This paper describes a numerical study of the g-jitter driven double diffusive convective flows, thermal and concentration distributions in binary alloy melt systems subject to an external magnetic field.The study is based on the finite element solution of transient magnetohydrodynamic equations governing the momentum, thermal and solutal transport in the melt pool. Numerical simulations are conducted using the synthesized single-and multifrequency g-jitter as well as the real g-jitter data taken during space flights with or without an applied magnetic field. It is found that for the conditions studied, the main melt flow follows approximately a lineal-superposition of velocity components induced by individual g-jitter components, regardless of whether a magnetic field exists or not. The flow field is characterized by a recirculating double diffusive convection loop oscillating in time with a defined frequency equal to that of the driving g-jitter force. An applied magnetic field has little effect on the oscillating recirculating pattern, except around the iiioiiient in time when the flow reverses its direction. The field has no eflect on the oscillation period, but it changes the phase angle. It is very effective in snppressing the flow intensity and produces a notable reduction of the solutal striation and time fluctuations in the melt. For a given magnetic field strength, the magnetic damping effect is more pronounced on the velocity associated with the largest g-jitter component present and/or the g-jitter spiking peaks. A stronger magnetic field is more effective in suppressing the melt convection and also is more helpful in bringing the convection in phase with the g-jitter driving force. The applied field is particularly useful in suppressing the effect of real g-jitter spikes on both flow and solutal distributions. With appropriately selected magnetic fields, the convective flows caused by g-jitter can be reduced sufficiently and diffusion dominant.solutal transport in the melt is possible.
SUMMARYThis paper presents a discontinuous Galerkin finite element computational methodology for solving the coupled phase-field and heat diffusion equations to predict the microstructure evolution during solidification. The phase-field modelling of microstructure formation is briefly discussed. The discontinuous Galerkin finite element formulation for the phase-field model systems for solidification microstructure formation is described in detail. Numerical stability is performed using the Neumann method. The accuracy of the discontinuous model is verified by the analytic solution of a simple 1-D solidification problem. Numerical calculations using the discontinuous finite element phase-field model have been performed for simulating the complex 2-D and 3-D dendrite structures formed in supercooled melts and the results are compared well with those in literature using the finite difference methods. Parallel computing algorithm is presented and results show that the minimization of the intercommunication between microprocessors is the key to increase the effectiveness in parallel computing with the discontinuous finite element phase-field model for solidification microstructure formation.
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