 Original Article
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Effect of RANS Turbulence Model on Aerodynamic Behavior of Trains in Crosswind
Chinese Journal of Mechanical Engineering volume 32, Article number: 85 (2019)
Abstract
The numerical simulation based on Reynolds timeaveraged equation is one of the approved methods to evaluate the aerodynamic performance of trains in crosswind. However, there are several turbulence models, trains may present different aerodynamic performances in crosswind using different turbulence models. In order to select the most suitable turbulence model, the intercity express 2 (ICE2) model is chosen as a research object, 6 different turbulence models are used to simulate the flow characteristics, surface pressure and aerodynamic forces of the train in crosswind, respectively. 6 turbulence models are the standard kε, Renormalization Group (RNG) kε, Realizable kε, Shear Stress Transport (SST) kω, standard kω and Spalart–Allmaras (SPA), respectively. The numerical results and the wind tunnel experimental data are compared. The results show that the most accurate model for predicting the surface pressure of the train is SST kω, followed by Realizable kε. Compared with the experimental result, the error of the side force coefficient obtained by SST kω and Realizable kε turbulence model is less than 1 %. The most accurate prediction for the lift force coefficient is achieved by SST kω, followed by RNG kε. By comparing 6 different turbulence models, the SST kω model is most suitable for the numerical simulation of the aerodynamic behavior of trains in crosswind.
Introduction
The aerodynamic characteristics of a highspeed train have an important impact on its economy, stability, and safety. Especially in the case of crosswind, the aerodynamic force changes significantly due to the variation of the flow field, and the train may be in a highrisk state of derailment and overturning [1,2,3,4,5]. Therefore, it is very important to study the aerodynamic characteristics of highspeed trains in crosswind. In the aerodynamics standards of the railway industry and the European railway application aerodynamics standard, the numerical simulation based on Reynoldsaveraged Navier–Stokes (RANS) equation is one of the approved methods to evaluate the aerodynamic performance of trains in crosswind. Up to now, many researchers have conducted numerical studies on the operation of highspeed trains in crosswind conditions [6,7,8,9,10]. Li et al. [11] investigated a numerical simulation method for the interaction between airflow and highspeed trains, indicating that it is necessary to consider the interaction between airflow and a highspeed train subjected to crosswind. Yu et al. [12] selected the aerodynamic drag force and wheel unloading rate as the optimization targets, and proposed a multiobjective shape optimization design method for highspeed train head. In computational fluid dynamics (CFD), the selection of the turbulence model is critical. The numerical results obtained by different turbulence models may be different, and the assumed turbulence model will be different according to the research object and flow characteristics.
The choice of turbulence models was different in the application of the numerical simulation of train flow fields. In previous studies, few have fully studied the influence of the turbulence model on the flow field around the train. Different turbulence models were chosen. For RANS, the standard kε and Realizable kε turbulence model were used to predict the aerodynamics of the vehicles [13, 14]. It has been verified that the SST kω turbulence model can better predict the aerodynamic forces and pressure on the train surface [15,16,17]. Large eddy simulation (LES) and detached eddy simulation (DES) method were also used to study the aerodynamic performances of trains [18,19,20,21,22]. The choice of the turbulence model plays a critical role in the calculation accuracy of the numerical simulation. Some researchers have conducted studies on the accuracy of different turbulence models for different research objects. As indicated in Fu et al. [23], the different turbulence models show different numerical simulation performances for a fullscale car. If considering the unsteady characteristics of the air flow, selecting the appropriate RANS turbulence model based on the flow characteristics can improve the accuracy of the unsteady simulation and reduce the calculation time [24]. When highspeed trains run at a high speed, different turbulence models have great differences in the simulation accuracy of the flow field around them. Wang et al. [25] investigates and evaluates the performance of three widely used turbulence models including the unsteady RANS, ScaleAdaptive Simulation (SAS) and DES to predict the slipstream of a generic train. MunozPaniagua et al. [26] analyzed the aerodynamic force coefficients of and pressure distribution on the train surface, the time average and instantaneous flow structures. The effect of SAS and improved delayed detached eddy simulation turbulence models on the aerodynamic characteristics of a train in crosswind was studied.
