Skip to main content Accessibility help
×
Home

Numerical study of bluntness effects on laminar leading edge separation in hypersonic flow

  • Amna Khraibut (a1), S. L. Gai (a1) and A. J. Neely (a1)

Abstract

Bluntness effects on laminar hypersonic leading edge separation are investigated numerically at Mach number $M\approx 10$ , unit Reynolds number $Re=1.3\times 10^{6}~\text{m}^{-1}$ , specific enthalpy $h_{o}=3.1~\text{MJ}~\text{kg}^{-1}$ and wall-to-stagnation temperature ratio $T_{w}/T_{o}=0.1$ . Such effects are important from an experimental point of view and because bluntness can affect a separated flow favourably or adversely. In this study, two blunt leading edge cases of small radius ( $15~\unicode[STIX]{x03BC}\text{m}$ ) and large radius ( $100~\unicode[STIX]{x03BC}\text{m}$ ) are investigated. A comparison with the idealised sharp leading edge case is also given. General flow features and surface parameters such as the shear stress, pressure and heat flux are presented and analysed. The results have also been interpreted in terms of Cheng’s displacement-bluntness similitude parameter affecting the size of separation. Previous experiments by Holden delineated small and large bluntness effects based on Cheng’s parameter and considering small to moderate separated regions. In this study, leading edge separation was found to suppress the favourable effect of bluntness in delaying separation. Bluntness, furthermore, seemed to promote the appearance of secondary vortices within a main separated region. Analysis of reverse flow boundary layer profiles such as velocity, pressure and temperature is also given. It is shown that bluntness accentuates large transverse gradients. This in turn adversely effects the reverse flow boundary layer leading to the appearance of secondary vortices.

