Simulation of a macrosegregation benchmark in a cylindrical coordinate system with a meshless method

Abstract

The main objective of the present paper is to define a new benchmark test for macrosegregation in axisymmetry and to verify a novel meshless method on it. The test case represents a solidification of Al4.5wt%Cu alloy in two different types of geometries, a solid and a hollow cylinder, cooled at the vertical boundaries. The volume averaging method is used to formulate the coupled mass, energy, momentum, and species transport equations for solid-liquid flow. The lever rule is used for determination of liquid and solid fraction. The meshless numerical approach, verified in this paper, is called the diffuse approximate method. The method is formed by using the weighted least squares approximation, where the second-order polynomial basis and Gaussians are used as trial and weight functions, respectively. The method is localised with the use of subdomains, each containing thirteen computational nodes. The explicit Euler scheme is used to perform the temporal integration. The fractional step method is used to couple the pressurevelocity fields. The stability of the method is attained by an adaptive shift of the computational node and Gaussian weight in the upstream direction. Results are presented for three geometrically different simulations. The results are compared with the classical finite volume method. All results show a very good agreement with the finite volume method. The simulations

Multi-Physics and Multi-Scale Meshless Simulation System for Direct-Chill Casting of Aluminium Alloys

“…Two different types of meshless approaches are used in this multi-scale system. The meshless diffuse approximate method (DAM) [16] to [19] is used for solving the thermofluid and the EMF model while the local radial basis function collocation method (LRBFCM) [20] to [23] is used for solving the thermomechanical model. Both methods are local, which means that local neighbourhoods are used to evaluate either approximation (DAM) or collocation (LRBFCM).…”

“…Both methods are local, which means that local neighbourhoods are used to evaluate either approximation (DAM) or collocation (LRBFCM). The details of the numerical implementation with meshless methods are given in the related publications [19] to [23].…”

“…In the first stage the conservation equations and the Poisson equation are solved in the cylindrical coordinate system for axial symmetry in case of round billets. Here the spatial discretization is performed with the local meshless diffuse approximate method [10] and [19] and the time stepping is performed with the explicit-Euler scheme. The liquid velocity, the volume-averaged enthalpy, and the volume-averaged species at the new time step are obtained in this stage.…”

“…The verification of the simulation system has been done by a spectrum of solidification related benchmark tests of which several have been originally proposed by our group [10] and [19].…”

Channel segregation during columnar solidification: Relation between mushy zone instability and mush permeability

“…Defects in casting processes depend critically on the permeability associated with the mushy zone that influences the interdendritic liquid flow [1]. Fluid flow in the mushy zone causes macrosegregation in the castings by redistributing the segregated solute elements [2][3][4][5][6][7][8][9][10] and in some cases, also forms channel segregates [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. The mushy zone is represented as a saturated porous medium with varying permeability [20][21][22][23].…”