Keywords

1 Introduction

In recent years, China’s transportation industry has developed rapidly, and the demand for cross-river bridges has become more and more prominent. According to statistics, Chongqing Maritime Bureau has built (under) 56 bridges. Lots of wading bridges not only promote the economic development on both sides of the Yangtze River, but also change the original channel conditions, which has a certain impact on the safety of ships crossing the bridge. Therefore, it is necessary to study the ship crossing the bridge and the interaction between the ship and the bridge from the mechanism, so as to design the navigation safety guarantee facilities according to the analysis results (Zhang Dan 2012; Tan Zhirong 2011; Wu Changsheng 2020).

There is a certain range of turbulent flow in the flow field around the bridge pier. The complex flow state of turbulence leads to the change of the water current force when the ship sails on the water, which brings some safety hazards. In order to alleviate navigation risks, researchers mostly use physical model tests and numerical simulations to study the turbulent characteristics of water flow caused by water blocking by piers in the channel (Liu Zhigang 2020; Raudkivi 1983). Comparing the distribution of the flow field around different pier types, it is found that the average velocity, turbulence intensity and Reynolds shear stress around the composite pier are lower than those around the single cylindrical pier. This is due to the existence of pile caps that limit the formation of vortices around the piers (Johnson 2003; Cautam 2019; Das 2013; Han Min 2010).

The angle between the normal direction of the cross-river bridge in the curved river section and the water flow direction changes periodically with the change of the water level all the year round. As a result, when the water flow velocity is large, a large steering pressure will be generated when the ship sails across the bridge. Therefore, in addition to the analysis from the perspective of the flow field, the ship sailing across the bridge in the curved river section also needs to be studied from the direction of flow-induced drift.

In this paper, we select typical bridges in the curved river section of the Three Gorges Reservoir area, and the water flow parameters in the bridge area are also selected. Numerical simulation is carried out through Fluent to analyze the relationship between the turbulent flow range of the bridge pier and the flow velocity and other parameters, so as to explore the effect of the turbulent flow of the pier on the curved river section on the navigation safety of ships. Then, the influence of flow-induced drift of ships under the action of different water flow and ship speeds was analyzed, and the influence of flow-induced drift on the navigation safety of ships was explored. Finally, referring to the existing mature multi-functional navigation aids and LED technology (Allen 2009; Zhao 2011; Liu Dianhong 2015; Chen Chen 2014), the optimization suggestions for navigation aid induction in the bridge area are put forward.

2 Flow Field Simulation of Bridge Pier

2.1 Simple Physical Scene

Using the usual practice of planar physical scene and grid scale [1, 2], a physical relationship diagram of small-scale pier waters with flow from upstream left to right is constructed. The diameter of the cylinder is D, the distance between the centers of the double piers in series is L, LI is the inflow scale, LH is the vertical scale, and LO is the outlet scale. The schematic diagram of the calculation grid of the single pier cylinder is shown as Fig. 1, and the calculation grid of the tandem double pier is shown as Fig. 2. Among them, the uniform free flow (its velocity is V) bypasses the cylinder from left to right, and the coordinates in the x-axis is along the flow direction, the y-axis is perpendicular to the incoming flow direction, and the coordinate origin is placed at the center of the cylinder.

Fig. 1.
figure 1

Schematic diagram of flow around the single pier cylinder

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2.2 Governing Equation

The fluid simulation uses the planar 2D flow conditions, the incompressible fluid continuity equation and the N-S equation:

Mass Conservation Equation:

$$ \nabla \cdot {\varvec{u}} = \frac{\partial u}{{\partial x}} + \frac{\partial v}{{\partial y}} = 0 $$
(1)

Momentum conservation equation:

$$ \frac{{\partial {\varvec{u}}}}{\partial t} + \left( {{\varvec{u}} \cdot \nabla } \right){\varvec{u}} = - \frac{\nabla p}{\rho } + \frac{\mu }{\rho }\nabla^{2} {\varvec{u}} $$
(2)

In (2), ▽ and u are the gradient operator and the velocity vector. It includes two velocity components u and v, p is the pressure, and μ is the hydrodynamic viscosity coefficient.

