Numerical study of the influence of synthetic turbulent inflow conditions on the aerodynamics of a train

Journal of Fluids and Structures 56 (2015) 134–151

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Numerical study of the influence of synthetic turbulent inflow conditions on the aerodynamics of a train J. García n, J. Muñoz-Paniagua, A. Jiménez, E. Migoya, A. Crespo Dpto. Ingeniería Energética, Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, C/ José Gutiérrez Abascal 2, 28006 Madrid, Spain

a r t i c l e in f o

abstract

Article history: Received 12 January 2015 Accepted 4 May 2015

The necessity of a more complete definition of the turbulent wind acting on a train is studied in this paper using computational fluid dynamics (CFD). A stochastic approach for the modeling of turbulent winds is proposed here. Synthetic winds are defined based on two different spectral models, namely the Kaimal spectrum and the Kraichnan spectrum. These are generated using Turbsim and ANSYS
FLUENT software, respectively. To complete the comparison, a third oncoming wind definition is considered, corresponding to a uniform (low-turbulence) wind. Large-Eddy Simulation (LES) and Scale-Adaptive Simulation (SAS) turbulence models have been used for the numerical simulation. Comparison is made of the average, standard deviations and extreme values of the loads calculated with the different methods. The corresponding flow fields are also studied and compared. The transient behavior is analyzed using the spectra of the velocity and loads, and the aerodynamic admittance curves. The results obtained for the last inlet condition are in good agreement with previous studies, while the importance of the spectral model choice is evidenced in the analysis of the velocity and force spectra, as well as in the aerodynamic admittance curves. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Synthetic turbulent wind Train aerodynamics Side-wind LES SAS Aerodynamic admittance

1. Introduction Operational safety of high-speed trains has been investigated assuming steady uniform cross-winds, attracting much attention from researchers (Diedrichs, 2008; Cheli et al., 2010; Hemida and Baker, 2010; Choi et al., 2014), as well as in road vehicles (Guilmineau et al., 2011). However, in windy conditions, the natural atmospheric wind can exhibit strong lateral gusts. Indeed, the wind in the atmospheric boundary layer is known to be distinctively turbulent and non-stationary. Thus, for a more precise evaluation of the cross-wind stability, unsteady turbulent oncoming wind should be considered. Furthermore, it has been observed that there can be substantial differences between the aerodynamic data obtained from steady and unsteady cases, so that the interest of an analysis considering unsteady inlet conditions is evident. Two approaches have been developed for the modeling of turbulent winds, namely deterministic and stochastic approaches. The former tackles the natural wind by means of an equivalent ideal wind gust that can adopt different shapes. These are the exponential shape (Larsen et al., 2003; TSI, 2008), the ‘1-cos’ shape (Carrarini, 2006), the ramp function (Lippert, 1999), a combination of a damping, a saturation and a sinusoidal function (Krajnovic, 2008), or the most commonly

n

Corresponding author. Tel.: þ34 1 3364156. E-mail address: [email protected] (J. García).

http://dx.doi.org/10.1016/j.jfluidstructs.2015.05.002 0889-9746/& 2015 Elsevier Ltd. All rights reserved.

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applied ‘Chinese hat’ (Proppe and Wetzel, 2010; TSI, 2008). The stochastic approach involves a description of the turbulent wind by its power spectrum density, so that the uncertainty and variability of the natural wind is somehow taken into account. Experimentally, this approach has been applied for high-speed trains (HST) by Baker et al. (2004), Quinn et al. (2007), Sterling et al. (2009) and Tomasini and Cheli (2013); analytically (Cooper, 1984; Yu et al., 2014); and numerically (Baker, 2010). However, there is no reference where the stochastic approach is considered in a computational fluid dynamic (CFD) study concerning HST. Large-eddy simulation (LES) has been used for transient simulations of HST (Hemida and Krajnovic, 2010), and here we use this method for the study of the train stability under a stochastic description of the oncoming cross-wind. The turbulent inflow problem, i.e. how to generate an artificial turbulent inflow condition for numerical simulations, has been faced considering a large variety of strategies. These may introduce different degrees of computational cost, and a review is given in the paper of Jarrin et al. (2006). More recent approaches rely on the fact that coherent structures embedded within the flow play a dominant role in the spatio-temporal dynamics of turbulent flows (Druault et al., 2004; Perret et al., 2008), where the generation of turbulent inflow boundary conditions is based on the use of an experimental database. Considering also a given reference turbulent flow, Hoepffner et al. (2011) have proposed a technique to produce a random field with exactly the same two-point two-time covariance as the reference one. Nevertheless, because of its relative simplicity, synthetic methods have reached a significant popularity. Kondo et al. (1997) create time series of velocity fluctuations by performing an inverse Fourier transform for prescribed spectral densities, where their phase is drawn randomly. The digital filtering technique is applied by Klein et al. (2003) and Xie and Castro (2008) for the superimposition of fluctuations, while Mathley et al. (2006) add perturbations from a 2D vortex method to a specified mean velocity profile. Based on the work of Kraichnan (1970), in the paper of Smirnov et al. (2001) a non-homogeneous turbulent flow field is obtained from simplified variants of a spectral method. The spectral synthesizer, implemented in ANSYS
FLUENT (ANSYS, 2013), is based on Smirnov's contribution. It involves scaling by some turbulent variables and applying orthogonal transformation operations to a continuous flow field generated by a superposition of harmonic functions, where the number of modes is limited to reduce the computational cost. Whereas the algorithm is relatively simple, the spectral density of the generated turbulent flow field only follows Gaussian's spectral model (Huang et al., 2010), so the energy in the inertial subrange and the dissipation subrange are too small compared to what is observed in real wind conditions. In contrast, other spectral models, like the von Karman (1948) or Kaimal et al. (1972) ones, do cover both the energy-containing and the inertial subrange. This characteristic is critical to ensure accurate LES for evaluation of wind effects on ground vehicles, as it is pointed out by Huang et al. (2010). Consequently, we compare the results obtained from the application of the spectral synthesizer with those considering the Kaimal spectral model. The latter has been simulated using the TurbSim (Jonkman, 2009) code, which is widely used in wind energy engineering. To complete the comparison, simulations have also been run with a uniform (low-turbulence) oncoming wind using the Scale-Adaptive Simulation (SAS) (Menter and Egorov, 2010) turbulence model. The motivation of using this turbulence model is based on previous works of the authors.

