Effects of the Turbulent Schmidt Number on the Mass Exchange of a Vegetated Lateral Cavity

Computational Fluid Dynamics (CFD) has been established as a relevant technique to investigate the qualitative and quantitative characteristics of complex environmental flows, such as transient storage zones. In numerical studies involving mass transport of solutes and sediment (e.g., mean retention time and mass exchange rate), one fundamental variable is the turbulent Schmidt number (Sct) which defines the ratio of momentum diffusivity to mass diffusivity in turbulent flows, and thus affects the concentration of solute within the solution impacting on the estimation of mass related variables. This is particularly important for transient storage zones, such as lateral cavities and groyne fields, as they are known for their role in nutrient retention and release, and sediment entrapment. This numerical study aims to examine the influence of the turbulent Schmidt number in the mean retention time and mass exchange rate between a channel and a vegetated/non-vegetated lateral cavity.

 

The cavity was L = 0.25m long (x-axis), W = 0.15m wide (y-axis) and had a depth of H = 0.10m (z-axis). The aspect ratio between the width and the length resulted in 0.6 which corresponded to a single circulation system (Sukhodolov et al., 2002). The flow had a bulk velocity of U = 0.101 m/s that corresponds to a Reynolds number of 9000. The vegetation drag was represented by an anisotropic porous media calculated with the Darcy-Forchheimer model (Yamasaki et al., 2019), the vegetation density was constant at a = 0.1332%. Large Eddy Simulation (LES) was applied to define the flow field in that domain, using the Wall Adapting Local Eddy-viscosity (WALE) to account subgrid effects. A passive scalar was injected inside the lateral cavity to investigate its transport and diffusion in a range of Sct from 0.1 to 2.0. The numerical results of the flow field were validated using literature experimental data considering 3 different meshes to achieve mesh independence (Xiang et al., 2019).

 

The effect of Sct variation was, then, analysed in both vegetated and non-vegetated scenarios, for a total of 40 different simulations. The volumetric average scalar concentration in the cavity was fitted into a first-order decay model (C = C₀.e^-t/T_D), where C₀ = 1 is the initial concentration, t  (s) is time and T_D  is the mean residence time. The mass exchange rate was defined as k = W/(T_D.U) . Preliminary results showed in the vegetated scenarios a limited effect of Sct on the mass exchange rate, which varied from 1% if the Sct value was doubled.

References

Sukhodolov, A., Uijttewaal, W. S. J. and Engelhardt, C.: On the correspondence between morphological and hydrodynamical patterns of groyne fields, Earth Surf. Process. Landforms, 27(3), 289–305, doi:10.1002/esp.319, 2002.

Xiang, K., Yang, Z., Huai, W. and Ding, R.: Large eddy simulation of turbulent flow structure in a rectangular embayment zone with different population densities of vegetation, Environ. Sci. Pollut. Res., 26(14), 14583–14597, doi:10.1007/s11356-019-04709-x, 2019.

Yamasaki, T. N., de Lima, P. H. S., Silva, D. F., Preza, C. G. de A., Janzen, J. G. and Nepf, H. M.: From patch to channel scale: The evolution of emergent vegetation in a channel, Adv. Water Resour., doi:10.1016/j.advwatres.2019.05.009, 2019.