Adjustment process of a contained gas to a change in the boundary temperature

Abstract

Numerical solutions are obtained for transient natural convection of a compressible fluid in a closed vessel at high Rayleigh number motions are driven by abruptly lowering the temperature at the entire walls of the vessel. Main emphasis will be placed on describing the flow evolutions of a non-Boussinesq fluid. Specifically, numerical solutions are sought by intergrating the full, time-dependent Navier-Stokes equations for nitrogen gas in a vertically-mounted circular cylinder. All terms are retained in the governing equations. Numerical results provided the details of flow and temperature are fields in the transient process. When the aspect ratio (height/diameter) is smaller than one, the evolution of the temperature field is highly oscillatory. The oscillation frequency is comparable to the internal gravity wave frequency; this is consistent with the previous analytical predictions. Numerically-constructed contour maps showing temperature and velocity fields are presented to illustrate the effect of the aspect ratio of the vessel.