1.1. The scope of the study

 Transient and wind gusts simulations are not exactly novel, but to our knowledge, this is the first CFD study considering







not a single ideal gust but a full turbulent cross-wind acting on a train. The complexity of experimentally setting a controlled fully turbulent cross-wind test emphasizes the interest of the numerical alternative. A description of the method, its requirements and capabilities are included. Three different scenarios are compared in the paper. These are a uniform oncoming cross-wind and two stochastic winds, namely a Gaussian-based and the Kaimal spectral model, covering in this paper the simplest and the most realistic approaches. The former and the Gaussian-based case correspond to a uniform mean wind profile, while in the Kaimal-based case a non-uniform mean wind profile, following a logarithmic law, is considered. The turbulence intensity is also varied in these three scenarios. In all the cases, the train is at rest, subjected to a synthetic turbulent wind at a 301 yaw angle. Substantial differences between the aerodynamic data obtained from steady and unsteady cases have been observed in other cases (Krajnovic et al., 2012), and one objective of the paper is to estimate and analyze these differences. Averaged aerodynamic quantities (mean, extreme values and the standard deviation of force and moments coefficients as well as pressure distributions) are used for this comparison, while the transient behavior is analyzed by the velocity and forces spectra, and the aerodynamic admittance curves. SAS and LES are used in this work for the transient simulation of the stated problem. For the validation of our simulations, results are compared with the experimental data given in the work of Wu (2004). While LES have been extensively used in train aerodynamics, SAS has not yet been applied for this particular problem, so it is encouraging the industrial interest it might cause.

2. Numerical method A detailed description of the flow structures around a train subjected to a 301 cross-wind is given by Chiu and Squire (1992) and Hemida and Krajnovic (2009). Capturing the vortex shedding in flows around trains requires simulation methods

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that resolve rather than model the small turbulent scales, so unsteady CFD methods are demanded. A review of transient numerical simulations for train aerodynamics is given by Krajnovic (2014). Among the different available approaches, SAS and LES are used in this paper. The former is considered as a second-generation Unsteady Reynolds-Averaged Navier–Stokes (URANS) model which results in a LES-like behavior in unsteady regions of the flow field, while the latter is already well known in the scientific community. A more detailed description of both is given below. 2.1. Scale-adaptive simulation (SAS) Based on the work of Rotta (1972), Menter and Egorov (2010) propose the Scale-Adaptive Simulation (SAS) model as a new alternative to modernize the kL-equation of Rotta. The SAS technique is considered as a new URANS turbulence model but, instead of just capturing large-scale flow structures while filtering out the small-scale turbulence eddies, the model is capable to resolve the turbulent spectrum in unstable flow conditions (ANSYS, 2013). The SST-SAS model is implemented in ANSYS
FLUENT as it is developed from the original k–ω SST turbulence model. The difference from the latter is the introduction of an additional source term QSAS in the transport equation for the specific dissipation rate ω, defined as "
2 L Q SAS ¼ ρmax 0; ξ2 κ S2 LvK
# 2 1 ∂ω ∂ω 1 ∂k ∂k
C c k max ; ð1Þ σϕ ω2 ∂xj ∂xj k2 ∂xj ∂xj where ξ2 ¼3.51, κ ¼0.41, Cc ¼2, σ ϕ ¼ 23 , and denoting ρ, ω and k the fluid density, the specific dissipation rate and the   turbulent kinetic energy, respectively. S is a scalar invariant of the rate-of-strain tensor S ¼ 12 ∇ðuÞ þ∇T ðuÞ , given as pffiffiffi 1=4 pffiffiffiffiffiffiffiffiffiffiffiffiffi S ¼ 2Sij Sij . The turbulent length scale is defined as L ¼ k=ðcμ ωÞ, with cμ ¼ 0:09, and LvK stands for the von Karman length. It is the information provided by the von Karman length that allows the SAS model to dynamically adjust to resolved structures in a URANS simulation. Indeed, the SAS term switches itself on when the ratio of the modeled turbulent length scale L to the von Karman length scale increases (Davidson, 2006). Thus, when the flow equations resolve unsteadiness, the SAS term detects the unsteadiness and leads to an increase of the production of ω and hence a decrease of the turbulent viscosity, which results in a LES-like behavior in unsteady regions of the flow field. In the implementation of the model in ANSYS
FLUENT 15.0, the explicit calibration of high wave number damping is provided by means of the limitation of the von Karman length, which is defined as 2 3 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u κξ 6 κS 7 u 6 7 2 LvK ¼ max6 ″ ; C SAS ð2Þ 7 s Δu
t β 4jU j 5
α cμ with the grid size Δ calculated as the cubic root of the control volume size Δ ¼ ðΔx Δy Δz Þ1=3 , with Δi being the local computational cell size in the i-Cartesian coordinate. U ″ refers to the second velocity derivative ∂2 u=∂y2 , β and α parameters SAS are set as default, with values of 0.09 and 1, respectively, while Cs ¼0.11 2.2. Large-eddy simulation (LES) The filtered continuity and momentum equations read ∇  u ¼ 0;

ð3Þ

∂u 1 þ ðu  ∇Þu ¼
∇p þ ν∇2 u
∇  τ; ∂t ρ

ð4Þ

with u being the filtered velocity vector, p the filtered pressure field, and ρ and ν the fluid density and kinematic viscosity, respectively. This filtering is based on the filter width determined by the grid size. Thus, the smallest scales (sub-grid scales) are modeled by means of the sub-grid stress tensor τ relating them to the local gradients of the resolved velocities via a subgrid scale eddy viscosity νsgs:

τ ¼
2νsgs S þ 13 ðτ: IÞI;

ð5Þ   where S ¼ 12 ∇ðu Þ þ ∇T ðu Þ is the filtered rate-of-strain tensor. The sub-grid scale eddy viscosity is defined as νsgs ¼ L2 jSj, where L is computed as L ¼ min½κ d; C LES s Δ

ð6Þ

¼ 0:1 (Krajnovic et al., 2012), and the with κ ¼ 0.41 being the von Karman constant, d the distance to the closest wall, C LES s filter width defined as Δ ¼ ðΔx Δy Δz Þ1=3 with Δi being the local computational cell size in the i-Cartesian coordinate.

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Fig. 1. Dimensions of the train model considered in this paper.

Fig. 2. (a) Computational domain and (b) details of mesh close to the train surface to capture the boundary layer. The coordinate system denoted with an acute superscript (x0 , y0 , z0 ) is aligned with the free-stream direction, while the coordinate system denoted as (x,y,z) is yawed 301 to the free-stream direction and consequently aligned with the train direction.

