A Two-dimensional Particle Dispersion Model for Prediction of Pollutant Mixing in Open Channels

Abstract

Simulation of the pollutant mixing in shallow water flow which has large width to depth ratio is usually conducted using the depth-averaged advection-dispersion equation. In the depth-averaged model, the mass transport term induced by the velocity deviations in vertical direction is treated using the Ficks law, in which the concentration flux is assumed to be proportional to the concentration gradient. The assumption is attained only after the Taylor period, where the balance is achieved between the shear advection and vertical diffusion. However, the initial period is not short enough to be neglected, and the mixing properties in the initial period have differences from the Taylor period. Therefore, the aim of this study is to develop the non-Fickian particle dispersion model for analysis of the pollutant mixing both in the initial and Taylor periods, and the mixing properties were analyzed by using the simulation results in open channel flows. The 2D non-Fickian Particle Dispersion Model (2D PDM) was developed using the step-by-step calculation of horizontal translation and vertical mixing based on the shear dispersion theory and particle tracking technique. In the horizontal translation stage, the vertical velocity profiles, which have logarithmic distribution in stream-wise direction and linear distribution in span-wise direction, were generated from the depth-averaged flow field for calculation of horizontal advection by shear flow. The transported particles in horizontal plane were allocated in vertical using the three particle allocation algorithms, which were the random mixing for turbulent mixing, fully mixing, and partial mixing. The results of 2D PDM applications show that the spatial concentration curves have skewed distribution in the initial period, and the curves gradually changed to the symmetric distribution during the Taylor period. Thus, the time evolution of variance shows the non-linear increase with time in the initial period, and the skewness coefficient was approached to 0 in the Taylor period. The calculation results of dispersion coefficients in various hydraulic conditions show that the longitudinal and transverse dispersion coefficients were increased in the initial period due to the advection dominant mixing, and the values were converged to the constant value in the Taylor period. The instantaneously introduced pollutant transport simulations were conducted in the complex open channel flow using the developed model. The application results in the meandering channels show that the breakthrough curves were well fitted with the measured concentration curves. Using the validated simulation results, the dispersion coefficients were calculated in various meandering channels using the 2D spatial routing procedure, which is not required the frozen cloud assumption. The calculation results of dispersion coefficients show that the transverse dispersion coefficients were increased on channel apex due to the increase of vertical velocity deviations, and the transverse dispersion coefficients show positive relation with the channel sinuosity. Furthermore, the simulation results of developed model were compared with the 2D tracer test results in the Sum River and the Hongcheon River, which have complex flow field due to the irregular geometry and recirculation zone. The simulation results reproduced the tail of concentration curves induced by the sidewall friction and dead zone, and the peak concentration and arrival time were properly predicted.