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Laminar hypersonic leading edge separation – a numerical study

Published online by Cambridge University Press:  25 May 2017

Amna Khraibut Open the ORCID record for Amna Khraibut [Opens in a new window] ,
S. L. Gai ,
L. M. Brown  and
A. J. Neely
Amna Khraibut*
Affiliation:
School of Engineering and Information Technology, Northcott Drive, Canberra ACT 2612, Australia
S. L. Gai
Affiliation:
School of Engineering and Information Technology, Northcott Drive, Canberra ACT 2612, Australia
L. M. Brown
Affiliation:
School of Engineering and Information Technology, Northcott Drive, Canberra ACT 2612, Australia
A. J. Neely
Affiliation:
School of Engineering and Information Technology, Northcott Drive, Canberra ACT 2612, Australia
*
†Email address for correspondence: [email protected]
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Abstract

This paper describes laminar hypersonic leading edge separation. Such a configuration of separated flow was originally studied by Chapman et al. (NACA Tech. Rep. 1356, 1958) at supersonic Mach numbers as it is particularly amenable to theoretical analysis and assumes no pre-existing boundary layer. It can be considered as a limiting case of much studied generic configurations such as separation at a compression corner and separated flow behind a base. A numerical investigation is described using a compressible Navier–Stokes solver assuming perfect gas air, no slip boundary condition and a non-catalytic surface. A moderate enthalpy flow of $3.1\times 10^{6}~\text{J}~\text{kg}^{-1}$ with a unit Reynolds number of $1.34\times 10^{6}~\text{ m}^{-1}$ and a Mach number of 9.66 was considered. The resulting separated flow is analysed in the context of viscous–inviscid interaction and interpreted in terms of ‘triple-deck’ concepts. Particular emphasis is given to wall temperature effects. The effects of strong to moderate wall cooling on flow in the separated region as well as on processes of separation, reattachment and separation length, are highlighted. The numerical simulations have also shown the existence of a secondary eddy embedded within the primary recirculation region, with its size, shape and position, being strongly affected by the wall temperature.

JFM classification

Boundary Layers: Boundary layer separation Mathematical Foundations: Computational methods Aerodynamics: High-speed flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 821 , 25 June 2017 , pp. 624 - 646
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© 2017 Cambridge University Press 

