Final Technical Report

on

INTERACTIVE CALCULATION PROCEDURES FOR

MIXED COMPRESSION INLETS

(NASA Grant NAG 3-140)

-Submitted by

Eli Reshotko

Professor of Engineering

Principal Investigator

Department of Mechanical and Aerospace Engineering

School of Engineering

Case Institute ot Technology

Case Western Reserve University

Cleveland, Ohio 44106

March 1983

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The proper design of engine nacelle installations for supersonic aircraft

depends on a sophisticated understanding of the interactions between the boundary layers and the bounding external flows. The successful operation of

mixed external-internal compression inlets depends significantly on the ability to

closely control the operation of the internal compression portion of the inlet.

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"This portion of the Inlet is one where compression is achieved by multiple reflection of oblique shock waves and weak compression waves in a converging

Internal flow passage. However weak these shocks and waves may seem gasdynamically, they are of sufficient strength to separate a laminar boundary layer

and generally even strong enough for separation or incipient separation of the

turbulent boundary layers.

Shock reflection without separation in inlets can however be obtained by

bleeding off a portion of the mass flow near shock impingement regions. This

is shown by Smeltzer and Sorenson (Ref. 1) describing on- and off-design

performance of a mixed compression inlet for N/ = 3.5. They Indicate that of

the order of 20% of the capture mass flow must be bled to achieve maximum

pressure recovery at the design Mach number. This is a very large fraction

of the flow when one considers that the bleed flow is dumped giving negligible

if any contribution to thrust. A NASA sponsored experimental study (Ref, 2)

showed that satisfactory results can be obtained for smaller bleed flows.

+An objective of the CWRU program was to develop sufficient understanding

of the viscous-lnvlscld Interactions and of the shock wave boundary layer Interactions and reflections.

During the many years of the subject grant, the Principal Investigator has

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participated with NASA-Lewis personnel in discussing their overall program in

mixed compression Inlets leading to specific identification of those portions to

be carried out under the subject grant.

Interaction Procedure for Two-D,im,ensi0nol and Axisvmmetric Inlets

Dr. Yehuda Tassa developed an Interaction calculation procedure using the

finite difference techniques or Cebeci and Smith (Refs. 3,4) for compressible

turbulent boundary layers together with a streamline-normal characteristics procedure clue to Mr. B.H. Anderson of NASA-Lewis, Since much of the boundary

layer flow Is supersonic, It Is desirable to trace Math waves Into the supersonic portion of the boundary layers so that the wave reflections are correctly

located. Accordingly, the characterlsitics procedure was modified to Include

step by step entropy changes due to viscous shear and the matching between

the characteristics region and the Inner turbulent boundary layer takes place

where the local Mach number Is about 1.2, Just outside the sonic line. This

procedure is essentially as described by Ferri and Dash (Ref. 5) and by Miller

(Ref. 6).

The procedure (Refs. 7-10) utilizes Anderson's characteristic procedure

whose streamline-normal network is more readily compatible with the mesh for

boundary calculations, and also a more sophisticated boundary layer program

than used by the previous Investigators. The Cebect-Smith procedure was augmented to include the leading longitudinal and transverse curvature terms so

that the procedure would be applicable for fairly thick boundary layers and

sharp longitudinal curvatures as often encountered on boattails and sometimes

on inlet centerbodies. The results show that although the interaction procedure
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does work and can provide flow field information without resorting to the much

more complicated and time-consuming Navier-Stokes calculation procedures, the

quality of the results is very sensitively dependent on the care and local massaging exercised by the operator. These difficulties were made very apparent

by the recent work of Ashpis (Ref. ll) completed under this grant. This procedure therefore shows little promise at this time of being adequate for use as

a design code.

Shock Boundary-Layer Intero_tion_

Since in a shock boundary layer interaction, there is a downstream condition that must be satisifed, a parabolic method cannot be adequate. The procedure must become elliptic thus requiring some kind of shooting technique to

approach the correct downstream condition. In work completed under the

grant, Goldberg (Ref. 12) has followed the suggestions of Wornom (Ref. 13)

and Dwoyer (Ref. 14) in using the second derivative of the displacement thickness (d28'_/dx 2) as a branching parameter, He was able to proceed through

the interaction zone to a converged solution even with zones of separation.

He also showed the effect of suction on the character of shock-boundary-layer

Interactions. Goldberg's work provides the basis for the development of an oblique shock-boundary-layer Interaction program to be incorporated into the

PEPSIS procedure.

