A numerical and analytical study of the effect of aspect ratio on the behavior of a round thermal

A round thermal is formed when an element of buoyant fluid is released instantaneously into a quiescent ambient. Although the thermal spreading rate is of primary importance to mathematical modeling, the reported values in the literature vary greatly. To identify possible factors affecting the thermal spreading rate, we investigated the effect of different initial conditions numerically by solving the unsteady Reynolds-averaged Navier-Stokes equations with a two-equation turbulence closure. The initial aspect ratio (i.e. length-to-diameter ratio) of the thermal was varied between 0.125-4.0, and the initial density differences was changed from 1 to 10 %. Results show that the spreading rate is greatly affected by the initial aspect ratio, which also explains the variations in earlier reported values. Following the numerical study, an analytical model using buoyant vortex ring theory is developed to predict the spreading rate of a thermal. The predictions show good agreement with the results from both the numerical simulations and previous experimental studies. Another simple analytical model is also presented to approximate the thermal induced flow, and is validated using the numerical simulations.