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Conditional analysis on extreme wall shear stress and heat flux events in compressible turbulent boundary layers

Published online by Cambridge University Press:  03 November 2023

Peng-Jun-Yi Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Zhen-Hua Wan*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Si-Wei Dong
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, PR China
Nan-Sheng Liu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
De-Jun Sun*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
*
Email addresses for correspondence: wanzh@ustc.edu.cn, dsun@ustc.edu.cn
Email addresses for correspondence: wanzh@ustc.edu.cn, dsun@ustc.edu.cn

Abstract

This study presents a comprehensive analysis on the extreme positive and negative events of wall shear stress and heat flux fluctuations in compressible turbulent boundary layers (TBLs) solved by direct numerical simulations. To examine the compressibility effects, we focus on the extreme events in two representative cases, i.e. a supersonic TBL of Mach number $M=2$ and a hypersonic TBL of $M=8$, by scrutinizing the coherent structures and their correlated dynamics based on conditional analysis. As characterized by the spatial distribution of wall shear stress and heat flux, the extreme events are indicated to be closely related to the structural organization of wall streaks, in addition to the occurrence of the alternating positive and negative structures (APNSs) in the hypersonic TBL. These two types of coherent structures are strikingly different, namely the nature of wall streaks and APNSs are shown to be related to the solenoidal and dilatational fluid motions, respectively. Quantitative analysis using a volumetric conditional average is performed to identify and extract the coherent structures that directly account for the extreme events. It is found that in the supersonic TBL, the essential ingredients of the conditional field are hairpin-like vortices, whose combinations can induce wall streaks, whereas in the hypersonic TBL, the essential ingredients become hairpin-like vortices as well as near-wall APNSs. To quantify the momentum and energy transport mechanisms underlying the extreme events, we proposed a novel decomposition method for extreme skin friction and heat flux, based on the integral identities of conditionally averaged governing equations. Taking advantage of this decomposition method, the dominant transport mechanisms of the hairpin-like vortices and APNSs are revealed. Specifically, the momentum and energy transports undertaken by the hairpin-like vortices are attributed to multiple comparable mechanisms, whereas those by the APNSs are convection dominated. In that, the dominant transport mechanisms in extreme events between the supersonic and hypersonic TBLs are indicated to be totally different.