3. Numerical set-up and boundary conditions The train geometry considered in this paper is a smooth, simplified model of the leading control unit of the ICE 2 train (class 808) of Deutsche Bahn AG, and is known as Aerodynamic Train Model (ATM). This geometry is widely accepted among the train aerodynamics community as a reference geometry. Similar to the wind tunnel experiments described in the work of Wu (2004) and the LES study from Hemida and Krajnovic (2009), the model is a scale 1:10 version of the actual train, so the total length of the numerical train model is L¼ 3.552 m, and the train height is H ¼0.358 m. Details like bogies, pantograph, spoiler or the pillar supports used in the experimental set-up are removed, as well as the inter-car gap. A endcar dummy identical to the nose is considered. The resulting model is presented in Fig. 1. The computational domain is an hexahedral box inside which the model is arranged as indicated in Fig 2. The domain has an extension of 55H in the stream-wise direction, a width of 45H and the height reads 5H. The train is yawed 301 to the freestream direction, and is placed 5H downstream of the inlet boundary. The ground clearance is set to 0.15H. The influence of the computational domain size has been analyzed in terms of pressure field, and the results are given in Fig. 3(a), where the perturbation of the pressure field because of the train and the lateral walls is observed, and how once the width and length of the domain are increased this perturbation is attenuated. No-slip condition is used at the train surface and the ground, while uniform ambient pressure is imposed at the top and lateral walls of the domain, as well as the outlet. Among the three inlet conditions considered in this paper, two different approaches are adopted to simulate a realistic atmospheric wind as similar as possible to an unsteady wind experienced by a train. The first of these two approaches is one of the algorithms available in ANSYS
FLUENT to model the fluctuating velocity at velocity inlet boundaries, namely the spectral synthesizer (ANSYS, 2013). This is based on a random flow generation technique, originally proposed by Kraichnan (1970) and modified by Smirnov et al. (2001). The second approach is to generate a synthetic wind using the Turbsim code (Jonkman, 2009). TurbSim is a stochastic inflow turbulence code developed at the National Renewable Energy Laboratory (NREL). The third inlet condition corresponds to a uniform (lowturbulence) oncoming wind. A more detailed description of the resulting velocity profiles is given below. It is important to remark that, as it can be observed in Fig. 2(a), two frames of reference are used in this paper. It is denoted with an acute superscript (x0 ; y0 ; z0 ) the coordinate system aligned to the computational domain (i.e. x0 corresponds to the stream-wise direction), while a second coordinate system (x, y, z) rotated 301 in the z-direction is used for the train loads definition (i.e x0 corresponds to the train longitudinal direction). In the following, the acute superscript is used for the inflow velocity profile definition. 3.1. Numerical details As it is said previously, the results of the present calculations are obtained with the commercial code ANSYS
Fluent. The SIMPLE method is used for solving the pressure–velocity coupling. The spatial discretization schemes are second order for the pressure equation and bounded central difference for the momentum equation. A bounded second order implicit scheme is chosen for the transient terms. Several meshes were tested to check the grid independency. The final mesh was an hexcore-type mesh generated with 20 prism layers around the model, with a growth rate of 1.15, and 35  106 cells. The mean n þ ¼ un n=ν, where un is the wall friction velocity and ν is the kinematic viscosity of air (ν ¼ 1.45  10
5 m2 s
1) and n

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Fig. 3. Independency analysis on the computational domain size and on the time step. In (a) the total pressure field at two different computational domain sizes is compared, showing how in the second case, once the width and the length of the domain are increased, the perturbation of the pressure field at the lateral walls is attenuated. Pressure is given in Pa. Note that, for the sake of aesthetics, the scale of the two computational domains is different so that the figures width is the same. In (b) the CFL number at the domain is given.

stands for the distance from the center of the first cell to the nearest wall, was 1.1 and the maximum n þ was 2.0. A fixed time step of 10
4 s was used for the time integration which gives a mean CFL value of 1. Fig. 3(b) is included here to show this distribution. 3.2. Smirnov-based turbulent wind As it has been mentioned before, the fluctuating velocity components are generated in ANSYS
FLUENT with the spectral synthesizer method (ANSYS, 2013). This method uses the random flow generation technique proposed by Smirnov et al. (2001). Not too much information about how the method is implemented in the software is given. Basically, on the basis of the work of Kraichnan (1970), the algorithm is developed from a variant of spectral method for generation of an isotropic continuous flow field with the target turbulence length and time scales defined in advance. The flow field is generated using the modified method of Kraichnan (1970): rffiffiffiffi N 2 X u~ i ðx0 ; y0 ; z0 ; t Þ ¼ Nn¼1 

 n xj n xj t t pni cos k~ j þ ωn þqni sin k~ j þ ωn ; ð7Þ l τ l τ n n where l and τ are the length and time-scales of turbulence, respectively, N refers to the spectral sample size, k~ j ¼ kj l=τcðjÞ , n n n n n n n n pi ¼ ϵijm ζ j km and qi ¼ ϵijm ξj km with ζi and ξi following a Normal distribution with mean 0 and standard deviation 1, ϵijk is n the permutation tensor used in vector product operation, and numbers kj and ωn, respectively, represent a sample of n

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139

wave-number vectors and frequencies of the modeled turbulent kinetic energy spectrum:
1=2

2 4 2 k exp
2k : EðkÞ ¼ 16

ð8Þ

π

Final fluctuating flow field is obtained by applying a scaling and orthogonal transformation to the flow field u~ i : ui ¼ aik cðkÞ u~ k ;

ð9Þ

where aik stands for an orthogonal transformation tensor that would diagonalize a given anisotropic velocity correlation tensor bij as ami anj bij ¼ δmn c2ðnÞ ;

aik akj ¼ dij :

ð10Þ

The outcome of the procedure is to produce a time-dependent flow field ui ðxj ; tÞ with correlation functions bij ¼ ui uj , and turbulence length and time scales l and τ, respectively. The average resulting velocity is uniform and has a value of U ¼ 70 m s
1 . The model is isotropic with a characteristic length Li ¼ 5.84 m, and a standard deviation of the velocity of 8.4 m s
1. Table 1 summarizes the most characteristic parameters of the resulting velocity profile. A realization of the resulting velocity profile is shown in Fig. 5, where the longitudinal and vertical fluctuations of the velocity are observed. The method offers a relatively inexpensive way to generate random velocity fluctuations, giving a more realistic representation of turbulence than that obtained with a simple Gaussian velocity distribution using a random-number generator (Smirnov et al., 2001). Nevertheless, the Gaussian nature of the considered spectrum is reflected in the spectral density of the generated turbulent flow field, and therefore the energy in the inertial subrange and the dissipation subrange may be neglected in the turbulent flow field obtained from Smirnov's method (Huang et al., 2010). Consequently, in our paper an alternative spectral model is considered. It is interesting to remark that, because of the Gaussian nature of the resulting spectrum, in the following Smirnov-based or Gaussian-based might be used indistinctively. 3.3. Turbsim turbulent wind A synthetic wind that varies both in time and space is generated in Turbsim v.1.50 (Jonkman, 2009). The input data used to simulate the synthetic wind involves the spectral model, stability conditions and ground surface roughness length. Among the different models that shape the spectrum density in wind engineering, the Kaimal spectral model is chosen in this paper (Kaimal et al., 1972). This model fits better to empirical observations in atmospheric turbulence, and gives better approach than von Karman model (von Karman, 1948), at lower levels than 150 m (Burton et al., 2001). Kaimal spectrum density is described in the following equation: Si ðf Þ ¼

