Experimental and Numerical Investigation on Ballast Flight from Perspective of Individual Particles

Abstract

Ballast flight significantly affects the safe operation of high-speed railway. A wind tunnel experiment and computational fluid dynamics simulation were performed to investigate the occurrence and development mechanism of ballast flight from the perspective of individual particles, which was based on the capture, reconstruction, and analysis approach of ballast features. The dynamic characteristics of ballast particles under wind load, the flow field characteristics such as the distribution of air pressure and streamline, and the influence of the ballast mass and shape, windward direction, and wind speed on the ballast flight were investigated. The results show that the critical velocity of the ballast weighing from 5 g to 200 g is between 14.22 m/s and 29.89 m/s. The massive ballast with the shape of an oblate is unlikely to fly. The air pressure difference is proportional to the square of the wind speed, and it increases 14.9 times when the wind speed increases from 10 m/s to 40 m/s. In order to avoid ballast flight, recommended suggestions include limiting the proportions of the small and the ellipsoid ballast praticles, laying the ballast with high density and a large size on the top of the ballast bed, and reducing the degradation and fouling of the ballast bed.

1. Introduction

The ballast track is one of the most important tracks of high-speed railway. It has been commonly applied in the world and has great potential for the advantages of low cost, small vibration and noise, and easy maintenance [1,2]. In addition, the ballast track could be used in areas such as large span bridges and poor geologic zones, which are inaccessible for other track structures. However, with the increase of the operation speed of trains, the problem of ballast flight becomes more and more significant [3,4,5]. The ballast flight is the phenomenon by which the ballast particle goes out of the ballast bed due to train aerodynamic behavior mainly. The flying ballast may strike the rail, train body, and the infrastructures near the railway line, which will increase the maintenance cost and threaten the safety of operation. There are some prevention methods of ballast flight in the market, such as using ballast glue and a protection net. However, these measures will also increase the construction cost and the maintenance difficulty. The ballast flight limits the further development of the ballast track in high-speed railway and it is necessary to be investigated.

The diverse reasons of ballast flight are complex, and some considerable research papers based on experiments and numerical simulations have been published recently. The experimental research includes field tests and laboratory tests, which concentrate on the flow above the ballast bed mainly. Quinn [4,5] set up some strips of lightweight plastic tape on the ballast shoulder of a railway line, and the movement of these strips before and after the train passage was monitored by a high-frequency video camera. The airflow direction and its rate of change were investigated qualitatively. Qie [6] set a view area of small ballast particles in a high-speed railway line to observe the occurrence and development of ballast flight at the train speed of 350 km/h. A set of sensors of air velocity and pressure were set up in the horizontal and vertical space above the ballast bed in a field experiment to monitor the flow during the train passage and to analyze the areas where ballast flight may occur easily [7,8,9,10,11,12,13]. The wind tunnel experiments of the ballast bed of both model scale and full scale were carried out to study the influence of track parameters on ballast flight [13,14,15,16,17]. The influence of sleeper type, track vibration, and snow on ballast flight was considered based on laboratory tests as well [17,18,19,20,21,22,23]. Moreover, numerical simulation models of the train and ballast bed were established with the method of computational fluid dynamics (CFD). The distribution characteristics of airflow above the ballast bed and the influence of the parameters such as the computational mesh size and track type on flow were discussed [6,16,17,24,25,26,27,28].

The essence of ballast flight is the ballast movement of individual particles. Most previous studies on ballast flight have analyzed the aerodynamic feature of flow from the macroscopic properties of the ballast bed, which ignored the dynamics characteristics of individual ballast particles under wind load. Besides, the ballast bed is formed by granular ballast particles with different shapes and sizes. If using the integral model of a ballast bed [6,24,25] to investigate the mechanism of ballast flight, the influence of particle shape, mass, volume, or other factors could not be considered properly. Therefore, some researchers investigated the mechanism of ballast flight from the perspective of individual particles. Kwon and Park [7] classified the ballast particles as flat, half-spherical, and spherical by shape. The influence of shape on ballast flight was investigated based on a wind tunnel experiment of individual particles. Jing [29] pointed out that the contact of the ballast and the platform had a marginal effect on ballast flight based on the CFD simulations of an individual ballast. However, the particle features had an obvious effect on ballast flight, but it was not simulated accurately in the previous CFD research. Besides, there was not a strict classification standard of ballast shape in the related study. So, the airflow around the ballast particle under wind load could not be obtained accurately, as well as the influence of ballast shape, size, and mass on ballast flight.