Copyright

Corresponding author

Email address for correspondence: amnakhraibut80@gmail.com

References

Hide All
Bertram, M. H. 1954 Viscous and leading-ddge thickness effects on the pressures on the surface of a flat plate in hypersonic flow. J. Aero. Sci. 21 (6), 430431.
Bertram, M. H. & Henderson, A. Jr 1958 Effects of boundary-layer displacement and leading-edge bluntness on pressure distribution, skin friction, and heat transfer of bodies at hypersonic speeds. NACA Tech. Note 4301.
Borovoy, V. Y., Mosharov, V. E., Radchenko, V. N., Skuratov, A. S. & Struminskaya, I. V. 2014 Leading edge bluntness effect on the flow in a model air-inlet. Fluid Dyn. 49 (4), 454467.
Borovoy, V. Y., Skuratov, A. S. & Struminskaya, I. V. 2008 On the existence of a threshold value of the plate bluntness in the interference of an oblique shock with boundary and entropy layers. Fluid Dyn. 43 (3), 369379.
Brinich, P. F.1956 Effect of leading-edge geometry on boundary-layer transition at mach 3.1. NACA Tech. Note 3659.
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.
Brown, S. N. & Stewartson, K. 1969 Laminar separation. Annu. Rev. Fluid Mech. 1 (1), 4572.
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), 336343.
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.
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.
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, 265285.
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, 189216.
Catherall, D. & Mangler, K. W. 1966 The integration of the two-dimensional laminar boundary-layer equations past the point of vanishing skin friction. J. Fluid Mech. 26 (1), 163182.
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.
Cheng, H. K., Hall, J. G., Golian, T. C. & Hertzberg, A. 1961 Boundary-layer displacement and leading-edge bluntness effects in high-temperature hypersonic flow. J. Aero. Sci. 28 (5), 353381.
Cheng, H. K. & Pallone, A. J. 1956 Inviscid leading-edge effect in hypersonic flow. J. Aero. Sci. 23 (7), 700702.
Coenen, E. G. M. 1999 Quasi-simultaneous coupling for wing and airfoil flow. In Domain Decomposition Methods in Science and Engineering, pp. 197205. Domain Decomposition Press.
Creager, M. O.1959 The effect of leading-edge sweep and surface inclination on the hypersonic flow field over a blunt flat plate. NASA-MEMO-12-26-58A.
Dietz, G. & Meijering, A. 1997 Numerical investigation of boundary-layer instabilities over a blunt flat plate at angle of attack in supersonic flow. In New Results in Numerical and Experimental Fluid Mechanics, pp. 103110. Springer.
Drayna, T. W., Nompelis, I. & Candler, G. V. 2006 Numerical simulation of the AEDC waverider at Mach 8. In 25th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, AIAA 2006–2816.
Edney, B. E. 1968 Effects of shock impingement on the heat transfer around blunt bodies. AIAA J. 6 (1), 1521.
Edwards, C. L. W & Anders, J. B.1968 Low-density, leading-edge bluntness, and ablation effects on wedge-induced laminar boundary layer separation at moderate enthalpies in hypersonic flow. NASA Tech. Note D-4829.
Gadd, G. E. 1957 An experimental investigation of heat transfer effects on boundary layer separation in supersonic flow. J. Fluid Mech. 2 (02), 105122.
Goldstein, S. 1948 On laminar boundary-layer flow near a position of separation. Q. J. Mech. Appl. Maths 1 (1), 4369.
Gray, J. D. & Rhudy, R. W.1972 Effects of wall cooling and leading-edge blunting on ramp-induced, laminar flow separations at Mach numbers from 3 through 6. Tech. Rep. Arnold Engineering Development Center. AEDC-TR-71-274.
Hama, F. R. 1968 Experimental studies on the lip shock. AIAA J. 6 (2), 212219.
Hayes, W. D. 1959 Viscous hypersonic similitude. J. Aero. Sci. 26 (12), 815824.
Hayes, W. D. & Probstein, R. F. 1959 Hypersonic Flow Theory. Elsevier.
Hirschel, E. H. 2005 Basics of Aerothermodynamics, 2nd edn. Springer.
Holden, M. S. 1966 Experimental studies of separated flows at hypersonic speeds. II – Two-dimensional wedge separated flow studies. AIAA J. 4 (5), 790799.
Holden, M. S. 1971 Boundary-layer displacement and leading-edge bluntness effects on attached and separated laminar boundary layers in a compression corner. II – Experimental study. AIAA J. 9 (1), 8493.
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. In 21st AIAA Computational Fluid Dynamics Conference, 24–27 June, San Diego, California, USA, AIAA-2013-2837, p. 2837.
Holloway, P. F., Sterrett, J. R. & Creekmore, H. S.1965 An Investigation of Heat Transfer within Regions of Separated Flow at a Mach Number of 6.0. NASA Tech. Note TN D-3074.
Hruschka, R. B. 2010 Optical Studies and Simulations of Hypervelocity Flow Fields Around Blunt Bodies. Citeseer.
John, B. & Kulkarni, V. 2014 Effect of leading edge bluntness on the interaction of ramp induced shock wave with laminar boundary layer at hypersonic speed. Comput. Fluids 96, 177190.
Kemp, J. H. 1969 Hypersonic viscous interaction on sharp and blunt inclined plates. AIAA J. 7 (7), 12801289.
Kerimbekov, R. M., Ruban, A. I. & Walker, J. D. A. 1994 Hypersonic boundary-layer separation on a cold wall. J. Fluid Mech. 274, 163195.
Khorrami, A. F. & Smith, F. T. 1994 Hypersonic aerodynamics on thin bodies with interaction and upstream influence. J. Fluid Mech. 277, 85108.
Khraibut, A.2018 Laminar hypersonic leading edge separation. PhD thesis, University of New South Wales.
Khraibut, A., Deepak, N. R., Gai, S. L. & Neely, A. J. 2014 Hypersonic leading edge separation. In 19th Australasian Fluid Mechanics Conference, vol. 1, pp. 268271. Australasian Fluid Mechanics Society.
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.
Khraibut, A., Gai, S. L. & Neely, A. J.2015 Numerical investigation of bluntness effects on hypersonic leading edge separation. In 53rd AIAA Aerospace Sciences Meeting, Kissimmee, Florida, AIAA-2015-0984.
