Simulation of air–water interfacial mass transfer driven by high-intensity isotropic turbulence

Abstract

Previous direct numerical simulations (DNS) of mass transfer across the air–water interface have been limited to low-intensity turbulent flow with turbulent Reynolds numbers of $R_{T}\leqslant 500$. This paper presents the first DNS of low-diffusivity interfacial mass transfer across a clean surface driven by high-intensity ($1440\leqslant R_{T}\leqslant 1856$) isotropic turbulent flow diffusing from below. The detailed results, presented here for Schmidt numbers $Sc=20$ and $500$, support the validity of theoretical scaling laws and existing experimental data obtained at high $R_{T}$. In the DNS, to properly resolve the turbulent flow and the scalar transport at $Sc=20$, up to $524\times 10^{6}$ grid points were needed, while $65.5\times 10^{9}$ grid points were required to resolve the scalar transport at $Sc=500$, which is typical for oxygen in water. Compared to the low-$R_{T}$ simulations, where turbulent mass flux is dominated by large eddies, in the present high-$R_{T}$ simulation the contribution of small eddies to the turbulent mass flux was confirmed to increase significantly. Consequently, the normalised mass transfer velocity was found to agree with the $R_{T}^{-1/4}$ scaling, as opposed to the $R_{T}^{-1/2}$ scaling that is typical for low-$R_{T}$ simulations. At constant $R_{T}$, the present results show that the mass transfer velocity $K_{L}$ scales with $Sc^{-1/2}$, which is identical to the scaling found in the large-eddy regime for $R_{T}\leqslant 500$. As previously found for a no-slip interface, also for a shear-free interface the critical $R_{T}$ separating the large- from the small-eddy regime was confirmed to be approximately $R_{T}=500$.