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Sub-filter-scale shear stress analysis in hypersonic turbulent Couette flow

Published online by Cambridge University Press:  08 April 2024

Takahiko Toki Open the ORCID record for Takahiko Toki [Opens in a new window] ,
Victor C.B. Sousa Open the ORCID record for Victor C.B. Sousa [Opens in a new window] ,
Yongkai Chen Open the ORCID record for Yongkai Chen [Opens in a new window]  and
Carlo Scalo Open the ORCID record for Carlo Scalo [Opens in a new window]
Takahiko Toki*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906, USA
Victor C.B. Sousa
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906, USA
Yongkai Chen
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906, USA
Carlo Scalo
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906, USA School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906, USA
*
†Email address for correspondence: ttoki@purdue.edu
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Abstract

Direct numerical simulations of hypersonic turbulent Couette flows are performed for top-wall Mach numbers of 6, 7 and 8, inspired by non-reactive high-enthalpy wind tunnel free-stream conditions, with the goal of analysing the physical processes driving the sub-filter-scale (SFS) stresses to inform development of large-eddy simulation techniques for hypersonic wall-bounded flows. Semi-local scaling laws collapse mean profiles and second-order turbulent statistics well, in spite of the strong wall-normal gradients of temperature and density. On the other hand, the SFS shear stresses exhibit an unexpected profile characterized by a region of pronounced shear stress deficit, which becomes more pronounced for higher Mach numbers. Instantaneous visualizations suggest that the SFS shear stress deficit is induced by the counter-gradient resolved momentum transport driven by residual velocity motions at the interface between high-density low-speed streaks being ejected away from the wall, and low-density high-speed ones replacing the displaced fluid, qualifying this as a compressibility effect. It is shown that the SFS shear stresses are primarily driven by second-order interactions between residual velocities, in spite of their triply nonlinear nature. This, in turn, motivated a statistical quadrant analysis revealing the presence of a SFS shear stress deficit, that is, SFS processes driving momentum transport of the resolved field towards the top wall. Additionally, higher-Reynolds-number simulations reveal that there is an upper limit of spatial filter widths to resolve large-scale structures, and such deficit is observable at any Reynolds number when a reasonable spatial filter is applied.

JFM classification

Compressible Flows: Hypersonic Flow Compressible Flows: Compressible boundary layers Turbulent Flows: Compressible turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 984 , 10 April 2024 , A53
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Bai, T., Griffin, K.P. & Fu, L. 2022 Compressible velocity transformations for various noncanonical wall-bounded turbulent flows. AIAA J. 60, 4325–4337.CrossRefGoogle Scholar
Bardina, J., Ferziger, J.H. & Reynolds, W.C. 1980 Improved subgrid scale models for large-eddy simulation. AIAA Paper 80-1357.CrossRefGoogle Scholar
Bhagwandin, V. & Martin, M.P. 2021 LES of shock-turbulent boundary layer interaction over a mach 10 hollow cylinder with flare. AIAA Aviation 2021 Forum, AIAA Paper 2021-2820.Google Scholar
Boerner, T.J., Deems, S., Furlani, T.R., Knuth, S.L. & Towns, J. 2023 ACCESS: advancing innovation: NSF's advanced cyberinfrastructure coordination ecosystem: services & support. Practice and Experience in Advanced Research Computing (PEARC ’23).CrossRefGoogle Scholar
Bose, S.T., Moin, P. & You, D. 2010 Grid-independent large-eddy simulation using explicit filtering. Phys. Fluids 22, 105103.CrossRefGoogle Scholar