In this paper, the information of ballast features was captured, reconstructed, and analyzed accurately by an experimental platform of the three-dimensional (3D) scanning system, which could also build the database of ballast particles. Then, a wind tunnel experiment of ballast particles was carried out to investigate the movement characteristics of ballast particles under wind load, as well as the influence of ballast mass and shape, wind direction, and speed on ballast flight. Finally, a CFD simulation was utilized to explore the aerodynamic characteristics of ballast particles such as the distribution of air pressure and streamline. The results could reveal the mechanism of occurrence and development of ballast flight from the perspective of individual particles and provide effective prevention suggestions for ballast flight.

2. Materials and Methods

2.1. Accurate Capture, Reconstruction, and Analysis of Ballast Features

The granular particles in the ballast bed have different sizes and shapes, which have a significant influence on the dynamic characteristics of the ballast bed [30]. The image recognition technology for obtaining particle features has been widely used in civil engineering in recent years [31,32,33]. Nevertheless, the previous research paid more attention to the mechanical properties of the ballast aggregate based on the image recognition method, which ignored the local morphological characteristics of particles, because the local features of individual particles had little effect on the mechanical property of the ballast aggregate. The traditional approach of image recognition is relatively time consuming as well. This paper aims to investigate the aerodynamic characteristics of individual ballast particles under wind load, which were influenced by the local particle features significantly. The 3D scanning platform was set up to capture the ballast features rapidly based on our previous research [34] in detail, as shown in Figure 1. It can capture the morphological particle characteristics such as the shape, size, angularity, and surface texture. Information on the ballast features was obtained in the format of a Standard Template Library (STL) by scanning a particle from double views.

Five hundred ballast particles with different sizes and shapes were selected randomly from a high-speed railway line, and their profiles were recorded by the 3D scanning system. An in-house program was developed using the graphic analysis algorithm to identify and extract the dimensions of the long axis, middle axis, and short axis of the ballast by obtaining the outline projection with three particle views. Then, the shape parameters such as the volume, surface area, acicular index, and flakiness index were calculated automatically based on MATLAB. The method of the accurate capture, reconstruction, and analysis of ballast features provides a technical support to analyze the movement characteristics of ballast particles in a wind tunnel experiment and to formulate an accurate CFD numerical simulation models.

The classification of particle shape was based on the relationship between the dimensions of the ballast axis, as listed in

Table 1. Grouping scheme of ballast shape.

Group	Shape	Classification Standard
A	Spherical	$\raisebox{1ex}{$b$}\!\left/ \!\raisebox{-1ex}{$a$}\right.>\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, $\raisebox{1ex}{$c$}\!\left/ \!\raisebox{-1ex}{$b$}\right.>\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$
B	Ellipsoid	$\raisebox{1ex}{$b$}\!\left/ \!\raisebox{-1ex}{$a$}\right.<\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, $\raisebox{1ex}{$c$}\!\left/ \!\raisebox{-1ex}{$b$}\right.>\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$
C	Oblate	$\raisebox{1ex}{$b$}\!\left/ \!\raisebox{-1ex}{$a$}\right.>\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, $\raisebox{1ex}{$c$}\!\left/ \!\raisebox{-1ex}{$b$}\right.<\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$
D	Prolate	$\raisebox{1ex}{$b$}\!\left/ \!\raisebox{-1ex}{$a$}\right.<\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, $\raisebox{1ex}{$c$}\!\left/ \!\raisebox{-1ex}{$b$}\right.<\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

a, b, and c represent the long axis, middle axis, and short axis dimensions of the ballast particles, respectively.

, proposed by Zingg [35], Krumbein, and Pettijohn [36], and most widespread around the world. The 500 ballast samples were divided into four groups based on the approach. Group A comprised the ballast particles with the spherical shape, while Group B was ellipsoid, Group C was oblate, and Group D was prolate. Then, 18 ballast particles were selected and numbered in each group according to the mass. The distribution gradient of particle mass in each group was similar; in other words, the mass of the ballast with the same number was similar between groups. For example, the particle mass of A15, B15, C15, and D15 was all about 150 g.

Figure 2 shows the ballast samples with the serial numbers of the four groups. The information of ballast features was calculated to form a database based on the automatic analysis algorithm. The four representative ballast samples are summarized in

Table 2. Database of ballast information.

