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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]

A kinetic equation (S-model) is used to solve the nonstationary problem of a monatomic rarefied gas flowing from a tank of infinite capacity into a vacuum through a long plane channel. Initially, the gas is at rest and is separated from the vacuum by a barrier. The temperature of the channel walls is kept constant. The flow is found to evolve to a steady state. The time required for reaching a steady state is examined depending on the channel length and the degree of gas rarefaction. The kinetic equation is solved numerically by applying a conservative explicit finite-difference scheme that is firstorder accurate in time and second-order accurate in space. An approximate law is proposed for the asymptotic behavior of the solution at long times when the evolution to a steady state becomes a diffusion process. [ABSTRACT FROM AUTHOR]

Flows of a rarefied gas between plane parallel walls with nonuniform surface properties are studied based on kinetic theory. It is assumed that one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundary whose accommodation coefficient varies periodically in the longitudinal direction. Four fundamental flows are studied, namely, Poiseuille flow, thermal transpiration, Couette flow, and the heat transfer problem. These flow problems are numerically studied based on the linearized Bhatnagar-Gross-Krook-Welander model of the Boltzmann equation over a wide range of the mean free path and the parameters characterizing the distribution of the accommodation coefficient. The flow fields, the mass and heat flow rates through a cross section or the wall surfaces, and the tangential force acting on the wall surfaces are studied. Due to the nonuniform surface properties, a longitudinal motion of the gas induces a local heat transfer through the wall surface in Poiseuille, thermal transpiration, and Couette flows; a temperature difference between the walls induces a motion of a gas and a local tangential stress on the walls in the heat transfer problem. However, the heat flow rate through the wall surface in the first three flow problems and the tangential force acting on the wall surface in the heat transfer problem vanish if integrated over one period. No net mass flow is induced in the heat transfer problem. Six reciprocity relations among the flow rates in the aforementioned four flows are numerically confirmed. Among the six relations, both hand sides of three relations vanish. The background of this phenomenon is discussed based on the flow field of the gas. [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]

Direct Simulation Monte Carlo (DSMC) is a powerful numerical method to study rarefied gas flows such as cometary comae and has been used by several authors over the past decade to study cometary outflow. However, the investigation of the parameter space in simulations can be time consuming since 3D DSMC is computationally highly intensive. For the target of ESA's Rosetta mission, comet 67P/Churyumov-Gerasimenko, we have identified to what extent modification of several parameters influence the 3D flow and gas temperature fields and have attempted to establish the reliability of inferences about the initial conditions from in situ and remote sensing measurements. A large number of DSMC runs have been completed with varying input parameters. In this work, we present the simulation results and conclude on the sensitivity of solutions to certain inputs. It is found that among cases of water outgassing, the surface production rate distribution is the most influential variable to the flow field. [ABSTRACT FROM AUTHOR]

An unstructured mesh Navier-Stokes solver employing a Maxwell slip boundary condition was developed. The present flow solver was applied to the simulation of flows around an axisymmetric hollow cylinder in a Mach 10.4 freestream, known as Calspan-UB Research Center (CUBRC) Run 14 case, and the velocity slip and the temperature jump on the cylinder surface were investigated. The effect of tangential momentum and thermal accommodation coefficients used in the Maxwell condition was also investigated by adjusting their values. The results show that the reverse flow region is developed on the body surface due to the interaction between the shock and the boundary layer. Also, the shock impingement makes pressure high. The flow properties on the surface agree well with the experimental data, and the velocity slip and the temperature jump vary consistently with the local Knudsen number change. The accommodation coefficients affect the slip phenomena and the size of the flow region. The slip phenomena become larger when both tangential momentum and thermal accommodation coefficients are decreased. However, the range of the reverse flow region decreases when the momentum accommodation coefficient is decreased. The characteristics of the momentum and thermal accommodation coefficients also are overlapped when they are altered together. [ABSTRACT FROM AUTHOR]

A rigorous asymptotic analysis of the Boltzmann equation for small Knudsen numbers leads, in the general case, to more complicated sets of differential equations than widely used to describe the behavior of gas in terms of classical fluid dynamics. The present paper deals with such one that is valid for significant temperature variations and finite Reynolds numbers at the same time (slow nonisothermal flow equations). A finite-volume solver developed on the open-source CFD platform OpenFOAM $${^ \circledR}$$ is proposed for computer simulation of a slightly rarefied gas in an arbitrary geometry. Typical temperature-driven flows are considered as numerical examples. A force acting on uniformly heated bodies is studied as well. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann (LB) method has been used to simulate rarefied gas flows in micro-systems as an alternative tool, and shown its application possibility. For the rarefied gas flows, the surface roughness plays an important role for the slip phenomenon at the wall. If the wall surface is sufficiently rough, the reflection of the molecules will be diffuse and the tangential momentum accommodation coefficient (TMAC) is equal to unity. However, it has been known that the reflections are not always fully diffuse. In this study, rarefied gas flows are simulated in the slip and the transition flow regime including the effect of the TMAC. For the simulations, new non-fully diffuse wall boundary treatments of the LB method are proposed. The results of 2D and 3D simulations are in excellent agreement with the analytical solutions for the slip flow regime. The solutions of the linearized Boltzmann equation and DSMC for the transition flow regime are compared with those of high order LB method with present boundary conditions, and they are in excellent agreement. The tangential momentum accommodation coefficient effect is also investigated. [ABSTRACT FROM AUTHOR]

A method of calculating rapidly forces and torques caused by rarefied gas flow acting on a space-craft is presented. The spacecraft surface is described mathematically in detail. Our results are in good agreement with results obtained by other methods. [ABSTRACT FROM AUTHOR]

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]

The direct simulation Monte Carlo method is used to study a plane-parallel supersonic gas flow through a grid formed by a series of parallel infinite cylinders. Characteristic features of the shock disturbance formation during the interaction of a supersonic flow with a permeable grid and the effect of this disturbance on the flow parameters behind the grid are revealed. The boundaries of the domain of supersonic flow breakup ahead of the grid and the laws of the total momentum loss on the grid are obtained. Kinetic and energetic characteristics of the flow behind the grid are determined. [ABSTRACT FROM AUTHOR]