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Transfer of internal energy fluctuation in compressible isotropic turbulence with vibrational non-equilibrium

Published online by Cambridge University Press:  27 May 2021

Qinmin Zheng Open the ORCID record for Qinmin Zheng [Opens in a new window] ,
Jianchun Wang Open the ORCID record for Jianchun Wang [Opens in a new window] ,
Md. Mahbub Alam Open the ORCID record for Md. Mahbub Alam [Opens in a new window] ,
Bernd R. Noack Open the ORCID record for Bernd R. Noack [Opens in a new window] ,
Hui Li  and
Shiyi Chen
Qinmin Zheng
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 School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, 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
Md. Mahbub Alam
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology, Shenzhen 518055, PR China
Bernd R. Noack
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology, Shenzhen 518055, PR China Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, Müller-Breslau-Straße 8, D-10623 Berlin, Germany
Hui Li
Affiliation:
School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, PR China
Shiyi Chen
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 State Key Laboratory of Turbulence and Complex Systems, Peking University, Beijing 100871, PR China
*
†Email address for correspondence: wangjc@sustech.edu.cn
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Abstract

The transfer of internal energy fluctuation is numerically investigated for the stationary compressible isotropic turbulence in vibrational non-equilibrium with large-scale thermal forcing. We observe the spectra of velocity, solenoidal pressure component, density and temperatures all exhibiting the $k^{-5/3}$ scaling in the inertial range. The Helmholtz decomposition results reveal that the solenoidal velocity component predominates over the dilatational component. Fluctuations of the solenoidal velocity and pressure components are nearly insensitive to the turbulent Mach number and vibrational relaxation, while those of the dilatational velocity and pressure components are closely related to them. In addition, the weak and strong acoustic equilibrium hypotheses are verified. On global average, the dissipation of translational–rotational energy fluctuation stems mainly from the thermal conduction and vibrational relaxation, while effects of the dilatation and viscosity are negligible. For the vibrational energy fluctuation, the dilatation effect is insignificant, while the dissipation due to the thermal conduction is roughly equivalent to the production owing to the vibrational relaxation. The cascades of translational–rotational and vibrational energy fluctuations are mainly dominated by the solenoidal component of filtered velocity. The direct subgrid-scale (SGS) fluxes of translational–rotational and vibrational energy fluctuations due to the dilatational component of filtered velocity in the compression region are balanced by the reverse SGS fluxes in the expansion region. On the other hand, the dependencies of the SGS fluxes due to the solenoidal component of filtered velocity on the local compressibility are closely related to the relaxation effect. The sensibility gradually disappears as the relaxation effect weakens.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Homogeneous turbulence

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JFM Papers
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Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A26
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© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alexakis, A. & Biferale, L. 2018 Cascades and transitions in turbulent flows. Phys. Rep. 767, 1–101.CrossRefGoogle Scholar
