Skip to main content

Dispersion within potable water networks for unsteady flows at Re<10000

Researcher: Mr James Hart
Project duration: 2009-2012
Supervisor: Prof. Ian Guymer
Funding body:

Project Overview

The aim of the project is to investigate solute transport, specifically longitudinal dispersion, within the dead-end regions of potable water networks. Within such regions discharge is contingent on the sporadic demand of the consumer. Current water quality models assume steady, highly turbulent flow, assumptions which are insufficient to accurately model these regions of the network. In such regions discharge is unsteady and flow velocities range from the relatively high main network velocity, through to zero. The focus of the project is to investigate the degree to which dispersion impacts solute transport in such regions, where flows are unsteady and Reynolds numbers are low (i.e. below 10000).

One crucial aspect of the project centres on investigating methods to accurately predict dispersion coefficients at low Reynolds numbers. Taylor (1953, 1954) proposed expressions to analytically determine the dispersivity in both laminar and turbulent pipe flow, expressions which are widely used within the field. However, Levenspiel (1958), Flint and Eisenklam (1969), Cutter (2004) and unpublished work undertaken at the University of Warwick have all demonstrated significant divergences between Taylor’s expression and experimentally obtained data for low turbulent flow (i.e. with Reynolds numbers below 10000), as shown in Figure 1. Therefore, before dispersion can be accurately modelled within low flow regions, the experimental and analytical data must be reconciled, which has become the short term goal of the project.

Following this, the focus of the project will move onto dispersion within unsteady flows. Tracer experiments will be conducted upon pipe flows where discharge patterns typical of network dead-ends are recreated. The overall aim of the project is firstly to assess the degree to which dispersion impacts solute transport under such conditions, and secondly, if dispersion is significant, to investigate whether a model can be proposed to accurately predict it under such circumstances.


Figure 1
Figure 1: Dispersion coefficients at low Reynolds numbers.

References

Cutter, M. R. (2004) Dispersion in Steady Pipe Flow with Reynolds Number Under 10000. MSc Thesis, University of Cincinnati, Cincinnati, Ohio.

Flint, L. F. and Eisenklam, P. (1958) Longitudinal gas dispersion in transitional and turbulent flow through a straight tube. Canadian Journal of Chemical Engineers, 47, 101-106.

Levenspiel, O. (1958) Longitudinal Mixing of Fluids Flowing in Circular Pipes. Industrial and Chemical Engineering Research, 50 (3), 343-346.

Taylor, G. I. (1953) Dispersion of Soluble Matter in Solvent Flowing Slowly Through a Tube. Proceedings of the Royal Society, 219, 186-203.

Taylor, G. I. (1954) The Dispersion of Matter in Turbulent Flow Through a Pipe. Proceedings of the London Mathematical Society, 223, 446-468.

Dye in the pipe
Figure 1: Transport of dye within a pipe.

Pic2
Figure 2: Fluorometer for measuring concentration of tracer within flow.

PIc3
Figure 3: Ultrasonic Velocity Profiler for measuring velocity profile across the pipe.