Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-19T11:33:27.923Z Has data issue: false hasContentIssue false
  • English
  • Français

A spectral inspection for turbulence amplification in oblique shock wave/turbulent boundary layer interaction

Published online by Cambridge University Press:  28 October 2022

Ming Yu Open the ORCID record for Ming Yu [Opens in a new window] ,
MingXiang Zhao ,
ZhiGong Tang ,
XianXu Yuan Open the ORCID record for XianXu Yuan [Opens in a new window]  and
ChunXiao Xu Open the ORCID record for ChunXiao Xu [Opens in a new window]
Ming Yu
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, PR China Key Laboratory of Applied Mechanics, Ministry of Education, Institute of Fluid Mechanics, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
MingXiang Zhao
Affiliation:
Key Laboratory of Applied Mechanics, Ministry of Education, Institute of Fluid Mechanics, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China Beijing Institute of Space Launch Technology, Beijing 100076, PR China
ZhiGong Tang
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, PR China
XianXu Yuan*
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang 621000, PR China
ChunXiao Xu*
Affiliation:
Key Laboratory of Applied Mechanics, Ministry of Education, Institute of Fluid Mechanics, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
†Email addresses for correspondence: yuanxianxu@cardc.cn, xucx@tsinghua.edu.cn
†Email addresses for correspondence: yuanxianxu@cardc.cn, xucx@tsinghua.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Turbulence amplification and the large-scale coherent structures in shock wave/turbulent boundary layer interaction flows have been studied at length in previous research, while the direct association between these two flow features is still lacking. In the present study, the transport equation of turbulent kinetic energy spectra is derived and utilized to analyse the scale-by-scale energy budget across the interaction zone, enabling us to reveal the association between the genesis of the large-scale motions and the turbulence amplification. For the presently considered flow with incipient shock-induced separation, we identified in turbulent kinetic energy spectra distribution that the most energetic motions are converted from the near-wall small-scale motions to large-scale motions consisting of velocity streaks and cross-stream circulations as they go through the interaction zone. The amplification of streamwise velocity fluctuation is triggered first, resulting in the emergence of large-scale velocity streaks, which is attributed to the adverse pressure gradient, as indicated by the spectra of the production term. The energy carried by large-scale velocity streaks is transferred to other velocity components by the pressure-strain term, producing large-scale cross-stream circulations. When large-scale motions are convected downstream, their energy is transferred via turbulent cascade to smaller scales and dissipated by viscosity. The spanwise uniform fluctuations, reminiscent of the unsteadiness of the separation bubble, are contributed primarily by the inter-scale energy transfer from the finite spanwise scale motions.

JFM classification

Aerodynamics: High-speed flow Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 951 , 25 November 2022 , A2
Check for updates
Copyright
© The Author(s), 2022. 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

Andreopoulos, Y., Agui, J.H. & Briassulis, G. 2000 Shock wave–turbulence interactions. Annu. Rev. Fluid Mech. 32 (1), 309–345.CrossRefGoogle Scholar
Anyiwo, J.C. & Bushnell, D.M. 1982 Turbulence amplification in shock-wave boundary-layer interaction. AIAA J. 20 (7), 893–899.CrossRefGoogle Scholar
Arun, S., Sameen, A., Srinivasan, B. & Girimaji, S. 2021 Scale-space energy density function transport equation for compressible inhomogeneous turbulent flows. J.Fluid Mech. 920, A31.CrossRefGoogle Scholar
Auléry, F., Dupuy, D., Toutant, A., Bataille, F. & Zhou, Y. 2017 Spectral analysis of turbulence in anisothermal channel flows. Comput. Fluids 151, 115–131.CrossRefGoogle Scholar
