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Numerical study of the impact of windblown sand particles on a high-speed train
J. Wind Eng. Ind. Aerodyn. 145 (2015) 87–93
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Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia
Numerical study of the impact of windblown sand particles on a high-speed train C. Paz n, E. Suárez, C. Gil, M. Concheiro School of Industrial Engineering, University of Vigo, Campus Universitario Lagoas-Marcosende, 36310, Spain
art ic l e i nf o
a b s t r a c t
Article history: Received 27 January 2015 Received in revised form 15 June 2015 Accepted 16 June 2015
This study develops an approach to evaluate the effect of particle impacts on the motion of high-speed trains in a sand-laden flow. For this purpose, external routines were implemented to extend the Discrete Phase Model (DPM) of the commercial simulation code ANSYS Fluent. Although the aerodynamics is an established concern in the design of high-speed trains, relatively few studies investigate the response of trains to demanding environments such as deserts. Several of the derived problems include potential effects on the aerodynamic performance or the wear of materials. Simulations with different values for the particle diameter, particle load and coefficient of restitution were performed. The analysis of the leading vehicle shows a greater impact probability on the train nose with small impact angles and high velocities on the sides, leading to a more pronounced wear of the surface. A logarithmic dependency of the drag coefficient with the particle diameter was also revealed, and a force reduction of 10% for each 0.2 decrease in the coefficient of restitution was noted. The results of the simulations confirm the feasibility of the presented methodology. & 2015 Elsevier Ltd. All rights reserved.
Keywords: High-speed train CFD Aerodynamics Windblown sand Impact Drag force
1. Introduction The motion of high-speed trains and their response to aerodynamic effects derived from increased velocities, such as crosswinds (Hemida and Krajnovic, 2010; Schetz, 2001), slipstreams (Muld, 2012; Weise et al., 2006), pressure variations (Gawthorpe, 2000; Ko et al., 2012) or ballast flying (Jing et al., 2012; Kaltenbach et al. 2008), have long been an important field of research in the railway industry (Baker, 2014a, 2014b; Raghunathan et al., 2002). The majority of these studies are focused mainly on the evaluation of the fluid field around the train under different conditions through full-scale (Baker et al., 2013) or scaled experiments (Gilbert et al., 2013) and numerical simulations (Hemida et al., 2014), analysing more deeply certain areas, e.g., the wake (Bell et al., 2014) or the underbody (García et al., 2011). In recent years, the development in countries such as China or Saudi Arabia has led to the construction of new tracks crossing desert areas, in which windblown sand has become a matter of concern. The motion of high-speed trains in particle-laden flows is affected by many factors such as the risk of overturning caused by sandstorms (Qian et al., 2002), the premature wear of train elements (Woldman et al., 2012) or potential effects on the aerodynamic performance. n
Corresponding author. Tel.: þ 34 986 813 754. E-mail addresses: [email protected] (C. Paz), [email protected] (E. Suárez), [email protected] (C. Gil), [email protected] (M. Concheiro). http://dx.doi.org/10.1016/j.jweia.2015.06.008 0167-6105/& 2015 Elsevier Ltd. All rights reserved.
In China, for example, many accidents have been reported. Other countries (e.g., Saudi Arabia) are dealing with this problem in new infrastructures, trying to avoid the plugging of the vents, the obstruction of moving elements or the damaging of the train surface. The collision forecast of sand particles on the train surface could establish a proper dimensioning and positioning of the ventilation and refrigeration grilles. Additionally, the impact angle points out areas with the highest risk of erosion, i.e., those areas requiring the use of specific countermeasures such as paintings or coatings. These two mentioned problems (wear of materials and aerodynamic effects) are related to the exchange of energy during the impact between the particles and the train surface. This impact is feasibly modelled through computational methods. The physics of the collision is a complex and well-studied process (Hertz, 1896; Kosinski et al., 2014; Kuwabara and Kono, 1987). When two elastic bodies collide, their surfaces are deformed as a function of their momentum and mechanical properties. The elastic wave generated by the impact promotes the energy exchange between solids and the dissipation of energy into the surroundings in the form of sound or heat. Different expressions have been proposed to measure the characteristics of the impact such as the contact time or the exerted force (Antonyuk et al., 2010; Cowell et al., 2015). From the point of view of computational fluid dynamics (CFD) simulations, two different strategies are generally accepted as the most suitable to evaluate this type of problem. On the one hand, the Eulerian–Eulerian (E–E) model treats both phases as
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continuous flows interpenetrating each other. This approach has been followed by Xiong et al. (2011) in their study of the performance of high-speed trains under different levels of sandstorms. On the other hand, the Eulerian–Lagrangian (E–L) model solves the fluid flow using Navier–Stokes equations, and the solid particles are injected into the flow and are then tracked individually to calculate their trajectories inside the gas (Valentine and Decker, 1995). This strategy offers a more comprehensive picture of the particle flow interaction but requires more powerful computational resources (Zhang and Chen, 2007). For this reason, the size and distribution of the particles must be properly characterised and the injections must be reduced to the minimum necessary (Kaufmann et al., 2008). In this paper, the E–L approach has been used to simulate the motion of a high-speed train in a sand-laden atmosphere. The objectives of this study are to quantify the force exerted on the train by sand grains (with different ranges of particle diameter, particle load and coefficient of restitution between particle and surface) and to determine the regions with a higher probability of suffering impacts, focusing on the leading vehicle, and the characteristics (angle, velocity and force) of these collisions. Because of the complexity of the dynamics of the collision, the computational costs of the CFD calculation of the detailed process are prohibitive (Stevens and Hrenya, 2005). The strategy followed here involves a feasible macroscopic approach using the average force during the interval of time between two consecutive impacts, retaining the desirable accuracy. The selected geometric model and the conditions of the simulation of the continuous phase are described in Section 2. In Section 3, the parameters for the particle tracking, including the characterisation of the sand grains, are detailed; additionally, the routines implemented for the assessment of the generated forces are provided. In Section 4, the contours of probability, normalised velocity, tangential velocity, angle and force of the impacts and the graphs for the drag force contribution are shown and discussed. Finally, the conclusions are summarised in Section 5.
