Modelling Dispersion Coefficient in Meandering Channels by Use of Dimensional Analysis

Abstract

Dispersion is the major means of determining pollutant transport in water bodies. Its effect is usually measured by dispersion coefficient, D, determined through tracer studies- a process that is cumbersome, time consuming and expensive. The parameter, D, is a most basic factor of measurement in hydraulic modeling of pollutants in rivers and its accuracy is important to measure the characteristic behavior of pollutants and preserve surface water quality. To circumvent the challenges of tracer studies, many researchers have used the geometric and hydraulic parameters of the river without considering the effect of meandering which is fundamental in river morphology. The aim of this research is to develop a robust dispersion coefficient model that accounts for the effect of bends in order to improve accuracy of the phenomenon. To do this, two out-door laboratory channels of 2 and 3 meanders respectively were constructed. Channel floor was covered with a layer of river sand and allowed to grow grass to perfectly mimick natural stream conditions. Tracer experiments were conducted on both channels at different velocities to obtain data for measured dispersion coefficient determined by Levenspiel and Smith method. Dimensional analysis was used to relate all the geometric and hydraulic parameters of the channels and MATLAB was used for calibration. Two models that include two new parameters namely, number of meanders (N) and ratio of radius of curvature to hydraulic radius ((R_c⁄R_h ) were developed, one for each of the channels. Predicted results by both models were compared with the measured and with those obtained from some existing models. Statistical measures of accuracy namely, RMSE; MAE; DR and percentage error, showed that the new models performed better. The improvement in the new models is result of inclusion of the two new terms that reflect bend characteristics. The implication is that incorporating parameters of bend geometry in dispersion coefficient models improves their accuracy in determining the phenomenon in meandering channels. In conclusion, it is now known that bend parameters increase accuracy of D. New models to be used in determining dispersion coefficient in meandering channels have been developed, implying that a reliable and more accurate prediction of the dispersive ability of channels with bends is now possible. This will ensure better and reliable designs of treatment plants, better water resources management and pollution control that will improve surface water quality in compliance with United Nations development goals for clean water and sanitation for all, and preserve aquatic communities throughout the river reach.