Parameter analysis and rapid design of porosity gradient distribution for open-cell metal foam in the latent thermal energy storage unit

The positive gradient porosity design of metal foam is used to improve the thermal performance of the vertical shell-and-tube latent thermal energy storage (LTES) unit. To optimize the gradient design, quantitative analysis is of vital importance. Therefore, the relative offset number EX is proposed in this study, which indicates the porosity difference between upper/down porosity and the mean porosity. Based on the numerical model of a shell-and-tube LTES unit filled with composite phase change material (CPCM) on the shell side, the effects of parameters, including the inlet HTF temperature and velocity, LTES dimensions, porosity, and thermal conductivity of the metal foam on the optimal gradient design are discussed. The optimal EX exhibits little relation with the inlet temperature but increases with the LTES height and thermal conductivity, while decreases with inlet velocity, porosity, and LTES outer radius. With the correlation between the optimal EX and the relative dimensionless number, the effects of these parameters on the optimal EX are integrated and quantified as experience equations so that the optimal porosity gradient of metal foam and the relative reduction melting time can be rapidly obtained under a wide variety of practical applications.