2. Geometric model and boundary conditions Although the main objective of this study is to evaluate the impacts on the leading vehicle, an entire train has been simulated to solve the continuous phase. The geometric model used is a simplified full-scale ETR 500, consisting of two power cars and six intermediate cars with a total length of 200 m. The geometry is a complete 3D model of the ETR500, including simplified bogies, in which all the details smaller than the surface cell size were not considered, and omitting singular elements such as the pantographs. This design, similar to the one used by Gil et al. (2008) and Muld et al. (2012), is considered sufficient to reproduce correctly the aerodynamics of a high speed train and to account for most of
the relevant effects, such as the boundary layer development around the train or the turbulence due to the asymmetry of the bogies. For a more realistic representation, the model is mounted on a single-track ballast and rail (STBR) scenario (CEN European Standard, 2009). Since this study is focused on the analysis of the leading vehicle and the flow in this region would be almost unaffected by the presence of a second track, an STBR scenario was chosen to reduce the computational cost of the simulations. The computational domain is extended 8 H beyond the nose of the leading vehicle and 30 H from the train tail to the outlet. The height and width of the outer box which limits the domain are 10 H and 20 H, respectively (Hemida et al., 2014) (shown in Fig. 1). Two different meshes were created to evaluate the influence of the grid resolution on the results. The scheme Cutcell, a utility within the software ANSYS Meshing, has been selected for both meshes with the intention of obtaining unstructured hexahedral grids aligned with the undisturbed upstream flow (Nemec et al., 2008). The coarse and fine meshes consist of 22 and 56 million elements with a cell size on the surface of the train of 0.012 H and 0.007 H, respectively. Based on the previous study of mesh convergence included in the paper of Paz et al. (2014), it is considered that both meshes have reached the convergence. However, both meshes were compared to evaluate their performance in the current geometrical model. A boundary layer around the model and the rails have also been included, leading to values of y þ between 50 and 100. Simulations were performed using the commercial software ANSYS Fluent. The k-epsilon Realisable viscous model (Cheli et al., 2010) was considered the most suitable for solving the continuous phase because of the balance between accuracy and computational cost. The inlet velocity was set uniformly to 300 km/h (83.33 m/s) and the outlet to atmospheric pressure. The STBR scenario and the ground were defined as moving walls with the identical speed as the air, reproducing the relative motion of the train and avoiding the use of sliding meshes (Flynn et al., 2014). To improve the convergence of the simulations, the cases were calculated first in steady-state and were afterwards changed to a transient mode. The time step was selected as a function of the oscillation frequency for a Strouhal number of 0.14 (Baker, 2010) and H as the characteristic length (see Fig. 1).
3. Particle impact approach For the simulation of sand particles, the DPM model implemented in Fluent has been used. This E–L approach is considered appropriate for this purpose because the discrete volume fraction is much lower than 10% and the computational resources are sufficiently powerful (ANSYS Inc., 2012). To reduce the simulation costs, a one-way coupling between phases was selected, treating the sand grains as solid particles; no additional forces were
Fig. 1. Computational domain (left) and geometrical model (right).
C. Paz et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 87–93
included in the force balance equation. The equation of motion for a spherical particle in a gas is given by Crowe et al. (2012) →
mg (ρs − ρc ) 1 π D2 → → → → m dv /dt = CD ρc (u − v ) u − v + ρs 2 4 →
(1)
where v is the particle velocity, u is the gas velocity, ρc is the density of the continuous phase, ρs is the density of the solid phase, g is the gravity acceleration, D is the particle diameter, m is the particle mass and CD is the drag coefficient of the particle. Defining the dispersed phase Reynolds number (relative Reynolds number) and the momentum (velocity) response time as
Rer =
τV =
→ → ρc D u − v μc
(2)
ρ d D2 18μ c
(3)
where μc is the molecular viscosity of the continuous phase; and dividing through by the particle mass gives →
→
dv /dt =
g (ρs − ρc ) 1 CD Rer → → (u − v ) + τV 24 ρs
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ranging from 1 to 100 g/m3 have been distributed among one hundred thousand injections. This process was considered sufficient to reach a good resolution in the results. The sand impact phenomena were evaluated using an intended external routine that calculates the force exerted by colliding particles. This routine also assesses the distribution, angle and velocity of the impacts on every cell of the train surface using contours. With this utility, estimating the change in the drag force is possible, producing a more accurate dimensioning of the extra energy consumption, if necessary, in the case of strong sandstorms involving high wind speeds. In addition, the elements of the highspeed trains that would suffer the highest amount of wear can be predicted, and their duty life can be estimated by considering their structural characteristics. This external implementation uses the time averaged momentum equation to calculate the force exerted by the load of particles, considering the change of momentum of every particle due to the impact and averaging it over the time between two consecutive impacts. For each particle, this time is defined as →
Δti = Δx/ u pi1 , where Δx is the distance between successive par-
→ ticles (which depends on the particle load), and u pi is the velocity
(4)
The particles have been released from a vertical plane placed near the forward nose of the train following an equally spaced distribution. The width of the plane is equal to the width of the train, and the height covers the distance from the ballast bed to the roof of the head. The purpose of this setup is to test the proposed approach by analysing the impacts on the leading vehicle. The injection of particles from other positions can also be simulated in future studies because the identical methodology can be applied. The dimensions of this plane have been set according to a previous evaluation of the region that would contain the particles that actually collide with the train, avoiding tracking useless injections. This simplification reduces the computational cost of the process. Another crucial aspect in the DPM process is the characterisation of the sand grains by fundamentally defining their diameter and concentration. The size of the particles corresponds to the classification of medium and fine sand, ranging from 0.1 to 0.5 mm according to the International Scale for the identification and classification of soils ISO 14688-1 (ISO, 2002). Considering these grain sizes, the velocities near the ground associated with the usual atmospheric wind would not be able to raise the particles to the top of the injection plane. Nevertheless, the passing of a highspeed train accelerates the surrounding air and generates in the wake air velocities near the ballast layer which magnitude is similar to the running speed of the train, 83.33 m/s in this case (Deeg et al., 2008; Kaltenbach et al., 2008). In desert areas, this generates a sand cloud behind the vehicle, which, considering the high frequency of some lines and the Stokes number of the particles (Crowe et al., 2012), remains in suspension until the passing of a later train. The case of crossing trains is the most critical situation. Knowing the velocity profile on the ground and the size of the sand grains, predicting the particle density at different heights of this sand cloud is possible. In this study, an extrapolation from the results of Liu and Dong (2004) estimates the sand concentration at the maximum speed of the train wake and at a height of 1 m, corresponding to the train nose. First, the original curves have been adjusted by a logarithmic function and the growth of these curves with velocity has been identified. Then, an asymptotic approach has been used to evaluate the function at the desired height. This extrapolation led to a particle density of the order of grams; therefore, concentrations
