A model for computing thermally-driven shallow flows

Abstract

In many natural disasters such as overland oil spills or lava flows, physical fluid properties as density change when considering non-homogeneous spatial and time variable distributions of the temperature. This effect is even more remarkable when these flows show a non-Newtonian behaviour due to the sensitivity of their rheological properties as viscosity or yield stress to temperature. In these cases, temperature becomes a significant variable that drives the fluid behaviour, which must be solved using an energy equation coupled with the free surface flow system. Special attention is devoted to thermal source terms which must include all the heat fluid exchanges, and their modelling sometimes can govern the complete flow behaviour. Fluid density, viscosity and yield stress, also affected by temperature, must be recomputed every time step. Summarizing, this work presents a 2D free surface flow model considering density and temperature variations, which could even modify viscosity and yield stress, with heat transfer mechanisms. The model is applied to oil spill overland simulations and heating/cooling test cases are carried out to ensure the system energy balance. As conclusions, it can be said that the numerical results demonstrate the importance of the heat exchange effects and those of the density, viscosity and yield stress variations.