Detached eddy simulation of flow characteristics around railway embankments and the layout of anemometers

Journal of Wind Engineering & Industrial Aerodynamics 193 (2019) 103968

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Detached eddy simulation of flow characteristics around railway embankments and the layout of anemometers Jie Zhang a, b, Jiabin Wang a, c, d, Xiaoming Tan a, c, d, Guangjun Gao a, c, d, *, Xiaohui Xiong a, c, d a

Key Laboratory of Traffic Safety on Track of Ministry of Education, School of Traffic & Transportation Engineering, Central South University, Changsha, 410075, China Division of Fluid Dynamics, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, SE-41296, Gothenburg, Sweden Joint International Research Laboratory of Key Technology for Rail Traffic Safety, Central South University, Changsha, 410075, China d National & Local Joint Engineering Research Center of Safety Technology for Rail Vehicle, Changsha, 410075, China b c

A R T I C L E I N F O

A B S T R A C T

Keywords: Railway embankment Flow structure Uniform wind profile Atmospheric boundary layer Speed-up factor IDDES

Anemometers are usually set up along railway embankments to monitor wind speeds, and the layout for them has to be investigated. This work used an improved delayed detached eddy simulation (IDDES) approach to explore the flow properties around railway embankments, and then a proposal was put forward for the layout of anemometers. The numerical method was validated against previous wind tunnel tests on the speed-up ratios of the flow around a 1/300 scale two-dimensional embankment with the slope gradient of 1:2. The effects of inlet velocity profiles, i.e., uniform velocity and atmospheric boundary layer velocity profiles, on the speed-up ratios around a 5 m high railway embankment were compared. The study indicates that using a uniform velocity profile to assess the operational safety of trains running across strong wind regions could be favourable, especially when complex local terrains contribute to different wind characteristics. The anemometers should be set upstream, i.e., at a well defined distance in locations with sufficient extent of open ground and on the electrification masts along railway lines. This is not in line with the anemometer layout of the existing SWEWS (Strong Wind Early Warning Systems), the difference being due to the speed-up effect of the railway embankment, which is usually not considered explicitly. Formulas have been developed on the basis of regression of the simulation results to express the relationships between e.g. top wind speed over the embankment (located in an area where it is not possible to install anemometers) and measured wind speeds. In this way it is possible to take into account the speed-up effect encountered by the wind passing over the embankment, which needs to be considered in the operational rules in order to ensure safe operations.

1. Introduction With rapid development of high-speed railways all over the world, the regular operational speed of a high-speed train has reached 300 km/h, sometimes even up to 350 km/h. At such a high speed, the trains travelling through wind regions are subjected to a risk of overturning with potentially extremely serious consequences. According to the investigation of train accidents caused by strong winds around the world, most derailment and overturning incidents happen at exposed locations, e.g., bridges, embankments, and special cuts (Fujii et al., 1999; Andersson et al., 2004; Diedrichs et al., 2007; Zhang et al., 2013; Zhang et al., 2015), where the flow structures around the trains are more turbulent and complicated. Therefore, how to maintain or to improve the operational

safety of the train under crosswinds has become of significant importance in the rail industry. In the present paper, the attention is paid to the railway embankment. To deal with this issue, research work has been conducted that focuses on the aerodynamic performance of trains on the railway embankments to understand the typical train flow characteristics. For example, Diedrichs et al. (2007) studied, by means of computation and wind tunnel tests, the aerodynamic performance of a high-speed train ICE2, when it stood on the windward and leeward tracks of a 6 m high embankment, at a crosswind of 30
yaw angle, and the Reynolds number was 4.6  106 based on the train height. They pointed out the LWC (leeward case) is more critical than the WWC (windward case) for the speed-up effect of the embankment, which is confirmed by Cheli et al.

* Corresponding author. Key Laboratory of Traffic Safety on Track of Ministry of Education, School of Traffic & Transportation Engineering, Central South University, Changsha, 410075, China E-mail address: [email protected] (G. Gao). https://doi.org/10.1016/j.jweia.2019.103968 Received 24 August 2018; Received in revised form 30 June 2019; Accepted 5 August 2019 Available online xxxx 0167-6105/© 2019 Elsevier Ltd. All rights reserved.

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lines, as shown in Fig. 1(a). However, given the strong fluctuation of natural wind and the distance between the location of anemometers and railway lines, the velocity measured by the anemometer cannot present the wind speed above railway lines in time. Additionally, due to the speed-up effect of embankment, the velocity measured is even much lower, although it is the real speed of the incoming flow. To solve this problem, now the anemometers are being installed on the electrification masts along railway lines, Fig. 1(b) (The specified set-up can be found in previous work (Zhang et al., 2016a; Xiong and Liang, 2016). Both are installed on a horizontal holder which is fixed on the electrification masts, and located 4 m or 4.5 m above the rail level. Each monitoring point has two anemometers longitudinally separated, as in some other countries for the flat ground case (SNCF I/SYSTRA, 2004; Gong and Wang, 2012; Hoppmann et al., 2002)). But due to the speed-up effect of the embankment, this leads to another problem that the velocity measured is much higher than that of the upstream flow with the same aerodynamic forces of the train. This is because the operational regulation is established according to the aerodynamic forces of the train and the forces are always obtained from the instant inlet velocity in wind tunnel tests and numerical simulations. As a result, the velocity measured would give an inaccurate warning and strictly limit the train speed. To summarize, two issues are included: (1) the anemometers located upstream cannot present the wind speed in time above the railway; (2) for embankment cases, the anemometers fixed on electrification masts show higher velocities, which may strictly low the transport capacity. Therefore, there is a hot debate about which velocity should be used to guide the operation of trains passing through wind regions, and this is the true aim in this paper to find out the relationship between the velocities of natural winds and the locations of anemometers, and investigate the layout of the anemometers in a railway embankment case.

