Predicting submerged hydraulic jump characteristics using machine learning methods

Hydraulic jump typically occurs downstream of hydraulic structures by converting the supercritical to subcritical flow regimes. If the tail-water depth is greater than the secondary depth of the hydraulic jump, the jump will be submerged (SHJ). In these conditions, the momentum equations will not have an analytical solution and a new solution is required. In this study, after dimensional analysis, an experimental study was conducted in a rectangular flume with a length of 9 m, a width of 0.5 m and a depth of 0.45 m in a wide range of Froude numbers (Fr = 3.5 to 11.5) and submergence ratios (Sr = 0.1 to 4). The data were then normalized and divided into two parts of training and testing. A new technique, DGMDH, was used to predict the submerged hydraulic jump characteristics. The results were then compared with the GMDH model. The results showed that DGMDH model estimated the relative submergence depth, jump length, and relative energy loss with accuracy of R2 = 0.9944 and MAPE = 0.038, R2 = 0.9779 and MAPE = 0.0387, and R2 = 0.9932 and MAPE = 0.0192, respectively. While the accuracy of GMDH model for relative submergence depth, jump length, and relative energy loss was respectively R2 = 0.9923 and MAPE = 0.043, R2 = 0.9671 and MAPE = 0.0527, and R2 = 0.9932 and MAPE = 0.0192. Due to superiority of the DGMDH model over the GMDH model, it is recommended to use this model to estimate the submerged hydraulic jump characteristics. Highlight The results showed that DGMDH model have more accurate results than the GMDH model in predicting the relative submergence depth, jump length, and relative energy loss.

Numerical Simulations of the Flow Field of a Submerged Hydraulic Jump over Triangular Macroroughnesses

The submerged hydraulic jump is a sudden change from the supercritical to subcritical flow, specified by strong turbulence, air entrainment and energy loss. Despite recent studies, hydraulic jump characteristics in smooth and rough beds, the turbulence, the mean velocity and the flow patterns in the cavity region of a submerged hydraulic jump in the rough beds, especially in the case of triangular macroroughnesses, are not completely understood. The objective of this paper was to numerically investigate via the FLOW-3D model the effects of triangular macroroughnesses on the characteristics of submerged jump, including the longitudinal profile of streamlines, flow patterns in the cavity region, horizontal velocity profiles, streamwise velocity distribution, thickness of the inner layer, bed shear stress coefficient, Turbulent Kinetic Energy (TKE) and energy loss, in different macroroughness arrangements and various inlet Froude numbers (1.7 < Fr1 < 9.3). To verify the accuracy and reliability of the present numerical simulations, literature experimental data were considered.

Case Study on Application of the Step with Non-Uniform Heights at the Bottom Using a Numerical and Experimental Model

Steps effectively dissipate the energy of water along a path and reduce the size of the stilling basin but are rarely used in curved spillways. The shore spillway of a reservoir, which is restricted by topography, must be arranged in a curved shape. At high flow velocity and low water depth, some areas of the base plate of the curved spillway were not covered by the water. The water flow into the stilling basin did not form a submerged hydraulic jump. It was proposed that a step with bottom non-uniform heights be placed in the smooth base plate of the curved spillway to improve these undesirable hydraulic phenomena. A physical model experiment with a length scale of 1:40 verified the feasibility of the curved stepped spillway in engineering. Based on the k-ε model and volume-of-fluid (VOF) method, a three-dimensional numerical model was established, and the reliability of the numerical model was verified by measured data. The main flow region, velocity field, cavitation on a step, and the energy loss rate of steps were discussed. The comparison between a curved spillway with and without steps shows that the steps balance the partial centrifugal force in the curved section, making the water depth of the cross-section evenly distributed, and the base plate was no longer covered by water. The flow pattern on the steps was skimming flow, and the velocity of the flow into the stilling basin was greatly reduced. The elevation of the concave bank of the base plate was raised, resulting in the formation of transverse flow, which in turn constituted a three-dimensional energy dissipation pattern with the longitudinal flow. The energy loss was significantly higher than that of the smooth curved spillway. However, the triangular region near to the concave bank on the base plate experienced negative pressure, and an aeration device in front of the steps was needed.