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References

Blottner, F. G., Johnson, M. & Ellis, M.1971 Chemically reacting viscous flow program for multi-component gas mixtures. Tech. Rep. Sandia Labs., Albuquerque, N. Mex.Google Scholar
Bodonyi, R. J. & Smith, F. T. 1986 Shock-wave laminar boundary-layer interaction in supercritical transonic flow. Comput. Fluids 14 (2), 97–108.Google Scholar
Brown, S. N., Cheng, H. K. & Lee, C. J. 1990 Inviscid–viscous interaction on triple-deck scales in a hypersonic flow with strong wall cooling. J. Fluid Mech. 220, 309–337.CrossRefGoogle Scholar
Brown, S. N. & Stewartson, K. 1969 Laminar separation. Annu. Rev. Fluid Mech. 1 (1), 45–72.Google Scholar
Brown, S. N., Stewartson, K. & Williams, P. G. 1975 Hypersonic self-induced separation. Phys. Fluids 18 (6), 633–639.Google Scholar
Burggraf, O. R. 1966 Analytical and numerical studies of the structure of steady separated flows. J. Fluid Mech. 24 (01), 113–151.CrossRefGoogle Scholar
Burggraf, O. R. 1973 Inviscid reattachment of a separated shear layer. In Proceedings of the 3rd International Conference on Numerical Methods in Fluid Mechanics, pp. 39–47. Springer.Google Scholar
Burggraf, O. R.1975 Asymptotic theory of separation and reattachment of a laminar boundary layer on a compression ramp. Tech. Rep. DTIC Document.Google Scholar
Burggraf, O. R., Rizzetta, D., Werle, M. J. & Vatsa, V. N. 1979 Effect of Reynolds number on laminar separation of a supersonic stream. AIAA J. 17 (4), 336–343.Google Scholar
Candler, G. V., Johnson, H. B., Nompelis, I., Gidzak, V. M., Subbareddy, P. K. & Barnhardt, M. 2015 Development of the US3D code for advanced compressible and reacting flow simulations. In 53rd AIAA Aerospace Sciences Meeting, p. 1893.Google Scholar
Candler, G. V., Subbareddy, P. K. & Brock, J. M. 2014 Advances in computational fluid dynamics methods for hypersonic flows. J. Spacecr. Rockets 52 (1), 17–28.CrossRefGoogle Scholar
Cassel, K. W., Ruban, A. I. & Walker, J. A. 1995 An instability in supersonic boundary-layer flow over a compression ramp. J. Fluid Mech. 300, 265–285.Google Scholar
Cassel, K. W., Ruban, A. I. & Walker, J. D. A. 1996 The influence of wall cooling on hypersonic boundary-layer separation and stability. J. Fluid Mech. 321, 189–216.Google Scholar
Chapman, D. R., Kuehn, D. M. & Larson, H. K.1958 Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition. NACA Tech. Rep. 1356.Google Scholar
Cheng, H. K. 1993 Perspectives on hypersonic viscous flow research. Annu. Rev. Fluid Mech. 25 (1), 455–484.CrossRefGoogle Scholar
Drayna, T. W., Nompelis, I. & Candler, G. V.2006 Numerical simulation of the aedc waverider at mach 8. AIAA Paper 2816.Google Scholar
Edney, B. E. 1968 Effects of shock impingement on the heat transfer around blunt bodies. AIAA J. 6 (1), 15–21.Google Scholar
Elliott, J. W. & Smith, F. T. 1986 Separated supersonic flow past a trailing edge at incidence. Comput. Fluids 14 (2), 109–116.Google Scholar
Gadd, G. E. 1957 An experimental investigation of heat transfer effects on boundary layer separation in supersonic flow. J. Fluid Mech. 2 (02), 105–122.Google Scholar
Gajjar, J. & Smith, F. T. 1983 On hypersonic self-induced separation, hydraulic jumps and boundary layers with algebraic growth. Mathematika 30 (1), 77–93.CrossRefGoogle Scholar
Hayes, W. D. & Probstein, R. F. 1959 Hypersonic Flow Theory. Elsevier.Google Scholar
Higdon, J. L. 1985 Stokes flow in arbitrary two-dimensional domains: shear flow over ridges and cavities. J. Fluid Mech. 159, 195–226.Google Scholar
Holden, M. S., Wadhams, T. P., MacLean, M. G. & Dufrene, A. T.2013 Measurements of real gas effects on regions of laminar shock wave/boundary layer interaction in hypervelocity flows for blindcode validation studies. Air Force Office of Scientific Research Rep. AFRL-OSR-VA-TR-2013-0134. Virginia, USA.CrossRefGoogle Scholar
Jackson, A. P., Hillier, R. & Soltani, S. 2001 Experimental and computational study of laminar cavity flows at hypersonic speeds. J. Fluid Mech. 427, 329–358.CrossRefGoogle Scholar
Katzer, E. 1989 On the lengthscales of laminar shock/boundary-layer interaction. J. Fluid Mech. 206, 477–496.Google Scholar
Kerimbekov, R. M., Ruban, A. I. & Walker, J. D. A. 1994 Hypersonic boundary-layer separation on a cold wall. J. Fluid Mech. 274, 163–195.CrossRefGoogle Scholar
Khorrami, A. F. & Smith, F. T. 1994 Hypersonic aerodynamics on thin bodies with interaction and upstream influence. J. Fluid Mech. 277, 85–108.Google Scholar
Korolev, G. L., Gajjar, J. B. & Ruban, A. I. 2002 Once again on the supersonic flow separation near a corner. J. Fluid Mech. 463, 173–199.Google Scholar
