Projection method for flows with large local density gradients: Application to dendritic solidification

Abstract

SUMMARYNumerical models of solidification including a mushy zone are notoriously inefficient; most of them are based on formulations that require the coupled solution to the velocity components in the momentum equation greatly restricting the range of applicability of the models. Initial attempts at modeling directional solidification in the presence of a developing mushy zone using a projection formulation encountered difficulties once solidification starts, which were traced to the inability of the method to deal with large local density differences in the vicinity of the fluid-mush interface. A modified formulation of the projection method has been developed that maintains the coupling between the body force and the pressure gradient and is presented in this work. This formulation is shown to be robust and extremely efficient; reducing very significantly the necessary storage and the computational time required for the simulation of problems involving very large meshes when compared with previously published data. This is illustrated in this work through its application to simulations involving a Pb-Sn alloy.

Element‐free Galerkin method for thermosolutal convection and macrosegregation

“…The method has been described earlier in the context of binary alloy solidification [50]. In the present work, appropriate changes are made in the governing equations to apply it for the solidification of multicomponent alloys.…”

Modeling Freckle Segregation with Mesh Adaptation

“…u * is the intermediate velocity. Following the formulation described by Heinrich et al, [19] the momentum equation can be split into the following steps:…”

“…Westra [18] presented the use of fractional step method in the simulation of freckle defects that occur in directional solidification processes. [18] A large three-dimensional calculation performed by Heinrich et al, [19] showed evidence that significant improvement in efficiency of macrosegregation computations is possible with the use of fractional step method for the solution of the momentum equation.…”

“…Solidification models that use the fractional step or projection method for the solution of the momentum equation in binary alloy solidification problems were also developed. [16][17][18][19] This method allows the decoupled solution of velocity and pressure and leads to better computational efficiency. Westra [18] presented the use of fractional step method in the simulation of freckle defects that occur in directional solidification processes.…”

14th International Conference on Finite Elements in Flow Problems

“…The work by Heinrich et al [9] focuses on the development of a projection method for the simulation of dendritic solidification in flows where large local density gradients are present. The modified projection method used in this work preserves the pressure gradient-body force coupling.…”