An approach for simulating the transport of spherical particles in a rarefied gas flow via the direct simulation Monte Carlo method

Abstract

An approach is presented for computing the force on and heat transfer to a spherical particle from a rarefied flow of a monatomic gas that is computed using the direct simulation Monte Carlo (DSMC) method. The particle concentration is taken to be dilute, and the gas flow around the particle (but not necessarily throughout the flow domain) is taken to be free-molecular. Green’s functions for the force and heat transfer are determined analytically, are verified by demonstrating that they yield certain well-known results, and are implemented numerically within a DSMC code. Simulations are performed for the case of gas confined between two parallel plates at different temperatures for broad ranges of pressures and particle velocities. The simulation results agree closely with analytical results, where applicable. A simple approximate expression relating the thermophoretic force to the gas-phase heat flux is developed, and the drag and thermophoretic forces are found to be almost decoupled for a wide range of particle velocities.

Rarefied gas flow in microtubes at different inlet-outlet pressure ratios

“…For highly rarefied flows, in which the deviation from Navier-Stokes predictions is significant, the direct simulation Monte Carlo ͑DSMC͒ method has been used. [8][9][10][11][12] DSMC is a particle-based method and is especially efficient in numerical solutions of transition flow. A hybrid DSMC and Navier-Stokes scheme 13 as well as hybrid continuum-particle methods based on computational fluid dynamics and DSMC ͑Ref.…”

Thermophoresis in Rarefied Gas Flows

“…They used a force Green's function (Gallis et al 2001b) to compute the force on a spherical particle directly from the molecular velocity distribution calculated by the direct simulation Monte Carlo (DSMC) method of Bird (1994). The selected geometry was that of a motionless, spherical particle suspended in a monatomic, quiescent gas lling the region between 2 in nite, parallel plates.…”

“…The DSMC calculations also showed that the magnitude of the thermophoretic force was nearly constant between the plates, contradicting earlier theoretical studies (Havnes et al 1994;Chen 1999Chen , 2000 that predicted signi cant variations in the thermophoretic force near the walls. Gallis et al (2001b) also used the DSMC/Green's function method to analyze the relation between gas heat ux and the thermophoretic force. Vestner (1974) appears to be the rst to have noticed that the thermophoretic force (in both the freemolecular and continuum limits) is proportional to the particle cross-sectional area and the local heat ux and inversely proportional to the mean molecular speed.…”

“…Vestner (1974) appears to be the rst to have noticed that the thermophoretic force (in both the freemolecular and continuum limits) is proportional to the particle cross-sectional area and the local heat ux and inversely proportional to the mean molecular speed. Based on theoretical arguments, Gallis et al (2001b) conjecture that the constant of proportionality depends on the form of the molecular velocity distribution. Even for apparently distinct velocity distributions, such as the Chapman-Enskog (nonequilibrium continuum) or the combination of 2 half-range Maxwellians (free molecular), the proportionality constant differs by only about 10%.…”

“…Even for apparently distinct velocity distributions, such as the Chapman-Enskog (nonequilibrium continuum) or the combination of 2 half-range Maxwellians (free molecular), the proportionality constant differs by only about 10%. Gallis et al (2001b) calculated the thermophoretic proportionality constant over the entire transition regime and found that the constant varied smoothly from the continuum to the free-molecular values for particles in argon in a parallel-plate geometry. Thus, the close relationship between the heat ux and the thermophoretic force was demonstrated in this geometry.…”