Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-17T23:23:56.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulence structures and statistics of a supersonic turbulent boundary layer subjected to concave surface curvature

Published online by Cambridge University Press:  18 February 2019

Mingbo Sun Open the ORCID record for Mingbo Sun [Opens in a new window] ,
Neil D. Sandham Open the ORCID record for Neil D. Sandham [Opens in a new window]  and
Zhiwei Hu
Mingbo Sun*
Affiliation:
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073, China Aerodynamics and Flight Mechanics, Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK
Neil D. Sandham
Affiliation:
Aerodynamics and Flight Mechanics, Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK
Zhiwei Hu
Affiliation:
Aerodynamics and Flight Mechanics, Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK
*
†Email address for correspondence: sunmingbo@nudt.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Supersonic turbulent flows at Mach 2.7 over concave surfaces for two different radii of curvature were investigated and compared with a flat plate turbulent boundary layer using direct numerical simulations. The streamwise velocity reduces in the outer part of the boundary layer due to compression, while it increases near the wall due to curvature, with a higher shape factor for the concave cases. The near-wall spanwise streak spacing reduces compared to the flat plate, with large-scale streaks and turbulence amplification also observed. Streamwise velocity iso-surfaces and streamlines show the generation of Görtler-like vortices, consistent with significant centrifugal effects. Abundant small vortices are shown to be associated with large baroclinic production of vorticity that is caused by the density and pressure gradients that are associated with concave compression. Profiles of turbulent kinetic energy and turbulent Mach number exhibit a characteristic two-layer structure in the concave boundary layer cases. In the outer layer, turbulence is greatly amplified, whereas a local balance exists in the inner layer. Turbulent energy budget analysis shows that both production and dissipation increase near the concave wall, whereas in the outer part of the boundary layer, the production is increased and ultimately balanced by convection and turbulent transport.

JFM classification

Boundary Layers: Boundary layer structure Compressible Flows: Compressible boundary layers Aerodynamics: High-speed flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 60 - 99
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

