Simulating the Effect of Space Vehicle Environments on Directional Solidification of a Binary Alloy
Space microgravity missions are designed to provide a microgravity environment for scientific experiments, but these missions cannot provide a perfect environment, due to vibrations caused by crew activity, on-board experiments, support systems (pumps, fans, etc.), periodic orbital maneuvers, and water dumps. Therefore, it is necessary to predict the impact of these vibrations on space experiments, prior to performing them. Simulations were conducted to study the effect of the vibrations on the directional solidification of a dendritic alloy. Finite element ca!cu!attie?ls were dme with a simd2titcr based on a continuum model of dendritic solidification, using the Fractional Step Method (FSM). The FSM splits the solution of the momentum equation into two steps: the viscous intermediate step, which does not enforce continuity; and the inviscid projection step, which calculates the pressure and enforces continuity. The FSM provides significant computational benefits for predicting flows in a directionally solidified alloy, compared to other methods presently employed, because of the efficiency gains in the uncoupled solution of velocity and pressure. finite differences, arises when the interdendritic liquid reaches the eutectic temperature and concentration. When a node reaches eutectic temperature, it is assumed that the solidification of the eutectic liquid continues at constant temperature until all the eutectic is solidified. With this approach, solidification is not achieved continuously across an element; rather, the element is not considered solidified until the eutectic isotherm overtakes the top nodes. For microgravity simulations, where the convection is driven by shrinkage, it introduces large variations in the fluid velocity. When the eutectic isotherm reaches a node, all the eutectic must be solidified in a short period, causing an abrupt increase in velocity. To overcome this difficulty, we employed a scheme to numerically predict a more accurate value for the rate of change of fraction of liquid as the liquid in an element solidifies. The new method enables us to contrast results of simulations in which the alloy is subjected to no gravity or a steady-state acceleration versus simulations when the alloy is subjected to vibration disturbances; therefore, the effect of vibration disturbances can be assessed more accurately. To assess the impact of these vibration-perturbations, transient accelerometer data from a space shuttle mission are used as inputs for the simulation model. These on-orbit acceleration data were obtained from the Microgravity Science Division at Glenn Research Center (GRC- MSD) and are applied to the buoyancy term of the momentum equation in a simulation of a Pb-5.8 wt. % Sb alloy that solidifies in a thermal gradient of 4000 K/m and a translation velocity of 3 p d s . Figure 2 shows the vertical velocity of a node that begins in the all-liquid region and subsequently solidifies; the vibrations are applied at 5000 seconds in this simulation. An important difficulty, common to all solidification models based on finite elements or 2 The magnitudes of the velocity oscillations that are vibration-induced are very small and acceptable. The biggest concern is whether the concentration of the liquid near the dendrite tips is distorted because of the vibration-induced perturbations. Results for this case show no concentration oscillations present in the all-liquid region.