Combined bulk and wall reactions in turbulent pipe flow: decay coefficients and concentration profiles

This study discusses the effect of combined first-order, bulk and wall reactions on the overall intensity of mass withdrawal in smooth pipes. A one-dimensional model for the transport of high Schmidt number compounds (where the Schmidt number is the ratio of the fluid viscosity to the solute diffusivity) is extended with the effect of a first-order bulk reaction. Profiles of velocity and eddy diffusivity are obtained with a standard high Reynolds number k –∊ closure in combination with a modified Van Driest wall function. By comparing the results of the 1D model to an analytical asymptotic high Sc approximation, it is shown that the interaction between bulk and wall reactions is very weak. In terms of the decay coefficient, a maximum deviation of 4% is observed for very high bulk demand due to the attenuation of the streamwise solute mass flux. The parameter range for which the concentration profiles can be safely assumed to be uniform, both in the viscous sublayer and in the bulk, is established.