Hostname: page-component-5c6d5d7d68-txr5j Total loading time: 0 Render date: 2024-08-14T10:07:44.212Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of wall temperature on hypersonic shock wave/turbulent boundary layer interactions

Published online by Cambridge University Press:  14 August 2024

Ji Zhang Open the ORCID record for Ji Zhang [Opens in a new window] ,
Tongbiao Guo Open the ORCID record for Tongbiao Guo [Opens in a new window] ,
Guanlin Dang  and
Xinliang Li
Ji Zhang
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
Tongbiao Guo
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Guanlin Dang
Affiliation:
AI for Science Institute, Beijing 100080, PR China
Xinliang Li*
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, PR China
*
†Email address for correspondence: lixl@imech.ac.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Wall temperature has a significant effect on shock wave/turbulent boundary layer interactions (STBLIs) and has become a non-negligible factor in the design process of hypersonic vehicles. In this paper, direct numerical simulations are conducted to investigate the wall temperature effects on STBLIs over a 34° compression ramp at Mach number 6. Three values of the wall-to-recovery-temperature ratio (0.50, 0.75 and 1.0) are considered in the simulations. The results show that the size of the separation bubble declines significantly as the wall temperature decreases. This is because the momentum profile of the boundary layer becomes fuller with wall cooling, which means the near-wall fluid has a greater momentum to suppress flow separation. An equation based on the free-interaction theory is proposed to predict the distributions of the wall pressure upstream of the corner at different wall temperatures. The prediction results are generally consistent with the simulation results (Reynolds number Reτ ranges from 160 to 675). In addition, the low-frequency unsteadiness is studied through the weighted power spectral density of the wall pressure and the correlation between the upstream and downstream. The results indicate that the low-frequency motion of the separation shock is mainly driven by the downstream mechanism and that wall cooling can significantly suppress the low-frequency unsteadiness, including the strength and streamwise range of the low-frequency motions.

JFM classification

Compressible Flows: Hypersonic Flow Compressible Flows: Shock waves Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 990 , 10 July 2024 , A21
Check for updates
Copyright
© The Author(s), 2024. Published by 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

