Natural Convection in Rectangular Cavities

General Overview

The subject of natural convection in rectangular-shaped cavities is important in several engineering applications like, for example, solar collectors, solidification of ingots, cooling of electronic equipment and air flow in buildings.

For these applications, is important to predict quantitative parameters, like the heat transfer rate, or qualitative features of the flow, like the flow regime (steady, periodic, quasi-periodic, chaotic and turbulent) and flow pattern (i.e. stratification, regions of laminar or turbulent behaviour etc.) .

Numerical Simulation

Work recently performed at DINMA - Sezione di Fisica Tecnica - has shown the feasability of accurate simulations of two-dimensional time-dependent natural convection in square cavities at values of the Rayleigh number in excess of 2x10E09 and Prandtl number of 0.7.

The calculations, performed on the CRAY X-MP/116se, have been done on a 256x256 finite volume grid, using an implicit primitive variable Additive Correction Multigrid, featuring second order accuracy in space and in time and mass conservation constantly satisfied, to machine accuracy, during the time-integration.

The figure (33 K) illustrates a snapshot of the time-evolution of the flow field in the cavity.

Movies

• Early Stages of the Flow

  (2 M MPEG movie) (Keep cursor inside movie frame to see proper colors)

  The evolution of the flow during start-up, is shown in this MPEG animation. The temperature field is visualized during the early stages, with an enlarged view of the left-bottom corner depicted on the left. The interaction of the cold intrusion with the hot boundary layer, on the left wall, is clearly visible, together with the subsequent formation of traveling waves along the walls. These structures take the form of characteristic hooks, and are modulated by the low frequency oscillation of the cavity core.

• Flow at Large Times

  (1.9 M MPEG movie) (Keep cursor inside movie frame to see proper colors)

  This short mpeg animation shows the evolution of the temperature and vorticity fields in the cavity at (statistical) steady state, illustrating the transition of the boundary layers at about 70 % of the cavity height, while most of the fluid is practically quiescent, or oscillating at low frequencies (gravity waves). The inserts at the left are enlarged views of the top-left corner of the cavity.