Camillo, G.P., Wagner, A., Toki, T. & Scalo, C. 2023 Combined experimental and numerical investigation of a hypersonic turbulent boundary layer by means of FLDI and large-eddy simulations. Aerospace 10, 570.10.3390/aerospace10060570CrossRefGoogle Scholar
Chapelier, J.-B. & Lodato, G. 2016 A spectral-element dynamic model for the large-eddy simulation of turbulent flows. J. Comput. Phys. 321, 279–302.CrossRefGoogle Scholar
Chen, P.E.S., Lv, Y., Xu, H.H.A., Shi, Y. & Yang, X.I.A. 2022 LES wall modeling for heat transfer at high speeds. Phys. Rev. Fluids 7, 014608.CrossRefGoogle Scholar
Chen, Y. & Scalo, C. 2021 a Effects of porous walls on near-wall supersonic turbulence. Phys. Rev. Fluids 6, 084607.CrossRefGoogle Scholar
Chen, Y. & Scalo, C. 2021 b Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls. J. Fluid Mech. 920, A24.CrossRefGoogle Scholar
Clark, R.A., Ferziger, J.H. & Reynolds, W.C. 1979 Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91 (1), 1–16.CrossRefGoogle Scholar
Comte-Bellot, G. & Corrsin, S. 1971 Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence. J. Fluid Mech. 48, 273–337.CrossRefGoogle Scholar
Danis, M.E. & Durbin, P. 2022 Compressibility correction to $k-\omega$ models for hypersonic turbulent boundary layers. AIAA J. 60 (11), 6225–6234.CrossRefGoogle 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.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
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.CrossRefGoogle Scholar
Franko, K.J. & Lele, S.K. 2013 Breakdown mechanisms and heat transfer overshoot in hypersonic zero pressure gradient boundary layers. J. Fluid Mech. 730, 491–532.10.1017/jfm.2013.350CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W.H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765.CrossRefGoogle Scholar
Gottlieb, S. 2005 On high order strong stability preserving Runge–Kutta and multi step time discretizations. J. Sci. Comput. 25, 105–128.Google Scholar
Gupta, P. & Scalo, C. 2018 Spectral energy cascade and decay in nonlinear acoustic waves. Phys. Rev. E 98, 033117.CrossRefGoogle Scholar
Helm, C.M. 2021 Direct and large-eddy simulation and analysis of shock separated flows. PhD thesis, University of Maryland, College Park.Google Scholar
Helm, C.M. & Martin, M.P. 2022 Large eddy simulation of two separated hypersonic shock/turbulent boundary layer interactions. Phys. Rev. Fluids 7, 074601.10.1103/PhysRevFluids.7.074601CrossRefGoogle Scholar
Hendrickson, T., Subbareddy, P.K. & Candler, G.V. 2022 Improving eddy viscosity based turbulence models for high speed, cold wall flows. AIAA Scitech 2022 Forum, AIAA Paper 2022-0589.Google Scholar
Hirai, R., Pecnik, R. & Kawai, S. 2021 Effects of the semi-local Reynolds number in scaling turbulent statistics for wall heated/cooled supersonic turbulent boundary layers. Phys. Rev. Fluids 6, 124603.CrossRefGoogle Scholar
Huang, J., Duan, L. & Choudhari, M.M. 2022 Direct numerical simulation of hypersonic turbulent boundary layers: effect of spatial evolution and Reynolds number. J. Fluid Mech. 937, A3.CrossRefGoogle 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
Kawai, S. 2019 Heated transcritical and unheated non-transcritical turbulent boundary layers at supercritical pressures. J. Fluid Mech. 865, 563–601.10.1017/jfm.2019.13CrossRefGoogle Scholar
Kim, K., Hickey, J.-P. & Scalo, C. 2019 Pseudophase change effects in turbulent channel flow under transcritical temperature conditions. J. Fluid Mech. 871, 52–91.10.1017/jfm.2019.292CrossRefGoogle Scholar
Knight, D., Zhou, G., Okong'o, N. & Shukla, V. 1998 Compressible large eddy simulation using unstructured grids. AIAA Paper 98-0535.CrossRefGoogle Scholar
Kolmogorov, A.N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13 (01), 82–85.CrossRefGoogle Scholar
Kraichnan, R.H. 1976 Eddy viscosity in two and three dimensions. J. Atmos. Sci. 33 (8), 1521–1536.2.0.CO;2>CrossRefGoogle Scholar
