# Aerodynamics of a Train and Flat Closed-Box Bridge System with Train Model Mounted on the Upstream Track

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## Abstract

**:**

## 1. Introduction

## 2. Configurations of Wind Tunnel Setup

#### 2.1. Wind Tunnels and Models

_{∞}= 2 m/s, and the corresponding Reynolds number (Re) based on U

_{∞}and d is of 2.5 × 10

^{3}. On the other hand, the second group of models scaled by 1:40 were used for pressure field and flow profile measurements as shown in Figure 1b in WT-II. The widths, heights, and lengths of the train and bridge-deck models are b × d × l = 81.6 mm × 92.3 mm × 2000.0 mm and B × D × L = 490.0 mm × 70.0 mm × 2000.0 mm, respectively, resulting in a maximum blockage ratio of 4.6%. For brevity, only the geometrics of this group of models are depicted in Figure 2. In the pressure field and profile measurement experiment, the train model was still made by 3D printing technique, whereas the bridge-deck model was made of wood with an aluminum spine embedded inside. The test range of α was also set in [−12°, 12°] with an interval of 2°, while the incoming flow velocity is U

_{∞}= 20 m/s corresponding to Re = 1.25 × 10

^{5}(based on U

_{∞}and d). Please note that, only the train’s shoulders are rounded without any sharp corners, thus all the Reynolds numbers in this paper are calculated based on d.

^{t}–y

^{t}and x

^{b}–y

^{b}denote the geometric coordinate systems of the train and bridge-deck models, respectively. The coordinate origins are fixed at the centroids of the cross sections of the test models.

#### 2.2. Testing Points and Instruments

^{t}/Δy

^{b}are the vertical coordinates of the test points.

## 3. Aerodynamic Interactions

#### 3.1. Train Model

#### 3.1.1. Underbody Flow Restraining Effect

#### 3.1.2. Bridge Deck Shielding Effect

^{t}≤ 0.5 could not be effectively tested and thus are not shown here. In Figure 5a, the streamlined component of the normalized mean velocity u/U

_{∞}is always smaller than 1.0 in Δy

^{t}= [0.5, 1.5], evidencing the above achieved shielding effect in all the test ranges of α = [−12°, 12°]. However, in the range of α = [−12°, −6°], this bridge-deck shielding effect was limited, as is evidenced by the u/U

_{∞}≈ 1.0 flow profile. With an increase in α = [−4°, 12°], this bridge deck shielding effect is remarkably enhanced as is evidenced by the noticeably decaying u/U

_{∞}profile and obviously intensifying turbulence intensities I

_{u}& I

_{v}profiles in Δy

^{t}= [0.5, 1.0], respectively.

#### 3.2. Bridge-Deck Model

#### 3.2.1. Flow Transition Promoting Effect

_{p}= 7.3~14.1 at α

_{i}in the train-bridge case is in line with that at α

_{i}− 4° in the bridge-only case. That is to say, the critical |α| of the flow transition of the lower half bridge-deck model is reduced by about 4° with the presence of the train model.

#### 3.2.2. Flow Separation Intensifying Effect

## 4. Aerodynamic Characteristics

#### 4.1. Aerodynamic Force Coefficients

- (a)
- In α = [0°, 12°], no abrupt changes, i.e., drag crisis (Figure 8a), jumping and recovering of lift, moment, and three fluctuating force coefficients (Figure 8b–f), can be observed in the present study. As concluded in Section 3, these differences shall be chiefly caused by the disappearance of the quasi-Reynolds number effect.
- (a)
- In α = [−12°, 0°], the ${\overline{C}}_{D}^{t}$, ${\overline{C}}_{L}^{t}$, and ${\overline{C}}_{M}^{t}$ in the two cases with train model mounted on the upstream and downstream tracks share almost the similar behaviors, as described in Figure 8a–c. However, the ${\overline{C}}_{L}^{t}$ in the present study is reduced by 0.23 in the range of α = [−12°, 0°].