Bradshaw, P. 1974 The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers. J. Fluid Mech. 63, 449–466.10.1017/S0022112074001728Google Scholar
Ciolkosz, L. & Spina, E.2006 An experimental study of Görtler vortices in compressible flow. AIAA Paper 2006-4512.Google Scholar
Donovan, J. F., Spina, E. F. & Smits, A. J. 1994 The structure of a supersonic turbulent boundary layer subjected to concave surface curvature. J. Fluid Mech. 259, 1–24.10.1017/S0022112094000017Google Scholar
Duan, L. & Beekman, I. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245–267.10.1017/S0022112010005902Google Scholar
Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C. & Poinsot, T. 1999 Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys 152 (2), 517–549.10.1006/jcph.1999.6238Google Scholar
Fernando, E. M. & Smits, A. J. 1990 A supersonic turbulent boundary layer in an adverse pressure gradient. J. Fluid Mech. 211, 285–307.10.1017/S0022112090001574Google Scholar
Fernholz, H. H. & Warnack, D. 1998 The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer. J. Fluid Mech. 359, 329–356.10.1017/S0022112097008513Google Scholar
Flaherty, W. & Austin, J. M. 2013a Scaling of heat transfer augmentation due to mechanical distortions in hypervelocity boundary layers. Phys. Fluids 25, 106–106.10.1063/1.4826476Google Scholar
Flaherty, W. & Austin, J. M. 2013b Scaling of heat transfer augmentation due to mechanical distortions in hypervelocity boundary layers. Phys. Fluids 25 (10), 379–409.10.1063/1.4826476Google Scholar
Flaherty, W. P. 2013 Effects of Local and Global Mechanical Distortions to Hypervelocity Boundary Layers. University of Illinois at Urbana-Champaign.Google Scholar
Franko, K. J. & Lele, S. 2014 Effect of adverse pressure gradient on high speed boundary layer transition. Phys. Fluids 26 (2), 176–183.10.1063/1.4864337Google Scholar
Görtler, H.1954 On the three-dimensional instability of laminar boundary layers on concave walls. NASA Tech. Mem. 1375.Google Scholar
Green, J. E. 1970 Interactions between shock waves and turbulent boundary layers. Prog. Aerosp. Sci. 11, 235–340.10.1016/0376-0421(70)90018-7Google Scholar
Grilli, M., Hickel, S. & Adams, N. A. 2013 Large-eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp. Intl J. Heat Fluid Flow 42 (8), 79–93.10.1016/j.ijheatfluidflow.2012.12.006Google Scholar
Guarini, S. E., Moser, R. D., Shariff, K. & Wray, A. 2000 Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5. J. Fluid Mech. 414, 1–33.10.1017/S0022112000008466Google Scholar
Harun, Z., Monty, J. P., Mathis, R. & Marusic, I. 2013 Pressure gradient effects on the large-scale structure of turbulent boundary layers. J. Fluid Mech. 715, 477–498.10.1017/jfm.2012.531Google Scholar
Hu, Z. W., Morfey, C. L. D. & Sandham, N. D. 2006 Wall pressure and shear stress spectra from direct numerical simulations of channel flow. AIAA J. 44 (7), 1541–1549.10.2514/1.17638Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.10.1017/S0022112095000462Google Scholar
Kim, J., Samimy, M. & Lee, S. 2001 Effects of compression and expansion on turbulence intensity in supersonic boundary layers. AIAA J. 39, 1071–1077.10.2514/2.1419Google Scholar
Lagha, M., Kim, J., Eldredge, J. D. & Zhong, X. 2011 A numerical study of compressible turbulent boundary layers. Phys. Fluids 23, 015106.10.1063/1.3541841Google Scholar
Lee, J. H. & Sung, H. J. 2009 Structures in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 639, 101–131.10.1017/S0022112009990814Google Scholar
Li, F., Choudhari, M., Chang, C.-L., Wu, M. & Greene, P. T.2010 Development and breakdown of Görtler vortices in high speed boundary layers. AIAA Paper 2010-705.Google Scholar
Luca, L., Cardone, G., Aymer de la Chevalerie, D. & Fonteneau, A. 1993 Goertler instability of a hypersonic boundary layer. Exp. Fluids 16, 10–16.10.1007/BF00188500Google Scholar
Luker, J. J., Hale, C. S. & Bowersox, R. D. W. 1998 Experimental analysis of the turbulent shear stresses for distorted supersonic boundary layers. J. Propul. Power 14, 110–118.10.2514/2.5256Google Scholar
Lumley, J. L. 1978 Computational modeling of turbulent flows. Arch. Appl. Mech. 18, 123–176.10.1016/S0065-2156(08)70266-7Google Scholar
Maeder, T., Adams, N. A. & Kleiser, L. 1998 Direct Numerical Simulation of Supersonic Turbulent Boundary Layers. Springer.10.1007/978-94-011-5118-4_47Google Scholar
Morkovin, M. V. 1962 Effects of compressibility on turbulent flows. In Mecanique de la Turbulence (ed. Favre, A.), p. 367C380. CNRS.Google Scholar
Neel, I., Leidy, A. N., Bowersox, R. D. W. & Tichenor, N. R.2016 Hypersonic boundary layer with streamline curvature-driven adverse pressure gradient. AIAA Paper 2016-4248.Google Scholar
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at m = 2. 25. J. Fluid Mech. 16, 530–545.Google Scholar
Ren, J. & Fu, S. 2015a Secondary instabilities of Görtler vortices in high-speed boundary layer flows. J. Fluid Mech. 781, 388–421.10.1017/jfm.2015.490Google Scholar