Lee, J., Jung, S.Y., Sung, H.J. & Zaki, T.A. 2013 Effect of wall heating on turbulent boundary layers with temperature-dependent viscosity. J. Fluid Mech. 726, 196–225.CrossRefGoogle Scholar
Lele, S.K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.CrossRefGoogle 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
Liu, C.-H. 2003 Turbulent plane Couette flow and scalar transport at low Reynolds number. Trans. ASME J. Heat Transfer 125, 988–998.10.1115/1.1571084CrossRefGoogle Scholar
Loginov, M.S., Adams, N.A. & Zheltovodov, A.A. 2006 Large-eddy simulation of shock-wave/ turbulent-boundary-layer interaction. J. Fluid Mech. 565, 135–169.CrossRefGoogle Scholar
Ma, P.C., Yang, X.I.A. & Ihme, M. 2018 Structure of wall-bounded flows at transcritical conditions. Phys. Rev. Fluids 3, 034609.10.1103/PhysRevFluids.3.034609CrossRefGoogle Scholar
Martin, M.P. 2007 Direct numerical simulation of hypersonic turbulent boundary layers. Part 1. Initialization and comparison with experiments. J. Fluid Mech. 570, 347–364.CrossRefGoogle Scholar
Martin, M.P., Piomelli, U. & Candler, G.V. 2000 Subgrid-scale models for compressible large-eddy simulations. Theor. Comput. Fluid Dyn. 13, 361–376.CrossRefGoogle Scholar
McDaniel, D.R., Nichols, R.H., Eymann, T.A., Starr, R.E. & Morton, S.A. 2016 Accuracy and performance improvements to Kestrel's near-body flow solver. AIAA Aviation 2021 Forum, AIAA Paper 2016-1051.Google Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.CrossRefGoogle Scholar
Meneveau, C., Lund, T.S. & Cabot, W.H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385.CrossRefGoogle Scholar
Moin, P., Squires, K., Cabot, W. & Les, S. 1991 A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3, 2746–2757.10.1063/1.858164CrossRefGoogle Scholar
Nagarajan, S., Lele, S.K. & Ferziger, J.H. 2003 A robust high-order compact method for large eddy simulation. J. Comput. Phys. 191, 392–419.CrossRefGoogle Scholar
Nagarajan, S., Lele, S.K. & Ferziger, J.H. 2007 Leading-edge effects in bypass transition. J. Fluid Mech. 572, 471–504.CrossRefGoogle Scholar
Nichols, R.H. 2019 A summary of the turbulence models in the CREATETM-AV Kestrel flow solvers. AIAA Scitech 2019 Forum, AIAA Paper 2019-1342.Google Scholar
Patel, A., Boersma, B.J. & Pecnik, R. 2016 The influence of near-wall density and viscosity gradients on turbulence in channel flows. J. Fluid Mech. 809, 793–820.CrossRefGoogle Scholar
Piomelli, U., Moin, P. & Ferziger, J.H. 1988 Model consistency in large eddy simulation of turbulent channel flows. Phys. Fluids 31, 1884–1891.10.1063/1.866635CrossRefGoogle Scholar
Piomelli, U., Rouhi, A. & Geurts, B.J. 2015 A grid-independent length scale for large-eddy simulations. J. Fluid Mech. 766, 499–527.10.1017/jfm.2015.29CrossRefGoogle Scholar
Piomelli, U. & Zang, T.A. 1991 Large-eddy simulation of transitional channel flow. Comput. Phys. Commun. 65, 224–230.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds numbers. J. Fluid Mech. 688, 120–168.CrossRefGoogle Scholar
Roys, C.J. & Blottner, F.G. 2006 Review and assessment of turbulence models for hypersonic flows. Prog. Aerosp. Sci. 42, 469–530.Google Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Sousa, V.C.B., Patel, D., Chapelier, J.-B., Wartemann, V., Wagner, A. & Scalo, C. 2019 Numerical investigation of second-mode attenuation over carbon/carbon porous surfaces. J. Spacecr. Rockets 56 (2), 319–332.CrossRefGoogle Scholar
Sousa, V.C.B. & Scalo, C. 2022 a A legendre spectral viscosity (LSV) method applied to shock capturing for high-order flux reconstruction schemes. J. Comput. Phys. 460, 111157.CrossRefGoogle Scholar
Sousa, V.C.B. & Scalo, C. 2022 b A unified quasi-spectral viscosity (QSV) approach to shock capturing and large-eddy simulation. J. Comput. Phys. 459, 111139.CrossRefGoogle Scholar