(2010). Moreover, Cheli et al. (2010) found that for small attack angles (up to 35
), the forces of the train on an embankment are higher than the ones on flat ground, ascribing this to the embankment speed-up effect. More interesting still is that if the forces are normalised with respect to the wind velocity measured over the track, the coefficients are highly close to those of the train on flat ground. Due to the speed-up effect associated with the geometry of the embankment, Liu and Zhang (2013) attempted to study the effect of different leeward landforms in cuttings on the aerodynamic performance of high-speed trains. They found that when the leeward side (LWS) of the cutting is a downhill (that is a half-embankment), the high-speed train would be in a more dangerous running environment. Also Miao et al. (2010) analysed the effects of railway environments on the aerodynamic performances of trains on a 10 m high embankment, and pointed out that the embankment slope is an important parameter for the train aerodynamic forces. There is also some work to obtain the velocity distributions around railway embankments. To explore the speed-up effects, field tests, wind tunnel tests and numerical simulations are always applied. For the field test, it can obtain the real wind speed in both inner and outer layers of the flow around an embankment quickly, as well as the speed-up ratio and the surface pressure perturbation (Frank et al., 1993; Baker, 1985). However, it is quite expensive and costs a large amount of resources. In Baker’s work (Baker, 1985), to save resources the wind characteristics over narrow railway embankments at both model and full scale were discussed. He concluded that only the velocity component normal to the embankment is accelerated. With the development of CFD (computational fluid dynamics), the numerical simulation is becoming a popular tool to solve flow issues. In the beginning, the standard k-ε turbulence model was used to simulate velocity distributions around the embankment with different slope angles and heights to propose the location of anemometers where the velocity gradient is 0 (Miao et al., 2013). After that, detached eddy simulations (DES) with standard Spalart–Allmaras (SA) model were conducted by Gao et al. (2014) who investigated the wind velocity and pressure distributions in front of the wind barrier at different embankment heights. They found that the optimal location for the anemometer is approximately 5 m in front of the wind barrier where the velocity reaches the minimum value. Overall, all these studies above usually focus on the crosswind stability of the train on an embankment, the speed-up effect of an embankment, and the locations of anemometers far from railways. In countries with highly developed railway systems, the anemometers, as an important part of Strong Winds Early Warning Systems (SWEWS) (Fujii et al., 1999; SNCF I/SYSTRA, 2004; Gong and Wang, 2012; Hoppmann et al., 2002), are either installed along the railway lines (e.g., a location of 4 m above the rail level and 4 m from the centre line of the near track) or a certain distance far from the railway lines (e.g., a distance of 10 times the height of the obstacle) (SNCF I/SYSTRA, 2004; Zhang et al., 2016a). At present, along the Lanzhou-Xinjiang railway and the Qinghai-Tibet railway in China, those anemometers are generally located upstream in locations with sufficient extent of open ground, but not far from railway

2. Numerical set-up 2.1. Numerical method In the present work, the commercial CFD software solver ANSYS FLUENT 15.0 with an improved delayed detached eddy simulation (IDDES) approach based on SST (shear stress transport) k-ω turbulence model (ANSYS Inc, 2015) was used to achieve an instantaneous and an accurate time-averaged view of the flow structure around the embankment. The IDDES (Shur et al., 2008) is an improvement over the original DES model that is a hybrid RANS–LES (Reynolds-averaged Navier-Stokes–large eddy simulation) approach, has been used successfully to study the slipstream of a high-speed train (Huang et al., 2016). The DES method was initially proposed by Spalart and Allmaras (Spalart et al., 1997), now has been widely considered to be a promising approach in modelling high-Reynolds number separated flows (Gao et al., 2014; Huang et al., 2016; Morden et al., 2015; Niu et al., 2017; Flynn et al., 2014; Zhu et al., 2016; Zhang et al., 2016b, 2017, 2018). It was developed to overcome the excessive computer demands of LES, while seeking

Fig. 1. Installation of anemometers: (a) On the top of an iron tower in a wide-open area; (b) On the electrification mast. 2

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to improve the accuracy of RANS in unsteady flow. For this hybrid method, a smooth transition is made from the regions where the unsteady Reynolds-averaged equations are solved to those where a LES is performed. The switching between the two models depends on the local grid-resolution. The DES approach is promising. However, it still has some drawbacks. For the wall bounded flows with thick boundary layers and small separation regions, the grid spacing parallel to the wall is often not larger than the boundary layer thickness to achieve RANS or fine enough to activate the pure LES. As a consequence the eddy viscosity would be reduced, as well as the modelled Reynolds stresses, leading to Modelled Stress Depletion (MSD) and Grid Induced Separation (GIS) phenomena (Spalart, 2009; Spalart and Allmaras, 1992). Therefore, an improved method IDDES is used in this paper. The IDDES model has the following goals in addition to the formulation of the standard DES model (ANSYS Inc, 2015):

discretized using the bounded second-order implicit scheme for unsteady flow calculations. The convergence criterion is based on the residual value of the continuity equation, which is less than 104 with minimal fluctuation. Also the convergence is monitored by plotting the x component of the wind speed at point “n" above the railway embankment (see Fig. 2). In all simulations, RANS simulations were performed to obtain initial flow fields so as to provide realistic inlet conditions for unsteady cases, and the number of iterations was dependent on the convergence criterion. For the unsteady cases, the time step used is Δt ¼ 2  104 s, showing maximum CFL number of around 1.0 all over the domain, and 20 iterations are performed for each time step to reduce the residuals. In order to obtain the instantaneous flow field, the number of time steps is 6000. After that, the flow field would be fully developed, so data sampling for time statistics is chosen to average the flow field. This averaging time is also 6000 time steps (It should be note for the cases applying perturbations at the inlet, more 4000 is needed to average the flow for eliminating the turbulent effect from the inlet), and the computational data are saved at each step.

