On the mesoscopic Eulerian formalism for the simulation of non-isothermal dilute turbulent two-phase flows

We address the numerical simulation of particle-laden turbulent flows in the dilute regime, i.e., when the volume fraction of the dispersed phase is small. However, because of the potentially large density difference between the two phases, the dispersed phase may be significantly inertial and not exactly follow the carrier. For a dilute two-phase flow (typically a cloud of droplets or solid particles in a turbulent gaseous flow), there are at least two effects of inertia: (1) Preferential concentration can result in steep gradients in the number density of particules and (2) Because inertial particles have a large ‘memory’ time scale, two particles that are very close can have drastically different properties, i.e., velocity, size and temperature. These peculiar characteristics call for specific modeling strategies and raise additional problems for the numerical simulation of dilute two-phase flows. A series of test cases are presented to evaluate the performance and robustness of two numerical strategies, in particular one called the PSI scheme that ensures the positiveness of the number density. Then a particle-laden turbulent planar jet is computed to evaluate the importance of the uncorrelated heat flux in the mesoscopic formalism.