Aluie, H. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106 (17), 174502.CrossRefGoogle ScholarPubMed
Aluie, H. 2013 Scale decomposition in compressible turbulence. Physica D 247 (1), 54–65.CrossRefGoogle Scholar
Aluie, H., Li, S. & Li, H. 2012 Conservative cascade of kinetic energy in compressible turbulence. Astrophys. J. Lett. 751 (2), L29.CrossRefGoogle Scholar
Anderson, J.D. Jr. 2006 Hypersonic and High-Temperature Gas Dynamics. American Institute of Aeronautics and Astronautics.CrossRefGoogle Scholar
Balsara, D.S. & Shu, C.-W. 2000 Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comput. Phys. 160 (2), 405–452.CrossRefGoogle Scholar
Bertolotti, F.P. 1998 The influence of rotational and vibrational energy relaxation on boundary-layer stability. J. Fluid Mech. 372, 93–118.CrossRefGoogle Scholar
Bose, T.K. 2014 High temperature gas dynamics. In High Temperature Gas Dynamics. Springer.CrossRefGoogle Scholar
Candler, G.V. 2019 Rate effects in hypersonic flows. Annu. Rev. Fluid Mech. 51 (1), 379–402.CrossRefGoogle Scholar
Cardy, J., Falkovich, G. & Gawedzki, K. 2008 Nonequilibrium Statistical Mechanics and Turbulence, vol. 355. Cambridge University Press.CrossRefGoogle Scholar
Colonna, G., Bonelli, F. & Pascazio, G. 2019 Impact of fundamental molecular kinetics on macroscopic properties of high-enthalpy flows: the case of hypersonic atmospheric entry. Phys. Rev. Fluids 4 (3), 033404.CrossRefGoogle Scholar
Dobler, W., Haugen, N.E.L., Yousef, T.A. & Brandenburg, A. 2003 Bottleneck effect in three-dimensional turbulence simulations. Phys. Rev. E 68 (2), 026304.CrossRefGoogle ScholarPubMed
Donzis, D. & Jagannathan, S. 2013 Fluctuations of thermodynamic variables in stationary compressible turbulence. J. Fluid Mech. 733, 221–244.CrossRefGoogle Scholar
Donzis, D.A. 2012 Shock structure in shock-turbulence interactions. Phys. Fluids 24 (12), 126101.CrossRefGoogle Scholar
Donzis, D.A. & John, J.P. 2020 Universality and scaling in homogeneous compressible turbulence. Phys. Rev. Fluids 5 (8), 084609.CrossRefGoogle Scholar
Donzis, D.A. & Maqui, A.F. 2016 Statistically steady states of forced isotropic turbulence in thermal equilibrium and non-equilibrium. J. Fluid Mech. 797, 181–200.CrossRefGoogle Scholar
Donzis, D.A. & Sreenivasan, K.R. 2010 The bottleneck effect and the kolmogorov constant in isotropic turbulence. J. Fluid Mech. 657, 171–188.CrossRefGoogle Scholar
Eyink, G.L. & Drivas, T.D. 2018 Cascades and dissipative anomalies in compressible fluid turbulence. Phys. Rev. X 8 (1), 011022.Google Scholar
Fiévet, R. & Raman, V. 2018 Effect of vibrational nonequilibrium on isolator shock structure. J. Propul. Power 34 (5), 1334–1344.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Gotoh, T. & Fukayama, D. 2001 Pressure spectrum in homogeneous turbulence. Phys. Rev. Lett. 86 (17), 3775–3778.CrossRefGoogle ScholarPubMed
Gotoh, T. & Rogallo, R.S. 1999 Intermittency and scaling of pressure at small scales in forced isotropic turbulence. J. Fluid Mech. 396, 257–285.CrossRefGoogle Scholar
Gottlieb, S. & Shu, C.-W. 1998 Total variation diminishing Runge–Kutta schemes. Maths Comput. 67 (221), 73–85.CrossRefGoogle Scholar
Hirschfelder, J.O., Curtiss, C.F., Bird, R.B. & Mayer, M.G. 1964 Molecular Theory of Gases and Liquids, vol. 165. Wiley.Google Scholar
Jagannathan, S. & Donzis, D. 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
Khurshid, S. & Donzis, D.A. 2019 Decaying compressible turbulence with thermal non-equilibrium. Phys. Fluids 31 (1), 015103.CrossRefGoogle Scholar
Knisely, C.P. & Zhong, X. 2020 Impact of vibrational nonequilibrium on the supersonic mode in hypersonic boundary layers. AIAA J. 58 (4), 1704–1714.CrossRefGoogle Scholar
Kolmogorov, A.N. 1991 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Proc. R. Soc. Lond. A 434 (1890), 9–13.Google Scholar
