Abstract
We present direct numerical simulation results of turbulent open channel flow at bulk Reynolds numbers up to 12 000, coupled with (passive) scalar transport at Schmidt numbers up to 200. Care is taken to capture the very large-scale motions which appear already for relatively modest Reynolds numbers. The transfer velocity at the flat, free surface is found to scale with the Schmidt number to the power ‘$-1/2$’, in accordance with previous studies and theoretical predictions for uncontaminated surfaces. The scaling of the transfer velocity with Reynolds number is found to vary, depending on the Reynolds number definition used. To compare the present results with those obtained in other systems, we define a turbulent Reynolds number at the edge of the surface-influenced layer. This allows us to probe the two-regime model of Theofanouset al.(Intl J. Heat Mass Transfer, vol. 19, 1976, pp. 613–624), which is found to correctly predict that small-scale vortices significantly affect the mass transfer for turbulent Reynolds numbers larger than 500. It is further established that the root mean square of the surface divergence is, on average, proportional to the mean transfer velocity. However, the spatial correlation between instantaneous surface divergence and transfer velocity tends to decrease with increasing Schmidt number and increase with increasing Reynolds number. The latter is shown to be caused by an enhancement of the correlation in high-speed regions, which in turn is linked to the spatial distribution of surface-parallel vortices.
Highlights
We present direct numerical simulation results of turbulent open channel flow at bulk Reynolds numbers up to 12 000, coupled with scalar transport at Schmidt numbers up to 200
Tsai et al (2013) and Turney (2016) found that at relatively low wind speeds Langmuir circulations (which are somewhat similar to very large-scale motions (VLSM) in open channel flow) contribute significantly to interfacial mass transfer
The series of direct numerical simulations (DNS) presented in this paper constitutes a significant leap forward by pushing the boundaries of both Reynolds and Schmidt numbers to 180 ≤ Reτ ≤ 630 and 7 ≤ Sc ≤ 200, respectively, as well as ensuring that the domain size was large enough to accommodate even the largest scales of motion that may occur in open channel flow
Summary
Transfer of gases across a gas–liquid interface is of fundamental importance in many research fields, such as civil engineering and environmental science. Bottom shear induced turbulence is generally the dominant gas transfer mechanism, which we aim to study here in detail To this end, highly accurate direct numerical simulations (DNS) of mass transfer across a shear-free surface in isothermal open channel flow were performed. The series of DNS presented in this paper constitutes a significant leap forward by pushing the boundaries of both Reynolds and Schmidt numbers to 180 ≤ Reτ ≤ 630 and 7 ≤ Sc ≤ 200, respectively, as well as ensuring that the domain size was large enough to accommodate even the largest scales of motion that may occur in open channel flow This was made possible due to the recent increases in computational power and the availability of the dual-meshing strategy in our KCFlo code (Kubrak et al 2013), which allows us to simultaneously solve multiple scalar transport equations.
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