In the case of crosswind, the flow characteristics of the train vary greatly. The extent and mechanism of the influence of the turbulence model on the aerodynamic performance of trains have not been studied comprehensively, therefore, most researchers choose the turbulence model based on experience. In this study, the ICE2 model is chosen as a research object, and 6 common RANS turbulence models are used to numerically simulate the train surface pressure, flow characteristics and aerodynamic performance under crosswind. By comparing the numerical simulation results with the experimental data obtained by the wind tunnel experiments, the most suitable turbulence model for simulating the train flow around crosswind is studied.
Governing Equations
Navier–Stokes Equations
The motion of the airflow around trains can be described by a continuity equation, a momentum equation, and an energy equation. The general governing equations are as follows:
where ρ is the density, t is the time variable, \(\varvec{\varPhi}\) is a general variable, which can represent u, v, w, T, and the others, V is the velocity vector, Γ is the general diffusion coefficient, S is the generalized source term. The left side of the equation is the transient term and the convection term, and the right side of the equation is the diffusion term and the source term.
Turbulence Model
When a train runs at a high speed, the flow around the train can be treated as a threedimensional incompressible flow process. A reasonable turbulent transport equation must be selected for the numerical simulation. The RANS simulation is currently the most widely used turbulent numerical method. The Reynolds stress term in the RANS equation is unknown, resulting in the unclosed equations. The eddy viscosity model introduces the turbulent viscosity μ_{t} based on the Boussinesq hypothesis and establishes the relationship of Reynolds stress with respect to the average velocity gradient. According to the number of differential equations that determine the turbulent viscosity μ_{t}, the eddy viscosity model is divided into zeroequation model, oneequation model, and twoequation model [27]. The oneequation model is mainly Spalart–Allmaras. Typical twoequation models include the standard kε, RNG kε, Realizable kε, SST kω, and standard kω. In this paper, the oneequation and 5 twoequation models commonly used in engineering are selected for comparison. The standard kε, RNG kε, Realizable kε, SST kω, standard kω, and Spalart–Allmaras turbulence models are respectively represented by SKE, RNG, RKE, SST, SKW, and SPA for simplicity.
Wall Function
Whether it is the standard kε model, RNG kε model or Realizable kε model, it is effective for fully developed turbulent flows, that is, these models are high Reynolds turbulence models, and they can only be used to solve the flow fully developed. In the nearwall region, the turbulent flow is not fully developed. In the region closer to the wall, the flow may be in a laminar flow state. Therefore, it is difficult to use the previous high Reynolds model for the calculation in the nearwall region, and special processing should be used. A wall function method or a kε model with a low Re number can be used. The wall function method is actually a set of semiempirical formulas used to directly relate the physical quantities on the wall to the unknowns, in conjunction with the high Re number kε model. A standard wall function is used when the dimensionless wall distance y+ is in the range of 30 and 200, and a reinforced wall function is used when y + is close to 1. For the kω turbulence model, y+ is guaranteed to be close to 1.
Numerical Information
Train Model
The model is an ICE2 train, as shown in Figure 1(a), which consists of a head car and a part of the tail car. The tail car is mainly used to ensure the flow field of the head car and between the head and tail cars. There is a 5 mm gap to ensure the separate measurement of the head and tail forces. The numerical simulation calculation model is consistent with the wind tunnel test model [28]. The scale size of the train model is 1:10, the total length of the scaled train L = 3.552 m, the width B = 0.302 m, the height H = 0.358 m, and the streamlined length L_{head} = 2.656 m, the incoming flow is shown in Figure 1(b). Taking the center of the section as the origin, it is divided into four parts according to the angle, as shown in Figure 1(b). 4 parts are the upper surface (0°‒45°, 315°‒360°), leeward surface (45°‒135°), bottom surface (135°‒225°) and windward surface (225°‒315°). Figure 2 illustrates the speed vector diagram, where U_{t} is the train’s running speed; U_{w} is the crosswind velocity; U_{R} is the air speed relative to the train; β is the yaw angle. The experimental data were obtained from the Bombardier Transportation Company of the Zhukovsky Central Aerodynamics Institute in Russia in 2003 in the T103 openair jet tunnel [28].
