(84e) Effective Reaction Rate and Mass Transfer for a Surface Reaction in Turbulent Flow

In this work, Lagrangian numerical methods are used to examine the effect of a chemical reaction on turbulent mass transfer. A direct numerical simulation (DNS) is used to describe the turbulent flow field in a channel with half-height equal to 150 in viscous units. After the fluid flow reaches fully developed, stationary state, the mass transfer is simulated by releasing a large number of reactant particles distributed randomly on a cross section of the channel at every time step. The reaction is such that the reactant can transform into a product when it comes in contact with the wall. The reaction equation can be written as: A -> B, where A is the reactant and B is the product, which is adsorbed by the wall In other words, a diffusion-controlled reaction between the fluid and the channel wall is simulated. This is also analogous to the case of a well-mixed reactant solution in the flow approaching a section of the wall where the solution can deposit, similar to a Chemical Vapor Deposition case. In each simulation time step, the reactant particles move due to convection, which is determined by the DNS of the flow, and due to diffusion, which is simulated by a random Brownian motion that depends on the Schmidt number (Sc) of the fluid. The rate of reaction between the fluid and the wall is related to the probability that a particle colliding with the wall will react with the wall. Applying this methodology, the bulk concentration, the wall concentration, and the mass transfer coefficient to the wall can be calculated as a function of the channel length.

The presentation will discuss the effects of the flow and the Schmidt number on the apparent reaction rate and on the mass transfer coefficient, as well as the entry effects on the rate of mass transfer. In the region very close to the reactant entrance, the wall concentration is found to be higher than the bulk concentration, and, therefore, there is mass transfer from the wall to the bulk flow. Beyond this region, the bulk concentration is higher than the wall concentration, and mass transfer occurs from the bulk flow to the wall. This region is a region where the mass transfer rate to the wall is stabilized. Although there is no effect of Schmidt number on the bulk concentration, the mass transfer coefficient is found to be higher for smaller Schmidt number fluids. In the stabilized region, it was found that the first order reaction is diffusion limited with larger Sc (50 and above). The mass transfer coefficient was found to be independent of the reaction rate, but has a strong dependence on Sc: K⁺ ~ Sc^{-0.529±0.037} for Sc ≤ 10 and K⁺ ~ Sc^{-0.825±0.026} for Sc ≥ 50.