MODELING OF CONSTITUENT TRANSPORT IN UNSTEADY FLOWS IN PIPE NETWORKS

A new computer model is presented to predict the spatial and temporal distribution of residual constituent in a pipe network under slowly va rying unsteady flow conditions. Unlike the other available models, whi ch use steady-state or extended-period simulation of steady flow condi tions, thus neglecting inertial effects, the presented model is truly dynamic, using a lumped-system approach to compute unsteady flow condi tions. This model also includes dispersion and constituent decay in pi pes. Slowly varying flow conditions are computed by numerically integr ating the governing equations by an implicit finite-difference scheme subject to the appropriate boundary conditions. The transport equation is solved to compute the propagation of a constituent with a first-or der decay rate. To avoid numerical diffusion, the advection and disper sion are solved in two steps: The Warming-Kutler-Lomax explicit scheme is used to solve pure advection while an explicit scheme is used to c alculate dispersion and decay. Complete mixing is assumed at the pipe junctions. The model is applied to two typical pipe networks to simula te the transport and decay of chlorine, and the results are compared w ith another model which uses the standard extended-period simulation t echnique. The results are found to be in good agreement at the beginni ng of the simulation. However, the chlorine concentrations at differen t nodes in the network differ when the flow becomes more unsteady and when reverse flows occur. The model may be used to analyze the propaga tion and decay of any substance with a first-order reaction rate.