TRANSPORT IN A CONFINED COMPRESSIBLE FLUID UNDER TIME-DEPENDENT VOLUMETRIC HEAT-SOURCES

The response of a confined compressible perfect gas to an uneven time-dependent volumetric heat source is studied. The low Mach number compressible Navier-Stokes equations are solved numerically by means of the pressure implicit with splitting of operators (P.I.S.O.) algorithm in the case where the characteristic time of the thermal perturbation is small compared to the diffusion time and large compared to the acoustic time. A comparison is made with first-order asymptotic results previously obtained. The asymptotic analysis is then carried out up to the second order in the bulk. It is shown that: (a) a flow is generated from one side of the cavity to the other, confirming the asymptotic results previously obtained; (b) a flow towards the walls is found in thermal boundary layers because of a sink effect due to the lower temperature in these regions; (c) comparison with analytical results in the bulk is quite satisfactory except for the velocity where some differences are shown; (d) the second-order asymptotic analysis shows that this approximation in the bulk is a mechanical perturbation caused by the contraction of the fluid layers near the boundaries; (e) the matching between analytical results and numerical results is improved by more than 50% when considering a second-order solution; (f) this analysis validates both numerical code and scaling laws. © 1990 American Institute of Physics.