4σ 2i Li =U h ð1 þ 6fLi =U h Þ5=3

;

ð11Þ

where the subscript i refers to each of the three components of the velocity field. U h represents the mean wind speed at a characteristic height h, while Li and σi are the integral length scale and the velocity standard deviation for each cartesian coordinate i, respectively. The cycling frequency is denoted as f. A more detailed description of the meaning of the parameters of Eq. (11) is given by Kaimal et al. (1972). It is important to remark that the turbulent wind is generated in Turbsim at full-scale so, as a scaled train model is used in the simulation in ANSYS
FLUENT, for similarity, to have equal Reynolds number in our simulations and considering in both cases air, the length-scale factor is 1:10 and the time-scale factor is 1:100, so that velocities obtained in Turbsim are multiplied by 10. In the following, data correspond to the scaled case. The value of h is 1.03 m, due to the original purpose of TurbSim related to wind engineering (Jonkman, 2009). Considering a logarithmic velocity profile, given as
 z ln z0 0 u ¼ U h
; ð12Þ h ln z0 where U h is chosen for the velocity of the wind at the train centroid height to be u0 ðH=2Þ ¼ U ¼ 70 m s
1 , where z0 is the ground surface roughness length. For a better validation of our simulations, and a comparison with the experimental data, z0 ¼0.002 m (in full scale, z0 ¼0.02 m, it corresponds to a open flat terrain, Holmes, 2001). The integral length scale Li is Table 1 Integral length scale and velocity standard deviation for each cartesian coordinate i. Lengths are given in m, while the velocity standard deviation in m s
1. Lu0

Lv0

Lw0

σ u0

σ v0

σ w0

5.84

5.84

5.84

8.4

8.4

8.4

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J. García et al. / Journal of Fluids and Structures 56 (2015) 134–151

function (different for each velocity component) of the turbulence scale parameter λu0 , which depends on the characteristic height h (Jonkman, 2009). Meanwhile, σ v0 and σ w0 are given as a function of the standard deviation for the streamwise velocity component σ u0 . The scaled resulting values of Li and σi are given in Table 2. The coherence function, which describes how turbulence is correlated as a function of spatial separation, mean wind speed and frequency, is given as 0 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 u
2
 u fr r ij 2 C ij B Cohfijg ¼ exp@
12t ð13Þ þ 0:12 A Lu0 Uh with rij being the distance between two points i and j, and Lu0 the coherence scale parameter for the mean wind direction. Once the spectra of the velocity components and spatial coherence are defined in the frequency domain, an inverse Fourier transform produces time series. A modified version of the Sandia method (Veers, 1988) is used to generate time series based on spectral representation. The underlying theory behind this method of simulating time series assumes a stationary process. A realization of the resulting velocity profile is shown in Fig. 5, where the longitudinal and vertical fluctuations of the velocity are observed. 3.4. Uniform turbulent wind Finally, a third scenario is considered in this paper. This is the simplest one, and correspond to a uniform turbulent wind. It is known that in spatially evolving flows, the choice of the inlet boundary condition is found to be critical for a successful simulation. Nevertheless, the use of simple stationary inflow conditions can still result in accurate simulations (Hemida and Krajnovic, 2009, 2010), and this is applied also in this paper. The turbulent intensity is limited to 0.3% and a uniform velocity profile is considered. The averaged profile coincides with the Smirnov-based case, as presented in Fig. 5. 3.5. Wind simulation In order to predict wind loads on ground vehicles, when LES is employed, the primary task would be to generate a proper turbulent inlet condition. In Fig. 4 the resulting turbulent wind from the two different stochastic approaches is analyzed, namely the one generated by the spectral synthesizer or Smirnov-based and the one generated in Turbsim or Kaimal-based approach. A comparison of the simulated oncoming wind and the corresponding theoretical or target models given in Eqs. (8) and (11) is also drawn in Fig. 4. For Eq. (8), a factor of 23 is used to transform the kinetic energy spectra into the power density spectra, while k ¼ 2fLi =U is applied to obtain the spectra as a function of frequency f, as done in the paper of Huang Table 2 Integral length scale and velocity standard deviation for each cartesian coordinate i. Lengths are given in m, while the velocity standard deviation in m s
1. Lu0

Lv0

Lw0

σ u0

σ v0

σ w0

5.84

1.93

0.47

14.35

11.48

7.18

Fig. 4. Comparison of velocity spectra obtained considering the Smirnov-based velocity spectrum (a) and the Kaimal-based velocity spectrum (b) as inlet condition. The three velocity components are given for each case, and they are compared with the corresponding theoretical target spectrum.