 Provide shielding against GIS, similar to the DDES model (Spalart et al., 2006).  Allow the model to run in Wall-Modelled LES (WMLES) mode in case unsteady inlet conditions are provided to simulate wall boundary layers in unsteady mode. The IDDES model is designed to allow the LES simulation of wall boundary layers at much higher Reynolds numbers than standard LES models. As an alternative to unsteady inlet conditions, unsteadiness could also be triggered by an obstacle (such as a backward facing step, or a rib inside or upstream of the boundary layer).

2.2. Computational details The cross-section of a conventional railway embankment at full scale in China is shown in Fig. 2. h represents the height of the embankment, which is 1 m, 3 m and 5 m, respectively, and its slope ratio is 1:1.5 (Diedrichs et al., 2007; Liu and Zhang, 2013; Schober et al., 2010; Tomasini et al., 2014). To obtain the distance of the proposed monitoring point from the railway line, point “m" is set at the windward side (WWS) of the ridge, and point “r" is at the base of the embankment, as shown in Fig. 2. Meanwhile, combined with the layout of anemometers on electrification masts for the overhead contact system of electrified railways all over the world, point “n" is fixed at 4.5 m above the rail level (Miao et al., 2013), and 4.25 m far from the centreline of the near track. In addition, point “p" is a symmetric point relative to point “n" above the centreline of the tracks. The model scale is 1/10th, however, all of the dimensions presented in the following sections are at full scale if not stated otherwise. The computational domain and coordinate definition are set up in Fig. 3. Measurements presented by Baker (1985) show that only the normal velocity to the embankment accelerates. Therefore, when an embankment is perpendicular to the wind direction, the speed-up factor is the largest. On this condition the layout of anemometers around the railway embankment is investigated in this work. To eliminate the effect of boundary conditions on the flow field around railway embankments, the inlet is 60 m upstream from the centre of the railway line. The height, given the full development of the flow field, is also chosen as 60 m. Taken the three-dimensional flow effect into account, a certain length, denoted by W which is 10 m, is extruded along the longitudinal direction. Then the coordinate system is defined. The coordinate origin is positioned in the middle plane, at the centre of the double railway lines and at 0.6 m above the ridge of the embankment, as shown in Fig. 2. A uniform velocity of 20 m/s was set at the front inlet, Fig. 3; the turbulent kinetic energy, k ¼ 3(IUin)2/2, and the specific dissipation rate, ω ¼ k1/2/(0.07LC1/4), were used to specify the properties of the incoming flow. Where, I is the turbulence intensity, Uin is the incoming flow velocity, L is the characteristic length, C is the empirical constant that is 0.09. The difference between a uniform and atmospheric boundary layer upwind velocity profile is considered. This is done by modelling the flow over a 5 m high embankment as described in section 3.2. It should be reminded that for the main cases in Section 3.3, perturbations were applied at the inlet to create turbulence, aiming to achieve a realistic inflow, whereas in Section 3.1 and 3.2 no perturbations were adopted to save computational costs. Here a spectral synthesizer method has been incorporated into ANSYS FLUENT, so to save computing time we did not use a precursory simulation or putting blocks on the upstream surface in the simulations to generate the turbulence. The spectral synthesizer

Similar to DES, the k-equation of the IDDES-SST model is modified to include information on the local grid spacing. In case the grid resolution is sufficiently fine, the model will switch to LES mode. However, the goal is to cover stable boundary layers (meaning no unsteady inlet conditions and no upstream obstacles generating unsteadiness) in RANS mode. In order to avoid affecting the SST model under such conditions, the IDDES function provides shielding similar to the DDES model, meaning it attempts to keep the boundary layer in steady RANS mode even under grid refinement (ANSYS Inc, 2015). The IDDES-SST model is based on modifying the sink term in the kequation of the SST model (The ω-equation remains unmodified.) (ANSYS Inc, 2015).

∂ðρkÞ ~ ¼ r ½ðμ þ μT Þrk þ Pk  ρβ* kωFIDDES þ r ðρUkÞ ∂t σ k3 ∂ðρωÞ ~ ωÞ ¼ r ½ðμ þ μT Þrω þ ð1  F1 Þ2ρ rkrω þ α3 ωPk þ r ðρU σ ω2 ω ∂t σ ω3 k  β3 ρω2 FIDDES ¼ lRANS ¼

lRANS lIDDES

pffiffiffi. * k β ω

(1)

(2)

(3)

(4)

where FIDDES is based on the RANS turbulent length scale and the LES grid length scales. Note in the DES formulation, turbulent boundary layer simulations, grid cells are anisotropic, and the grid spacing (Δ) is based on the largest grid space in the x, y or z directions forming the computational cell, that is Δ ¼ max (Δx, Δy, Δz). However, in the IDDES formulation, the sub-grid length scale Δ differs from the DES formulation, a more general formulation for Δ is used that combines local grid scales and the wall distance dw. In all simulations, the SIMPLEC (Semi-Implicit Method for PressureLinked Equations Consistent) algorithm is used to couple the pressure and the velocity fields. A bounded central differencing scheme is chosen for solving the momentum equation. A second-order upwind scheme is applied for solving the k and ω equations. The time derivative is 3

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Fig. 2. Cross-section of a conventional railway embankment at full scale (unit: m).

