Energy dissipation is one of the most important factors in choosing stepped spillways. However, very few studies have investigated energy dissipation with different horizontal face angles. In this paper, the realizable k-ε turbulent model was used to study the flow field, energy dissipation rates and turbulent kinetic energy and its dissipation rate for different stepped spillways with five horizontal face angles in the skimming flow regions. Results showed that the field and direction of the flow were changed by the horizontal face angles of the stepped spillway, which produced some unique characteristics and thus caused better energy dissipation. The fluctuation of free water surface will be larger with increasing horizontal face angles and the energy dissipation rate decreases with an increasing unit discharge and increases for the enlargement of the horizontal face angles. This conclusion could provide a reference for the relevant research of V shaped stepped spillways.

Water wave dynamics and its engineering application have always been a key issue in the field of hydraulics, and effective and efficient numerical methods need to be proposed to perform three-dimensional (3-D) simulation of large-scale water fluctuation in engineering practice. A single-phase free-surface lattice Boltzmann method (SPFS-LB method) is coupled with a large-eddy simulation approach for simulating large-scale free water surface flows, and the simulation is accelerated on a GPU (graphic processing unit). The coupling model is used to simulate the evolution process of dam-break wave after complete and partial dam-break. The formation mechanism of horizontal and vertical vortices in water after partial dam-break and the advance and evolution process of dam-break flow on non-contour riverbed are analyzed. The method has been verified to be reasonable and can obtain a more accurate time curve of water level fluctuation. Applying this method to practical arch dams, discharge coefficients consistent with empirical formulas can be obtained by comparison and analysis, and the surface flow phenomena (such as tongue diffusion, surface fragmentation, and surface fusion) can be well simulated by this method. In addition, based on the key technology of parallel computing on a GPU, the implementation of the SPFS-LB model on a GPU unit achieves tens of millions of lattice updates per second, which is over fifty times higher than that on a single CPU chip. It is proved that the proposed method for large-scale water fluctuations can be used to study practical engineering problems. The mathematical model method realizes the efficient and accurate simulation of practical physical problems.

Vertical jet in flowing water is a common phenomenon in daily life. To study the flow and turbulent characteristics of different jet orifice shapes and under different velocity ratios, the realizable k-ε turbulent model was adopted to analyze the three-dimensional (3D) flow, turbulence, and vortex characteristics using circular, square, and rectangular jet orifices and velocity ratios of 2, 5, 10, and 15. The following conclusions were drawn: The flow trajectory of the vertical jet in the channel exhibits remarkable 3D characteristics, and the jet orifice and velocity ratio have a significant influence on the flow characteristics of the channel. The heights at which the spiral deflection and maximum turbulent kinetic energy (TKE) occur for the circular jet are the smallest, while those for square jets are the largest. As the shape of the jet orifice changes from a circle to a square and then to a rectangle, the shape formed by the plane of the kidney vortices and the region above it gradually changes from a circle to a pentagon. With the increase in the velocity ratio, the 3D characteristics, maximum TKE, and kidney vortex coverage of the flow all gradually increase.