MASS DISPERSION IN INTERMITTENT LAMINAR FLOW
Mass dispersion in unsteady laminar flow is common in dead-end regions of water distribution systems. However, dispersion has not been included in network models and this omission can lead to inaccurate predictions of water quality in regions where laminar flow prevails. Incorporating dispersion in network models is a challenge because it requires solving a two-dimensional (2-D) governing equation numerically. The present work introduces and verifies a new analytical equation that can estimate the rate of dispersion in unsteady laminar flow. Existing analytical solutions for one-dimensional mass transport in steady flow were investigated. Dispersive transport of non-conservative solutes in pipe networks was found to be important when the dimensionless group m=(1+4KE/U ^2 ) 1/2 >1.2, where K is reaction rate, E is dispersion rate and U is average velocity. A new analytical expression for the instantaneous rate of dispersion in unsteady laminar flow was developed. The instantaneous rate of dispersion in pulsating laminar flow through a pipe is a dynamic weighted average of two factors: (i) the dispersion memory from previous pulses with the factor of R(t)=exp(-t/? 0 ) where ? 0 =a ^2 /16D is a Lagrangian time scale reflecting molecular diffusivity D across the pipe radius a and (ii) the nonlinear excitation from the current pulse with the factor of 1-R(t). Analytical predictions of dispersion agree well with results obtained from the 2-D governing equation for conservative solute transport in a pipe. When dimensionless average pulse duration ? ?0.025 ( ? =D ? /a ^2 where ?=pulse duration), analytical estimates of time-averaged dispersion E in unsteady laminar flow with two or three repeating pulses are within 15% of E 0 in steady flow with the same average velocity. For these pulse conditions, the analytical equation also agrees very well with experimental data. When ? >0.0625, the steady and unsteady estimates of dispersion diverge. As ? approaches one, E converges toward its maximum rate of dispersion, E 0 (1+? U ^2 ) where ? U is the coefficient of variation of velocity. A field example from EPANET demonstrated that addition of dispersion improved prediction of fluoride concentrations in dead-end pipes with laminar flow. Water utilities can improve predictions of water quality in the periphery of distribution systems by incorporating dispersive transport in their current network models.
School:University of Cincinnati
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:water distribution networks quality dispersion advection models
Date of Publication:01/01/2004