Chen Wenxue and Xie Xingzong
China Institute of Water Resources and Hydropower Research, Beijing, China, 100038
Tel.
86-10-63204115
Abstract:
This paper concerns with the numerical simulation method of turbulent flows
around the ogee valve of Three Gorges ship lock. At first the calculating domain
is divided into several sub-domains by multi-block matching method, and in each
sub-domain structured orthogonal grids are generated by T&M and Hilgenstock
method, finally the turbulent flow field is simulated by Hybrid Finite Analytic
Method (HFAM) with the standard k-εmodel.
The numerical results are in agreement with two-component laser-Doppler
measurements.
Keywords: multi-block matching method; numerical simulation; turbulent flow field; HFAM
The double-line five-stage ship lock is one of the three main projects in Three Gorges hydrocomplex and it is also the largest inland navigation structure in the world. The total head of the ship lock is 113m, and the head of the mid-stage reaches to 45.2m. Phenomena such as cavitation and vibration may occur when the ship lock is operated under such high head. For safe operation of the ship lock, the structure and hydraulic performance of the ship lock have been widely studied[1] and the turbulent flow field around the ship lock should be deeply studied for structure optimization of the ship lock.
Numerical simulation of the turbulent flows around the ship lock is difficult, since the unsteady turbulent flows and the flow boundary are very complicated. Furthermore, the high speed jet in the small clearance between the ogee valve of the ship lock and the lintel increases the complexity of the flow downstream of the ogee valve. And when the small clearance is taken into account in numerical simulation, structured grid generation becomes very difficult. For solving this problem, the computational domain is divided into several blocks[2,3], in each block grids are generated individually, and finally the turbulent flows are calculated by means of the Hybrid Finite Analytic Method (HFAM)[4].
For complex
computational domain, when structured grids are used in numerical simulation,
the computation domain is usually divided into several sub-blocks for
convenience of grid generation and numerical simulation. The sub-blocks can be
classified into two types, that is overlapped one and patched one. For two
patched blocks, there should be a connecting block which is used to transmit
information of the adjacent blocks for getting continuous pressure field if
staggered grids are used in the numerical simulation[8]. This domain
dividing method is named as multi-block and matching method. Grids in sub-blocks
can be numbered individually and fluid flows in different blocks are calculated
separately. Fig. 1 depicts the divided blocks of the computational domain around
the ogee valve with bottom expansion gallery of the Three Gorges ship lock.
Obviously, block 5 and block 6 are
connecting blocks.
Fig. 1 Multi-blocks of the computational domain
In structured grid generation, two problems are very important for numerical simulation. One is grid distribution, the other is the grid orthogonality. For improving meshes quality, many grid generation methods had been presented, such as TTM method[5], T&M method[6] and Hilgenstock 3D1 and 3D2 method[7]. TTM method is inconvenient since the source terms and the values of the adjustable parameters for controlling grid distribution require artful selection and are problem dependent. While T&M method can automatically adjust interior grid distribution according to grid point distribution along boundaries, but it is not good at grid orthogonal control. And in Hilgenstock method some parameters such as angles between girds and boundaries are used to modify the source terms for improving grid orthogonality. In this paper, T&M method and Hilgenstock method are combined to generate computational grids, that is the initial grids are calculated by means of T&M method, and then the source terms in the Poisson equations are modified by Hilgenstock method. Thus meshes with suitable grid distribution and good orthogonality can be gotten.
For two dimensional problems, grid coordinates in physical space can be determined by the following equations[6]:
(1)
(2)
, on the boundary of η=const
(3)
, on the boundary of ξ=const
(4)
where (x,y) is the coordinate of the grid point in physical space, while (ξ,η) is the coordinate of the grid point in computation domain. The source terms φand ψof the interior grids can be calculated by linear interpolation of that on the boundaries
Grids calculated by equation (1) are usually non-orthogonal. For improving orthogonality of grids, the source terms in equation (1) should be modified. According to Hilgenstock method[7], the source terms can be calculated by the following formula:
(5)
(6)
here,
and
are angles between grids and boundaries
and
respectively. Subscript b denotes
boundary, and σis
a constant which is usually smaller than 1 for stability of calculation.
Superscripts n and n+1 denote iteration number.
Fig.2 depicts partial grids around the ogee valve with opening of 0.3. Obviously, the grids are orthogonal.
(a) (b)
Fig. 2 (a) Grids near the ogee valve, (b) grids in the clearance
The Hybrid Finite Analytic Method was first proposed by Li[4], which has merits as auto upwind and low numerical dissipation, and had been widely used in numerical simulation of laminar and turbulent flows. In this paper HFAM is used to simulate the complex turbulent flows around the ogee valve of Three Gorges ship lock.
For two dimensional steady turbulent flows, the relevant continuity and momentum equations in arbitrary curvilinear coordinates (ξ,η) can be written as the following generalized form[8]:
(7)
where,
, A and B are coefficients related with variables of U, V, k and ε,
and S is source terms.
