Internal Entropy Generation Limits for Direct Sensible Thermal Storage

This paper presents results for the entropy generated internally during the charging and discharging processes of a direct, sensible thermal energy store. The two processes correspond to the inflow of either a low or high temperature liquid stream into an enclosure initially filled with a uniformly high or low temperature liquid, respectively. The level of internal entropy generation due to thermal mixing between the inflow and the initial liquid volume corresponds to losses in the usable fraction of the stored volume and therefore decreased efficiency. Empirically, the observed behavior of direct sensible storage devices spans the range of nearly mixed to highly stratified. In the present work, analytical models for the fully-mixed and ideally-stratified limits are used to bound these behaviors and to analytically determine the corresponding entropy generation levels. The ratio of total entropy generation for the ideally-stratified limit relative to that of the fully-mixed limit is shown to vary as $8/πPe.$ The limiting behaviors therefore define a continuum of entropy generation levels separated by up to several orders of magnitude for typical Peclet numbers. A published numerical model which accounts for aspects of the observed thermal mixing is then examined in relation to these limits. The model predicts entropy generation levels midway between the limiting behaviors which suggests significant potential for improvements in the efficiency of direct sensible storage devices.