Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-12-01T02:09:43.472Z Has data issue: false hasContentIssue false
  • English
  • Français

The amplification of large-scale motion in a supersonic concave turbulent boundary layer and its impact on the mean and statistical properties

Published online by Cambridge University Press:  29 January 2019

Qian-Cheng Wang Open the ORCID record for Qian-Cheng Wang [Opens in a new window] ,
Zhen-Guo Wang ,
Ming-Bo Sun Open the ORCID record for Ming-Bo Sun [Opens in a new window] ,
Rui Yang ,
Yu-Xin Zhao  and
Zhiwei Hu
Qian-Cheng Wang
Affiliation:
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China
Zhen-Guo Wang
Affiliation:
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China
Ming-Bo Sun*
Affiliation:
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China
Rui Yang
Affiliation:
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China
Yu-Xin Zhao
Affiliation:
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China
Zhiwei Hu
Affiliation:
Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Direct numerical simulation is conducted to uncover the response of a supersonic turbulent boundary layer to streamwise concave curvature and the related physical mechanisms at a Mach number of 2.95. Streamwise variations of mean flow properties, turbulence statistics and turbulent structures are analysed. A method to define the boundary layer thickness based on the principal strain rate is proposed, which is applicable for boundary layers subjected to wall-normal pressure and velocity gradients. While the wall friction grows with the wall turning, the friction velocity decreases. A logarithmic region with constant slope exists in the concave boundary layer. However, with smaller slope, it is located lower than that of the flat boundary layer. Streamwise varying trends of the velocity and the principal strain rate within different wall-normal regions are different. The turbulence level is promoted by the concave curvature. Due to the increased turbulence generation in the outer layer, secondary bumps are noted in the profiles of streamwise and spanwise turbulence intensity. Peak positions in profiles of wall-normal turbulence intensity and Reynolds shear stress are pushed outward because of the same reason. Attributed to the Görtler instability, the streamwise extended vortices within the hairpin packets are intensified and more vortices are generated. Through accumulations of these vortices with a similar sense of rotation, large-scale streamwise roll cells are formed. Originated from the very large-scale motions and by promoting the ejection, sweep and spanwise events, the formation of large-scale streamwise roll cells is the physical cause of the alterations of the mean properties and turbulence statistics. The roll cells further give rise to the vortex generation. The large number of hairpin vortices formed in the near-wall region lead to the improved wall-normal correlation of turbulence in the concave boundary layer.

JFM classification

Boundary Layers: Boundary layer control Compressible Flows: Compressible boundary layers Aerodynamics: High-speed flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 454 - 493
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

Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.10.1017/S0022112000001580Google Scholar
Barlow, R. S. & Johnston, J. P. 1988a Local effects of large-scale eddies on bursting in a concave boundary layer. J. Fluid Mech. 191, 177–195.10.1017/S0022112088001557Google Scholar
Barlow, R. S. & Johnston, J. P. 1988b Structure of a turbulent boundary layer on a concave surface. J. Fluid Mech. 191, 137–176.10.1017/S0022112088001545Google Scholar
Bradshaw, P.1973 Effects of streamline curvature on turbulent flow. AGARDograph 169.Google Scholar
Bradshaw, P. 1974 The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers. J. Fluid Mech. 63, 449–464.10.1017/S0022112074001728Google Scholar
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214.10.1017/S0022112005004726Google Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimentional flow fields. Phys. Fluids 2, 765–777.10.1063/1.857730Google Scholar
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aeronaut. Sci. 21, 91–108.10.2514/8.2938Google Scholar
Dempsey, L. J., Hall, P. & Deguchi, K. 2017 The excitation of Görtler vortices by free stream coherent structures. J. Fluid Mech. 826, 60–96.10.1017/jfm.2017.380Google 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
Elsinga, G. E., Adrian, R. J., Oudheusden, B. W. & Van Scarano, F. 2010 Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer. J. Fluid Mech. 644, 35–60.10.1017/S0022112009992047Google Scholar
Fernholzh, H. H. & Finley, P. J.1980 A critical commentary on mean flow data for two dimensional compressible turbulent boundary layers. AGARDograph 253. North Atlantic Treaty Organization.Google Scholar
Flaherty, W. & Austin, J. M. 2013 Scaling of heat transfer augmentation due to mechanical distortions in hypervelocity boundary layers. Phys. Fluids 25, 106106.10.1063/1.4826476Google Scholar
Floryan, J. M. 1991 On the Görtler instability of boundary layers. Prog. Aerosp. Sci. 28, 235–271.10.1016/0376-0421(91)90006-PGoogle Scholar
Franko, K. J. & Lele, S. 2014 Effect of adverse pressure gradient on high speed boundary layer transition. Phys. Fluids 26, 024106.10.1063/1.4864337Google Scholar
Görtler, H.1954 On the three dimensional instability of laminar boundary layers on concave walls. NACA TM 1375.Google 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
Hall, P. 1983 The linear development of Görtler vortices in growing boundary layers. J. Fluid Mech. 130, 41–58.10.1017/S0022112083000968Google Scholar
Harun, Z., Mont, 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
Hoffmann, P. H., Muck, K. C. & Bradshaw, P. 1985 The effect of concave surface curvature on turbulent boundary layers. J. Fluid Mech. 161, 371–403.10.1017/S0022112085002981Google Scholar
Hopkins, E. J. & Inouye, M. 1971 An evaluation of theories for predicting turbulent skin friction and heat transfer on flat plates at supersonic and hypersonic mach numbers. AIAA J. 9 (6), 993–1003.10.2514/3.6323Google Scholar
Humble, R. A., Peltier, S. J. & Bowersox, R. D. W. 2012 Visualization of the structural response of a hypersonic turbulent boundary layer to convex curvature. Phys. Fluids 24, 106103.10.1063/1.4761833Google Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.10.1017/S0022112006003946Google Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.10.1017/S0022112009007721Google Scholar
Jayaram, M., Taylor, M. W. & Smits, A . J. 1987 The response of a compressible turbulent boundary layer to short regions of concave surface curvature. J. Fluid Mech. 175, 343–362.10.1017/S0022112087000429Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.10.1017/S0022112087000892Google Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417–423.10.1063/1.869889Google Scholar
Laderman, A. J. 1980 Adverse pressure gradient effects on supersonic boundary layer turbulence. AIAA J. 18 (10), 1186–1195.10.2514/3.50870Google Scholar
Lee, J. H. & Sung, H. J. 2011 Very-large-scale motions in a turbulent boundary layer. J. Fluid Mech. 673, 80–120.10.1017/S002211201000621XGoogle Scholar
Lewis, J. E., Gran, R. L. & Kubota, T. 1972 An experiment on the adiabatic compressible turbulent boundary layer in adverse and favourable pressure gradients. J. Fluid Mech. 51, 657–672.10.1017/S0022112072001296Google Scholar
Lu, S. S. & Willmarth, W. W. 1973 Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60 (3), 481–511.10.1017/S0022112073000315Google Scholar
Maeder, T., Adams, N. A. & Kleiser, L. 2001 Direct simulation of turbulent supersonic boundary layers by an extended temporal approach. J. Fluid Mech. 429, 187–216.10.1017/S0022112000002718Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31, 418–428.10.1016/j.ijheatfluidflow.2010.01.005Google Scholar
Mokhtarzadeh-Dehghan, M. R. & Yuan, Y. M. 2002 Measurements of turbulence quantities and bursting period in developing turbulent boundary layers on the concave and convex walls of a 90° square bend. Exp. Therm. Fluid Sci. 27, 59–75.10.1016/S0894-1777(02)00213-3Google Scholar
Monty, J. P., Harun, Z. & Marusic, I. 2011 A parametric study of adverse pressure gradient turbulent boundary layers. Intl J. Heat Fluid Flow 32, 575–585.10.1016/j.ijheatfluidflow.2011.03.004Google Scholar
