The axisymmetric Taylor-vortex flow of a rarefied gas between two coaxial circular cylinders, a rotating inner cylinder and a resting outer one, is investigated numerically for small Knudsen numbers on the basis of the compressible Navier-Stokes (CNS) equations and their appropriate slip boundary conditions. The accuracy of the result as an approximate solution to the Boltzmann equation is confirmed by comparing it with the result obtained by the direct simulation Monte Carlo (DSMC) method for Knudsen numbers of the order of . The flow field for smaller Knudsen numbers (of the order of ) exhibits a boundary-layer like structure near the cylinders. It is shown that, compared with the cylindrical Couette flow, the velocity slip in the circumferential direction is enhanced in the Taylor-vortex flow.
@article{SLSEDP_2015-2016____A1_0,
author = {Aoki, Kazuo and Kagaya, Ryo and Kosuge, Shingo and Yoshida, Hiroaki},
title = {Numerical analysis of the {Taylor-vortex} flow of a slightly rarefied gas},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:1},
pages = {1--12},
publisher = {Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique},
year = {2015-2016},
doi = {10.5802/slsedp.94},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.94/}
}
TY - JOUR AU - Aoki, Kazuo AU - Kagaya, Ryo AU - Kosuge, Shingo AU - Yoshida, Hiroaki TI - Numerical analysis of the Taylor-vortex flow of a slightly rarefied gas JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:1 PY - 2015-2016 SP - 1 EP - 12 PB - Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique UR - http://www.numdam.org/articles/10.5802/slsedp.94/ DO - 10.5802/slsedp.94 LA - en ID - SLSEDP_2015-2016____A1_0 ER -
%0 Journal Article %A Aoki, Kazuo %A Kagaya, Ryo %A Kosuge, Shingo %A Yoshida, Hiroaki %T Numerical analysis of the Taylor-vortex flow of a slightly rarefied gas %J Séminaire Laurent Schwartz — EDP et applications %Z talk:1 %D 2015-2016 %P 1-12 %I Institut des hautes des scientifiques & Centre de mathtiques Laurent Schwartz, ole polytechnique %U http://www.numdam.org/articles/10.5802/slsedp.94/ %R 10.5802/slsedp.94 %G en %F SLSEDP_2015-2016____A1_0
Aoki, Kazuo; Kagaya, Ryo; Kosuge, Shingo; Yoshida, Hiroaki. Numerical analysis of the Taylor-vortex flow of a slightly rarefied gas. Séminaire Laurent Schwartz — EDP et applications (2015-2016), Exposé no. 1, 12 p. doi : 10.5802/slsedp.94. http://www.numdam.org/articles/10.5802/slsedp.94/
[1] G. I. Taylor, Phil. Trans. R. Soc. London Ser. A 223, 289 (1923).
[2] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, London, 1961.
[3] P. Chossat and G. Iooss, The Couette-Taylor Problem, Springer-Verlag, New York, 1994.
[4] G. A. Bird, Molecular Gas Dynamics, Oxford University Press, Oxford, 1976.
[5] G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford University Press, Oxford, 1994.
[6] S. Stefanov and C. Cercignani, J. Fluid Mech. 256, 199 (1993).
[7] D. Riechelmann and K. Nanbu, Phys. Fluids A 5, 2585 (1993).
[8] G. A. Bird, in Rarefied Gas Dynamics, edited by C. Shen, Peking University Press, Beijing, 1997, p.149.
[9] K. Aoki, Y. Sone, and M. Yoshimoto, in Rarefied Gas Dynamics, edited by R. Brun, R. Campargue, R. Gatignol, J.-C. Lengrand, Cépaduès-Éditions, Toulouse, 1999, Vol. 2, p.109.
[10] Y. Sone, in Rarefied Gas Dynamics, edited by L. Trilling and H. Y. Wachman, Academic Press, New York, 1969, p. 243.
[11] Y. Sone, in Rarefied Gas Dynamics, edited by D. Dini, Editrice Tecnico Scientifica, Pisa, 1971, Vol. 2, p. 737.
[12] Y. Sone, Kinetic Theory and Fluid Dynamics, Birkhäuser, Boston, 2002.
[13] Y. Sone, Molecular Gas Dynamics: Theory, Techniques, and Applications, Birkhäuser, Boston, 2007.
[14] B. Larignon, K. Marr, and D. B. Goldstein, J. Therm. heat Trans. 20, 544 (2006).
[15] H. Yoshida and K. Aoki, Phys. Rev. E 73, 021201 (2006).
[16] A. Manela and I. Frankel, J. Fluid. Mech. 588, 59 (2007).
[17] T. Ohwada, Y. Sone, and K. Aoki, Phys. Fluids A 1, 1588 (1989).
[18] Y. Sone, T. Ohwada, and K. Aoki, Phys. Fluids A 1, 236 (1989).
[19] R. M. Beam and R. F. Warming, An implicit factored scheme for the compressible Navier-Stokes equations, AIAA J. 16, 393 (1978).
[20] Y. Sone, C. Bardos, F. Golse, and H. Sugimoto, Eur. J. Mech. B/Fluids 19, 325 (2000).
Cité par Sources :
