# The Effects of Aerodynamic Interference on the Aerodynamic Characteristics of a Twin-Box Girder

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

#### 2.1. Section Model Geometrical Information and Surface Pressure Measurements

_{s}= 480 mm, and the geometric scale ratio of the section model is 1:120. Figure 2a shows a 3D sketch of the twin-box girder used in the present study. To obtain the surface pressure distributions, 46 pressure taps with a 0.5 mm radius were installed in the slice, which is 230 mm away from the right end of the bridge deck, as shown in Figure 2b. It should be noted that the experiments on the twin-box girder were stationary in this paper.

_{p}can be calculated by nondimensionalization of the time-averaged pressure p

_{m}, which can be written as:

_{i}denotes the instantaneous pressure, ${p}_{\infty}$ is the pressure of the free stream, ${\rho}_{air}$ is the density of air, ${U}_{\infty}$ is the flow velocity of the free stream, and T is the sample period.

^{3}); hence, the boundary layer around the solid structure becomes turbulent and the pressure drag force dominates the skin drag force [21]. Thus, the pressure drag force is the dominant component of total drag, and the skin friction drag can be neglected.

**P**

_{i}is the pressure force,

**P**

_{xi}and

**P**

_{zi}are the pressure force components along the x and z directions, respectively, ds

_{i}denotes the element area, and ζ

_{i}is the moment arm. It should be noted that, when the gap exists, the pressure forces at pressure taps 9–11 and 32–34 should be considered.

_{D}, the lift force coefficient C

_{L}, and the moment force coefficient C

_{m}are defined as:

_{D}, F

_{L}, and F

_{m}are the drag, lift, and moment forces, respectively, and B is the width of the twin-box girder.

_{D mean}), the fluctuating drag force coefficients (C

_{D rms}), the mean lift force coefficients (C

_{L mean}), the fluctuating lift force coefficients (C

_{L rms}), the mean moment force coefficients (C

_{m mean}), and the fluctuating moment force coefficients (C

_{m rms}). It should be noted that the root mean square of the specific value is adopted to represent the fluctuation.

#### 2.2. Aerodynamic Interference Measurements

#### 2.2.1. Leading Body-Height Grid Aerodynamic Interference

#### 2.2.2. Leading Circular Cylinder Aerodynamic Interference

#### 2.3. Turbulence Intensity Measurement

## 3. Results and Discussions

#### 3.1. Undisturbed Surface Pressure Distribution and Aerodynamic Forces

^{3}, the profile of the surface pressure indicates that the pressure of the upstream girder reaches a peak near the windward corner A, because the incoming flow passes through the windward slope on the upper surface and the incoming flow is affected by the forward pressure gradient, which enhances the flow speed and promotes the continuous increase in suction. After the windward corner, the flow velocity gradually decreases, and the negative pressure also decreases. It should be noted that a short-term pressure plateau is formed after the windward corner on the upper surface of the upstream girder at low Reynolds numbers (e.g., Re = 6.13 × 10

^{3}), but this pressure plateau will disappear at high Reynolds numbers. The pressure plateau is formed by the separation bubble, because the internal and external fluids of the separation bubble are relatively stable; thus, the pressure in the separation bubble is almost identical. Moreover, the endpoint of the pressure platform could be regarded as the reattachment point. Figure 8 also shows that the amplitude of the surface pressure increases with the Reynolds number, and the pressure on the lower surface of downstream girder has a common tendency to decrease first and then increase at different Reynolds numbers.

^{3}, while the time-averaged lift force coefficient significantly increases first and then flattens with the increase in the Reynolds number. With the Re rising, the time-averaged moment force coefficient first increases rapidly, and then decreases. The fluctuating lift force coefficient and the fluctuating moment force coefficient show a similar tendency to the fluctuating drag coefficient with increasing Re.

#### 3.2. Modulation of Surface Pressure Distribution by Leading Body-Height Grids

^{4}), because the boundary layer transitioned to the turbulent boundary layer. At low turbulence intensity (I = 3.57–5.15%), the amplitude of the pressure peak was enhanced. It is also noteworthy that, at the upstream girder, the pressure plateaus (appearing in the undisturbed surface pressure distribution) in the upper and lower surfaces were eliminated, because the vortices generated by the body-height grid broke the separation bubbles, and the laminar boundary layer was transformed into turbulence, which cannot maintain a stable pressure to form the separation bubbles. At moderate turbulence intensity (I = 16.9–18.3%), the negative pressures are enhanced when x/0.5B > −0.7, indicating that the high turbulence intensity contains more energy to strengthen the flow velocity around the box girder. When the turbulence intensity is further increased (I = 27.9–31.4%), the negative pressures are also increased.

