Thermal Entrainment in the Core Regions of Transitional Plane Fountains in Linearly Stratified Ambient Fluids

Abstract

Thermal entrainment is an integral feature of free-shear flows involving temperature changes, including fountains (negatively buoyant jets). The understanding of thermal entrainment is essential for applications involving thermal stratification such as that in a solar water storage tank. In this study, thermal entrainment in the core regions of transitional plane fountains in linearly-stratified ambient fluids is studied numerically over a range of the Froude number, Reynolds number, and dimensionless thermal stratification parameter. The results show that thermal entrainment has a negligible effect on the inner core region, but is significant in the outer core region, particularly at the interfaces among the upflow, downflow, and ambient fluid, and the thermal entrainment parameter, which quantifies the extent of thermal entrainment, decreases with height or in a stronger stratification, but increases with increasing Froude number or Reynolds number. Several numerical relations are obtained with the numerical results for the thermal entrainment parameter.