1. Introduction
Tornadoes are common all over the world. They have great destructive power, though they normally do not last long. A tornado is a micro-scale and strong convective weather phenomenon: a quickly rotating column of air that extends from a thunderstorm and touches the ground. The number of tornadoes reported in China is lower than that in the United States; nevertheless, the damage caused by them is very great. They caused a total economic loss of more than 9.1 billion CNY from 2007 to 2017, and at least 1772 people died from 1961 to 2011 [
1,
2,
3]. For example, Yang et al. [
4] reported that on 23 June 2016, an EF4 tornado killed at least 99 people and injured 846 others in Yancheng City, Jiangsu Province, China. In addition, more than 3000 buildings were destroyed, and hundreds of high-voltage transmission towers were damaged. According to reported statistics, approximately 17 provinces in China have suffered from tornadoes over the last two decades. Annually, the number of deaths is more than 10 and the number of injuries exceeds 1000 [
5]. The direct economic loss amounts to billions of CNY. The railway infrastructures are also vulnerable to these extreme local strong winds, and trains in Japan are often affected by strong tornadoes [
6,
7]. For instance, a high-speed train was hit by a tornado on 25 December 2005 near Sakata, and it overturned, killing 5 people and injuring 32 more. Another train encountered a tornado on 17 September 2006 when traveling at a speed of 25 km/h on the Japanese National Railroad. The first two wagons overturned, and six people were injured. In China, to the author’s knowledge, there are few records of extremely strong winds hitting trains, such as tornadoes. On 1 June 2021, a tornado was generated between the Mao’ershan West Railway Station and the Shangzhinan Railway Station along the Harbin–Mudanjiang High-Speed Railway, which caused equipment failure, and many trains were delayed. In recent years, the density of railway lines in China has been increasing. Global warming also leads to higher frequencies of extreme weather phenomena, such as tornadoes. Therefore, it is necessary to evaluate tornado-induced aerodynamic forces and strengthen the meteorological monitoring technology to ensure the operational safety of trains, especially in the areas where tornadoes are most common [
8].
Due to the difficulties and dangers associated with field measurements, and the complexity of tornadoes’ boundary conditions, the parameters defining the characteristics of tornadoes have not been well investigated. Physical modeling of tornado-like vortices has become a powerful tool for investigating tornado-induced wind forces on a structure. This modelling approach is similar to boundary-layer wind tunnel experiments, and has advantages such as controllable conditions and repeatability [
9]. Ying and Chang [
10] designed and developed a tornado-like-vortex simulator based on basic knowledge of tornado structure, and analyzed the tangential and radial velocities of tornadoes. The tornado-vortex simulator was improved by Ward [
11], becoming known as the Ward-type tornado-vortex simulator. Haan et al. [
12] designed, built, and tested the Iowa State University (ISU) tornado-vortex simulator. Its design and construction were based on two important requirements; i.e., it needed to accommodate physical models of a reasonable size to measure wind loads on different structures, and the tornado needed to be able to move along a path on the ground, enabling the simulation of realistic scenarios.
Most existing studies on the structural wind load caused by tornadoes have been related to building structures, cooling towers, transmission towers, bridges, etc. For example, Haan et al. [
13] used the ISU tornado-vortex simulator to investigate the wind loads on a one-story gable-roof structure and compared them to the provisions of the ASCE-7-05 building standard. Yang et al. [
14] conducted an experimental study to investigate the characteristics of wake vortex, flow structures, and wind loads acting on a high-rise building model in tornado-like winds. Sabareesh et al. [
15,
16] used the tornado-vortex simulator of the Tokyo Institute of Technology to study the effects of building location and ground roughness on the surface pressures of a cubic building. Razavi and Sarkar [
17] studied the influences of three roof geometries on tornado-induced structural actions on five equally-spaced wood frames of a low-rise building, and the maximum structural actions were calculated and compared with predictions of the ASCE7-16 building standard. Cao et al. [
9] and Wang et al. [
18] investigated the wind pressure distributions and wind forces on the inner and outer surfaces of a cooling tower structure that was subjected to stationary and translating tornado-like vortices. Ezami et al. [
19] tested an aerodynamic, self-supported lattice transmission tower model under tornado-like vortices. The tornado-like wind field was measured using cobra probes, and the aerodynamic structural responses were also measured to understand the dynamic responses of self-supported transmission towers to the tornado-induced loads. Cao et al. [
20] conducted wind pressure measurements on a rigid streamlined bridge deck model to determine the tornado-induced surface pressure distributions and aerodynamic load coefficients for each test section, and total force coefficients.
