Simplified Numerical and Analytical Approach for Solutes in Turbulent Flow Reacting with Smooth Pipe Walls

Kaveh Sookhak Lari, Maarten van Reeuwijk, Čedo Maksimović

Journal of Hydraulic Engineering · 2010

Abstract

A large group of reactions that affect water quality in distribution networks occur on the pipe wall surface. Existing simulation models are usually based on cross-sectionally averaged variables that use mass-transfer coefficients derived for constant-concentration (Dirichlet) boundary conditions to account for cross-sectional variations. In the case of a first-order wall-demand problem, the boundary condition is however of Robin type. We derive a simple one-dimensional (1D) model for the radial concentration profile of a solute of arbitrary Schmidt number (Sc) reacting with pipe walls in a fully developed turbulent flow. A modified van Driest mixing length model was used to approximate the Reynolds-averaged velocity and eddy diffusivity. Numerical solutions of the 1D model agree well with a two-dimensional mass transport model and experimental data. An asymptotic solution for high Sc is derived, which is in excellent agreement with the 1D model for Sc>100 . A comparison with the mass-transfer coefficients for constant-concentration boundary conditions shows that the differences between the two boundary conditions are small.