Comparison of dns of compressible and incompressible turbulent droplet-laden heated channel flow with phase transition

In this paper a turbulent channel flow with dispersed droplets is examined. The dispersed phase is allowed to have phase transition, which leads to heat and mass transfer between the phases, and correspondingly modulates turbulent flow properties. As a point of reference we examine the flow of water droplets in air, containing also the vapor of water. The key element of this study concerns the treatment of the carrier phase as either a compressible or an incompressible fluid. We compare simulation results obtained with a pseudo-spectral discretization for the incompressible flow to those obtained with a finite volume approach for the compressible flow. The compressible formulation is not tailored for low Mach flow and we need to resort to a Mach number that is artificially high for simulation feasibility. We discuss differences in fluid flow, heat- and mass transfer and dispersed droplet properties. The main conclusion is that both formulations give a good general correspondence. Flow properties such as velocity fields agree very closely, while heat transfer as characterized by the Nusselt number differs by around 25%. Droplet sizes are shown to be slightly larger, particularly in the center of the channel, in case the compressible formulation is chosen. A low-Mach compressible formulation is required for a fully quantitative comparison.