Computational studies of the three-dimensional, hypersonic flow of rarefied, strongly stratified gas past an obstacle are carried out, the incident gas stratified in a direction transverse to the mean flow. An “ N-body” computational code based on Monte Carlo techniques is developed for these purposes. Our primary interest is centered on the three-dimensional effects induced in the gas flow by a solid obstacle comparable in size to the gas scale height and collisional mean free path. Of the different types and shapes of obstacles studied, we focus herein on a cylindrical obstacle, assumed to be a diffuse elastic scatterer. The cylindrical obstacle is a short uniform pipe whose upstream end is fully open, facing directly into the flow, and whose downstream end is covered by a flat circular endplate containing an “orifice” at its center. For different choices of “orifice” diameter, the obstacle serves as a useful model of an impact probe (closed orifice) or scoop (closed, partially open, or fully open orifice) in a rapidly rotating strongly stratified gas (as in a gas centrifuge). The computed results show that the obstacle (in all cases studied, spanning the range from completely closed orifice to fully open orifice) induces large systematic motions in the gas, with strong radially inward driven flow in the direction of the gradient of density stratification, and correspondingly large density perturbations in these regions. The radial inflow of gas is prominent not only in the neighborhood of the obstacle and downstream from it but also at considerable distances radially inward from it and at z-heights well above and below. The radially driven gas inflow is a striking three-dimensional effect induced when strongly stratified gas impinges upon an obstacle; it constitutes a major characteristic common to all the hypersonic, stratified flows studied despite differences in Mach number and gas scale height and regardless of whether the obstacle is a flat plate, a “long” solid rod, or a “short” cylindrical pipe. The resultant density distribution of the obstructed molecular gas exhibits a striking “asymmetry” in the (radial) direction of the gradient of density stratification but retains “symmetry” in the z-direction perpendicular to the stratification gradient. The “ r-asymmetry” is in striking contrast to the characteristic rotation-symmetry exhibited about the obstructing pipe's central axis in corresponding cases of unstratified flows investigated. The bow shock that forms near the obstacle exhibits a characteristic thickness that broadens with mean free path in the direction of the gradient of density stratification and a characteristic shape that is substantially warped (in that direction) from the paraboloid-shaped bow shock that forms (with axis of revolution coincident with the pipe's central axis) in corresponding cases of unstratified flows. The redirection of the gas flow at the shock away from the direction of the incident mean flow is particularly strong along that portion of the warped bow shock most closely aligned with the (radial) direction of the stratification gradient; the postshock density ridge in this direction is masked considerably by the strongly stratified density background.
Read full abstract