Study of the effects of the local roughness on the transverse diffusion of pollution in a straight rectangular channel

Understanding the processes of mixing and transporting materials in rivers has been accounted as a main activity in the water resources management. Among the mixing processes, the transverse diffusion is considered as the second important process, after the longitudinal diffusion, affecting the longitudinal and transverse distribution of pollutants in river flows. Determination of the rate of material diffusion and their density are usually carried out based on solving mass conservation equations. The available analytical solutions were only provided for uniform flows in straight channels, so there are needs for numerical methods to solve the governing equations for non-uniform flow in complicated forms of channel geometries. The results from studies on rectangular straight channels show that the transverse diffusion coefficient (TDC) increases with increasing friction factor, while no specific relation between TDC and the ratio of width to depth is provided. Meanwhile, based on laboratory studies, an empirical relationship for estimation of transverse mixing coefficient is introduced for straight channels in uniform flow. An equation is also introduced to show the relationship among the longitudinal dispersion coefficient of pollutants, flow depth, river width, flow velocity, and shear velocity of river flows. Since increasing the amount of roughness of the channel boundaries, provides additional flow turbulence, which in turn results in reducing the perfect mixing length of the pollutant, some laboratory researches have been carried out using the spatial artificial roughness in flumes with single or combined cross sections to investigate the effects of roughness on the coefficient of transverse mixing of pollutants. However, all related tests were mainly carried out within laboratory channels with small widths where the tracer injection was made in the middle of the channels. In this research, we carried out tests in a wider channel, including artificial roughness on the bed to reduce the effects of channel walls where the tracer injection was made from the channel center. In this study, the laboratory tests were carried out in a channel with a length of 7.3, and width of 0.6 meters. The channel had been installed on a metal platform with adjustable slope, but the tests were carried out using a fixed slope. A set of square wooden blocks in three rows and two layouts with upstream ramp were used to make artificial channel bed roughness for increasing the transverse mixing of the pollutants. Salt solution at a concentration of approximately 27 grams per liter was used as the pollutant and an electrical conductivity instrument was used to measure the density of samples taken from two sections (i.e. 135 and 365 cm) downstream of the injection point as well as the density of the tracer concentration inside the tank. For each layout, three discharges of 20, 30, and 35 liter per second have been considered. Due to time and financial constraints, and consequently, limitation on evaluating the various conditions of the flow, number of rows, and different points in laboratory-scale, the FLUENT software was used to improve the results of the present research. The results of the laboratory tests showed that the local roughness has a considerable effect on the reduction of full mixing length. Also, the results of the dimensional analysis showed that the transverse diffusion coefficient is directly related to the ratio of width to depth as well as friction coefficient. As a whole, the results of this research show that the friction factor and the flow depth have a significant effect on the amount of TDC of the pollutant, so that by increasing the amount of friction coefficient, the TDC was increased, the perfect mixing length was reduced and dilution was done in a shorter distance. Moreover, increasing the flow velocity led to increase in the pollutant transport by flow, reduce the amount of TDC of the pollutant, and consequently, increase the perfect mixing length. Based on the results from laboratory experiments and dimensional analysis, a new relationship was introduced to estimate TDC with a mean relative error of 0.059. As mentioned previously, to extend the applications of the results to various situations, using data obtained from laboratory experiments, the abilities of FLUENT software for simulating the different conditions were investigated. It is found that the FLUENT software is able to simulate and predict the mixing processes in rivers with a reasonable accuracy.