Application of Dual-Grid Level Set Method Based in-house code for Simulation of Casting Process: Filling and Solidification

Abstract

Casting is a paramount process which is practiced since centuries for manufacturing of automobile parts, locomotives, turbine shafts, foundations, machinery, heavy equipment, antiques, artistic objects etc. Due to its diversified industrial application, the importance of this particular manufacturing process will always remain intact. Majority of the components cast every year are complex in nature. Many of the Indian Foundry Industries are focusing in to the development of ‘Smart Casting’ process wherein the design of the mold box as well as the gating system is optimized with the application of Computational Multi-Fluid Dynamics in order to obtain defect free cast products. Present study mainly focuses on modifying the developed in-house code of 2-D, Dual Grid Diffused Interface Level Set method, developed at CFDHT Lab, I.I.T. Bombay and applying it to the Casting and Solidification process in order to identify the location of the Hot Spot formations, evaluate Feed Paths and defects like shrinkage cavity, porosity and miss-run. After literature study it is found that solidification process is not only governed by the thermal conduction but natural convection due to gravity as well as the residual flow developed from the incoming molten metal also have a strong impact on the same. Over and above, in casting, various intricate and complicated geometries are encountered and it becomes difficult to generate the grid for such shapes using the present code as it has capability of generating a uniform Cartesian Grid. A novel approach of Ghost Boundary Method is proposed and demonstrated to handle the intricate shapes. In this approach any required domain is modeled computationally with its maximum dimension in both, x and y direction and a uniform Cartesian Grid is generated. Certain grid points are then assigned zero values wherein no solution is required and are blanked. The boundary conditions are treated and are applied to intermediate cells in a manner such that it can easily depict the physical wall boundary present in the actual part. The major limitation found in the Ghost Boundary Method is that it can be implemented only for geometries having straight edges (either horizontal or vertical). The geometries having inclined edges or curved edges cannot be handled. Hence another technique, widely known as “Immersed Boundary Method” is implemented in the present code with the Cut-Cell approach to handle all sorts of geometries having inclined or curved edges. The concept of using Multi-Level Set function is established for the first time where in the Level Set function one (two) is used to bifurcate between two fluids and Level Set function two (one) is used to bifurcate between the fluid domain and solid domain where no governing equations are to be solved. The method to calculate modified, cell volumes, cell areas, cell node distances, advection flux and diffusion flux for the Cut Cell is explained in the corresponding sections. For simulating the entire casting process, a module by module approach in the development is adopted which includes individual modeling of filling and solidification process respectively. For simulating filling process, the continuity, momentum, and Level Set equation is solved assuming no heat transfer and the results are validated with the standard experimental and numerical Benchmark results of the filling geometry of J. Campbell as well with few other geometries in terms of filling time and interface contours. The results obtained are in acceptable range using Ghost Boundary and Immersed Boundary Method. The solidification process is modeled by adding the Boussinesq approximation to account for the natural circulation, in the Navier Stokes equation as a source term. The sharp jump boundary condition is applied for evaluating the temperature in energy equation. Only single Level Set function is solved here rather than two with proper implementation of the Interfacial boundary condition as the Navier Stokes equation is solved in the fluid domain. The results are validated with the experimental and numerical results of unidirectional solidification of Tin in terms of interface location, temperature contours, streamlines and vector plot with respect to time. After developing the individual module, the coupling of both the codes is done in order to analyze the effect of filling process in terms of residual flow over the solidification process, which is the actual case in real casting process. In depth analysis is shown in terms of impact of residual flow and its direction on the solidification process and interface advection at different Grashoff's to Reynaldo number ratio. Simulations are performed in order to identify a critical Grashoff's to Reynolds number ratio beyond which the phenomena replicates the results in terms of planar interface advection (as in case of solving pure diffusion).