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et al. (2010). The three velocity components are represented, showing that in the Smirnov-based case an isotropic turbulent wind is obtained while an anisotropic turbulent wind is generated in Turbsim for the Kaimal-based case. The anisotropic behavior of the Kaimal-based spectrum is observed as the turbulence lengths and standard deviations used in Fig. 4(b) for the normalization in the three directions are different, as given in Table 2. The spectrum of the simulated series fits well with the target spectrum in the three principal directions; indicating that the anisotropy of the spectra is well represented by the proposed method. On the other hand, for the Gaussian model, the turbulence is isotropic and the turbulent length and standard deviations are equal for the three directions (see Table 1). The simulated turbulent wind matches the target model for the two approaches, confirming the validity of the wind generation. The differences between the two stochastic approaches are evident. In Fig. 4(a), the turbulent flow field, generated by the spectral synthesizer implemented in ANSYS
FLUENT, follows a Gaussian distribution, whereas in Fig. 4(b) a very accurate representation of the Kaimal spectrum is given from Turbsim. The spectral synthesizer is based on the work of Smirnov et al. (2001), who proposed a modified version of the basic model of Kraichnan (1970), origin of the Gaussian nature. Huang et al. (2010) point out that the Gaussian model was initially designed to approximate the energy-containing sub-range of turbulence only. Therefore, it may not capture satisfactorily the inertial and dissipation sub-ranges. Indeed, this is noted in Fig. 4(a), where the Smirnov-based spectrum, for any velocity component, has a roll-off in the inertial subrange compared with the Kaimal-based obtained from Turbsim. This rapid decay is expected to have a significant effect on the admittance curve, as it will be examined in Section 4.4. Nevertheless, we estimate opportune to remark that the simplicity and computational economy of generating the turbulent wind by the spectral synthesizer compared with the Turbsim is still an important factor when simulating this inlet condition. The difference lies not in the generation code but in the spectral model itself, so the choice of the spectral model will influence both time and accuracy. In Fig. 5, the average and instantaneous velocity profiles in the average incident wind direction are given. The Smirnovbased case corresponds to a uniform average incident wind, whereas in the Kaimal-based case there is a logarithmic profile for the average velocity of the form given in Eq. (12). 4. Results 4.1. Time-averaged coefficients and pressure distribution The time-averaged surface pressure distribution and the time-averaged surface shear stress are used to calculate the aerodynamic coefficients. These (force and moments) are computed with respect to the coordinate system with the origin set at the ground plane, in the middle plane of the train (distance L=2 from the nose tip) and at the longitudinal symmetry plane (Fig. 2). The free-stream velocity used for normalization is U ¼ 70 m s
1 , while the reference area is A¼0.1 m2 and the reference length is h¼0.3 m, (TSI, 2008), once considered the 1:10 model scale: Ci ¼

Fi 1 2

C mi ¼

ρU

2

A;

Fi 1 2

ρU

2

Ah;

ð14Þ

ð15Þ

where subscript i denotes each Cartesian coordinate for the frame denoted as (x,y,z) aligned with the train direction, see Fig. 2. Table 3 compiles the information obtained in the three cases considered in this paper, namely the uniform turbulent wind and the previous two stochastic approaches. In this table the average values, standard deviations and maximum

Fig. 5. Averaged (bold line) and instantaneous (dashed line) velocity profiles for the three inlet conditions considered in this paper: (a) uniform and Smirnov-based profiles (both uniform averaged velocity profile) and (b) Kaimal-based profile (logarithmic averaged velocity profile).

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Table 3 Averaged force and moment coefficients for the three oncoming turbulent wind conditions. Wind model

Cx

Cy

Avr. Uniform Smirnov-based Kaimal-based

0.065 0.113 0.085

Max. 0.088 0.448 0.394

rms 0.010 0.113 0.130

Cmx Avr. Uniform Smirnov-based Kaimal-based


2.632
3.172
3.502

Cz

Avr. 3.755 4.549 4.935

Max. 3.814 6.035 6.809

rms 0.032 0.599 0.789

Cmy Max.
2.669
4.137
4.916

rms 0.021 0.394 0.557

Avr.
2.512
3.963
3.026

Avr. 1.732 1.750 1.965

Max. 1.799 3.777 3.454

rms 0.030 0.785 0.719

Cmz Max.
2.789
9.336
5.691

rms 0.146 1.959 1.230

Avr.
11.069
10.517
10.825

Max.
11.375
16.149
15.199

rms 0.127 1.980 1.695

(absolute) values of the force and moment coefficients are presented. The maximum value corresponds to an integration period of 0.9 s (90 s in full scale). As it was expected, it is observed that the standard deviation and the maximum value for any aerodynamic coefficient are lower in the uniform case than in any stochastic one. Comparing the two stochastic approaches, the lower turbulent intensity in the x- and y-direction for the Smirnov-based case is reflected in a lower rms of Cx and Cy, while the fluctuation in Cz is larger than in the Kaimal-based one conforming to how the turbulent wind was defined, see Section 3.3. This influences the variation of Cmy as well, whereas Cmx follows the same trend as Cy. The standard deviation of the forces and moments and the maximum values follow a similar trend, except for the axial force coefficient, Cx, where the Smirnov based case gives a lower extreme load than the Kaimal case. The reason for this may be that the average load is also lower in the Kaimal case. Concerning the averaged values, it is interesting to compare the uniform and the Smirnov-based cases, as these have the same mean velocity profile although different turbulent intensities. The uniform case implies a low-turbulence wind (I u0 ¼ 0:3%) and the Smirnov-based case is a mean-turbulence case (I u0 ¼ 12%), thus the interest lies in comparing the influence of the turbulence or unsteadiness of the cross-wind. The increment observed for the Smirnov-based case in Cx and Cy is remarkable (about a 74% for the former and 21% for the latter), while negligible for Cz. Since the train is yawed 301 to the free-stream direction, the larger influence of the velocity fluctuations in the stream-wise direction in Cx than those in the span-wise direction in Cy is obvious. Nevertheless, the low value of the drag coefficient Cx should be taken into account for the discussion of the observed increment. The rolling moment Cmx is found to be one of the most important aerodynamic coefficients regarding cross-wind stability. In consequence, it is vital to stress the increase of 20% observed for this coefficient when simulating a higher turbulence. This increase is still more significant when the Kaimal-based turbulent wind is adopted, reaching a 33% larger than the uniform one. It is important to remark that the Kaimal spectrum is analog to the von Karman one, which is accepted as a wind spectrum very similar to that of natural wind, (Tomasini and Cheli, 2013). Therefore, a simulation of the natural wind as close to the reality as possible is required for the cross-wind stability. The comparison between the two stochastic approaches is not limited to the spectra they are based on, but to the turbulence intensity and the mean velocity profile as well. The latter is supposed to have an influence on the lift force coefficient Cz, where a larger value is obtained for the logarithmic velocity profile compared with the mean-uniform profile from the Smirnov-based representation. Table 3 illustrates the increase of the two most important coefficients for crosswind stability, namely Cy and Cmx when the Kaimal spectrum and a high-turbulence wind are considered as inlet condition. The effect of this on the train aerodynamics is also explained analyzing the pressure distribution along the train. The conclusions here presented include observations related to the maximum values obtained during the simulation. Nevertheless, it is worth mentioning that these maximum values depend on the integration period, and thus it may be more informative if the corresponding probability density functions are given. For this purpose, the integration period has been divided into 16 fractions, to elaborate a cumulative probability distribution of the maximum (absolute) values of all the loads during the sub-period tc ¼0.056 s (i.e. 5.625 s at full scale). It has been fitted with a Gumbel or Fisher–Tippet distribution:  ( !)  