Speziale, C.G., Erlebacher, G., Zang, T.A. & Hussaini, M.Y. 1988 The subgrid-scale modeling of compressible turbulence. Phys. Fluids 31, 940–942.CrossRefGoogle Scholar
Stolz, S. & Adams, N.A. 1999 An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11 (7), 1699–1701.CrossRefGoogle Scholar
Stolz, S., Adams, N.A. & Kleiser, L. 2001 a An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows. Phys. fluids 13 (4), 997–1015.CrossRefGoogle Scholar
Stolz, S., Adams, N.A. & Kleiser, L. 2001 b The approximate deconvolution model for large-eddy simulations of compressible flows and its application to shock-turbulent-boundary-layer interaction. Phys. Fluids 13, 2985–3001.CrossRefGoogle Scholar
Toki, T. & Bellan, J. 2021 Investigation of species-mass diffusion in binary-species boundary layers at high pressure using direct numerical simulations. J. Fluid Mech. 928, A18.CrossRefGoogle Scholar
Toki, T. & Bellan, J. 2022 Effects of thermophoresis on high pressure binary-species boundary layers with uniform and non-uniform compositions. J. Fluid Mech. 952, A37.CrossRefGoogle Scholar
Toki, T., Teramoto, S. & Okamoto, K. 2020 Velocity and temperature profiles in turbulent channel flow at supercritical pressure. J. Propul. Power 36, 3–13.CrossRefGoogle Scholar
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28, 026102.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1995 a A priori tests of large eddy simulation of the compressible plane mixing layer. J. Engng Math. 29, 299–327.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1995 b Subgrid-modelling in LES of compressible flow. Appl. Sci. Res. 54, 191–203.CrossRefGoogle Scholar
Wadhams, T., Holden, M. & Maclean, M. 2014 Comparisons of experimental and computational results from ‘blind’ turbulent shock wave interaction study over cone flare and hollow cylinder flare configurations. 14th AIAA Aviation Technology, Integration and Operations Conference.Google Scholar
Wallace, J.M. 2016 Quadrant analysis in turbulence research: history and evolution. Annu. Rev. Fluid Mech. 48, 131–158.CrossRefGoogle Scholar
Wallace, J.M., Eckelmann, H. & Brodkey, R.S. 1972 The wall region in turbulent shear flow. J. Fluid Mech. 54, 39–48.10.1017/S0022112072000515CrossRefGoogle Scholar
Wang, J., Wan, M., Chen, S. & Chen, S. 2018 Kinetic energy transfer in compressible isotropic turbulence. J. Fluid Mech. 841, 581–613.CrossRefGoogle Scholar
Wilcox, D.C. 2006 Turbulence Modeling for CFD, 3rd edn. DCW Industries.Google Scholar
Xu, D., Wang, J. & Chen, S. 2022 Skin-friction and heat-transfer decompositions in hypersonic transitional and turbulent boundary layers. J. Fluid Mech. 941, A4.10.1017/jfm.2022.269CrossRefGoogle Scholar
Xu, D., Wang, J., Wan, M., Yu, C., Li, X. & Chen, S. 2021 a Compressibility effect in hypersonic boundary layer with isothermal wall condition. Phys. Rev. Fluids 6, 054609.10.1103/PhysRevFluids.6.054609CrossRefGoogle Scholar
Xu, D., Wang, J., Wan, M., Yu, C., Li, X. & Chen, S. 2021 b Effect of wall temperature on the kinetic energy transfer in a hypersonic turbulent boundary layer. J. Fluid Mech. 929, A33.CrossRefGoogle Scholar
Yao, J. & Hussain, F. 2023 Study of compressible turbulent plane couette flows via direct numerical simulation. J. Fluid Mech. 964, A29.CrossRefGoogle Scholar
Yerragolam, G.S., Stevens, R.J.A.M., Verzicco, R., Lohse, D. & Shishkina, O. 2022 Passive scalar transport in Couette flow. J. Fluid Mech. 943, A17.CrossRefGoogle Scholar
Yoshizawa, A. 1986 Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29, 2152–2164.CrossRefGoogle Scholar
Zhang, C., Duan, L. & Choudhari, M.M. 2018 Direct numerical simulation database for supersonic and hypersonic turbulent boundary layers. AIAA J. 56 (11), 4297–4311.10.2514/1.J057296CrossRefGoogle Scholar
Zonta, F., Marchioli, C. & Soldati, A. 2012 Modulation of turbulence in forced convection by temperature-dependent viscosity. J. Fluid Mech. 697, 150–174.CrossRefGoogle Scholar