Auléry, F., Toutant, A., Bataille, F. & Zhou, Y. 2015 Energy transfer process of anisothermal wall-bounded flows. Phys. Lett. A 379 (24–25), 1520–1526.CrossRefGoogle Scholar
Babinsky, H. & Harvey, J.K. 2011 Shock Wave–Boundary-Layer Interactions. Cambridge Aerospace Series, vol. 32. Cambridge University Press.CrossRefGoogle Scholar
Baidya, R., Scharnowski, S., Bross, M. & Kähler, C.J. 2020 Interactions between a shock and turbulent features in a Mach 2 compressible boundary layer. J.Fluid Mech. 893, A15.CrossRefGoogle 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 (8), 084403.CrossRefGoogle Scholar
Bernardini, M., Modesti, D., Salvadore, F. & Pirozzoli, S. 2021 STREAmS: a high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows. Comput. Phys. Commun. 263, 107906.CrossRefGoogle Scholar
Bernardini, M., Pirozzoli, S. & Grasso, F. 2011 The wall pressure signature of transonic shock/boundary layer interaction. J.Fluid Mech. 671, 288–312.CrossRefGoogle Scholar
Cho, M., Choi, H. & Hwang, Y. 2016 On the structure of pressure fluctuations of self-sustaining attached eddies. In APS Division of Fluid Dynamics Meeting Abstracts, pp. A33–003.Google Scholar
Cho, M., Hwang, Y. & Choi, H. 2018 Scale interactions and spectral energy transfer in turbulent channel flow. J.Fluid Mech. 854, 474–504.CrossRefGoogle Scholar
Clemens, N. & Narayanaswamy, V. 2014 Low-frequency unsteadiness of shock wave/turbulent boundary layer interactions. Annu. Rev. Fluid Mech. 46, 469–492.CrossRefGoogle Scholar
Délery, J., Marvin, J.G. & Reshotko, E. 1986 Shock-wave boundary layer interactions. Tech. Rep. Advisory Group for Aerospace Research and Development Neuilly-Sur-Seine (France).Google Scholar
Dolling, D.S. 2001 Fifty years of shock-wave/boundary-layer interaction research: what next? AIAA J. 39 (8), 1517–1531.CrossRefGoogle Scholar
Domaradzki, J.A., Liu, W., Härtel, C. & Kleiser, L. 1994 Energy transfer in numerically simulated wall-bounded turbulent flows. Phys. Fluids 6 (4), 1583–1599.CrossRefGoogle Scholar
Doohan, P., Willis, A.P. & Hwang, Y. 2021 Minimal multi-scale dynamics of near-wall turbulence. J.Fluid Mech. 913, A8.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martin, M.P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J.Fluid Mech. 672, 245–267.CrossRefGoogle 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.CrossRefGoogle Scholar
Dupont, P., Haddad, C., Ardissone, J.P. & Debieve, J.F. 2005 Space and time organisation of a shock wave/turbulent boundary layer interaction. Aerosp. Sci. Technol. 9 (7), 561–572.CrossRefGoogle Scholar
Dupont, P., Haddad, C. & Debieve, J.F. 2006 Space and time organization in a shock-induced separated boundary layer. J.Fluid Mech. 559, 255–277.CrossRefGoogle Scholar
Dupont, P., Piponniau, S. & Dussauge, J.P. 2019 Compressible mixing layer in shock-induced separation. J.Fluid Mech. 863, 620–643.CrossRefGoogle Scholar
Dupont, P., Piponniau, S., Sidorenko, A. & Debiève, J.F. 2008 Investigation by particle image velocimetry measurements of oblique shock reflection with separation. AIAA J. 46 (6), 1365–1370.CrossRefGoogle Scholar
Dupuy, D., Toutant, A. & Bataille, F. 2018 a Equations of energy exchanges in variable density turbulent flows. Phys. Lett. A 382 (5), 327–333.CrossRefGoogle Scholar
Dupuy, D., Toutant, A. & Bataille, F. 2018 b Turbulence kinetic energy exchanges in flows with highly variable fluid properties. J. Fluid Mech. 834, 5–54.CrossRefGoogle Scholar
Fang, J., Zheltovodov, A.A., Yao, Y., Moulinec, C. & Emerson, D. 2020 On the turbulence amplification in shock-wave/turbulent boundary layer interaction. J. Fluid Mech. 897, A32.CrossRefGoogle Scholar
Hamba, F. 2019 Inverse energy cascade and vortical structure in the near-wall region of turbulent channel flow. Phys. Rev. Fluids 4 (11), 114609.CrossRefGoogle 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.CrossRefGoogle Scholar
Helm, C., Martin, M.P. & Dupont, P. 2014 Characterization of the shear layer in a Mach 3 shock/turbulent boundary layer interaction. J. Phys.: Conf. Ser. 506, 012013.Google Scholar
Humble, R.A., Scarano, F. & Van Oudheusden, B.W. 2007 Particle image velocimetry measurements of a shock wave/turbulent boundary layer interaction. Exp. Fluids 43 (2), 173–183.CrossRefGoogle Scholar
