The Prediction of Velocity and Temperature Profiles in Gravity Currents for Use in Chilled Water Storage Tanks

It has been demonstrated that one way of producing thin thermoclines (temperature gradients) in a chilled water storage tank is by introducing the water horizontally in the form of a gravity current. A gravity current is a fluid intrusion into a body of stagnant fluid at a different density. The incoming fluid is introduced at the bottom of the body of fluid if it is more dense; it is introduced at the top if it is less dense. In the application considered here, chilled water is to be stored in an efficient manner under the original body of warmer water. Vertical profiles of velocity and temperature in transient, two-dimensional, laminar, thermally driven, constant inflow gravity currents are studied. This provides a basis for understanding the initial stages of the formation of a thermocline in a chilled water storage tank. Two laminar flow formulations were developed to predict velocity and temperature profiles in the inertia-buoyancy regime. One formulation uses a strictly numerical approach, while the other uses a singular perturbation method to analyze the flow. Experimental temperature profiles are compared with the results from both formulations, and show good agreement.