Numerical simulation and analysis of water flow over stepped spillways

Abstract

Numerical simulation of water flow over the stepped spillway is conducted using Mixture multiphase flow model. Different turbulence models are chosen to enclose the controlling equations. The turbulence models investigated are realizable k-ε model, SST k-ω model, v 2 -f model and LES model. The computational results by the four turbulence models are compared with experimental ones in the following aspects: mean velocity, the spanwise vorticity and the growth of the turbulent boundary layer thickness in the streamwise direction. It is found from the comparison that the realizable k-ε model, in which the rotation tensor is included, shows good performance for simulation of flows involving rotation, boundary layer and recirculation. The realizable k-ε model is the most efficient in simulating flow over stepped spillways. Further, the characteristics of water flow on the stepped spillway are studied in terms of the mean velocity profile normal to the pseudo-bottom and the pressure field on the steps based on the simulation results using realizable k-ε model. stepped spillway, turbulence model, numerical simulation, boundary layerAs an important energy dissipation structure, stepped spillways are widely used in recent years due to the development of roller-compacted concrete (RCC) technique. When the water skims over the steps, steady vortices appear in triangular zone formed by the step faces and the pseudo-bottom, and air entrainment occurs due to high turbulence. Momentum exchange exists between the recirculating fluid trapped on the steps and the upper skimming flows.It can be tracked back to the 1970s the first studies that payed attention to the hydraulic design of stepped spillway [1] . In the following 30 years, very active experimental research has been done on the air-water flow characteristics over stepped spillways, such as flow patterns, inception of air entrainment, air concentration, velocity field, pressure field and energy dissipation [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . The complexity of the flow structure and the investigation on scale effects has caused uncertainties in transposing the experimental results to prototype. The minimum Reynolds and Weber numbers required to minimize scale effects in physical modeling of air-water two-phase flows on stepped spillways were given by Boes and Hager [16] . With the development of computational fluid dynamics (CFD), complex multiphase flows can be simulated numerically and the results are reliable and integrated. The flow over stepped spillways was simulated using the VOF (Volume of Fluid) method in conjunction with standard k-ε turbulence model by Chen et al. [17] . Cheng et al. [18,19] used the VOF and Mixture models respectively to simulate flow over stepped spillways and reported that the Mixture model has an obvious advantage over the VOF model. The steps behave as macroroughness and the flow is highly turbulent, therefore the definition of a correct turbulence model is fundamental to get reliable results. In this paper, the Mix

Hydraulics of the Developing Flow Region of Stepped Spillways. II: Pressure and Velocity Fields

“…6). The occurrence of higher pressures at the lower edge of the cavity was consistent with numerical simulations (Qian et al 2009, Bombardelli 2015. Figure 6 also shows a few regions with a nearly-constant pressure gradient, implying that the streamlines were parallel despite the non-hydrostatic pressure distributions.…”

“…The observations were consistent with the velocity data of Amador et al (2006) and numerical modelling (Qian et al 2009). A close examination of Figure 6 showed longitudinal variations in pressure profiles across step cavities: for example, the step cavity 2-3 was generally governed by positive pressures, while a negative pressure core was observed in step cavity 3-4.…”

“…The data showed maximum turbulence levels just behind the step edges, where the separation of the shear layer developed. Numerical simulations of these experiments suggested rapidlyvaried velocity and pressure fields in the developing flow (Qian et al 2009). …”

Comparison of Different Turbulence Models for Numerical Simulation of Pressure Distribution in V-Shaped Stepped Spillway

“…Chen et al [2] studied the pressure distribution of traditional stepped spillway using -turbulence model and satisfactory results were obtained. Qian et al [18] compared four turbulence models (realizable -model, SST -model, V 2 -model and LES model) and found that the realizable -model was the most efficient in simulating flow overstepped spillways which involves rotation. And the pressure field was studied using the realizable -model.…”

Application of Displacement Height and Surface Roughness Length to Determination Boundary Layer Development Length over Stepped Spillway

“…A CFD model complements experimental and theoretical fluid dynamics by providing an alternative cost-effective means of simulating real flows. Substantive CFD research has been conducted for simulation of flow over a stepped spillway, especially for the flow field upstream of the air entrainment inception, e.g., [36][37][38][39][40][41][42][43][44][45]. In this paper, the commercial software Fluent 6.2 [46] was used to process the numerical simulation.…”