C^
μj   ^ P C j  o C ¼ exp exp ;  βj

ð16Þ

pffiffiffi where C^ is the argument of the probability density function, with μj being the mode and β j π = 6 the standard deviation, and the subscript j stands for each of the components of the force and moment acting on the train (x, y, z, mx, my, mz), see Eqs. (14) and (15). The values of μj and βj for each load are given in Table 4. The corresponding return period for an

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Table 4 Values of μ and β parameters for each force and moment coefficient to calculate the probability of exceedance and return period of a extreme value. Cx

Uniform Smirnov-based Kaimal-based

Cy

μ

β

μ

β

0.071 0.183 0.144

0.007 0.084 0.079

3.775 4.095 4.981

0.018 0.466 0.613

Cmx

Uniform Smirnov-based Kaimal-based

Cz

Cmy

μ 1.752 2.091 2.218

β 0.016 0.566 0.574

Cmz

μ

β

μ

β

2.644 3.345 3.524

0.013 0.278 0.483

2.613 4.430 3.629

0.074 1.762 1.134

μ 11.156 11.714 11.412

β 0.080 1.458 1.348

Fig. 6. Probability density function of the maximum (absolute) value of (a) Cy and (b) Cmx fitted by a Gumbel distribution. Blue dots refer to the numerical results (in (a) from the Kaimal-based case and in (b) from the Smirnov-based case), showing the cumulative maximum (absolute) value, while red line is the Gumbel distribution, as given in Eq. (16). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

Fig. 7. Location of the measured time-averaged pressure distributions and the orientation of angle θ.

extreme load is tr ¼

1 1
PðjC j j o C^ Þ

tc :

ð17Þ

In Fig. 6, the probability density functions of maximum (absolute) value for Cy and Cmx obtained from the numerical results are compared with the analytical ones from Eq. (16). For the sake of generality, only two representative cases are plotted. Fig. 6(a) corresponds to the results obtained for the maximum (absolute) Cy from the Kaimal-based case, while Fig. 6(b) shows those for the maximum (absolute) Cmx from the Smirnov-based case. The acceptable fit of the numerical results to the Gumbel distribution is evident. The averaged surface pressure distribution (in terms of pressure coefficient) at different cross-sections (see Fig. 7) is plotted in Fig. 8 for the three inlet conditions considered in this paper and compared with the experimental data from (Wu, 2004). The latter is used for the validation of the simulation of the uniform (low-turbulence intensity) case. The objective is

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Fig. 8. Comparison of Cp at different cross-sections, see Fig. 7, obtained considering the uniform velocity profile (black), the Smirnov-based velocity spectrum (red) and the Kaimal-based velocity spectrum (blue) as inlet condition. These are compared also to experimental results from Wu (2004). (a) x=L ¼ 0:03, (b) x=L ¼ 0:07, (c) x=L ¼ 0:14, (d) x=L ¼ 0:44, (e) x=L ¼ 0:58 and (f) x=L ¼ 0:75. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

to regard the accuracy of the SAS simulation considering the uniform oncoming wind, while at the same time to confirm the differences between this inlet condition and the LES simulations with mean and high-turbulence winds. The SAS prediction is significantly correlated with the experimental data, although differences are identified in the range θ  135–2251 for some cross-sections. It is important to remark that the train model used in our simulations reproduces the geometry considered in the paper of Hemida and Krajnovic (2009), which does not take into account some geometric details included in the experimental case. These are the spoiler, the bogies and inter-car gap, as well as the support pillars. It was not possible for the authors to find any detailed reference where results for the experimental case were reported, neither any paper where the numerical simulation had reproduced exactly the experimental model. This issue has already being pointed by Diedrichs (2008), where a summary of the conclusions of four investigations with four different numerical

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145

models is given for this aerodynamic problem. Thus, we choose Hemida and Krajnovic (2009) as a reference, and consequently our results are also affected by the lack of these geometric details, in particular at the train underbody, where bigger discrepancies are obtained. This explains a better agreement with the experimental data at planes x/L ¼0.44, 0.58 and 0.75, where less influenced by spoiler or bogies. Indeed, the correlation with the experimental data validates our simulation, capturing the main flow features. In general terms, the pressure distribution for the three cases is quite similar, although notable differences are identified at the lee-ward side and more slightly at the underbody. A stronger suction peak is observed at the lee-ward side, while a second suction peak is generated close to the lower lee-ward corner at x/L ¼0.03. The intensity of these peaks is even higher at x/L ¼0.07, where the peaks are displaced upwards. Differences of the pressure distribution between the low-turbulence and the mean- and high-turbulence cases is mainly detected at x/L¼0.07 and x/L ¼0.14. These sections are place at the end of the train nose, where the vortex structures originate. While in the former a suction peak clearly appears for the Smirnovand Kaimal-based cases (i.e. mean- and high-turbulence cases, respectively), in the latter the observed trend is confusing. It is in this section where the turbulence of the oncoming wind has a larger influence on the detached structures from the train body, and consequently it is not straightforward to note a general behavior. Discrepancies between the three cases attenuate at x/L¼ 0.44, while they again are more evident at x/L ¼0.58 and x/L¼ 0.75, where a high pressure distribution is observed in the underbody. 4.2. Instantaneous flow description A short description of the main vortices detached from the train and observed in the wake region is given in this section. Among the different methods proposed for identifying coherent structures of the flow, here the Q-criterion (Hunt et al., 1988) is used. Fig. 9 presents instantaneous flow structures at the train wake for the three simulated cases. The structures are visualized by iso-surfaces of positive values of the second invariant of the velocity gradient tensor   Q ¼ 12 ‖Ω‖2
‖S‖2 ð18Þ where Ω is the rate-of-rotation tensor and S the rate-of-strain tensor. The iso-surfaces are colored by the static pressure, with Q¼1.0  10
3. In Fig. 9(a) the low-turbulence case is presented. In this case, the vortical structures shedding from the body are clearly identified. As observed by Hemida and Krajnovic (2010), numerous vortices originate on the lee-side of the upper edge of the train, and these roll up and merge with the vortex born in the lee-ward A-pillar of the train nose. This structure is attached to the vehicle for a large fraction of the train length. Meanwhile, a second vortex generated at the train nose, in this case from the lower part of the nose, rapidly detaches from the surface and is convected downstream in the wake. It is observed that this vortex interacts with a third strong vortex shed from the underbody. Several vortices are shed from the lee-ward underbody edge, and the interaction of them is detected in Fig. 9(a) by a structure growing in size at the lee-side of the train. These main vortices extend far beyond the train tail before breaking into smaller structures. Similar results are found by Wu (2004) for the upper nose vortex. While the upper vortices are strong and steady, the lower vortices are highly unsteady (Hemida and Krajnovic, 2010), and these are the responsible for the vortex shedding in the wake. When the oncoming wind has a larger turbulence, this effect is damped and unsteadiness is also observed at the upper vortices. In Fig. 9(b) and (c) a mean- and a high-turbulence wind are considered, respectively. These figures illustrate how the strong vortices mentioned before are broken not so far from their onsets. The upper vortex originated at the A-pillar of the train nose vanishes when merging with a vast number of small eddies detached from the upper lee-ward edge. It is clear that the length at which the vortex keeps steady is reduced as the turbulence intensity increases. The lower vortices are also broken immediately and small structures are convected

