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Effect of wall temperature on the kinetic energy transfer in a hypersonic turbulent boundary layer

Published online by Cambridge University Press:  27 October 2021

Dehao Xu Open the ORCID record for Dehao Xu [Opens in a new window] ,
Jianchun Wang Open the ORCID record for Jianchun Wang [Opens in a new window] ,
Minping Wan ,
Changping Yu Open the ORCID record for Changping Yu [Opens in a new window] ,
Xinliang Li  and
Shiyi Chen
Dehao Xu
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China
Jianchun Wang*
Affiliation:
Guangdong Provincial Key Laboratory of Fundamental Turbulence Research and Applications, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
Minping Wan
Affiliation:
Guangdong Provincial Key Laboratory of Fundamental Turbulence Research and Applications, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
Changping Yu
Affiliation:
Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Xinliang Li
Affiliation:
Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Shiyi Chen*
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China Guangdong Provincial Key Laboratory of Fundamental Turbulence Research and Applications, Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

The effect of wall temperature on the transfer of kinetic energy in a hypersonic turbulent boundary layer for different Mach numbers and wall temperature ratios is studied by direct numerical simulation. A cold wall temperature can enhance the compressibility effect in the near-wall region through increasing the temperature gradient and wall heat flux. It is shown that the cold wall temperature enhances the local reverse transfer of kinetic energy from small scales to large scales, and suppresses the local direct transfer of kinetic energy from large scales to small scales. The average filtered spatial convection and average filtered viscous dissipation are dominant in the near-wall region, while the average subgrid-scale flux of kinetic energy achieves its peak value in the buffer layer. It is found that the wall can suppress the inter-scale transfer of kinetic energy, especially for the situation of a cold wall. A strong local reverse transfer of fluctuating kinetic energy is identified in the buffer layer in the inertial range. Helmholtz decomposition is applied to analyse the compressibility effect on the subgrid-scale flux of kinetic energy. A strong transfer of the solenoidal component of fluctuating kinetic energy is identified in the buffer layer, while a significant transfer of the dilatational component of fluctuating kinetic energy is observed in the near-wall region. It is also shown that compression motions have a major contribution to the direct transfer of fluctuating kinetic energy, while expansion motions play a marked role in the reverse transfer of fluctuating kinetic energy.

