Influence of acoustic streaming on the stability of melt flows in horizontal Bridgman configurations

We study the effect of acoustic streaming (steady flow generated by progressive acoustic waves) on the stability of convective flows associated with crystal growth from melt in horizontal Bridgman configurations. We consider two simple configurations: an extended fluid layer submitted to a horizontal temperature gradient and a laterally heated parallelepipedic cavity. In both cases, the dependence of the critical Grashof number Grc on the acoustic intensity (monitored through the acoustic parameter A) is determined for given values of the Prandlt number and of the dimension of the acoustic source Hb. In the case of the extended fluid layer, it is shown that for rather small beam widths Hb, the acoustic streaming destabilizes the buoyant flows, but for a large beam width, a range of acoustic intensities A is found for which the buoyant flows are stabilized. An adequate decentring of the beam can also enhance the stabilization. In the case of the parallelepipedic cavity, the numerical calculations for a quite large beam width have shown that the critical thresholds for the two first (steady, and then oscillatory) bifurcations clearly increase when the acoustic streaming contribution is enhanced.