Ozalp, A. A. & Umur, H. 2003 An experimental investigation of the combined effects of surface curvature and streamwise pressure gradients both in laminar and turbulent flows. Heat Mass Transfer 39, 869–876.10.1007/s00231-003-0413-4Google Scholar
Patel, V. C. & Sotiropoulos, F. 1997 Longitudinal curvature effects in turbulent boundary layers. Prog. Aerosp. Sci. 33, 1–70.10.1016/S0376-0421(96)00001-2Google 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. Phys. Fluids 16, 530–545.10.1063/1.1637604Google Scholar
Pokrajac, D., Campbell, L. J., Nikora, V., Manes, C. & Mcewan, I. 2007 Quadrant analysis of persistent spatial velocity perturbations over square-bar roughness. Exp. Fluids 42, 413–423.10.1007/s00348-006-0248-0Google Scholar
Ren, J. & Fu, S. 2015 Secondary instabilities of Görtler vortices in high-speed boundary layer flows. J. Fluid Mech. 781, 388–421.10.1017/jfm.2015.490Google Scholar
Ringuette, M. J., Wu, M. & Martin, M. P. 2008 Coherent structures in direct numerical simulation of turbulent boundary layers at mach 3. J. Fluid Mech. 594, 59–69.10.1017/S0022112007009020Google Scholar
Roghelia, A., Olivier, H., Egorov, I. & Chuvakhov, P. 2017 Experimental investigation of Görtler vortices in hypersonic ramp flows. Exp. Fluids 58 (10), 139.10.1007/s00348-017-2422-yGoogle 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., Li, Q. & Yee, H. C. 2002 Entropy splitting for high-order numercial simulation of compressible turbulence. J. Comput. Phys. 178, 307–322.10.1006/jcph.2002.7022Google Scholar
Sandham, N. D., Schlein, 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. & Orlu, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid. Mech. 659, 116–126.10.1017/S0022112010003113Google Scholar
Schrader, L., Brandt, L. & Zaki, T. A. 2011 Receptivity, instability and breakdown of Görtler flow. J. Fluid Mech. 682, 362–396.10.1017/jfm.2011.229Google Scholar
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27–54.10.1017/S0022112083000634Google Scholar
Smith, D. R. & Smits, A. J. 1995 A study of the effects of curvature and a supersonic turbulent boundary layer. Exp. Fluids 18, 363–369.10.1007/BF00211393Google 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
Smits, A. J. & Wood, D. H. 1985 The response of turbulent boundary layers to sudden pertubations. Annu. Rev. Fluid Mech. 17, 321–358.10.1146/annurev.fl.17.010185.001541Google Scholar
Spalding, D. B. 1961 A single formula for the law of the wall. J. Appl. Mech. 28, 455–457.10.1115/1.3641728Google Scholar
Sturek, W. B. & Danberg, J. E. 1972a Supersonic turbulent boundary layer in adverse pressure gradient, part 2: data analysis. AIAA J. 10 (5), 630–635.10.2514/3.50167Google Scholar
Sturek, W. B. & Danberg, J. E. 1972b Supersonic turbulent boundary layer in adverse pressure gradient, part I: the experiment. AIAA J. 10 (4), 475–480.10.2514/3.50167Google Scholar
Sun, M. B., Hu, Z. & Sandham, N. D. 2017 Recovery of a supersonic turbulent boundary layer after an expansion corner. Phys. Fluids 29, 076103.10.1063/1.4995293Google Scholar
Swearingen, J. D. & Blackwelder, R. F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255–290.10.1017/S0022112087002337Google Scholar
Tandiono, T., Winoto, S. H. & Shah, D. A. 2008 On the linear and nonlinear development of Görtler vortices. Phys. Fluids 20, 094103.10.1063/1.2980349Google Scholar
Tichenor, N. R., Humble, R. 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, Southampton, UK.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
Vinokur, M.1980 On one-dimensional stretching functions for finite-difference calculations. NASA Contractor Report 3313.Google Scholar
Wang, B., Sandham, N. D., Hu, Z. & Liu, W. 2015b Numerical study of oblique shock-wave/boundary-layer interaction considering sidewall effect. J. Fluid Mech. 767, 526–561.10.1017/jfm.2015.58Google Scholar
Wang, J. S., Feng, L. H., Wang, J. J. & Li, T. 2018 Görtler vortices in low-Reynolds-number flow over multi-element airfoil. J. Fluid Mech. 835, 898–935.10.1017/jfm.2017.781Google 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, 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, 116101.10.1063/1.4968527Google Scholar
Wang, Q. C., Wang, Z. G. & Zhao, Y. X. 2017 The impact of streamwise convex curvature on the supersonic turbulent boundary layer. Phys. Fluids 29, 116106.10.1063/1.4994928Google Scholar
White, F. M. 2006 Viscous Fluid Flow, 3rd edn. McGraw-Hill.Google Scholar
Wu, X., Zhao, D. & Luo, J. 2011 Excitation of steady and unsteady Görtler vortices by free-stream vortical disturbances. J. Fluid Mech. 682, 66–100.10.1017/jfm.2011.224Google Scholar
Wu, Y. & Christensen, K. T. 2006 Population trends of spanwise vortices in wall turbulence. J. Fluid Mech. 568, 55–76.10.1017/S002211200600259XGoogle Scholar
Xie, Z. T. & 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., Vinokur, M. & Djomehri, M. J. 2000 Entropy splitting and numerical dissipation. J. Comput. Phys. 162, 33–81.10.1006/jcph.2000.6517Google Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.10.1017/S002211209900467XGoogle Scholar