Investigating the simultaneous effect of divergence and bed roughness on hydraulic jump characteristics

Introduction: Hydraulic jump is a fast and irreversible variable flow that occurs downstream of hydraulic structures and the result of which is the rapid transformation of supercritical flow into subcritical flow, which increases the depth of the flow and causes a significant loss of energy. By examining the previous studies, it is clear that the roughness bed or the divergence plays an important role in hydraulic jump characteristics. Methodology: FLOW-3D is one of the suitable software in hydraulic Phenomenon modeling. In order to ensure the appropriate capability of FLOW-3D software in simulating hydraulic jump, first, a research related to this issue which has been investigated in the past in a laboratory, is simulated in the software. Then, by comparing the results of the numerical simulations with the laboratory data and ensuring the proper functioning of the software, new simulations are made. The experiments related to the physical model used were carried out in a laboratory flume with walls and floors made of transparent plexiglass, 5 meters long, 0.3 meters wide, 0.45 meters high, and zero longitudinal slope. To create a supercritical flow, a steel valve with a height of 0.65 meters and a thickness of 3 mm and an opening height of 1.7 cm was used for a non-prismatic channel with a divergence ratio of 0.33. In order to create symmetrical opening ratios of 0.33, glass boxes with a length of 0.5, a height of 0.2 and a width of 0.1 meters were placed on both sides of the flume. After the simulation and by checking the R², MAE and RMSE parameters, the k-ɛ model and the mesh with the number of 687600 cells were selected as the optimal mesh. In this research, according to the selection of four types of bed (smooth bed, rough bed with hemispherical roughness and diameter of 3, 4 and 5 cm) and three divergence angles (7, 14 and 90 degrees) and five Froude numbers (Froude number: 4.34, 5.71, 6.95, 8.17, and 9.37) in total, Simulated for 60 different experiments. Results and discussion: The results showed that for the maximum discharge for the sudden divergent channel, the roughness of the bed with a diameter of 5 cm causes the amount of the flow depth to decrease by 19.77% compared to the smooth bed. Also, the sudden divergence of the bed reduces the flow level by 23.75%. In all cases, the value of y₂/y₁ increases with increasing Froude number. With the increase of the Froude number from 4.34 to 9.37, the value of y₂/y₁ on the flat bed increases by 15.54%. With the increase of the Froude number from 4.34 to 9.37, the value of y₂/y₁ on the rough bed with a diameter of 3 cm decreases by 5.67% on average compared to the smooth bed. As the roughness diameter increases from 3 to 5 cm, the value of (L_j/y₁) decreases by 15.58% on average. The results show that the (E_L/E₁) ratio increases with the application of bed roughness. So that by applying a roughness with a diameter of 5 cm, the value of (E_L/E₁) compared to a smooth bed increases by about 5% on average, and by applying a sudden divergence, the value of (E_L/E₁) compared to a bed diverging under an angle of 7 degrees The average increases by 4.58%. Conclusion: FLOW-3D is a good software to prediction of hydraulic jump characteristics in divergent channel with smooth bed and rough bed and The k-ɛ turbulence model was selected as the optimal turbulence model. Increasing the bed roughness size decreases the secondary depth for all values ​​of 𝐹𝑟₁. The sudden expanding of the rough bed with a roughness of 4 cm reduces the y₂/y₁ by 12.98% compared to the bed with a divergence under 7 degrees. Increasing the size of the roughness decreases the length of the hydraulic jump. According to the results, the length of the hydraulic jump in the rough bed with a diameter of 5 cm compared to the smooth bed decreased by 26.12%. Also, by increasing the roughness diameter from 3 to 5 cm, the value of (L_j/y₁) decreases by 15.58% on average. By applying roughness with a diameter of 5 cm, the value of (E_L/E₁) increases by about 5% on average compared to the smooth bed. Results show that the divergence angle of the bed is effective on streamlines. But, increasing the roughness of the bed, there is no noticeable change in the streamlines. However, increasing the bed roughness size, increases the amount of disturbance energy in the section.