In addition, studies have also been carried out on the wind loads on trains under boundary-layer cross-winds. For instance, Baker et al. [
21,
22,
23] conducted wind tunnel tests to study the aerodynamic forces and moments of a train under cross-winds. Using different ground simulation techniques, Kwon et al. [
24] performed a large number of wind tunnel tests on Korean high-speed railway trains to investigate the effect of the train shape on wind resistance. Tian [
25] studied the effects of wind speed and wall height on the aerodynamic performance and overturning stability of trains.
The available literature concerning tornado-induced wind loads on trains is limited. Suzuki et al. [
26,
27,
28] and Bourriez et al. [
29] conducted preliminary model experiments to investigate the aerodynamic forces acting on a train traveling through a tornado. The results showed that the aerodynamic forces changed magnitude and direction depending on the position of the train in the swirling flow, and the train itself may deform the flow field. In another study, Baker et al. [
30] proposed a risk analysis method for the overturning of a train by a tornado, and the probability of overturning was determined based on specified statistical distributions of tornado parameters and vehicle operation parameters. Cao et al. [
31] investigated the spatially varied aerodynamic load characteristics of the high-speed train with different locations of the tornado’s center, along with the effects of the viaduct and wind screen on the wind loads. It was found that the wind screen alters the mechanism of the tornado-vortices–train-viaduct interaction, and therefore changes the most unfavorable location of the tornado’s center for total force coefficients. Additionally, some studies have been carried out to investigate the wind loads on train cars under the action of tornadoes via numerical simulation. For example, Xu et al. [
32] investigated the interaction between a high-speed train and a tornado-like vortex numerically using detached eddy simulations and model analysis considering the operation path, tornado intensity, and train speed. Kohei et al. [
33] conducted a computational simulation for the flow around a train passing through stationary tornado-like vortices and the resulting aerodynamics forces acting on the train, and compared it with the experimental results. However, the research on the wind loading characteristics of a train under the action of tornadoes is in the exploratory stage, and some important parameters related to the tornado airflow, such as the swirl ratio and ground roughness, were not taken into account.
In this study, pressure measurements on a rigid train car model under stationary tornadoes were performed to investigate the effects of the distance between the tornado’s core and the longitudinal axis of the train car, the swirl ratio, and the ground roughness on the wind pressure distributions on the train car’s surface and wind load characteristics. The findings can be helpful to determining the threshold conditions for raising the alarm when safety is compromised. The rest of this paper is structured as follows:
Section 2 introduces the experimental setup and the definitions of the main parameters and influential coefficients;
Section 3 presents the pressure distributions across the train car under tornado-like flow;
Section 4 and
Section 5 present, respectively, the sectional aerodynamic load coefficients and total force coefficients of the train car under the action of a tornado; finally,
Section 6 draws the main conclusions.
5. Overall Force Coefficients
Since the sectional aerodynamic loads are not distributed consistently along the car’s axis due to the tornado flow characteristics, it was necessary to propose overall force coefficients for the train car, in order to thoroughly assess the effects of tornadoes on trains. To this end, this section investigates the effects of the distance between the train car and the tornado’s center, swirl ratio, and ground roughness on the overall force coefficients of the train car.
5.1. Effect of Distance between Car and Tornado Center
Figure 18 depicts the overall force coefficients as functions of the distance between train car and the tornado’s center when
S = 0.35 and
λ = 0, and under boundary-layer cross-wind conditions represented by the dashed lines.
For the results of boundary-layer cross-wind, all the five overall force coefficients do not change with the distance, because the boundary-layer cross-wind field remained constant with horizontal distance. The side force coefficient CFX of the train car was the largest; the rolling moment coefficient CMY and lift coefficient CFZ were relatively small—i.e., −0.37 and 0.16, respectively; and the pitching moment coefficient CMX and yaw moment coefficient CMZ were almost zero.
As for tornado-like wind, the overall force coefficients are significantly affected by the distance between the car and the tornado’s center. Near the tornado’s center, at which the tangential wind velocities were extremely small, the side force coefficient CFX was close to zero. As the distance between the train car and the tornado’s center increased, the side force coefficient CFX of the car increased due to the combined effects of pressure drop and tangential wind velocity. When R/Rc = 1.5, the side force coefficient CFX reached its maximum value, and then it decreased with increasing distance. The changes in the rolling moment coefficient CMY were the same as those of the side force coefficient, though its values were approximately half those of the side force coefficient. The absolute value of the pitching moment coefficient CMX increased first and then decreased with increasing distance; i.e., it reached its maximum value when R/Rc = 1.5, and became almost zero when R/Rc > 2.
