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 $R_{T}=500$.

Bubble-mediated transfer of dilute gas in turbulence

“…1976), further discussed by Magnaudet & Calmet (2006) and Katul & Liu (2017). These two regimes and their crossover have been observed experimentally and numerically by Herlina & Wissink (2016, 2019), following earlier experimental work by Fortescue & Pearson (1967) (who used the root mean square of the fluctuating velocity as characteristic velocity).…”

Direct numerical simulation of turbulent mass transfer at the surface of an open channel flow

“…From the surface (y = H) down to a depth of (H − y) ≈ 2 δ , the normalised mean vertical profiles of the scalar quantities shown in figure 11 were found to nearly collapse with the profiles reported in Herlina & Wissink (2019), hereafter HW19 (not included in the plot), where the interfacial mass transfer was driven by isotropic turbulence diffusing upwards from the opposite boundary. For the highest Reynolds number case (G09), the agreement between the open channel profiles produced here and in the case driven by isotropic turbulence remains reasonably well up to a distance of at least 10 δ from the free surface.…”

“…Recently, DNS of highly realistic Schmidt numbers (e.g. Sc ≈ 500 for O 2 and Sc ≈ 600 for CO 2 in water) have been performed in buoyancy-driven flow by Wissink & Herlina (2016), Fredriksson et al (2016) and in isotropic-turbulence driven flow by Herlina & Wissink (2014) and Herlina & Wissink (2019). Note that the latter is often used to produce a near-surface turbulent flow field that, despite the lack of streamwise anisotropy, is used to mimic the flow field generated by bottom shear, such as in open channel flow.…”

Local gas transfer rate through the free surface in spatially accelerated open-channel turbulence

“…8 to increase with the flow acceleration. Herlina and Wissink 48 asserted that local surface-attached vortex structures (SAVS) having the surface-normal axis are stretched and strengthened. In the smallscale converging zone accompanied with downwelling currents, gas transfer is expected to be related to the interactions between the SAVS that promote the horizontal mixing and the longitudinal secondary vortex that promotes the vertical mixing.…”