Theoretical Calculation and Experimental Verification of Wind-Driven Rain Aerodynamic Forces on the Bridge Main Beam
Abstract
:1. Introduction
2. Summary of Raindrop Characteristics
3. Derivation of Wind-Driven Rain Aerodynamic Forces of the Main Beam
3.1. Rain Drop Impact Analysis and Simplified Calculation Model
3.2. Water Accumulation Model on the Main Beam Surface
3.3. Analysis of the Wind-Driven Rain Pneumatic Three-Component Force of Main Beam
4. Wind-Driven Rain Aerodynamic Force Test of the Main Beam
4.1. Overview of the Test
4.2. Test Results and Analysis
5. Discussion
- Firstly, the water content in a unit volume of air, the raindrop size, the raindrop spectral characteristics, and the falling velocity of experimental rainfall and natural rainfall may not be completely consistent, while theoretical calculations ideally use natural rainfall characteristic parameters, which will inevitably lead to a deviation in the results.
- Secondly, under the wind axis coordinate system used in this article, the aerodynamic drag force of the experimental model is mainly affected by the impact force of raindrops, while the aerodynamic lift and torque force, especially for the aerodynamic lift force, are more affected by the gravity of surface water accumulation. This conclusion is consistent with the literature [35,36]. Therefore, the error of surface water accumulation, especially under heavy rain, can cause significant deviation in the results of the surface runoff model. However, the surface water accumulation runoff model used in this article is an empirical model (Equation (20)), but for water accumulation on the surface of the main beam, its accuracy and applicability still need to be verified.
- Thirdly, the reasons for differences in the consistency between theoretical and experimental values of two types of cross-sections is that the side of the streamlined section is in a broken line form, and the lower edge of the side may not be fully impacted by raindrops, due to the obstruction of the upper edge. However, in theoretical calculations, the entire side is treated as a straight line, resulting in an increase in error.
- Finally, the reason the error tends to increase with the increase in rain intensity may be related to the more complex water accumulation state on the surface of the main beam under heavy rain intensity and its influence on the impact force of raindrops. This reason has been mentioned and analyzed in detail in the literature [21,23]. So, in Figure 10, the two maximum deviation values (116% and 81%) both occurred during a rain intensity of 120 mm/h, barring any problems with the rainfall equipment.
6. Conclusions
- 1.
- Even when the rainfall intensity reaches 709 mm/h (extreme value in China), the increase in density of air is less than 2%, and the change in density of air caused by rainfall can be ignored.
- 2.
- This article proposes the mass-weighted equivalent method (MWEM) to simplify the calculation process of raindrop impact force. Compared with the theoretical method, the error of the simplified calculation method (MWEM) increases with the increase in rainfall intensity, but even if the rainstorm intensity reaches 709 mm/h, the error is only about 4%, which can meet the accuracy of engineering applications. At the same time, the accuracy of the MWEM is verified through wind-driven rain experiments of two typical bridge main beam sections. It can be used for engineering applications.
- 3.
- For the additional aerodynamic force of the main beam under the action of wind-driven rain, in the wind axis coordinate system used in this article, the drag force mainly considers the impact force of raindrops, which is different from the lift and torque force that must simultaneously consider the impact force of raindrops and the complex water accumulation on the surface of the main beam. Therefore, under the existing empirical formulas for calculating the thickness of accumulated water, there is a significant deviation between the theoretical and experimental results of lift and torque force. Furthermore, it is worth noting that as the rainfall intensity increases, there is also a trend toward an increase in the deviation between theoretical and experimental results. So, the more complex water accumulation state on the surface of the main beam under heavy rain intensity and its influence on the impact force of raindrops need to be further studied.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Rain Intensity Level | Light Rain | Moderate Rain | Heavy Rain | Rainstorm | Weak Heavy Rainstorm | Medium Heavy Rainstorm | Strong Rainstorm | Domestic Extreme Value |
---|---|---|---|---|---|---|---|---|
Precipitation (mm/h) | 2.5 | 8 | 16 | 32 | 64 | 100 | 200 | 709.2 |
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Lei, X.; Shen, L.; Chen, Z.; Zhang, X.; Wei, C.; Han, Y. Theoretical Calculation and Experimental Verification of Wind-Driven Rain Aerodynamic Forces on the Bridge Main Beam. Atmosphere 2023, 14, 1535. https://doi.org/10.3390/atmos14101535
Lei X, Shen L, Chen Z, Zhang X, Wei C, Han Y. Theoretical Calculation and Experimental Verification of Wind-Driven Rain Aerodynamic Forces on the Bridge Main Beam. Atmosphere. 2023; 14(10):1535. https://doi.org/10.3390/atmos14101535
Chicago/Turabian StyleLei, Xu, Lian Shen, Zhengqing Chen, Xuewen Zhang, Chenglong Wei, and Yan Han. 2023. "Theoretical Calculation and Experimental Verification of Wind-Driven Rain Aerodynamic Forces on the Bridge Main Beam" Atmosphere 14, no. 10: 1535. https://doi.org/10.3390/atmos14101535