Serbest yüzey akımında pürüzlü taban üzerinde ağır parçacıkların boyuna dispersiyonu

Turbulent flow has been observed by humans throughout history, and was studied by science since at least the time of Leonardo Da Vinci. Although it is yet to be fully explained, causes and effects of this natural phenomenon are covered to an extent that we are able to acquire viable and applicable data, via analytical or numerical models. One significant result of turbulence is the dispersion of material along the flow, namely longitudinal dispersion. This is also being studied along with turbulence, as it has a very significant practical importance; being very closely related to environmental pollution. This study intends to numerically solve the dispersion of heavy particles in free surface flows over rough beds, and acquire accurate results compared to those of the physical experiments. Previous models numerically solved the turbulent dispersion of heavy particles over smooth bed. Most importantly, this study will be investigating the effect of rough beds on the dispersion. The software product of this thesis will be using somewhat refined methods from the previous ones to determine the variants used to calculate the dispersion. Finally, longitudinal dispersion coefficients for particles with different settling velocities in a free surface flow with various bed roughness values are intended to be acquired. The law of the wall by Theodore Von Karman (1930), and the Van Driest velocity profile and the turbulent diffusion and dispersion physics lie fundamentally in the background of this study. Random walk method will be modelled numerically for this thesis to use one particle analysis to determine dispersion coefficients for different variations of particle settling velocities and bed roughness values. What we will need is the velocity profile across the cross-section of the flow, the wall-normal turbulence velocities and particle behavior at the upper and lower boundaries (bed and surface). For the mean x velocity, Van Driest profile has to be corrected with a wake function to be valid across the whole section of the flow. Present model will also be using Cebeci and Chang (1978) coordinate shift to inspect roughness effect on dispersion, which has never been applied on a numerical model before. For wall-normal turbulence, the model will be using Nezu and Nakagawa (1993) semi-theoretical curve based on experimental data, modified to cover the inner region of the flow by Kirca (2013) For heavy particles, a characteristic parameter representing the effect of gravity, called the Rouse parameter will be used. As the particles will be moving upwards and downwards randomly along the cross section of the flow for the random walk method, we will be using a scale to determine the length of this movement, namely the penetration length scale, which is basically the vertical size of the turbulent eddy, which carries the particle vertically. The model will be using Sayre (1968) and Sumer (1973) approximation of this length scale, smoothened by Kirca (2013) for using continuous and a differentiable value across the depth, with a tangent-hyperbolic function. Particles will encounter flow boundaries across the way. They will be considered to bounce back into the flow. For any energy loss that would occur in nature, the model will be using a tuning parameter. To model the bouncing effect, a piecewise function by Kirca (2013) will be used. The model is tested for naturally buoyant particles over smooth bed, for various Ref values from 500 to 50000, for heavy particles such as β = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1 and 1,5 over smooth wall (ks+ ˂ 5) and for ks+ roughness values from 5 to 2000 and β = 0.1, 0.2, to 0.9 and 1. The software model seems to provide results that agree with the previous studies both numerical and analytical. As for the innovative part of this study, Cebeci-Chang coordinate shift was included in the model along with the Coleman and Alanso wake function correction to have a refined profile and be able to inspect the effect of bed roughness on the dispersion of the heavy particles. Results show that, for neutrally buoyant particles, as roughness increases, dispersion coefficient tends to slightly decrease, especially when the roughness elements penetrates deeper into the flow domain (i.e. for high ks/h values). As the settling velocity of the particles increase, however, the effect of roughness on the dispersion seems to fade.