- (a)
- In α = [0°, 12°], no abrupt changes, i.e., jumping and recovering of ${\overline{C}}_{L}^{b}$, ${\overline{C}}_{M}^{b}$, ${\tilde{C}}_{D}^{b}$, ${\tilde{C}}_{L}^{b}$, and ${\tilde{C}}_{M}^{b}$ can be observed in the present study relative to those of [34]. Obviously, this difference shall also be caused by the disappearance of the quasi-Reynolds number effect as concluded in Section 3.1.2.
- (b)
- In α = [−12°, 0°], ${\overline{C}}_{M}^{b}$, ${\tilde{C}}_{D}^{b}$, ${\tilde{C}}_{L}^{b}$, and ${\tilde{C}}_{M}^{b}$ in the two cases with train model mounted on the upstream and downstream tracks display similar behaviors, while the values of |${\overline{C}}_{D}^{b}$| and |${\overline{C}}_{L}^{b}$| in the present study are much smaller than those of [34].

#### 4.2. Strouhal Numbers

^{t}, St

^{b}, and St

^{w}for the train, bridge-deck, and whole train-bridge models, respectively) are calculated via the power spectral densities (PSDs) of the model lifts based on d, D, and d + D, respectively.

^{t}and St

^{b}in the range of α = [−12°, 12°]. The results of an infinite prism tested by [40] and the train model in the train-only case are also demonstrated here for comparison. Generally, the train-only results highly mimic those of [40], again suggesting a validation of the present investigation.

^{5}belonging to the large Reynolds number [41]. Thus, the underlying mechanism of this Strouhal number disappearance shall be this ILEV flow pattern. In α = [−4°, 12°], both the Strouhal numbers of the train and bridge-deck models decreases gradually.

## 5. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Mode installations: (

**a**) Models for flow visualization, and (

**b**) Models for pressure field and flow profile measurements.

**Figure 2.**Model geometric parameters: (

**a**) pressure test points in the lateral direction; (

**b**) pressure test sections in the longitudinal direction; and (

**c**) flow profile test points. (Unit: mm).

**Figure 3.**Instantaneous flow patterns: (

**a**–

**h**) Train-only case at α = −12°~2°, (

**i**–

**p**) Bridge-only case at α = −12°~2°, and (

**q**–

**x**) Train-bridge case at α = −16°~−2°.

**Figure 4.**Instantaneous flow patterns: (

**a**–

**e**) Train-only case at α = 4°~12°, (

**f**–

**j**) Bridge-only case at α = 4°~12°, and (

**k**–

**o**) Train-bridge case at α = 0°~8°.

**Figure 5.**Profiles of flow approaching the train model at various angles of attack: (

**a**) Normalized mean velocity in streamwise direction; (

**b**) Turbulence intensity in streamwise direction; and (

**c**) Turbulence intensity in vertical direction.

**Figure 6.**Pressure distributions around the bridge-deck model at various angles of attack: (

**a**–

**c**) Mean pressure coefficients; (

**d**–

**f**) Fluctuating pressure coefficients.

**Figure 8.**Aerodynamic force coefficients of the train model: (

**a**) Mean drag coefficients; (

**b**) Mean lift coefficients; (

**c**) Mean moment coefficients; (

**d**) Fluctuating drag coefficients; (

**e**) Fluctuating lift coefficients; and (

**f**) Fluctuating moment coefficients.

**Figure 9.**Aerodynamic force coefficients of the bridge-deck model: (

**a**) Mean drag coefficients; (

**b**) Mean lift coefficients; (

**c**) Mean moment coefficients; (

**d**) Fluctuating drag coefficients; (

**e**) Fluctuating lift coefficients; and (

**f**) Fluctuating moment coefficients.

**Figure 10.**Strouhal numbers of the models: (

**a**) the train model; (

**b**) the bridge-deck model; and (

**c**) the whole system.

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**MDPI and ACS Style**

Wang, H.; Li, H.; He, X.
Aerodynamics of a Train and Flat Closed-Box Bridge System with Train Model Mounted on the Upstream Track. *Appl. Sci.* **2022**, *12*, 276.
https://doi.org/10.3390/app12010276

**AMA Style**

Wang H, Li H, He X.
Aerodynamics of a Train and Flat Closed-Box Bridge System with Train Model Mounted on the Upstream Track. *Applied Sciences*. 2022; 12(1):276.
https://doi.org/10.3390/app12010276

**Chicago/Turabian Style**

Wang, Hui, Huan Li, and Xuhui He.
2022. "Aerodynamics of a Train and Flat Closed-Box Bridge System with Train Model Mounted on the Upstream Track" *Applied Sciences* 12, no. 1: 276.
https://doi.org/10.3390/app12010276