Fig. 3. Computational domain (unit: m).

provides an alternative method of generating fluctuating velocity components. It is based on the random flow generation technique originally proposed by Kraichnan (1970) and modified by Smirnov et al. (2001). In this method, fluctuating velocity components are computed by synthesizing a divergence-free velocity-vector field from the summation of Fourier harmonics. In ANSYS FLUENT, the number of Fourier harmonics is fixed to 100 (ANSYS Inc, 2015). A pressure outlet boundary condition with 0 Pa was applied at the outlet. The top was treated as a symmetry wall and the sides were treated as periodic boundaries. No-slip walls were applied at the ground, embankment, and ballast. The computational domain consisted of a structured grid which was generated by the commercial grid generator software ANSYS ICEM CFD. In order to capture the flow structure near the railway embankment correctly, a prism layer of 10 cells was created in a belt. The maximum thickness of the first layer is 1 mm. This gives a value of y þ over the majority of the embankment surface in the range of 20–100. In addition, for the numerical predictions, the grids that were near the embankment were refined. Fig. 4 shows the mesh distributions around the embankment.

lX2 lie at the centre of the windward and leeward lines (WWL and LWL), respectively. Line lY1 is a horizontal line at a height of 4.5 m from the rail top, line lY2 locates at 10 m from the ground, and line lY3 is on the top of the rail (TOR). Fig. 6 shows the mean speed-up ratio RU on the coarse and fine meshes, and the details of the two different resolution meshes are listed in Table 1. Those trends presented are similar to these obtained by Diedrichs et al. (2007). The speed-up ratio RU is defined as: RU ¼ Uxy/Uin

(5)

Where, Uxy is the mean velocity component (z m above the rail top) in the xy plane consisting of the combination of the X and Y components of velocity, which is different from the definition used by Baker (1985) who considered the Z component. Uin is the incoming flow velocity. Note that in the simulations, Uin is the inlet velocity at the corresponding height, e.g., for the horizontal lines, it is the velocity at the height of (h þ z) m, while as to the vertical lines, it is the velocity at the height of z m above the ground level. Although slight differences are observed in the two cases, the results on the coarse mesh closely meet these on the fine mesh. Thus, it can be determined that the results are not a function of mesh resolution and the coarse mesh is sufficient in the analysed cases. Unfortunately, no wind tunnel test concerning the same railway embankment has been conducted to validate the numerical method used in this paper. Here a simulation of the flow around a 1/300 scale twodimensional embankment with a slope gradient of 1:2 was used to

3. Results and discussion 3.1. Grid independence and program validation To determine the effect of mesh resolutions on the solution, a grid sensitivity study was conducted. Five lines in the middle plane located around a 5 m high railway embankment are shown in Fig. 5. Lines lX1 and

4

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phenomenon occurred in the region close to the top surface of the embankment, so three monitoring points are set over the embankment. To obtain the speed-up ratio, a new formula is used as follows: ΔKL ¼ u/u0 – 1 (Kraichnan, 1970). Where u is the velocity z m above the embankment top, and u0 is velocity z m above ground level upstream of the embankment. The speed-up ratios from the simulation and wind tunnel test are presented in Fig. 8. The ratios calculated in the simulation, with smaller values, are close to those in the wind tunnel tests, and the maximum error between the numerical and experimental values is less than 6%. This similarity in shape suggests that the comparison of results in the validation case gives a reasonable understanding of the modelling uncertainties and flow patterns also in the analysed case, although the sizes at full scale, as well as the slope gradient, are not exactly the same. Overall, the numerical results show good agreement with those in wind tunnel tests, and the IDDES used in the present paper can give a high accuracy to predict this kind of flow around the embankment. 3.2. Effect of inlet velocity profiles on speed-up ratios around a 5 m high railway embankment The embankment that is built on ground is affected by the atmospheric boundary layer (ABL), so it is better to understand the effect of inlet velocity profiles (Both uniform and atmospheric boundary layer) on the speed-up ratios around the railway embankment. Generally, the wind profile of the ABL (from surface to around 200 m) is logarithmic in nature and is best approximated using the log wind profile equation that accounts for surface roughness and atmospheric stability (Cook, 1985). However, sometimes the surface roughness or stability information is not available, so the wind profile power law relationship is often used as a substitute for the log wind profile. In this section, a power law is used to describe the vertical distribution of horizontal mean wind speeds. In order to estimate the wind speed at a certain height z, the wind profile power law relationship can be written as (Cook, 1985): u ¼ uref (z/zref) α

Fig. 4. Mesh distributions: (a) mesh around the embankment; (b) close-ups of figure (a); (c) mesh on the railway embankment.

