Subsonic rarefied gas flow over a rack of flat transverse plates

Abstract

Parameters of a rarefied gas flow through a rack of flat plates aligned across the flow are studied by means of the joint numerical solution of the Boltzmann and Navier-Stokes equations. A subsonic flow regime is considered. The changes in flow characteristics are calculated as functions of the freestream velocity and plate temperature.Introduction. Akin'shin et al.[1] performed a pioneering experimental study of a rarefied gas flow in a capillary sieve in the range of Knudsen numbers Kn = 10 −4 -10 −1 at different temperatures for several inert gases and determined the dependence of the flow rate on the flow geometry and the character of interaction between molecules and capillary walls. A supersonic flow with Mach numbers M = 2-3 and a Reynolds number Re = 10 6 over perforated screens was studied in [2] by analyzing the effect of injection into the base region on the flow structure. Theoretical results based on the presentation of the perforated screen as a discontinuity surface with relations that take into account the flow structure inside the perforation and the mechanisms of interaction between the gas and the walls were published in [3], and this analytical approach was further developed in [4,5].The results of numerical experiments performed by means of direct statistical modeling of one-dimensional rarefied gas flows through a permeable flat surface can be found in [6]. Steady-state flows in the range of Mach numbers M = 3-10 with different temperatures of the target and accommodation numbers were studied under the assumption that the gas molecule passes through the surface without interacting with the latter with a probability P and becomes scattered with a probability 1−P . In particular, the laws of variation of flow parameters in the "shockdisturbance front" formed ahead of the target were determined, and the difference of this front from the shock-wave structure was found.The necessity of studying subsonic rarefied gas flows is inspired by their importance for practical purposes (motion of the gas in porous solids and capillary membranes in devices for gas separation and cooling). The flow characteristics are determined by interaction of flows around the target elements. These are normally threedimensional structures consisting of cylindrical channels or a set of finite-length plates aligned along or across the flow.It seems of interest to consider systems designed for controlling (generating) flows with prescribed properties without any changes in geometry, by varying the temperature or gas-flow parameters on the wetted surfaces. Such systems are analyzed in the present paper.The numerical solution of the Boltzmann equation, which describes the rarefied nonequilibrium gas dynamics, requires a large volume of computations, because the distribution function to be determined includes a threedimensional space of velocities in addition to spatial variables. Two-dimensional formulations can be currently used for numerical simulations of rarefied gas flows. Even in comparatively simple cases, however, the...

Supersonic rarefied gas flow through a wire grid

“…Popov and Tcheremissine [10] performed a numerical study of a supersonic rarefied gas flow through an infinite periodic grid consisting of flat plates aligned across the flow. Stationary regimes in the case of a shock wave attached to the grid and nonstationary regimes with an upstream moving shock wave were studied.…”