# Hydrodynamic Characteristics at Intersection Areas of Ship and Bridge Pier with Skew Bridge

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## Abstract

**:**

## 1. Introduction

## 2. Model Test

#### 2.1. Model Test of Flow around a Round-Ended Pier

#### 2.1.1. Flow Patterns and Fields around a Pier on a Fixed Bed

_{L}of 200 was adopted. Figure 3c,d show the measuring frame of the self-made ADV profile current meter. The ADV acquisition probe was fixed to the measuring frame and calibrated with a leveling ruler to ensure it was vertical. A scale was laid around the measuring frame in all directions.

#### 2.1.2. Analysis of Test Results

- Analysis of the flow around a pier when the flow angle of attack is 0°

_{y}is in the legend, in mm/s. The changing process of the ADV measurement probe from Figure 4a–c shows that when α = 0°, the trailing vortex of the round-ended pier alternately falls off and forms a zigzag streamline. At T = 0 s, the boundary layer of the flow around the right side of the pier separates and forms a wake vortex, which then falls off downstream. When T = 0.387 s, a vortex is formed around the left side of the pier, and the flow states at these two moments have an approximate mirror image relationship based on the pier axis. When T = 0.780 s, the flow pattern is the same as that when T = 0 s; therefore, it can be concluded that the quasi-period of vortex formation and shedding around the circular end pier is approximately 0.78 s when α = 0°.

- Effect of flow angle of attack on the flow pattern around the round-ended pier

#### 2.2. Physical Model Test of Ship–Bridge Intersection

#### 2.2.1. Test Model and Equipment

#### 2.2.2. Analysis of the Test Results

## 3. Numerical Modeling

#### 3.1. Establishment of a Geometric Model and the Arrangement of Simulation Groups

#### 3.1.1. Analysis of Test Results

#### 3.1.2. Numerical Simulation

#### 3.2. Governing Equation

#### 3.2.1. Flow Governing Equation

#### 3.2.2. Flow Governing Equation

#### 3.3. Meshing Methods and Application of Self-Compiled UDFs

#### 3.3.1. Grid Division and Dynamic Grid Method

#### 3.3.2. Self-Compiling UDF Process

## 4. Verification and Analysis of Numerical Simulation Results

#### 4.1. Verification of Numerical Simulation Results

#### 4.1.1. Verification of Flow Field and Vorticity Field around Flow

#### 4.1.2. Verification of Trailing Vortex Shedding Frequency and Transverse Velocity behind a Round-Ended Pier

_{L}, which is the force perpendicular to the flow direction of the pier, fluctuates, and its fluctuation frequency is consistent with the wake vortex shedding frequency and transverse flow velocity fluctuation frequency. In this study, the fluctuation period of the lift coefficient ${C}_{L}=\frac{{F}_{L}}{0{.5\mathsf{\rho}\mathrm{V}}^{2}D}$ around the flow was found to be 0.8 s through simulation (Figure 20), which is consistent with the experimental result of 0.78 s discussed in Section 3.1.2. Here, V is the river velocity, and D is the characteristic length of the blunt body.

#### 4.1.3. Numerical Verification of Bow Roll Moment and Its Evolution Law

#### 4.2. Verification of Numerical Simulation Results

_{L}fluctuations. As shown in Figure 24, when the flow angle of attack increases from 0° to 15°, the lift fluctuation period of the bridge pier increases, and the lift direction almost points toward the back flow side. This is because the separation point of the boundary layer on the back flow side advances, while the separation point on the upstream side of the pier drops back, because of which, the upstream side of the pier is subjected to a relatively stable water pressure and counteracts the periodic negative water pressure, due to the wake vortex on the back flow side.

#### 4.3. Influence of Flow around a Round-Ended Pier with α = 0° on Moving Ship

#### 4.4. Analysis of the Influence of Flow around a Circular-Ended Pier on Moving Ship

#### 4.5. Influence of Flow Angle of Attack on Ships Sailing on Both Sides of a Round-Ended Pier

#### 4.5.1. Influence of Flow Angle of Attack on Ships Sailing on the Upstream Side of a Round-Ended Pier

#### 4.5.2. Influence of Flow Angle of Attack on Ships Sailing on the Back Side of a Round-Ended Pier

#### 4.5.3. Influence of Transverse Distance between the Ship and Pier on a Ship Sailing in a Skew Bridge Area

## 5. Discussion

_{y}> 0.3 m/s are unsuitable for ships sailing at low speeds in inland rivers. There is no limit standard for navigable flow conditions in bridge areas, regarding bridge design and other navigable specifications. Hence, based on the limit of the transverse flow velocity in navigable standards for inland rivers, this study defines the water areas B1 and B2 (Figure 34a) with a transverse flow velocity of V

_{y}> 0.3 m/s on both sides of the bridge pier as areas with a significant influence on navigable ships. Based on the flow rate scale calculation, the transverse flow velocity V

_{y}suitable for navigable waters in the PIV test and corresponding numerical model in this study should not exceed 0.02 m/s.