of the ith particle. This way, the mean force that a particle load would exert on the train in steady conditions is calculated (see Fig. 2). Only the component of the force normal to the surface on which the force is applied is considered, since the tangential component is much smaller; therefore, the projection of this normal force on the longitudinal axis determines the contribution of the force to drag resistance. →
Favg =
∑ i
(
→
Δp /Δt
)
i
=
∑ i
→ → ⎛ ⎜ m p u p2n − u p1n ⎜ Δt ⎜ ⎝
(
) ⎞⎟⎟
⎟ ⎠i
(5)
→
where, for the ith particle, Δp is the variation of momentum, → → m p is the particle mass and u p1n and u p2n are the normal components of the velocity of the particle before and after the collision, respectively. → → When the collision is totally elastic, u p1 = u p2 and the force is the maximum for the current particle size. In a real case, however, → → the impact is partially inelastic, u p1 > u p2 . This fact is considered through the coefficient of restitution, defined as the ratio between the velocity normal to the surface before and after the impact. This coefficient is a characteristic for each pair of materials and is an important factor in the selection of the coatings and paints that cover the surface of the train. A more elastic material reduces the exerted force and, consequently, the wear produced by the sand impacts.
Leading vehicle
Fig. 2. Sketch of the impact of particles on the train surface.
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4. Results and discussion 4.1. Validation To ensure the validity of the simulation of the continuous phase, the results were compared to both the numerical and experimental data from Rocchi et al. (2013). Fig. 3 shows the position of the validation probe relative to the top of rail (TOR) and the centre of track (COT). The values of the normalised velocity (U) obtained from this probe are depicted in Fig. 4. The normalised velocity is given by
U=
(u
x
case, the finer mesh captures the flow behaviour better in the bogies region; the complexity of this region requires a smaller cell size in the surface grid to produce accurate results. Unfortunately, no reference data are available in the field of particle impacts in aerodynamics to validate the implemented approach (Zhang and Chen, 2007). The existing studies investigate the penalties caused on airfoils by heavy rain (because of the liquid film) (Valentine and Decker, 1995) or the effect of dust on wind turbines and solar thermal collectors (because of increasing roughness) (Torres García et al., 2014); the nature of these problems are therefore unsuitable for comparison with the present work.
− u∞ )2 + u y2 + u z 2 u∞
(6)
where u x , u y and u z are the longitudinal, lateral and vertical components, respectively, of the velocity, and u∞ is the freestream velocity that corresponds to the train speed. The data from Rocchi et al. (2013) are represented as an interval of possible values of normalised velocities in the region that corresponds to the passing of the leading vehicle and half an intermediate car. The simulations agreed with the provided data in the nose region, producing results within the upper and lower limit. However, when moving backwards, some fluctuations appear. These fluctuations might be caused by slight differences in the underbody geometry which result from the simplification process. When comparing the coarse and fine meshes, the results are identical in the nose region; however, after the passing of the first bogies, differences between the meshes are noted. In this
Fig. 3. Position of the validation probe.
Fig. 4. Comparison of the normalised velocity between the results of the current study for both a coarse and a fine mesh and the results obtained by Rocchi et al. (2013).
4.2. Characterisation of the impacts Prior to tracking the discrete phase, the simulation of the fluid field was performed. The solution was considered converged when the scaled residuals were smaller than the Fluent's recommendation of 10 3 and the fluctuations in drag force were within 1% of the total value. Regarding the DPM simulations, the assessment of the effect of the discrete phase consisted of a series of particle injections when varying three main parameters: particle diameter (0.1–0.5 mm), particle load (0.001–0.1 kg/m3) and the coefficient of restitution (0.6, 0.8 and 1). The particle diameters selected correspond to Stokes numbers ranging from 1.96 to 49.06, and the particle loads represent volume fractions of sand between 4E-07 and 4E-05. As expected, the leading vehicle suffered the majority of sand grain impacts. Nevertheless, collisions were also noted on the roof of the last few cars. These collisions occur because after the particles strike the train's head, they are mainly displaced upwards and to the sides. These particles return to the surface of the ETR 500 model because of gravity and the fluid stream. As the most affected region, a deeper analysis of the leading vehicle was performed. Fig. 5 displays a map of the impact distribution for three different particle sizes. These contours reveal two main characteristics: around the nose, the collisions are distributed along a line in the vertical and lateral direction; and in the flat region between the windshield and the nose, a radial decrease of impacts appears. Focusing on the comparison of these three cases, both the impact probability and the affected region increase as the diameter of the particle increases. The relative weight of the right hand terms of Eq. (1) is responsible for the different contours pictured in Fig. 5. When the sand grains are sufficiently small, the displacement of air generated by the train nose is capable of carrying the particles with the stream, avoiding the collision. For this reason, a particle diameter of 0.1 mm shows almost no impact on the sides of the head and also on the lower part of the windshield because the geometry displaces the particles upwards, reaching the surface only on higher areas. By contrast, for a particle size of 0.5 mm, a regular distribution of impacts appears on the entire windshield. In addition to the impact probability, the routines implemented allow for a wider analysis of the simulation, as shown in Fig. 6. The map of normalised velocity (Fig. 6(a)) shows a stagnation point on the lower part of the windshield by reason of the geometry of the model; this map also shows higher speeds in the transition between the frontal face and the rest of the head. This tendency agrees with the behaviour of the flow in this region. Moreover, the tangential component of the velocity (Fig. 6(b)) shows that the borders of the head are the most susceptible to wear. These areas have the greatest speeds in the surface plane. Regarding the angle of impact (Fig. 6(c)), defined as the angle complementary to the one between the particle terminal velocity and the vector normal to each surface, the values on the sides are lower than 45°, implying a more tangential collision because of the relative
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Fig. 5. Distribution of impacts in the leading vehicle for a particle density of 0.1 kg/m3 and particle sizes of 0.1, 0.3 and 0.5 mm, respectively.
