FVM

The Aim of this paper is to investigate numerically the simulation of ice melting in one and two dimension using the cell-centered finite volume method. The mathematical model is based on the heat conduction equation associated with a fixed grid, latent heat source approach. The fully implicit time scheme is selected to represent the time discretization. The ice conductivity is chosen to be the value of the approximated conductivity at the interface between adjacent ice and water control volumes. The predicted temperature distribution, percentage melt fraction, interface location and its velocity is compared with those obtained from the exact analytical solution. A good agreement is obtained when comparing the numerical results of one dimensional temperature distribution with the analytical results.

The Weighted-Sum-of-Gray-Gases (WSGG) model is used to investigate radiative heat transfer in non- gray media. The finite volume method (FVM) is used to solve the radiative transfer equation. Validations with benchmarks show satisfactory results when coupling the WSGG model to the FVM. A scattering analysis is then presented where the effects of the scattering albedo and the phase function are studied. Finally, the WSGG model is applied to a gas turbine combustion simulator (GTCS) for prediction of the incident wall radiative heat flux. Comparison of the experimental measurements with the non-gray WSGG numerical results shows satisfactory agreement of the wall radiative heat flux.