BIFURCATION AND STABILITY ANALYSES FOR A 2-PHASE RAYLEIGH-BENARD PROBLEM IN A CAVITY

Stability and bifurcation analyses of a partially melted or solidified material heated from below and cooled from above in a cavity, the so- called two-phase Rayleigh-Benard problem, are conducted by a finite-vo lume/Newton's method. Bifurcation analysis techniques using a numerica l Jacobian and an iterative matrix solver suitable to this large compl icated system are adopted. The onset and evolution of melt flows coupl ing with the heat conduction in the solid and a deformable melt/solid interface are illustrated through detailed bifurcation diagrams, and t he linear stability of each flow family is carefully examined. Some co mparison with the one-phase system is performed. Results are presented for a variety of parameters of interest, including the Rayleigh numbe r, aspect ratio, and tilt angle. Although most calculations are presen ted for the melt with a Prandtl number of one, the effects of Prandtl number on the onset of cellular convection and the sensitivity of symm etry breaking by tilting are examined. Furthermore, the dynamic respon ses of an unstable static state to stable solutions after small distur bances are illustrated, and the effect of heat of fusion is discussed. (C) 1998 American Institute of Physics.