	A15	B15	C15	D15
Long axis	5.53 cm	7.34 cm	9.18 cm	10.39 cm
Middle axis	5.45 cm	4.46 cm	8.69 cm	5.16 cm
Short axis	3.86 cm	3.97 cm	1.86 cm	2.61 cm
Mass	149 g	151 g	148 g	150 g
Volume	54.18 cm3	55.66 cm3	52.86 cm3	53.96 cm3
Surface area	80.39 cm2	89.86 cm2	120.52 cm2	102.94 cm2
Acicular index	1.02	1.65	1.06	2.01
Flakiness index	0.71	0.89	0.21	0.51
Actual ballast
Reconstructed ballast

.

2.2. Wind Tunnel Experiment

The wind tunnel experiment of ballast particles was carried out to investigate the occurrence and development of ballast flight from the perspective of individual particles. The ballast dynamics characteristics under wind load, as well as the influence of mass, shape, and windward direction on ballast flight were analyzed.

As shown in Figure 3, a board (2.5 m × 2 m) was fixed as the test bench in the wind tunnel laboratory. It was 0.35 m between the test bench and ground, which was the same as the thickness of the ballast bed. A transparent plexiglass plate was fixed above the test bench to simulate the bottom of a train carriage, through which the movement of the ballast could be observed clearly. The wind speed from the inlet of the wind tunnel laboratory could be adjusted by controlling the fan voltage. A Pitot tube was set up to monitor the wind speed above the test bench. The test bench, plexiglass board, and Pitot tube were fixed firmly in case of vibration under the strong wind. In addition, the multi-layer protective nets were installed at the end of the test bench as well as the outlet of the wind tunnel laboratory, which could prevent the ballast from flying out of the bench and causing damage to the fan.

The ballast samples in the four groups were tested respectively, and there were eight ballast particles to be tested in each case because of the tremendous number of samples. The light particles were easy to be blown off if light and heavy ballast particles were tested simultaneously. So, the light samples (A1, A2, B1, B2, C1, C2, D1, and D2) were arranged in a single test. The remaining ballast samples were tested in the order of A3–A10, A11–A18, B3–B10, B11–B18, C3–C10, C11–C18, D3–D10 and D11–D18. The ballast samples were arranged at the front of the test bench in accordance with their sequence in each group, as shown in Figure 4.

The shapes and sizes of the surface were similar in different placement directions between the spherical ballast (Group A) and oblate ballast (Group C), while these properties of ellipsoid ballast (Group B) and prolate ballast (Group D) were affected by the placement direction greatly. For this reason, the ballast samples of Groups B and D were set as the long side faces the wind and short side faces the wind, respectively, as shown in Figure 5, to investigate the influence of the windward direction of the ballast on its dynamics and critical velocity.

The mean velocity above the ballast bed is close to 1/3 of the train speed [12]. Therefore, the input velocity ν in the experiment could represent the airflow generated by the train with a speed of 3ν. The wind speed was increased step by step during the test. The movement of each ballast sample under wind load was recorded by the high-speed camera in the wind tunnel laboratory, and the wind speed was obtained correspondingly. It was difficult to prevent the ballast flying once it had the initial displacement under wind load. Therefore, it was necessary to control the initial displacement of the ballast to prevent ballast flight. In this paper, the wind speed of initial particle displacement was defined as the critical velocity. Each test was repeated three times to reduce the influence of random errors. Meanwhile, the placement sequence and windward direction of ballast particles should be consistent in repeated tests.

2.3. Computational Fluid Dynamics Simulation

Ballast flight is mainly affected by the airflow around the ballast surface during the passage of high-speed trains. In order to investigate the air pressure and streamline around the ballast with different shapes, sizes, and windward directions, as well as the influence of the wind speed on ballast flight, the CFD numerical simulation of ballast particles was established using Fluent v18.1 software.

2.3.1. Model Formulation

The shape and size of the test bench in the numerical simulations were consistent with those in the wind tunnel experiment. The height from the test bench to the top of the computational boundary was 0.419 m, which was same as the height from the ballast bed surface to the train underbody [6]. The size of the calculation domain was 4 m × 2 m × 0.419 m, as shown in Figure 6.

