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

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.

Experimental Analysis on the Use of Counterflow Jets as a System for the Stabilization of the Spatial Hydraulic Jump

This study presents an investigation on the use of submerged counterflow jets as a means for stabilizing the spatial hydraulic jump occurring in abruptly expanding channels. The characteristics of the flow downstream from the stilling basin and the main parameters influencing the effectiveness of the device in improving flow uniformity and reducing scouring potential are examined in laboratory tests, under several geometric configurations and hydraulic boundary conditions. The position within the stilling basin and the jet density (i.e., the number of orifices issuing the counterflow jets) were found to be important parameters influencing the performance of the device. Overall, the results indicate that this dissipation system has promising capabilities in forcing the transition from supercritical to subcritical flow, by significantly shortening the protection length needed to limit the phenomena of instability associated with spatial hydraulic jumps.

Numerical Simulations of 2D Hydraulic Jumps by a Parallel SPH Model

Hydraulic jumps are a rapid transition from supercritical to subcritical flow and generally occur in rivers or spillways. Owing to the high energy dissipation rate, hydraulic jumps are widely applied as energy dissipators in hydraulic projects. To achieve efficient and accurate simulations of 2D hydraulic jumps in open channels, a parallel Weakly Compressible Smoothed Particle Hydrodynamics model (WCSPH) with Shepard Density filter was established in this study. The acceleration of the model was obtained by OpenMP to reduce execution time. To further reduce execution time, a suitable and efficient scheduling strategy was selected for the parallel numerical model by comparing parallel speed-ups under different scheduling strategies in OpenMP. Following this, two test cases of uniform flow in open channels and hydraulic jumps with different inflow conditions were investigated to validate the model. The comparison of the water depth and velocity fields between the numerical results and the analytical solution generally showed good agreement, although there was a minor discrepancy in conjugate water depths. The numerical results showed free surface undulation with decreasing amplitude, which is more consistent with physical reality, with a low inflow Froude number. Simultaneously, the Shepard filter was able to smooth the pressure fields of the hydraulic jumps with a high inflow Froude number. Moreover, the parallel speed-up was generally able to reach theoretical maximum acceleration by analyzing the performance of the model according to different particle numbers.

Uncertainty analyses regarding evaluating effective parameters on the hydraulic jump characteristics of different shape channels

The hydraulic jump phenomenon is a beneficial tool in open channels for dissipating the extra energy of the flow. The sequent depth ratio and hydraulic jump length critically contribute to designing hydraulic structures. In this research, the capability of Support Vector Machine (SVM) and Gaussian Process Regression (GPR) as kernel-based approaches was evaluated to estimate the features of submerged and free hydraulic jumps in channels with rough elements and various shapes, followed by comparing the findings of GPR and SVM models and the semi-empirical equations. The results represented the effect of the geometry (i.e., steps and roughness elements) of the applied appurtenances on hydraulic jump features in channels with appurtenances. Moreover, the findings confirmed the significance of the upstream Froude number in the sequent depth ratio estimating in submerged and free hydraulic jumps. In addition, the immersion was the highest contributing variable regarding the submerged jump length on sloped smooth bed and horizontal channels. Based on the comparisons among kernel-based approaches and the semi-empirical equations, kernel-based models showed better performance than these equations. Finally, an uncertainty analysis was conducted to assess the dependability of the best applied model. The results revealed that the GRP model possesses an acceptable level of uncertainty in the modeling process.