Ren, J. & Fu, S. 2015b Study of the discrete spectrum in a Mach 4.5 Görtler flow. Flow Turbul. Combust. 94, 339–357.10.1007/s10494-014-9575-zGoogle Scholar
Sandham, N. D. 2016 Effects of compressibility and shock-wave interactions on turbulent shear flows. Flow Turbul. Combust. 97, 1–25.10.1007/s10494-016-9733-6Google Scholar
Sandham, N. D., Schülein, E., Wagner, A., Willems, S. & Steelant, J. 2014 Transitional shock-wave/boundary-layer interactions in hypersonic flow. J. Fluid Mech. 752, 349–382.10.1017/jfm.2014.333Google Scholar
Saric, W. S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26, 379–409.10.1146/annurev.fl.26.010194.002115Google Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.10.1017/S0022112010003113Google Scholar
Smith, D. R. & Smits, A. J.1994 The effects of steamline curvature and pressure gradient on the behavior of turbulent boundary layers in supersonic flow. AIAA Paper 94-2227.Google Scholar
Smith, D. R. & Smits, A. J. 1995 A study of the effects of curvature and compression on the behavior of a supersonic turbulent boundary layer. Exp. Fluids 18, 363–369.10.1007/BF00211393Google Scholar
Smits, A. J. & Dussauge, J.-P. 2006 Turbulent Shear Layers in Supersonic Flow, 2nd edn. Springer.Google Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.10.1146/annurev-fluid-122109-160753Google Scholar
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337–371.10.1017/S002211209300120XGoogle Scholar
Spina, E. F., Smits, A. J. & Robinson, S. K. 1994 The physics of supersonic turbulent boundary layers. Annu. Rev. Fluid Mech. 26, 287–319.10.1146/annurev.fl.26.010194.001443Google Scholar
Sun, M. B. & Hu, Z. W. 2018a Formation of surface trailing counter-rotating vortex pairs downstream of a sonic jet in a supersonic cross-flow. J. Fluid Mech. 850, 551–583.10.1017/jfm.2018.455Google Scholar
Sun, M. B. & Hu, Z. W. 2018b Generation of upper trailing counter-rotating vortices of a sonic jet in a supersonic crossflow. AIAA J. 56 (3), 1047–1059.10.2514/1.J056442Google Scholar
Sun, M. B. & Hu, Z. W. 2018c Mixing in nearwall regions downstream of a sonic jet in a supersonic crossflow at Mach 2.7. Phys. Fluids 30, 106102.10.1063/1.5045752Google Scholar
Sun, M. B., Hu, Z. W. & Sandham, N. D. 2017 Recovery of a supersonic turbulent boundary layer after an expansion corner. Phys. Fluids 29 (7), 076103.10.1063/1.4995293Google Scholar
Sun, M. B., Zhang, S. P., Zhao, Y. X. & Liang, J. H. 2013 Experimental investigation on transverse jet penetration into a supersonic turbulent crossflow. Sci. China Technol. Sci. 56, 1989–1998.10.1007/s11431-013-5265-7Google Scholar
Thompson, K. W. 1990 Time dependent boundary conditions for hyperbolic systems. J. Comput. Phys. 89 (2), 439–461.10.1016/0021-9991(90)90152-QGoogle Scholar
Tichenor, N. R., Humble, R. A. A. & Bowersox, R. D. W. 2013 Response of a hypersonic turbulent boundary layer to favourable pressure gradients. J. Fluid Mech. 722, 187–213.10.1017/jfm.2013.89Google Scholar
Tong, F., Li, X., Duan, Y. & Yu, C. 2017 Direct numerical simulation of supersonic turbulent boundary layer subjected to a curved compression ramp. Phys. Fluids 29, 125101.10.1063/1.4996762Google Scholar
Touber, E.2010 Unsteadiness in shock-wave/boundary-layer interactions. PhD thesis, University of Southampton.Google Scholar
Touber, E. & Sandham, N. D. 2009 Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble. Theor. Comput. Fluid Dyn. 23, 79–107.10.1007/s00162-009-0103-zGoogle Scholar
Vallikivi, M., Ganapathisubramani, B. & Smits, A. J. 2015a Spectral scaling in boundary layers and pipes at very high Reynolds numbers. J. Fluid Mech. 771, 303–326.10.1017/jfm.2015.181Google Scholar
Vallikivi, M., Hultmark, M. & Smits, A. J. 2015b Turbulent boundary layer statistics at very high Reynolds number. J. Fluid Mech. 779, 371–389.10.1017/jfm.2015.273Google Scholar
Wang, B., Sandham, N. D., Hu, Z. W. & Liu, W. 2015 Numerical study of oblique shock-wave/boundary-layer interaction considering sidewall effects. J. Fluid Mech. 767, 526–561.10.1017/jfm.2015.58Google Scholar
Wang, Q. C. & Wang, Z. G. 2016 Structural characteristics of the supersonic turbulent boundary layer subjected to concave curvature. Appl. Phys. Lett. 108, 114102.Google Scholar
Wang, Q. C., Wang, Z. G. & Zhao, Y. X. 2016a An experimental investigation of the supersonic turbulent boundary layer subjected to concave curvature. Phys. Fluids 28 (9), 096104.10.1063/1.4962563Google Scholar
Wang, Q. C., Wang, Z. G. & Zhao, Y. X. 2016b On the impact of adverse pressure gradient on the supersonic turbulent boundary layer. Phys. Fluids 28 (11), 116101.10.1063/1.4968527Google Scholar
White, F. M. 2007 Viscous Fluid Flow, 3rd edn. McGraw-Hill.Google Scholar
Xie, Z. & Castro, I. P. 2008 Efficient generation of inflow conditions for large eddy simulation of street-scale flows. Flow Turbul. Combust. 81, 449–470.10.1007/s10494-008-9151-5Google Scholar
Yee, H. C., Sandham, N. D. & Djomehri, M. J. 1999 Low-dissipative high-order shock-capturing methods using characteristic-based filters. J. Comput. Phys. 150 (1), 199–238.10.1006/jcph.1998.6177Google Scholar