Water droplet condensation and evaporation in turbulent channel flow

Abstract

We propose a point-particle model for two-way coupling of water droplets dispersed in the turbulent flow of a carrier gas consisting of air and water vapour. We adopt an Euler-Lagrangian formulation based on conservation laws for the mass, momentum and energy of the continuous phase and on empirical correlations describing momentum, heat and mass transfer between the droplet phase and the carrier gas phase. An incompressible flow formulation is applied for direct numerical simulation of differentially heated turbulent channel flow. The two-way coupling is investigated in terms of its effects on mass and heat transfer characteristics and the resulting droplet size distribution. Compared to simulations without droplets or those with solid particles with the same size and specific heat as the water droplets, a significant increase in Nusselt number is found, arising from the additional phase changes. The Nusselt number increases with increasing ambient temperature and is almost independent of the heat flux applied to the walls of the channel. The time-averaged droplet size distribution displays a characteristic dependence on position expressing the combined effect of turbophoresis and phase changes in turbulent wall-bounded flow. In the statistically steady state that is reached after a long time, the resulting flow exhibits a mean motion of water vapour from the warm wall to the cold wall, where it condenses on average, followed by a net mean mass transfer of droplets from the cold wall to the warm wall.

Effect of droplet interaction on droplet-laden turbulent channel flow

“…In order to describe the temperature and vapor mass fraction in the continuous phase, apart from the Navier-Stokes equation also convection-diffusion equations for the temperature and vapor mass fraction have been solved. It has been shown 4 that for the test cases studied by Russo et al, 2 a compressible and an incompressible formulation for the continuous phase yield very similar results for most quantities of interest. For each droplet apart from the usual equations of motion, equations for its temperature and its mass have been solved, which take into account the convective heat transfer between the two phases, the enthalpy of evaporation when phase change occurs, and the deviation from saturation.…”

“…Apart from the collision model, that will be described in Subsection II D, the method is the same as used by Russo et al 2 and based on a method for incompressible particle-laden turbulent channel flow. 28 The method is pseudo-spectral, consisting of a Fourier-Galerkin method in the periodic streamwise and spanwise direction and a Chebyshev-collocation method in the wall-normal direction.…”

“…1 This increase is caused by the temperature difference between the particles and the continuous phase close to the wall, where the particle concentration is higher than average due to turbophoresis. In a later paper, 2 it has been shown that the increase in heat transfer can be further augmented if the particles are replaced by droplets which can grow and shrink by phase change when the continuous phase consists of a mixture of dry air and the vapor of the dispersed phase. This further increase in heat transfer can be understood from the larger temperature difference between the two phases caused by the enthalpy of evaporation, which cools the droplets close to the hot wall where evaporation occurs, and heats the droplets close to the cold wall, where condensation of the vapor occurs.…”

“…In this paper, the effect of droplet collisions on the properties of droplet-laden turbulent flow in a differentially heated channel will be studied for the reference test cases considered by Russo et al 2 In particular, it will be shown how droplet collisions influence the droplet concentration and how this affects the temperature profile of the continuous phase in the steady state.…”

DNS of turbulent channel flow subject to oscillatory heat flux

“…In the statistically steady state this momentum component is close to zero and this result is confirmed by averaging continuity equation (1) over the periodic directions and time. In the incompressible formulation this averaged quantity is always equal to zero [17]. The net wall-normal gas movement during the initial stage motivates us to use the compressible formulation.…”