Leite, P. H. M. & Santos, W. F. N. 2015 Computational analysis of the flow field structure of a non-reacting hypersonic flow over forward-facing steps. J. Fluid Mech. 763, 460–499.Google Scholar
Lewis, J. E., Kubota, T. & Lees, L. 1968 Experimental investigation of supersonic laminar, two-dimensional boundary-layer separation in a compression corner with and without cooling. AIAA J. 6 (1), 7–14.Google Scholar
Lighthill, M. J. 1953 On boundary layers and upstream influence. II. Supersonic flows without separation. Proc. R. Soc. Lond. A 217 (1131), 478–507.Google Scholar
Messiter, A. F. 1970 Boundary-layer flow near the trailing edge of a flat plate. SIAM J. Appl. Maths 18 (1), 241–257.Google Scholar
Millikan, R. C. & White, D. R. 1963 Systematics of vibrational relaxation. J. Chem. Phys. 39 (12), 3209–3213.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18 (01), 1–18.Google Scholar
Mohri, K. & Hillier, R. 2011 Computational and experimental study of supersonic flow over axisymmetric cavities. Shock Waves 21 (3), 175–191.Google Scholar
Neiland, V. Y. 1969 Theory of laminar boundary layer separation in supersonic flow. Fluid Dyn. 4 (4), 33–35.Google Scholar
Neiland, V. Y. 1970 Asymptotic theory of plane steady supersonic flows with separation zones. Fluid Dyn. 5 (3), 372–381.CrossRefGoogle Scholar
Neiland, V. Y. 1973 Boundary-layer separation on a cooled body and its interaction with a hypersonic flow. Fluid Dyn. 8 (6), 931–939.Google Scholar
Neiland, V. Y., Boglepov, V. V., Dudin, G. N. & Lipatov, I. 2008 Asymptotic Theory of Supersonic Viscous Gas Flows. Butterworth-Heinemann.Google Scholar
Neiland, V. Y., Sokolov, L. A. & Shvedchenko, V. V. 2009 Temperature factor effect on separated flow features in supersonic gas flow. In BAIL 2008-Boundary and Interior Layers, pp. 39–54. Springer.Google Scholar
Nompelis, I. & Candler, G. V. 2014 US3D predictions of double-cone and hollow cylinder-flare flows at high enthalpy. In 44th AIAA Fluid Dynamics Conference.Google Scholar
Park, C. 1993 Review of chemical-kinetic problems of future nasa missions in earth entries. J. Thermophys. Heat Transfer 7 (3), 385–398.Google Scholar
Park, G., Gai, S. L. & Neely, A. J. 2010 Laminar near wake of a circular cylinder at hypersonic speeds. AIAA J. 48 (1), 236–248.Google Scholar
Rizzetta, D. P.1976 Asymptotic solution for two-dimensional viscous supersonic and hypersonic flows past compression and expansion corners. PhD thesis, Ohio State University.Google Scholar
Rizzetta, D. P., Burggraf, O. R. & Jenson, R. 1978 Triple-deck solutions for viscous supersonic and hypersonic flow past corners. J. Fluid Mech. 89 (03), 535–552.Google Scholar
Roy, C. J. 2003 Grid convergence error analysis for mixed-order numerical schemes. AIAA J. 41 (4), 595–604.CrossRefGoogle Scholar
Seddougui, S. O., Bowles, R. I & Smith, F. T. 1991 Surface-cooling effects on compressible boundary-layer instability. Eur. J. Mech. (B/Fluids) 10 (2), 117–145.Google Scholar
Shvedchenko, V. V. 2009 About the secondary separation at supersonic flow over a compression ramp. TsAGI Sci. J. 40 (5), 587–607.Google Scholar
Smith, F. T. 1986 Steady and unsteady boundary-layer separation. Annu. Rev. Fluid Mech. 18 (1), 197–220.Google Scholar
Smith, F. T. 1988 A reversed flow dingularity in interacting boundary layers. Proc. R. Soc. Lond. A 420 (1858), 21–52.Google Scholar
Smith, F. T. & Khorrami, A. F. 1991 The interactive breakdown in supersonic ramp flow. J. Fluid Mech. 224, 197–215.Google Scholar
Sridhar, V., Gai, S. L. & Kleine, H. 2016 Oscillatory characteristics of shallow open cavities in supersonic flow. AIAA J. 54 (11), 3495–3508.Google Scholar
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Fluids, vol. 3. Cambridge University Press.Google Scholar
Stewartson, K. 1974 Multistructured boundary layers on flat plates and related bodies. Adv. Appl. Mech. 14, 145–239.Google Scholar
Stewartson, K. 1975 On the asymptotic theory of separated and unseparated fluid motions. SIAM J. Appl. Maths 28 (2), 501–518.Google Scholar
Stewartson, K. & Williams, P. G. 1969 Self-induced separation. Proc. R. Soc. Lond. A 312 (1509), 181–206.Google Scholar
Stewartson, K. & Williams, P. G. 1973 On self-induced separation II. Mathematika 20 (01), 98–108.CrossRefGoogle Scholar
Sychev, V. V., Ruban, A. I., Sychev, V. V. & Korolev, G. L. 1998 Asymptotic Theory of Separated Flows. Cambridge University Press.Google Scholar
Van Leer, B. 1979 Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32 (1), 101–136.Google Scholar
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18 (4), 517–519.CrossRefGoogle Scholar
Wright, M. J., Candler, G. V. & Bose, D. 1998 Data parallel line relaxation method for the Navier–Stokes equations. AIAA J. 36 (9), 1603–1609.CrossRefGoogle Scholar