Dynamic models for subgrid-scale transport and mixing of reactants in atmospheric turbulent reacting flows

The effects of the sub-grid scales on chemical transformations in large-eddy simulations of the convective atmospheric boundary layer (CBL) are investigated. A set of simulations of CBLs with two reactants involved in a second-order irreversible reaction are performed to study how subgrid-scale chemistry is affected by two factors: reaction rate and resolution (grid size). To quantify the relative importance of subgrid-scale turbulent mixing on the chemical transformations, we introduce the non-dimensional 'sub-grid' Damköhler number, defined as the ratio between the time scale associated with the smallest scales resolved by LES and the chemical time scale. For values of the sub-grid Damköhler number on the order of 1 or larger, simulation results become scale dependent when the effect of subgrid-scale mixing of the reactants on the reaction rate is ignored. In order to account for that effect, dynamic similarity subgrid-scale models are developed and used to calculate the sub-grid fluxes and also the sub-grid reactant covariance. The dynamic procedure allows for simulations free of parameter tuning since the model coefficients are computed based on the resolved reactant concentrations. A scale-dependent procedure is proposed that allows relaxing the assumption of scale invariance used in the dynamic similarity model.