Numerical Method
The size of the computational domain should satisfy the requirement that it will not affect the flow field around the train. The computational domain shown in Figure 3 is established. The gap between the train and ground is 0.0503 m, and the length, width, and height of the computational domain are 16 m, 12 m and 4 m, respectively. The entrance plane in front of the train is 4 m from the nose of the head car, and the distance between the center line of the train and the left and right sides is 4 m and 8 m, respectively.
The boundary conditions are set as follows: the two entrances of the computational domain are specified as the inlet boundary conditions with a speed of 60.62 m/s and the crosswind velocity of 35 m/s. The two exits are set as the pressure outlets, and the ground and train surfaces are fixed wall boundaries. The top surface of the computational domain is symmetry, as shown in Figure 3. The air density is 1.205 kg/m^{3} and the kinematic viscosity is 1.81 × 10^{−5} Pa∙s. The SIMPLE algorithm of pressurevelocity coupling is used, and the secondorder scheme is chosen for the discretization for all variables.
The pressure coefficient c_{p}, aerodynamic side force coefficient c_{s} and lift force coefficient c_{l} are defined as:
where \(p\) is the static pressure, \(p_{\infty }\) is the reference pressure, \(\rho\) is the air density; \(u_{\infty }\) is the incoming flow velocity, F_{s} and F_{l} are the aerodynamic side and lift forces, respectively; A is the characterized area of the train.
Computational Mesh
In order to simulate the flow around the train better, the flow field is multilayered and refined. The grid size is gradually increased to ensure a fine grid. The refined region is shown in Figure 4. Since the fluid variable in the near wall region has a large gradient, a fine mesh near wall region can basically determine the true physical phenomenon of the rear wall. A boundary layer is created on the surface of the train to simulate the flow near the wall. The first layer of the boundary layer has a height of 0.01 mm, a growth rate of 1.2. There are 12 layers in total, ensuring that y+ is close to 1. After selecting the reasonable mesh size for meshing, the mesh of the flow field around the train model is shown in Figure 4. The mesh in the boundary layer of the train surface is shown in Figure 5.
The accuracy of the numerical results is related to the number and quality of the mesh, therefore, the mesh independence is studied firstly. Three sets of grids were divided by changing the size of the train components. The SST kω turbulence model is used for the numerical calculation. The side force coefficients c_{s} obtained using different grids are shown in Table 1. The relative error of the side force coefficients is within 3%. When the number of meshes increases from 23.81 million to 29.85 million, the relative error in the side force coefficient is less than 2%. It can be seen that the further increase of the mesh has little effect on the side force coefficient, therefore, the grid with a number of 23.81 million is chosen for the remaining numerical calculations.
Results
The numerical simulations were carried out with 6 turbulence models, which are SKE, RNG, RKE, SKW, SST and SPA, and the flow characteristics of ICE2 train in crosswind are analyzed.
Flow Distribution
When the train is running in a crosswind environment, its surrounding flow field is shown in Figure 6. When the airflow is blocked by the train, it is divided into two parts sourced from the windward side of the train, a part of the airflow bypasses the roof and the other flows from the bottom of the train (see Figure 6(a)). A large number of eddies are formed on the leeward side of the train, and the flow field is extremely complicated (see Figure 6(b)).
