Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-10T20:37:56.889Z Has data issue: false hasContentIssue false
  • English
  • Français

Skin-friction and heat-transfer decompositions in hypersonic transitional and turbulent boundary layers

Published online by Cambridge University Press:  25 April 2022

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]  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:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
Shiyi Chen*
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China 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]
Get access Rights & Permissions [Opens in a new window]

Abstract

The decompositions of the skin-friction and heat-transfer coefficients based on the twofold repeated integration in hypersonic transitional and turbulent boundary layers are analysed to give some major reasons of the overshoot phenomena of the wall skin friction and heat transfer. It is shown that the overshoot of the skin-friction coefficient is mainly caused by the drastic change of the mean velocity profiles, especially the strong negative streamwise gradient of the mean streamwise velocity far from the wall; and the overshoot of the heat-transfer coefficient is primarily due to the viscous dissipation, especially the strong positive vertical gradient of the mean streamwise velocity near the wall. These observations are different from the previous observations that the Reynolds shear stress and Reynolds heat flux are the reasons, respectively. Further investigations show that the above observations are independent of the set-up of the wall blowing and suction parameters, which indicates the universality of the major reasons of the overshoot phenomena in our numerical simulations. In the hypersonic turbulent boundary layers, it is observed that the strongly cooled wall temperature and the high Mach number can slightly enhance the contribution of the Reynolds shear stress, and weaken the contribution of the mean convection, mainly due to the strong compressibility effect. Moreover, the magnitudes of the relative contributions of the mean convection, pressure dilatation, viscous dissipation and the Reynolds heat flux increase as the wall temperature increases.

JFM classification

Compressible Flows: Compressible boundary layers Compressible Flows: Hypersonic Flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 941 , 25 June 2022 , A4
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

REFERENCES

Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.CrossRefGoogle Scholar
Arntz, A., Atinault, O. & Merlen, A. 2015 Exergy-based formulation for aircraft aeropropulsive performance assessment: theoretical development. AIAA J. 53, 1627–1639.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
Brandt, L. & Henningson, D.S. 2002 Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech. 472, 229–261.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
Fan, Y., Li, W. & Pirozzoli, S. 2019 Decomposition of the mean friction drag in zero-pressure-gradient turbulent boundary layers. Phys. Fluids 31, 086105.Google Scholar
Franko, K.J., Bhaskaran, R. & Lele, S.K. 2011 Direct numerical simulation of transition and heat-transfer overshoot in a Mach 6 flat plate boundary layer. In 41st AIAA Fluid Dynamics Conference and Exhibit, pp. 2011–3874. AIAA.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.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14, L73–L76.CrossRefGoogle Scholar
Ghosh, S., Foysi, H. & Friedrich, R. 2010 Compressible turbulent channel and pipe flow: similarities and differences. J. Fluid Mech. 648, 155–181.CrossRefGoogle 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, 035301(R).CrossRefGoogle Scholar
Horvath, T.J., Berry, S.A. & Hollis, B.R. 2002 Boundary layer transition on slender cones in conventional and low disturbance Mach 6 wind tunnels. AIAA Paper 2002-2743.CrossRefGoogle Scholar
Hunt, J.C.R., Wray, A.A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Studying Turbulence Using Numerical Simulation Databases, 2, pp. 193–208. Center for Turbulence Research, Ames Research Center.Google 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, 101–123.CrossRefGoogle 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
Mayer, C.S.J., Von Terzi, D.A. & Fasel, H.F. 2011 Direct numerical simulation of complete transition to turbulence via oblique breakdown at Mach 3. J. Fluid Mech. 674, 5–42.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, 1656.CrossRefGoogle Scholar
Mehdi, F. & White, C.M. 2011 Integral form of the skin friction coefficient suitable for experimental data. Exp. Fluids 50, 43–51.CrossRefGoogle Scholar
Peeters, J.W.R. & Sandham, N.D. 2019 Turbulent heat transfer in channels with irregular roughness. Intl J. Heat Mass Transfer 138, 454–467.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
Rai, M.M., Gatski, T.B. & Erlebacher, G. 1995 Direct simulation of spatially evolving compressible turbulent boundary layers. AIAA Paper 95-0583.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, 339–367.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
Shu, C.-W. & Osher, S. 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (2), 439–471.CrossRefGoogle Scholar
Sun, D., Guo, Q., Yuan, X., Zhang, H., Li, C. & Liu, P. 2021 A decomposition formula for the wall heat flux of a compressible boundary layer. Adv. Aerodyn. 3, 33.CrossRefGoogle Scholar
Wadhams, T.P., Mundy, E., Maclean, M.G. & Holden, M.S. 2008 Ground test studies of the HIFiRE-1 transition experiment part 1: experimental results. J. Spacecr. Rockets 45, 1134–1148.CrossRefGoogle Scholar
Wang, L. & Lu, X. 2012 Flow topology in compressible turbulent boundary layer. J. Fluid Mech. 703, 255–278.CrossRefGoogle Scholar
Wenzel, C., Gibis, T. & Kloker, M. 2021 a About the influences of compressibility, heat transfer, and pressure gradients in compressible turbulent boundary layers. J. Fluid Mech. 930, A1.CrossRefGoogle Scholar
Wenzel, C., Gibis, T., Kloker, M. & Rist, U. 2021 b Reynolds analogy factor in self-similar compressible turbulent boundary layers with pressure gradients. J. Fluid Mech. 907, R4.CrossRefGoogle Scholar
Xia, Z., Zhang, P. & Yang, X.I.A. 2021 On skin friction in wall-bounded turbulence. Acta Mech. Sin. 37, 589–598.CrossRefGoogle 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.CrossRefGoogle 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
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
Zhang, P., Song, Y. & Xia, Z. 2022 Exact mathematical formulas for wall-heat flux in compressible turbulent channel flows. Acta Mech. Sin. 38, 1–10.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, 043107.CrossRefGoogle ScholarPubMed