(1)
Zheng Jinhai1, Yan
Yixin1 and
Zhu Yuliang1
1
Research Institute of Coastal & Ocean Engineering, Hohai Univ.,
Nanjing 210098, China
Tel.: +86-25-3713777 ex.50637, Fax.: +86-25-3701905
E-mail:
jhzheng@china.com
Abstract:
After construction of the pipeline segment of the submerged cross-river tunnel,
the level of riverbed is raised in the deep-water side of the curved reach in
the Huangpu River Estuary and the bed elevation is then changed. A
three-dimensional finite-difference hydrodynamic model is developed to simulate
tidal flow of the curved reach with complex bathymetry, and it is applied to
evaluate the influence of a submerged cross-river tunnel on the adjacent flow
domain. The mode-splitting technique is employed to solve the three-dimensional
tidal flow problem. The modified Double-Sweep-Implicit method is adopted to
improve the computational stability and accuracy. In order to obtain the
satisfactory open boundary conditions, the mathematical models of the East China
Sea and the Yangtze Estuary are also established to give a control boundary.
Based on the calibration and verification of these models, variable water level
and the velocity tensors including the plane velocity field and the vertical
transverse flow pattern are studied numerically. It is concluded that the
submerged cross-river tunnel has little influence on the flooding control
structure and the boat sailing safety, although the longitudinal and transverse
flow have some changes, which are favourable for the project.
Keywords: submerged cross-river tunnel, three-dimensional hydrodynamic model, improved Double-Sweep-Implicit method, tidal curved reach, transverse flow, flood control, boat sailing safety
Due to the restraint of the general design of the peripheral circuit highway of Shanghai metropolis, the pipeline segment of the submerged cross-river tunnel is raised in the deep pool of the tidal curved reach of the Huangpu River Estuary to ensure the utilization of the tunnel. After the completion of project, the top elevation of the segment in the deep pool is -15.500m and 90m wide, with 1:10 slope upstream and contiguous to the natural riverbed in other directions. In the engineering site, the river bed elevation is changed from -21.500m to -15.500m, the raising amplitude up to 6m, which is the rare case of the submerged cross-river tunnel project. Would the change of the river bed elevation result in the alternation of the water level, the flow pattern and the river bed evolution in the adjacent water area of the project? Would the project affect the use of the flood control installations and the water transportation facilities, such as the navigation channel, the anchorage space and the harbour? Furthermore, the submerged cross-river tunnel is so close to Wusongkou and Yuncaobang mouth, therefore it is an important problem whether the influence sphere would go beyond them or not. Those are followed with interest by the municipal administration, the navigation and the water conservancy departments.
Many researchers have been carried out on curved channel flows, but the three-dimensional nature of the curved channel flow phenomenon is still difficult to analyze mathematically. Experimental and/or analytical studies were conducted by Yen(1965), Krishnappan & Lau(1977), De Vriend(1981), Odgaard(1986), Johannesson & Parker(1989), and Chang(1992). Various three-dimensional numerical models have been used to simulate the curved channel flows, notably Leschziner & Rodi(1979), Demurea & Rodi(1986), Shinizu et al.(1990), Demuren(1993), Meselhe et al.(1995), Olsen & Stokesth(1995), Ye & McCorquodale(1998), Sinha et al.(1998), Meselhe & Sotiropoulos(2000). Leschziner & Rodi(1979) and Demurea & Rodi(1986) employed a partially parabolic version of the Reynolds-average Navier-Stokes and the k -ε turbulence closure equations — assuming a predominant flow direction and negligible stream-wise diffusion — to calculate flows through a strongly curved 180°bend and a meandering channel, respectively. The parabolic flow assumptions and the cylindrical coordinate system employed to formulate the governing equations restrict the applicability of both methods to non-separated flows through open channels of simple cross section. Shinizu et al.(1990) applied the 3D continuity and momentum equation in an orthogonal, curvilinear coordinate system with hydrostatic approximation to compute the flow field in a 180°curved, rectangular cross-sectional channel with 6-m-long straight approach and a 3-m-long straight exist. Meselhe et al.(1995) employed the full elliptic form of the governing equations — the Reynolds-average Navier-Stokes and the standard k-ε turbulence closure — formulated in generalized curvilinear coordinates to simulate flow through a meandering channel of trapezoidal cross section, and focused primarily on proposing a simplified approach for calculating the water surface elevation as part of overall solution procedure. Ye & McCorquodale(1998) developed a 3D hydraulic model with a curved-channel-fitted coordinate system in horizontal plane and a σ-coordinate in z-direction to simulate the curved channel flows in a 270°open channel bend with a 2:1 sloped outer bank and a meandering channel with hydraulic smooth bed and walls and rectangular cross sections had uniform 90°bends in alternating directions interconnected by straight reaches. Meselhe & Sotiropoulos(2000) advanced a numerical model to predict three-dimensional turbulent flow in open channel taking into account the deformation of the free surface. Although through their methodology is, in principle, capable of handing arbitrary cross-section, the model is validated by application to a meandering channel comprised two identical 90°curves of opposite direction connected by a straight reach, with the cross section is trapezoidal with 1:1 bank, and rectangular cross-sectional channel with 180°bend.