(6)

where, u is the wind speed at height z, and uref is the known wind speed, with the same value of the uniform wind speed in Section 2.2, at a reference height z ¼ 10 m above the ground based on the Chinese Standard – Load code for the design of building structures (Standard, 2012). The exponent (α) is an empirically derived coefficient that varies dependent on the stability of the atmosphere. For flat terrain and open land cover conditions, α is approximately 0.15 (Standard, 2012). Therefore, in this paper, α ¼ 0.15 is used. Fig. 9 shows the mean RU and Uxy distributions around a 5 m high railway embankment using two different inlet velocity profiles. Note that in formula (5), Uin that is the velocity at the height of (h þ z) m is a constant for the horizontal line, while it is the velocity at the height of z m above the ground level that is a constant at the uniform inlet velocity profile, but being variable with the height at the ABL along the vertical

make a comparison with the results of wind tunnel tests conducted by Shiau and Hsieh (Shiaua and Hsieh, 2002). Fig. 7 shows the embankment model that is similar to the shape of the railway embankment. The origin is set at ground level of the centre of the embankment top. The height of the embankment is h1 ¼ 5 cm. Because the rural terrain type of neutral turbulent boundary layer flow was simulated as the approaching flow in the tests, the inlet velocity profile is approximated by the power law in the simulation, as shown in eq. (6) of Section 3.2. Where u is the wind speed at height z, and uref is the free stream velocity of 5 m/s, at a reference height zref ¼ 100 cm (with a scale of 1/300) above the ground. The exponent α is approximately 0.16. According to previous work (Diedrichs et al., 2007; Frank et al., 1993; Baker, 1985), the speed-up

Fig. 5. Location of five reference lines. 5

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Fig. 6. Mean RU along lines. (a) RU along lY1; (b) close-ups of figure (a); (c) RU along lX1 (WWL) and lX2 (LWL); (d) close-ups of figure (c). Flow is from left to right in these images.

embankment and obtaining a smaller speed-up effect. As to the mean RU and Uxy along lX1 and lX2, much larger ΔKL below the train height is obtained by using the atmospheric boundary layer at the inlet, Fig. 9(c), while much smaller Uxy below the train height is shown in Fig. 9(d). As reported in (Mao et al., 2011), although using a uniform velocity profile to assess the operational safety of trains may limit the train speed, it could be much safer for a train running across the strong wind regions, especially when the wind characteristics are quite complex due to the different local terrain around the railway. Therefore, in this paper, to guarantee train safety and reduce train accidents, the uniform velocity profile is used to investigate the flow characteristics around railway embankments and attempt to obtain the layout of anemometers.

Table 1 Details of two different resolution meshes. Embankment height

Grid

Nodes

Cells

5 m at full scale

Coarse mesh Fine mesh

1249  253  51 1301  298  61

15,724,800 23,166,000

line. This is why lower velocities are observed in ABL in Fig. 9(d), but higher speed-up factors are shown in Fig. 9(c). For the mean RU and Uxy along lY1 in the same inlet velocity profile, there is no difference as a constant is used to normalize Uxy, as shown in Fig. 9(a) and (b). The speed-up ratios present similar changes with the variation of horizontal distance, especially in the upstream. However, above the track, the uniform velocity profile contributes to a more significant speed-up effect, which is not favourable for a running train (Mao et al., 2011). This is because below the reference height z ¼ 10 m, the inlet velocity profiles comes from the ABL follows the power law relationship, so the velocity near the ground is much lower than that of the uniform inlet velocity profile. As a result, less flow volume per unit that comes from the inlet below this height, thereby less flow flowing over the

3.3. Flow structures around the embankment 3.3.1. Instantaneous flow structures The iso-surfaces of the second invariant of velocity gradient Q is often used to describe the instantaneous flow structures (Hunt et al., 1988). It can be defined as: Q ¼  0:5ðSij Sij  Ωij Ωij Þ

Fig. 7. Embankment model with a slope gradient of 1:2 (Kraichnan, 1970). The origin is set at ground level of the centre of the embankment top. 6

(7)

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Fig. 8. ΔKL at z/h1 ¼ 1:2 (Kraichnan, 1970).

Journal of Wind Engineering & Industrial Aerodynamics 193 (2019) 103968

from

the

IDDES

and

wind

tunnel

bridge of the Kansai airport line (Fujii et al., 1999), the leeward wind velocities sometimes exceed the windward ones by 20%, and their oscillation magnitudes are obvious. Meanwhile, when the height of the embankment is over 3 m, the velocity magnitude of iso-surfaces of Q behind the embankment and below the ridge is much less due to the shielding effect of the embankment. The turbulent flow characteristics also can be seen from the turbulence intensity around the embankment, as shown in Fig. 11. Note that the moderate turbulence intensity is fully filled into the domain, except of the wake region, indicating that the incoming flow is turbulent. Much larger red regions with high turbulence intensity are observed behind a higher embankment. This confirms that the shielding effect of the embankment leads to massive separations, resulting in higher fluctuations. Fig. 12 shows several turbulence intensity profiles along lines. In general, the turbulence intensity at less disturbed regions is around 5% that has been given at the inlet boundary condition. Higher turbulence intensity is observed near the top of the embankment without considering higher fluctuations in the wake region. A higher embankment basically contributes to higher turbulence intensity except of small particular regions.

