Direct numerical simulation of gas transfer across the air–water interface driven by buoyant convection

A series of direct numerical simulations of mass transfer across the air–water interface driven by buoyancy-induced convection have been carried out to elucidate the physical mechanisms that play a role in the transfer of heat and atmospheric gases. The buoyant instability is caused by the presence of a thin layer of cold water situated on top of a body of warm water. In time, heat and atmospheric gases diffuse into the uppermost part of the thermal boundary layer and are subsequently transported down into the bulk by falling sheets and plumes of cold water. Using a specifically designed numerical code for the discretization of scalar convection and diffusion, it was possible to accurately resolve this buoyant-instability-induced transport of atmospheric gases into the bulk at a realistic Prandtl number ($\mathit{Pr}=6$) and Schmidt numbers ranging from$\mathit{Sc}=20$to$\mathit{Sc}=500$. The simulations presented here provided a detailed insight into instantaneous gas transfer processes. The falling plumes with highly gas-saturated fluid in their core were found to penetrate deep inside the bulk. With an initial temperature difference between the water surface and the bulk of slightly above$2$ K, peaks in the instantaneous heat flux in excess of$1600~\text{W}~\text{m}^{-2}$were observed, proving the potential effectiveness of buoyant-convective heat and gas transfer. Furthermore, the validity of the scaling law for the ratio of gas and heat transfer velocities$K_{L}/H_{L}\propto (\mathit{Pr}/\mathit{Sc})^{0.5}$for the entire range of Schmidt numbers considered was confirmed. A good time-accurate approximation of$K_{L}$was found using surface information such as velocity fluctuations and convection cell size or surface divergence. A reasonable time accuracy for the$K_{L}$estimation was obtained using the horizontal integral length scale and the root mean square of the horizontal velocity fluctuations in the upper part of the bulk.

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Direct numerical simulation of turbulent scalar transport across a flat surface

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.68 ◽

2014 ◽

Vol 744 ◽

pp. 217-249 ◽

Cited By ~ 17

Author(s):

H. Herlina ◽

J. G. Wissink

Keyword(s):

Mass Transfer ◽

Isotropic Turbulence ◽

Reynolds Numbers ◽

Gas Transfer ◽

Computational Domain ◽

Atmospheric Gases ◽

Transfer Velocity ◽

Physical Mechanisms ◽

Schmidt Numbers ◽

Large Eddies

AbstractTo elucidate the physical mechanisms that play a role in the interfacial transfer of atmospheric gases into water, a series of direct numerical simulations of mass transfer across the air–water interface driven by isotropic turbulence diffusing from below has been carried out for various turbulent Reynolds numbers ($R_T=84,195,507$). To allow a direct (unbiased) comparison of the instantaneous effects of scalar diffusivity, in each of the DNS up to six scalar advection–diffusion equations with different Schmidt numbers were solved simultaneously. As far as the authors are aware this is the first simulation that is capable to accurately resolve the realistic Schmidt number, $\mathit{Sc}=500$, that is typical for the transport of atmospheric gases such as oxygen in water. For the range of turbulent Reynolds numbers and Schmidt numbers considered, the normalized transfer velocity $K_L$ was found to scale with $R_T^{-{1/2}}$ and $\mathit{Sc}^{-{1/2}}$, which indicates that the largest eddies present in the isotropic turbulent flow introduced at the bottom of the computational domain tend to determine the mass transfer. The $K_L$ results were also found to be in good agreement with the surface divergence model of McCready, Vassiliadou & Hanratty (AIChE J., vol. 32, 1986, pp. 1108–1115) when using a constant of proportionality of 0.525. Although close to the surface large eddies are responsible for the bulk of the gas transfer, it was also observed that for higher $R_T$ the influence of smaller eddies becomes more important.

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