The approximate simulation method [29] was used in some numerical studies to reconstruct the simulation model of the ballast particles, which could only represent the ballast size roughly and ignored the local features of the ballast particles. In this paper, a refined numerical simulation model of ballast particles was developed based on the 3D scanning results. The principle and method were as follows. The STL file of ballast features obtained by the 3D scanning system was a geometric model, which could represent the ballast contour by a set of triangles, and the simulation precision could be adjusted by controlling the number of triangles. The information in each triangle contained only the 3D coordinates of vertices and the normal vector of the plane. That was, the ballast model obtained by scanning only recorded the geometric position information of the ballast surface, but not the topological information of the relationship between the geometries. Therefore, it was necessary to decompose and reconstruct the regular geometric voxels from the ballast contour information, rebuild the topological relationship based on the position information, and establish the whole body model of the ballast particles. In addition, the validity and closure of the geometric voxels of the ballast model should be checked to repair the geometric defects such as the cracks and isolated edges.

The “body” was created to determine the generated scale of mesh after reconstructing the ballast model in the calculation domain. The computational space was divided by the tetrahedral unstructured mesh because the geometric shape of the ballast was extremely complicated. In order to analyze the flow around the ballast particles, a boundary layer mesh was generated on the surface of the ballast model with an initial height of 0.2 mm, a growth rate of 1.2, and a mesh level of 3. Figure 7 shows the surface mesh and the spatial mesh of the numerical model.

The mesh near the contour of the ballast was refined by building a density box to improve the accuracy of calculation. In order to improve the computational efficiency and convergence, the mesh size changed smoothly from the density box to the computational boundary with a growth rate of 1.2. Figure 8 shows the final numerical simulation model with approximate 5.74 million mesh elements.

The $k-\epsilon$ two-equation turbulence model of the incompressible fluid was used as the mathematical model because the Mach number of the flow was less than 0.3 [37]. The governing equations of the flow field were established to solve the airflow according to the conservation law. The continuous equation is as follows:

$$\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$$

(1)

The momentum equation is as follows:

$$\frac{\partial u}{\partial t}+(u\frac{\partial u}{\partial x}+\nu \frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z})=-\frac{1}{\rho }\frac{\partial P}{\partial x}+(\upsilon +{\upsilon }_T)(\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}+\frac{{\partial }^{2}u}{\partial z^2})$$

(2)

$$\frac{\partial \nu }{\partial t}+(u\frac{\partial \nu }{\partial x}+\nu \frac{\partial \nu }{\partial y}+w\frac{\partial \nu }{\partial z})=-\frac{1}{\rho }\frac{\partial P}{\partial y}+(\upsilon +{\upsilon }_T)(\frac{{\partial }^2\nu }{\partial x^2}+\frac{{\partial }^2\nu }{\partial y^2}+\frac{{\partial }^2\nu }{\partial z^2})$$

(3)

$$\frac{\partial w}{\partial t}+(u\frac{\partial w}{\partial x}+\nu \frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z})=-\frac{1}{\rho }\frac{\partial P}{\partial z}+(\upsilon +{\upsilon }_T)(\frac{{\partial }^{2}w}{\partial x^2}+\frac{{\partial }^{2}w}{\partial y^2}+\frac{{\partial }^{2}w}{\partial z^2})$$

(4)

The turbulent kinetic energy ($k$) equation is as follows:

$$\begin{array}{ll}& \frac{\partial k}{\partial t}+\frac{\partial (uk)}{\partial x}+\frac{\partial (vk)}{\partial y}+\frac{\partial (wk)}{\partial z}\\ =& (G-\rho \epsilon )+\frac{\partial }{\partial x}(\frac{{\upsilon }_T}{{\sigma }_k}\frac{\partial k}{\partial x})+\frac{\partial }{\partial y}(\frac{{\upsilon }_T}{{\sigma }_k}\frac{\partial k}{\partial y})+\frac{\partial }{\partial z}(\frac{{\upsilon }_T}{{\sigma }_k}\frac{\partial k}{\partial z})\end{array}$$

(5)

The turbulence dissipation ($\epsilon$) equation is as follows:

$$\begin{array}{ll}& \frac{\partial \epsilon }{\partial t}+\frac{\partial (u\epsilon )}{\partial x}+\frac{\partial (v\epsilon )}{\partial y}+\frac{\partial (w\epsilon )}{\partial z}\\ =& \frac{\epsilon }{k}(C_{1}G-C_2\rho \epsilon )+\frac{\partial }{\partial x}(\frac{{\upsilon }_T}{{\sigma }_{\epsilon }}\frac{\partial \epsilon }{\partial x})+\frac{\partial }{\partial y}(\frac{{\upsilon }_T}{{\sigma }_{\epsilon }}\frac{\partial \epsilon }{\partial y})+\frac{\partial }{\partial z}(\frac{{\upsilon }_T}{{\sigma }_{\epsilon }}\frac{\partial \epsilon }{\partial z})\end{array}$$

(6)

where $u$, $v$ and $w$ are the local velocity components of the flow field in each coordinate direction; $\rho$, $P$ and $\upsilon$ is the density, the pressure and the viscosity coefficient of the airflow respectively; ${\upsilon }_T$ is the effective viscosity coefficient; $G$ is the production term of the turbulent kinetic energy ($k$); ${\sigma }_k$, ${\sigma }_{\epsilon }$, $C_1$ and $C_2$ are the empirical constants.