Type
JFM Papers
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Adams, N.A. 1998 Direct numerical simulation of turbulent compression ramp flow. Theor. Comput. Fluid Dyn. 12 (2), 109129.10.1007/s001620050102CrossRefGoogle Scholar
Bannier, A., Garnier, É. & Sagaut, P. 2015 Riblet flow model based on an extended fik identity. Flow Turbul. Combust. 95 (2), 351376.10.1007/s10494-015-9624-2CrossRefGoogle 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, 107906.10.1016/j.cpc.2021.107906CrossRefGoogle Scholar
Blonigan, P.J., Farazmand, M. & Sapsis, T.P. 2019 Are extreme dissipation events predictable in turbulent fluid flows? Phys. Rev. Fluids 4 (4), 044606.10.1103/PhysRevFluids.4.044606CrossRefGoogle Scholar
Cardesa, J.I., Monty, J.P., Soria, J. & Chong, M.S. 2019 The structure and dynamics of backflow in turbulent channels. J. Fluid Mech. 880, R3.10.1017/jfm.2019.774CrossRefGoogle Scholar
Chi, S.W. & Spalding, D.B. 1966 Influence of temperature ratio on heat transfer to a flat plate through a turbulent boundary layer in air. In International Heat Transfer Conference Digital Library. Begel House, 41–49.Google Scholar
Coleman, G.N., Kim, J. & Moser, R.D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159183.10.1017/S0022112095004587CrossRefGoogle Scholar
Deck, S., Renard, N., Laraufie, R. & Weiss, P. 2014 Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to 13 650. J. Fluid Mech. 743, 202248.CrossRefGoogle Scholar
Drela, M. 2009 Power balance in aerodynamic flows. AIAA J. 47 (7), 17611771.CrossRefGoogle Scholar
Duan, L., Beekman, I. & Martín, M.P. 2010 Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech. 655, 419445.CrossRefGoogle Scholar
Farazmand, M. & Sapsis, T.P. 2017 A variational approach to probing extreme events in turbulent dynamical systems. Sci. Adv. 3 (9), e1701533.10.1126/sciadv.1701533CrossRefGoogle ScholarPubMed
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73L76.10.1063/1.1516779CrossRefGoogle Scholar
Gomez, T., Flutet, V. & Sagaut, P. 2009 Contribution of Reynolds stress distribution to the skin friction in compressible turbulent channel flows. Phys. Rev. E 79 (3), 035301.10.1103/PhysRevE.79.035301CrossRefGoogle Scholar
Gomit, G., de Kat, R. & Ganapathisubramani, B. 2018 Structure of high and low shear-stress events in a turbulent boundary layer. Phys. Rev. Fluids 3 (1), 014609.10.1103/PhysRevFluids.3.014609CrossRefGoogle Scholar
Guerrero, B., Lambert, M.F. & Chin, R.C. 2020 Extreme wall shear stress events in turbulent pipe flows: spatial characteristics of coherent motions. J. Fluid Mech. 904, A18.10.1017/jfm.2020.689CrossRefGoogle Scholar
Hirasaki, G.J. & Hellums, J.D. 1970 Boundary conditions on the vector and scalar potentials in viscous three-dimensional hydrodynamics. Q. Appl. Maths 28 (2), 293296.10.1090/qam/99793CrossRefGoogle 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), 9931003.10.2514/3.6323CrossRefGoogle Scholar
Hu, S. & Zhong, X. 1998 Linear stability of viscous supersonic plane Couette flow. Phys. Fluids 10 (3), 709729.10.1063/1.869596CrossRefGoogle 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, A3.10.1017/jfm.2022.80CrossRefGoogle Scholar
Huang, P.G., Coleman, G.N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185218.10.1017/S0022112095004599CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Proc. R. Soc. Lond. A 365 (1852), 647664.Google ScholarPubMed
Hutchins, N., Monty, J.P., Ganapathisubramani, B., Ng, H.C. & Marusic, I. 2011 Three-dimensional conditional structure of a high-Reynolds-number turbulent boundary layer. J. Fluid Mech. 673, 255285.10.1017/S0022112010006245CrossRefGoogle Scholar
Iwamoto, K., Fukagata, K., Kasagi, N. & Suzuki, Y. 2005 Friction drag reduction achievable by near-wall turbulence manipulation at high Reynolds numbers. Phys. Fluids 17 (1), 011702011702.CrossRefGoogle Scholar
Jiang, G.-S. & Shu, C.-W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202228.CrossRefGoogle Scholar
Jiménez, J., Hoyas, S., Simens, M. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335360.CrossRefGoogle Scholar
Kametani, Y. & Fukagata, K. 2011 Direct numerical simulation of spatially developing turbulent boundary layers with uniform blowing or suction. J. Fluid Mech. 681, 154172.CrossRefGoogle Scholar
Kametani, Y., Fukagata, K., Örlü, R. & Schlatter, P. 2015 Effect of uniform blowing/suction in a turbulent boundary layer at moderate Reynolds number. Intl J. Heat Fluid Flow 55, 132142.CrossRefGoogle Scholar
Lenaers, P., Li, Q., Brethouwer, G., Schlatter, P. & Örlü, R. 2012 Rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence. Phys. Fluids 24 (3), 035110.CrossRefGoogle Scholar
Li, W., Fan, Y., Modesti, D. & Cheng, C. 2019 Decomposition of the mean skin-friction drag in compressible turbulent channel flows. J. Fluid Mech. 875, 101123.CrossRefGoogle Scholar
Marley, C.D. & Riggins, D.W. 2011 Numerical study of novel drag reduction techniques for hypersonic blunt bodies. AIAA J. 49 (9), 18711882.CrossRefGoogle Scholar
Mehdi, F., Johansson, T.G., White, C.M. & Naughton, J.W. 2014 On determining wall shear stress in spatially developing two-dimensional wall-bounded flows. Exp. Fluids 55 (1), 19.CrossRefGoogle Scholar