Lele, S.K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.CrossRefGoogle Scholar
Li, D., Zhang, X. & He, G. 2013 Temporal decorrelations in compressible isotropic turbulence. Phys. Rev. E 88 (2), 021001.CrossRefGoogle ScholarPubMed
Liao, W., Peng, Y. & Luo, L.-S. 2010 Effects of multitemperature nonequilibrium on compressible homogeneous turbulence. Phys. Rev. E 81 (4), 046704.CrossRefGoogle ScholarPubMed
Martin, M.P., Piomelli, U. & Candler, G.V. 2000 Subgrid-scale models for compressible large-eddy simulations. Theor. Comput. Fluid Dyn. 13 (5), 361–376.Google Scholar
Meldi, M. & Sagaut, P. 2013 Pressure statistics in self-similar freely decaying isotropic turbulence. J. Fluid Mech. 717, R2.CrossRefGoogle Scholar
Ni, Q. 2015 Compressible turbulent mixing: effects of schmidt number. Phys. Rev. E 91, 053020.CrossRefGoogle ScholarPubMed
Nompelis, I., Candler, G.V. & Holden, M.S. 2003 Effect of vibrational nonequilibrium on hypersonic double-cone experiments. AIAA J. 41 (11), 2162–2169.CrossRefGoogle Scholar
Pan, S. & Johnsen, E. 2017 The role of bulk viscosity on the decay of compressible, homogeneous, isotropic turbulence. J. Fluid Mech. 833, 717–744.CrossRefGoogle Scholar
Passot, T., Vázquez-Semadeni, E. & Pouquet, A. 1995 A turbulent model for the interstellar medium. II. Magnetic fields and rotation. Astrophys. J. 455, 536–555.CrossRefGoogle Scholar
Rich, J.W. & Treanor, C.E. 1970 Vibrational relaxation in gas-dynamic flows. Annu. Rev. Fluid Mech. 2 (1), 355–396.CrossRefGoogle Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Springer.CrossRefGoogle Scholar
Samtaney, R., Pullin, D.I. & Kosović, B. 2001 Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids 13 (5), 1415–1430.CrossRefGoogle Scholar
Schmidt, W. & Grete, P. 2019 Kinetic and internal energy transfer in implicit large-eddy simulations of forced compressible turbulence. Phys. Rev. E 100 (4), 043116.CrossRefGoogle ScholarPubMed
Sciacovelli, L., Cinnella, P. & Grasso, F. 2017 Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence. J. Fluid Mech. 825, 515–549.CrossRefGoogle Scholar
Shi, L., Shen, H., Zhang, P., Zhang, D. & Wen, C. 2017 Assessment of vibrational non-equilibrium effect on detonation cell size. Combust. Sci. Technol. 189 (5), 841–853.CrossRefGoogle Scholar
Tsuji, Y. & Ishihara, T. 2003 Similarity scaling of pressure fluctuation in turbulence. Phys. Rev. E 68 (2), 026309.CrossRefGoogle ScholarPubMed
Urzay, J. 2018 Supersonic combustion in air-breathing propulsion systems for hypersonic flight. Annu. Rev. Fluid Mech. 50, 593–627.CrossRefGoogle Scholar
Vedula, P. & Yeung, P.K. 1999 Similarity scaling of acceleration and pressure statistics in numerical simulations of isotropic turbulence. Phys. Fluids 11 (5), 1208–1220.CrossRefGoogle Scholar
Vincenti, W.G. & Kruger, C.H. 1965 Introduction to Physical Gas Dynamics. Wiley.Google Scholar
Wang, J., Gotoh, T. & Watanabe, T. 2017 Spectra and statistics in compressible isotropic turbulence. Phys. Rev. Fluids 2 (1), 013403.CrossRefGoogle Scholar
Wang, J., Shi, Y., Wang, L.-P., Xiao, Z., He, X. & Chen, S. 2011 Effect of shocklets on the velocity gradients in highly compressible isotropic turbulence. Phys. Fluids 23 (12), 125103.CrossRefGoogle 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
Wang, J., Wan, M., Chen, S., Xie, C., Wang, L.-P. & Chen, S. 2019 Cascades of temperature and entropy fluctuations in compressible turbulence. J. Fluid Mech. 867, 195–215.CrossRefGoogle Scholar
Wang, J., Wang, L.-P., Xiao, Z., Shi, Y. & Chen, S. 2010 A hybrid numerical simulation of isotropic compressible turbulence. J. Comput. Phys. 229 (13), 5257–5279.CrossRefGoogle Scholar
Zheng, Q., Wang, J., Noack, B.R., Li, H., Wan, M. & Chen, S. 2020 Vibrational relaxation in compressible isotropic turbulence with thermal nonequilibrium. Phys. Rev. Fluids 5, 044602.CrossRefGoogle Scholar