Wang Ling-Ling
Hohai University, Nanjing, 210098, China
Abstract:
A 2D-3D combining turbulent model with complicated boundary is developed, in
which some new techniques are used to treat the free surface and boundary
condition .The important hydraulic parameters of flow field is obtained with
this model. The results are more reasonable than thadw traditional models. In
the traditional models, some parameters such as pressure cannot be obtained in
2D simulation and exact free surface is difficult to be obtained in 3D
simulation, since 2D and 3D turbulent flow fields are simulated separately. The
model has been used to simulate the flow field of the diversion open channel of
THREE-GORGE-PROJECT. The numerical results are verified by the actual
measurement and adopted by the construction authority in choosing the navigation
route of the diversion open channel.
Keywords: turbulence, model building, Navier-stokes equation;orthogonal curvilinear meshes, shallow water equation
Numerical method is widely used to simulate flow field of large body of water. When the depth is smaller than plane dimension, the water governing equation is shallow water equation. It has been well solved by the fraction steps. The results can provide water level and depth-average velocity at any point in the calculating zone except the velocity distribution along depth of water. Sometimes, this kind of results may be too rough when it is used as the decisive factor of underwater engineering. In this case, 3D flow field information is needed and it can be obtained only when 3D turbulent governing equation is solved.
Up to now, the calculating method of 3D is not mature and the accuracy is low In hydraulic engineering, the boundary condition of 3D simulation is difficult to present out. This will undoubtedly decline the accuracy. In this paper, a 2D-3D combining turbulent model is used to deal with free surface and the complicated boundary condition. By using this method, the calculated results are in good agreement with the measured data.
In order to improve the accuracy, the technique of orthogonal curvilinear grid generation is used to divide the calculating zone.
Shallow water equation under boundary fitted curvilinear system are:
(1)
where x and y are horizontal coordinates of physical plane and x, h of the computational plane; t is time; h is water level; H is local water depth; AB is stand for partial derivative of A to B.
indicate the length and width of
numerical grid in physical plane. U, V are depth-averaged velocity components in
the x
-direction and h-direction
respectively. The velocities u (in the x-direction) and v (in the y-direction)
are related to U and V by
(2)
Supposing that j is a general variable. It can stand for velocity u, v, w, turbulence energy
k and its dissipation rate e. Thus the governing equation in 3D flow can be written as below:
(3)
where: Gis diffusion parameter, Sjis source term. The calculating grid is generated by divide
boundary-fitted grid in 2D numerical calculating into several layer along depth. The water governing equation in 3D spatial can be written as
(4)
where
The boundary condition may be presented:
on inflow and outflow section:
on land boundary: v = 0
The results of 2D can be used as initial values of 3D numerical calculating. Boundary condition along depth on the inflow section can be gained by transfer the depth-average values into the parabola distribution. While on the outflow section is second condition.
Since the free surface has been obtained from 2D results and the accuracy is relative high. It can be used as initial condition in 3D simulation. On land boundary: velocity on tangential direction is zero and for k, e , the boundary function method is used.
The governing equation (1) can be separated into three parts by using the technique of fractional steps. From the calculating, we can obtain the depth-average velocity U, V and water level h. The details of calculation are written in reference [1]. By using k-e model and SIMPLE procedure, we can solve equation (4). The details are written in reference [2 ].
The numerical method has been used to simulate the flow field of THREE-GORGE-PROJECT diversion-channel flow. The computed results are in good agreement with the experimental data.
The distance between the water intake section and outflow section is about 5000 meters; The region concerned is divided into 51´43 elements. The physical plane is shown in Fig.l.
In the calculation, the size of space step Ds is 25.0 meters to 140.0 meters; the roughness n is about 0.020; the time step. Dt is 20 minutes to 60 minutes; the water level of the inflow and outflow are given by the measured value of SHU JIA AO and SHAN DOU PING hydrometric station.
Calculation grid of 3D is gained by divided the mesh in Fig.l 11 layers in vertical. Thus the results in 2D simulation can be used in 3D simulation directly. The initial condition and the boundary condition are in parabolic distribution in depth.
The distribution of computational velocity vectors in Fig. 2 is obtained in plane 2D calculation when the discharge is 14000m3/s . Fig. 3 shows the flow field of different layers of 3D calculating results. Comparisons between computed results and experimental data are shown in Table 1. The position of the points is shown in Fig.2.
On the upstream of diversion-channel, the river meanders right obviously. The flow here is in high velocity and the gradient of water surface is the biggest also. On the down-stream of diversion-channel, the velocity is larger along the right bank. while in the left bank, there is a large domain vortex. All these characters are proved to be right.
Table 1 comparisons between computed velocity and experimental data
|
Point Velocity(m/s) |
A |
B |
C |
D |
E |
F |
|
Measured |
2.74 |
2.85 |
2.94 |
3.04 |
2.67 |
1.19 |
|
Computed |
2.76 |
2.90 |
3.03 |
3.01 |
2.63 |
0.96 |
|
Error |
0.02 |
0.05 |
0.09 |
0.03 |
0.04 |
0.23 |
Fig. 1 Physical plane
Fig. 2 Computational velocity vectors of 2D flow field
Fig. 3 Computational velocity vectors of 3D flow field
(1) The method presented in this paper has many advantages; it can deal with the problem of the surface simulation and boundary condition easy.
(2) The orthogonal curvilinear coordinate system can be used to treat the complicated contour of natural river boundary. Thus, the computational accuracy will be increased largely.
(3) The numerical method presented here can be used in many aspects of engineering, such as environmental engineering, tidal river flow, river flow with sediment deposition, etc.
References
XU Wei-Xin and Jin Zhong-Qing, Numerical Simulation of High Turbulent Free Surface Flow Under the Curvilinear Coordinates, Journal of Hydrodynamics,Ser.B.3(l 995)65-71.
Jin Zhong-Qing, 1989: Numerical Solution to the Navier-Stokes Equations and Turbulence Models, Hohai University Publishing Corporation, (in Chinese).