Numerical Study of Thermosolutal Convection in Enclosures Used for Directional Solidification (Bridgman Cavity)

Abstract

The present work is devoted to the numerical investigation of the interaction between thermal and solutal convection in enclosures used for modeling directional solidification. The full transient Navier-Stokes, energy and species con- servation equations are solved numerically by us- ing finite volumes technique. The effect of parameters governing the problem (namely the Rayleigh number, Ra, Lewis number, Le, and thermal to solutal ratio, N) on the tran- sition to oscillatory modes is studied for thermal and solutal buoyancy forces opposing each other. In steady regimes and for moderate Lewis value (Le=10), the flow structure and intensity are found to depend strongly on N (N is considered to vary between 0 and 10 2 ) .F orN = 1, the transition to oscillatory mode is studied as a function of the Lewis number. We show the existence of three distinct behaviours of the critical Rayleigh num- ber. In the first domain (Le > 100), the critical Rayleigh number tends to an asymptotic constant value. In the second domain (for intermediate 4< Le < 100), the evolution of the critical Rayleigh number can be correlated by RaC × Le −1/2 ∝ 1. In the third domain (Le < 4), where the scale for mass and energy diffusion are of the same order; a complex scenario caused by the strong competi- tion between the solutal and the thermal forces is observed.