Figure 7 shows the streamlines at different crosssections of the train using SST kω turbulence model. The corresponding crosssectional location is shown in Figure 1(a). When the steady airflow under certain conditions bypasses the train, a vortex is formed from the surface, that is, the boundary layer is detached, and the airflow over the roof and bottom is collected on the leeward side of the train, generating a lot of vortices. At different crosssections, the number and scale size of vortices are different. When the air flows over the roof and the bottom of the vehicle, the shedding eddy is likely to occur on the leeward side of the train. It can be seen from different sections that as the airflow develops downstream, the scale of the vortex shedding becomes larger and larger, and the vortices are gradually far from the vehicle body. There are many largescale vortices on the leeward side of the train. These vortices consume energy and generate a large suction pressure on the leeward side of the train.
The surrounding flow field obtained using different turbulence models are shown in Figure 8. Due to the similarity, only the flow field distribution at the crosssection x_{5} = − 2.06 m is given. Different turbulence models have different simulation capabilities for the flow field. As shown in Figure 8(e), the SST kω turbulence model captures four typical vortices, defined as V_{c1}, V_{c2}, V_{c3}, and V_{c4}, respectively. Three turbulence models including RNG, SKW and SST have the ability to capture the above vortices. The other three turbulence models do not capture the V_{c1} vortex, and the SKE turbulence model also has poor recognition of several other vortices. The V_{c3} vortex is not obtained using RNG turbulence model, and the V_{c3} and V_{c4} vortices identified by SKW turbulence model are interconnected.
In order to further analyze the flow field, Figure 9 shows the comparison of the velocity distributions at different crosssections. When the airflow is blocked by the train, the flow velocity is significantly reduced, and the airflow speed increases significantly when the airflow bypasses the roof and the vehicle bottom. As there are many vortex structures on the leeward side of the train, the flow velocity in the above regions is relatively low. Obviously, the calculation results show that the velocity distribution obtained using different turbulence models are different. The SKE turbulence model performs poorly compared with the other turbulence models. The other turbulence models show higher gradients in velocity. 4 turbulence models including RNG, SKW, SST and SPA show a lower velocity near the leeward side of the train, and RNG and SST turbulence models present a higher resolution of the velocity gradient.
Train Surface Flow
Figures 10 and 11 show the flow pattern on the train surface including the leeward side and the bottom. The airflow branches off from the windward surface of the train, some flows over the roof and the others over the bottom of the train, as shown in Figure 6(a). There are many separation lines (red) and reattachment lines (black) on the surface of the train, mainly including separation lines S1, S2, S3 and reattachment lines A1, A2, A3, as shown in Figure 10(e). For the upper surface, airflow is separated at the separation line S1, and reattached at the reattachment line A2, and then separated again from the separation line S3. The airflow adheres to the surface of the train body at the reattachment line A2, and then separates at the separation line S3, and reattaches again at the reattachment line A1, and the airflow flows downstream to the separation line S1. The underneath airflow is separated at the separation line S2 and reattached at the reattachment line A3. The flow pattern around the bogie is more complicated, and the airflow has multiple separation and reattachment lines. The separation and reattachment of the airflow at the front end of the train will form bubbles. The air bubbles will fall off and develop to the downstream along the train. Once the air bubbles fall off, new air bubbles will be generated. When these air bubbles flow backward, the airflow on the leeward side of the train will be intensified, forming a large vortex.
The simulation results of the separation lines (S1 and S3) and the reattachment line (A1) for SKE and RKE are poor. RNG and SPA turbulence models predict a higher position of the separation line S3, and RNG turbulence model also has a higher predicted position for the reattachment line A2. However, the SPA turbulence model has a lower predicted position for the reattachment line A2. The three turbulence models including RKE, SKW and SST have similar predictions for the reattachment line A2. The length of the separation line S3 predicted using SKW turbulence model is significantly larger than the other models. The position and length of these surface flow lines represent the position and the size of the region for the airflow varied from the twodimensional surface to the threedimensional flow field. Obviously, different turbulence models have different predictions in surface flow.
