Axial Dispersion Coefficients for Laminar Flows in Water Distribution Systems

A dispersive transport component has recently been incorporated into the constituent transport equation used for modeling water quality in pressurized distribution systems. Among the various issues that arose from this major development, dispersion coefficients (E) relevant to water distribution systems still remain unknown. In order to quantify E values, researchers have considered the long-established Taylor's theory (E^*) and time-dependent functions. However, discrepancies between theoretical and experimental approaches still exist because the former does not consider the transient nature of dispersion whereas the latter derives from the analytical relations that overestimate dispersion rates. The present study quantifies dispersion coefficients in pressurized pipes under laminar conditions by using Computational Fluid Dynamics (CFD). Assumptions made with CFD are few and mostly related to the velocity field in pipe flows. Consequently, the mass transports are obtained by solving the species equation over an axi-symmetric domain. Next, the resulting spatial-temporal constituent concentrations are used to estimate dispersion coefficient values determined by the method of moments (MOM) at equally-spaced locations along the length of the pipe. With the aim of building a quasi-analytical relation of E/E^* = β f_E = f(Re,T,Sc), transient simulations at a series of Reynolds numbers for laminar flows (Re < 2,100) were carried out in consideration of constituents with different molecular diffusivity in water. Among the various challenges that this study confronts, two are thoroughly described here: (i) the pre-analysis needed to obtain a solution that is independent of the numerical setup and (ii) the CFD benchmarking solution required under conditions when Taylor's theory applies (T > 0.30).