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Viscous simulation of shock-reflection hysteresis in overexpanded planar nozzles

Published online by Cambridge University Press:  10 September 2009

E. SHIMSHI ,
G. BEN-DOR  and
A. LEVY
E. SHIMSHI
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel
G. BEN-DOR
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel
A. LEVY*
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel
*
†Email address for correspondence: avi@bgu.ac.il
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Abstract

A computational fluid dynamics simulation of the flow in an overexpanded planar nozzle shows the existence of Mach-reflection hysteresis inside the nozzle. Previous simulations have dealt only with the flow outside the nozzle and thus concluded that the hysteresis phenomenon takes place outside the nozzle even when viscous effects are introduced. When including the geometry of the nozzle in the simulation it becomes evident that flow separation will occur before the transition from regular to Mach reflection for all relevant Mach numbers. The simulation reveals complex changes in the flow structure as the pressure ratio between the ambient and the jet is increased and decreased. The pressure along the nozzle wall downstream of the separation point is found to be less than the ambient pressure, and a modification of the Schilling curve fit is suggested for cases of extensive flow separation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 635 , 25 September 2009 , pp. 189 - 206
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Abramovich, G. N. 1976 Applied Gas Dyanamics. Nauka, Moscow.Google Scholar
Ashwood, P. F. & Crosse, G. W. 1957 The influence of pressure ratio and divergence angle on the shock position in two-dimensional, over-expanded, convergent-divergent nozzles. C.P. No. 327, British ARC.Google Scholar
Chpoun, A., Passerel, D., Li, H. & Ben-Dor, G. 1995 Reconsideration of oblique shock wave reflections in steady flows. Part 1. Experimental investigation. J. Fluid Mech. 301, 19–35.Google Scholar
Clauser, F. H. 1956 The turbulent boundary layer. In Advances in Applied Mechanics (ed. Dryden, H. L., Karman, Th. von & Kuerti, G.), Academic.Google Scholar
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. Interscience.Google Scholar
Frey, M. 2001 Investigation of flow problems in rocket nozzles at overexpansion. PhD thesis, Institute of Aerodynamics and Gasdynamics, University of Stuttgart, Stuttgart, Germany.Google Scholar
Hadjadj, A. 2004 Numerical investigation of shock reflection phenomena in overexpanded supersonic jets. AIAA J. 42, 570–577.CrossRefGoogle Scholar
Hornung, H. G., Oertel, H. & Sandeman, R. J. 1979 Transition to Mach reflection of shock waves in steady and pseudosteady flow with and without relaxation. J. Fluid Mech. 90, 541–560.CrossRefGoogle Scholar
Hunter, C. A. 1998 Experimental, theoretical, and computational investigation of separated nozzle flows. In Thirty-Fourth AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Cleveland, OH.Google Scholar
Ivanov, M. S., Vandromme, D., Fomin, V. M., Kudryavtsev, A. N., Hadjadj, A. & Khotyanovsky, D. V. 2001 Transition between regular and Mach reflection of shock waves: new numerical and experimental results. Shock Waves 11, 99–107.Google Scholar
Kudryavtsev, A. N., Khotyanovsky, D. V., Hadjadj, A., Vandromme, D. & Ivanov, M. S. 2002 Numerical investigation of shock wave interactions in supersonic imperfectly expanded jets. In Proceedings of the International Conference on Methods of Aerophysical Research, 29 June 1998 – 3 July 1998, Akademiya Nauk SSSR Novosibirsk Inst Teoreticheskoi I Prikladnoi Mekhaniki, p. 138. See also: http://www.itam.nsc.ru/ENG/Conf/ICMAR/IR98/icmar98.htmlGoogle Scholar