Modesti, D., Pirozzoli, S., Orlandi, P. & Grasso, F. 2018 On the role of secondary motions in turbulent square duct flow. J. Fluid Mech. 847, R1.CrossRefGoogle Scholar
Morkovin, M.V. 1962 Effects of compressibility on turbulent flows. Méc. Turbul. 367 (380), 26.Google Scholar
Nagib, H.M., Chauhan, K.A. & Monkewitz, P.A. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Proc. R. Soc. Lond. A 365 (1852), 755770.Google Scholar
Pan, C. & Kwon, Y. 2018 Extremely high wall-shear stress events in a turbulent boundary layer. J. Phys.: Conf. Ser. 1001, 012004.Google Scholar
Peet, Y. & Sagaut, P. 2009 Theoretical prediction of turbulent skin friction on geometrically complex surfaces. Phys. Fluids 21 (10), 105105.CrossRefGoogle Scholar
Pirozzoli, S. 2010 Generalized conservative approximations of split convective derivative operators. J. Comput. Phys. 229 (19), 71807190.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech. 688, 120168.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2013 Probing high-Reynolds-number effects in numerical boundary layers. Phys. Fluids 25 (2), 021704.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, 361393.CrossRefGoogle Scholar
Poinsot, T.J. & Lele, S.K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101 (1), 104129.CrossRefGoogle Scholar
Renard, N. & Deck, S. 2016 A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer. J. Fluid Mech. 790, 339367.CrossRefGoogle Scholar
Roy, C.J. & Blottner, F.G. 2006 Review and assessment of turbulence models for hypersonic flows. Prog. Aerosp. Sci. 42 (7–8), 469530.CrossRefGoogle Scholar
Rumsey, C.L. 2010 Compressibility considerations for $k$-$\omega$ turbulence models in hypersonic boundary-layer applications. J. Spacecr. Rockets 47 (1), 1120.CrossRefGoogle Scholar
Sheng, J., Malkief, E. & Katz, J. 2009 Buffer layer structures associated with extreme wall stress events in a smooth wall turbulent boundary layer. J. Fluid Mech. 633, 1760.CrossRefGoogle Scholar
Spalart, P.R., Moser, R.D. & Rogers, M.M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96 (2), 297324.CrossRefGoogle Scholar
Spina, E.F., Smits, A.J. & Robinson, S.K. 1994 The physics of supersonic turbulent boundary layers. Annu. Rev. Fluid Mech. 26 (1), 287319.CrossRefGoogle Scholar
Stroh, A., Hasegawa, Y., Schlatter, P. & Frohnapfel, B. 2016 Global effect of local skin friction drag reduction in spatially developing turbulent boundary layer. J. Fluid Mech. 805, 303321.CrossRefGoogle Scholar
Subbareddy, P. & Candler, G. 2011 DNS of transition to turbulence in a hypersonic boundary layer. In 41st AIAA Fluid Dynamics Conference and Exhibit, AIAA paper, p. 3564.Google Scholar
Tang, J., Zhao, Z., Wan, Z.-H. & Liu, N.-S. 2020 On the near-wall structures and statistics of fluctuating pressure in compressible turbulent channel flows. Phys. Fluids 32 (11), 115121.CrossRefGoogle Scholar
Tong, F., Dong, S., Lai, J., Yuan, X. & Li, X. 2022 Wall shear stress and wall heat flux in a supersonic turbulent boundary layer. Phys. Fluids 34 (1), 015127.CrossRefGoogle Scholar
Van Driest, E.R. 1956 On turbulent flow near a wall. J. Aeronaut. Sci. 23 (11), 10071011.CrossRefGoogle Scholar
Wallace, J.M. 2016 Quadrant analysis in turbulence research: history and evolution. Annu. Rev. Fluid Mech. 48, 131158.CrossRefGoogle Scholar
Walz, A. 1969 Boundary Layers of Flow and Temperature. MIT Press.Google Scholar
Wenzel, C., Gibis, T. & Kloker, M. 2022 About the influences of compressibility, heat transfer and pressure gradients in compressible turbulent boundary layers. J. Fluid Mech. 930, A1.CrossRefGoogle 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.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
Yu, M., Liu, P., Fu, Y., Tang, Z. & Yuan, X. 2022 Wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence. Part 1. One-point statistics. Phys. Fluids 34 (6), 065139.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, C., Duan, L. & Choudhari, M.M. 2017 Effect of wall cooling on boundary-layer-induced pressure fluctuations at Mach 6. J. Fluid Mech. 822, 530.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), 42974311.CrossRefGoogle Scholar
Zhang, P., Song, Y. & Xia, Z. 2022 a Exact mathematical formulas for wall-heat flux in compressible turbulent channel flows. Acta Mechanica Sin. 38 (1), 110.Google Scholar
Zhang, P. & Xia, Z. 2020 Contribution of viscous stress work to wall heat flux in compressible turbulent channel flows. Phys. Rev. E 102 (4), 043107.CrossRefGoogle ScholarPubMed
Zhang, P.-J.-Y., Wan, Z.-H., Liu, N.-S., Sun, D.-J. & Lu, X.-Y. 2022 b Wall-cooling effects on pressure fluctuations in compressible turbulent boundary layers from subsonic to hypersonic regimes. J. Fluid Mech. 946, A14.CrossRefGoogle Scholar
Zhang, P.-J.-Y., Wan, Z.-H. & Sun, D.-J. 2019 Space-time correlations of velocity in a Mach 0.9 turbulent round jet. Phys. Fluids 31 (11), 115108.CrossRefGoogle Scholar
Zhang, S., Li, X., Zuo, J., Qin, J., Cheng, K., Feng, Y. & Bao, W. 2020 Research progress on active thermal protection for hypersonic vehicles. Prog. Aerosp. Sci. 119, 100646.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, 392420.CrossRefGoogle Scholar
Zhao, X. & He, G.-W. 2009 Space-time correlations of fluctuating velocities in turbulent shear flows. Phys. Rev. E 79 (4), 046316.CrossRefGoogle ScholarPubMed