Kinetic Theory of the Transient Couette Flow Problem

The transient Couette flow problem of rarefied binary gas mixtures is studied for the nonlinear case, Mi ≥ 1: one of the plates with equal plate temperatures is accelerated impulsively. The method of solution is the Monte Carlo method. The physical space is divided into macroscopically small cells. The change in the distribution function in a cell during a time interval Δt, which should be sufficiently small in comparison with the characteristic times (τD)iα, (τF)iα, and (τC)ij, is obtained by following the test particles for each molecular event through the event; i.e., molecular drift, external force, or molecular collision. The flow field is calculated for Maxwellian molecules and the range of Knudsen number Kn ≥ 0.1 (from free molecular to transition flow regime). The relaxation phenomena of a gas mixture with the boundary effects are observed. Of particular interest are an epochal relaxation due to the molecule-surface collision and the temperature “overshoot” near the moving plate. The steady-state solutions, which are obtained from the long-time results, are also presented. The effects of Knudsen number, mixture ratio, and gas-surface interaction are investigated, and the separation phenomena between the species are observed.

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Transient Couette flow of a rarefied gas between plane parallel walls with different surface properties

Doi

2016

Physics of Fluids

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Transient Couette flow of a rarefied gas between plane parallel walls with different surface properties induced by a sudden start-up of one of the walls is studied based on kinetic theory. The linearized Boltzmann equation for a hard sphere molecular gas is analyzed under the assumptions that one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundary. The initial and boundary value problem is solved numerically by using a modified hybrid scheme of characteristic coordinate and finite difference methods, to describe the discontinuities in the velocity distribution function correctly. The time evolution of the flow and the approach to the final time-independent state are studied over a wide range of the mean free paths and the accommodation coefficient of the boundary. In the transient process, the shear force acting on the moving wall depends on which wall moves. In contrast, the shear force acting on the wall at rest is independent of which wall moves; this property is a consequence of the symmetric relation of the Boltzmann equation [S. Takata, “Symmetry of the unsteady linearized Boltzmann equation in a fixed bounded domain,” J. Stat. Phys. 140, 985 (2010)]. The speed of approach to the time-independent state is fastest at an intermediate value of the mean free path. The behavior of the gas in the final time-independent state, including the heat flow in the isothermal gas, is also discussed.

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Kinetic Theory of the Transient Couette Flow Problem

Abstract: The discrete ordinate method is used to solve the linearized Bhatnagar-Gross-Krook Boltzmann equation for the transient Couette flow problem. Of particular interest is the velocity “overshoot” at the wall which occurs for d/μ < 2.

Cited by 3 publications

References 2 publications

The Transition Regime

The Transition Regime

Transient Couette Flow of Rarefied Binary Gas Mixtures

Transient Couette flow of a rarefied gas between plane parallel walls with different surface properties

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Kinetic Theory of the Transient Couette Flow Problem

Abstract: The discrete ordinate method is used to solve the linearized Bhatnagar-Gross-Krook Boltzmann equation for the transient Couette flow problem. Of particular interest is the velocity “overshoot” at the wall which occurs for d/μ &lt; 2.

Cited by 3 publications

References 2 publications

The Transition Regime

The Transition Regime

Transient Couette Flow of Rarefied Binary Gas Mixtures

Transient Couette flow of a rarefied gas between plane parallel walls with different surface properties

Contact Info

Product

Resources

About

Abstract: The discrete ordinate method is used to solve the linearized Bhatnagar-Gross-Krook Boltzmann equation for the transient Couette flow problem. Of particular interest is the velocity “overshoot” at the wall which occurs for d/μ < 2.