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Uncertainty quantification in rarefied dynamics of molecular gas: rate effect of thermal relaxation

Published online by Cambridge University Press:  04 May 2021

Qi Li ,
Jianan Zeng ,
Wei Su  and
Lei Wu Open the ORCID record for Lei Wu [Opens in a new window]
Qi Li
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Jianan Zeng
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Wei Su
Affiliation:
School of Engineering, University of Edinburgh, EdinburghEH9 3FB, UK
Lei Wu*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen518055, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The thermal conductivity of a molecular gas consists of the translational and internal parts. Although in continuum flows the total thermal conductivity itself is adequate to describe the heat transfer, in rarefied gas flows they need to be modelled separately, according to the relaxation rates of translational and internal heat fluxes in an homogeneous system. This paper is dedicated to quantifying how these relaxation rates affect rarefied gas dynamics. The kinetic model of Wu et al. (J. Fluid Mech., vol. 763, 2015, pp. 24–50) is adapted to recover the relaxation of heat fluxes, which is validated by the direct simulation Monte Carlo method. Then the model of Wu et al., which has the freedom to adjust the relaxation rates, is used to investigate the rate effects of thermal relaxation in problems such as the normal shock wave, creep flow driven by Maxwell's demon and thermal transpiration. It is found that the relaxation rates of heat flux affect rarefied gas flows significantly, even when the total thermal conductivity is fixed.