Lawrence, R. A. & Weynand, E. E. 1968 Factors affecting flow separation in contoured supersonic nozzles. AIAA J. 6, 1159–1160.CrossRefGoogle Scholar
Li, H. & Ben-Dor, G. 1997 A parametric study of Mach reflection in steady flows. J. Fluid Mech. 341, 101–125.Google Scholar
Menter, F. R. 1994 Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32, 1598–1605.Google Scholar
Molder, S., Gulamhassein, A., Timofeev, E. & Voinovich, P. 1997 Focusing of conical shocks at the centreline of symmetry. In Twenty-First International Symposium on Shock Waves, Great Keppel Island, Australia.Google Scholar
Morrisette, E. L. & Goldberg, T. J. 1978 Turbulent-flow separation criteria for overexpanded supersonic nozzles. Rep. No. NASA-TP-1207, p. 40. NASA Langley Research Center.Google Scholar
Mulvany, N. J., Chen, L., Tu, J. Y. & Anderson, B. 2004 Steady-state evaluation of two-equation RANS (Reynolds-averaged Navier–Stokes) turbulence models for high-Reynolds number hydrodynamic flow simulations. Sci. Lab. Rep. No. DSTO-TR-1564, 66. DSTO.Google Scholar
Nasuti, F., Onofri, M. & Pietropaoli, E. 2004 The influence of nozzle shape on the shock structure in separated flows. In Proceedings of the Fifth European Symposium Aerothermodynamics for Space Vehicles 8–11 November 2004, Cologne, Germany. (ed. Danesy, D.), p. 353.Google Scholar
von Neumann, J. 1943 Oblique reflection of shocks. In John von Neumann's Collected Works (ed. Taub, A. H.), 1st edn., p. 238. Pergamon.Google Scholar
Ralov, A. I. 1990 On the impossibility of regular reflection of a steady-state shock wave from the axis of symmetry. J. Appl. Math. Mech. 54, 200–203.Google Scholar
Reshotko, E. & Tucker, M. 1955 Effect of a discontinuity on turbulent boundary-layer-thickness parameters with application to shock-induced separation. Rep. No. TN 3454. NACA.Google Scholar
Romine, G. L. 1998 Nozzle flow separation. AIAA J. 36, 1618–1625.Google Scholar
Schilling, M. 1962 Flow separation in a rocket nozzle. MS thesis, Graduate School of Arts and Sciences, University of Buffalo, Buffalo, NY.Google Scholar
Schotz, M., Levy, A., Ben-Dor, G. & Igra, O. 1997 Analytical prediction of the wave configuration size in steady flow Mach reflections. Shock Waves 7, 363–372.Google Scholar
Shimshi, E., Ben-Dor, G. & Levy, A. 2008 Viscous simulation of shock reflection hysteresis in overexpanded planar nozzles. In Eighteenth International Shock Interaction Symposium, Rouen, France.Google Scholar
Sivells, J. C. 1978 A computer program for the aerodynamic design of axisymmetric and planar nozzles for supersonic and hypersonic wind tunnels. Rep. No. AEDC-TR-78-63. Arnold Engineering Development Center.Google Scholar
Skews, B. W. 1997 Aspect ratio effects in wind tunnel studies of shock wave reflection transition. Shock Waves 7, 373–383.CrossRefGoogle Scholar
Speziale, C. G. & Thangam, S. 1992 Analysis of an RNG based turbulence model for separated flows. Intl J. Engng Sci. 30, 1379–1388.CrossRefGoogle Scholar
Summerfield, M., Foster, C. R. & Swan, W. C. 1954 Flow separation in overexpanded supersonic exhaust nozzles. Jet Propul. 24, 319–321.Google Scholar
Uskov, V. N. & Chernyshov, M. V. 2006 Differential characteristics of the flow field in a plane overexpanded jet in the vicinity of the nozzle lip. J. Appl. Mech. Tech. Phys. 47, 366–376.Google Scholar
Vuillon, J., Zeitoun, D. & Ben-Dor, G. 1995 Reconsideration of oblique shock wave reflections in steady flows. Part 2. Numerical investigation. J. Fluid Mech. 301, 37–50.Google Scholar