Fig. 9. Instantaneous flow structure around the train. Iso-surface of the instantaneous second-invariant of the velocity gradient Q ¼0.001 colored by the static pressure. (a) Uniform turbulent wind, (b) Smirnov-based turbulent wind, and (c) Kaimal-based turbulent wind. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

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Fig. 10. Pressure field and pathlines at x/L ¼ 0.14 (left) and x/L ¼ 0.75 (right) from the nose tip. Low-turbulence corresponds to the uniform case, meanturbulence to the Smirnov-based case and high-turbulence to the Kaimal-based case. (a) Low-turbulence (x=L ¼ 0:14), (b) low-turbulence (x=L ¼ 0:75), (c) mean-turbulence (x=L ¼ 0:14), (d) mean-turbulence (x=L ¼ 0:75), (e) high-turbulence (x=L ¼ 0:14), and (f) high-turbulence (x=L ¼ 0:75).

downstream. A different behavior between Fig. 9(b) and (c) is due to the different spectral models the turbulent wind is based on, as well discrepancies in the wake structures may be also attributed to the differences of spatial correlations in the turbulent flows generated by the two stochastic approaches. The pressure field at two different cross-sections from the nose tip and the pathlines around the train body are shown in Fig. 10. These are at x/L ¼0.14 and x/L¼0.75 far from the nose tip. The pressure field at the wind-ward side is notably similar in the three scenarios contemplated here, which validate the comparison of them. The stagnation point position is not significantly different, making possible a comparison of the resulting moments acting on the train. In the lee-ward side, at x/ L ¼0.14, the pressure field is nearly the same, although the position and the intensity of the vortex core are different, increasing the vortex core width with the turbulence intensity. At x/L ¼0.75, the vortex shedding from the train body and the interaction of these structures with the oncoming turbulent wind are more evident. In consequence, as the turbulence intensity is different in the three cases, the wake flow is not similar anymore. As it is illustrated in Fig. 9, the vortices detached from the train nose and along the train body are more intense and better defined that in the mean- and highturbulence cases, where smaller structures are captured.

4.3. Force and moments spectra Useful information can be obtained from a spectral analysis of the forces and moments acting on the train. Fig. 11 gives n the normalized spectra of all the loads as a function of the non-dimensional frequency f ¼ fL=U , where L is the train length
1 and U is adopted as 70 m s for both the Smirnov-based and the Kaimal-based case. Loads are referred to the (x,y,z)-axis, along and across the train, respectively, see Fig. 2. The spectra of the loads have been made non-dimensional with the frequency and their respective standard deviations, given previously in Table 3. The non-dimensional frequency range is

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147

(a)

Fig. 11. Comparison of forces and moments spectra obtained considering the Smirnov-based velocity spectrum (red) and the Kaimal-based velocity spectrum (blue) as inlet condition. (a) Cx, (b) Cmx, (c) Cy, (d) Cmy, (e) Cz, and (f) Cmz. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

defined from 0.1 to 10, because harmonics whose period is larger than 1/10 or shorter than 10 times the integration time are not correctly simulated by the numerical computation. In all the cases represented in Fig. 11, the spectra decrease for non-dimensional frequencies larger than one. This decrease is more than a tenth of their value at lower frequencies and about two orders of magnitude lower than the maximum value observed at frequencies of 0.6–1.0. This behavior is expected, since at higher frequencies the smaller

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turbulent eddies have shorter wavelengths and thus have a more rapid loss of coherence than for the larger eddies (Bouferrouk, 2013). The maximum value of the force (or moment) spectrum is observed at the vortex shedding frequency induced by the train body. This frequency range is in good agreement with that obtained by Hemida and Krajnovic (2010) taking into account that the normalization is done with the train height and not with the length as in this paper. A similar decrease is observed in all the cases, with a slightly lower slope for the drag and the rolling moment (Cx and Cmx, respectively). It is interesting to remark that, although two different turbulent spectra have been considered, with significant discrepancies between them, the force spectra are similar in both the Smirnov- and the Kaimal-based case, especially at higher frequencies. This behavior has also been noted by Huang et al. (2010) where the comparison between the Smirnov and the von Karman spectra is performed. In Fig. 11, it can be observed that it is at low frequencies, up to one, where differences are more evident. The spectra of the two horizontal forces, (drag and side forces) and of their associated moments (rolling and yaw moment, Cmx and Cmz, respectively) when calculated with the uniform velocity profile (Smirnovbased case) are lesser than those calculated with the logarithmic model for non-dimensional frequencies smaller than 0.5. As the total area under the spectrum curves has to be one, the opposite behavior is observed for non-dimensional frequencies larger than 0.5. This behavior may be due to the larger coherence of the incident wind in the uniform case. Although in both cases, uniform and logarithmic, the length scale for the velocity in the wind direction is the same, Lu0 , the length scale for the other component of the wind velocity, Lv0 , is larger in the uniform case, see Tables 1 and 2, and when projected in coordinates along and across the train, both horizontal velocity components are somewhat correlated with Lv0 . This behavior is not observed for the lift force and the pitch moment, where the spectra calculated with both model are very similar. 4.4. Aerodynamic admittance This section is concerned with evaluating the aerodynamic admittances obtained when considering the two different stochastic turbulent winds as the inlet condition. The admittance function used in this paper is the one proposed by Cooper (1984), Baker (2010) or Tomasini and Cheli (2013), and it is defined as the ratio of the force or moment spectrum to the velocity spectrum of the oncoming wind, normalized conveniently: !2 SC F C F ðf Þ 1 U jX F ðf Þj2 ¼ ; ð19Þ Suu ðf Þ 4 CF where C F is any of the non-dimensional force or moment acting on the train. The main difference with the previously mentioned references is that in this case the oncoming turbulent wind is not a cross-wind at 901 incidence but at a 301 yaw angle, considering the train at rest. Eq. (19) is based on a first-order version of the quasi-steady theory where the second-order terms are neglected. The quasi-steady theory makes the simple but inaccurate assumption that the train responds to the atmospheric turbulence as if they were steady changes of mean wind speed and direction, so that the fluctuations of force correspond exactly with the variations of the incident wind (Thomas, 1996). However, the presence of a bluff body in the flow regime results into a modification of the frequency characteristics of the upstream flow. Indeed, the train induces a filtering of the high frequency energy present in the oncoming wind as the dimensions of the vehicle are greater than the small eddies in the wind (Quinn et al., 2007). Besides, the quasi-steady approach assumes the train induced force fluctuations as a result of the turbulence in the approaching wind (Sterling et al., 2009) and neglects the influence of flow separation and vortex shedding. Furthermore, when no full spatial correlation is observed in the oncoming turbulent wind over the entire exposed area of the train, the quasi-steady theory needs to be corrected (Baker, 2010). These features are the base for the introduction of the aerodynamic admittance concept. Fig. 12(a) and (b) shows the drag and side force aerodynamic admittance functions, respectively, obtained for the Smirnov-based case and the Kaimal-based case. The aerodynamic admittance is plotted as a function of the nonn dimensional frequency f ¼ fL=U , where L is the train length and U is adopted as 70 m s
1 for both cases previously defined. In Fig. 12(a), at low frequencies the admittance is greater than unity for both inlet conditions, while only the admittance curve corresponding to the Smirnov-based case is greater than unity in Fig. 12(b), where it is observed that the Kaimal-based curve tends to unity although there is an irregular behavior because of the shortness of total integration period. This is the expected behavior, i.e. the curve should be expected to tend to unity at low frequencies since the large scale fluctuations in the wind directly affect the train aerodynamic forces, but in the works of Quinn et al. (2007) and Sterling et al. (2009), where an analysis of the yaw-angle influence is presented, the same behavior for small yaw angles (up to 301) has also been presented. Sterling et al. (2009) give several reasons why the admittance curve might be different from unity at low frequencies are pointed out. Among these, the train induced vortex shedding and the force fluctuations caused by lateral and vertical turbulence fluctuations would explain the larger value of the admittance in Fig. 12(a). Nevertheless, concerning the Smirnov-based curves, an extra explanation is given to the increase of the admittance function at both low and high frequencies. As the admittance function is defined as the ratio of the force or moment spectrum to the velocity spectrum of the oncoming wind, the definition of the latter is evidenced in the admittance function. Indeed, in Fig. 4 and in virtue of Eq. (8), it is observed that the Smirnov-based case results into a Gaussian model with a rapid decay at the inertial subrange.

