The model proposed by Felicelli, Heinrich, and Poirier is used to simulate the solidification of a small two-dimensional domain of Pb-10 wt pct Sn alloy in the presence of electromagnetic stirring by different traveling fields, with or without gravity. Results show (a) enrichment of the bulk liquid by mush solute draining; (b) spontaneous formation of vertical channels, acting as ducts, significantly modified by the electromagnetic flow; and possibly (c) a finer periodic structure of subchannels. Only the last feature is sensitive to the mesh size and permeability value. Scaling analysis is used to balance Darcy, buoyancy, and electromagnetic phenomena. Attention is focused on the gradient zone at the solidification front. Electromagnetic forces can change the flow structure in the bulk liquid. In this way, they modify the pressure differences at the solidification front, changing the channel segregation pattern. Although they cannot eliminate the channels, they can control their positions and partly prevent the unsteadiness of buoyancy effects.
We deal with the prediction of electromagnetically-driven turbulent flows by means of a large-eddysimulation method (LES). The model is applied in the case of a liquid metal pool submitted to a polyphase linear electromagnetic stirrer. We investigate two cases: (i) the effects of the pulsating part of the Lorentz forces are neglected, the frequency of the applied magnetic field being high enough; (ii) the oscillating part of the electromagnetic forces is taken into account, the frequency of the magnetic field being sufficiently low. The LES predictions agree well with the mean velocity measurements, as does the standard k-e model. However, as for the turbulent kinetic energy predictions, there is a large discrepancy between the two models. When the oscillating part of the Lorentz forces is taken into account, the computations show that the fluid flow is sensitive to the unsteady part of the forces provided the frequency of the magnetic field is sufficiently low. The mean velocity is not affected by the fluctuating component of the force. As for the turbulence parameters, the presence of the pulsating part leads to a significant reduction of the turbulent kinetic energy, whilst the turbulence length scale decreases. The effect of the oscillating part of the Lorentz forces becomes negligible when the magnetic field frequency exceeds approximately 5 Hz.
During the solidification of metal alloys, chemical heterogeneities at the scale of the product develop. It is referred to as "macrosegregation". Numerical simulation tools exist in the industry. However, their predictive capabilities are not validated and are still limited. A 2D numerical benchmark is presented, based on the solidification of metallic Pb-Sn alloys. Concerning the numerical benchmark, a "minimal" common model of solidification is assumed, including columnar growth without undercooling, fixed solid, isotropic permeability of the mushy region, local thermodynamic equilibrium, lever-rule assumption for the local average composition. We focus our attention on the numerical method used to solve the average conservation equations: Finite Volume, Finite Element, Velocity-Pressure coupling treatment, scheme for convective terms, etc. At this stage of the work, we cannot exhibit a reference solution. However we draw some conclusions on the effects of the grid dependency, in particular on the location and sizes of the segregate channels. The development of both thermally and solutal driven convections in the first stage of the process (cf. low Prandtl and high Lewis numbers) and the relative independency of the convective scheme are also discussed. This presentation also have the goal to call other contributors to join this benchmark [1] in order to enrich the exercise and to reach a reference solution for this important problem in metallurgy.
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