Monte Carlo Calculation of Molecular Flow Rates through a Cylindrical Elbow and Pipes of Other Shapes

Abstract

A method is devised for the calculation of molecular flow rates through pipes where the mean free path for intermolecular collisions is large compared to the dimensions of the pipes. Results of the calculation are given for a straight cylindrical pipe, a cylindrical elbow, the annulus between two concentric cylinders, a straight cylindrical pipe with restricted openings, and a straight cylindrical pipe with restricted openings and a plate to block the direct beam between the openings.

Effective Kundsen diffusivities in structures of randomly overlapping fibers

“…Experiments with small, nearly spherical synthetic crystals (Barrer and Grove, 1950) gave tortuosity factors 18% higher in the slip region than in the Knudsen regime, while Carman's (19.56) experiments in powder beds suggested lower tortuosity factors for slip flow. Figure 15 also presents simulation results for Knudsen diffusion in structures of randomly oriented fibers, clbtained by Melkote and Jensen (1989) using the transmission probability method (Davis, 1960;Abbasi, 1981;Burganos and Sotirchos, 1988). There is good agreement between their results and those obtained in this study at low porosities, but significant differences are observed in the high-porosity region.…”

Multiscale modeling of transport and residence times in nanostructured membranes

“…Therefore, a simulation of a pure Knudsen regime does not require calculation of the interactions between the gas particles or between the pore wall and the gas particles; consequently, the simulations are less computationally intensive and will allow accessing longer time and length scales than molecular dynamics. Simulations following this idea have been performed for pores of different shapes [33][34][35][36] and roughness. [37][38][39] In all of these works the particle trajectories were considered one at a time, taking advantage of the lack of interaction among particles.…”

Monte Carlo Functional Expansion Calculation of Free Molecular Flows

“…In this technique the coefficients of a polynomial expansion of the collision density are estimated by a stochastic process. Compared to the technique introduced by Davis [1] our code gives comparable accuracy with a considerable saving in computer time. A preliminary report on this method has appeared earlier [2].…”

“…For example, Davis [1] and Garelis and Wainwright [3] have applied it to free molecular flow, Fleck [4] to photon flow in a superradiant laser rod, Blechschmidt [5] to light transmission in a cylindrical tube and Berceanu [6] to the flow of cold neutrons. The calculation of view factors in heat transfer problems [7] is also amenable to MC estimation and the heat flow resulting can be determined as we shall describe.…”

“…Ordinarily, we choose ak to be the cumulative area along Sk from one end to the point considered, with values ak = 0 and ak = Sk at the two ends of the subsurface. The collision density 0k on each subsurface is expanded in a set of orthogonal polynomials as follows (1) 0k(ak) = Z WMr Ordinarily, we choose pk by…”