A Numerical Investigation of Transpiration Cooling with Liquid Coolant Phase Change

Abstract

This article presents a numerical approach to investigate the transpiration cooling problems with coolant phase change within porous matrix. A new model is based on the coupling of the two-phase mixture model (TPMM) with the local thermal nonequilibrium (LTNE), and used to describe the liquid coolant phase change and heat exchange processes in this article. The effects of thermal conductivity, porosity, and sphere diameter of the porous matrix on the temperature and saturation distributions within the matrix are studied. The results indicate that an increase in the porosity or sphere diameter can lead to an area dilation of two-phase region and a rise of liquid temperature; whereas an increase in the thermal conductivity of the porous matrix results only in a rise of liquid temperature, but drops of solid temperature and temperature gradient on the hot surface. The influence of hot surface pressure on cooling effect is discussed by numerical simulations, and numerical results show that the effect of the transpiration cooling will be worse under higher pressure. The investigation also discovers an inverse phenomenon to the past investigations on the transpiration cooling without coolant phase change, namely in two-phase region, coolant temperature may be higher than solid temperature. This inversion can be captured only by the new LTNE-TPMM.

Numerical simulation of complete liquid–vapour phase change process inside porous media using smoothing of diffusion coefficient

“…Several other researchers [30e36], on the other hand, used the second modification from Wang [28] for the simulation of phase change processes under different flow conditions. More recently, Shi and Wang [37] presented a thermal non-equilibrium model, based mainly on the formulation of Wang [28]. However, to the best of present authors' knowledge, other than the investigations of Wang [28] and Shi and Wang [37], there is no study that dealt with the phase change process from a sub-cooled liquid state to the superheated vapour state inside a porous medium, where the phase change takes place [28] dealt with a two dimensional problem with localised heater using the thermal equilibrium model, Shi and Wang [37] obtained results with one-dimensional formulation under thermal non-equilibrium condition.…”

“…More recently, Shi and Wang [37] presented a thermal non-equilibrium model, based mainly on the formulation of Wang [28]. However, to the best of present authors' knowledge, other than the investigations of Wang [28] and Shi and Wang [37], there is no study that dealt with the phase change process from a sub-cooled liquid state to the superheated vapour state inside a porous medium, where the phase change takes place [28] dealt with a two dimensional problem with localised heater using the thermal equilibrium model, Shi and Wang [37] obtained results with one-dimensional formulation under thermal non-equilibrium condition. However, a careful examination of results, presented by Wang [28] for steel and glass beads, shows the occurrence of temperature differences in the range of 100 C to 500 C within a very short distance in the vapour phase.…”

“…Wang [28] identified this zone as the dry-out region although its existence could not be experimentally substantiated since they were carried out only for phase change from the sub-cooled liquid to the two-phase condition. In the thermal non-equilibrium model of Shi and Wang [37], owing to the presence of volumetric heat exchange term, uniformity of temperature could be better ensured. 3 Nevertheless, they also observed a very high temperature change within a very short distance in the vapour phase.…”

Simulation of complete liquid–vapour phase change process inside porous evaporator using local thermal non-equilibrium model

“…According to the best of the present authors' knowledge, only Wang [8] and Shi and Wang [20] numerically investigated the complete phase change assuming the process occurring at a constant (i.e., fixed) saturation temperature. 2 While Wang [8] presented results for the phase change due to localised heat source in a two-dimensional channel using LTE model, Shi and Wang [20] extended the numerical simulations for one-dimensional problem adopting LTNE model.…”

“…According to the best of the present authors' knowledge, only Wang [8] and Shi and Wang [20] numerically investigated the complete phase change assuming the process occurring at a constant (i.e., fixed) saturation temperature. 2 While Wang [8] presented results for the phase change due to localised heat source in a two-dimensional channel using LTE model, Shi and Wang [20] extended the numerical simulations for one-dimensional problem adopting LTNE model. Nevertheless, in both these studies, although Nomenclature a s specific surface of the porous medium, 1/m A c cross-sectional area of the pipe per unit radian ¼R 2 /2, m 2 b body force per unit mass, m/s 2 b normalized body force per unit mass ¼b/g C p specific heat, J/kgK d p characteristic pore size of porous matrix, m D capillary diffusion coefficient, m 2 /s f hindrance function Fr…”