The objective of the present work is to develop and validate a three-dimensional model for simulating flows through tidal curved river reach of complex bathymetry, and to evaluate the influence of a submerged cross-river tunnel on the adjacent water area. The numerical study is accompanied by a parallel experimental test and an analysis of the fluvial processes to provide a basis for the design and construction of the submerged cross-river tunnel.
For the submerged cross-river tunnel is only
1500m away from Wusongkou and 800m from Yuncaobang mouth, the tidal data at
Wusong tidal station could not be employed to provide the boundary conditions
before the influence sphere of the project is determined. In order to obtain the
sound open boundary conditions, the mathematical models of the East China Sea
and the Yangtze Estuary are also established (Zhu, et al., 2000). The present
three-dimensional hydrodynamic model covers the domain from the Huangpu Park to
the Yangtze River, in which a 4000m stretch of the Huangpu River upstream of
Wusongkou is the most interesting domain.
Governing
equations
For a three-dimensional turbulent flow of an incompressible Newtonian fluid with the Boussinesq eddy viscosity approximation, the Reynolds-average Navier-Stokes equations in Cartesian Coordinates are as follows:
(1)
(2)
where
is the velocity components in the
horizontal x-, y-
and vertical z-direction, respectively;
,
are the eddy viscosity which reflect the anisotropy effects in the horizontal
direction and vertical direction, respectively; t
is time; the source term
, in which p is the hydrostatic
pressure, f is the Corolis parameter, g
is the gravitational acceleration, ρ
is the density of water.
Since the vertical acceleration are usually
gental in rivers and estuaries, it is reasonable to assume the pressure
distribution is hydrostaic, the z-direction
momentum equation reduces to the hydrostatic law.
(3)
In the vertical direction, a σ-transformation is introduced to map the irregular bottom topography and the surface water level into a flat domain where the free surface boundary conditions could be precisely applied and the difficulties for shape depth variations are overcame. The transformed vertical velocity becomes
(4)
Then a new set of governing equations is obtained.
(5)
(6)
(7)
(8)
whereη
is the water surface elevation;
, increasing upward and σ=0
locating at the water surface; D=h+η
is the total water depth; Ah
and Av are the horizontal
and vertical eddy viscosity coefficients of turbulent flow, respectively.
A finite-difference numerical scheme is developed by means of the improved Double-Sweep-Implicit method to improve the computational stability and accuracy. The computation domain is staggered both in time and space: in time, the velocity component in x-direction are calculated at half-time step distance, while free surface elevation and the velocity component in y-direction are computed at full-time step distance; in space, velocity components are computed respectively in the centre of the y-σ, x-σ, x-y face of each mesh, while free surface elevation is calculated in the x-y face of each vertical column of water. The convective term in the momentum equations is discretizated by the Eulerian-Lagrangian method. The details of numerical implementation are described by Zhu et al.(2000).
The kinematic boundary conditions at the free surface and seabed are that the vertical component velocity equals to zero.
