Three-Dimensional Rayleigh-Benard Convection of a Rarefied Gas: DSMC and Navier-Stokes Calculations

摘要

The three-dimensional Rayleigh-Benard convection of a rarefied gas is studied numerically by using DSMC and Navier-Stokes finite difference methods. We present the results obtained in a three-dimensional box with an aspect ratio A=Lx:Ly:Lz at a fixed wall temperature ratio r=Tc/Th=0.1. In general, the three-dimensional results confirm the validity of the zone of convection obtained in the previous author's two-dimensional considerations. A detailed analysis has been performed for Knudsen number Kn=0.02 and A=2:2:1, A=3:3:1, and A= 4:4:1 and different Froude numbers ranged within the zone of convection. As result, a variety of different stable convection patterns in form of rolls and squares has been obtained. For the lowest Knudsen numbers computed, Kn=0.001 and Kn=0.002 , Froude number Fr= 1.0, and a fixed aspect ratio A=2:2:1, an irregular (chaotic) flow in form of unstable polygonal patterns has been observed.