Phase field study of the tip operating state of a freely growing dendrite against convection using a novel parallel multigrid approach

Alloy dendrite growth during solidification with coupled thermal-solute-convection fields has been studied by phase field modeling and simulation. The coupled transport equations were solved using a novel parallel-multigrid numerical approach with high computational efficiency that has enabled the investigation of dendrite growth with realistic alloy values of Lewis number ∼104 and Prandtl number ∼10−2. The detailed dendrite tip shape and character were compared with widely recognized analytical approaches to show validity, and shown to be highly dependent on undercooling, solute concentration and Lewis number. In a relatively low flow velocity regime, variations in the ratio of growth selection parameter with and without convection agreed well with theory

Determination of interfacial heat transfer coefficient and its application in high pressure die casting process

In this paper, the research progress of the interfacial heat transfer in high pressure die casting (HPDC) is reviewed. Results including determination of the interfacial heat transfer coefficient (IHTC), influence of casting thickness, process parameters and casting alloys on the IHTC are summarized and discussed. A thermal boundary condition model was developed based on the two correlations: (a) IHTC and casting solid fraction and (b) IHTC peak value and initial die surface temperature. The boundary model was then applied during the determination of the temperature field in HPDC and excellent agreement was found

Feature study of body-fitted Cartesian grids used in casting numerical simulation

A type of mesh called a body-fitted Cartesian mesh, very different from the traditional structured body-fitted mesh, is established. At first, the right parallelepiped mesh is generated, then, a feature analysis is done on the cross sections. These cross sections are the intersections of the casting shape with the right parallelepiped grids (under the Cartesian coordinate system). On the basis of the feature analysis, two sorts of body-fitted boundary grids, shape-keeping grids and shape-distortion grids, are defined. Shape-distortion grids can be removed or weaken by increasing the number of grids or moving the coordinates of the mesh generation region, so actually the body-fitted Cartesian mesh generation is to get shape-keeping grids. A shape-keeping grid mainly consists of two sorts of surfaces (I type face and II type face), and each of them is joined by two types of points (I type point and II type point). If only these two types of points were given, the shape-keeping mesh would be constructed. In this paper, the cases of the above two boundary grids being generated were discussed. An algorithm was put forward to get the shape-keeping grids. Several body-fitted Cartesian meshes generated on castings show the validity of the algorithm. The mesh generation examples show that the body-fitted Cartesian mesh is more excellent than the right parallelepiped mesh in aspects of decreasing grids number and being closer to the shape of the casting solid

Atomistic Determination of Anisotropic Surface Energy-Associated Growth Patterns of Magnesium Alloy Dendrites

Because of the existence of anisotropic surface energy with respect to the hexagonal close-packed (hcp) lattice structure, magnesium alloy dendrite prefers to grow along certain crystallographic directions and exhibits a complex growth pattern. To disclose the underlying mechanism behind the three-dimensional (3-D) growth pattern of magnesium alloy dendrite, an anisotropy function was developed in light of the spherical harmonics and experimental findings. Relevant atomistic simulations based on density functional theory were then performed to determine the anisotropic surface energy along different crystallographic directions, and the corresponding anisotropic strength was quantified via the least-square regression. Results of phase field simulations showed that the proposed anisotropy function could satisfactorily describe the 3-D growth pattern of the α-Mg dendrite observed in the experiments. Our investigations shed great insight into understanding the pattern formation of the hcp magnesium alloy dendrite at an atomic level