Numerical investigation on energy loss in vertical drop with horizontal serrated edge

Introduction: Due to the simplicity of construction, vertical drops are widely used to reduce the steep slope of the canal and the volume of earthworks in irrigation and drainage canals. The upstream regime of flow in structures can be subcritical or supercritical. Stilling basins are usually used to dissipate the energy and prevent the bed erosion. Due to the fact that concrete materials are used in the construction of the stilling basin, Hydraulic engineers are always looking for a way to minimize the construction cost of downstream stilling basin and increase downstream energy loss of these structures. The dimensions of the downstream stilling basin depend on the geometry and hydraulic parameters of vertical drop. So In the present study, the effect of serrated drop edge on energy dissipation is investigated numerically using Flow3D software.
Methodology: Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses computers to analyze and simulate complex fluid problems. Flow-3D software is one of the most widely used software in the field of computational fluid dynamics.One of the prominent features of this software is the ability to simulate free-surface flow by VOF method. The governing equations of fluid flow are continuity and momentum equations. In Flow 3D software, several turbulence models are implemented. In the present study, k-ε and RNG turbulence models were used to perform the simulation. An experimental vertical drop set up with a height of 25 cm, width of 46 cm and a relative critical depth ranging from 0.2 to 0.35 was used for simulation. Total relative energy loss was used to validate the numerical results. Afterwards, different arrangements of dented (serrated) edge were used to simulate the flow on a vertical drop. The squared shapes in plan were used. The dimensions of dented edges which distributed symmetrically along the width were 6.9 and 4.6 cm (0.15 and 0.1 times the width of the flume) and their thicknesses were 2 cm. So, the number of dented edges was 3 and 4, respectively. The total number of meshes was considered to be 1237500. According to the dimensional analysis, the relative energy loss can be expressed as equation (1):
ΔE/Eu=f(yc/h, n, α) (1)
where, yc/h is the relative critical depth, n is the number of serrated edge and α is the relative dimensions of the serrated edge.
Results and Discussion: The RNG turbulence model showed better agreement with laboratory values compared to the k-ε turbulence model. The results showed that the use of dented vertical drop increases the energy loss for the same relative depth in downstream, length of falling jet and the turbulence intensity compared to the simple vertical drop. In the dented model, irregularities in the streamlines of downstream increased significantly. Increasing in dimensions of the dented edges and decreasing their number caused more irregularity in streamline and augmentation of the turbulence. So, the model with 3 dented edges (relative dimension of 0.15) performed the most turbulence and irregularity in the downstream streamlines. Energy losses in vertical drop with 3 and 4 dented edges and ordinary vertical drop are compared. The average energy losses were 26, 38, 15 and 25 percent, respectively. Although the use of dented edges increases the length of falling jet, but the stilling basin length for energy loss in models with dented edges is less than the ordinary model.
Conclusion: According to the results of the present study, the vertical drop with 3 dented edges and relative dimension of 0.15 performs the highest energy loss as compared to the ordinary vertical drop and other models of the present study. In this study, the Froude number ranged from 3.7 to 4.5 in the ordinary vertical drop to 2.7 to 2.9. Since a stilling basin is usually constructed at downstream of the vertical drop to dissipate the destructive kinetic energy of the flow and the dimensions of the stilling basin depends on the Froude number, so the use of dented edges in the vertical drop has such advantages as reduction in basin dimensions, augmentation in energy loss and lower depth for tail-water to form the hydraulic jump. Therefore, considering the hydraulic and economic conditions of the design, it is possible to use dented edges in practice to reduce the dimensions of the stilling basins and increasing the energy loss of flow in downstream of vertical drops. Some other features and conditions are not considered in this study. So, it is suggested that the effect of angle of dented edges on energy loss and other hydraulic parameters could be investigated.