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Mixing layers for highly underexpanded supersonic jets in hypersonic streams

Published online by Cambridge University Press:  29 March 2006

James P. Moran
James P. Moran
Affiliation:
Aerodyne Research, Inc., Burlington, Massachusetts 01803
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Abstract

The mixing layer bounding the exhaust plume associated with hypersonic highaltitude rockets is analysed as a laminar binary mixture of perfect gases with Lewis and Prandtl numbers of unity. A far-field approximation to the undisturbed jet core and a Newtonian pressure balance between the jet and ambient gases are used to construct the mixing-layer location. Longitudinal pressure variations are neglected and resultant errors are evaluated. Boundary conditions at the edge of the mixing layer are evaluated by streamline tracing to shock entry points. The sensitivity of properties in the mixing layer to variations in the plume angle of attack, engine nozzle efficiency and engine thrust are examined, and an approximate density and thrust scaling of mixing-layer overall properties is developed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 1 , 12 August 1974 , pp. 153 - 175
Copyright
© 1974 Cambridge University Press

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References

Albini, F. A. 1965 Approximate computation of underexpanded jet structure A.I.A.A. J. 3, 1535.Google Scholar
Alden, H. L. & Habert, R. H. 1964 Gas dynamics of high-altitude rocket plumes. MITHRAS Inc. Rep. MC-63-80-R1.Google Scholar
Alden, H. L., Habert, R. H. & Hill, J. A. F. 1963 Gas dynamics of high-altitude rocket plumes. MITHRAS Inc. Rep. MC-63-80.Google Scholar
Altshuler, S., Moe, M. M. & Molund, P. 1958 The electromagnetics of the rocket exhaust. Space Tech. Lab. Inc. Rep. GM-TR-0165-00397.Google Scholar
Ashkenas, H. & Sherman, F. S. 1966 The structure and utilization of supersonic free jets in low density wind tunnels. In Rarefied Gas Dynamics, vol. 2 (ed. J. J. de Leeuw), pp. 84–105. Academic.
Boynton, F. P. 1967 Highly underexpanded jet structure: exact and approximate calculations. A.I.A.A. J. 5, 1703.Google Scholar
Boynton, F. P. 1968 Exhaust plumes from nozzles with wall boundary layers J. Spacecraft, 5, 1143.Google Scholar
Boynton, F. P. 1971 Numerical calculations of viscous, high-altitude exhaust plume flow fields. Res. Inst. Engng Sci. College of Engng, Wayne State University, Detroit, Michigan Rep.Google Scholar
Casaccio, A. 1963 Similar solutions for the turbulent compressible mixing of two streams with streamwise pressure gradient. Republic Aviation Corp. Rep. RAC 882A.Google Scholar
Chernyi, G. G. 1961 Introduction to Hypersonic Flow (trans. & ed. R. F. Probstein), chap. 3. Academic.
Dorrance, W. H. 1962 Viscous Hypersonic Flow, chap. 2. McGraw-Hill.
Draper, J. S. & Moran, J. P. 1973a Evaluation of modelling and simulation of viscous effects in high-altitude plumes. Proc. 7th JANNAF Plume Tech. Meeting.
Draper, J. S. & Moran, J. P. 1973b A study of wind tunnel simulation of high-altitude rocket plumes. Air Force Rocket Propulsion Lab. Rep. AFRPL TR-72-111.Google Scholar
Greenberg, A. A. 1966 Laminar mixing of two streams in a pressure gradient. M.I.T. Aerophys. Lab. Tech. Rep. no. 117.Google Scholar
Hartmann, J. & Lazarus, F. 1941 The air-jet with a velocity exceeding that of sound Phil. Mag. 31, 35.Google Scholar
Hayes, W. D. 1947 On hypersonic similitude Quart. Appl. Math. 5, 105.Google Scholar
Hayes, W. D. & Probstein, R. F. 1959 Hypersonic Flow Theory, chap. 3. Academic.
Hill, J. A. F. & Draper, J. S. 1966 Analytical approximation for the flow from a nozzle into a vacuum J. Spacecraft, 3, 1552.Google Scholar
Hill, J. A. F. & Habert, R. H. 1963 Gas dynamics of high-altitude missile trails. MITHRAS Inc. Rep. MC-61-18-R1.Google Scholar
Hubbard, E. W. 1966 Approximate calculation of highly underexpanded jets A.I.A.A. J. 4, 1877.Google Scholar
Jarvinen, P. O. & Dyner, H. B. 1969 Rocket exhaust plume dimensions J. Spacecraft, 6, 1309.Google Scholar
Jarvinen, P. O. & Hill, J. A. F. 1970 Universal model for underexpanded rocket plumes in hypersonic flow. Proc. 12th JANNAF Liquid Propulsion Meeting.
Li, T. Y. & Geiger, R. E. 1957 Stagnation point of a blunt body in hypersonic flow J. Aero. Sci. 24, 25.Google Scholar
Lock, R. C. 1951 The velocity distribution in the laminar boundary layer between parallel streams Quart. J. Mech. Appl. Math. 4, 42.Google Scholar
Mirels, H. & Mullen, J. F. 1962 Expansion of gas clouds and hypersonic jets bounded by a vacuum. Aerospace Corp. Rep. TDR-169 (3230–12) TR-1.Google Scholar
Moran, J. P. 1967 Similarity in high-altitude jets A.I.A.A. J. 5, 1343.Google Scholar
Owen, P. L. & Thornhill, C. K. 1948 The flow of an axially symmetric supersonic jet from a nearly sonic orifice into a vacuum. Aero. Res. Counc. R. & M. no. 2616.Google Scholar
Rosenberg, N. W. Hamilton, W. M., Lovell, D. J. & Bang, B. A. 1961 High-altitude visible missile trails. In Project Firefly 1960, vol. 3. Missile Trail Mechanisms, Air Force Camb. Res. Lab. Rep. AFCRL 256 (III).
Rudman, S. 1973 Numerical study of highly underexpanded three dimensional plumes. Adv. Tech. Lab. Rep. ATL TR 184.Google Scholar
Sedov, L. I. 1959 Similarity and Dimensional Methods in Mechanics (trans. & ed. M. Holt), chap. 4. Academic.
Sibulkin, M. & Gallaher, W. H. 1963 Far-field approximation for a nozzle exhausting into a vacuum A.I.A.A. J. 1, 1452.Google Scholar
Simons, G. A. 1972 Effect of nozzle boundary layers on rocket exhaust plumes A.I.A.A. J. 10, 1534.Google Scholar
Taylor, G. I. 1950 The formation of a blast wave by a very intense explosion Proc. Roy. Soc. A 201, 159.Google Scholar
Thomson, A. 1965 High-altitude rocket plume structure. General Dyn. Corp. Convair Div. Rep. GD-C-DBE65-023.Google Scholar
Thomson, A. & Harshbarger, F. 1961 Some comments on the fluid dynamics of missile trails. In Project Firefly 1960, vol. 3. Missile Trail Mechanisms, Air Force Camb. Res. Lab. Rep. AFCRL 256 (III).
Ting, L. 1959 On the mixing of two parallel streams J. Math. & Phys. 38, 153.Google Scholar
Wilson, K. H. 1973 Target phenomenology. Task I–Mixing layer analysis. Lockheed Missiles & Space Co. Rep. LMSC-B305172.Google Scholar