2.3 Simulation Conditions

According to the data of the special report, the calculation conditions are taken from the observation data. The calculation conditions are simplified to:

  • Pier diameter: D = 10 m;

  • Bending radius: R = 800 m;

  • flow velocity: V = 1, 1.5, 2.0, 3.0 (m/s)

3 Comparison and Analysis of Numerical Simulation

3.1 Flow Field Analysis of Single Pier

Through the change of flow velocity parameters under the condition of variable water level, the flow velocity cloud map, pressure map, velocity streamline map and vorticity field around the bridge pier are compared between the single pier and the tandem double pier. We analyzed the relationship between the turbulent range of the pier and the flow velocity and other parameters, and explored the influence of the turbulence of the pier in the curved river section on the navigation safety of ships.

3.1.1 Flow Field Analysis

Velocity nephogram and vector analysis reflect the changing law of the turbulent range.

Fig. 2.
figure 2

Nephogram of different inflow velocities

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Fig. 3.
figure 3

Vector distribution map of different inflow velocities

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In Fig. 2 and Fig. 3, the overall trend of the influence of velocity on the flow field can be seen, and the characteristics of the velocity nephogram are as follows:

  1. (1)

    With the increase of the incoming flow velocity, the phenomenon of flow around the pier becomes more obvious, the flow pattern in the downstream direction of the pier becomes more complex, and the turbulent flow width further increases. Under different working conditions, with the increase of the incoming flow velocity, the influence range of the two sides on the downstream also further increases.

  2. (2)

    There are also differences in turbulent flow patterns on the concave and convex banks of the curved river reach. It can be analyzed by the quantification of the X/Y axis coordinates: When V = 1 m/s, the concave bank side piers have a significant impact on the flow regime in the downstream range of about 10D, and gradually weakened until disappearing at 35D.The pier on the side of the convex bank has a significant impact on the flow regime in the downstream 18D range, and the velocity isosurface is dense, indicating that in the river section from the bridge pier to the downstream 18D range, the flow regime is changeable and the ship’s heading stability is poor. From the follow-up of the pier to 40D, the flow disorder gradually weakens to basically no effect.

  3. (3)

    During the flood period, when the flow velocity increases, for example, under the conditions of V = 2 m/s and V = 3 m/s, the significant influence range of the concave bank side is 19D and 22D, and the significant influence range of the convex side is 23D and 36D, respectively. That is to say, with the increase of the incoming flow speed, the water flow field of the bridge pier changes more significantly, and the scope of influence on the ship’s navigation also increases.

3.1.2 Pressure Field Analysis

The pressure field is a high-pressure area and a low-pressure area inside and outside the pier, which can easily lead to the deflection moment of the ship (Tan Zhirong 2022).

Fig. 4.
figure 4

Pressure distribution diagram of different inflow velocities

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Figure 4 depicts the change in the distribution of the pressure field on the downstream side of the pier under different flow velocity conditions. With the increase of the flow velocity, the low pressure area under the bridge pier increases, and the spread is more obvious in the downstream direction. The pressure in the low-pressure area is relatively small, and when the ship travels in the continuous low-pressure area, it is easy to deflect to the side of the pier, resulting in the danger of touching the pier.

3.1.3 Vorticity Field Analysis

Fig. 5.
figure 5

Vorticity distribution map of different inflow velocities

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It can be seen from Fig. 5 that when D remains unchanged, with the increase of the flow velocity, the more vortices generated after the piers on the convex bank side and the concave bank side, the greater the vorticity, and the area extending to the downstream also further increases (vorticity legend in FIG. F increases to some extent).

4 Analysis of Ship Crossing Bridge Motion Based on Flow-Induced Drift

To study the flow-induced drift under the action of different water flows, a coordinate system needs to be established. Let the y-axis of the coordinates be parallel to the axis of the bridge, and the x-axis to be parallel to the normal of the bridge, as shown in Fig. 6 (a), (b).

Fig. 6.
figure 6

Schematic diagram of ships sailing across the bridge and drifting in the waters of the bridge area

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The ship speed is Vs and the water flow velocity is Vf, according to the flow-induced drift formula in “The Navigation Standard of the Yangtze River Trunk Line 2020”.

