Large-eddy simulation of high-Schmidt number mass transfer in a turbulent channel flow

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Abstract
Mass transfer through the solid boundary of a turbulent channel flow is analyzed by means of large-eddy simulation (LES) for Schmidt numbers Sc=1, 100, and 200. For that purpose the subgrid stresses and fluxes are closed using the Dynamic Mixed Model proposed by Zang et al. [Phys. Fluids A 5, 3186 (1993)]. At each Schmidt number the mass transfer coefficient given by the LES is found to be in very good quantitative agreement with that measured in the experiments. At high Schmidt number this coefficient behaves like Sc−2/3, as predicted by standard theory and observed in most experiments. The main statistical characteristics of the fluctuating concentration field are analyzed in connection with the well-documented statistics of the turbulent motions. It is observed that concentration fluctuations have a significant intensity throughout the channel at Sc=1 while they are negligible out of the wall region at Sc=200. The maximum intensity of these fluctuations depends on both the Schmidt and Reynolds numbers and is especially influenced by the intensity of the velocity fluctuations present in the buffer layer of the concentration field. At Sc=1, strong similarities are observed between the various terms contributing to the turbulent kinetic energy budget and their counterpart in the budget of the variance of concentration fluctuations. At high Schmidt number, the latter budget is much more influenced by the small turbulent structures subsisting in the viscous sublayer. The instantaneous correlation between the spatial characteristics of the concentration field and those of the velocity field is clearly demonstrated by the presence of low- and high-concentration streaks close to the wall. The geometrical characteristics of these structures are found to be highly Sc dependent. In particular their spanwise wavelength is identical to that of the streamwise velocity streaks at Sc=1 while it is reduced by half at Sc=200. Analysis of the co-spectra between concentration and normal velocity fluctuations emphasizes the fact that the large-scale structures play an essential role in the turbulent mass transfer process at high Schmidt number. Overall the picture that emerges from this investigation fully confirms the conclusions of Campbell and Hanratty [AIChE J. 29, 221 (1983)]: high-Schmidt-number mass transfer at a solid wall is governed by the low-frequency part of the normal velocity fluctuation gradient at the wall, i.e., by the large-scale structures observed in planes parallel to the wall in the viscous sublayer.