diff --git a/src/fvOptions/sources/derived/solidificationMeltingSource/solidificationMeltingSource.H b/src/fvOptions/sources/derived/solidificationMeltingSource/solidificationMeltingSource.H index 441ee1a08..7b3b0f400 100644 --- a/src/fvOptions/sources/derived/solidificationMeltingSource/solidificationMeltingSource.H +++ b/src/fvOptions/sources/derived/solidificationMeltingSource/solidificationMeltingSource.H @@ -31,10 +31,28 @@ Description The isotherm phase change occurs at the melting temperature, \c Tsol (= \c Tliq). The not isotherm phase change occurs between solidus and liquidus temperature, \c Tsol < \c Tliq respectively, as long as the melt fraction is - greater than the max eutectic melt fraction, \c alpha1e (0 = - pure_substance, 1 = eutectic_mixture is not permitted) , i.e. eutectic to - initial solvent concentration difference, where a linear eutectic melt - fraction to temperature relation is considered - lever rule. + greater than the max eutectic melt fraction, \c alpha1e (0 = pure_substance, + 1 = eutectic_mixture is not permitted), where a linear eutectic melt + fraction to temperature relation is considered; e.g. given a specific + quantity of a binary system, \c alpha1 is its melt fraction and \c alpha0 is + its solid fraction, such that \c alpha0 = 1 - \c alpha1 therefore, assuming + infinite solute diffusion, the quantity of a component in solid phase is (1 + - \c alpha1) * \c CS where \c CS is the solid concentration of the + considered component and the quantity of a component in liquid phase is \c + alpha1 * \c CL where \c CL is the melt concentration of the considered + component; considering that the total quantity of a component must be equal + to the sum of the quantities of the considered component in the liquid and + solid phases, if \c C0 is the initial concentration of the considered + component before the phase change, then: + \c C0 = (1 - \c alpha1) * \c CS + \c alpha1 * \c CL (lever rule) + from which: \c alpha1 = (\c C0 - \c CS) / (\c CL - \c CS) + and thus: + - for a miscible binary system \c alpha1e = 0; + - for a binary system not miscible at solid state + \c alpha1e = \c C0 / \c CLE where \c CLE is eutectic melt concentration; + - for a binary system partially-miscible at solid state + \c alpha1e = (\c C0 - \c CSE) / (\c CLE - \c CSE) where CSE is eutectic + solid concentration of the relative solid solution. The presence of the solid phase in the flow field is incorporated into the model as a momentum porosity contribution; the energy associated with the