An analytical model for transport from quasi-steady and periodic accelerations on spacecraft (Q1579249)

This paper considers an analytical model of coupled flow, heat, and mass transfer in the core region of a rectangular low aspect ratio (length to height) flow channel, which represents a simplified Bridgman configuration. This model problem can predict the convective transport resulting from small transverse steady and periodic accelerations (\(g\)-jitter flow) typically associated with manned spacecraft. On the other hand, this simplified model problem eliminates analytical difficulties in describing two-dimensional turning flows near the channel ends, and can focus instead on one-dimensional turning flows near the channel midpoint for which closed-form analytical solution can be obtained. The non-dimensional time-dependent equations of motion, energy and solutal transport in the core region are derived using the assumptions of parallel laminar flow and constant thermal or solutal gradients. Closed-form analytical solutions are then obtained for three cases of constant or variable gravitational acceleration. The effects of stabilizing and destabilizing axial gradients are determined for both steady and time-dependent transverse gravitational accelerations. The author shows that a large stabilizing axial gradient will significantly damp very low frequency transport, but this damping effect diminishes as frequency is increased. This suggests the possibility to test high-frequency predictions of \(g\)-jitter model by applying horizontal periodic accelerations to a test cell, or by performing solidification experiments with vertical stabilizing thermal gradient. It is also shown that the effects of multi-frequency disturbances are additive, making it possible to integrate over a properly weighted power spectral density spectrum in order to obtain the net flow and transport. Finally, it is shown that the start-up transients can have profoundly different effects depending on the phase of acceleration at the starting time.