Three-Dimension_l Flow (_alcul_tlons

In order to properly start aa three-dimensional flow calculation, say for an

axi-symmetric centerbody at angle of attack, it is necessary to have an in-
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teracted solution at the first station of a numerical program. The development

of such a starting program was undertaken within the grant, The suggested

technique substitutes a 3/4 power law tip for the leading portion of the cone,

For such a tlp. the shock-wave and boundary-layer also have a 3/4 power

shape according to strong interaction theory (Ref. 15) and so the entire flow

field is self-similar. The extension of the procedure to angle-of-attack follows

MIrels and Thronton (Ref. ]6). In an M.S. thesis by Mr. R. SrinJvasan now

nearing completion, it becomes apparent that the strong-interaction theory is

valid only for hypersonic non-slender shapes (M282 >> 1) and cannot be applied properly to Inlet centerbodles at supersonic speeds.
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REFERENCES

°

2,

.

.

,

,

.

,

.

10.

11.

Smeltzer, D.B. and Sorensen, N, E. : Investigation of a Mixed-Compression

Axisymmetrlc Inlet System at Math Numbers 0.6 to 3.5, NASA TN D-6078,

Nov. ]970.

Fukuda, Michael K. : Control of Shock Wave-Boundary Layer Interactions by

Bleed in Supersonic Mixed Compression Inlets. M.S. Thesis, Case

Western Reserve University. May 1975.

Cebeci, T. and Smith, _A.M.O. and Mosinkis, G. : Calculations of Compressible Adiabatic Turbulent Boundary Layers. AIAA Journal 8, Nov. 1970, pp.

1007-10010

Cebeci, T.: Behavior of Turbulent Flow Near a Porous Wall with Pressure

Gradient. AIAA Journal 8. 12, Dec. 1970, pp. 2152-2156.

Ferri, A. and Dash, S.: Viscous Flow at High Mach Numbers with Pressure

Gradients. Proceedings of the 1969 Symposium on Viscous Interaction

Phenomena in Supersonic and Hypersonic Flow. University of Dayton

Press. 1970.

Miller, G.: Mathematical Formulation of Viscous-lnviscid Interactions Problems in Supersonic Flow. AIAA Journal, Vol. 11. No. 7, July 1973, pp.

938-942.

Tassa, Y., Anderson, B.H. and Reshotko, E. : Improved Interactive Calculation Procedure for Supersonic Flows. Presented at the 19th israel Annual Conference on Aviation and Astronautics, May 1976.

Anderson, B.H., Tassa, Y. and Reshotko, E. : Characteristics Procedure for

Supersonic Flows Including Consideration of Viscous Contributions to Flow

Rationality. AIAA Paper 76-426. Presented at AIAA 9th Fluid and Plasma Dynamics Conference, July 1976.

Tassa, Y., Anderson, B.H., and Reshotko, E. : Finite Difference Procedure

for Boundary Layers Including Effects of Longitudinal and Transverse Curvatures. AIAA Paper 76-427. Presented at AIAA 9th Fluid and Plasma

Dynamics Conference, July ]976.

Tassa, Y., Anderson, B.H., and Reshotko, E. : Interactive Calculation Procedure for Supersonic Flows. NASA TMX-73653, May 1977.

Ashpls, David: Examination of an Interactive Computational Procedure for

Second Order Boundary Layer Flows. M.S. Thesis, Case Western Reserve

University, Aug. 1981.

12. Goldberg, U., and Reshotko, E.: Calculation of Oblique-Shock-Wave Laminar
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13.

14,

15.

16.

Boundary-Layer Interaction on a Flat Plate.

1980.

NASA CR-] 59829, March

Wornom, S.F. : A Numerical Study of Displacement Body and Curvature Effects on Incompressible and Compressible Laminar Boundary Layers.

Ph, D. Thesis, VPI & SU, Blacksburg, VA, May 1971.

Dwoyer, D. L, : Supersonic and Hypersonic Two-Dimensional Laminar Flow

over a Compression Corner. Proc. AIAA Computatinal Fluid Dynamics

Conference, July ]9-20, ]973, pp. 69-83.

Mlrels, H. : Hypersonic Flow over Slender Power Law and Related Bodies.

Advances in Applied Mechar_ics, Vol. 7, 1962, ]-54.

Mlrels, H., and Thornton, P.R.: Effect of Body Perturbations on Hypersonic

Flow over Slender Power Low Bodies. NASA TR R-45, ]959.