Heat and mass transfer in turbulent multiphase channel flow

Abstract

Direct numerical simulation is used to assess the importance of compressibility in turbulent channel flow of a mixture of air and water vapor with dispersed water droplets. The dispersed phase is allowed to undergo phase transition, which leads to heat and mass transfer between the phases. We compare simulation results obtained with an incompressible formulation with those obtained for compressible flow at various low values of Mach number. Results for flow properties obtained with the compressible model converge quickly to the incompressible results in case the Mach number is reduced. In contrast, thermal properties such as the Nusselt number, display a systematic difference between the two formulations on the order of 15%, even in the low-Mach limit. Second, a new efficient numerical algorithm for droplet-laden turbulent channel flow at low Mach numbers is proposed. In order to avoid very small time steps at low Mach numbers that would arise from stability requirements associated with explicit time-stepping we propose a new semi-explicit time integration method. We perform a perturbation analysis in powers of the Mach number of the system of governing equations. An important feature of the new numerical approach is the independence of the maximum allowed time step on the Mach number. We validate the new method by comparing it with a fully explicit code for compressible flow at general Mach numbers showing a good agreement in all quantities of interest. Finally, we consider turbulent droplet-laden channel flow with phase transition in the presence of gravity in the wall-normal direction and a thin film of water at the bottom wall. We maintain the film thickness constant by draining water from the bottom wall to compensate for (a) the droplets that fall onto the film and (b) evaporation/condensation. We also maintain on average the total mass of water in the channel by inserting new droplets at the top wall to compensate for the water that has been drained from the bottom wall. We analyze the behavior of the statistically averaged gas and droplet quantities focusing on the heat exchange between the two phases.