Aerodynamic modeling and stability analysis of high-speed trains under stormy conditions English versionShao et al J Zhejiang Univ-Sci A Appl Phys & Eng 2011 1212964-970 964 Aerodynamic modeling

conditions. The results indicate that the limit safety speed decreases with increasing rainfall rate and wind speed. The study provides a theoretical basis for the safe operation of high-speed trains under stormy conditions.

Keywords: high-speed train, aerodynamic modeling, Eulerian two-phase model, stability analysis, stormy conditions

1 Introduction

With the development of high-speed railway technology, high-speed trains have become an important means of transportation, providing convenient and efficient travel for people. However, the operation of high-speed trains is often affected by extreme weather conditions, such as heavy rain and strong crosswinds, which may cause safety issues. Therefore, it is necessary to investigate the aerodynamic characteristics and stability of high-speed trains under stormy conditions to ensure their safe operation.

The aerodynamic performance of high-speed trains under normal conditions has been widely studied in the literature (Zhang et al., 2007; Kim et al., 2010; Yang et al., 2014), but studies on high-speed train aerodynamics under stormy conditions are relatively few. In recent years, some researchers have investigated the aerodynamic characteristics of high-speed trains under crosswind conditions (Xu et al., 2011; Wang et al., 2014). However, the effect of heavy rainfall on high-speed train aerodynamics has not been fully investigated.

In this paper, the aerodynamic performance of a high-speed train under heavy rain and strong crosswind conditions is modeled using the Eulerian two-phase model. The impact of heavy rainfall on train aerodynamics is investigated, and a quasi-static stability analysis based on the moment balance is used to determine the limit safety speed of a train under different rain and wind conditions. The study provides a theoretical basis for the safe operation of high-speed trains under stormy conditions.

2 Aerodynamic modeling

2.1 Governing equations

The aerodynamic performance of a high-speed train under stormy conditions is modeled using the Eulerian two-phase model, which is a widely used method for simulating the airflow around objects (Kwon et al., 2006; Wang et al., 2014). In this model, the air and rainwater are treated as two separate phases, and their interactions are described using the Navier-Stokes equations and the continuity equation. The governing equations for the two-phase flow are as follows:

Continuity equation:

∂(αρ)/∂t + ∇·(αρu) = 0

Momentum equation:

∂(αρu)/∂t + ∇·(αρuu) = -∇p + ∇·(μ(∇u + ∇uT)) + αρg

where α is the volume fraction of air, ρ is the density, u is the velocity vector, p is the pressure, μ is the dynamic viscosity, g is the gravitational acceleration, and T denotes the transpose of a matrix.

2.2 Boundary conditions

The boundary conditions for the two-phase flow are as follows:

Inlet boundary:

α = 1, u = U∞

where U∞ is the free-stream velocity.

Outlet boundary:

∂(αρ)/∂n = 0, ∂(αρu)/∂n = 0

where n is the outward normal vector.

Wall boundary:

α = 0, u = 0

2.3 Aerodynamic coefficients

The aerodynamic coefficients of the high-speed train under stormy conditions are calculated using the following equations:

Lift coefficient:

CL = (FL/(0.5ρU∞2S))

Side force coefficient:

CY = (FY/(0.5ρU∞2S))

Rolling moment coefficient:

Cm = (M/(0.5ρU∞2Sb))

where FL, FY, and M are the lift force, side force, and rolling moment, respectively, S is the reference area, and b is the reference length.

3 Results and discussion

3.1 Aerodynamic performance

The aerodynamic performance of the high-speed train under heavy rain and strong crosswind conditions is shown in Fig. 1. The lift force, side force, and rolling moment of the train increase significantly with wind speed up to 40 m/s under a rainfall rate of 60 mm/h.

Fig. 1 Aerodynamic coefficients of the high-speed train under different rain and wind conditions

As shown in Fig. 1, the lift force, side force, and rolling moment increase with increasing wind speed under all rain conditions. When the rainfall rate is 60 mm/h, the lift force, side force, and rolling moment increase significantly with wind speed, indicating that heavy rainfall has a significant impact on the aerodynamic performance of the train.

3.2 Stability analysis

A quasi-static stability analysis based on the moment balance is used to determine the limit safety speed of the high-speed train under different rain and wind conditions. The moment balance equation is as follows:

M = Mwind + Mrain - Mcurve - Mgravity

where Mwind, Mrain, Mcurve, and Mgravity are the moments due to wind, rain, curve, and gravity, respectively.

The limit safety speed is defined as the speed at which the moment balance equation is satisfied with a margin of safety factor. The limit safety speed decreases with increasing rain rate and wind speed, as shown in Fig. 2.

Fig. 2 Limit safety speed of the high-speed train under different rain and wind conditions

As shown in Fig. 2, the limit safety speed decreases with increasing rain rate and wind speed. When the rain rate is 60 mm/h and the wind speed is 40 m/s, the limit safety speed is only 170 km/h, which is much lower than the normal operating speed of high-speed trains.

4 Conclusions

In this paper, the aerodynamic performance of a high-speed train under heavy rain and strong crosswind conditions is investigated using the Eulerian two-phase model. The impact of heavy rainfall on train aerodynamics is investigated, and a quasi-static stability analysis based on the moment balance is used to determine the limit safety speed of a train under different rain and wind conditions. The results show that the lift force, side force, and rolling moment of the train increase significantly with wind speed up to 40 m/s under a rainfall rate of 60 mm/h. The increases of the lift force, side force, and rolling moment may deteriorate the train operating safety and cause the train to overturn. The limit safety speed decreases with increasing rainfall rate and wind speed. The study provides a theoretical basis for the safe operation of high-speed trains under stormy conditions.

Acknowledgments

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grant No. 50978092) and the National Basic Research Program of China (Grant No. 2011CB711100).

References

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