Stochastic modeling of surface scalar-flux fluctuations in turbulent channel flow using one-dimensional turbulence

Abstract

Accurate and economical modeling of near-surface transport processes is a standing challenge for various engineering and atmospheric boundary-layer flows. In this paper, we address this challenge by utilizing an economical stochastic one-dimensional turbulence (ODT) model. ODT aims to resolve all relevant scales of a turbulent flow for a one-dimensional domain. Here ODT is applied to turbulent channel flow as stand-alone tool. The ODT domain is a wall-normal line that is aligned with the mean shear. The free model parameters are calibrated once for the turbulent velocity boundary layer at a fixed Reynolds number. After that, we use ODT to investigate the Schmidt (Sc), Reynolds (Re), and Peclet (Pe) number dependence of the scalar boundary-layer structure, turbulent fluctuations, transient surface fluxes, mixing, and transfer to a wall. We demonstrate that the model is able to resolve relevant wall-normal transport processes across the turbulent boundary layer and that it captures state-space statistics of the surface scalar-flux fluctuations. In addition, we show that the predicted mean scalar transfer, which is quantified by the Sherwood (Sh) number, self-consistently reproduces established scaling regimes and asymptotic relations with respect to Sc,Re, and Pe. For high asymptotic Sc and Re, ODT results fall between the Dittus–Boelter, Sh∼Re4/5Sc2/5, and Colburn, Sh∼Re4/5Sc1/3, scalings but they are closer to the former. For finite Sc and Re, the model prediction reproduces the relation proposed by Schwertfirm and Manhart (Int. J. Heat Fluid Flow, 28, 1204–1214, 2007) that is based on boundary-layer theory and yields a locally steeper effective scaling than any of the established asymptotic relations. The model extrapolates the scalar transfer to small asymptotic Sc≪Reτ-1 (diffusive limit) with a functional form that has not been previously described.