Nonlinear phenomena in a rarefied gas in Couette problem

Fluid, gas and plasma mechanics


Аuthors

Vuong V. T.1*, Gorelov S. L.2**

1. Moscow Institute of Physics and Technology, 9, Institutskiy per., Dolgoprudny, Moscow region, 141701, Russia
2. Central Aerohydrodynamic Institute named after N.E. Zhukovsky, TsAGI, 1, Zhukovsky str., Zhukovsky, Moscow Region, 140180, Russia

*e-mail: tienbom@mail.ru
**e-mail: gorelovsl@yandex.ru

Abstract

Heat and momentum transfer processes in a rarefied gas enclosed between two infinite parallel plates with different temperatures and moving relative to each other are studied. The Direct Simulation Monte Carlo (DSMC) method was applied to calculate the distribution of density, velocity, temperature, heat fluxes and viscous stress tensor over a wide range of Knudsen numbers and at different values of plates’ temperatures and velocities. The obtained results were compared with the analytical results for the free-molecular case and for a wide range of the Knudsen numbers. Calculations of the heat flux and friction stress (tangential component of the viscous stress tensor) were performed by the self-similar interpolation method. It was established, that there is a normal component (which is not presented both in the free-molecular flow and in the case of a continuous flow) in the transition region between the free-molecular flow and continuous flow in addition to the tangential component of the viscous stress tensor. This effect was explained by the fact, that the gas density and temperature distributions in the transition region flow were not uniform. Moreover, both normal and tangential components have essentially non-monotonous behavior in the considered range of the Knudsen numbers. Maximum magnitude of the normal and tangential components depends on the plates’ velocity and their temperatures ratio. In addition, the heat flux to the hot wall depends on the Knudsen number and can change its’ sign at a certain temperature drop ratio and the plates velocity.

Keywords:

Couette problem, rarefied gas, moments of momentum and heat

References

  1. Kogan M.N. Dinamika razrezhennogo gaza (Rarefield Gas Dynamics), Moscow, Nauka, 1967, 440 p.

  2. Cercignani C. The Boltzmann Equation and Its Applications, Springer, New York/Berlin, 1988, 476 p.

  3. Yoshio Sone. Molecular Gas Dynamics: Theory, Techniques and Applications, Birkhäuser, 2007, 667 p.

  4. Gorelov S.L., Kogan M.N. Uchenye zapiski TsAGI, 1970, vol. 1, no. 6, pp. 126 – 130.

  5. Gorelov S.L., Vyong Van T’en. Matematicheskoe modelirovanie, 2014, vol. 26, no. 10, pp. 33 – 46.

  6. Vyong Van T’en, Gorelov S.L. Mekhanika zhidkosti i gaza, 2016, no. 6, pp. 101 – 107.

  7. Haviland J.K., Lavin M.L. Application of the Monte Carlo Method to Heat Transfer in a Rarefied Gas, Physics of Fluids, 1962, vol. 5, no. 11, pp. 1399 – 1405.

  8. Ivchenko I.N., Loyalka S.K., Tompson R.N. Analytical methods for problems of molecular transport, Springer, 2007, 409 p.

  9. Abramov A.A., Butkovskii A.V. Mekhanika zhidkosti i gaza, 2010, no. 1, pp. 168 – 175.

  10. Abramov A.A., Butkovskii A.V. Teplofizika vysokikh temperatur, 2010, vol. 48, no. 2, pp. 274 – 278.

  11. Chernyak V.G., Polikarpov A.F. Zhurnal eksperimental’noi i tekhnicheskoi fiziki, 2010, vol. 137, no. 1, pp. 165 – 176.

  12. Shlikhting G. Teoriya pogranichnogo sloya (Boundary-Layer Theory), Moscow, Nauka, 1974, 711 p.

  13. William W. Liou, Yichuan Fang. Microfluid Mechanics: Principles and Modeling, The McGraw-Hill Companies, Inc, 2006, 353 p.

  14. Koshmarov Yu.A., Ryzhov Yu.A. Prikladnaya dinamika razrezhennogo gaza (Applied rarefied gas dynamics), Moscow, Mashinostroenie, 1977, 184 p.

  15. Shidlovskii V.P. Vvedenie v dinamiku razrezhennogo gaza (Introduction to the Dynamics of Rarefied Gases), Moscow, Nauka, 1965, 220 p.

  16. Bird G.A. Molecular gas dynamics and the direct simulation of gas flows, Clarendon press, Oxford, 1994, 458 p.

  17. Berd G. Molekulyarnaya gazovaya dinamika (Molecular gas dynamics), Moscow, Mir, 1981, 320 p.

  18. Bird G.A. Monte Carlo simulation of gas flows, Annual Reviev of Fluid Mechanics, 1978, vol. 10, pp. 11 – 31.

  19. Berezko M.E., Nikitchenko Yu.A., Tikhonovets A.V. Trudy MAI, 2017, no. 94, available at: http://trudymai.ru/eng/published.php?ID=80922

  20. Sharipov F., Cumin L.M.G., and Kalempa D. Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number, European Journal of Mechanics B/Fluids, 2004, no. 23, pp. 899 – 906.

  21. Egorov I.V., Erofeev A.I. Uchenye zapiski TsAGI, 1997, no. 2, pp. 23 – 39.

  22. Shen C. Rarefied Gas Dynamics: Fundamentals, Simulations and Micro Flows, Springer, Berlin Heidelberg, New York, 2005, 406 p.


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