_{y}> 0.02 m/s. Table 6 shows the width of the restricted water area on both sides of the pier. As shown, the scale of the restricted water area on both sides of the bridge pier with α = 0° is approximately 1b in the Y direction. With an increase in the flow angle of attack, B1 and B2 on both sides of the bridge pier increase. When α = 15°, 30°, and 45°, the widths of the restricted water area on the back side of the bridge pier are 1.5b, 1.9b, and 3b, respectively. Notably, the width of the restricted water area at α = 15° and α = 45° is consistent with the simulation results of the spacing between the ship and pier in this study, while the width of the restricted water area at α = 30° slightly deviates, with a difference of only 0.6b. This indicates that the discriminant method of critical lateral velocity may also be suitable for the channel design of skew bridge areas.

## 6. Conclusions

- (1)
- The PIV flume test and numerical model test were conducted to study the influence of the flow angle of attack on the flow field and pressure field around a round-ended pier without vessel. The results showed that the fluctuation period of the downstream transverse velocity of the round-ended pier is consistent with the trailing vortex shedding period of the flow around the pier. This period is prolonged with the increase in the flow angle of attack of the pier, but the trailing vortex shedding period tends to be stable at α ≥ 15°. The trailing vortex shedding periods of α = 0°, 15°, 30°, and 45° are 0.8, 1.4, 1.5, and 1.6 s, respectively. Due to the water-blocking effect of the round-ended pier, a positive water pressure area is generated in front of the pier, and this area swings back and forth to the left and right banks when the flow angle of attack α ≥ 30°. A negative water pressure area is generated downstream of the boundary layer separation point of the flow around both sides of the pier, and the pressure area is different on both sides of the pier with the increase in the flow angle of attack. The negative water pressure area of the trailing vortex on the back flow side of the pier is larger than that on the upstream side, and the negative water pressure area generated by the shedding vortex system shifts to the back flow side of the pier with the increase in α.
- (2)
- The accuracy of the numerical simulation results of the ship–bridge intersection was verified based on the ship–bridge intersection model test. The process of the ship drifting through the bridge pier in the channel with a flow rate of 0.283 m/s was deduced by numerical simulation, when the ship–bridge transverse spacing was 1b. The results showed that the ship will be affected by three continuous fluctuation peaks of the bow roll moment, and the ship will experience a change in the bow roll moment direction, from ‘positive’ to ‘negative’ and then from ‘negative’ to ‘positive’. Moreover, the center of gravity position trajectory presents a ‘straw hat’ shape, and the ship will then maintain its attitude, to leave the bridge area.
- (3)
- Through a numerical simulation, the process of a ship passing both sides of the pier with different flow angles of attack at a speed of 0.566 m/s and ship–bridge spacing of 1b was deduced, and the change laws of the bow roll moment and the position of the center of gravity were analyzed. The results showed that the first positive peak value and the second positive peak value of the bow roll moment decrease with the increase in α when the transverse spacing between the ship and pier is constant, and the ship’s attitude is stable. When the ship moves from the back flow side of the bridge pier, although the increase in α has little influence on the overall positive peak value of the bow roll moment, the changes in the negative peak value and second positive peak value are significant, the ship’s navigation attitude is unstable, and the ship has a risk of colliding with the bridge pier and sweeping.
- (4)
- The width of the area that has a significant influence on navigable ships, judged by the hydrodynamic action of the ship on the skew bridge area, is the same as the result judged from the transverse velocity. For the ship class referred to in this study, it is reasonable to take the range of the transverse velocity limit of 0.3 m/s in the bridge area as the area having a significant influence on navigable ships. Combined with the analysis of the impact of the flow angle of attack, this study provides a reference for the width of channel design in skew bridge areas.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Schematic of the test instrument layout: (