#### 3.3. Modulation of Surface Pressure Distribution by Leading Circular Cylinders

#### 3.4. Modulation of Aerodynamic Forces by Leading Body-Height Grids

_{D mean}is sensitive to the Reynolds number when Re ≤ 1.0 × 10

^{4}. Moreover, the hypotenuse of the contour at the corner indicates that the turbulence intensity can reduce the Reynolds number effects of C

_{D mean}. When the Reynolds number is further increased, the C

_{D mean}shows slight Reynolds number sensitivity, which is consistent with the bare deck (see Figure 9a). At moderate turbulence intensity (5% ≤ I ≤ 20%), the C

_{D mean}is enhanced, and the C

_{D mean}presents slight Reynolds number dependence. It should be noted that there exists a lock-up region of C

_{D mean}. At high turbulence intensity (I > 20%), the C

_{D mean}is further promoted, and is only associated with the turbulence intensity.

^{4}(see Figure 14b), and with the increase in turbulence intensity, the lift force is enhanced, which implies that the strength of turbulent flow can effectively promote the lift force. Meanwhile, at Re > 1e4, the lift force is insensitive to both Reynolds number and turbulence intensity, because the boundary layer transitions to full turbulence.

_{D rms}and C

_{L rms}show different distribution characteristics. At low turbulence intensity (I < 2.5%), C

_{D rms}shows Reynolds number dependence at low Re, i.e., Re < 1.0 × 10

^{4}. With the increase in turbulence intensity, the C

_{D rms}is enhanced by the strong fluctuating component of incoming flow, and the Reynolds number sensitivity of the C

_{D rms}is eliminated (see Figure 14d). However, the C

_{L rms}depends on the Reynolds number and turbulence intensity, because the increase in Re or turbulence intensity can enhance the vertical fluctuating force.

^{4}and turbulence intensity I ≤ 12.5%, the mean moment force coefficient increases significantly with the turbulence intensity, which may be due to the increase in the vertical and horizontal fluctuating velocity of the flow field caused by the turbulence. However, in other regions, the mean moment force coefficient does not show strong turbulence intensity sensitivity, because the turbulence mainly affects and increases the horizontal and vertical velocities, but has a small impact on the moment force. The fluctuating moment force coefficient and the fluctuating lift force coefficient exhibit similar trends, indicating that the fluctuating lift force is the dominant component of the fluctuating moment force.

#### 3.5. Modulation of Aerodynamic Forces by Leading Circular Cylinders

^{3}. Moreover, the fluctuating drag force is insensitive to the Reynolds number, and the disturbed fluctuating drag force at low Re is closer to that of the undisturbed fluctuating force at high Re. Furthermore, the fluctuating drag force is independent of the spacing ratio ε.

_{L mean}shows less sensitivity to the Reynolds number, because the turbulence in the wake of cylinder has been fully developed, which causes the boundary layer of the body surface to transition to turbulence. When the cylinder is close to the twin-box girder, the wake of the cylinder cannot fully develop into turbulence to change the boundary layer, which explains why the Reynolds number effect still exists. In conclusion, when the spacing ratio ε > 2, the turbulence generated by the wake of the cylinder effectively eliminates the Reynolds number effects on the time-averaged lift force.

^{3}. This may be because the vertical pulsation component in the cylindrical wake is very small and the turbulence generated by the cylinder suppresses the vortex shedding of the twin-box girder to reduce the fluctuation of the lift force.

_{m mean}is slightly enhanced. Meanwhile, with the increase in the spacing ratio, the absolute value of C

_{m mean}decreases gradually. When the spacing ratio ε = 5, the C

_{m mean}is smaller than the undisturbed mean moment force. This indicates that the fully developed turbulence wake generated by a large spacing ratio can effectively suppress the time-averaged moment force.

_{m rms}of the twin-box girder with cylinder interference. At Re ≤ 9.0 × 10

^{3}, the interfered C

_{m rms}is greater than the undisturbed C

_{m rms}. When the spacing ratio ε ≤ 3, the C

_{m rms}is insensitive to the diameter, and the C

_{m rms}decreases slightly with the increase in the Reynolds number.

