Thermal Convection in an Enclosure Due to Vibrations Aboard Spacecraft

Abstract

This paper discusses thermal convection in an enclosure induced by spacecraft vibrations (#-jitter). Under normal circumstances (no maneuvers, no intentional spinning of the spacecraft) the ^-jitter generates predominantly oscillatory velocity and temperature fields with zero time-mean values. The ^-jitter can also generate secondary flows with nonzero mean, but they are of much smaller order. Some implications of the g- jitter on materials processing in space are discussed. NE of the primary advantages foreseen for processing of materials in space is the reduction of natural convection associated with the Earth's gravity. However, there have been some indications (e.g., Apollo 14 experiments 1'2) that spacecraft vibrations might cause appreciable thermal con- vection. Such convection may be important in fluids ex- periments and also affect the quality of crystals grown in space. Therefore, to study the effectiveness of spacecraft vibrations in generating fluid flows, the present work theoretically investigates a case in which a fluid-filled con- tainer with differentially heated walls is subjected to spacecraft vibrations. Implications of the results for space processing are discussed. In an attempt to evaluate the effects of g-jitter on fluid motions Spradley el al. 3 made a numerical analysis for various configurations. They considered three g-jitter profiles, sinusoidal, absolute sinusoidal and saw tooth, and compared the flowfields with that for constant g level. They found that if the g-jitter is decomposed into a time mean part and an oscillatory part, the mean part is more important than the oscillatory part in determining the flowfield and heat- transfer rate. A somewhat related work has been done by Forbes4 where the effect of sinusoidal vibrations on natural convective heat transfer in a rectangular enclosure is studied experimentally as well as numerically under 1-g conditions. The results indicate that the vibrations have very little effect on the heat transfer when the flow is laminar. The present study is more comprehensive than the work by Spradley et al.,3 and is meant to give a better physical insight into the g-jitter in space. Some of the material presented herein is taken from the work by Prasad and Ostrach.5 Formulation of the Problem g-Jitter Consider an experimental setup which is in a spaceship orbiting the Earth (Fig. 1). The coordinates (X0,Y0,Z0) are fixed at the center of the Earth with origin 0 (fixed frame of reference), and the coordinates (X'f Y',Z') are attached to the spacecraft with origin 0' at its center of mass. The coor-