Le Balleur, J. C. 1977 Viscous-inviscid flow matching: Analysis of the problem including separation and shock waves. La Rech. Aerospatialele 1977‐6, 349358.
Le Balleur, J. C. 1978 Viscous-inviscid flow matching: Numerical method and applications to two-dimensional, transonic and supersonic flows. La Rech. Aerospatiale, Bull. Bimestriel, (Paris) 183, 6576.
Le Page, L. M., Barret, M., O’Byrne, S. & Gai, S. L. 2019 Rotational temperature imaging of a leading-edge separation in hypervelocity flow. In 31st International Symposium on Rarefied Gas Dynamics, AIP Conference Proceedings 2132. 110001.
Lees, L. & Probstein, R. F. 1952 Hypersonic viscous flow over a flat plate. In Physical Review, vol. 86, pp. 600600.
Lighthill, M. J.1953 On boundary layers and upstream influence. II. Supersonic flows without separation. 217 (1131), 478–507.
Mallinson, S. G., Gai, S. L. & Mudford, N. R. 1996 High-enthalpy, hypersonic compression corner flow. AIAA J. 34 (6), 11301137.
Marini, M.1998 Effects of flow and geometry parameters on shock-wave boundary-layer interaction phenomena. In 8th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Norfolk, VA, USA, AIAA-98-1570.
Mason, W. H. & Lee, J. 1994 Aerodynamically blunt and sharp bodies. J. Spacecr. Rockets 31 (3), 378382.
Messiter, A. F. 1970 Boundary-layer flow near the trailing edge of a flat plate. SIAM J. Appl. Maths 18 (1), 241257.
Moeckel, W. E.1957 Some effects of bluntness on boundary-layer transition and heat transfer at supersonic speeds. NACA Tech. Rep. TR-1312.
Nagamatsu, H. T., Graber, B. C. & Sheer, R. E. 1966 Roughness, bluntness, and angle-of-attack effects on hypersonic boundary-layer transition. J. Fluid Mech. 24 (1), 131.
Neiland, V. Y. 1969 Theory of laminar boundary layer separation in supersonic flow. Fluid Dyn. 4 (4), 3335.
Neiland, V. Y. 1970 Asymptotic theory of plane steady supersonic flows with separation zones. Fluid Dyn. 5 (3), 372381.
Neiland, V. Y. 1973 Special features of boundary-layer separation on a cooled body and its interaction with a hypersonic flow. Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 6, 99109 (translation in Fluid Dyn. 8 (6), 931–939).
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. 3954. Springer.
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, Atlanta, GA, USA, AIAA 2014-3366.
Oswatitsch, K. 1957 The conditions for the separation of boundary layers. In Contributions to the Development of Gasdynamics, pp. 618. Springer.
Pate, S. R.1977 Dominance of radiated aerodynamic noise on boundary-layer transition in supersonic-hypersonic wind tunnels: theory and application. PhD thesis, University of Tennessee, Knoxville, TN.
Prandtl, L. 1904 On fluid motions with very small friction. Verhldg 3, 484491.
Roy, C. J. 2003 Grid convergence error analysis for mixed-order numerical schemes. AIAA J. 41 (4), 595604.
Santos, W. F. N. 2005 Leading-edge bluntness effects on aerodynamic heating and drag of power law body in low-density hypersonic flow. J. Braz. Soc. Mech. Sci. Engng 27 (3), 236242.
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), 117145.
Shvedchenko, V. V. 2009 About the secondary separation at supersonic flow over a compression ramp. TsAGI Sci. J. 40 (5), 587607.
Smith, F. T. 1986 Steady and unsteady boundary-layer separation. Annu. Rev. Fluid Mech. 18 (1), 197220.
Smith, F. T. 1988 A reversed flow singularity in interacting boundary layers. Proc. R. Soc. Lond. A A420, 2152.
Softley, E. 1969 Boundary layer transition on hypersonic blunt, slender cones. In 2nd Fluid and Plasma Dynamics Conference, San Francisco, CA, USA, AIAA 1969-705.
Stetson, K. F.1978 Effect of bluntness and angle of attack on boundary layer transition on cones and biconic configurations. In Proceedings of 17th Aerospace Sciences Meeting, New Orleans, LA, USA, AIAA-1979-269.
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Fluids, vol. 3. Clarendon Press.
Stewartson, K. 1970 On laminar boundary layers near corners. Q. J. Mech. Appl. Maths 23 (2), 137152.
Stewartson, K. 1974 Multistructured boundary layers on flatplates and related bodies. Adv. Appl. Mech. 14, 145239.
Stewartson, K. & Williams, P. G. 1969 Self-induced separation. Proc. R. Soc. Lond. A 312 (1509), 181206.
Stollery, J. L. 1972 Viscous interaction effects on re-entry aerothermodynamics: theory and experimental results. AGARD Lecture Series 42, 10-1–10-28.
Sychev, V. V. 1972 Laminar separation. Fluid Dyn. 7 (3), 407417.
Taylor, G. 1950 The formation of a blast wave by a very intense explosion. I. Theoretical discussion. Proc. R. Soc. Lond. A 201 (1065), 159174.
Townsend, J. C.1966 Effects of leading-edge bluntness and ramp deflection angle on laminar boundary-layer separation in hypersonic flow. NASA Tech. Note D-3290.
Tsien, H. 1946 Similarity laws of hypersonic flows. Stud. Appl. Maths 25 (1–4), 247251.
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.
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.
Veldman, A. E. P.1979 A numerical method for the calculation of laminar, incompressible boundary layers with strong viscous-inviscid interaction. Tech. Rep. NLR TR 79023. National Aerospace Laboratory.
Veldman, A. E. P. 1980 Boundary layers with strong interaction: from asymptotic theory to calculation method. In BAIL 1 Conf. on Boundary and Interior Layers – Computation and Asymptotic Methods, pp. 149163. Boole Press.
Werle, M. J. & Vasta, V. N. 1974 New method for supersonic boundary-layer separations. AIAA J. 12 (11), 14911497.
Wright, M. J., Candler, G. V. & Bose, D. 1998 Data parallel line relaxation method for the Navier–Stokes equations. AIAA J. 36 (9), 16031609.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

Numerical study of bluntness effects on laminar leading edge separation in hypersonic flow

  • Amna Khraibut (a1), S. L. Gai (a1) and A. J. Neely (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.