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Fig. 12. Comparison of aerodynamic admittance curves for (a) Cx and (b) Cy considering the Smirnov-based velocity spectrum (red) and the Kaimal-based velocity spectrum (blue) as inlet condition. (a) Cx and (b) Cy. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

Consequently, this is translated into a sharp increase of the admittance function at this range. That Gaussian shape is also reflected at low frequencies in the admittance function. For non-dimensional frequencies smaller than 0.2 and larger than 3, the corresponding spectrum is smaller than 10
6, thus the admittance function losses its physical significance out of this range. This explains the larger values of the admittance at low frequencies and why the curve is removed out of the range in Fig. 12. This observation is important if the spectral model considered for the generation of the turbulent wind is not the Kaimal model or any analog (von Karman spectrum) since confusing conclusions might be obtained when regarding the admittance function. At higher frequencies, the smaller turbulent eddies have shorter wavelengths and thus have a more rapid loss of coherence than for the larger eddies (Bouferrouk, 2013). Consequently, a decrease of the admittance function at high frequencies is observed in Fig. 12(a) and (b). Such decrease is about three orders of magnitude compared to the value at low frequencies for the drag while one order for the side force. The admittance decreases more rapidly in the drag aerodynamic admittance function than the side force one.

5. Conclusions The effect that atmospheric turbulence can exert on cross-wind vehicle aerodynamics has long been recognized, and here a more precise definition of the turbulent wind acting on a train is adopted using computational fluid dynamics (CFD). The influence of synthetic turbulent inflow conditions on the aerodynamics of a train has been studied, considering three approaches that are compared in terms of several parameters. The three inlet conditions cover the simplest and the most realistic approaches, namely a uniform (low-turbulence) mean wind profile, a stochastic Gaussian (based on Kraichnan spectrum) definition of the atmospheric wind with a uniform mean wind profile, and a stochastic Kaimal-based definition with a non-uniform mean wind profile, following a logarithmic law. The Gaussian velocity profile is generated directly in ANSYS
FLUENT using the spectral synthesizer developed on the basis of Smirnov proposal, while the Kaimal spectrum is generated in Turbsim at full-scale and then scaled to be used for the simulation in ANSYS
FLUENT. The uniform (lowturbulence) case is simulated using the Scale-Adaptive Simulation (SAS) turbulence model, while the other two cases are run in Large-Eddy Simulation (LES). Results obtained from the former are in good agreement with previous studies, which validates our numerical set-up. SAS proved to be valid in train aerodynamics simulation, being a good alternative to LES for transient simulations. Averaged aerodynamic quantities (mean, extreme values and the standard deviation of force and moments coefficients as well as pressure distributions) are used for the comparison of using these turbulent inflow conditions, while the transient behavior is analyzed by the velocity and forces spectra, and the aerodynamic admittance curves. Related to the time-averaged aerodynamic coefficients, the standard deviation and the maximum value for any aerodynamic coefficient are lower in the uniform case than in any stochastic one. Comparing the two stochastic approaches, the differences on the turbulent intensities (lower turbulent intensity in the x- and y-direction for the Gaussian case while larger in z-direction) are reflected in the standard deviations and maximum values of the force coefficients, where a similar trend is observed for any force and moment coefficient except for the axial force coefficient Cx. The rolling moment Cmx is found to be one of the most important aerodynamic coefficients regarding cross-wind stability. In consequence, it was vital to stress the increase of 20% observed for this coefficient when simulating the Smirnov-based case (higher turbulence than the uniform case). This increase is still more significant when the Kaimal-based turbulent wind is adopted, reaching a 33%

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larger than the uniform one. Concerning the pressure distribution, in general terms, it is quite similar for the three cases, although notable differences are identified at the lee-ward side and more slightly at the underbody. The influence of the spectral model is more evident when analyzing the velocity spectra. It is noted that the Smirnovbased spectrum, for any velocity component, has a roll-off in the inertial subrange compared with the Kaimal-based case. Although no significant effect is observed on the force spectra, it is clearly illustrated in the aerodynamic admittance curve that the choice of the spectral model is critical.

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