Humble, R.A., Scarano, F. & Van Oudheusden, B.W. 2009 Unsteady aspects of an incident shock wave/turbulent boundary layer interaction. J. Fluid Mech. 635, 47–74.CrossRefGoogle Scholar
Hwang, Y. & Bengana, Y. 2016 Self-sustaining process of minimal attached eddies in turbulent channel flow. J. Fluid Mech. 795, 708–738.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010 Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105 (4), 044505.CrossRefGoogle ScholarPubMed
Jammalamadaka, A., Li, Z. & Jaberi, F. 2014 Numerical investigations of shock wave interactions with a supersonic turbulent boundary layer. Phys. Fluids 26 (5), 87–108.CrossRefGoogle Scholar
Jiang, G.S. & Shu, C.W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202–228.CrossRefGoogle Scholar
Jiménez, J. 2015 Direct detection of linearized bursts in turbulence. Phys. Fluids 27 (6), 065102.CrossRefGoogle Scholar
Kawata, T. & Tsukahara, T. 2021 Scale interactions in turbulent plane Couette flows in minimal domains. J. Fluid Mech. 911, A55.CrossRefGoogle Scholar
Kitsios, V., Sekimoto, A., Atkinson, C., Sillero, J.A., Borrell, G., Gungor, A.G., Jiménez, J. & Soria, J. 2017 Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation. J. Fluid Mech. 829, 392–419.CrossRefGoogle Scholar
Klein, M., Sadiki, A. & Janicka, J. 2003 A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys. 186 (2), 652–665.CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2015 Spectral analysis on Reynolds stress transport equation in high Re wall-bounded turbulence. In International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9).CrossRefGoogle Scholar
Lee, M. & Moser, R.D. 2019 Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number. J. Fluid Mech. 860, 886–938.CrossRefGoogle Scholar
Li, X.L., Fu, D.X., Ma, Y.W. & Liang, X. 2010 Direct numerical simulation of shock/turbulent boundary layer interaction in a supersonic compression ramp. Sci. China Phys. Mech. Astron. 53 (9), 1651–1658.CrossRefGoogle Scholar
Ligrani, P.M., McNabb, E.S., Collopy, H., Anderson, M. & Marko, S.M. 2020 Recent investigations of shock wave effects and interactions. Adv. Aerodyn. 2 (1), 4.CrossRefGoogle Scholar
Liu, S.H., Cheng, Z.Q., Jiang, Y., Lu, J.F., Zhang, M.P. & Zhang, S.H. 2022 Numerical simulation of a complex moving rigid body under the impingement of a shock wave in 3D. Adv. Aerodyn. 4 (1), 8.CrossRefGoogle Scholar
Loginov, M.S., Adams, N.A. & Zheltovdov, A.A. 2006 Large-eddy simulation of shock-wave/turbulent-boundary-layer interaction. J. Fluid Mech. 565, 135–169.CrossRefGoogle Scholar
Lumley, J.L. 1964 Spectral energy budget in wall turbulence. Phys. Fluids 7 (2), 190–196.CrossRefGoogle Scholar
Mizuno, Y. 2016 Spectra of energy transport in turbulent channel flows for moderate Reynolds numbers. J. Fluid Mech. 805, 171–187.CrossRefGoogle Scholar
Musker, A.J. 1979 Explicit expression for the smooth wall velocity distribution in a turbulent boundary layer. AIAA J. 17 (6), 655–657.CrossRefGoogle Scholar
Nichols, J.W., Larsson, J., Bernardini, M. & Pirozzoli, S. 2017 Stability and modal analysis of shock/boundary layer interactions. Theor. Comput. Fluid Dyn. 31 (1), 33–50.CrossRefGoogle 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
Pirozzoli, S. 2010 Generalized conservative approximations of split convective derivative operators. J. Comput. Phys. 229 (19), 7180–7190.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2011 a Direct numerical simulation database for impinging shock wave/turbulent boundary-layer interaction. AIAA J. 49 (6), 1307–1312.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2011 b Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech. 688, 120–168.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2010 Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation. J. Fluid Mech. 657, 361–393.CrossRefGoogle Scholar
Pirozzoli, S. & Colonius, T. 2013 Generalized characteristic relaxation boundary conditions for unsteady compressible flow simulations. J. Comput. Phys. 248, 109–126.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.CrossRefGoogle Scholar
Plotkin, K.J. 1975 Shock wave oscillation driven by turbulent boundary-layer fluctuations. AIAA J. 13 (8), 1036–1040.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows, 1st edn. Cambridge University Press.CrossRefGoogle Scholar
