https://profdoc.um.ac.ir/articles/a/1057659.pdf

Collision partner selection schemes in DSMC: From micro/nano flows to hypersonic flows

A numerical study of three-dimensional effects on the performance of a micronozzle fabricated from e at silicon wafers is performed by use of both continuum and kinetic approaches. The nozzle operates in a low-Reynoldsnumber regime, and viscous effects dominate the gas expansion. Thrust losses occur because the shear on the wall is greater in a e at nozzle cone guration than in an axisymmetric conical nozzle. Therefore, the prediction of the micronozzle performance based on axisymmetric or two-dimensional modeling can lead to signie cant design errors.Comparisonofsimulationwithrecentdatashowsgood agreementintermsofthrustpredictionsforcold-gas thrusters at Reynolds numbers of approximately 2 ££ 102.

Numerical Modeling of Axisymmetric and Three-Dimensional Flows in Microelectromechanical Systems Nozzles

A numerical study of three-dimensional effects on the performance of a micronozzle fabricated from flat silicon wafer is performed by both continuum and kinetic approaches. The nozzle operates in a low Reynolds numbers regime and viscous effects dominate the gas expansion. Thrust losses occur because the shear on the wall is greater in the nozzle of a flat configuration compared to an axisymmetric conical nozzle. Therefore, the prediction of the micronozzle performance based on axisymmetric or two-dimension al modeling can lead to significant design errors.

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Numerical modeling of axisymmetric and three-dimensional flows in MEMS nozzles

Gaseous flow through a microchannel is treated numerically and analytically in order to assess pressure and mass flow losses due to a constriction of a finite length. Numerical modeling of two-dimensional (2-D) microchannel flow in the slip and transitional regimes is carried out using the direct simulation Monte Carlo (DSMC) method. The prediction of pressure losses and mass flow based on a simple analytic model for constriction microchannel flow are found to be in excellent agreement with DSMC simulations. Constriction has a dramatic effect on pressure loss and mass flow rate for the considered cases. The DSMC results indicate that the flow in the constriction microchannel separates in the transition section, but the separation does not significantly impact pressure distributions.

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Reconsideration of low Reynolds number flow-through constriction microchannels using the DSMC method

The direct simulation Monte Carlo (DSMC) method is a stochastic approach to solve the Boltzmann equation and is built on various numerical schemes for transport, collision and sampling. This work aims to compare and contrast two popular O(N) DSMC collision schemes - no-time-counter (NTC) and majorant collision frequency (MCF) - with the goal of identifying the fundamental differences. MCF and NTC schemes are used in DSMC simulations of a spatially homogeneous equilibrium gas to study convergence with respect to various collision parameters. While the MCF scheme forces the reproduction of the exponential distribution of time between collisions, the NTC scheme requires larger number of simulators per cell to reproduce this Poisson process. The two collision schemes are also applied to the spatially homogeneous relaxation from an isotropic non-Maxwellian given by the Bobylev exact solution to the Boltzmann equation. While the two schemes produce identical results at large times, the initial relaxation shows some differences during the first few timesteps.

/pdf/a-comparative-study-of-no-time-counter-and-majorant-3erd5banq0.pdf

A comparative study of no-time-counter and majorant collision frequency numerical schemes in DSMC

In this work the direct statistical simulation method for spatially uniform relaxation in rarefied gas is developed on the basis of a probabilistic interpretation for the integral representation of the master kinetic equation (Kats equation). It is shown that under certain conditions the conventional schemes for the relaxation simulation follow directly from this equation. A new accurate simulation scheme is proposed, the majorant frequency scheme, which requires a computing capacity that scales directly with the number of sampling particles. The relation between the solutions of the master kinetic equation of rarefied gas and the Boltzmann equation is studied for the uniform case. It is shown that the correlations occurring in the finite-number particle system affect significantly the statistical simulation results. The criterion for estimating the influence of such correlations during the computation process is suggested. Introduction At present, the direct statistical simulation method, based on splitting up the evolution of a gas system in two stages, is widely used in the dynamics of rarefied gas. The method is realized in the following way. The flowfield computed is divided into cells of a finite size Ax and, according to the initial distribution function, N sampling particles are placed into each cell. Then the spatially-uniform relaxation stage and the stage of a free-molecular transition are successively carried out in all the cells. The free-molecular transition simulation can be performed without difficulties. In this case, the realization of the spatially-uniform relaxation stage is of primary importance. Copyright © 1989 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. * Institute of Theoretical and Applied Mechanics. t Computing Center, 171 172 M. S. IVANOV ET AL For the simulation of collisional relaxation, the numerical schemes suggested in Refs. 1-4 are used. All these schemes are derived from heuristic considerations on the basis of physical understanding of the relaxation process in an actual gas; as a result there is no direct relation with the Boltzmann kinetic equation. The heuristic character of these schemes allow comparative analysis only qualitatively, with the use of the "Boltzmannian" collision frequency as the main criterion." The stochastic process for an approximate solution of the Boltzmann equation is constructed in Ref. 8 using the Euler scheme for the Boltzmann spatiallyuniform equation with its further randomization. In such an approach, for colliding particles the conservation laws are not valid, and this is the basic difference from the schemes given in Refs. 1-4. It seems reasonable to consider the known numerical schemes for the statistical simulation of rarefied gas flows in light of a general theory of Monte Carlo techniques. Such a unified consideration enables one to carry out a comparative analysis to show the inner relation between these schemes and also justifies the use of various Monte Carlo weight techniques.^ Derivation of Simulation Technique from Master Kinetic Equation In the construction of the Monte Carlo numerical technique we shall directly proceed from the master kinetic equation for the N-particle distribution function, which in the spatially-uniform case has the following r°° {fN(t,cjj) fN(t,c)} | vi-vj | by dbij dey l C) K2(t'->t I c) cp (t,c) dc dt + cp0(t,c) /2) Jo J where 9 (t,c) = t) (c) f^ (t,c) is the collision density. DIRECT SIMULATION AND MASTER KINETIC EQUATION 173 9o(t,c)=fN(o,c)\)(c)exp{-\)(c)t} _ . _ • _ _ N _ _• '-* C) = -^Y D'^WCv^V;' I Vi,Vj) II 5(vm-Vm)

S. V. Rogasinskii

Papers

Direct statistical simulation method and master kinetic equation