Simplified theoretical model to predict the melting time of a shell-and-tube LHTES

A theoretical model to predict the complete melting time of a Latent Heat Thermal Energy Storage (LHTES) considering a shell-and-tube configuration is presented and applied to several geometries. The shape of the device has been modified according to the internal radius (r i ), external radius (r e ) and total height (L) retaining constant the volume of the storage and the heat exchange area. The model has been validated by means of multiphase numerical simulations of the charging phase. The numerical simulations have been performed considering four configurations, with a radii ratio, r e /r i , equal to 1.5, 2, 4.375 and 6. The comparison between the model predictions and the numerical simulations confirms the reliability of the theoretical model in terms of melting time within the range investigated. The study reveals that, even considering the same storage volume, heat exchange area and wall temperature, for low values of radii ratio (r e /r i ), the shape of the device is able to reduce the charging time of the LHTES up to 50% for a radii ratio r e /r i =1.5 with respect to r e /r i =4.375. Increasing further the radii ratio from r e /r i =4.375 to 6, the melting time decreases. The unsteady numerical simulations support the prediction of the theoretical model. Thus, in the here studied geometrical configurations the proposed approach represents a simplified and accurate design tool to predict the charging time of a LHTES shell-and-tube device.