## 4. Conclusions

- (1)
- The leading body-height grid generates the turbulent incoming flow, which effectively breaks the separation bubbles and the flow reattachment, and the laminar boundary layer in the undisturbed case at low Re is forced to transition to turbulent flow. Moreover, the characteristics of surface pressure distribution with body-height grid interference are similar to those of bare deck at high Re;
- (2)
- The Reynolds number sensitivity of time-averaged drag force decreases with the increase in turbulence intensity, and the C
_{D mean}is dominated by the turbulence intensity. While the C_{L mean}and C_{m mean}are dependent on the Re and turbulence intensity at low Re, at high Re, the C_{L mean}and C_{m mean}are insensitive to the Re and turbulence intensity. The fluctuating drag force C_{D rms}depends on the turbulence intensity, and is insensitive to the Reynolds number, while the C_{L rms}and C_{m rms}are related to both turbulence intensity and the Reynolds number. In addition, the characteristics of C_{L rms}and C_{m rms}are similar, indicating that the C_{L rms}is the dominant component of the C_{m rms}; - (3)
- The coherent turbulence generated by the leading circular cylinders effectively changes the boundary layer of the twin-box girder. The Reynolds number sensitivity of surface pressure distribution is reduced by the interference of cylinders, and it is insensitive to the diameter and the spacing ratio. Moreover, the separation bubbles are also broken by the wake of the cylinder;
- (4)
- The time-averaged drag force C
_{D mean}is significantly reduced by the interference of the leading cylinder, and its Reynolds number sensitivity is diminished. Moreover, the time-averaged lift force C_{L mean}with cylinder interference is drastically decreased, and it is also insensitive to the Reynolds number. With the increase in the spacing ratio, the time-averaged moment force C_{m mean}is weakened, and its Reynolds number sensitivity is reduced. In addition, the fluctuating drag force C_{D rms}and lift force C_{L rms}are both insensitive to the Re, the spacing ratio, and the diameter, while the fluctuating moment force is closely related to these three parameters.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Schematic diagrams of the section model: (

**a**) 3D sketch of the twin-box girder, and (

**b**) spanwise location of the pressure tap (unit: mm).

**Figure 4.**Sketch view of the section model in the test section and the body-height grid in the flow inlet.

**Figure 6.**The sketch views of the leading circular cylinder and the twin-box girder (D is the diameter of the circular cylinder).

**Figure 8.**The mean surface pressure distribution of the twin-box girder at different Re: (

**a**) the pressure surface distribution of the upper surface, and (

**b**) the pressure surface distribution of the lower surface.

**Figure 9.**(

**a**–

**c**) The time-averaged drag force coefficient, time-averaged lift force coefficient, and time-averaged moment coefficient at different Reynolds numbers, respectively. (

**d**–

**f**) The fluctuating drag force coefficient, fluctuating lift force coefficient, and fluctuating moment coefficient at different Reynolds numbers, respectively.

**Figure 10.**Comparisons of the time-averaged surface pressure distribution of the twin-box girder with body-height grid interference and bare deck.

**Figure 11.**The time-averaged surface pressure distributions of the twin-box girder with body-height grid interference at different Reynolds numbers when turbulence intensities are close.

**Figure 12.**Comparisons of the time-averaged surface pressure distribution of the twin-box girder with circular cylinder interference and bare deck.

**Figure 13.**The time-averaged surface pressure distributions of the twin-box girder with circular cylinder interference at different Reynolds numbers with the same spacing ratio.

**Figure 14.**(

**a**–

**c**) The distributions of the time-averaged drag, lift, and moment, respectively, in the phase plane of Reynolds number and turbulence intensity. (

**d**–

**f**) The distributions of the fluctuating drag, lift, and moment, respectively, in the phase plane of Reynolds number and turbulence intensity.

**Figure 15.**(

**a**–

**d**) The relationship between the time-averaged drag force coefficient and the Reynolds number at different spacing ratios and cylinder diameters.

**Figure 16.**(

**a**–

**d**) The relationship between the fluctuating drag force coefficient and the Reynolds number at different spacing ratios and cylinder diameters.

**Figure 17.**(

**a**–

**d**) The relationship between the time-averaged lift force coefficient and the Reynolds number at different spacing ratios and cylinder diameters.

**Figure 18.**(

**a**–

**d**) The relationship between the fluctuating lift force coefficient and the Reynolds number at different spacing ratios and cylinder diameters.

**Figure 19.**(

**a**–

**d**) The relationship between the time-averaged moment force coefficient and the Reynolds number at different spacing ratios and cylinder diameters.

**Figure 20.**(

**a**–

**d**) The relationship between the fluctuating moment force coefficient and the Reynolds number at different spacing ratios and cylinder diameters.

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**MDPI and ACS Style**

Wu, B.; Xue, G.; Feng, J.; Laima, S.
The Effects of Aerodynamic Interference on the Aerodynamic Characteristics of a Twin-Box Girder. *Appl. Sci.* **2021**, *11*, 9517.
https://doi.org/10.3390/app11209517

**AMA Style**

Wu B, Xue G, Feng J, Laima S.
The Effects of Aerodynamic Interference on the Aerodynamic Characteristics of a Twin-Box Girder. *Applied Sciences*. 2021; 11(20):9517.
https://doi.org/10.3390/app11209517

**Chicago/Turabian Style**

Wu, Buchen, Geng Xue, Jie Feng, and Shujin Laima.
2021. "The Effects of Aerodynamic Interference on the Aerodynamic Characteristics of a Twin-Box Girder" *Applied Sciences* 11, no. 20: 9517.
https://doi.org/10.3390/app11209517