1
1
0.95
0.5
0.9
0
90
1
45
0.5
0
0
Fig. 6. Contours of (a) normalised velocity, (b) tangential velocity, (c) impact angle and (d) normalised drag force for a particle density of 0.1 kg/m3, a particle diameter of 0.5 mm and a restitution coefficient of 1.
position between the surface and flow. These impacts agree with the contour of the tangential velocity. However, the values on the nose are close to 90°, revealing a frontal impact. In this case, the energy carried by the particle will contribute almost entirely to increasing the drag resistance. This fact is confirmed by the image that represents the drag force contribution of particles (Fig. 6(d)) depending on the collision point. This map can be understood as a composition of the previous maps considering that drag force depends on the amount, the velocity and the angle of impacts (in addition to particle characteristics). In this figure, the nose is the
most affected region because it is impacted by a higher number of particles and the collisions are normal to the surface, although the velocity is not at a maximum. By contrast, despite suffering several impacts with a high velocity, the sides of the head remain almost unaffected in terms of the drag contribution since the surfaces are nearly parallel to the longitudinal axis. 4.3. Contribution of sand to the drag resistance The contribution of the windblown sand to the drag resistance of the train varies considerably depending on the size and
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Fig. 7. Graphs of the drag force ratio as a function of particle diameter for different values of the particle density and coefficient of restitution.
with the expected behaviour because for situations without a train passing, the wind velocities do not usually exceed 20 m/s and only micrometric particles are raised. These conditions differed from the high speeds considered in this study.
5. Conclusions
Fig. 8. Graphs of the drag force ratio as a function of particle load for different values of the particle diameter and coefficient of restitution of 1.
concentration of the particles and the coefficient of restitution of the train. The results from the DPM simulations are shown in the following graphs (Fig. 7 and Fig. 8). The values of the drag force are given by a ratio between the resistance generated by the particles and the overall aerodynamic drag. In this way, the extra amount of energy necessary to overcome the effect of the sand and keep a constant running speed is therefore estimated. The sand force is chiefly applied to the leading car, but the ratio given depends on the geometry of the entire train. Therefore, a longer train would suffer the identical particle resistance, although its proportion of the total train aerodynamic force would be smaller. The curves show a logarithmic dependency with particle diameter for all concentrations and coefficients of restitution within the tested range of particles. Larger particles or higher particle densities produce stronger drag resistances. For a particle size of 0.5 mm (a medium sand) and a particle density of 100 g/m3 , the drag contribution represents more than 10% of the aerodynamic force. However, with lower concentrations, the drag force represents less than 1% for all diameters. These magnitudes appear negligible, but considering the duration and frequency of the train routes in such a demanding environment, this 1% represents a substantial sum of energy. Therefore, the use of coatings and paints (in addition to minimising the wear of materials) can reduce the coefficient of restitution by retaining a fraction of the energy carried by the particles, which would reduce their momentum variation. As shown in the graph, these coatings are important because a decrease of 0.2 in the coefficient of restitution indicates a 10% reduction in the drag contribution due to sand, following a linear dependency. Finally, several publications analysing the characteristics of windblown dust (unaltered by the passing of a train and in different deserts, e.g., in Mali (Gillies et al., 1996) or Gobi (Jugder et al., 2011)) were selected and compared with the results obtained in this study. In these cases, the concentration and particle size of the grains were smaller than the considered ones for the simulations, producing almost no increase in the drag force. The distribution of the impacts shows a high probability in the train nose and the upper part of the windshield; the rest of the leading vehicle was practically unaffected. This behaviour agrees
The performance of a high-speed train in a particle-laden flow was investigated using numerical simulations to evaluate the effect of windblown sand in desert areas on the drag resistance and the wear of the surface of a train. The DPM model in Fluent was taken as a base model and extended with external routines that allowed for a broader analysis of the results. The fluid field was solved and validated against experimental and reference data; a series of simulations of the discrete phase with different parameters of particle diameter, particle load and coefficient of restitution were performed. A feasible and valid methodology to predict the impact zones of particles on the train was developed. The analysis of the leading vehicle shows a greater impact probability in the train nose, at which the particles would exert a larger drag force; additionally, smaller impact angles and higher velocities occur on the sides, which would lead to a more pronounced wear of the surface. The evaluation of the drag contribution of the sand reveals a logarithmic dependency with the diameter of the particle; moreover, a reduction of 10% in the total amount occurs for each 0.2 decrease in the coefficient of restitution. For the range of sand grains simulated, the values of the drag force varied from 0.02% to 11% of the total aerodynamic resistance. In this paper, the simulations performed reproduce the running of a high-speed train in a still atmosphere with sand particles in suspension, being therefore the leading vehicle the most affected part of the train. Further work could extend this study to consider the elevation of sand lying in the track or the effect caused by sand carried in crosswinds or sandstorms. Additionally, the presented approach could be fitted with experimental results for further validation.