Anderson, J.D. 1982 Modern Compressible Flow, with Historical Perspective. McGraw-Hill.Google Scholar
Babinsky, H. & Harvey, J.K. 2011 Shock Wave–Boundary-Layer Interactions. Cambridge University Press.10.1017/CBO9780511842757CrossRefGoogle Scholar
Bernardini, M., Asproulias, I., Larsson, J., Pirozzoli, S. & Grasso, F. 2016 Heat transfer and wall temperature effects in shock wave turbulent boundary layer interactions. Phys. Rev. Fluids 1, 084403.10.1103/PhysRevFluids.1.084403CrossRefGoogle 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 Rep. 1356.Google Scholar
Clemens, N.T. & Narayanaswamy, V. 2014 Low-frequency unsteadiness of shock wave/turbulent boundary layer interactions. Annu. Rev. Fluid Mech. 46 (1), 469–492.10.1146/annurev-fluid-010313-141346CrossRefGoogle Scholar
Dang, G., Liu, S., Guo, T., Duan, J. & X, L.I. 2022 a Direct numerical simulation of compressible turbulence accelerated by graphics processing unit: an open-source high accuracy accelerated computational fluid dynamic software. Phys. Fluid 34, 126106.10.1063/5.0127684CrossRefGoogle Scholar
Dang, G., Liu, S., Guo, T., Duan, J. & Li, X. 2022 b Direct numerical simulation of compressible turbulence accelerated by graphics processing unit: an open-access database of high-resolution direct numerical simulation. AIP Adv. 12, 125111.10.1063/5.0132489CrossRefGoogle Scholar
Dolling, D.S. 2001 Fifty years of shock-wave/boundary-layer interaction research: what next? AIAA J. 39 (8), 1517–1531.10.2514/2.1476CrossRefGoogle Scholar
Dolling, D.S. & Murphy, M.T. 1983 Unsteadiness of the separation shock wave structure in a supersonic compression ramp flowfield. AIAA J. 21 (12), 1628–1634.10.2514/3.60163CrossRefGoogle Scholar
van Driest, E.R. 1951 Turbulent boundary layer in compressible fluids. J. Aeronaut. Sci. 18 (3), 145–216.10.2514/8.1895CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martin, M.P. 2010 Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech. 655, 419–445.10.1017/S0022112010000959CrossRefGoogle Scholar
Duan, L. & Martin, M.P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 4. Effect of high enthalpy. J. Fluid Mech. 684, 25–59.10.1017/jfm.2011.252CrossRefGoogle Scholar
Elena, M. & Lacharme, J.P. 1988 Experimental study of a supersonic turbulent boundary layer using a laser Doppler anemometer. J. Mec. Theor. Appl. 7, 175–190.Google Scholar
Erengil, M.E. & Dolling, D.S. 1991 Unsteady wave structure near separation in a Mach 5 compression ramp interaction. AIAA J. 29, 728–735.10.2514/3.10647CrossRefGoogle Scholar
Erm, L.P. & Joubert, P.N. 1991 Low-Reynolds-number turbulent boundary layers. J. Fluid Mech. 230, 1–44.10.1017/S0022112091000691CrossRefGoogle Scholar
Fang, J., Zheltovodov, A.A., Yao, Y., Moulinec, C. & Emerson, D.R. 2020 On the turbulence amplification in shock-wave/turbulent boundary layer interaction. J. Fluid Mech. 897, A32.10.1017/jfm.2020.350CrossRefGoogle Scholar
Gonsalez, J.C. & Dolling, D.S. 1993 Correlation of interaction sweepback effects on the dynamics of shock-induced turbulent separation. AIAA Paper 1993-0776.10.2514/6.1993-776CrossRefGoogle Scholar
Guo, T., Fang, J., Zhang, J. & Li, X. 2022 Direct numerical simulation of shock-wave/boundary layer interaction controlled with convergent-divergent riblets. Phys. Fluids 34, 086101.10.1063/5.0102261CrossRefGoogle Scholar
Huang, P.G., Coleman, G.N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218.10.1017/S0022112095004599CrossRefGoogle Scholar
Humble, R., Scarano, F. & Van Oudheusden, B. 2009 Unsteady aspects of an incident shock wave/turbulent boundary layer interaction. J. Fluid Mech. 635, 47–74.10.1017/S0022112009007630CrossRefGoogle Scholar
Jameson, A., Schmidt, W. & Turkel, E. 1981 Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA Paper 1981-1259.10.2514/6.1981-1259CrossRefGoogle Scholar
Jaunet, V., Debieve, J.F. & Dupont, P. 2014 Length scales and time scales of a heated shock-wave/boundary-layer interaction. AIAA J. 52 (11), 2524–2532.10.2514/1.J052869CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.10.1017/S0022112095000462CrossRefGoogle Scholar
Jiang, G. & Shu, C. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228.10.1006/jcph.1996.0130CrossRefGoogle Scholar
Li, X., Fu, D. & Ma, Y. 2008 Direct numerical simulation of hypersonic boundary-layer transition over a blunt cone. AIAA J. 46 (11), 2899–2913.10.2514/1.37305CrossRefGoogle Scholar