The second-order upwind style of the finite volume method (FVM) was used to discretize the governing equations. The algebraic equations with discretized initial conditions and boundary conditions were solved by the semi-implicit method for pressure linked equations (SIMPLE), based on which the numerical solution of airflow was obtained.

2.3.2. Model Validation

A test device of air pressure with the shape of a pentahedron was developed for the model validation, as shown in Figure 9a. The height of the test device was 2 cm, which was the same with the average size of the actual ballast particle. The surfaces of the top and bottom were equilateral triangles with side lengths of 3 cm and 4 cm, respectively. The measuring point of air pressure was arranged at the center of each surface, and it was connected to the collecting instrument of air pressure through a conduit. A standard pressure sensor was used to calibrate the measuring data of the test device before the experiment. The test device was fixed on the test bench, and the air pressure data of each surface was recorded. The test device was simulated accurately in the CFD numerical simulation as well, as shown in Figure 9b.

The wind speed was set as 10 m/s, 20 m/s, and 30 m/s respectively both in the wind tunnel experiment and the numerical simulation. Then, the data of the air pressure in the CFD simulation was compared with that in the wind tunnel experiment, as listed in

Table 3. Comparison of data from the calculations and measurements.

		Top	Left	Right	Back
10 m/s	Measurement	−18.3 Pa	5.1 Pa	5.2 Pa	−20.4 Pa
	Calculation	−17.8 Pa	5.3 Pa	4.9 Pa	−19.7 Pa
	Deviation	−2.7%	3.9%	−5.8%	−3.4%
20 m/s	Measurement	−67.1 Pa	29.7 Pa	26.3 Pa	−75.1 Pa
	Calculation	−69.8 Pa	28.6 Pa	25.1 Pa	−76.2 Pa
	Deviation	4.0%	−3.7%	−4.6%	1.5%
30 m/s	Measurement	−162.7 Pa	60.7 Pa	58.1 Pa	−143.2 Pa
	Calculation	−153.6 Pa	57.6 Pa	60.8 Pa	−135.2 Pa
	Deviation	−5.6%	−5.1%	4.6%	−5.6%

. Table 3 shows that the simulation results agree well with the experimental data.

3. Results and Discussions

3.1. Experimental Results

3.1.1. Ballast Dynamics under Wind Load

The wind tunnel experiment of ballast particle was carried out according to the test scheme. It can be seen in the video from the real-time monitor that most of the ballast particles produce slight vibration and violent vibration generally one after another under wind load. As the wind speed increases, the particles roll or move slowly, then slide away quickly along the wind direction, and finally adhere to the protective net at the end of the test bench. Figure 10 shows the change of ballast position under wind load.

In the test of the acicular ballast (Group B and D) with the short side facing the wind, the ballast samples have an axial rotation perpendicular to the test bench after the vibration as the wind speed increases step by step. The axial rotation causes the windward surface of the ballast to change from the short side to the long side, resulting in an increase of the windward surface area. The ballast particles after rotation have a relatively stable contact with the test bench, and it is not easy to generate further displacement. As the wind speed increases further, the ballast particles continue to have movements of roll, slow slide, and fast slide successively.

3.1.2. Influence of Ballast Properties

The critical velocity could judge the difficulty of ballast flight, and the data of ballast particles with different mass and shapes are shown in Figure 11. It can be seen that the critical velocity increases with the ballast mass in general. The ellipsoid ballast B1 (5 g) is the first to move at the wind speed of 14.22 m/s, and it is the easiest to fly under wind load. When the wind speed is 29.89 m/s, all the particles are blown off. The oblate ballast C18 (200 g) moves at last, and it is the least likely to fly under wind load. The critical velocity of ballast particles with similar quality but different shapes is quite different. The ellipsoid ballast (Group B) has the minimum critical velocity, and it is the easiest to fly. The spherical ballast (Group A) and the prolate ballast (Group D) are the second sequentially. The oblate ballast (Group C) has the maximum critical velocity, and it is the least likely to fly. In other words, the critical velocity turns higher as the ballast particles become smaller and more flat. When the mass of ballast particles in different shapes increases from 5 g to 200 g, the largest increase of the critical velocity is the oblate ballast, reaching 84.2%. It is concluded that the influence of the mass change of the oblate ballast on its critical velocity is more significant than that of the other shapes, so the oblate ballast is unlikely to fly with the same mass increasing.

