Numerical simulation of immersion of a tunnel element - downscaling by CFD technology

During the immersion process of tunnel elements in the sea, the surrounding currents would inevitably be changed. A large scale ocean circulation model, which can simulate the sea currents, usually do not solve underwater structures. Thus, in this chapter, we use a downscaling Computational Fluid Dynamics model to simulate the flow characteristics around an immersed tunnel element for Shenzhong Link in China, under different velocity inlets and at different depths. Since E1 element is shielded from diversion dike and the flow velocity around is small, this paper focus on simulation of the flow field during the immersion process of E2 element after the completion of E1.


Introduction
To safeguard the cross-sea immersed tunnel constructions, a weather-ocean forecasting system is usually constructed, in order to forecast appropriate time windows when the marine environment satisfy for the flotation transportation and installation of tunnel elements [1] .National Marine Environmental Forecasting Center have provided forecasting service for the construction of the Hong Kong-Zhuhai-Macau Bridge and Shenzhong Link.To satisfy the strict demand for the current accuracy.An high-resolution ocean forecasting systems have been constructed based on geophysical fluid dynamics (GFD) models, including Regional Ocean Model System (ROMS) and Finite Volume Community Ocean Model (FVCOM) [2][3] .
During the immersion process of tunnel elements in the sea, the surrounding background currents would inevitably be changed.However, the ocean forecasting models would not solve underwater structures.Computational Fluid Dynamics (CFD) dynamic downscaling technology are used widely for high-precision analysis in Meteorological numerical simulations [4][5] .Whereas, there were few study on integration of CFD and GFD models [6][7] .The paper aim to construct a CFD model to simulate the flow characteristics around an immersed tunnel element.The model was applied to simulate the immersion process of E2 element after the completion of E1 in Shenzhong Link in China, Since E1 element is shielded from diversion dike and the flow velocity around is small.Uniform and linear currents were used as boundaries of the CFD model.For further work, current profiles produced from GFD can be used as the boundaries.

Mathematical model
The CFD model in this paper solves the continuity equation and Reynolds-averaged Navier-Stokes momentum equation for incompressible fluid, and is closed with the standard k-epsilon turbulence equation.The simulations are implemented in ANSYS Fluent [8] .
The continuity equation reads: where,  is the density of the water, i x is coordinate direction , p is pressure,  is molecular viscosity, g is gravitational constant.
Through the Boussinesq hypothesis, the turbulent stress is represented by: ' ' 2 3 where, k is turbulent kinetic energy, t  is turbulent viscosity.
The turbulent kinetic energy (TKE) transport equation reads: ( ) The turbulent dissipation transport equation reads: where are given values of 0.09, 1.0, 1.3, 1.44 and 1.92 respectively as in Launder and Spalding [9] .The CFD model is a more refined model with respect to GFD model.Uniform and linear currents were used as boundaries of the CFD model.For further work, current profiles produced from the ocean forecasting system can be used as the boundaries.

