ON THE ONSET OF NATURAL CONVECTION IN A PARTIALLY COOLED CYLINDER

Recent experimental configurations like the liquid metal electrode for the development of a liquid metal battery and the inverted Bridgman configuration for growing crystals involve natural convection of fluids confined in vertical cylinders heated from below and partially cooled from above. A cylindrical cavity subjected to such conditions is studied from a numerical point of view, assuming the Rayleigh number, the noncooled size, and the aspect ratio (height/diameter) parameters over ranges 10(3) <= Ra <= 10(5), 0 <= gamma <= 0.875, and 0.5 <= a <= 1.25, respectively, for all cases with Pr = 6.67 being assumed. The governing equations for natural convection are discretized employing a mixed Fourier-Finite volume method using the SIMPLEC algorithm as velocity decoupling strategy. Steady flow transitions from axisymmetric to nonaxisymmetric were obtained; interestingly, the average Nusselt number shows a monotonic decreasing behavior as a function of gamma while an increasing behavior as function of Ra is observed. In particular, symmetry breaking instability as a function of critical parameters of the convective flow is determined by a numerical stability analysis. Finally, a stability map for Ra vs. gamma is constructed for a = 1.0.