Numerical solution of solidification in a square prism using an algebraic grid generation technique |
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Authors: | Z Dursunkaya G Odaba?? |
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Institution: | (1) Associate Professor of Mechanical Engineering, Middle East Technical University, Inonu Bulvari 06531, Ankara, Turkey,;(2) Senior Engineer, Roketsan A.Ş., Elmadağ 06780, Ankara, Turkey, |
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Abstract: | The solidification of an infinitely long square prism was analyzed numerically. A front fixing technique along with an algebraic
grid generation scheme was used, where the finite difference form of the energy equation is solved for the temperature distribution
in the solid phase and the solid–liquid interface energy balance is integrated for the new position of the moving solidification
front. Results are given for the moving solidification boundary with a circular phase change interface. An algebraic grid
generation scheme was developed for two-dimensional domains, which generates grid points separated by equal distances in the
physical domain. The current scheme also allows the implementation of a finer grid structure at desired locations in the domain.
The method is based on fitting a constant arc length mesh in the two computational directions in the physical domain. The
resulting simultaneous, nonlinear algebraic equations for the grid locations are solved using the Newton-Raphson method for
a system of equations. The approach is used in a two-dimensional solidification problem, in which the liquid phase is initially
at the melting temperature, solved by using a front-fixing approach. The difference of the current study lies in the fact
that front fixing is applied to problems, where the solid–liquid interface is curved such that the position of the interface,
when expressed in terms of one of the coordinates is a double valued function. This requires a coordinate transformation in
both coordinate directions to transform the complex physical solidification domain to a Cartesian, square computational domain.
Due to the motion of the solid–liquid interface in time, the computational grid structure is regenerated at every time step. |
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Keywords: | Two dimensional solidification Moving boundary problem Coordinate transformation Front fixing |
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