Pressure Distribution
Figure 12 shows the pressure distribution around the train at the crosssection x_{4} = − 1.57 m. From the previous flow field analysis, it is only obvious that the results obtained using different turbulence models are different. 3 turbulence models including RNG kε, standard kω and SST kω show lower negative pressure on the leeward surface of the train, and the pressure gradient on the leeward surface is larger, while the other three turbulence models show a higher negative pressure, and a smaller pressure gradient.
Figure 13 shows the comparison of the surface pressure coefficient c_{p} and the experimental ones on different crosssections of the train. The pressure coefficient on the windward surface and the top surface of the train at all crosssections for different turbulence models are in a good agreement with the experimental results. The leeward surface also presents a reasonable match in pressure with the experimental data, indicating the rationality of the numerical method. As there are some differences in geometry between the numerical model and the experimental model, such as the bogie, the cylindrical support, and so on, a slight difference is observed on the bottom surface of train for the numerical results and experimental data.
At the crosssection x_{1} = − 0.107 m, the different turbulence models show a large difference at the bottom of the train due to the exist of the spoiler. It can be seen from Figure 13(b) that the bogie has a greater influence on the airflow underneath the train, and it shows a higher suction pressure than the experimental value. Due to the presence of the bogie, there is no experimental data for comparison at the crosssection x_{3} = − 0.50 m. Compared with the three crosssections near the streamlined nose, the pressure on the latter three crosssections are more intuitive than the experimental data due to the influence derived from the spoiler, the bogie and the cylindrical support. It can be seen from Figure 13(a) and (b) that the maximum negative pressure appears on the upper part of the leeward surface, and the maximum suction pressure appears on the windward surface of the streamlined part, indicating that the aerodynamic forces are concentrated in the streamlined part of the train. It can be seen that the pressure on the three crosssections x_{2} = − 0.25 m, x_{3} = − 0.50 m and x_{4} = − 1.57 m are different in a certain for different turbulence models. These areas are relatively less affected by the spoiler, bogies and cylindrical supports. It can be seen from Figure 13(b) that SST turbulence model exhibits the largest suction pressure, which can be confirmed from the previous analysis of flow field. Therefore, SST turbulence model shows a more accurate prediction in the flow separation in the boundary layer. Meanwhile, the pressure obtained using SST turbulence model agrees well with the experimental one at the other crosssections. At the nonstreamlined crosssection (x_{3} = − 0.50 m), the suction pressure on the upper part of the leeward surface for SKE turbulence model is much lower than that of the other turbulence models, and SST and RNG turbulence models exhibit a higher suction pressure. On the bottom surface at the crosssection x_{4} = − 1.57 m, SST and SKW turbulence models agree well with the experimental values. Comprehensive comparison of the pressure on all crosssections, SST turbulence model shows a better prediction on the surface pressure and also the flow field.
Aerodynamic Force
The difference in the side force coefficient c_{s} and lift force coefficient c_{l} between the numerical results and the experimental value [28] is studied. The results are given in Table 2. For the side force coefficient, the error is within 10% compared with the experimental value. Compared with the experiment results, the error for SST turbulence model is 0.5%, and for SKE turbulence model is 8.06%, followed by RNG with an error of 4.53%.
For the lift force coefficient, SST shows a more accurate result with an error of 21.8%, followed by RNG model, the error is 26.3%, and SKE predicts the worst. The deviation could be induced by a considerable geometric difference between the numerical and the experimental models. Some researchers have studied the aerodynamic performance of ICE2 trains [13]. The relative error in the lift force coefficient between the numerical result and the experimental ones is from − 31.1% to − 47.6%. In this study, it provides a more accurate result with an error of − 21.8%.
