Monolithic simulation of convection-coupled phase-change - verification and reproducibility

Phase interfaces in melting and solidification processes are strongly affected by the presence of convection in the liquid. One way of modeling their transient evolution is to couple an incompressible flow model to an energy balance in enthalpy formulation. Two strong nonlinearities arise, which account for the viscosity variation between phases and the latent heat of fusion at the phase interface. The resulting coupled system of PDE's can be solved by a single-domain semi-phase-field, variable viscosity, finite element method with monolithic system coupling and global Newton linearization. A robust computational model for realistic phase-change regimes furthermore requires a flexible implementation based on sophisticated mesh adaptivity. In this article, we present first steps towards implementing such a computational model into a simulation tool which we call Phaseflow. Phaseflow utilizes the finite element software FEniCS, which includes a dual-weighted residual method for goal-oriented adaptive mesh refinement. Phaseflow is an open-source, dimension-independent implementation that, upon an appropriate parameter choice, reduces to classical benchmark situations including the lid-driven cavity and the Stefan problem. We present and discuss numerical results for these, an octadecane PCM convection-coupled melting benchmark, and a preliminary 3D convection-coupled melting example, demonstrating the flexible implementation. Though being preliminary, the latter is, to our knowledge, the first published 3D result for this method. In our work, we especially emphasize reproducibility and provide an easy-to-use portable software container using Docker.Comment: 20 pages, 8 figure

Integrated modeling and validation for phase change with natural convection

Water-ice systems undergoing melting develop complex spatio-temporal interface dynamics and a non-trivial temperature field. In this contribution, we present computational aspects of a recently conducted validation study that aims at investigating the role of natural convection for cryo-interface dynamics of water-ice. We will present a fixed grid model known as the enthalpy porosity method. It is based on introducing a phase field and employs mixture theory. The resulting PDEs are solved using a finite volume discretization. The second part is devoted to experiments that have been conducted for model validation. The evolving water-ice interface is tracked based on optical images that shows both the water and the ice phase. To segment the phases, we use a binary Mumford Shah method, which yields a piece-wise constant approximation of the imaging data. Its jump set is the reconstruction of the measured phase interface. Our combined simulation and segmentation effort finally enables us to compare the modeled and measured phase interfaces continuously. We conclude with a discussion of our findings

Analytical, numerical, and experimental analysis of inverse macrosegregation during upward unidirectional solidification of Al-Cu alloys

The present work focuses on the influence of alloy solute content, melt superheat, and metal/mold heat transfer on inverse segregation during upward solidification of Al-Cu alloys. The experimental segregation profiles of Al 4.5 wt pet Cu, 6.2 wt pet Cu, and 8.1 wt pet Cu alloys are compared with theoretical predictions furnished by analytical and numerical models, with transient h(i) profiles being determined in each experiment. The analytical model is based on an analytical heat-transfer model coupled with the classical local solute redistribution equation proposed by Flemings and Nereo. The numerical model is that proposed by Voller, with some changes introduced to take into account different thermophysical properties for the liquid and solid phases, time variable metal/mold interface heat-transfer coefficient, and a variable space grid to assure the accuracy of results without raising the number of nodes. It was observed that the numerical predictions generally conform with the experimental segregation measurements and that the predicted analytical segregation, despite its simplicity, also compares favorably with the experimental scatter except for high melt superheat.35228529

The effect of impurities on the evolution of the melting front analyzed in a two-dimensional representation for the eutectic Pt–C

The paper discusses the effect of two-front melting on the liquidus temperature of the eutectic Pt–C and the eutectic temperature of the system in its pure state. This influence factor has not been considered thus far in the uncertainty budget associated with the assignment of thermodynamic temperatures to the eutectics Co–C (1597.15 K), Pt–C (2011.05 K), and Re–C (2747.35 K), selected in the European Metrology Research Programme project Implementing the New Kelvin. For Pt–C, simulation of the effect of two-front melting on the melting process has been done before in a 1D analytical model, and this formed the starting point to the present study. In this study the melting process is analyzed by means of a 2D axisymmetrical finite-volume model. In the model, freezing and melting are considered for an impure ingot and for a pure ingot. As to the impure ingot, the impurity concentrations are the concentrations met in current practice of the realization of the high-temperature reference fixed point, but formulated in terms of an effective concentration and associated effective distribution coefficient k<1, related to a Scheil fit to the melting curve at given melting conditions as measured for the eutectic Pt–C. Heat injection rates for melting varied from 15000 W·m-2 down to 3000 W·m-2. In any case for the impure system, two melting fronts are showing up. For the pure system, only one melting front is generated, traveling from the outside of the ingot toward its inside

A Dual Scale Model for Macrosegregation in Alloy Solidification

A numerical approach for coupling the temperature and concentration fields using a micro/macro dual scale model for a solidification problem is presented. The dual scale modeling framework is implemented on a hybrid explicit-implicit solidification scheme. The advantage of this model lies in more accurate consideration of microsegregation occurring at micro-scale using a subgrid model. The model is applied to the case of solidification of a Pb-40% Sn alloy in a rectangular cavity. The present simulation results are compared with the corresponding experimental results reported in the literature, showing improvement in macrosegregation predictions. Subsequently, a comparison of macrosegregation prediction between the results of the present method with those of a parameter model is performed, showing similar trends

Two-dimensional numerical model for the analysis of macrosegregation during solidification

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)This paper presents a 2D extension of a one-dimensional model proposed initially for the analysis of macrosegregation of multicomponent alloys. Some simulations were carried out to compare the performance of an explicit/implicit time integration scheme for coupling thermal-solutal fields with a fully implicit one. Simulations carried out for the analysis of a two-dimensional solidification problem has fitted the unidirectional and two-dimensional experimental data very well. (C) 2009 Elsevier B.V. All rights reserved.462358366Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAEPEX-UNICAMPFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

An explicit–implicit time stepping scheme for solidification models

A numerical scheme with hybrid explicit and implicit time stepping in solidification problems is presented. An explicit time stepping scheme is used for solving coupled temperature and concentration fields, while an implicit scheme is used for solving equations of motion.The explicit approach results in a local point-by-point coupling scheme for the temperature and concentration fields that uses constitutive model for back diffusion in solid. The present method offers distinct advantages of simplicity and flexibility in incorporation of microscale models, as demonstrated by the use of a back diffusion parameter in the microsegregation model. Results from the present method are compared with those in the literature using a fully implicit method, and they show significant improvement in final macrosegregation prediction