Li, X., Fu, D., Ma, Y. & Liang, X. 2010 Direct numerical simulation of shock/turbulent boundary layer interaction in a supersonic compression ramp. Sci. China Phys. Mech. Astron. 53, 1651–1658.10.1007/s11433-010-4034-xCrossRefGoogle Scholar
Liang, X. & Li, X. 2015 Direct numerical simulation on Mach number and wall temperature effects in the turbulent flows of flat-plate boundary layer. Commun. Comput. Phys. 17, 189–212.10.4208/cicp.221113.280714aCrossRefGoogle Scholar
Liu, W., Zhang, C.A. & Wang, F.M. 2018 Modification of hypersonic waveriders by vorticity-based boundary layer displacement thickness determination method. Aerosp. Sci. Technol. 75, 200–214.10.1016/j.ast.2017.12.020CrossRefGoogle 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/S0022112000002718CrossRefGoogle Scholar
Marusic, I., Mckeon, B.J., Monkewitz, P.A., Nagib, H.M., Smits, A.J. & Sreenivasan, K.R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 65103.10.1063/1.3453711CrossRefGoogle Scholar
Morkovin, M.V. 1962 Effects of compressibility on turbulent flows. In Mécanique de la Turbulence (ed. Favre, A.), pp. 367–380. CNRS.Google Scholar
Pasquariello, V., Hickel, S. & Adams, N.A. 2017 Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number. J. Fluid Mech. 823, 617–657.CrossRefGoogle Scholar
Piponniau, S., Dussauge, J., Debiève, J. & Dupont, P. 2009 A simple model for low-frequency unsteadiness in shock-induced separation. J. Fluid Mech. 629, 87–108.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech. 688, 120–168.CrossRefGoogle Scholar
Pirozzoli, S. & Grasso, F. 2006 Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at M = 2.25. Phys. Fluids 18 (6), 065113.10.1063/1.2216989CrossRefGoogle 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 (3), 530–545.CrossRefGoogle Scholar
Priebe, S. & Martín, M.P. 2021 Turbulence in a hypersonic compression ramp flow. Phys. Rev. Fluids 6, 034601.CrossRefGoogle Scholar
Roy, C.J. & Blottner, F.G. 2006 Review and assessment of turbulence models for hypersonic flows. Prog. Aerosp. Sci. 42, 469–530.CrossRefGoogle Scholar
Smits, A.J. & Dussauge, J.P. 1996 Turbulent Shear Layers in Supersonic Flow. Springer.Google Scholar
Spaid, F.W. & Frishett, J.C. 1972 Incipient separation of a supersonic, turbulent boundary layer, including effects of heat transfer. AIAA J. 10 (7), 915–922.CrossRefGoogle Scholar
Spalart, P.R. 1988 Direct simulation of a turbulent boundary layer up to R θ = 1410. J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
Steger, J.L. & Warming, R.F. 1981 Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods. J. Comput. Phys. 40 (2), 263–293.CrossRefGoogle Scholar
Thomas, F.O., Putnam, C.M. & Chu, H.C. 1994 On the mechanism of unsteady shock oscillation in shock wave/turbulent boundary layer interactions. Exp. Fluids 18, 69–81.CrossRefGoogle 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.CrossRefGoogle Scholar
Touré, P.S.R. & Schülein, E. 2023 Interaction of a moving shock wave with a turbulent boundary layer. J. Fluid Mech. 964, A28.CrossRefGoogle Scholar
Volpiani, P.S., Bernardini, M. & Larsson, J. 2020 Effects of a nonadiabatic wall on hypersonic shock/boundary-layer interactions. Phys. Rev. Fluids 5 (1), 014602.CrossRefGoogle Scholar
Walz, A. 1969 Boundary Layers of Flow and Temperature. MIT Press.Google Scholar
Wu, M. & Martin, M.P. 2007 Direct numerical simulation of supersonic turbulent boundary layer over a compression ramp. AIAA J. 45 (4), 879–889.CrossRefGoogle Scholar
Wu, M. & Martin, M.P. 2008 Analysis of shock motion in shockwave and turbulent boundary layer interaction using direct numerical simulation data. J. Fluid Mech. 594, 71–83.CrossRefGoogle Scholar
Xu, D., Wang, J., Wan, M., Yu, C., Li, X. & Chen, S. 2021 Effect of wall temperature on the kinetic energy transfer in a hypersonic turbulent boundary layer. J. Fluid Mech. 929, A33.CrossRefGoogle Scholar
Zhang, J., Guo, T., Dang, G. & Li, X. 2022 Direct numerical simulation of shock wave/turbulent boundary layer interaction in a swept compression ramp at Mach 6. Phys. Fluids 34, 116110.CrossRefGoogle Scholar
Zhang, Y., Bi, W., Hussain, F. & She, Z. 2014 A generalized Reynolds analogy for compressible wall-bddounded turbulent flows. J. Fluid Mech. 739, 392–420.CrossRefGoogle Scholar
Zhang, Z., Cui, G. & Xu, C. 2005 Turbulence Theory and Simulation. Tsinghua University Press.Google Scholar
Zhu, X., Yu, C., Tong, F. & Li, X. 2017 Numerical study on wall temperature effects on shock wave/turbulent boundary-layer interaction. AIAA J. 55 (1), 131–140.10.2514/1.J054939CrossRefGoogle Scholar