After a brief review of current source-based methods for modeling solidification phase change systems, a new source-based method for the treatment of latent heat evolution is presented. The essential feature of the proposed method is linearization of the discretized source term. This results in a robust and accurate computational method that can deal efficiently with a wide range of latent heat evolution mechanisms (i.e., liquid fraction temperature relationships). The proposed method is illustrated on application to a test problem in which various liquid fraction temperature relationships are employed.

Eral source-based method for solidification phase change

SUMMARY The aim of this paper is to categorize the major fixed grid formulations and solution methods for conduction controlled phase change problems. Using a two phase model of. a solid/liquid phase change, the basic enthalpy equation is derived. Starting from this equation, a number of alternative formulations are obtained. All the formulations are reduced to a standard form. From this standard form, finite element and finite volume discretizations are developed. These discretizations are used as the basis for a number of fixed grid numerical solution techniques for solidification phase change systems. In particular, various apparent capacity and source based enthalpy methods are explored.

Fixed grid techniques for phase change problems: A review

The major methods of mathematical modelling of solidification and melting problems are reviewed in this paper. Different analytical methods, nowadays still used as standard references to validate numerical models, are presented. Various mathematical formulations to numerically solve solidification and melting problems are categorized. Relative merits and disadvantages of each formulation are analysed. Recent advances in modelling solidification and melting problems associated with convective motion of liquid phase are discussed. Based on this comprehensive survey, basic guidelines are outlined to choose a correct mathematical formulation for solving solidification and melting problems.

https://iopscience.iop.org/article/10.1088/0965-0393/4/4/004/pdf

Mathematical modelling of solidification and melting: a review

Deposition of tin droplets on a steel plate: simulations and experiments

Thermal energy storage (TES) has the capability to absorb, store and release heat based on dynamic surrounding environmental conditions. Sensible energy storage captures or releases heat with changes in material’s temperature while latent heat is associated with a phase change at an isotherm or near isothermal temperature. Latent heat storage such as using a phase change material (PCM) gains growing attentions recently due to its ability of storing significant thermal energy within a small volume, making it one of most promising technologies for developing energy efficient buildings. To quantify their technical and economic feasibility for building’s applications, computational models of TES that can be integrated into whole building energy simulations are highly demanded. This paper reviews the different modeling methods generally used for PCM simulations. A few numerical modeling methods are observed in literature for modeling PCMs including the enthalpy method, the heat capacity method, the temperature transforming model, and the heat source method. The study compares and highlights the advantages, disadvantages and limitations of these models and methods. It particularly explores the viability of these methods for building applications. The paper further reviews the PCM models that have been integrated into prevalent whole building simulation programs such as EnergyPlus, TRNSYS, ESP-r etc. The study reveals that the heat capacity method is mostly used in programs, despite of its limitations on time and spatial resolutions. Further research is found necessary to identify the efficiency and accuracy of these methods in building applications.

Modeling phase change materials embedded in building enclosure: A review

An extensive amount of work has been published on the treatment of heat transfer associated with phase change. A few recent advances are discussed in this paper with some emphasis on the phase change of metals. The apparent capacity, effective capacity, enthalpy, post iterative, source based and semi-analytical methods are discussed and relative advantages and disadvantages of each are analysed. Recent developments in nodelling the flow during pouring and natural convection with applications of two widely used convective liffusive codes, the Los Alamos MAC and the Imperial College TEACH, are presented. An alternative tream function–vorticity approach is also discussed. Applications of these methods to turbulent convection during mould filling and continuous casting are presented. Areas of interest for further research work are identified as modelling of turbulence in liquid metals, flow through mushy regions and improvement of the performance of weak methods in multidimensional problems when the ratio of latent heat to sensible heat is large.

Z. Abdullah

Papers

On the numerical modelling of heat transfer during solidification processes