The convergence behavior of the direct simulation Monte Carlo (DSMC) method is systematically investigated for near-continuum, one-dimensional Fourier flow. An argon-like, hard-sphere gas is confined between two parallel, fully accommodating, motionless walls of unequal temperature. The simulations are performed using four variations based on Bird’s DSMC algorithm that differ in the ordering of the move, collide, and sample operations. The primary convergence metric studied is the ratio of the DSMC-calculated bulk thermal conductivity to the infinite-approximation Chapman-Enskog (CE) theoretical value, although temperature and heat flux are also considered. Ensemble, temporal, and spatial averaging are used to reduce statistical errors to levels that are small compared to the discretization errors from the time step (Δt), the cell size (Δx), and the number of computational particles per cell (Nc). The errors from these three parameters are determined using over 700 individual cases selected from the ranges 0.05<Δt∕to<1 (to is the molecular mean collision time), 0.05<Δx∕λo<1 (λo is the molecular mean free path), and 7≤Nc≤480. The infinite-particle-number (Nc→∞) convergence behavior for the thermal-conductivity ratio is found to be second-order in both time step and cell size, in good agreement with previous theoretical predictions based on Green-Kubo theory. For vanishing time step and cell size, the finite-particle-number convergence behavior is found to be O(1∕Nc) if ∼30 or more particles per cell are used. The observed convergence behavior is found to be more complicated when all three discretization parameters are finite. As discretization errors are systematically reduced, the DSMC-calculated conductivity is shown to approach the infinite-approximation CE theoretical value to within 1 part in 104.

An experimental apparatus has been developed to determine thermal accommodation coefficients for a variety of gas-surface combinations. Results are obtained primarily through measurement of the pressure dependence of the conductive heat flux between parallel plates separated by a gas-filled gap. Measured heat-flux data are used in a formula based on Direct Simulation Monte Carlo (DSMC) simulations to determine the coefficients. The assembly also features a complementary capability for measuring the variation in gas density between the plates using electron-beam fluorescence. Surface materials examined include 304 stainless steel, gold, aluminum, platinum, silicon, silicon nitride, and polysilicon. Effects of gas composition, surface roughness, and surface contamination have been investigated with this system; the behavior of gas mixtures has also been explored. Without special cleaning procedures, thermal accommodation coefficients for most materials and surface finishes were determined to be near 0.95, 0.85, and 0.45 for argon, nitrogen, and helium, respectively. Surface cleaning by in situ argon-plasma treatment reduced coefficient values by up to 0.10 for helium and by ∼0.05 for nitrogen and argon. Results for both single-species and gas-mixture experiments compare favorably to DSMC simulations.

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.

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