tests

Where, S ij and Ωij are the symmetric and anti-symmetric parts of the velocity gradient tensor. Thus, Q represents the local balance between shear strain rate and vorticity magnitude. Vortex shells may then be visualized as an iso-surface of Q > 0. Fig. 10 shows the highly unsteady flow above the ballast and behind the railway embankment at different heights, using Q ¼ 10,000 coloured with the velocity magnitude. The mainly vortex regions exist above the ballast and in the wake behind the embankment. For the sharp edges that would not occur in reality, some separation vortices are generated from the ridges of the embankment and ballast. These shedding vortices detach and progress downstream, which makes flow in the regions above and close to the track bed more turbulent. However, their influences are limited, compared with the vortex region in the wake. Due to the shielding effect of the embankment, a number of vortices appear behind it, contributing to making the flow field much more complex. With the increase of height, the number of vortices grows sharply. Apparently, if the anemometers are installed in these areas, the measured data would be doubtful and full of errors, as shown in Section 3.4. These results are in accord with Fujii’s experimental research (Fujii et al., 1999), which proposes judging wind directions and controlling train operation by wind velocities observed with windward anemometers. According to the field test results on the

3.3.2. Mean pressure and velocity Fig. 13 presents the mean pressure and velocity contours in different embankment heights. For the blockage effect of the embankment, positive pressure is generated at its base, although above the embankment there is negative pressure. The closer the distance above it is, the greater the pressure value is, especially at the corners. Based on Fig. 10, at these corners flow separations are induced by the edges, which contributes to the negative pressure. As the embankment height increases, the pressure peaks at the base, the top and in the wake become large. From the velocity contours, it is observed that the flow rising over the top of the embankment accelerates considerably. In the near ridge and track bed region, the speed-up factor is significant, which can be used to explain why negative pressure exists above the embankment. Meanwhile, at the base of the embankment and behind it, the velocity magnitude is much

Fig. 9. Mean RU and Uxy around a 5 m high railway embankment using two different inlet velocity profiles: (a) RU along lY1; (b) Uxy along lY1; (c) RU along lX1 and lX2; (d) Uxy along lX1 and lX2. Flow is from left to right in these images. 7

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Fig. 10. Instantaneous flow structures: An iso-surfaces of Q: (a) h ¼ 1 m; (b) h ¼ 3 m; (c) h ¼ 5 m. Flow is from bottom left to top right in these images.

shown in Fig. 14. Points p1 and p2 are at the centre of the windward line with the height of 5.3 m (the height of the overhead contact line) and 2.2 m (almost in the middle of a passenger train) above the rail level. Points p3 and p4 are at the centre of the leeward line with the full scale height of 5.3 m and 2.2 m. Points n and p can be found in Fig. 2. To make a comparison and understand the velocity fluctuation in the wake of the embankment, 3 monitoring points are built upstream with the distance of 40 m from the centreline of the railway line, while other 3 points are in the downstream with the distance of 60 m, as shown in Fig. 14. Fig. 15 shows the instantaneous speed-up ratios at different monitoring points for the 3 m height embankment. The non-dimensional time “tUin/W00 is used, where t is the computation time in simulations. The time histories of speed-up ratios show that the amplitudes in the monitoring points above the embankment at a certain height and in the upstream are smaller than the amplitudes in the monitoring points downstream. Due to the vortex separation as shown in Fig. 10, the velocities at monitoring points p2 and p4 are a little higher. The standard deviation (SD) values of speed-up ratios at different monitoring points are used to show the intensity of fluctuation in the velocity. Here the SD is defined as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX  σ ¼ t ðxi  μÞ2 N

(8)

i¼1

Fig. 11. Turbulence intensity around the embankment: (a) h ¼ 1 m; (b) h ¼ 3 m; (c) h ¼ 5 m. Flow is from left to right in these images.

Where, σ is the SD, N is the number of the sample, μ is the mean value and xi is the individual sample value. When the monitoring points are set upstream, their SD values are less than 0.045, as shown in Table 2. However, when the points are downstream, the maximum reaches 0.081, which means the oscillation is quite significant. For the points above the embankment the largest one is 0.059, since the perturbations coupling with the flow separation lead to more turbulence. Note that the velocities of points at undisturbed regions show consistent trends, e.g. Points p-1

less, being close to 0. With the increase of the embankment height, the velocity magnitude peaks above the railway line increase. 3.4. Velocities at monitoring points Several monitoring points were set up around the embankments, as 8

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Journal of Wind Engineering & Industrial Aerodynamics 193 (2019) 103968

Fig. 12. Turbulence intensity profiles along (a) line lY3; (c) line lY2; (c) line lX1; (d) line lX2.

between them, and establish an effective conversion method. In addition, it is obviously found that the maxima of speed-up factors along the lines increase with the increase of the embankment height. Also when the monitoring point moves close to the embankment, the speed-up effect above the embankment is more significant. Over a 5 m high embankment, the maximum velocity at 4.5 m above the rail level even exceeds at least 20%.

and p-2 in Fig. 15(a), and Points p-4 and p-5 in Fig. 15(b).

3.5. Speed-up ratios around embankments In the following section the layouts for the anemometers around railway embankments at different heights are derived from the mean speed-up ratios along the specified lines. For the horizontal ones, the chosen heights of the monitoring lines are 4.5 m above the rail level, and 10 m above the flat ground. For the vertical ones, the windward monitoring one is located at the centre line of the WWL, and the leeward monitoring one is located at the centre line of the LWL, respectively.