However, the critical velocities shown in Figure 11 also have some abnormal fluctuations, such as those of ballast A8, B5, C7, and D14. Although the mass of ballast B5 is larger than that of B4, B5 is more likely to fly under wind load. The abnormal fluctuation is not derived from the accidental error, because the data is the result of repeat tests under the same condition. Figure 12 shows the stability analysis of ballast B5. B5 will be in the most stable situation when it stands on the plane on which its long axis and middle axis are located. The plane is defined as “the stable placed surface”, which is shown by the red area in Figure 12b. B5 was placed with the bottom of its stable placed surface in the wind tunnel test. However, there are two raised edges on the stable placed surface of B5, as shown in Figure 12c. The contact between the ballast and test bench is a point-to-surface contact with three points (P1, P2, and P3) on the raised edges of the stable placed surface. Therefore, the ballast similar to B5 is easy to vibrate under wind load. As the wind speed increases gradually, the ballast particle is more likely to fly. For this reason, although the mass of B5 is larger than that of B4, its critical velocity is still lower, which results in the irregular fluctuation of the critical velocity in Figure 11. The irregular fluctuations of other ballast particles are similar, and they are not described here.

In order to investigate the influence of the windward direction of the particles on ballast flight, the ellipsoid ballast (Group B) and prolate ballast (Group D) with different windward surfaces were tested respectively. The critical velocities of the ballast particles with different windward surfaces are shown in Figure 13. It can be seen that the particles with large acicular indexes have different critical velocities when they are in different windward directions. When the windward surface of the ballast is adjusted from the long side to the short side, the critical velocity of the ellipsoid ballast and prolate ballast increase by 0.45–0.59 m/s and 0.32–0.44 m/s, respectively.

3.2. Simulation Results

3.2.1. Pressure Difference of Ballast Particle

There is a pressure difference between different ballast surfaces under different wind conditions. When the pressure is larger than that keeping the ballast stable, the particle would fly. The parameter P is introduced to analyze the flow characteristics of ballast particles, which could represent the pressure difference as follows:

$$P=P_p-P_n$$

(7)

where $P_p$ and $P_n$ refer to the maximum air pressure of positive and negative acting on the ballast surface respectively.

All numerical models of ballast samples were simulated according to the grouping scheme in the wind tunnel experiment. Then, the air pressure difference P was calculated based on Equation (7). Figure 14 shows the pressure difference of ballast particles with four shapes and two windward directions at a wind speed of 30 m/s. B_1 and D_1 represent the long sides of particle B and D facing the wind, while B_2 and D_2 represent the short sides facing the wind.

The mass and volume of ballast samples increase with their number sequence in Figure 14. Since the flow characteristic is independent of the mass in CFD simulation, the pressure difference among the ballast particles in each group increases with their volume. The reason is that the windward surface of the ballast particles increases with their enlarged volume, and the maximum positive and negative pressure increase at the same time under the condition of the constant wind speed and ballast shape. Thus, the pressure difference among the ballast surfaces increases accordingly. Compared with Figure 11, the pressure difference in Figure 14 gets higher with the increase of ballast volume, which indicates that the ballast particle is easy to fly. In Figure 11, the critical velocity gets higher with the increase of ballast mass, which is unlikely to trigger ballast flight. However, the ballast volume increases with its mass on the basis of the same shape, so the rule in Figure 14 is in contradiction with that in Figure 11. The result shows that although the pressure difference increases with the ballast volume, the ballast mass would increase with it as well. The ballast flight will occur only when the pressure is large enough to overcome the larger load derived from its increased mass. That is, although the ballast volume increases with its mass, the influence of mass on ballast flight is more significant than that of the volume. Therefore, the ballast with a higher density on the top of ballast bed is more effective than the ballast with a larger size to prevent ballast flight.