JFM classification

Compressible Flows: Compressible boundary layers Compressible Flows: Hypersonic Flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 929 , 25 December 2021 , A33
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alizard, F., Pirozzoli, S., Bernardini, M. & Grasso, F. 2015 Optimal transient growth in compressible turbulent boundary layers. J. Fluid Mech. 770, 124–155.CrossRefGoogle Scholar
Aluie, H. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106, 174502.CrossRefGoogle ScholarPubMed
Aluie, H. 2013 Scale decomposition in compressible turbulence. Phys. D 247, 2013.CrossRefGoogle Scholar
Aluie, H. & Eyink, G.L. 2009 Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter. Phys. Fluids 21, 115108.CrossRefGoogle Scholar
Aluie, H., Li, S. & Li, H. 2012 Conservative cascade of kinetic energy in compressible turbulence. Astrophys. J. Lett. 751, L29.CrossRefGoogle Scholar
Anderson, J.D. 2006 Hypersonic and High-Temperature Gas Dynamics. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Balsara, D.S. & Shu, C. 2000 Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comput. Phys. 160, 405–452.CrossRefGoogle Scholar
Bradshaw, P. 1977 Compressible turbulent shear layers. Annu. Rev. Fluid Mech. 9, 33–54.CrossRefGoogle Scholar
Cebeci, T. & Smith, A.M.O. 1974 Analysis of Turbulent Boundary Layers. Academic.Google Scholar
Cerutti, S. & Meneveau, C. 1998 Intermittency and relative scaling of subgrid-scale energy dissipation in isotropic turbulence. Phys. Fluids 10, 928–937.CrossRefGoogle Scholar
Chen, S., Wang, J., Li, H., Wan, M. & Chen, S. 2018 Spectra and Mach number scaling in compressible homogeneous shear turbulence. Phys. Fluids 30, 065109.CrossRefGoogle Scholar
Chen, S., Wang, J., Li, H., Wan, M. & Chen, S. 2019 a Effect of compressibility on small scale statistics in homogeneous shear turbulence. Phys. Fluids 31, 025107.Google Scholar
Chen, S., Wang, X., Wang, J., Li, H., Wan, M. & Chen, S. 2019 b Effects of bulk viscosity on compressible homogeneous turbulence. Phys. Fluids 31, 085115.Google Scholar
Chen, L., Xu, C. & Lu, X. 2010 Numerical investigation of the compressible flow past an aerofoil. J. Fluid Mech. 643, 97–126.CrossRefGoogle Scholar
Chu, Y. & Lu, X. 2013 Topological evolution in compressible turbulent boundary layers. J. Fluid Mech. 733, 414–438.CrossRefGoogle Scholar
Chu, Y., Zhuang, Y. & Lu, X. 2013 Effect of wall temperature on hypersonic turbulent boundary layer. J. Turbul. 14, 37–57.CrossRefGoogle Scholar
Domaradzki, J.A., Liu, W. & Brachet, M.E. 1993 An analysis of subgrid-scale interactions in numerically simulated isotropic turbulence. Phys. Fluids A: Fluid Dyn. 5, 1747–1759.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
Erm, L.P. & Joubert, P.N. 1991 Low-Reynolds-number turbulent boundary layers. J. Fluid Mech. 230, 1–44.CrossRefGoogle Scholar
Eyink, G.L. 2005 Locality of turbulent cascades. Phys. D: Nonlinear Phenom. 207, 91–116.CrossRefGoogle Scholar
Eyink, G.L. & Aluie, H. 2009 Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining. Phys. Fluids 21, 115107.CrossRefGoogle Scholar
Gatski, T.B. & Bonnet, J.P. 2009 Compressibility, Turbulence and High Speed Flow. Elsevier.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.CrossRefGoogle Scholar
Hamman, C.W., Klewicki, J.C. & Kirby, R.M. 2008 On the lamb vector divergence in Navier–Stokes flows. J. Fluid Mech. 610, 261–284.CrossRefGoogle Scholar
Hirasaki, G. & Hellums, J. 1970 Boundary conditions on the vector and scalar potentials in viscous three-dimensional hydrodynamics. Q. Appl. Maths 28, 293–296.CrossRefGoogle Scholar
Howe, M.S. 1975 Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute. J. Fluid Mech. 71, 625–673.CrossRefGoogle Scholar
Jagannathan, S. & Donzis, D.A. 2016 Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations. J. Fluid Mech. 789, 669–707.CrossRefGoogle Scholar
Josyula, E. 2015 Hypersonic Nonequilibrium Flows: Fundamentals and Recent Advances. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Kerr, R.M., Domaradzki, J.A. & Barbier, G. 1996 Small-scale properties of nonlinear interactions and subgrid-scale energy transfer in isotropic turbulence. Phys. Fluids 8, 197–208.CrossRefGoogle Scholar
Lagha, M., Kim, J., Eldredge, J.D. & Zhong, X. 2011 A numerical study of compressible turbulent boundary layers. Phys. Fluids 23, 015106.CrossRefGoogle Scholar
Li, Q. & Coleman, G.N. 2012 DNS of an Oblique Shock Wave Impinging upon a Turbulent Boundary Layer. Springer.Google Scholar
Li, X., Fu, D. & Ma, Y. 2008 Direct numerical simulation of hypersonic boundary layer transition over a blunt cone. AIAA J. 46, 2899–2913.CrossRefGoogle Scholar
Li, X., Tong, F., Yu, C. & Li, X. 2019 Statistical analysis of temperature distribution on vortex surfaces in hypersonic turbulent boundary layer. Phys. Fluids 31, 106101.Google Scholar
Liang, X. & Li, X. 2013 DNS of a spatially evolving hypersonic turbulent boundary layer at Mach 8. Sci. China Phys. Mech. Astron. 56, 1408–1418.CrossRefGoogle 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.CrossRefGoogle Scholar
Lighthill, M.J. 1952 On sound generated aerodynamically. Part I. General theory. Proc. R. Soc. Lond. A 211, 564–587.Google 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.CrossRefGoogle Scholar