The above controlling equations can be discreted into the 5-point scheme of HFAM[4,8]:
(8)
in which,
By means of the numerical method
mentioned above, the turbulent flows around the ogee valve of Three Gorges ship
lock were calculated by the standard k-εmodel.
With reference to Figure 1, there are four kinds of boundaries in the solution
domain, those are inlet, outlet, the upper surface of the ogee valve well and
solid boundaries. Uniform velocity profiles were specified at the inlet, that is
U=1, and V=0. The turbulent kinetic energy k at the inlet was determined by the
experiment data, and the dissipation rate at the inlet was specified as 0.8kinlet.
At the outlet the turbulent flow was supposed to be fully developed, and
was specified. At the solid surfaces, the ordinary wall functions were used. And
on the upper surface of the valve well, symmetry conditions were used.
In this paper, we only present the numerical results of the flow field around the ogee valve with opening of 0.3. And the downstream gallery is a kind of bottom expansion gallery. For detail results see Reference [9]. Figure 3 shows that there are two main vortices, one with small voritcity is in the valve well, the other with strong vorticity is in the expansion gallery. And in the left bottom corner of the expansion gallery, there is also a small vortex. The flow pattern is coincident with the visualized results[1]. In the clearance between the valve and the lintel, there is a high speed jet with maximum speed of 2.45, thus the pressure in the clearance is very low. The numerical simulation also shows that the minimum pressure is located in the clearance. Therefore cavitation may occur in the clearance.
Fig. 3 Streamlines near the ogee valve
For further understand the turbulent flows around the ogee valve, ensemble-averaged statistics have been obtained from two-component laser-Doppler measurements which were carried out in the high speed hydraulics national laboratory of Sichun University. Figure 4 and Figure 5 show comparisons between computed and experimented velocity profiles at various locations along the bottom expansion gallery. Near the ogee valve, agreement is seen to be very close, while at the further downstrem of the ogee valve, agreement is not very good. One main reason of the difference between calculated and measured results may be the turbulent model used in the calculation. The turbulent flow downstream of the ogee valve is a kind of strong shear flow which is anisotropy and inhomogeneous. While the standard k-εbased on Boussinesq hypothesis cannot depicts the anisotropy of turbulence. Thus for accurately simulating turbulent flows around the ogee valve, other turbulent models such as RSM, nonlinear k-εmodels[10,11] should be used.
A numerical method was presented for simulating turbulent flows with complex boundaries. This method is very simple, and it is easy to control grid distribution and grids orthogonality. By means of this method, turbulent flow field around the ogee valve of Three Gorges ship lock was calculated. The simulated results are in agreement with 2D LDV measurements. For accurately simulation of the complicated turbulent flows, better turbulent models should be used.
Fig. 4 Streamwise velocity distribution
(▲--measured value, the coordinate origin is set at the bottom edge of the ogee valve)
Fig. 5 Vertical velocity distribution
(▲--measured value)
References
[1] Q.H. Xu, R.K. Zhang, Application foundation study of navigation structure, China hydraulic and electrical press, Beijing, 1999.
[2] Chesshire,G., Henshaw, D., Composite overlapping meshes for the solution of partial differential equations, J. Comp. Phys. 90, 1-64, 1990.
[3] Steinthorsson, E., Ameri, A. A., Computations of viscous flows in complex geometries using multiblock grid systems, AIAA, 95-0177, 1995.
[4] W. Li, Hybrid finite analytic method of viscous fluid, Science press, Beijing, 2000.
[5] Thompson, J.F., Thames, F.C., Mastin, C.S., Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two dimensional bodies, J. Computational Physics, Vol.15, 1974, pp299-319.
[6] Thomas, P.D., Middlecoff, J.F., Direct control of the grid point distribution in meshes generated by elliptic equations, AIAA J., Vol.18, No.2, 1980, pp652-656.
[7] Z.K. Zhang, F.G. Zhuang et al, Study on grid distribution and orthogonality control in three dimension flow around combination of wing-body-tail, Computational Physics, Vol.14, No.2, 1997, in Chinese.
[8] W.X., Chen, Numerical simulation on stress-induced secondary flows and flows around axisymmetric bodies, Ph.D. thesis, 1997, Wuhan University of Hydraulic and Electrical Engineering, in Chinese.
[9] W.X., Chen, Study on the flow field around the ogee valve of Three Gorges ship lock, China Institute of Water Resources and Hydropower Research, HY-2000-03-005, December, 1998.
[10] Speziale, C.G., On nonlinear k-l and k-εmodels of turbulence, J.F.M., Vol.178, pp159-175, 1987.
[11] Yakhot, V., S.A. Orszag, et al, Development of turbulence models for shear flows by a double expansion technique, Physics Fluids, A4(7), pp1510-1520, 1992.