Simplified prediction model of the discharging time of a shell-and-tube LHTES

We present a simplified theoretical model able to predict the discharging performance of a shell-and-tube latent heat thermal energy storage. The model is validated against two-dimensional axi-symmetric numerical simulations. Here, the heat exchange area, A, the whole PCM volume, V, and the heat exchange wall temperature have been kept constant. According to these constraints, the shell-and-tube shape depends on just one geometrical parameter. Thus, six values of the ratio between the external and internal radius of the PCM module, re/ri, in the range between 2 and 6, are considered. The simplified model matches the discharging time predicted by the numerical simulations. Details of the sensible and the latent heat contribution to the discharging time is provided with respect to the radius ratio. Hence, the latent heat contribution represents about the 70% of the overall discharging time in the range 2⩽re/ri⩽6. The results reveal a scaling law between the Fourier number related to the complete solidification and the radius ratio, Fo∝(re/ri)-5.5, supported by the numerical simulations. Moreover, the rescaled dimensionless time, Fo/(re/ri)-5.5, leads to the self-similar behaviour of the liquid fraction βl time series for all the geometries here investigated. Thus, it represents a promising prediction tool for the design of latent heat thermal energy storage in shell-and-tube configuration.