3.5.2. Mean speed-up ratios along vertical lines Fig. 17 shows the Uxy along vertical lines at height hz from 0 m to 5 m, at different locations in the time-averaged flow field. A uniform velocity, that is 20 m/s, is set at the inlet. Moving forward a certain distance, due to the boundary layer effect of the ground, the wind speed close to the wall is less than 20 m/s. As it is far enough away from the embankment, the blockage influence is limited, and the speed-up ratios are almost the same for different embankment heights. The velocities along the vertical centrelines of the WWL and LWL coincide with increasing embankment height, while a maximum speed-up factor along each centreline can be found. Comparing the conditions at 1 m and 5 m embankment height, the speed-up effect of the higher embankment is more significant, as shown in Fig. 18. Through these figures, it is clear that the higher the embankment, the larger the speed-up factor. When this flow acts on the train body, it would lead to greater forces which expose the train to greater risk of overturning. Therefore, the major concern for regulatory purposes is the embankments of greater height. Meanwhile, for the same embankment height with double railway lines, the speed-up effect of the WWL is more significant than that of the LWL, below a standard sized train height from the track bed, which shows potential inconsistency with those reported in Diedrichs et al. (2007) and Cheli et al. (2010) who mentioned that the LWC (leeward case) is more critical than the WWC (windward case) for the speed-up effect of the embankment. However, to the authors’ knowledge, for the train on the embankment under strong winds, its side force mainly comes from the difference of the pressure on the windward and leeward of the train. Although the speed-up effect leads to slightly different pressure on the windward, the pressure on the leeward mostly depends on the configuration downstream (Cheli et al., 2010). The flat

3.5.1. Mean speed-up ratios along horizontal lines Fig. 16 shows the mean speed-up ratios along lY1 and lY2. The maxima along both lines are shown in Table 3. When the incoming airflow approaches the embankment, it is blocked, and its velocity decreases gradually to the lowest at the WWS of the embankment. After that, as the cross-section for the flow passing diminishes, the air climbs along the slope with extrusion, which contributes to the speed-up effect. Then the maximum comes out above the rail level. Subsequently, the flow speed slows down. With the increase of embankment heights, the position of the maximum wind speed tends to move toward the WWS. Considering the Chinese railways criterion of allowed wind-measurement deviation of 10% (Zhang et al., 2016a), as well as the speed-up ratios, it would be possible to locate the monitoring points both upstream and downstream of the embankment. However, based on the investigation in Section 3.3, Section 3.4 and Fujii’s research (Fujii et al., 1999), it is proposed that the point should be set in the upstream where the flow is less fluctuant. Meanwhile, there is a key point with zero gradient of wind speed along the horizontal velocity curve, where the velocity would not lead to a major change in a certain distance so as to avoid variability in the measurements. The monitoring point can be located at this place, as reported in previous work (Miao et al., 2013; Gao et al., 2014). Since the values measured in such a location would be less than those of the incoming flow and above the embankment, it would be conservative to use them directly as a basis for regulating the operations of high-speed trains. It is thus necessary to find out the relationship 9

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Journal of Wind Engineering & Industrial Aerodynamics 193 (2019) 103968

Fig. 13. Time-averaged flow structures: (a) h ¼ 1 m; (b) h ¼ 3 m; (c) h ¼ 5 m. Left: pressure (unit: Pa); right: velocity magnitude (unit: m/s). Flow is from left to right in these images.

10

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Fig. 14. Schematic diagram of monitoring points at full scale (unit: m).

Fig. 15. Instantaneous RU at different monitoring points: (a) Points around the embankment; (b) Points in the upstream and downstream.

embankment, and point “m" - at the WWS of the ridge (see Tables 4–6). The corresponding horizontal wind velocities are also given in the tables. Where, Xd-4.5m and Xd-10m are the designated distances away from the fixed points r and m along the x axis at the height of 4.5 m above the rail level and 10 m above ground, respectively, their corresponding horizontal wind velocities denoted separately by Uxy-d-4.5m and Uxy-d-10m. Uin is the incoming flow speed, which is set at 20 m/s, and Uxy-pole-n and Uxy-pole-p are the horizontal wind velocities at the electrification masts. The relationships between the positions of the upstream monitoring points and embankment height are expressed by the following approximate formulas: For the point r,

Table 2 Standard deviation (SD) values of speed-up ratios at different monitoring points. Point

p-1

p-2

p-3

p-4

p-5

p-6

SD Point

0.039 p1

0.039 p2

0.045 p3

0.047 p4

0.052 n

0.081 p

SD

0.039

0.059

0.037

0.055

0.040

0.037

ground (e.g. the WWC) in the leeward contributes to less side forces than the down slope (the LWC), which has reported in (Cheli et al., 2010). This is why the WWC is subjected to higher speed wind but it is still safer than the LWC.

Xd-4.5m 0.45 h þ 5.94 3.6. Proposed monitoring layout

Xd-10m 1.07h þ 13.54

(9) (10)

For the point m,

Based on the above investigation, the proposed monitoring points are situated at the point at which the horizontal wind velocity gradient is zero, at two different heights, and on the electrification masts, on both the WWS and the LWS of the embankment, with longitudinal separation of 0.8 m as defined in former work (Zhang et al., 2016a). The former is defined by its upstream distance from point “r" - at the base of the

Xd-4.5m 1.95 h þ 5.94

(11)

Xd-10m 0.43 h þ 13.54

(12)

The relationships between key velocities are expressed by the 11

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Journal of Wind Engineering & Industrial Aerodynamics 193 (2019) 103968

Fig. 16. Mean RU along horizontal lines: (a) 4.5 m above rail level; (b) 10 m above ground. Flow is from left to right in these images.

following:

Table 3 Maxima RU above the embankment at two heights. Height

4.5 m high above rail level 10 m high above ground

Maxima RU h¼1m

h¼3m

h¼5m

1.084 1.052

1.179 1.148

1.251 1.254

Uin (0.003h þ 1.01) Uxy-d-4.5m

(13)

Uin (0.0049h þ 1.00) Uxy-d-10m

(14)

Uin (0.031h þ 0.99) Uxy-pole-n

(15)

Uin (0.028 h þ 0.97) Uxy-pole-p

(16)

Fig. 17. Vertical time-averaged velocity distributions at different locations: (a) h ¼ 1 m; (b) h ¼ 3 m; (c) h ¼ 5 m. Flow is from left to right in these images. 12

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Journal of Wind Engineering & Industrial Aerodynamics 193 (2019) 103968

Fig. 18. Mean RU alonge vertical lines: (a) Along lX1; (b) Along lX2. Flow is from left to right in these images.

validation was conducted to find out a suitable mesh method for the research, and carefully determined mesh resolutions adjacent to the walls of the ground, track bed, and embankment were used. The numerical method was validated against the results of wind tunnel tests (Schober et al., 2010) on the speed-up ratios of flow around a 1/300 scaled two-dimensional embankment with a slope gradient of 1:2. To understand the effect of inlet velocity profiles (Both uniform and atmospheric boundary layer) on the speed-up ratios around a railway embankment, a brief comparison was carried out. The instantaneous flow structure around the railway embankment at different heights was analysed, and the time histories of speed-up ratios at monitoring points were discussed. After that, the speed-up ratios along horizontal and vertical lines were calculated and the appropriate layout of anemometers derived for different embankment heights. The study shows that the anemometers should be installed upstream at a well-defined distance (i.e., the distance of the point with zero horizontal velocity gradient.) in locations with a wide-open area and on the electrification masts along the railway lines. Each monitoring point should have two anemometers separated by a minimum distance that has been reported in the previous work (Zhang et al., 2016a; Xiong and Liang, 2016). Over the embankment, the velocity accelerates considerably, particularly in the near ridge and track bed region. With the increase in embankment heights, the position of the maximum wind speed above the embankment tends to move toward the WWS. At the same embankment height with double railway lines, the speed-up effect of the WWL is more significant than that of the LWL, below a standard sized train height from the track bed. Finally, formulas were established to relate the monitoring point positions with embankment height and the key velocities upstream and above the embankment, as a guide for establishing rules of high-speed train operations. Since the layout of anemometers is important for the running train and there are some differences of flow characteristics around the railway embankments when using two different wind profiles, i.e., the uniform velocity profile and the power law velocity profile, in the next work a detailed comparison will be conducted. The effect of different wind speeds will also be taken into consideration for studying the flow structures and layout of anemometers.

Table 4 Upstream distances of proposed monitoring points from point “r" and point “m" along the x axis. From point “r"

h/m

1 3 5

From point “m"

Xd-4.5 m/m

Xd-10 m/m

Xd-4.5 m/m

Xd-10 m/m

6.46 7.14 8.26

12.52 10.23 8.24

7.96 11.64 15.76

14.02 14.73 15.74

Table 5 Wind speeds at different positions. h/m

Uxy-d-4.5 m/(m/s)

Uxy-d-10 m/(m/s)

Uxy-pole-n/(m/s)

Uxy-pole-p/(m/s)

1 3 5

19.78 19.60 19.56

19.96 19.72 19.58

20.74 22.36 23.77

21.18 22.91 24.06

Table 6 Velocity magnitude ratio at different positions. h/ m

Uin/Uxy-

Uin/Uxy-

Uin/Uxy-

d-10m

pole-n

Uxy-pole-n/ Uxy-d-4.5m

Uin/Uxy-

d-4.5m

pole-p

Uxy-pole-p/ Uxy-d-4.5m

1 3 5

1.011 1.020 1.022

1.002 1.014 1.021

0.964 0.894 0.841

1.049 1.141 1.216

0.944 0.873 0.831

1.071 1.169 1.231

Uxy-pole-n (0.0418 h þ 1.01) Uxy-d-4.5m

(17)

Uxy-pole-p (0.04h þ 1.04) Uxy-d-4.5m

(18)

Generally, for the new SWEWS along railway lines, Uxy-d from the anemometers that are in the upstream of the embankment with a wideopen area can be used to monitor the wind speed along the railways, and according to the formula the velocity of the incoming flow Uin and the Uxy-pole can be deduced. On the other hand, it is better that the anemometers can be installed in the upstream and above the ridge of the embankment, i.e., on the electrification masts along the railway lines, which gives an accurate wind speed measurement above the railways. The above formulas, derived through regression of the simulation results, may be used as a reference when choosing upstream monitoring positions along railway lines with embankments of different heights, within the explored range.

Funding The research described in this paper was supported by the China Scholarship Council, the National key R & D program of China (Grant No. 2016YFB1200506-03) and the National Natural Science Foundation of China (Grant Nos. U1534210 and 51605044).

4. Conclusions

Acknowledgements

This work studied the flow field around railway embankments, based on improved delayed detached eddy simulation (IDDES), which is a 3-D time-dependent numerical simulation method. A grid-independent

The authors acknowledge the computing resources provided by the Department of Mechanical and Aerospace Engineering of Monash 13

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Journal of Wind Engineering & Industrial Aerodynamics 193 (2019) 103968

University, Australia and the High-speed Train Research Center of Central South University, China.

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