Unsteady numerical simulation of the cooling process of vertical storage tanks under laminar natural convection

The transient cooling of a fluid initially at rest inside a vertical cylinder submitted to heat losses through the walls is studied. The study is restricted to laminar flow conditions. In order to identify the relevant non-dimensional groups that define the unsteady natural convection phenomenon that occurs, a non-dimensional analysis is carried out. The long-term behaviour of the fluid is modelled by formulating a prediction model based on global balances. A parametric study by means of several multidimensional numerical simulations led to correlate the Nusselt number and the transient mean fluid temperature, in order to feed the global model proposed. Special attention is given to the appropriateness of the spatial and time discretisation adopted, the verification of the numerical solutions and the post-processing tasks carried out in order to obtain the correlations. The most relevant particularities of the numerical model developed are also pointed out.