Besides, the shape of the ballast also has an influence on the pressure difference, and the influence is consistent with the conclusion in the wind tunnel experiment. As shown in Figure 14, under the condition of the same volume, the pressure difference of the ellipsoid ballast is the largest, and it is the easiest to fly, followed by the sphere ballast and prolate ballast. The pressure difference of the oblate ballast is the smallest, and it is the least likely to fly. When the ballast volume (number) is the minimum, the pressure difference of the six ballast models is similar, which is from 701 Pa (C1) to 757 Pa (B1_1). With the increasing of the volume (number), there is a significant difference in the increasing range of the pressure difference between various groups. When the volume increases to the maximum, the increase of the pressure difference of sample B with the long side facing the wind is the largest (90.6%), followed by that of sample B with the short side facing the wind (86.8%), and sample C is the smallest (49.6%). The results show that the volume increase of the ellipsoid ballast has the most significant effect on ballast flight, especially when the long side faces the wind. In addition, in order to prevent ballast flight, the height of ballast bed level could be reduced, and the space between sleepers could be optimized. These measures could decrease the pressure acting on the ballast particles on the top of the ballast bed, and then prevent their initial displacements.

3.2.2. Flow Characteristic around Ballast Particle

The four ballast particles with the number of 15 in different shapes (A15, B15, C15, D15) were selected, and the different windward surfaces of the ellipsoid ballast and prolate ballast were considered (B15_1, B15_2, D15_1, D15_2). The simulation of ballast samples mentioned above was conducted based on the model in Figure 6. For the sake of comparing and analyzing, Figure 15 is the schematic diagram of the ballast samples, which shows the six numerical models from different views. The distance between particles in the simulation experiment was same with that of the wind tunnel experiment.

Based on the model in Figure 15, the airflow around the ballast particle was calculated at a wind speed of 30m/s. The pressure contour and the streamline of the ballast are shown in Figure 16 and Figure 17, respectively. It can be seen from Figure 16 that the pressure on the windward surface is positive, and that on the top, side, and back of the ballast is negative. The maximum positive pressure generates at the apex of the convex region on the windward surface of the ballast, and its magnitude is mainly affected by the local angular features of the particles. The maximum positive pressure increases with the sharpness of the ballast apex. Meanwhile, the maximum negative pressure generates at the common edge of the two adjacent surfaces on the top, side, or back of the ballast, and its magnitude is mainly affected by the angle formed by the two sides of the particle. The maximum negative pressure gets higher with the decrease of the ballast angle. Since the angle of the ballast samples is approximate, the maximum positive pressure of each ballast in Figure 16 is similar, and it is all about 530 Pa. However, the maximum negative pressure of each ballast is noticeably different. The maximum negative pressure of B15_1 is the highest (−781 Pa), which exists on its side. Therefore, the ellipsoid ballast (B15_1) has the largest pressure difference (1312 Pa) when its long side faces the wind, and it is the most likely to fly under the condition of the same mass.

Figure 17 shows the streamline around the ballast, and the airflow is blocked by the ballast to induce a disturbing flow when the wind blows parallel to the test bench. The airflow deflects upward and laterally, causing the streamline bending and forming a flow separation at the boundary of the ballast. Both the side and the top of the ballast are in the domain of flow separation, where the air pressure is negative, and the maximum negative pressure is just at the point of the flow separation.

The shape and placement direction of the ballast also have an effect on its streamline distribution. In Figure 17, a wide (from top view) and high (from side view) airflow generates behind the ballast particles with the shape of ellipsoid and spherical after the flow separation stage. The vortex formed by the flow separation sheds into the airflow on the top, side, and rear of the ballast, which increases the wind suction acting on the particle and enlarges the negative pressure further. On the contrary, the flow around the oblate ballast and the prolate ballast is along their contours. It generates less flow separation and wake flow, and it is less prone to occur ballast flight. Compared with the ballast that had its long side facing the wind, the ballast that had its short side facing the wind had a large depth in its downwind direction. The incoming airflow produces a flow separation at the corner of the windward side and then attaches to somewhere on the long axis of the particle. Finally, the airflow separates again at the end of the ballast and forms a narrow turbulent wake flow, which reduces the negative pressure and wind suction acting on the ballast surface. Therefore, the ballast of the long side facing the wind is more likely to fly, and it is consistent with the conclusion from the wind tunnel experiment.

3.2.3. Influence of Wind Speed

The pressure difference on the ballast surface of each group at wind speeds of 10 m/s, 20 m/s, 30 m/s, and 40 m/s respectively are shown in Figure 18.

