Turbulent channel flow concentration profile and wall deposition of a large Schmidt number passive scalar

Abstract

The transport of a passive scalar within a turbulent plane channel flow has been theoretically analyzed by assuming that the Schmidt number Sc, associated to the molecular diffusivity of the passive scalar, is a large parameter. Throughout most of the channel cross-section the mean passive scalar density is constant, but adjacent to the walls a thin boundary layer develops embedded in the viscous sublayer, with a relative thickness of order Sc(-1/3). In this narrow region a passive scalar profile arises due to the non-vanishing flux normal to the wall. This profile is parameter independent (universal) and leads to a constant flux of passive scalar that results from the addition of both the molecular diffusion flux and the turbulent transport one. The Sc-asymptotic matching of this profile with the constant core value provides an analytical expression for the wall-normal flux that depends on the fluid dynamics of the carrier flow. By using a DNS code to solve the external turbulent flow, the analytical expression has been quantified and compared with empifical expressions based on experimental data, showing excellent agreement.