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Rarefied gas dynamics - International Symposium, Institute for Aerospace Studies, University of Toronto, July 1964, Volume 1
Stationary rotation of rarefied gas mass gravitating in magnetic field
Monte Carlo method solution of heat transfer in rarefied gas between infinite flat plates
Sealing coefficient and leakage performance model for multiple thread rarefied gas viscoseals
Rarefied gas couette flow and heat transfer between parallel plates analyzed by model sampling procedures
Hypersonic rarefied gas flow near stagnation point investigated to predict drag on sphere in high speed gas stream with densities in transition regime
Molecular diffusion through a rarefied gas is analyzed by using the theory of Markov random walks. The Markov walk is simulated on the computer by using random numbers to find the new states from the appropriate transition probabilities. As the sample molecule during its random walk passes a scoring position, which is a location at which the macroscopic diffusing flow variables such as molecular flux and molecular density are desired, an appropriate payoff is scored. The payoff is a function of the sample molecule velocity. For example, in obtaining the molecular flux across a scoring position, the random walk payoff is the net number of times the scoring position has been crossed in the positive direction. Similarly, when the molecular density is required, the payoff is the sum of the inverse velocity of the sample molecule passing the scoring position. The macroscopic diffusing flow variables are then found from the expected payoff of the random walks.
Drag and heat transfer predicted by kinetic theory for rarefied gas flow over sphere at low Mach numbers, analyzing flow field
Viscoseal performance as predicted by three different analytical models is compared with experimental data for a rarefied gas sealant. An experimental investigation has been conducted on two multiple grooved two-inch diameter viscoseals over a wide range of gas densities and shaft speeds up to 30,000 rpm. The two seal geometries considered differ significantly insofar as groove aspect ratio is concerned. Two types of seal performances are presented in the form of net leakage operation and sealing coefficient performance as functions of the degree of gas rarefication. Although the analytical models correctly predict sealing trends, all of the models are shown to have some deficiencies which prevent their indiscriminate application.
A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.
Rarefied gas dynamics - Conference, Cambridge, Mass., July 1968, Volume 2
Rarefied gas dynamics - Conference, Cambridge, Mass., July 1968, Volume 1
The direct Monte Carlo method is used to simulate the transient motion of a confined rarefied gas as a container wall is rapidly heated or cooled. Results show that, for the rapid wall temperature changes, the gas response is better measured by an acoustic, rather than conduction, timescale, with steady state conditions being achieved after about ten wave crossing times.
The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.
Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.
Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.
An analytic study is made of the flow a rarefied monatomic gas through a two dimensional slot. The parameters of the problem are the ratios of downstream to upstream pressures, the Knudsen number at the high pressure end (based on slot half width) and the length to slot half width ratio. A moment method of solution is used by assuming a discontinuous distribution function consisting of four Maxwellians split equally in angular space. Numerical solutions are obtained for the resulting equations. The characteristics of the transition regime are portrayed. The solutions in the free molecule limit are systematically lower than the results obtained in that limit by more accurate numerical methods.
A kinetic-theory analysis is made of the flow of a rarefied monatomic gas through a two-dimensional slot connecting two reservoirs. Numerical solutions are obtained by the moment and discrete-ordinate methods. The former method portrays the transition-regime characteristics well but has limitations in the free-molecule regime. The latter method gives accurate results in the free-molecule and slip regimes and bolsters confidence in the accuracy of the transition-regime results. The numerical solution for the mass flux through the slot agrees well with an approximate analytical solution of the moment equations for length-to-width ratios from 6 to 0.5, pressure ratios from 0.8 to 0.1, and Knudsen numbers from 5 to 0.5.