The time for the ship to cross the bridge is T:

$$ {\text{T}} = {\text{S}}/\left( {V_{s} \cos \alpha + V_{f} \cos \beta } \right) $$
(3)

The flow-induced drift of the ship in the y-axis direction is B:

$$ {\text{B}} = \left( {V_{s} \sin \alpha + V_{f} \sin \beta } \right) \times {\text{S}}/\left( {V_{s} \cos \alpha + V_{f} \cos \beta } \right) $$
(4)

It can be seen from Fig. 7 that when other conditions are constant, the greater the water velocity, the greater the flow-induced drift. At the same time, the greater the boat speed, the smaller the flow-induced drift. When the flow rate is high, the captain should keep sailing cautiously, increase the speed at an appropriate time, and adjust the sailing in real time, so as to reduce the amount of drift.

Fig. 7.
figure 7

Drift value at different speed and flow velocity (m)

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The experimental conditions where the calculated river length is 1500 m, the water velocity is 3 m/s, and the ship speed is 14 km/h are selected to study the influence of different ship yaw angles on the drift. The results are shown in Fig. 8. It can be seen that when other conditions at a certain time, the larger the yaw angle of the ship is, the flow-induced drift will be reduced accordingly, and the larger the water-current included angle, the flow-induced drift will increase accordingly.

Fig. 8.
figure 8

Drift value due to different yaw angles and angles of water flow

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5 Optimization Suggestions for Navigation Beacon Induction in Bridge Area

5.1 Multifunctional Beacon for Real-Time Flow Velocity Collection

In the waters of the bridge area, we can install some multi-function beacons. The real-time hydrological and meteorological data can be measured by various sensors on the multi-functional beacon. This data is then sent to passing ships, waterway authorities and maritime regulators by AIS equipment. After receiving the data sent by the multi-function beacon, the captain can judge the real-time status of the channel, provide information decision support for the ship’s maneuvering, and ensure the safe navigation of the ship.

5.2 Recommended Route Guidance Based on LED Warning Signs

  1. (1)

    Install 3 lamps of different colors above the bridge navigation holes, so as to illuminate a section of water before entering the water area of ​​the bridge area. Ships traveling in different areas can observe the guiding lights of different colors, so as to judge the optimal route.

  2. (2)

    ABCD is a parallelogram representing the water in the bridge area. The ship travels in the direction of Q, the crew on duty observes the waters ahead, and the visual navigation system is located at point P on the side of the bridge above the bridge navigation hole Q to illuminate the water surface. The illuminated area is EFGH and the light colors are red, yellow-green and blue. Among them, the most sensitive yellow-green light of the human eye at night represents the best driving route. The red light is on the right side of the best route, the blue light is on the left. The red and blue lights flash quickly, and the yellow-green lights flash slowly.

  3. (3)

    By observing the light color and flickering frequency, the crew can judge which area the ship is traveling in, and adjust the course in time so that they can travel to the correct route before entering the bridge area waters. So it can pass the bridge area waters safely according to the instructions of the bridge area beacon.

6 Conclusions

  1. (1)

    From a microscopic perspective, this paper uses FLUENT to simulate the flow field of the bridge pier in two dimensions, and clarify the mechanism of the influence between the ship and the bridge when the ship crosses the bridge. Then, the relationship between the turbulent range and the flow velocity after the single pier and the tandem double pier under the condition of variable water level is obtained: with the increase of the incoming flow speed, the water flow field of the bridge pier changes more significantly, and the influence range of ship navigation gradually increases. Under the same flow velocity, the turbulent flow is more complex in the tandem double pier than the single pier, but the range is reduced.At the same flow rate, the turbulence of the tandem double pier is more complicated than that of the single pier, but the range is reduced.

  2. (2)

    From a macro point of view, the flow-induced drift under different flow rates and different ship speeds is discussed. It is obtained that the greater the water flow speed, the greater the flow-induced drift, and the greater the ship speed, the smaller the flow-induced drift.

  3. (3)

    From the perspective of navigation, it is proposed that the data such as the velocity of the bridge area during the high water level should be provided to the ship in time. Then, with the help of information technology, especially the popularized LED warning, which can be used as a directional light source to induce the recommended route.

Subsequent research can analyze the pier-water interaction under three-dimensional conditions.