Modification and improvement of equations to estimate the scour hole formation due to 2D wall jets using PSO algorithm

Abstract
Abstract:

The interaction between the jets and the loose beds may cause scour hole formation. The scour hole developments may cause structural instability of the structures and increases the damage probability of the structures. Hence the scour hole dimensions estimation is an important subject for engineers. Many investigators worked on the effective parameters on scour hole dimensions due to plane wall jets. They have presented many different equations to estimate the scour hole dimensions. The equations may be used on a specific range of the effective parameters. Using the width range of the available experimental data the appropriate equations are developed. Using the dimensional analysis the non dimensional parameters such as Froude densimetric, Reynolds number, non-dimensional form of the sediment size, standard deviation of the sediment mixture, tailwater depth, non dimensional form of the channel width and non dimensional form of the time were obtained. Authors tried to use an optimization procedure to develop the equations. As, generally, solving the optimization models is impossible using the analytical procedure, recently new metaheuristic methods are used to find the optimum results. So, in this research PSO algorithm was used to find of the unknown exponents and coefficients leading to the best result of proposed equations. Two different algorithms local PSO (LPSO) and Global PSO (GPSO) were used to find the unknown coefficients and exponents. Sensitivity analysis of the algorithms showed that the algorithms proposed different coefficients and exponents for different values population. Among the proposed coefficients and exponents one set of them are the best with minimum error. Comparsion between the experimental data and previouse prposed equations confirms strong scatter. Hence, in this type of problem using the metaheuristic algorithm and sensitivity analysis are recommended. The analysis of the results showed that the scour hole depth due to plane wall jets, is increasing funcions of densimetric Froude number, tailwater depth, time, and non dimensional form of the channel width. However, this parameter is a decreasing function of sediment gradation and non dimensional form of the sediment size. Similar trends were also observed for maximum ridge height formed at the downstream of the scour hole. The distance of the maximum height of the ridge is also an increasing function of densimetric Froude number, time, non dimensional form of the channel width, and Reynolds number of the jet. However this parameter is an decreasing function of standard deviation of the sediment mixture and tailawter depth. The sensitivity analysis of the effective parameters on scour hole dimension to find the more effective parameters were conducted. The latter analysis showed that Reynolds number, non dimensional form of the sediment size and non dimensional form of time has secondary effect on scour hole dimensions due to plane wall jets. However, the jet Reynolds number has the secondary effect on temporal variations of scour hole dimensions. The latter parameters were omitted from the effective parameters on scour hole dimensions without sensitive decreasing of equation accuracy.

Keywords

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Modares Civil Engineering journal
Volume 17, Issue 4
November and December 2017
Pages 229-239