DNS of turbulent Schmidt number and eddy diffusivity for reactive concentrations

Abstract

The gradient diffusion hypothesis for turbulent mass fluxes of reactive scalar is investigated by using direct numerical simulations (DNS) of a planar jet with a second-order chemical reaction A+B→R. Reactants A and B are separately supplied in the jet and ambient fluids, respectively. DNS is performed at three different Damköhler numbers, i.e, Da=0.1, 1, and 10. Eddy diffusivity and turbulent Schmidt number of reactive species are calculated from the DNS results. The results show that the longitudinal (x-direction) eddy diffusivity of reactant A near the jet centerline is always positive, whereas the longitudinal eddy diffusivities of reactant B and product R can be negative near the jet centerline. Near the jet centerline, the lateral (y-direction) eddy diffusivity of reactant A, DtA,y, becomes small, but the lateral eddy diffusivity of reactant B, DtB,y, becomes large because of the chemical reaction. In the outer region of the jet flow, the chemical reaction has the opposite effect on DtA,y and DtB,y, and the chemical reaction makes DtA,y large, but DtB,y small. It is concluded that the gradient diffusion hypothesis is largely affected by the chemical reaction, and this effect of chemical reaction should be taken into account when the gradient diffusion model is used to estimate turbulent mass fluxes of reactive scalar.

Keywords

• turbulent flow
• chemical reaction
• direct numerical simulation
• jet
• gradient diffusion model