In the streamlined part of the head car, when the airflow transitions from the top of the train to the leeward surface, the airflow separates and a negative highpressure zone is formed at the separation point. On the leeward surface at the crosssection x_{1} = − 0.107 m, the different negative pressure is generated using different turbulence models. The pressure predicted using SST is the largest, which results in the closest forces to the experimental ones. At the crosssection x_{2} = − 0.25 m, the pressure for SST turbulence model is also the largest, and that for SKE model is also the smallest, which matches the deviation. For the SKE turbulence model, the flow assumed is completely turbulent regardless of the role of molecular viscous, the viscous effect dominates the near wall of the train, and the turbulent development is not sufficient, and the calculation produces distortion. In the transition zone of the curved surface and the nearwall area of the surface, SKE is distorted by the low Reynolds number, and the pressure on the surface of the fitted body is small. It is shown in Table 2 that the SKE model shows the largest error, and SST model gives a minimum error. At the crosssection x_{4} = − 1.57 m, SST turbulence model gives the closest prediction in pressure on the bottom surface of the train, followed by SKW. Meanwhile, at the crosssection x_{6} = − 2.49 m, the pressure obtained using RNG and SST is close to the experimental one. It can be concluded from the above analysis that the SST and RNG models have better predictions in the lift force coefficient.
Conclusions
The accuracy of the numerical simulation of the external flow around trains by means of different turbulence models is analyzed with comparison to the wind tunnel experimental data. The results are as follows.

(1)
In the numerical simulation of the external flow around trains subjected to crosswind, different turbulence models show quite different performances at specific regions. The pressure on the windward surface is quite similar for all turbulence models. Compared with the experimental results, the side force coefficient obtained using SST kω turbulence model is the closest to the experimental one, and the error is within 1%. The error of the side force coefficient for both standard kε and RNG kε models is large, and the error is large than 4%, the standard kε model shows the worst prediction in the side force coefficient. Meanwhile, SST kω model gives a relatively small error in the prediction of the lift force coefficient.

(2)
The standard kε turbulence model is established for complete turbulence. As a high Reynolds number model, the calculation results in distortion in the nearwall region where viscous action dominates. The standard kε model is not suitable for surface curved flow and complex vortex flow. As a modification of the standard kε model, the Realizable kε model is a good simulation of the low Reynolds number flow in the nearwall region, and has the ability in the accurate prediction of the lift force coefficient, however, it fails to predict accurately in the side force coefficient. The standard kω and SST kω models are suitable for the low Reynolds number, and the separation prediction caused by the inverse pressure gradient is more accurate, however, the predicted separation region using the standard kω model is larger. SST kω model combines the advantages of the standard kω and standard kε models, and presents the closest results for both the lift and side forces among 6 turbulence model mentioned in this study.
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Authors’ Contributions
TL was in charge of the whole trial and wrote the manuscript; DQ assisted with the post process of the data and analysis; JZ revised the manuscript and gave some advices. All authors read and approved the final manuscript.
Authors’ Information
Tian Li, born in 1984, is currently a Research Associate at State Key Laboratory of Traction Power, Southwest Jiaotong University, China. He received his doctor degree from Southwest Jiaotong University, China, in 2012. His research interests include train aerodynamics.
Deng Qin, born in 1996, is currently a master candidate at State Key Laboratory of Traction Power, Southwest Jiaotong University, China.
Jiye Zhang, born in 1965, is currently a professor at State Key Laboratory of Traction Power, Southwest Jiaotong University, China. He received his PhD degree from Southwest Jiaotong University, China, in 1998. His research interests include train aerodynamics, stability and control of complex systems.
Competing Interests
The authors declare that they have no competing interests.
Funding
Supported by National Natural Science Foundation of China (Grant No. 51605397), Sichuan Provincial Science and Technology Program of China (Grant No. 2019YJ0227), and Selfdetermined Project of State Key Laboratory of Traction Power (Grant No. 2019TPL_T02).
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Li, T., Qin, D. & Zhang, J. Effect of RANS Turbulence Model on Aerodynamic Behavior of Trains in Crosswind. Chin. J. Mech. Eng. 32, 85 (2019). https://doi.org/10.1186/s1003301904022
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Keywords
 Turbulence model
 Crosswind
 High speed train
 Numerical simulation
 Aerodynamic