**a**) Double exposure camera layout; (

**b**) Schematic of laser emitter placement; (

**c**) ADV test frame; (

**d**) ADV measuring probe.

**Figure 4.**Instantaneous velocity vector diagram and flow diagram of the round-ended pier with α = 0: (

**a**) T = 0 s; (

**b**) T = 0.387 s; (

**c**) T = 0.780 s.

**Figure 7.**Instantaneous surface flow diagram of the flow around a single circular ended pier with α = 0°. (

**a**) T = 0 s; (

**b**) T = 0.387 s; (

**c**) T = 0.780 s.

**Figure 8.**Instantaneous surface flow diagram of flow around a single circular ended pier with α = 15°. (

**a**) T = 0 s; (

**b**) T = 0.684 s; (

**c**) T = 1.357 s.

**Figure 9.**Instantaneous surface flow diagram of flow around a single circular ended pier with α = 30°. (

**a**) T = 0 s; (

**b**) T = 0.711 s; (

**c**) T = 1.396 s.

**Figure 10.**Instantaneous surface flow diagram of flow around a single circular ended pier with α = 45°. (

**a**) T = 0 s; (

**b**) T = 0.783 s; (

**c**) T = 1.592 s.

**Figure 11.**Transverse velocity duration curves downstream of bridge pier: (

**a**) α = 0°; (

**b**) α = 15°; (

**c**) α = 30°; (

**d**) α = 45°.

**Figure 12.**Physical model test site and key equipment: (

**a**) Layout; (

**b**) Layout; (

**c**) Ship model; (

**d**) Static torque sensor.

**Figure 16.**Schematic of 2D numerical model meshing for ship–bridge intersection: (

**a**) Schematic of a subregional grid; (

**b**) Grid near the wall of a ship; (

**c**) Grid near the wall of a round-ended pier.

**Figure 17.**Diagrams of the flow field around a circular end pier: (

**a**) Physical model test results; (

**b**) Numerical simulation results.

**Figure 18.**Schematic of the vorticity field around a circular-ended pier surface: (

**a**) Physical model test results; (

**b**) Numerical simulation results.

**Figure 19.**Comparison diagrams of the transverse velocity–duration curves between model test and numerical simulation, measured at points: (

**a**) b1; (

**b**) b2; (

**c**) b3.

**Figure 21.**Schematics of the flow pressure distribution around the pier: (

**a**) No ship; (

**b**) Ship bowled up to the pier; (

**c**) Bow moves over the pier; (

**d**) Stern sailing over the pier.

**Figure 24.**Distribution diagrams of C

_{L}flow around a circular-ended pier: (

**a**) α = 0°; (

**b**) α = 15°.

**Figure 25.**Vorticity field and pressure field distribution diagrams of the flow around a circular-ended pier: (

**a**) α = 30°, T = 0 s; (

**b**) α = 30°, T = 0.0705 s; (

**c**) α = 45°, T = 0 s; (

**d**) α = 45°, T = 0.0775 s.

**Figure 26.**Distribution diagrams of C

_{L}flow around a circular-ended pier: (

**a**) α = 30°; (

**b**) α = 45°.

**Figure 27.**Diagrams of the flow pressure distribution and bow roll moment variation of a ship moving through a circular-ended pier at α = 0°: (

**a**) Variation law of the bow roll moment; (

**b**) Ship bowled up to the pier; (

**c**) Bow moving over the pier; (

**d**) Stern moving over the pier.

**Figure 28.**Change diagram of the barycenter position of the moving ship in the area of a circular-ended pier bridge with α = 0°.

**Figure 29.**Change laws of the bow roll moment and center of gravity position on both sides of the circular-ended pier α = 30°: (

**a**) Bow roll moment; (

**b**) Center of gravity position.

**Figure 30.**Diagrams of the water pressure distribution of the ship passing the left and right sides of the round-ended pier with α = 30°: (

**a**) Ship bowled up to the pier; (

**b**) Bow moving past the pier; (

**c**) Stern sailing past the pier.

**Figure 31.**Schematic of the bow roll moment and center of gravity position of a ship passing through a round-ended pier with different flow angles of attack: (

**a**) Bow roll moment; (

**b**) Center of gravity position.

**Figure 32.**Schematic of bow roll moment and center of gravity position of a ship passing a round-ended pier with different flow angles of attack: (

**a**) Bow roll moment; (

**b**) Center of gravity position.

**Figure 33.**Variation in the bow roll moment of a round-ended pier under different bridge spacings: (

**a**) α = 15°; (

**b**) α = 30°; (

**c**) α = 45°.

**Figure 34.**Transverse velocity distribution of flow around a round-ended pier with different flow angles of attack: (

**a**) α = 0°; (

**b**) α = 15°; (

**c**) α = 30°; (

**d**) α = 45°.

V = 0.141 m/s | Flow Angle of Attack of Round-Ended Pier (α) | |||
---|---|---|---|---|

0° | 15° | 30° | 45° | |

PIV/ADV | √ | √ | √ | √ |

Set Time Category | Pier Section Shape | Driving Area | Transverse Spacing between a Ship and Pier | Flow Angle of Attack of the Pier α |
---|---|---|---|---|

Validation group | Circular shape (diameter = 1 m) | / | 1b | / |

Different flow angles of attack | Rounded shape | (1) The backflow side of the pier (2) The upstream side of the pier | 1b | 0° 15° 30° 45° |

Distance between different ships and piers | Rounded shape | The backflow side of the pier | 1b, 1.2b, 1.5b, 2b 1b, 1.5b, 2b, 2.5b, 3b 1b, 2b, 3b, 4b | 15° 30° 45° |

