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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, Shenzhen518055, PR China School of Power and Mechanical Engineering, Wuhan University, Wuhan430072, 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, Shenzhen518055, PR China
Md. Mahbub Alam
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology, Shenzhen518055, PR China
Bernd R. Noack
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology, Shenzhen518055, PR China Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin, Müller-Breslau-Straße 8, D-10623Berlin, Germany
Hui Li
Affiliation:
School of Power and Mechanical Engineering, Wuhan University, Wuhan430072, 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, Shenzhen518055, PR China State Key Laboratory of Turbulence and Complex Systems, Peking University, Beijing100871, 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
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , A26
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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