An Eulerian multiphase frost model based on heat transfer measurements

Abstract

In this paper, a laminar numerical model is developed to predict frost formation over a horizontal cold flat surface. An Eulerian-Eulerian multiphase approach is followed to model humid air and ice phases separately. Frost accumulation on the cold surface is modeled with an empirical mass source term. Model constants were tuned in a systematic way using experimental heat flux and frost thickness data. A velocity dependent model constant is introduced into the mass source term. The heat flux rise observed experimentally at the initial stages of the frosting could be captured with the use of the velocity dependent model constant and the addition of this term considerably improved the accuracy of the frost model at the initial stages of frosting. It was also observed that the selected particle diameter for the solid ice phase has a considerable effect on the velocity profile over the frost layer. This requires tuning of the velocity dependent model constant parameters according to the selected ice particle diameter. The developed numerical model was tested with three different frost thermal conductivity models. Using the thermal conductivity of solid ice for the frost thermal conductivity resulted in the most accurate prediction at the early stages of the frost growth process indicating a rather column-wise vertical growth of ice crystals with very low lateral branching. However, the overprediction of the numerical heat flux with the thermal conductivity of solid ice points out a decrease in the thermal conductivity of the newly added frost layers indicating a more pronounced lateral branching of ice crystals within the frost layer. The effect of the diffusion coefficient of the water vapor in humid air on frosting is also investigated. An artificial increase in the diffusion coefficient improved the accuracy of the heat flux prediction of the model at the initial stages of frosting which might indicate an eddy-driven enhanced mixing in the boundary layer which might not be captured in the laminar flow model. Finally, the developed numerical model is also tested on another scenario with the surface temperature held at -30 °C. Detailed analysis of the numerical simulations showed a more porous frost layer with the surface temperature at -30 °C as compared to the frost porosity formed on the surface at -20 °C.