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The problem of rarefied gas flow through a long cylindrical channel as a function of the pressure and the temperature maintained at the channel ends is considered on the basis of the S-model of the Boltzmann kinetic equation. The pressure and temperature drops between the channel ends vary from small values at which the linear transport theory is valid to large values at which the gas molecule mean free path ceases to be constant along the channel. The solution to the model kinetic equation is found by means of the collocation method using the Chebyshev polynomials and rational functions. The mass flow and the pressure in the channel are obtained. Isobaric and isothermal flows are investigated. [ABSTRACT FROM AUTHOR]

Flows of a simple rarefied gas and gas mixtures are computed on the basis of the Boltzmann kinetic equation, which is solved by applying various versions of the conservative projection method, namely, a two-point method for a simple gas and gas mixtures with a small difference between the molecular masses and a multipoint method in the case of a large mass difference. Examples of steady and unsteady flows are computed in a wide range of Mach and Knudsen numbers. [ABSTRACT FROM AUTHOR]

The sound propagation through a binary mixture of rarefied gases in a semi-infinite space is investigated on the basis of the McCormack model to the linearized Boltzmann equation. The source of sound waves is an infinite and flat plate oscillating in the direction normal to its own plane. It is considered a fully established oscillation so that the solution of the kinetic equation depends on time harmonically. The diffuse scattering gas–surface interaction law is assumed as the boundary condition on the oscillatory plate. A realistic intermolecular potential based on experimental data for the transport coefficients of the mixture is employed in the calculations. Two mixtures of noble gases, namely, Helium–Argon and Helium–Xenon, are considered in order to investigate the influence of the molecular mass ratio of species on the problem. A wide range of the oscillation speed parameter, defined as the ratio of intermolecular collision frequency to sound frequency, is considered. The amplitudes and phases of the macrocharacteristics of the gas flow are calculated and the results are compared to those obtained for a single gas. [ABSTRACT FROM AUTHOR]

A numerical analysis of the rarefied gas flow caused by a temperature gradient in the direction tangential to a wall through a planar channel of finite length is carried out based on the nonlinear Shakhov model of the Boltzmann kinetic equation. The Maxwell diffuse and Cercignani–Lampis gas–surface interaction models are provided as a boundary condition at solid walls. An implicit scheme for solution of the S-model kinetic equation was applied and the algorithm has been optimized for the use of massive parallelization in both physical and velocities spaces. The competition between rarefaction, gas–surface scattering model and temperature gradient effects on a gas flow is discussed in terms of both mass flow rate and streamwise heat flux. A comparison with available literature results has been carried out and showed a good agreement. It was found that the temperature gradient as well as the gas–surface scattering dynamics play a significant role for the highly rarefied gas flow, beginning from the transition flow regime. At the same time, under certain gas–surface scattering conditions a change of the value of temperature gradient does not affect the heat flux. For the weakly rarefied flow the temperature gradient effect on the mass flow rate is small for any gas–surface scattering condition, while the heat flux does not depend neither on value of temperature gradient nor choice and details of gas–surface scattering dynamics. [ABSTRACT FROM AUTHOR]

Poiseuille flow and thermal transpiration of a rarefied gas between parallel plates with nonuniform suiface properties in the transverse direction are studied based on kinetic theory. We considered a simplified model in which one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundaty on which the accommodation coefficient varies periodically and smoothly in the transverse direction. The spatially two-dimensional (2D) problem in the cross section is studied numerically based on the linearized Bhatnagar-Gross-Krook-Welander (BGKW) model of the Boltzmann equation. The flow behavior, i.e., the macroscopic flow velocity and the mass flow rate of the gas as well as the velocity distribution function, is studied over a wide range of the mean free path of the gas and the parameters of the distribution of the accommodation coefficient. The mass flow rate of the gas is approximated by a simple formula consisting of the data of the spatially one-dimensional (ID) problems. When the mean free path is large, the distribution function assumes a wavy variation in the molecular velocity space due to the effect of a nonuniform surface property of the plate. [ABSTRACT FROM AUTHOR]

Transient flow of rarefied gas through an orifice caused by various pressure ratios between the reservoirs is investigated for a wide range of the gas rarefaction, varying from the free molecular to continuum regime. The problem is studied on the basis of the numerical solution of unsteady S-model kinetic equation. It is found that the mass flow rate takes from 2.35 to 30.37 characteristic times, which is defined by orifice radius over the most probable molecular speed, to reach its steady state value. The time of steady flow establishment and the steady state distribution of the flow parameters are compared with previously reported data obtained by the Direct Simulation Monte Carlo (DSMC) method. A simple fitting expression is proposed for the approximation of the mass flow rate evolution in time. [ABSTRACT FROM AUTHOR]

Plane thermal transpiration o f a rarefied gas between two walls of Maxwell-type boundaries with different accommodation coefficients is studied based on the linearized Boltzmann equation for a hard-sphere molecular gas. The Boltzmann equation is solved numerically using a finite difference method, in which the collision integral is evaluated by the numerical kernel method. The detailed numerical data, including the mass and heat flow rates of the gas, are provided over a wide range of the Knudsen number and the entire range of the accommodation coefficients. Unlike in the plane Poiseuille flow, the dependence of the mass flow rate on the accommodation coefficients shows different characteristics depending on the Knudsen number. When the Knudsen number is relatively large, the mass flow rate of the gas increases monotonically with the decrease in either of the accommodation coefficients like in Poiseuille flow. When the Knudsen number is small, in contrast, the mass flow rate does not vary monotonically but exhibits a minimum with the decrease in either of the accommodation coefficients. The mechanism of this phenomenon is discussed based on the flow field of the gas. [ABSTRACT FROM AUTHOR]

Abstract: The method, proposed previously by other authors, is applied here to calculate a mass flow rate of rarefied gas through a long rectangular channel of variable cross-section aspect ratio. The gas flow through this channel is generated by the pressure and/or temperature gradient. The method is based on the results obtained previously on the basis of the kinetic equation and it requires very modest computational efforts. As a demonstration of its application some examples of the mass flow rate calculations for the isothermal and non-isothermal flows through the channels with variable rectangular cross sections are given. The analytical expressions in the case of the hydrodynamic and free molecular flow regimes are proposed. [Copyright &y& Elsevier]

Abstract: A transient gas flow through a rectangular slit is simulated on the basis of unsteady S-model kinetic equation. The flow into vacuum and at two pressure ratios between the reservoirs are considered for a wide range of the rarefaction parameter lying from the free molecular to the near continuum regime. The time of steady flow establishment is obtained and it is found that this time depends on the pressure ratio between the reservoirs and on the gas rarefaction. The time evolution of the macroscopic flow parameters is analyzed in detail. The present results are compared with the results on the orifice flow previously obtained by other authors. [Copyright &y& Elsevier]

The kinetic S-model is used to study the steady rarefied gas flow through a long pipe of variable cross section joining two tanks with arbitrary differences in pressure and temperature. The kinetic equation is solved numerically by applying a second-order accurate conservative method on an unstructured mesh. The basic quantity to be computed is the gas flow rate through the pipe. The possibility of finding a solution based on the assumption of the plane cross sectional flow is also explored. The resulting solutions are compared with previously known results. [ABSTRACT FROM AUTHOR]