Finite volume simulation framework for die casting with uncertainty quantification

Abstract

The present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due to natural convection are modeled. Empirical relations are used to estimate the microstructure parameters and mechanical properties. The fractional step algorithm is modified to deal with the numerical aspects of solidification by suitably altering the coefficients in the discretized equation to simulate selectively only in the liquid and mushy zones. This brings significant computational speed up as the simulation proceeds. Complex domains are represented by unstructured hexahedral elements. The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence. State of the art uncertainty quantification technique is included in the framework to incorporate the effects of stochastic variations in the input parameters. Rigorous validation is presented using published 1 Corresponding Author

Uncertainty quantification in three dimensional natural convection using polynomial chaos expansion and deep neural networks

“…The governing equations (1-3) are solved using the software OpenCast [37] with finite volume method on a collocated grid. The fractional step method [38] is used to integrate the equations.…”

Optimization of solidification in die casting using numerical simulations and machine learning

“…(5) to (7) are solved to get the final grain size. Equations (1) to (7) are solved numerically using the software OpenCast [15] with a finite volume method on a collocated grid. The variations of thermal conductivity, density and specific heat due to temperature are taken into account.…”

“…In our work, we have first generated a tetrahedral mesh using GMSH [20] and then divided into a hexahedral mesh using TETHEX [21]. The details of the numerical algorithm and verification and validation of OpenCast are discussed in previous publications [15,22]. A model geometry representing a clamp [15] has been considered to illustrate the methodology.…”

“…In die casting, there is a lot of stochastic variation in the wall and initial temperatures. Shahane et al [15] have performed parameter uncertainty propagation and global sensitivity analysis and found that the die casting outputs are sensitive to the input uncertainty. Thus, from a practical point of view, it is sensible to choose a Pareto optimal design which is least sensitive to the inputs.…”

“…In this paper, we consider the heat transfer and solidification processes in die casting of a complex model geometry. The computer program [15] solves the fluid flow and energy equations, coupled with the solid fraction-temperature relation, using a finite volume numerical method. When not significant, natural convection flow is neglected and only the energy equation is solved.…”