Parameter | Flow Angle of Attack (α°) | First Positive Peak (N·m) | The Incremental (N·m) | Negative Peak (N·m) | The Incremental (N·m) | Second Positive Peak (N·m) | The Incremental (N·m) |
---|---|---|---|---|---|---|---|

Bow roll moment | 0 | 0.0189 | / | −0.0238 | / | 0.0236 | / |

15 | 0.0319 | 0.0130 | −0.0271 | −0.0033 | 0.0317 | 0.0081 | |

30 | 0.0364 | 0.0045 | −0.0371 | −0.0100 | 0.0358 | 0.0041 | |

45 | 0.0422 | 0.0058 | −0.0495 | −0.0124 | 0.0530 | 0.0172 |

Parameter | Flow Angle of Attack (α°) | First Positive Peak (N·m) | The Incremental (N·m) | Negative Peak (N·m) | The Incremental (N·m) | Second Positive peak (N·m) | The Incremental (N·m) |
---|---|---|---|---|---|---|---|

Bow roll moment | 0 | 0.0189 | / | −0.0238 | / | 0.0236 | / |

15 | 0.0180 | −0.0009 | −0.0287 | −0.0049 | 0.0353 | 0.0117 | |

30 | 0.0190 | 0.0040 | −0.0411 | −0.0124 | 0.0398 | 0.0045 | |

45 | 0.0277 | 0.0087 | −0.0539 | −0.0128 | 0.0625 | 0.0227 |

Flow Angle of Attack (α°) | Transverse Spacing between Ship and Pier | First Positive Peak (N·m) | The Incremental (N·m) | Negative Peak (N·m) | The Incremental (N·m) | Second Positive Peak (N·m) | The Incremental (N·m) |
---|---|---|---|---|---|---|---|

15 | 1.0b | 0.0150 | / | −0.0287 | / | 0.0353 | / |

1.2b | 0.0123 | −0.0027 | −0.0271 | 0.0016 | 0.0302 | −0.0051 | |

1.5b | 0.0081 | −0.0042 | −0.0257 | 0.0014 | 0.0240 | −0.0062 | |

2.0b | 0.0069 | −0.0012 | −0.0254 | 0.0003 | 0.0231 | −0.0009 | |

30 | 1.0b | 0.0190 | / | −0.0411 | / | 0.0398 | / |

1.5b | 0.0129 | −0.0061 | −0.0377 | 0.0034 | 0.0396 | −0.0002 | |

2.0b | 0.0104 | −0.0025 | −0.0262 | 0.0115 | 0.0383 | −0.0013 | |

2.5b | 0.0082 | −0.0010 | −0.0222 | 0.0040 | 0.0282 | −0.0101 | |

3.0b | 0.0079 | −0.0003 | −0.0216 | 0.0006 | 0.0253 | −0.0029 | |

45 | 1.0b | 0.0277 | / | −0.0539 | / | 0.0625 | / |

2.0b | 0.0133 | −0.0144 | −0.0291 | 0.0248 | 0.0383 | −0.0242 | |

3.0b | 0.0076 | −0.0057 | −0.0199 | 0.0092 | 0.0244 | −0.0139 | |

4.0b | 0.0069 | −0.0007 | −0.0188 | 0.0011 | 0.0242 | −0.0002 |

**Table 6.**Navigation limits of the width of the water area on either side of a round-ended pier with different flow angles of attack.

Flow Angle of Attack (α) | 0° | 15° | 30° | 45° |
---|---|---|---|---|

Ship on the backflow side of the pier (B1) | 1b | 1.5b | 1.9b | 3b |

Ship on the upstream side of the pier (B2) | 1b | 1.4b | 2.2b | 2b |

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## Share and Cite

**MDPI and ACS Style**

Li, A.; Zhang, G.; Liu, X.; Yu, Y.; Zhang, X.; Ma, H.; Zhang, J.
Hydrodynamic Characteristics at Intersection Areas of Ship and Bridge Pier with Skew Bridge. *Water* **2022**, *14*, 904.
https://doi.org/10.3390/w14060904

**AMA Style**

Li A, Zhang G, Liu X, Yu Y, Zhang X, Ma H, Zhang J.
Hydrodynamic Characteristics at Intersection Areas of Ship and Bridge Pier with Skew Bridge. *Water*. 2022; 14(6):904.
https://doi.org/10.3390/w14060904

**Chicago/Turabian Style**

Li, Anbin, Genguang Zhang, Xiaoping Liu, Yuanhao Yu, Ximin Zhang, Huigang Ma, and Jiaqiang Zhang.
2022. "Hydrodynamic Characteristics at Intersection Areas of Ship and Bridge Pier with Skew Bridge" *Water* 14, no. 6: 904.
https://doi.org/10.3390/w14060904