Numerical Simulation of Flow Characteristics in Vertical and Inclined Rectangular Drops Using RNG k-ε

Abstract
Abstract
Background and Objectives
This study employs computational fluid dynamics (CFD) to investigate the hydraulic behavior and energy dissipation efficiency of rectangular drop structures, encompassing both vertical and inclined configurations. Drop structures are integral to irrigation and flood control systems, serving to reduce water velocity and mitigate channel bed erosion. Vertical drop structures promote significant energy loss through the formation of hydraulic jumps, whereas inclined drops enable smoother flow transitions. Hydraulic jumps facilitate a reduction in the total energy of a moving fluid, thereby preventing scouring of channel banks and converting a portion of the fluid's kinetic energy to stabilize downstream flow conditions. The primary objective of this research is to numerically evaluate flow patterns and energy dissipation rates in vertical and inclined rectangular drop structures, with an emphasis on the influence of slope angle and geometric configuration. The study aims to provide practical insights for optimizing drop structure design to maximize energy dissipation with minimal construction costs. To validate the reliability of the CFD models, experimental data from prior studies are utilized. The flow characteristics, including water depth, energy loss, and jump length, are compared between both vertical and inclined drop structures.

Methodology
The computational domain for the simulation geometry, comprising a rectangular channel with an integrated drop structure, was developed and meshed using GAMBIT (ANSYS). The length of the rectangular channel (L) was set to 2 m. The simulations were performed using ANSYS FLUENT software, employing the finite volume method (FVM) for numerical analysis. The RNG k-ε turbulence model was selected due to its established accuracy in simulating turbulent open-channel flows. A structured mesh was generated for the computational domain of both vertical and inclined drop geometries to ensure accurate numerical simulations. Boundary conditions were established to simulate steady-state, incompressible turbulent flow, incorporating the assumption of free-surface flow with air-water interaction. The Volume of Fluid (VOF) model was employed to precisely capture and track the free surface in the simulations. The investigated geometries encompassed drop heights of 4 cm, 8 cm, and 12 cm, with inclined drops configured at slope ratios of 1.5:1 and 2:1. The simulations encompassed a range of flow discharges and drop configurations to thoroughly evaluate hydraulic behavior. Inlet flow depth (H) and approach flow velocity (V) were determined, with the Reynolds number ranging from 9000 to 28000. A mesh sensitivity analysis was conducted to verify the accuracy and reliability of the numerical results. The numerical model was validated by comparing the simulation results with experimental data reported by Sholichin and Akib (2010). Accordingly, a mesh consisting of approximately 20000-30000 elements was determined to be optimal for all developed models to effectively capture the flow characteristics. Boundary conditions were specified for all models. Pressure inlet and outlet boundary conditions were applied at the channel inlet and outlet, respectively. For the free surface, a symmetry boundary condition was applied, while wall boundary conditions were assigned to the channel bed, and the drop structure. Principal parameters, including velocity vectors, flow depths before and after the hydraulic jump, energy dissipation percentage, and turbulence, intensity were computed and analyzed. The numerical model demonstrated strong agreement with experimental results, exhibiting error margins within 9.8%, thereby validating the model accuracy. The comparison between simulated secondary depth values and experimental data revealed that the relative error for secondary flow depths across all stilling basins ranges from 0% to 9.5%. This demonstrates the satisfactory accuracy of the conducted simulations.

Findings
Numerical simulations reveal that the velocity vector patterns in vertical and inclined drop structures vary depending on the slope angle. The inclined drop structures exhibited a more uniform velocity distribution and reduced energy dissipation compared to vertical drop structures. Vertical drop structures produced more intense vortices at the onset of the hydraulic jump, resulting in greater localized energy loss. The RNG k-ε model effectively captured the turbulent characteristics and flow separation phenomena. Water surface profiles and energy loss values closely aligned with experimental measurements, with the average relative error for predicted secondary flow depths remaining below 9.5 % across all configurations. Energy loss in drop structures decreases with increasing drop number, as higher flow discharges result in hydraulic jumps characterized by weaker vortices. The highest energy dissipation efficiency was observed in vertical drops with larger step heights.

Conclusion
The results indicate that the RNG k-ε turbulence model, combined with the VOF method, is well-suited for predicting energy dissipation in both vertical and inclined drop structures. Vertical rectangular drop structures exhibit enhanced energy dissipation effectiveness relative to inclined drops under similar hydraulic conditions. The validated CFD model serves as a reliable tool for optimizing the design of energy dissipation structures. Choosing an optimal slope improves flow control and enhances the structural safety of the system.