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Numerical study of the impact of windblown sand particles on a high-speed train C. Paz n, E. Suárez, C. Gil, M. Concheiro School of Industrial Engineering, University of Vigo, Campus Universitario Lagoas-Marcosende, 36310, Spain
art ic l e i nf o
a b s t r a c t
Article history: Received 27 January 2015 Received in revised form 15 June 2015 Accepted 16 June 2015
This study develops an approach to evaluate the effect of particle impacts on the motion of high-speed trains in a sand-laden flow. For this purpose, external routines were implemented to extend the Discrete Phase Model (DPM) of the commercial simulation code ANSYS Fluent. Although the aerodynamics is an established concern in the design of high-speed trains, relatively few studies investigate the response of trains to demanding environments such as deserts. Several of the derived problems include potential effects on the aerodynamic performance or the wear of materials. Simulations with different values for the particle diameter, particle load and coefficient of restitution were performed. The analysis of the leading vehicle shows a greater impact probability on the train nose with small impact angles and high velocities on the sides, leading to a more pronounced wear of the surface. A logarithmic dependency of the drag coefficient with the particle diameter was also revealed, and a force reduction of 10% for each 0.2 decrease in the coefficient of restitution was noted. The results of the simulations confirm the feasibility of the presented methodology. & 2015 Elsevier Ltd. All rights reserved.
Keywords: High-speed train CFD Aerodynamics Windblown sand Impact Drag force
1. Introduction The motion of high-speed trains and their response to aerodynamic effects derived from increased velocities, such as crosswinds (Hemida and Krajnovic, 2010; Schetz, 2001), slipstreams (Muld, 2012; Weise et al., 2006), pressure variations (Gawthorpe, 2000; Ko et al., 2012) or ballast flying (Jing et al., 2012; Kaltenbach et al. 2008), have long been an important field of research in the railway industry (Baker, 2014a, 2014b; Raghunathan et al., 2002). The majority of these studies are focused mainly on the evaluation of the fluid field around the train under different conditions through full-scale (Baker et al., 2013) or scaled experiments (Gilbert et al., 2013) and numerical simulations (Hemida et al., 2014), analysing more deeply certain areas, e.g., the wake (Bell et al., 2014) or the underbody (García et al., 2011). In recent years, the development in countries such as China or Saudi Arabia has led to the construction of new tracks crossing desert areas, in which windblown sand has become a matter of concern. The motion of high-speed trains in particle-laden flows is affected by many factors such as the risk of overturning caused by sandstorms (Qian et al., 2002), the premature wear of train elements (Woldman et al., 2012) or potential effects on the aerodynamic performance. n
Corresponding author. Tel.: þ 34 986 813 754. E-mail addresses: [email protected] (C. Paz), [email protected] (E. Suárez), [email protected] (C. Gil), [email protected] (M. Concheiro). http://dx.doi.org/10.1016/j.jweia.2015.06.008 0167-6105/& 2015 Elsevier Ltd. All rights reserved.
In China, for example, many accidents have been reported. Other countries (e.g., Saudi Arabia) are dealing with this problem in new infrastructures, trying to avoid the plugging of the vents, the obstruction of moving elements or the damaging of the train surface. The collision forecast of sand particles on the train surface could establish a proper dimensioning and positioning of the ventilation and refrigeration grilles. Additionally, the impact angle points out areas with the highest risk of erosion, i.e., those areas requiring the use of specific countermeasures such as paintings or coatings. These two mentioned problems (wear of materials and aerodynamic effects) are related to the exchange of energy during the impact between the particles and the train surface. This impact is feasibly modelled through computational methods. The physics of the collision is a complex and well-studied process (Hertz, 1896; Kosinski et al., 2014; Kuwabara and Kono, 1987). When two elastic bodies collide, their surfaces are deformed as a function of their momentum and mechanical properties. The elastic wave generated by the impact promotes the energy exchange between solids and the dissipation of energy into the surroundings in the form of sound or heat. Different expressions have been proposed to measure the characteristics of the impact such as the contact time or the exerted force (Antonyuk et al., 2010; Cowell et al., 2015). From the point of view of computational fluid dynamics (CFD) simulations, two different strategies are generally accepted as the most suitable to evaluate this type of problem. On the one hand, the Eulerian–Eulerian (E–E) model treats both phases as
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continuous flows interpenetrating each other. This approach has been followed by Xiong et al. (2011) in their study of the performance of high-speed trains under different levels of sandstorms. On the other hand, the Eulerian–Lagrangian (E–L) model solves the fluid flow using Navier–Stokes equations, and the solid particles are injected into the flow and are then tracked individually to calculate their trajectories inside the gas (Valentine and Decker, 1995). This strategy offers a more comprehensive picture of the particle flow interaction but requires more powerful computational resources (Zhang and Chen, 2007). For this reason, the size and distribution of the particles must be properly characterised and the injections must be reduced to the minimum necessary (Kaufmann et al., 2008). In this paper, the E–L approach has been used to simulate the motion of a high-speed train in a sand-laden atmosphere. The objectives of this study are to quantify the force exerted on the train by sand grains (with different ranges of particle diameter, particle load and coefficient of restitution between particle and surface) and to determine the regions with a higher probability of suffering impacts, focusing on the leading vehicle, and the characteristics (angle, velocity and force) of these collisions. Because of the complexity of the dynamics of the collision, the computational costs of the CFD calculation of the detailed process are prohibitive (Stevens and Hrenya, 2005). The strategy followed here involves a feasible macroscopic approach using the average force during the interval of time between two consecutive impacts, retaining the desirable accuracy. The selected geometric model and the conditions of the simulation of the continuous phase are described in Section 2. In Section 3, the parameters for the particle tracking, including the characterisation of the sand grains, are detailed; additionally, the routines implemented for the assessment of the generated forces are provided. In Section 4, the contours of probability, normalised velocity, tangential velocity, angle and force of the impacts and the graphs for the drag force contribution are shown and discussed. Finally, the conclusions are summarised in Section 5.
