Low Prandtl number convection in a rectangular cavity with longitudinal thermal gradient and transverse [formula omitted

Abstract

MATERIALS processing in space, such as crystal growth, may be sometimes disturbed by residual accelerations, or g-jitters, which act on the space carrier: atmospheric drag, gravity gradient effect, vibrations, crew activities, etc. Because of the presence of thermal gradients (and thus of density gradients) in the liquid phase of the experiment these residual accclerations may give rise to convective motions ; in turn, these convective flows may act on the solute field and lead to heterogeneities of dopant in the grown crystal. Thus it is important to be able to predict the possible influence of gjitters on solidification experiments, and to forecast whether or not they may lead to a lower quality of space-grown crystals. With this aim, this note will be devoted to g-jitter convection in an ideal crystal growth configuration. A second paper (to be published) will be devoted to the influence of ,qjitter convection on the distribution of solute (or dopant) in the liquid phase. Here we shall assume that the liquid alloy is dilute enough to enable a separate computation of velocity and solute fields (no solutal convection). The crystal growth experiment is modelled by a hidimensional, rectangular cavity (Fig. I), with end walls held at temperatures T,,-AT/2 and T,+AT/2, and totally filled with a Newtonian, low Prandtl number liquid at mean temperature To ; side walls are adiabatic and all surfaces are rigid no-slip boundaries. We shall study convective flows induced by gjitters transverse to the thermal gradient ; we chose this orientation of the g-jitters because it is the most ‘critical’, i.e. there is no threshold for the onset of convection as there would be in a ‘Rayleigh-BCnard’ configuration. The pioneering work