Priebe, S., Wu, M. & Martin, M.P. 2009 Direct numerical simulation of a reflected-shock-wave/turbulent-boundary-layer interaction. AIAA J. 47 (5), 1173–1185.CrossRefGoogle Scholar
Rose, W.C. & Childs, M.E. 1974 Reynolds-shear-stress measurements in a compressible boundary layer within a shock-wave-induced adverse pressure gradient. J. Fluid Mech. 65 (1), 177–188.CrossRefGoogle Scholar
Saric, W.S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26 (1), 379–409.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.CrossRefGoogle Scholar
Selig, M.S., Andreopoulos, J., Muck, K.C., Dussauge, J.P. & Smits, A.J. 1989 Turbulence structure in a shock wave/turbulent boundary-layer interaction. AIAA J. 27 (7), 862–869.CrossRefGoogle Scholar
Smits, A.J. & Muck, K.C. 1987 Experimental study of three shock wave/turbulent boundary layer interactions. J. Fluid Mech. 182, 291–314.CrossRefGoogle Scholar
Tong, F.L., Yu, C.P., Tang, Z.G. & Li, X.L. 2017 Numerical studies of shock wave interactions with a supersonic turbulent boundary layer in compression corner: turning angle effects. Comput. Fluids 149, 56–69.CrossRefGoogle Scholar
Touber, E. & Sandham, N. 2009 Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble. Theor. Comput. Fluid Dyn. 23 (2), 79–107.CrossRefGoogle Scholar
Volpiani, P.S., Bernardini, M. & Larsson, J. 2018 Effects of a nonadiabatic wall on supersonic shock/boundary-layer interactions. Phys. Rev. Fluids 3 (8), 083401.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
Wang, X., Wang, Z., Sun, M., Wang, Q. & Hu, Z. 2019 b Direct numerical simulation of a supersonic turbulent boundary layer subject to adverse pressure gradient induced by external successive compression waves. AIP Adv. 9 (8), 085215.CrossRefGoogle Scholar
Wang, Q.C., Wang, Z.G., Sun, M.B., Yang, R., Zhao, Y.X. & Hu, Z. 2019 a The amplification of large-scale motion in a supersonic concave turbulent boundary layer and its impact on the mean and statistical properties. J. Fluid Mech. 863, 454–493.CrossRefGoogle Scholar
Wray, A.A. 1990 Minimal storage time advancement schemes for spectral methods. NASA Ames Research Center, California, Report No. MS Vol. 202.Google Scholar
Wu, X., Liang, J. & Zhao, Y. 2019 Direct numerical simulation of a supersonic turbulent boundary layer subjected to a concave surface. Phys. Rev. Fluids 4 (4), 044602.CrossRefGoogle 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
Yoon, M., Hwang, J. & Sung, H.J. 2018 Contribution of large-scale motions to the skin friction in a moderate adverse pressure gradient turbulent boundary layer. J. Fluid Mech. 848, 288–311.CrossRefGoogle Scholar
Yoon, M., Hwang, J., Yang, J. & Sung, H.J. 2020 Wall-attached structures of streamwise velocity fluctuations in an adverse-pressure-gradient turbulent boundary layer. J. Fluid Mech. 885, A12.CrossRefGoogle Scholar
Yu, M. & Xu, C.X. 2021 Compressibility effects on hypersonic turbulent channel flow with cold walls. Phys. Fluids 33 (7), 075106.CrossRefGoogle Scholar
Yu, M., Xu, C.X. & Pirozzoli, S. 2019 Genuine compressibility effects in wall-bounded turbulence. Phys. Rev. Fluids 4 (12), 123402.CrossRefGoogle Scholar
Yu, M., Xu, C.X. & Pirozzoli, S. 2020 Compressibility effects on pressure fluctuation in compressible turbulent channel flows. Phys. Rev. Fluids 5 (11), 113401.CrossRefGoogle Scholar
Zhang, Y.S., Bi, W.T., Hussain, F. & She, Z.S. 2014 A generalized Reynolds analogy for compressible wall-bounded turbulent flows. J. Fluid Mech. 739, 392–420.CrossRefGoogle Scholar
Zheltovodov, A.A., Lebiga, V.A. & Yakovlev, V.N. 1989 Measurement of turbulence characteristics in compressible boundary layers near separation zones. J. Appl. Mech. Tech. Phys. 30 (3), 442–447.CrossRefGoogle Scholar
Zhuang, Y., Tan, H.J., Li, X., Sheng, F.J. & Zhang, Y.C. 2018 Görtler-like vortices in an impinging shock wave/turbulent boundary layer interaction flow. Phys. Fluids 30 (6), 061702.CrossRefGoogle Scholar
Zuo, F.Y., Memmolo, A., Huang, G.P. & Pirozzoli, S. 2019 Direct numerical simulation of conical shock wave–turbulent boundary layer interaction. J. Fluid Mech. 877, 167–195.CrossRefGoogle Scholar