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Random Walk Particle Tracking to Model Dispersion in Steady Laminar and Turbulent Pipe Flow
Citation:
Shang, F., J. Burkhardt, AND R. Murray. Random Walk Particle Tracking to Model Dispersion in Steady Laminar and Turbulent Pipe Flow. JOURNAL OF HYDRAULIC ENGINEERING. American Society of Civil Engineers (ASCE), Reston, VA, 149(7):04023022, (2023). https://doi.org/10.1061/JHEND8.HYENG-13405
Impact/Purpose:
A two dimensional modeling approach to get an accurate simulation of how the solute particles are transported within a drinking water pipe. It provides insightful information about the contaminant transport in both longitudinal and radial direction. The information generated is helpful for the sampling design and contaminant source identification.
Description:
A random walk particle tracking approach was developed to analyze the advection and dispersion processes of the solute transport in a circular pipe. Stochastic difference equations were derived to model a solute particle’s two-dimensional random movement in the cross-section of a pipe. The random movement is caused by the molecular or turbulent diffusion. Combined with the radial difference of the advection velocities, it leads to the solute dispersion on the longitudinal direction. This two-dimensional modeling approach can be applied to any mixing time and can accurately model both the longitudinal distribution of the solute concentration as a function of the mixing time and the residence time distribution as a function of the pipe length. The simulation results approach the asymptotic solution analytically derived by Taylor (1953, 1954) when the mixing time is long enough. And simulations confirm that, under laminar flow conditions, the impact of the molecular diffusion on the solute transport is negligible for short mixing times. For turbulent flow conditions, the simulation studies showed that the longitudinal dispersion of the solute is very sensitive to the cross-sectional velocity profiles assumed. The presented random walk particle tracking approach is easy to implement programmatically and unconditionally stable. It can be used to predict mixing characteristics of a pipe under both laminar and turbulent conditions and can easily account for different types of initial conditions. One dimensional effective dispersion coefficient in longitudinal direction can be estimated from the RWPT simulation results and the validity of applying one-dimensional advection-dispersion model to simulate solute transport within a pipe can also be checked.
URLs/Downloads:
DOI: Random Walk Particle Tracking to Model Dispersion in Steady Laminar and Turbulent Pipe Flow
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