In Figure 18, the scattered points in dotted circles are the computational results of the air pressure difference, and the coordinates of the dotted circles are the average pressure difference of the six ballast models. It can be seen that the pressure difference of the ballast increases with the wind speed. The average pressure difference increases 373 Pa, 643 Pa, and 860 Pa respectively when the wind speed increases from 10 m/s to 40 m/s, and increases 14.9 times in total. The increasing range of the pressure difference also increases gradually with the wind speed. That is, there is a nonlinear relationship between the pressure difference and the wind speed, which is fitted by the power function. The fitting curve as well as the regression equation of each ballast is shown in Figure 18. The pressure difference of the ballast is proportional to the square of the wind speed based on the analysis of regression, which can be expressed with the power function as

$$P=k{v}^2$$

(8)

where $v$ is the wind speed, $k$ is the fitting coefficient. The value of $k$ is related to the shape and windward direction of ballast. The ellipsoid ballast (B15_1) with long side facing the wind has the largest $k$ of 1.3799, and the oblate ballast (C15) has the smallest $k$ of 1.1360. The ballast with a higher $k$ is easier to fly when the ballast mass is similar.

It can be seen from Figure 18 and Equation (8) that the wind speed has a significant effect on ballast flight. Therefore, with the increasing of the train running speed, it is necessary to take measures to reduce the air pressure above the ballast bed, which could improve the stability of the ballast on the ballast bed surface and then avoid ballast flight. In case of special natural conditions such as strong wind, freezing weather, and heavy snow that might induce ballast flight, the running speed of train must be limited.

4. Conclusions

The occurrence and development mechanisms of ballast flight were investigated from the particle perspective of aerodynamics. A wind tunnel experiment and CFD numerical simulation of ballast particles were utilized to analyze the movement characteristics of ballast particles under wind load, the flow around ballast particles, and the influence of the ballast mass and shape, as well as windward direction and wind speed on ballast flight. Besides, a series of preventive suggestions of ballast flight were proposed, which had been adopted in the high-speed railway line of Beijing–Zhangjiakou in China and had a good effect. The main conclusions are as follows:

(1)

The local features of ballast particles can be obtained accurately and efficiently based on the capture, reconstruction, and analysis method, which provides reliable technical means for investigating the mechanism of ballast flight in a wind tunnel experiment and CFD numerical simulation.

(2)

The phenomenon of slight vibration, violent vibration, roll, slow movement, and fast movement occur successively in the initial stage of ballast flight. The massive ballast is less likely to fly. The ballast of 5 g was blown off first at the wind speed of 14.22 m/s, and the ballast of 200 g was blown off last at the wind speed of 29.89 m/s.

(3)

The oblate ballast is the least prone to fly under wind load, which has the smallest flow separation, wake flow, and surface pressure difference; in contrast, the ellipsoid ballast is the easiest to fly, followed by the spherical and prolate ballast particles. A ballast particle that has its short side facing the wind is less likely to fly than one that has its long side facing the wind. The pressure difference of the ballast is proportional to the square of the wind speed. The average pressure difference of the ballast increases 14.9 times when the wind speed increases from 10 m/s to 40 m/s.

(4)

In order to avoid ballast flight, the ballast gradation could be adjusted by limiting the ballast particles with small size as well as with the shape of ellipsoid, and the ballast particles with high density or large size could be laid on the top of ballast bed before the operation of a high-speed railway line. During the operation, the ballast bed should be cleaned in time to reduce the ballast breakage and contamination caused by deterioration. The compaction operation should be carried out in a timely manner after tamping to improve the stability of the ballast bed.

It should be noted that the intensity and distribution of the airflow underneath a high-speed train varies significantly over time. The purpose of this paper is to investigate the influence of the particle properties on the ballast flight. For this reason, the equivalent wind load was applied to the model in the wind tunnel experiment and the CFD simulation, rather than the actual wind load underneath high-speed train. Moreover, the test bench instead of the ballast bed was set up to place the ballast samples in this paper, which could eliminate the interference between particles on the ballast bed surface and focus on the influence of quality and shape on ballast flight. However, the mechanical characteristics of the ballast particles under wind load on the test bench were different from those of the ballast bed. Therefore, future work should consider the particles in the ballast bed under the actual wind load underneath a high-speed train on the basis of this paper. Furthermore, the ballast flight is the phenomenon of ballast particles flying off the track. The future research could focus on the coupling method of CFD and DEM (discrete element method), which could simulate and analyze the flying behavior of ballast particles directly.