The dynamic boundary condition at the free
surface induced by the surface wind stress vector is taken as zero, and at the
seabed induced by the bottom frictional stress vector is computed by the
emprical formula (Zhu et al., 2000).
The lateral boundary conditions are set to be
zero of the flow normal to the shoreline. The given tidal levels obtained from
the mathematical model of the Yangtze Estuary are applied along the open
boundaries.
The three-dimensional numerical model solves Eqs.(5)~(8) by application of the mode splitting technique advanced by Simons(1974). The computational strategy is as follows.
Step 1: The external mode, a two-dimensional
depth-integrated model, is solved to obtain the free surface elevation and the
depth-integrated velocities. On the first sweep in the x-direction, U n+1 and
ηn+1/2
are found, and on next sweep in the y-direction,
V n+1 and ηn+1
are obtained.
Step 2: The internal mode, a three-dimensional model, is solved to obtain the three-dimensional velocities un+1,vn+1 and Wn+1 , by knowing U n+1 ,V n+1 andηn+1.
Step 3: The vertical component of velocity in physical domain, wn+1, is found by insertion ofηn+1, un+1 , vn+1 and Wn+1 into Eq.(4).
Since the geometry is complex and the submerged cross-river tunnel is narrower than 50m, the grid size nearby the project is determined to be 12.5m, while the larger grid size to be 75.0m is used far away from it. The time step is set to be 5s for this computation.
For the calibration of present model, the topographic data of Step.,1999 is provided by the Shanghai Survey and Research Institute of Navigation, also the tidal level data and the synchronous hydrometric measurements from Step.,11 to 18 in the flood season. From the calibration, the Manning roughness is chosen as 0.012.
For the calibration of present model, the topographic data of Jan., 2000 and the tidal level data and the synchronous hydrometric measurements from Jan., 15 to 23 in the dry season are employed.
From the comparisons of the field survey data and computations, as shown in Fig.1 to Fig.4, a satisfactory agreement is obtained. Fig.5 shows ebb maximum tidal flow pattern near the project. Results demonstrated that the present model is efficient and capable of reflecting the tidal motion in the Huangpu River.
Fig. 1 Comparison of water level
(— computational data ╂ measurement data)
Fig.2 Comparison of discharge
(— computational data ╂ measurement data)
Fig.3 Comparison of Longitudinal Velocity
(— computational data ╂ measurement data)
Fig.4 Comparison of Transverse Velocity
(— computational data
╂
measurement
data)
Fig.5 Ebb maximum tidal flow pattern near project
After the completion of project, the tidal level will raise 5mm at the site, which is the maximum change. This illustrates that the submerged cross-river tunnel has little influence on the flood control.
After the completion of project, the maximum change of the flow direction is about 9 degree. Comparison of the plane velocity field before and after the project shows that no obvious change occurs. This demonstrates that the submerged cross-river tunnel has little influence on the boat sailing safety.
Fig.6 and Fig.7 show that the longitudinal flow profile along the talweg before and after the completion of project. It can be seen that the longitudinal flow after the completion of project is plainer than that in the natural situation, due to the change of riverbed elevation.
Fig. 6 Longitudinal flow along talweg in natural situation
Fig. 7 Longitudinal flow along talweg after completion of tunnel
The transverse flows along the project axis before and after the completion of project are shown in Fig.8 and Fig.9. From the comparison of them, it is found that the transverse flow has some change. The velocity in the bottom layer nearby Pudong becomes larger, while that nearby Puxi becomes smaller. This change will be beneficial to deepening the channel nearby Pudong and ensuring the safety of the submerged cross-river tunnel.
Fig. 8 Transverse flow along project axis in natural situation
Fig. 9 Transverse flow along project axis after completion of tunnel
Both calibration and validation demonstrate that the present three-dimensional finite-difference hydrodynamic model is efficient to simulate tidal flows through curved river reach of complex bathymetry.
In order to obtain the sound open boundary conditions, the model in a larger domain such as the East China Sea model and the Yangtze Estuary model is necessary.
Computations illustrate that the submerged cross-river tunnel has little influence on the flood control and the boat sailing safety. The changes of the longitudinal and the transverse flow are favourable for the project.
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