Calculation of channel flows of gases by the Monte-Carlo method with correction for collisions

Steady flow of a moderately rarefied gas in a circularly cylindrical channel was considered for the case of the flow being produced by the interaction of two flows colliding head-on. An iterative procedure based on the Monte Carlo method was used to solve the five-dimensional equations describing molecules with an arbitrary collisional cross section dependent on the relative velocity of a colliding pair. A Maxwellian initial distribution of the molecules was assumed, and various collision velocities were examined. A total of 4000-5000 trial trajectories were run to attain a 95% level of accuracy. The countercurrent flows were found to diffuse independent of one another. Transmissivity (Clausing) coefficients were calculated in terms of the Knudsen and Mach numbers, the channel length, the diffusion coefficient, and density and temperature distributions along the channel. The quantitative results are considered significant for calibrating pitot tube measurements in a transition zone.