JFM classification

Rarefied Gas Flow: Rarefied Gas Flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 917 , 25 June 2021 , A58
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Bird, G.A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford University Press Inc., Oxford Science Publications.Google Scholar
Borgnakke, C. & Larsen, P. 1975 Statistical collision model for Monte Carlo simulation of polyatomic gas mixture. J. Comput. Phys. 18 (4), 405–420.CrossRefGoogle Scholar
Boyd, I.D. 1991 Rotational-translational energy transfer in rarefied nonequilibrium flows. Phys. Fluids A 2, 447–452.CrossRefGoogle Scholar
Candler, G.V. 2018 Rate effects in hypersonic flows. Annu. Rev. Fluid Mech. 51, 379–402.CrossRefGoogle Scholar
Chapman, S. & Cowling, T.G. 1970 The Mathematical Theory of Non-uniform Gases. Cambridge University Press.Google Scholar
Eucken, A. 1913 Über das Wärmeleitvermögen, die spezifische Wärme und die innere Reibung der Gase. Phys. Z 14, 324–332.Google Scholar
Frezzotti, A. & Ytrehus, T. 2006 Kinetic theory study of steady condensation of a polyatomic gas. Phys. Fluids 18, 027101.CrossRefGoogle Scholar
Gimelshein, N.E., Gimelshein, S.F. & Lavin, D.A. 2002 Vibrational relaxation rates in the direct simulation Monte Carlo method. Phys. Fluids 14, 4452–4455.CrossRefGoogle Scholar
Gorji, M.H. & Jenny, P. 2013 A Fokker–Planck based kinetic model for diatomic rarefied gas flows. Phys. Fluids 25, 062002.CrossRefGoogle Scholar
Gupta, A.D. & Storvick, T.S. 1970 Analysis of the heat conductivity data for polar and nonpolar gases using thermal transpiration measurements. J. Chem. Phys. 52 (2), 742–749.CrossRefGoogle Scholar
Haas, B.L., Hash, D.B., Bird, G.A., Lumpkin III, F.E. & Hassan, H.A. 1994 Rates of thermal relaxation in direct simulation Monte Carlo methods. Phys. Fluids 6, 2191–2201.CrossRefGoogle Scholar
Hanson, F.B. & Morse, T.F. 1967 Kinetic models for a gas with internal structure. Phys. Fluids 10, 345–353.CrossRefGoogle Scholar
Holway, L.H. 1966 New statistical models for kinetic theory: methods of construction. Phys. Fluids 9, 1658–1673.CrossRefGoogle Scholar
Kolluru, P.K., Atif, M. & Ansumali, S. 2020 Extended BGK model for diatomic gases. J. Comput. Sci. 45, 101179.CrossRefGoogle Scholar
Kosuge, S. & Aoki, K. 2018 Shock-wave structure for a polyatomic gas with large bulk viscosity. Phys. Rev. Fluids 3, 023401.CrossRefGoogle Scholar
Mason, E.A. 1963 Molecular relaxation times from thermal transpiration measurements. J. Chem. Phys. 39, 522–526.CrossRefGoogle Scholar
Mason, E.A. & Monchick, L. 1962 Heat conductivity of polyatomic and polar gases. J. Chem. Phys. 36, 1622–1639.CrossRefGoogle Scholar
McCormack, F.J. 1968 Kinetic equations for polyatomic gases: the 17-moment approximation. Phys. Fluids 11, 2533–2543.CrossRefGoogle Scholar
Morse, T.F. 1964 Kinetic model for gases with internal degrees of freedom. Phys. Fluids 7, 159–169.CrossRefGoogle Scholar
Porodnov, B.T., Kulev, A.N. & Tuchvetov, F.T. 1978 Thermal transpiration in a circular capillary with a small temperature difference. J. Fluid Mech. 88 (4), 609–622.CrossRefGoogle Scholar
Rykov, V. 1975 A model kinetic equation for a gas with rotational degrees of freedom. Fluid Dyn. 10, 959–966.CrossRefGoogle Scholar
Su, W., Zhang, Y.H. & Wu, L. 2021 Multiscale simulation of molecular gas flows by the general synthetic iterative scheme. Comput. Meth. Appl. Mech. Engng 373, 113548.CrossRefGoogle Scholar
Su, W., Zhu, L.H. & Wu, L. 2020 Fast convergence and asymptotic preserving of the general synthetic iterative scheme. SIAM J. Sci. Comput. 42, B1517–B1540.CrossRefGoogle Scholar
Taniguchi, S., Arima, T., Ruggeri, T. & Sugiyama, M. 2014 Thermodynamic theory of the shock wave structure in a rarefied polyatomic gas: beyond the Bethe–Teller theory. Phys. Rev. E 89, 013025.CrossRefGoogle Scholar
Tcheremissine, F.G. & Agarwal, R.K. 2009 Computations of hypersonic shock waves in diatomic gases using the generalized Boltzmann equation. In 26th International Symposium on Rarefied Gas Dynamics, Kyoto, Japan, 21–25 July (ed. Takashi Abe). American Institute of Physics.CrossRefGoogle Scholar
Vargo, S.E., Muntz, E.P., Shiflett, G.R. & Tang, W.C. 1999 Knudsen compressor as a micro-and macroscale vacuum pump without moving parts or fluids. J. Vac. Sci. Technol. A 17, 2308–2313.CrossRefGoogle Scholar
Wagner, W. 1992 A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation. J. Stat. Phys. 66, 1011–1044.CrossRefGoogle Scholar
Wang-Chang, C.S. & Uhlenbeck, G.E. 1951 Transport Phenomena in Polyatomic Gases, Rept. No. CM-681. University of Michigan Engineering Research.Google Scholar
Wu, L., Li, Q., Liu, H. & Ubachs, W. 2020 Extraction of the translational Eucken factor from light scattering by molecular gas. J. Fluid Mech. 901, A23.CrossRefGoogle Scholar
Wu, L., Reese, J.M. & Zhang, Y.H. 2014 Solving the Boltzmann equation by the fast spectral method: application to microflows. J. Fluid Mech. 746, 53–84.CrossRefGoogle Scholar
Wu, L., White, C., Scanlon, T.J., Reese, J.M. & Zhang, Y.H. 2013 Deterministic numerical solutions of the Boltzmann equation using the fast spectral method. J. Comput. Phys. 250, 27–52.CrossRefGoogle Scholar
Wu, L., White, C., Scanlon, T.J., Reese, J.M. & Zhang, Y.H. 2015 A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases. J. Fluid Mech. 763, 24–50.CrossRefGoogle Scholar