Four-equation turbulence model for prediction of 2-dimensional unsteady thermal discharge into a reservoir

Abstract

Computational 4-equation turbulence model is described here for prediction of 2-dimensional unsteady heated surface jet into a reservoir. Turbulent stresses and heat fluxes in the momentum and energy equations are determined from transport equations for the turbulent kinetic energy (k), isotropic rate of kinetic energy dissipation ($\varepsilon$), mean square temperature variance ($\overline{\theta^2}$), and rate of destruction of the temperature variance ($\varepsilon_e$). Computational results by 4-equation model are favorably compared with those obtained by 2- and 3-equation models. Added advantage of the 4-equation model is that it yields quantitative information about the ratio between the velocity time scale and the thermal time scale. Predicted time scale ratio is within experimental observations by others. Although the mean velocity and temperature fields are similarly predicted by three different models, second order quantities are more realistically evaluated by the 4-equation model.