A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems—I. Model formulation

A new approach to the modelling of grain structure formation in solidification processes is proposed. Based upon a two-dimensional cellular automata technique, the model includes the mechanisms of heterogeneous nucleation and of grain growth. Nucleation occurring at the mould wall as well as in the liquid metal are treated by using two distributions of nucleation sites. The location and the crystallographic orientation of the grains are chosen randomly among a large number of cells and a certain number of orientation classes, respectively. The growth kinetics of the dendrite tip and the preferential 〈100〉 growth directions of cubic metals are taken into account. The model is then applied to small specimens of uniform temperature. The columnar-to-equiaxed transition, the selection and extension of columnar grains which occur in the columnar zone and the impingement of equiaxed grains are clearly shown by this technique. The calculated effect of the alloy concentration and cooling rate upon the resultant microstructure agree with experimental observations.

Probabilistic modelling of microstructure formation in solidification processes

A basic model of the transport phenomena occurring during solidification of multicomponent mixtures is presented. The model is based on a two-phase approach, in which each phase is treated separately and interactions between the phases are considered explicitly. The macroscopic transport equations for each phase are derived using the technique of volumetric averaging. The basic forms of the constitutive relations are developed. These relations link the macroscopic transport phenomena to microscopic processes such as microstructure development, interfacial stresses, and interfacial heat and mass transfer. Thermodynamic relations are presented, and it is shown that nonequilibrium effects can be addressed within the framework of the present model. Various simplifications of the model are examined, and future modeling needs are discussed.

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A volume-averaged two-phase model for transport phenomena during solidification

Modelling of heat flow has become a standard practice in many solidification processes. Effort is currently being made to couple heat flow calculations to related macroscopic phenomena such as mould filling, fluid flow, macrosegregation, or thermal stresses. If these macroscopic aspects are important in predicting formation of macroscopic defects or optimising process conditions, then microstructural features such as phase appearance, morphology, grain size, spacings, or microdefects are certainly no less important in determining the ultimate mechanical properties of the solidified product. The aim of the present paper is to introduce the basic concepts of macroscopic and microscopic phenomena which enter normally into any solidification process. At the macroscopic level, i.e. at the scale of the whole process (casting, weldment, … ), the latest developments in numerical techniques which are used to solve the continuity equations are briefly presented together with the advantages and inconvenience...

Modelling of microstructure formation in solidification processes

The modelling of heat, mass and solute transport in solidification systems

A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems. II: Application to solidification in a rectangular cavity

A widely accepted numerical finite-difference scheme for the solution of coupled elliptic partial differential equations has been extended to accommodate binary solid-liquid phase change. Through the adoption of a recently developed continuum model, the solution of the multiconstituent, multiphase problem has been reduced to a level of computational requirements generally associated with strongly coupled single-phase problems. Example calculations have been performed to illustrate use of the model for static phase change systems, as well as to illustrate the significance of bulk and mushy region fluid motion for macroscopic phase change behavior.

W.D. Bennon

Papers

A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems—I. Model formulation

A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems. II: Application to solidification in a rectangular cavity

Numerical analysis of binary solid-liquid phase change using a continuum model

Solidification of an aqueous ammonium chloride solution in a rectangular cavity—II. Comparison of predicted and measured results