Numerical analysis of the Taylor-vortex flow of a slightly rarefied gas. (English) Zbl 1360.35136
Summary: 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 \(10^{-2}\). The flow field for smaller Knudsen numbers (of the order of \(10^{-3}\)) 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.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35A35 | Theoretical approximation in context of PDEs |
| 76N15 | Gas dynamics (general theory) |
| 35Q20 | Boltzmann equations |
| 76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
| 76B47 | Vortex flows for incompressible inviscid fluids |
| 65C05 | Monte Carlo methods |
| 76F65 | Direct numerical and large eddy simulation of turbulence |
| 76M28 | Particle methods and lattice-gas methods |
Keywords:
compressible Navier-Stokes (CNS) equations; Boltzmann equation; Monte Carlo method; Couette flow; vortex flowReferences:
| [1] | G. I. Taylor, Phil. Trans. R. Soc. London Ser. A223, 289 (1923). · JFM 49.0607.01 |
| [2] | S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, London, 1961. · Zbl 0142.44103 |
| [3] | P. Chossat and G. Iooss, The Couette-Taylor Problem, Springer-Verlag, New York, 1994. · Zbl 0817.76001 |
| [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). · Zbl 0785.76068 |
| [7] | D. Riechelmann and K. Nanbu, Phys. Fluids A5, 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. · Zbl 0925.76510 |
| [11] | Y. Sone, in Rarefied Gas Dynamics, edited by D. Dini, Editrice Tecnico Scientifica, Pisa, 1971, Vol. 2, p. 737. · Zbl 0245.76063 |
| [12] | Y. Sone, Kinetic Theory and Fluid Dynamics, Birkhäuser, Boston, 2002. · Zbl 1021.76002 |
| [13] | Y. Sone, Molecular Gas Dynamics: Theory, Techniques, and Applications, Birkhäuser, Boston, 2007. · Zbl 1144.76001 |
| [14] | B. Larignon, K. Marr, and D. B. Goldstein, J. Therm. heat Trans.20, 544 (2006). |
| [15] | H. Yoshida and K. Aoki, Phys. Rev. E73, 021201 (2006). |
| [16] | A. Manela and I. Frankel, J. Fluid. Mech.588, 59 (2007). · Zbl 1141.76471 |
| [17] | T. Ohwada, Y. Sone, and K. Aoki, Phys. Fluids A1, 1588 (1989). · Zbl 0695.76032 |
| [18] | Y. Sone, T. Ohwada, and K. Aoki, Phys. Fluids A1, 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). · Zbl 0374.76025 |
| [20] | Y. Sone, C. Bardos, F. Golse, and H. Sugimoto, Eur. J. Mech. B/Fluids19, 325 (2000). · Zbl 0973.76076 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