Under the tornado wind loading, the lift coefficient CFZ and yaw moment coefficient CMZ of the train car exhibited the most unfavorable values near the tornado’s center (R/Rc = 0). This is mainly attributed to the strong rotation effect of the tornado and the large pressure drop at the tornado’s center, due to which the train car is subjected to strong upward suction and counterclockwise torque. As the radial distance increased, the absolute value of the pressure drop decreased, resulting the lift and yaw moment coefficients of the car decreasing as well.
5.2. Effect of Swirl Ratio
Figure 19 demonstrates the variations in overall force coefficients with the distance between the train car and the tornado’s center under three different swirl ratios (
S = 0.15,
S = 0.35 and
S = 0.72) when
λ = 0. It can be observed that the general variation trends of the wind force coefficients with the radial position under different swirl ratios are basically the same; however, there are apparent differences in the values.
- (1)
Side force coefficient CFX and rolling moment coefficient CMY
When the swirl ratio increased from 0.15 to 0.35, the peak value of the side force coefficient
CFX increased significantly. Inconspicuous variation was observed when it was increased from 0.35 to 0.72. Under different swirl ratios, the positions of the peak
CFX value were different. The side force coefficient
CFX reached its maximum value at around
R/Rc = 2.5 when the swirl ratio was 0.15, and at around
R/Rc = 1.5 when the swirl ratio was 0.35 or 0.72. The effect of swirl ratio on the rolling moment coefficient
CMY was the same as that on the side force coefficient
CFX, indicating that the side force contributed a lot to the rolling moment. The value of the rolling moment coefficient was approximately half that of the side force coefficient. This tendency agrees well with the results of sectional side force coefficients and rolling moment coefficients in
Figure 15.
- (2)
Lift force coefficient CFZ
When R/Rc < 1.5, the lift force coefficient CFZ increased first and then decreased with increasing swirl ratio. When 1.5 < R/Rc < 3, the lift coefficient decreased with increasing swirl ratio. When R/Rc > 3, the lift coefficient was almost unaffected by the swirl ratio. Moreover, for higher swirl ratios, the lift force coefficient CFZ attenuated rapidly with increasing distance between car and the tornado’s center within a certain range.
- (3)
Pitching moment coefficient CMX
The peak value of the pitching moment coefficient CMX increased significantly when the swirl ratio increased from 0.15 to 0.35, whereas it was slightly decreased when the swirl ratio increased from 0.35 to 0.72. In general, the higher the swirl ratio, the closer the position of the peak CMX value appears to the center of the vortex core.
- (4)
Yawing moment coefficient CMZ
When R/Rc < 1.5, the yawing moment coefficient CMZ increased with increasing swirl ratio. When 1.5 < R/Rc < 3, the yawing moment coefficient decreased with increasing swirl ratio. When R/Rc > 3, the yawing moment coefficient was nearly not affected by the swirl ratio.
In summary, when the swirl ratio increased from 0.15 to 0.35, the absolute values of the force coefficients of the car increased significantly, which was mainly observed within R/Rc < 1.5. When the swirl ratio increased from 0.35 to 0.72, the lift force coefficient CFZ and yawing moment coefficient CMZ changed significantly when R/Rc < 1.5, whereas the other wind force coefficients remained rather unaffected.
5.3. Effect of Ground Roughness
Similarly to the analysis in the previous subsection,
Figure 20 demonstrates the variations in the overall force coefficients with the distance between the train car and the tornado’s center under three different ground roughness levels (
λ = 0.15,
λ = 0.35, and
λ = 0.72) when
S = 0.35. It can be observed that the general variation trends of the wind force coefficients with the radial position under different ground roughness levels were essentially the same. Generally, when within the vicinity of the vortex core radius (i.e.,
R/Rc < 1.5), there is uncertainty about the trends of overall force coefficients with different ground roughness values, which may be caused by the uncertainty from the combined effect of pressure drop and aerodynamic effects, though the overall force coefficients decrease with the increasing of the ground roughness further away from the core boundary (i.e.,
R/Rc > 2) as the aerodynamic effects become primary. Additionally, the peak values of all force coefficients decrease as roughness increases, implying that a train exposed to roughness will suffer less damage. On the other hand, the extent of the effect of roughness on different force coefficients is not consistent.
