Hostname: page-component-5c6d5d7d68-qks25 Total loading time: 0 Render date: 2024-08-18T20:25:28.921Z Has data issue: false hasContentIssue false

Hypersonic compression corner flow with large separated regions

Published online by Cambridge University Press:  27 August 2019

Sudhir L. Gai
Affiliation:
University of New South Wales, Canberra, 2612, Australia
Amna Khraibut*
Affiliation:
University of New South Wales, Canberra, 2612, Australia
*
Email address for correspondence: amnakhraibut80@gmail.com

Abstract

The structure of large-scale hypersonic boundary layer separation and reattachment is studied numerically using a flat plate/compression corner geometry. Apart from verifying the large scale separation characteristics in hypersonic flow, a detailed discussion of secondary separation and fragmentation into multiple vortices embedded within the main recirculation region is presented. The unique relation between the second minimum in shear stress and the scaled angle is highlighted in the context of the reverse flow singularity of Smith (Proc. R. Soc. Lond. A, vol. A420, 1988, pp. 21–52) and it appears that for a small wall temperature ratio, such a singularity is unlikely. It is shown that the size of the separation can be estimated in terms of Burggraf’s expression based on asymptotic theory.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Benay, R., Chanetz, B., Mangin, B., Vandomme, L. & Perraud, J. 2006 Shock wave/transitional boundary-layer interactions in hypersonic flow. AIAA J. 44 (6), 12431254.10.2514/1.10512Google Scholar
Blottner, F. G., Johnson, M. & Ellis, M.1971 Chemically reacting viscous flow program for multi-component gas mixtures. Tech. Rep. No. SC-RR-70-754. Sandia Labs.10.2172/4658539Google 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, 309337.10.1017/S0022112090003275Google Scholar
Burggraf, O. R.1975 Asymptotic theory of separation and reattachment of a laminar boundary layer on a compression ramp. Tech. Rep. AGARD-CP-168. AGARD.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, AIAA Paper 2015-1893. AIAA.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), 1728.10.2514/1.A33023Google 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, 455484.10.1146/annurev.fl.25.010193.002323Google Scholar
Daniels, P. G. 1979 Laminar boundary-layer reattachment in supersonic flow. J. Fluid Mech. 90 (2), 289303.10.1017/S0022112079002214Google Scholar
Deepak, N. R., Gai, S. L. & Neely, A. J. 2013 A computational investigation of laminar shock/wave boundary layer interactions. Aeronaut. J. 117 (1187), 2756.10.1017/S0001924000007740Google Scholar
Degrez, G., Boccadoro, C. H. & Wendt, J. F. 1987 The interaction of an oblique shock wave with a laminar boundary layer revisited. An experimental and numerical study. J. Fluid Mech. 177, 247263.10.1017/S0022112087000946Google Scholar
Délery, J. & Marvin, J. G.1986 Shock-wave boundary layer interactions. Tech. Rep. AGARDograph 280. AGARD.Google Scholar
Drayna, T. W., Nompelis, I. & Candler, G. V.2006 Numerical simulation of the AEDC waverider at Mach 8. AIAA Paper 2005–2816.10.2514/6.2006-2816Google Scholar
Druguet, M. C., Candler, G. V. & Nompelis, I. 2005 Effects of numerics on Navier–Stokes computations of hypersonic double-cone flows. AIAA J. 43 (3), 616623.10.2514/1.6190Google Scholar
Egorov, I., Neiland, V. & Shvedchenko, V. 2011 Three-dimensional flow structures at supersonic flow over the compression ramp. In 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, p. 730. AIAA.Google Scholar
Gittler, Ph. & Kluwick, A. 1987 Triple-deck solutions for supersonic flows past flared cylinders. J. Fluid Mech. 179, 469487.10.1017/S0022112087001617Google Scholar
Holden, M. S. 1966 Experimental studies of separated flows at hypersonic speeds. II-two-dimensional wedge separated flow studies. AIAA J. 4 (5), 790799.10.2514/3.3548Google Scholar
Holden, M. S., Wadhams, T. P., Harvey, J. K. & Candler, G. V.2003 Comparisons between DSMC and Navier–Stokes solutions on measurements in regions of laminar shock wave/boundary layer interactions in hypersonic flows. AIAA Paper 2003-0435.10.2514/6.2002-435Google Scholar
Hung, C. M. & MacCormack, R. W. 1976 Numerical solutions of supersonic and hypersonic laminar compression corner flows. AIAA J. 14 (4), 475481.10.2514/3.61386Google Scholar
Jacobs, P. A. & Gollan, R. J.2010 The Eilmer3 code. Tech. Rep. 2008/07. University of Queensland.Google Scholar
Katzer, E. 1989 On the lengthscales of laminar shock/boundary-layer interaction. J. Fluid Mech. 206, 477496.10.1017/S0022112089002375Google Scholar
Khraibut, A.2018 Laminar hypersonic leading edge separation. PhD thesis, University of New South Wales, Canberra.10.1017/jfm.2017.204Google Scholar
Khraibut, A., Gai, S. L., Brown, L. M. & Neely, A. J. 2017 Laminar hypersonic leading edge separation – a numerical study. J. Fluid Mech. 821, 624646.10.1017/jfm.2017.204Google Scholar
