Transition from gravity- to inertia-dominated behavior computed for the turbulent stably-stratified filling of an open enclosure

This paper treats the unsteady mixed convection processes occurring during the stably-stratified bottom filling of an open enclosure with application to stratified thermal storage devices. Central to the performance of these devices is the extent of thermal mixing which occurs at the interface between the hot and cold fluid volumes as one or the other is displaced from the vessel. Useful volume fraction, a parameter reflecting the temperature limited usefulness of the stored fluid, and internal entropy generation are used to characterize the extent of thermodynamic losses in time and their variation with flow rates ranging from well-stratified to highly-mixed conditions. The transition to highly-mixed behavior is critically important since it limits the achievable energy discharge rates. Distinct trends in the variation of cumulative performance with Reynolds number indicate this transition occurs at Froude numbers of approximately one and lead to identification of a gravity-dominated and an inertia-dominated regime. In the gravity-dominated regime, the useful volume fraction increases linearly with time after an initial adjustment period and the turbulent diffusivity affects the variation of entropy generation only at the edges of the relatively distinct thermocline. Within the thermocline, the turbulent kinetic energy is completely damped by gravity. However, in the inertia-dominated or highly-mixed regime, the useful volume fraction starts to drop in the later stages of the filling process and appreciable entropy generation levels are distributed across a relatively wide thermocline with turbulent diffusivity playing a significant role throughout.