- (1)
Side force coefficient CFX and rolling moment coefficient CMY
It can be observed that as the ground roughness increased, the peak value of the side force coefficient CFX decreased. The positions of the peak CFX value under different ground roughness levels were different. The side force coefficient CFX reached its maximum value at about R/Rc = 1.5 when on smooth ground, and at about R/Rc = 1.2 when the roughness was 5% or 25%. The effect of ground roughness on the rolling moment coefficient CMY was the same as that on the side force coefficient CFX.
- (2)
Lift force coefficient CFZ
When near the tornado’s center, the lift force coefficient CFZ with rough ground was larger than that with smooth ground. In addition, at other positions, the lift coefficient decreased with increasing roughness. When R/Rc > 3, the lift coefficient was almost unaffected by the ground’s roughness.
- (3)
Pitching moment coefficient CMX
When the car was located within the vortex core radius, the pitching moment coefficient CMX increased first and then decreased with increasing roughness. When 1.5 < R/Rc < 2, the pitching moment coefficient CMX decreased with increasing roughness. In general, the higher the ground roughness, the closer the position of the peak pitching moment coefficient CMX to the center of the vortex core.
- (4)
Yawing moment coefficient CMZ
When R/Rc < 3, the yawing moment coefficient CMZ decreased with increasing ground roughness. When R/Rc > 3, the yawing moment coefficient remained unaffected.
6. Conclusions
In this study, the wind loading characteristics of a train model under tornado-like vortices were investigated through wind pressure measurements using a tornado-vortex simulator. Aerodynamic parameters, including the surface pressure distributions, aerodynamic load coefficients for different sections, and the force coefficients of a train car affected by the tornado-like vortices were identified. Furthermore, the effects of distance between the train car and the tornado’s center, swirl ratio of tornado-like vortices, and ground roughness were taken into consideration. The main conclusions are as follows.
The mean wind pressure coefficients across the train car are negative regardless of the position of the pressure taps. This is attributed to the combined effects of the pressure drop accompanying a tornado and the aerodynamic flow–structure interaction. The mean and fluctuating pressure distribution across the train car varies with the horizontal distance from the tornado’s center to the centerline of the train car model, and the variation trends of them are almost the same. When the train car is at the center of the tornado vortex core, the pressure drop is the main factor. When the train car is located at a distance equal to 1.5 times the vortex core’s radius, the tornado airflow and the aerodynamic effects between train car and tornado are the main factors. When the distance from the train car to the tornado’s center exceeds three times vortex core’s radius, the impact of tornado-like vortices on the train car is almost negligible. These features exhibit obvious discrepancies from results obtained through conventional boundary-layer wind tunnel tests.
The mean sectional force coefficients along the train car axis are position-dependent and reach their peak values near the middle section. The sectional side force coefficients and rolling moment coefficients reach their peak values when the train car is located within the tornado’s core, and the largest sectional lift force coefficients are obtained when the train car is at the tornado’s center. The overall distributions of the wind force coefficients of the train car under different swirl ratios and ground roughness levels are basically the same, though their values are different. The peak aerodynamic force value increases with increasing swirl ratio, but this peak value may not change significantly when the swirl ratio is high; on the other hand, this peak value changed little with increasing ground roughness.
The lift force and yawing moment coefficients of the train car decrease with increasing radial distance, and exhibit their peak values at the center of the vortex core. The absolute values of the side force, rolling moment, and pitching moment coefficients increase first and then decrease with increasing radial distance. They reached their maximum values at a radial distance of 1.5 times the vortex core’s radius. The change trends of the overall force coefficients of the train car under different ground roughness levels and different swirl ratios are nearly the same as those of the sectional force coefficients. The peak values of all force coefficients decreased as roughness increased, implying that a train in rough terrain will suffer less damage.
The present investigation revealed some interesting results of wind loading characteristics of a train car model under tornado-like vortices. One limitation of this study was that the simulated tornado did not have translation speed, which needs to be taken into consideration in further research to provide a comprehensive understanding of wind loads of train cars under the action of tornadoes. Additionally, future works considering more statistical measures, such as median and 84.13th percentile of the pressure and force coefficients, may provide better insights into the wind loading characteristics.