2. Geometric model and boundary conditions Although the main objective of this study is to evaluate the impacts on the leading vehicle, an entire train has been simulated to solve the continuous phase. The geometric model used is a simplified full-scale ETR 500, consisting of two power cars and six intermediate cars with a total length of 200 m. The geometry is a complete 3D model of the ETR500, including simplified bogies, in which all the details smaller than the surface cell size were not considered, and omitting singular elements such as the pantographs. This design, similar to the one used by Gil et al. (2008) and Muld et al. (2012), is considered sufficient to reproduce correctly the aerodynamics of a high speed train and to account for most of
the relevant effects, such as the boundary layer development around the train or the turbulence due to the asymmetry of the bogies. For a more realistic representation, the model is mounted on a single-track ballast and rail (STBR) scenario (CEN European Standard, 2009). Since this study is focused on the analysis of the leading vehicle and the flow in this region would be almost unaffected by the presence of a second track, an STBR scenario was chosen to reduce the computational cost of the simulations. The computational domain is extended 8 H beyond the nose of the leading vehicle and 30 H from the train tail to the outlet. The height and width of the outer box which limits the domain are 10 H and 20 H, respectively (Hemida et al., 2014) (shown in Fig. 1). Two different meshes were created to evaluate the influence of the grid resolution on the results. The scheme Cutcell, a utility within the software ANSYS Meshing, has been selected for both meshes with the intention of obtaining unstructured hexahedral grids aligned with the undisturbed upstream flow (Nemec et al., 2008). The coarse and fine meshes consist of 22 and 56 million elements with a cell size on the surface of the train of 0.012 H and 0.007 H, respectively. Based on the previous study of mesh convergence included in the paper of Paz et al. (2014), it is considered that both meshes have reached the convergence. However, both meshes were compared to evaluate their performance in the current geometrical model. A boundary layer around the model and the rails have also been included, leading to values of y þ between 50 and 100. Simulations were performed using the commercial software ANSYS Fluent. The k-epsilon Realisable viscous model (Cheli et al., 2010) was considered the most suitable for solving the continuous phase because of the balance between accuracy and computational cost. The inlet velocity was set uniformly to 300 km/h (83.33 m/s) and the outlet to atmospheric pressure. The STBR scenario and the ground were defined as moving walls with the identical speed as the air, reproducing the relative motion of the train and avoiding the use of sliding meshes (Flynn et al., 2014). To improve the convergence of the simulations, the cases were calculated first in steady-state and were afterwards changed to a transient mode. The time step was selected as a function of the oscillation frequency for a Strouhal number of 0.14 (Baker, 2010) and H as the characteristic length (see Fig. 1).
3. Particle impact approach For the simulation of sand particles, the DPM model implemented in Fluent has been used. This E–L approach is considered appropriate for this purpose because the discrete volume fraction is much lower than 10% and the computational resources are sufficiently powerful (ANSYS Inc., 2012). To reduce the simulation costs, a one-way coupling between phases was selected, treating the sand grains as solid particles; no additional forces were
Fig. 1. Computational domain (left) and geometrical model (right).
C. Paz et al. / J. Wind Eng. Ind. Aerodyn. 145 (2015) 87–93
included in the force balance equation. The equation of motion for a spherical particle in a gas is given by Crowe et al. (2012) →
mg (ρs − ρc ) 1 π D2 → → → → m dv /dt = CD ρc (u − v ) u − v + ρs 2 4 →
(1)
where v is the particle velocity, u is the gas velocity, ρc is the density of the continuous phase, ρs is the density of the solid phase, g is the gravity acceleration, D is the particle diameter, m is the particle mass and CD is the drag coefficient of the particle. Defining the dispersed phase Reynolds number (relative Reynolds number) and the momentum (velocity) response time as
Rer =
τV =
→ → ρc D u − v μc
(2)
ρ d D2 18μ c
(3)
where μc is the molecular viscosity of the continuous phase; and dividing through by the particle mass gives →
→
dv /dt =
g (ρs − ρc ) 1 CD Rer → → (u − v ) + τV 24 ρs
89
ranging from 1 to 100 g/m3 have been distributed among one hundred thousand injections. This process was considered sufficient to reach a good resolution in the results. The sand impact phenomena were evaluated using an intended external routine that calculates the force exerted by colliding particles. This routine also assesses the distribution, angle and velocity of the impacts on every cell of the train surface using contours. With this utility, estimating the change in the drag force is possible, producing a more accurate dimensioning of the extra energy consumption, if necessary, in the case of strong sandstorms involving high wind speeds. In addition, the elements of the highspeed trains that would suffer the highest amount of wear can be predicted, and their duty life can be estimated by considering their structural characteristics. This external implementation uses the time averaged momentum equation to calculate the force exerted by the load of particles, considering the change of momentum of every particle due to the impact and averaging it over the time between two consecutive impacts. For each particle, this time is defined as →
Δti = Δx/ u pi1 , where Δx is the distance between successive par-
→ ticles (which depends on the particle load), and u pi is the velocity
(4)
The particles have been released from a vertical plane placed near the forward nose of the train following an equally spaced distribution. The width of the plane is equal to the width of the train, and the height covers the distance from the ballast bed to the roof of the head. The purpose of this setup is to test the proposed approach by analysing the impacts on the leading vehicle. The injection of particles from other positions can also be simulated in future studies because the identical methodology can be applied. The dimensions of this plane have been set according to a previous evaluation of the region that would contain the particles that actually collide with the train, avoiding tracking useless injections. This simplification reduces the computational cost of the process. Another crucial aspect in the DPM process is the characterisation of the sand grains by fundamentally defining their diameter and concentration. The size of the particles corresponds to the classification of medium and fine sand, ranging from 0.1 to 0.5 mm according to the International Scale for the identification and classification of soils ISO 14688-1 (ISO, 2002). Considering these grain sizes, the velocities near the ground associated with the usual atmospheric wind would not be able to raise the particles to the top of the injection plane. Nevertheless, the passing of a highspeed train accelerates the surrounding air and generates in the wake air velocities near the ballast layer which magnitude is similar to the running speed of the train, 83.33 m/s in this case (Deeg et al., 2008; Kaltenbach et al., 2008). In desert areas, this generates a sand cloud behind the vehicle, which, considering the high frequency of some lines and the Stokes number of the particles (Crowe et al., 2012), remains in suspension until the passing of a later train. The case of crossing trains is the most critical situation. Knowing the velocity profile on the ground and the size of the sand grains, predicting the particle density at different heights of this sand cloud is possible. In this study, an extrapolation from the results of Liu and Dong (2004) estimates the sand concentration at the maximum speed of the train wake and at a height of 1 m, corresponding to the train nose. First, the original curves have been adjusted by a logarithmic function and the growth of these curves with velocity has been identified. Then, an asymptotic approach has been used to evaluate the function at the desired height. This extrapolation led to a particle density of the order of grams; therefore, concentrations