Korolev, G. L. 1991 Asymptotic theory of laminar flow separation at a corner. Fluid Dyn. 26 (1), 150152.Google Scholar
Korolev, G. L. 1992 Nonuniqueness of separated flow past nearly flat corners. Fluid Dyn. 27 (3), 442444.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, 173199.10.1017/S0022112002008777Google 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), 714.Google Scholar
Logue, R. P., Gajjar, J. & Ruban, A. I. 2014 Instability of supersonic compression ramp flow. Phil. Trans. R. Soc. Lond. A 372 (2020), 20130342.Google Scholar
MacCormack, R. W. 2014 Numerical Computation of Compressible and Viscous Flow. AIAA.10.2514/4.102646Google Scholar
MacLean, M. G., Holden, M. S. & Dufrene, A. T.2014 Measurements of real gas effects on regions of laminar shock wave/boundary layer interactions in hypervelocity flows presented in AIAA Aviation 2014: Experimental Overview Paper. Available at: https://www.cubrc.org/_iassets/docs/laminar-xx-paper.pdf.Google Scholar
Mallinson, S. G.1994 Shock wave/boundary layer interaction at a compression corner in hypervelocity flows. PhD thesis, University of New South Wales, Canberra.10.1007/978-3-642-78829-1_13Google Scholar
Mallinson, S. G., Gai, S. L. & Mudford, N. R. 1997 The interaction of a shock wave with a laminar boundary layer at a compression corner in high-enthalpy flows including real gas effects. J. Fluid Mech. 342, 135.10.1017/S0022112097005673Google Scholar
Neiland, V. Y. 1970 Asymptotic theory of plane steady supersonic flows with separation zones. Fluid Dyn. 5 (3), 372381.Google Scholar
Neiland, V. Y., Sokolov, L. A. & Shvedchenko, V. V. 2008 Temperature factor effect on the structure of the separated flow within a supersonic gas stream. Fluid Dyn. 43 (5), 706717.Google Scholar
Nompelis, I. & Candler, G. V.2014 US3D predictions of double-cone and hollow cylinder-flare flows at high enthalpy. AIAA Paper 2014-3366.10.2514/6.2014-3366Google Scholar
Nompelis, I., Candler, G. V. & Holden, M. S. 2003 Effect of vibrational nonequilibrium on hypersonic double-cone experiments. AIAA J. 41 (11), 21622169.10.2514/2.6834Google Scholar
Olejniczak, J. & Candler, G. V. 1998 Computation of hypersonic shock interaction flow fields. In 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, AIAA Paper 1998-2446.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, Columbus, OH.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, 535552.10.1017/S0022112078002724Google Scholar
Roy, C. J. 2003 Grid convergence error analysis for mixed-order numerical schemes. AIAA J. 41 (4), 595604.10.2514/2.2013Google Scholar
Rudy, D., Thomas, J., Kumar, A., Gnoffo, P. A. & Chakravarthy, S. 1989 A validation study of four Navier–Stokes codes for high-speed flows. In 20th Fluid Dynamics, Plasma Dynamics and Lasers Conference, AIAA Paper 1989-1838.Google Scholar
Shrestha, P., Hildebrand, N. J., Dwivedi, A., Nichols, J. W., Jovanovic, M. R. & Candler, G. V. 2016 Interaction of an oblique shock with a transitional Mach 5.92 boundary layer. In 46th AIAA Fluid Dynamics Conference, AIAA Paper 2016-3647.Google Scholar
Shvedchenko, V. V. 2009 About the secondary separation at supersonic flow over a compression ramp. TsAGI Sci. J. 40 (5), 587607.10.1615/TsAGISciJ.v40.i5.60Google Scholar
Smith, F. T. 1988 A reversed flow singularity in interacting boundary layers. Proc. R. Soc. Lond. A A420, 2152.10.1098/rspa.1988.0116Google Scholar
Smith, F. T. & Khorrami, A. F. 1991 The interactive breakdown in supersonic ramp flow. J. Fluid Mech. 224, 197215.10.1017/S0022112091001714Google Scholar
Smith, F. T. & Khorrami, A. F. 1994 Hypersonic aerodynamics on thin bodies with interaction and upstream influence. J. Fluid Mech. 277, 85108.Google Scholar
Stewartson, K. 1970 On laminar boundary layers near corners. Q. J. Mech. Appl. Maths 23 (2), 137152.10.1093/qjmam/23.2.137Google Scholar
Stewartson, K. 1975 On the asymptotic theory of separated and unseparated fluid motions. SIAM J. Appl. Maths 28 (2), 501518.10.1137/0128039Google Scholar
Swantek, A. B. & Austin, J. M. 2012 Heat transfer on a double wedge geometry in hypervelocity air and nitrogen flows. In 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA Paper 2012-0284.Google Scholar
Tumuklu, O., Levin, D. A. & Theofilis, V. 2018 Investigation of unsteady, hypersonic, laminar separated flows over a double cone geometry using a kinetic approach. Phys. Fluids 30 (4), 046103.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), 101136.10.1016/0021-9991(79)90145-1Google Scholar
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18 (4), 517519.10.1063/1.1747673Google Scholar
Wright, M. J., Candler, G. V. & Bose, D. 1998 Data parallel line relaxation method for the Navier–Stokes equations. AIAA J. 36 (9), 16031609.10.2514/2.586Google Scholar
Yao, Y., Krishnan, L., Sandham, N. D. & Roberts, G. T. 2007 The effect of Mach number on unstable disturbances in shock/boundary-layer interactions. Phys. Fluids 19 (5), 054104.10.1063/1.2720831Google Scholar