Simulation Results
A three-dimensional physical model was setup as shown in Figure 1.The x direction is parallel to the direction of the ocean current, the y direction is parallel to the water depth direction, and the z direction is parallel to the length direction of the E1 and E2 tunnel elements.The physical domain is 250 m * 19.3 m * 450 m (x*y*z).The width, height and length of E1 and E2 tunnel element are 46 m * 10.6 m * 123.8 m (x*y*z) and 46 m * 10.6 m * 165 m (x*y*z) respectively.Before the immersing process, E2 would be floated 5 meters away from E1 at the sea surface.The average depth where E2 element located is 19.3m.The grid was refined around E2 tunnel element, with a minimum grid of 0.33 m and a maximum grid of 1 m (Figure 2).The boundaries in x direction is set as velocity inlet and outflow.E1 and E2 are set as no slip wall.The simulations are transient with time step range of 0.15-0.5 s, and run until steady state.
The background currents considered in the numerical experiments are 0.1 m/s, 0.5 m/s and 1 m/s respectively.Three working conditions are considered, in which E2 was gradually immersed, located at 1 m below the sea surface (referred to as "upper"), the middle position (referred to as "middle"), and 1 m above the trench (referred to as "lower").Under different background ocean currents, the flow patterns when passing through E2 are similar.Thus the paper presents the flow field distribution under background ocean current of 0.5 m/s (Figure 3-Figure 6).Besides the uniform velocity inlets, a linearly-decreased current with 1 m/s at the surface and zero at the bottom was also used as the boundary (Figure 7).Under the three different uniform background currents, the maximum flow velocities in the zone around the E2 tunnel element section are 0.3 m/s, 1.4 m/s and 2.9 m/s respectively; the maximum flow velocity is about three times of the background current.
Figure 3-Figure 6 shows the streamlines and the flow field distribution at different sections.Seen from the XY cross-section, due to the existence of the tunnel element, a low-speed "dead water" vortex zone was formed behind the immersed tunnel in all three working conditions.(Figure 3).Highspeed zones are formed above and below the immersed tunnel element, with a maximum current speed of about 1.4 m/s; in the two working conditions of "upper" and "lower", the extent high-speed zones is longer than that of the tunnel element in the middle (Figure 4).Seen from XZ cross-section (Figure 5), a high-speed zone is formed on both sides of E2; The length of the high-speed zone on the open sea side is about 40% of the length of tunnel element, and the maximum flow velocity is about 0.9 m/s.when the current passes the gap between E1 and E2, the flow velocity can reach to 1.4 m/s, among which the high flow velocity zone in the "upper" working condition is significantly longer than the other two working conditions.In summary, seen from YZ cross-section (Figure 6), when the immersed tunnel is located at different depths, high-speed zones appear on the upper, lower, left, and right sides of the tunnel element, with magnitude of 0.9-1.4 m. /s, which is about 2-3 times of the background current.

Conclusions and discussions
A downscaling CFD model was constructed to analyse the flow field distribution around an immersed tunnel, and present the zones where high-speed currents are located, thereby support decision making for immersed tunnel operations.Three uniform background velocities of 0.1 m/s, 0.5 m/s and 1 m/s were used in the simulations.Under different background currents, the flow patterns passing through the E2 tunnel element are similar.High-speed zones appear above, below, left, and right of the tunnel element, and a low-speed vortex zone would be formed behind the tunnel element.The maximum flow velocities in the zone around the tunnel element are 0.3 m/s, 1.4 m/s and 2.9 m/s respectively, that is, the maximum flow velocity is about three times of the background current.
The paper aim to show that a CFD model can be used as downscaling technology, when there is need for the refined simulations with respect to the larger scale ocean circulation model.The simulations in the paper used velocity inlet boundary condition, where the velocity is vertically uniform.For further work, current profiles produced from the ocean forecasting system can be used as the boundaries of the CFD model.

Figure 1 .Figure 2 .
Figure 1.Schematic of the physical model

Figure 3 .
Figure 3. Streamline diagram (black line) of the XY section when E2 is in the upper, middle and lower working conditions, and the background current direction is from right to left; E2 and the boundary of the physical domain are marked in red.

Figure 4 .
Figure 4.The flow vector distribution of the XY cross-section when E2 is in the upper, middle and lower working conditions; the colour represents the velocity magnitude; the cross-section is taken from the middle of the E2 tunnel element, and the background current direction is from right to left.

Figure 5 .
Figure 5.The flow vector distribution of the XZ section when E2 is in the upper, middle and lower working conditions; the colour represents the velocity magnitude; the section is taken from the water depth where E1 and E2 intersect, that is Y=10 m (top), 11.6 m (middle), 13.2 m (bottom), respectively; the background current direction is from top to bottom.

Figure 6 .
Figure6.The velocity magnitude distribution of the YZ cross-section when E2 is in the upper, middle and lower working conditions.The cross-section is taken from the middle of the tunnel element.The background sea current direction is vertical to the paper plane.

Figure 7 .
Figure 7.The velocity magnitude distribution of the YZ cross-section when E2 is in the middle working condition.The cross-section is taken from the middle of the tunnel element.The background sea current direction is vertical to the paper plane, and the magnitude linearly decrease from the surface to the bottom.