of the ith particle. This way, the mean force that a particle load would exert on the train in steady conditions is calculated (see Fig. 2). Only the component of the force normal to the surface on which the force is applied is considered, since the tangential component is much smaller; therefore, the projection of this normal force on the longitudinal axis determines the contribution of the force to drag resistance. →
Favg =
∑ i
(
→
Δp /Δt
)
i
=
∑ i
→ → ⎛ ⎜ m p u p2n − u p1n ⎜ Δt ⎜ ⎝
(
) ⎞⎟⎟
⎟ ⎠i
(5)
→
where, for the ith particle, Δp is the variation of momentum, → → m p is the particle mass and u p1n and u p2n are the normal components of the velocity of the particle before and after the collision, respectively. → → When the collision is totally elastic, u p1 = u p2 and the force is the maximum for the current particle size. In a real case, however, → → the impact is partially inelastic, u p1 > u p2 . This fact is considered through the coefficient of restitution, defined as the ratio between the velocity normal to the surface before and after the impact. This coefficient is a characteristic for each pair of materials and is an important factor in the selection of the coatings and paints that cover the surface of the train. A more elastic material reduces the exerted force and, consequently, the wear produced by the sand impacts.
Leading vehicle
Fig. 2. Sketch of the impact of particles on the train surface.
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4. Results and discussion 4.1. Validation To ensure the validity of the simulation of the continuous phase, the results were compared to both the numerical and experimental data from Rocchi et al. (2013). Fig. 3 shows the position of the validation probe relative to the top of rail (TOR) and the centre of track (COT). The values of the normalised velocity (U) obtained from this probe are depicted in Fig. 4. The normalised velocity is given by
U=
(u
x
case, the finer mesh captures the flow behaviour better in the bogies region; the complexity of this region requires a smaller cell size in the surface grid to produce accurate results. Unfortunately, no reference data are available in the field of particle impacts in aerodynamics to validate the implemented approach (Zhang and Chen, 2007). The existing studies investigate the penalties caused on airfoils by heavy rain (because of the liquid film) (Valentine and Decker, 1995) or the effect of dust on wind turbines and solar thermal collectors (because of increasing roughness) (Torres García et al., 2014); the nature of these problems are therefore unsuitable for comparison with the present work.
− u∞ )2 + u y2 + u z 2 u∞
(6)
where u x , u y and u z are the longitudinal, lateral and vertical components, respectively, of the velocity, and u∞ is the freestream velocity that corresponds to the train speed. The data from Rocchi et al. (2013) are represented as an interval of possible values of normalised velocities in the region that corresponds to the passing of the leading vehicle and half an intermediate car. The simulations agreed with the provided data in the nose region, producing results within the upper and lower limit. However, when moving backwards, some fluctuations appear. These fluctuations might be caused by slight differences in the underbody geometry which result from the simplification process. When comparing the coarse and fine meshes, the results are identical in the nose region; however, after the passing of the first bogies, differences between the meshes are noted. In this
Fig. 3. Position of the validation probe.
Fig. 4. Comparison of the normalised velocity between the results of the current study for both a coarse and a fine mesh and the results obtained by Rocchi et al. (2013).
4.2. Characterisation of the impacts Prior to tracking the discrete phase, the simulation of the fluid field was performed. The solution was considered converged when the scaled residuals were smaller than the Fluent's recommendation of 10 3 and the fluctuations in drag force were within 1% of the total value. Regarding the DPM simulations, the assessment of the effect of the discrete phase consisted of a series of particle injections when varying three main parameters: particle diameter (0.1–0.5 mm), particle load (0.001–0.1 kg/m3) and the coefficient of restitution (0.6, 0.8 and 1). The particle diameters selected correspond to Stokes numbers ranging from 1.96 to 49.06, and the particle loads represent volume fractions of sand between 4E-07 and 4E-05. As expected, the leading vehicle suffered the majority of sand grain impacts. Nevertheless, collisions were also noted on the roof of the last few cars. These collisions occur because after the particles strike the train's head, they are mainly displaced upwards and to the sides. These particles return to the surface of the ETR 500 model because of gravity and the fluid stream. As the most affected region, a deeper analysis of the leading vehicle was performed. Fig. 5 displays a map of the impact distribution for three different particle sizes. These contours reveal two main characteristics: around the nose, the collisions are distributed along a line in the vertical and lateral direction; and in the flat region between the windshield and the nose, a radial decrease of impacts appears. Focusing on the comparison of these three cases, both the impact probability and the affected region increase as the diameter of the particle increases. The relative weight of the right hand terms of Eq. (1) is responsible for the different contours pictured in Fig. 5. When the sand grains are sufficiently small, the displacement of air generated by the train nose is capable of carrying the particles with the stream, avoiding the collision. For this reason, a particle diameter of 0.1 mm shows almost no impact on the sides of the head and also on the lower part of the windshield because the geometry displaces the particles upwards, reaching the surface only on higher areas. By contrast, for a particle size of 0.5 mm, a regular distribution of impacts appears on the entire windshield. In addition to the impact probability, the routines implemented allow for a wider analysis of the simulation, as shown in Fig. 6. The map of normalised velocity (Fig. 6(a)) shows a stagnation point on the lower part of the windshield by reason of the geometry of the model; this map also shows higher speeds in the transition between the frontal face and the rest of the head. This tendency agrees with the behaviour of the flow in this region. Moreover, the tangential component of the velocity (Fig. 6(b)) shows that the borders of the head are the most susceptible to wear. These areas have the greatest speeds in the surface plane. Regarding the angle of impact (Fig. 6(c)), defined as the angle complementary to the one between the particle terminal velocity and the vector normal to each surface, the values on the sides are lower than 45°, implying a more tangential collision because of the relative
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Fig. 5. Distribution of impacts in the leading vehicle for a particle density of 0.1 kg/m3 and particle sizes of 0.1, 0.3 and 0.5 mm, respectively.
