Model Discussion of Transpiration Cooling with Boiling

The two-phase mixture model has been widely used to describe the performances of fluid flow and heat transfer within porous media with liquid phase change. However, this model was based on two important assumptions: the temperature is constant (T-f = const) in two phase region, while fluid temperature is locally equal to the solid matrix temperature (T-s = T-f). These assumptions result in an inveracious numerical phenomenon, i.e.,: a thermal insulating layer within the porous matrix in numerical simulations. This numerical phenomenon is not real, because the solid matrix is made of thermal conductive material. To modify the mathematical model of the transpiration cooling problem with boiling, this paper presents an improved model, which is based on that the Gibbs free energy of liquid phase and vapor phase are equal in two-phase region. Temperature variation in two-phase region is considered, and fluid temperature is locally different from the solid matrix temperature (T-s not equal T-f), therefore the local heat transfer through the convection between solid and fluid is considered as well. Numerical calculations of the transpiration cooling problem with boiling are carried out with the improved model. The numerical results such as the variations of temperatures of fluid and solid, the saturation and pressure of fluid within porous media, are reasonable, and the inveracious issue of the thermal insulating layer is successfully resolved.