Prediction of Hydraulic Jumps on a Triangular Bed Roughness Using Numerical Modeling and Soft Computing Methods

Mehdi Dasineh,Amir Ghaderi,Alban Kuriqi,Mohammad Ahmadi,Mohammad Bagherzadeh

doi:10.3390/math9233135

Abstract

This study investigates the characteristics of free and submerged hydraulic jumps on the triangular bed roughness in various T/I ratios (i.e., height and distance of roughness) using CFD modeling techniques. The accuracy of numerical modeling outcomes was checked and compared using artificial intelligence methods, namely Support Vector Machines (SVM), Gene Expression Programming (GEP), and Random Forest (RF). The results of the FLOW-3D® model and experimental data showed that the overall mean value of relative error is 4.1%, which confirms the numerical model’s ability to predict the characteristics of the free and submerged jumps. The SVM model with a minimum of Root Mean Square Error (RMSE) and a maximum of correlation coefficient (R2), compared with GEP and RF models in the training and testing phases for predicting the sequent depth ratio (y2/y1), submerged depth ratio (y3/y1), tailwater depth ratio (y4/y1), length ratio of jumps (Lj/y2*) and energy dissipation (ΔE/E1), was recognized as the best model. Moreover, the best result for predicting the length ratio of free jumps (Ljf/y2*) in the optimal gamma is γ = 10 and the length ratio of submerged jumps (Ljs/y2*) is γ = 0.60. Based on sensitivity analysis, the Froude number has the greatest effect on predicting the (y3/y1) compared with submergence factors (SF) and T/I. By omitting this parameter, the prediction accuracy is significantly reduced. Finally, the relationships with good correlation coefficients for the mentioned parameters in free and submerged jumps were presented based on numerical results.

Highlights

The hydraulic jump is a natural phenomenon in an open channel, sometimes regarded as an effective method of energy dissipation near structures such as gates, chutes, and spillways [1]
The results showed that the equation terms have little influence in determining the location of the hydraulic jump
The results showed that for energy dissipation for (ΔE/E1)f, the Support Vector Machines (SVM) model with R2 = 0.9848 and Root Mean Square Error (RMSE) = 0.0313, and for the testing phase (ΔE/E1)S, R2 =

Summary

Introduction

The hydraulic jump is a natural phenomenon in an open channel, sometimes regarded as an effective method of energy dissipation near structures such as gates, chutes, and spillways [1]. If the tailwater depth equals the subcritical sequent depth, it is called a free hydraulic jump. If the tailwater depth is greater than the subcritical sequent depth, the jump is submerged (submerged hydraulic jump). Enormous research studies dealing with the free and submerged hydraulic jumps such as McCorquodale and Khalifa [3], Smith [4], Graber et al [5], Vallé and Pasternack [6], Dey and Sarkar [7], Tokyay et al [8], and Samadi-Boroujeni et al [9] were carried out. Ead and Rajaratnam [10] experimentally studied hydraulic jumps on corrugated beds

Objectives

Methods

Results

Conclusion