Coriolis effect on the stability of convection in mushy layers during the solidification of binary alloys.

Abstract

We consider the solidification of a binary alloy in a mushy layer subject to Coriolis effects. A near-eutectic approximation and large far-field temperature is employed in order to study the dynamics of the mushy layer in the form of small deviations from the classical case of convection in a horizontal porous layer of homogenous permeability. The linear stability theory is used to investigate analytically the Corio lis effect in a rotating mushy layer for, a diffusion time scale used by Amberg & Homsey (1993) and Anderson & Worster (1996), and for a new diffusion time scale proposed in the current study. As such, it is found that in contrast to the problem of a stationary mushy layer, rotating the mushy layer has a stabilising effect on convection. For the case of the new diffusion time scale proposed by the author, it is established that the viscosity at high rotation rates has a destabilising effect on the onset of stationary convection, ie. the higher the viscosity, the less stable the liquid. Finite amplitude results obtained by using a weak non-linear analysis provide differential equations for the amplitude, corresponding to both stationary and overstable convection. These amplitude equations permit one to identify from the post-transient conditions that the fluid is subject to a pitchfork bifurcation in the stationary case and to a Hopf bifurcation associated with the overstable convection. Heat transfer results were evaluated from the amplitude solution and are presented in terms of the Nusselt number for both stationary and overstable convection. They show that rotation enhances the convective heat transfer in the case of stationary convection and retards convective heat transfer in the oscillatory case, but only for low values of the parameter X I = 8 Pr ~ 0 So· The parameter 1/ X I represents the coefficient of the time derivative term in the Darcy equation. For high X I values, the contribution from the time derivative term is small (and may be neglected), whilst for small X I values the time derivative term may be retained.