93, 113, 154, 169, 191

United States (Continued)

Lone Star Laboratory, 35

Marquardt Aircraft Co., 166

Massachusetts Institute of Technology,

26, 49, 51, 57, 64, 71, 108, 123, 134,

137, 140, 145, 148, 159

Montana State University, 258, 261,

264

NACA, 128

NACA,Ames, 56, 66

NACA,Langley, 3, 9, 30, 37, 80, 98,

146

NACA,Lewis, 36, 62, 72, 99, 101,

112, 114, 117, 119

NASA, 241

NASA,Ames, 257

NASA,HQ, 274

NASA,Langley, 233, 237, 238, 244,

253, 256, 260, 265, 268, 270, 272,

273, 278, 279, 280, 283, 285, 289, 294

NASA,Lewis, 212, 214, 240, 242

Naval Ordnance Laboratory, 45, 69,

79, 87, 115, 160, 194, 207, 230

New York University, 25, 29, 61

North American Aviation Inc., 40, 74,

83, 173

North Carolina State College, 186

North Carolina State University, 210

Northern Research and Engineering

Corp., 235

Northrop Corp., 231

Ohio State University, 75

Ordnance Aerophysics Laboratory,

141, 155

Packard Motor Car Co., 39

Philco Corp., 203

Polytechnic Institute of Brooklyn, 136

78
United States (Continued)

Pratt and Whitney Aircraft, 183

Princeton University, 60, 85, 104

Purdue University, 254, 263

Sandberg-Serrell Corp., 143

Sandia Corp., 177, 195

Sverdrup Technology Inc., 277

Texas A&M University, 262

TRW Systems, 215

United Aircraft Corp., 53, 55, 58, 178

United Aircraft Research Laboratory,

196

University of California, 77, 90

University of California, Berkeley, 67,

86, 181

University of California, Los Alamos,

239, 248

University of Michigan, 59, 88, 92,

94, 150, 205

University of Oklahoma, 291, 296

University of Tennessee, 116, 122,

187

Virginia Polytechnic Institute, 247,

251

Vought Corp., 252

79
IXl/ A Nalon_ A_mat_oa a_a

1. Report No.

NASA CR-4294

Report Documentation Page

2. Government Accession No. 3. Reciplent's Catalog No.

4. Title and Subtitle

Supersonic Wind Tunnel Nozzles--

A Selected, Annotated Bibliography To Aid in the Development

of Quiet Wind Tunnel Technology

7. Author(s)

Stephen W. D. Wolf

9. Performing Organization Name and Address

MCAT Institute

Moffett Field, CA 94035-1000

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, DC 20546-0001

5. Report Date

July 1990

6. Performing Organization Code

8. Performing Organization Report No.

A-90163

10. Work Unit No.

505-60-61

11. Contract or Grant No.

NCC2-604

13. Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

Sandford S. Davis, Ames Research Center, MS 260-1,

Moffett Field, CA 94035-1000

(415) 604-4197 or FFS 464-4197

15. Supplementary Notes

Point of Contact:

16. Abstract

This bibliography, with abstracts, consists of 298 citations arranged in chronological order.

le,c.ted the citations_ to be helpful to persons engaged in the design and development of quiet (low

disturbance) nozzles for modem supersonic wind tunnels. We include author, subject, and corporate

source indexes to assist with the location of specific information.

17. Key Words (Suggested by Author(s))

Supersonic nozzles

Supersonic quiet flows

Supersonic wind tunnels

Nozzle design

19. Security Classif. (of this report)

Unclassified

NASA FORM 1626 OCTee

18. Distribution Statement

Unclassified--Unlimited

Subject category---09

20. Secudty Classif. (of this page)

Unclassified

21. No. of Pages

84

22. Price

A05

For sate by the National Technical Information Service, Springfield, Virginia 22161

NASA-[_ogley, 1990