A new approach to front tracking on a fixed grid in solidification problems
Abstract
This work presents a method for solving phase change problems featuring a moving boundary through explicit interface tracking that involves the reconstruction and advection of a moving interface on a fixed grid. The method consists of three distinct steps: interface reconstruction and advection (tracking), calculation of normal velocities, and the solution of the governing equations for different phases. Details of the approach and algorithms and their implementation are discussed. Several two-dimensional transient solidification problems are chosen as benchmark problems here. Front tracking in a simulated melting problem using the present approach is compared to the exact solution as a first verification. Then, conduction-driven solidification of pure aluminum under several different growth conditions is demonstrated with both one set and two sets of marker points. Convection effects in the liquid domain for the solidification problem are also incorporated into the model. Natural convection effects are driven by buoyancy forces, which comprises the Boussinesq approximation for the creation of momentum from density changes caused by thermal gradients. Two other problems (solidification of pure tin and horizontal Bridgman crystal growth of succinonitrile) are considered and compared to numerical results and experimental data in the literature to support the accuracy and applicability of the numerical techniques developed. The new method couples Lagrangian and Eulerian methods for the interface tracking and provides a flexible and general computational approach for solving moving boundary problems. The algorithm can be extended to three-dimensional problems as well. As an extension to this work, alloy solidification problems are being addressed, with the inclusion of a concentration solver into the model.
Degree
Ph.D.
Advisors
Garimella, Purdue University.
Subject Area
Mechanical engineering
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