1
1
0.95
0.5
0.9
0
90
1
45
0.5
0
0
Fig. 6. Contours of (a) normalised velocity, (b) tangential velocity, (c) impact angle and (d) normalised drag force for a particle density of 0.1 kg/m3, a particle diameter of 0.5 mm and a restitution coefficient of 1.
position between the surface and flow. These impacts agree with the contour of the tangential velocity. However, the values on the nose are close to 90°, revealing a frontal impact. In this case, the energy carried by the particle will contribute almost entirely to increasing the drag resistance. This fact is confirmed by the image that represents the drag force contribution of particles (Fig. 6(d)) depending on the collision point. This map can be understood as a composition of the previous maps considering that drag force depends on the amount, the velocity and the angle of impacts (in addition to particle characteristics). In this figure, the nose is the
most affected region because it is impacted by a higher number of particles and the collisions are normal to the surface, although the velocity is not at a maximum. By contrast, despite suffering several impacts with a high velocity, the sides of the head remain almost unaffected in terms of the drag contribution since the surfaces are nearly parallel to the longitudinal axis. 4.3. Contribution of sand to the drag resistance The contribution of the windblown sand to the drag resistance of the train varies considerably depending on the size and
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Fig. 7. Graphs of the drag force ratio as a function of particle diameter for different values of the particle density and coefficient of restitution.
with the expected behaviour because for situations without a train passing, the wind velocities do not usually exceed 20 m/s and only micrometric particles are raised. These conditions differed from the high speeds considered in this study.
5. Conclusions
Fig. 8. Graphs of the drag force ratio as a function of particle load for different values of the particle diameter and coefficient of restitution of 1.
concentration of the particles and the coefficient of restitution of the train. The results from the DPM simulations are shown in the following graphs (Fig. 7 and Fig. 8). The values of the drag force are given by a ratio between the resistance generated by the particles and the overall aerodynamic drag. In this way, the extra amount of energy necessary to overcome the effect of the sand and keep a constant running speed is therefore estimated. The sand force is chiefly applied to the leading car, but the ratio given depends on the geometry of the entire train. Therefore, a longer train would suffer the identical particle resistance, although its proportion of the total train aerodynamic force would be smaller. The curves show a logarithmic dependency with particle diameter for all concentrations and coefficients of restitution within the tested range of particles. Larger particles or higher particle densities produce stronger drag resistances. For a particle size of 0.5 mm (a medium sand) and a particle density of 100 g/m3 , the drag contribution represents more than 10% of the aerodynamic force. However, with lower concentrations, the drag force represents less than 1% for all diameters. These magnitudes appear negligible, but considering the duration and frequency of the train routes in such a demanding environment, this 1% represents a substantial sum of energy. Therefore, the use of coatings and paints (in addition to minimising the wear of materials) can reduce the coefficient of restitution by retaining a fraction of the energy carried by the particles, which would reduce their momentum variation. As shown in the graph, these coatings are important because a decrease of 0.2 in the coefficient of restitution indicates a 10% reduction in the drag contribution due to sand, following a linear dependency. Finally, several publications analysing the characteristics of windblown dust (unaltered by the passing of a train and in different deserts, e.g., in Mali (Gillies et al., 1996) or Gobi (Jugder et al., 2011)) were selected and compared with the results obtained in this study. In these cases, the concentration and particle size of the grains were smaller than the considered ones for the simulations, producing almost no increase in the drag force. The distribution of the impacts shows a high probability in the train nose and the upper part of the windshield; the rest of the leading vehicle was practically unaffected. This behaviour agrees
The performance of a high-speed train in a particle-laden flow was investigated using numerical simulations to evaluate the effect of windblown sand in desert areas on the drag resistance and the wear of the surface of a train. The DPM model in Fluent was taken as a base model and extended with external routines that allowed for a broader analysis of the results. The fluid field was solved and validated against experimental and reference data; a series of simulations of the discrete phase with different parameters of particle diameter, particle load and coefficient of restitution were performed. A feasible and valid methodology to predict the impact zones of particles on the train was developed. The analysis of the leading vehicle shows a greater impact probability in the train nose, at which the particles would exert a larger drag force; additionally, smaller impact angles and higher velocities occur on the sides, which would lead to a more pronounced wear of the surface. The evaluation of the drag contribution of the sand reveals a logarithmic dependency with the diameter of the particle; moreover, a reduction of 10% in the total amount occurs for each 0.2 decrease in the coefficient of restitution. For the range of sand grains simulated, the values of the drag force varied from 0.02% to 11% of the total aerodynamic resistance. In this paper, the simulations performed reproduce the running of a high-speed train in a still atmosphere with sand particles in suspension, being therefore the leading vehicle the most affected part of the train. Further work could extend this study to consider the elevation of sand lying in the track or the effect caused by sand carried in crosswinds or sandstorms. Additionally, the presented approach could be fitted with experimental results for further validation.
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