Marco, A., Camussi, R., Bernardini, M. & Pirozzoli, S. 2013 Wall pressure coherence in supersonic turbulent boundary layers. J. Fluid Mech. 732, 445–456.CrossRefGoogle 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. & Hussaini, M.Y. 2000 Subgrid-scale models for compressible large-eddy simulations. Theor. Comput. Fluid Dyn. 13, 361–376.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
Modesti, D. & Pirozzoli, S. 2016 Reynolds and mach number effects in compressible turbulent channel flow. Intl J. Heat Fluid Flow 59, 33–49.CrossRefGoogle Scholar
Piomelii, U., Cabot, W.H., Moin, P. & Lee, S. 1991 Subgrid-scale backscatter in turbulent and transitional flows. Phys. Fluids A 3, 1766–1771.CrossRefGoogle Scholar
Pirozzoli, S. 2012 On the size of the energy-containing eddies in the outer turbulent wall layer. J. Fluid Mech. 702, 521–532.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., Bernardini, M. & Grasso, F. 2008 Characterization of coherent vortical structures in a supersonic turbulent boundary layer. J. Fluid Mech. 613, 205–231.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2010 On the dynamical relevance of coherent vortical structures in turbulent boundary layers. J. Fluid Mech. 648, 325–349.CrossRefGoogle 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.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Ringuette, M., 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.CrossRefGoogle Scholar
She, Z., Zou, H., Xiao, M., Chen, X. & Hussain, F. 2018 Prediction of compressible turbulent boundary layer via a symmetry-based length model. J. Fluid Mech. 857, 449–468.CrossRefGoogle Scholar
Simens, M.P., Jiménez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228, 4218–4231.CrossRefGoogle Scholar
Smits, A.J. & Dussauge, J.P. 2006 Turbulent Shear Layers in Supersonic Flow. Springer.Google Scholar
Teng, J., Wang, J., Li, H. & Chen, S. 2020 Spectra and scaling in chemically reacting compressible isotropic turbulence. Phys. Rev. Fluids 5, 084601.CrossRefGoogle Scholar
Teng, J., Wang, J., Li, H. & Chen, S. 2021 Inter-scale kinetic energy transfer in chemically reacting compressible isotropic turbulence. J. Fluid Mech. 912, A36.CrossRefGoogle Scholar
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28, 026102.CrossRefGoogle Scholar
Van Driest, E.R. 1951 Turbulent boundary layer in compressible fluids. J. Aeronaut. Sci. 18 (3), 145–160.CrossRefGoogle Scholar
Volpiani, P., Iyer, P., Pirozzoli, S. & Larsson, J. 2020 Data-driven compressibility transformation for turbulent wall layers. Phys. Rev. Fluids 5, 052602(R).CrossRefGoogle Scholar
Wang, J., Shi, Y., Wang, L., Xiao, Z., He, X. & Chen, S. 2012 a Effect of compressibility on the small-scale structures in isotropic turbulence. J. Fluid Mech. 713, 588–631.CrossRefGoogle Scholar
Wang, J., Shi, Y., Wang, L., Xiao, Z., He, X. & Chen, S. 2012 b Scaling and statistics in three-dimensional compressible turbulence. Phys. Rev. Lett. 108, 214505.CrossRefGoogle ScholarPubMed
Wang, J., Wan, M., Chen, S. & Chen, S. 2018 Kinetic energy transfer in compressible isotropic turbulence. J. Fluid Mech. 841, 581–613.CrossRefGoogle Scholar
Wang, J., Wan, M., Chen, S., Xie, C., Zheng, Q., Wang, L. & Chen, S. 2020 Effect of flow topology on the kinetic energy flux in compressible isotropic turbulence. J. Fluid Mech. 883, A11.CrossRefGoogle Scholar
Wang, J., Yang, Y., Shi, Y., Xiao, Z., He, X. & Chen, S. 2013 Cascade of kinetic energy in three-dimensional compressible turbulence. Phys. Rev. Lett. 110, 214505.CrossRefGoogle ScholarPubMed
Wang, L. & Lu, X. 2012 Flow topology in compressible turbulent boundary layer. J. Fluid Mech. 703, 255–278.CrossRefGoogle Scholar
White, F.M. 2006 Viscous Fluid Flow, 3rd edn. McGraw-Hill.Google Scholar
Xu, D., Wang, J., Wan, W., Yu, C., Li, X. & Chen, S. 2021 Compressibility effect in hypersonic boundary layer with isothermal wall condition. Phys. Rev. Fluids 6, 054609.CrossRefGoogle Scholar
Yu, M. & Xu, C. 2021 Compressibility effects on hypersonic turbulent channel flow with cold walls. Phys. Fluids 33, 075106.CrossRefGoogle Scholar
Yu, M., Xu, C. & Pirozzoli, S. 2019 Genuine compressibility effects in wall-bounded turbulence. Phys. Rev. Fluids 4, 123402.CrossRefGoogle Scholar
Zhang, C., Duan, L. & Choudhari, M. 2018 Direct numerical simulation database for supersonic and hypersonic turbulent boundary layers. AIAA J. 56, 4297–4311.CrossRefGoogle Scholar
Zhang, Y., Bi, W., Hussain, F., Li, X. & She, Z. 2012 Mach-number-invariant mean-velocity profile of compressible turbulent boundary layers. Phys. Rev. Lett. 109, 054502.CrossRefGoogle ScholarPubMed
Zhang, Y., Bi, W., Hussain, F. & She, Z. 2014 A generalized Reynolds analogy for compressible wall-bounded turbulent flows. J. Fluid Mech. 739, 392–420.CrossRefGoogle Scholar
Zheng, W., Ruan, S., Yang, Y., He, L. & Chen, S. 2019 Image-based modelling of the skin-friction coefficient in compressible boundary-layer transition. J. Fluid Mech. 875, 1175–1203.CrossRefGoogle Scholar
Zheng, Q., Wang, J., Noack, B.R., Li, H., Wan, M. & Chen, S. 2020 Vibrational relaxation in compressible isotropic turbulence with thermal non-equilibrium. Phys. Rev. Fluids 5, 044602.CrossRefGoogle Scholar
Zheng, Q., Wang, J., Noack, B.R., Mahbub, A., Li, H. & Chen, S. 2021 Transfer of internal energy fluctuation in compressible isotropic turbulence with vibrational nonequilibrium. J. Fluid Mech. 919, A26.CrossRefGoogle Scholar