Vshaped stepped spillway is a new shaped stepped spillway, and the pressure distribution is quite different from that of the traditional stepped spillway. In this paper, five turbulence models were used to simulate the pressure distribution in the skimming flow regimes. Through comparing with the physical value, the realizable
The unique structure of the stepped spillways causes abundant vortices near the steps [
Considering that the flow pattern of the stepped spillway reflects the hydraulic characteristics of the flow, many scholars have also studied the flow regimes. The flow regimes of a stepped spillway can be divided into nappe flow, transition flow, and skimming flow [
In this paper, the stepped spillways of
The numerical model layout.
Fluent software was used to perform these simulations using the finite volume method (FVM). The numerical model of the stepped spillway (shown in Figure
The volume of fluid (VOF) was used to track the airwater interface, which was presented by Hirt and Nichols [
In this approach, the tracking interface between air and water was accomplished by the solution of the continuity equation for the volume fraction of water:
The standard (ST)
This model is a semiempirical model based on transport equations for turbulence kinetic energy and turbulence kinetic energy dissipation rate. For its assumption of fully turbulent, it is valid only for fully turbulent flows.
The renormalization group (RNG)
This model was derived using a rigorous statistical technique. Although it is similar in form to the ST
The realizable (Rl)
This model can accurately simulate the spreading rate of both planar and round jets and the flows involving rotation, boundary layers under strong adverse pressure gradients, separation, and recirculation.
The standard (ST)
This model is an empirical model based on model transport equations for the turbulence kinetic energy and turbulence kinetic energy dissipation rate.
The shearstress transport (SST)
A physical model of Vshaped stepped spillway is shown in Figure
The physical model layout.
Figure
The pressure distribution on steps ((a) on Vshaped step, (b) on traditional step).
Since the pressure distribution changed along the cross section in Vshaped stepped spillway, three rows of pressure measurement points were adopted, and the position of rows was in
Pressure measurement points on steps.
In this section, we take the pressure distribution on one step (#43) when Fr = 5.99 as an example to illustrate. Figure
The pressure distribution of profiles on step ((a) on horizontal surface, (b) on vertical surface, Fr = 5.997).
For comparing the turbulence models performance statistically, the root mean square error (RMSE) criterion was estimated using
Table
The RMSE values of different turbulence models.
Step surface  Profile  St 
RNG 
Rl 
St 
SST 

Horizontal surface 

0.98  1.93  1.30  2.25  2.81 

2.00  1.39  1.20  1.71  1.93  

2.56  1.63  1.11  1.98  1.80  


Vertical surface 

0.82  0.75  0.53  0.67  0.59 

1.15  1.06  0.99  1.15  1.12  

1.70  2.49  1.51  1.96  1.85 
Figure
The free water surface of physical model and numerical model ((a) physical model, (b) Rl
For stepped spillway, when the flow transitions from one step to the next step, a part of the flow travels in the downstream direction, and the other part changes direction because of the collision between the water and the steps. The flow that changes direction forms a reflux and collides with the vertical step surface. Then, the flow is forced to climb and blocked by the mainstream, forming stable vortices.
To clearly show the spiral flow and downstream flow, the streamlines are shown in different steps in Figure
The velocity vectors and streamlines on steps ((a, c) traditional steps, (b, d) Vshaped steps; Rl
Velocity vector
Velocity vector
Streamline
Streamline
This flow field in Vshaped stepped spillway increases the turbulence intensity; therefore, there will be better energy dissipation rate and aeration properties and this will be studied in the future.
In this paper, the pressure distribution of Vshaped stepped spillway was studied using five turbulence models. The following conclusions can be drawn:
(
(
Chute width
Inlet height of the model
Turbulent kinetic energy
Turbulent kinetic energy dissipation rate
Volume fractions of air
Volume fractions of water
Generation of turbulence kinetic energy due to the mean velocity gradients
Generation of turbulence kinetic energy due to buoyancy
Mean velocity component in the
Turbulent viscosity
Userdefined source terms
Inverse effective Prandtl numbers
Turbulent kinematic viscosity
Generation of
Effective diffusivity of
Dissipation of
Userdefined source term
Crossdiffusion term
Width of the step
Height of the step
Froude number.
The authors declare that they have no conflicts of interest.
This project was supported by the National Key Research and Development Program of China (no. 2016YFC0401707), the National Natural Science Foundation of China (no. 51579165), and the National Science Fund for Distinguished Young Scholars (no. 51625901). The authors acknowledge the working of Dr. Yong Peng.