Numerical Analysis of the Effect of Different Nose Shapes on Train Aerodynamic Performance

Abstract

This study investigates the aerodynamic performance of various trains with different nose shapes, using as the design variables two angles $\alpha ,\beta$ for the head shape and the bluntness angle $\gamma$, without crosswind. The effects on aerodynamic performance, such as the train drag coefficient, pressure distribution along the train surface, flow structures around the train and the wake, and head pressure pulse, are analyzed. The results indicate that the increase in the train nose length for flat shapes decreases the $C_D$ values by $21.47\%$ and $19.11\%$, decreasing the high-pressure region in the leading head. The duck nose configuration emerges as a compromise between drag reduction and nose length. Increasing the angle $\gamma$, a further drag reduction of $8.5\%$ is featured. Drag formation along the train is also analyzed. The steeper the variation in the geometry, the higher the peak intensity and the slope of the curve. Regarding the flow features around the train, two main counter-rotating vortices are captured in the wake. Moreover, the higher the nose length and the higher the bluntness angle $\gamma$, the weaker and narrower the wake. Again, a longer nose shape yields a softer jump in terms of pressure difference, crucial for train homologation and safety.

1. Introduction

High-speed trains have become essential in modern transportation due to continuous advancements in railway technology. Researchers have been particularly focused on the aerodynamic performance of these trains, with studies identifying the train’s shape as a key factor. Features such as bluntness, A-pillar roundness, and nose length are critical in shaping aerodynamic performance (Niu et al. [1], Chen et al. [2], Munoz-Paniagua et al. [3], and Oh et al. [4]). Using numerical simulations and wind tunnel experiments, researchers have examined how variables like train speed, cross-sectional area, and ground clearance influence aerodynamic drag (Rocchi et al. [5], Meng et al. [6], and Zampieri et al. [7]).

Many experts and scholars have performed various optimization studies on the nose shape of trains to improve the aerodynamic performance of trains in open air and tunnels (Yang et al. [8], Yao et al. [9], Suzuki and Nakade [10], and Li et al. [11]). One of the most important factors is the length of the train’s nose. A longer, streamlined nose has been shown to significantly reduce drag, minimize wake flow, and create a minor positive pressure zone in the nose cone (Xu et al. [12], Baker [13], Flynn et al. [14], Osth et al. [15], and Bell et al. [16]). This becomes particularly relevant as the train speed increases. Studies demonstrate that a more streamlined shape not only improves aerodynamic forces but also reduces slipstream and wake flow (Hemida et al. [17], Schetz [18], and Raghunathan et al. [19]).

Choi and Kim [20] revealed that shaping the nose from blunt to streamlined at speeds between 100 and 200 km/h can reduce drag by up to $50\%$. Hemida and Krajnovic [21] explored how the shape of the nose affects flow under crosswind conditions, showing that shorter noses generate more vortex structures in the wake. The pressure distribution on the train surface also varies based on the nose length, with longer noses providing better pressure reduction at both at the front and rear of the train (Hemida and Krajnovic [22], and Chen et al. [23,24]).

Tian [25] emphasized the importance of a streamlined shape as the most effective means of reducing drag. As the length of the train’s nose increases, air pressure pulses decrease logarithmically, while aerodynamic drag on both the head and tail cars is reduced significantly (Tian et al. [26]). These findings are backed by wind tunnel tests, which have proven to be vital for studying the aerodynamics of high-speed trains (Niu et al. [27] and Kwon et al. [28]). Stucki and Maynes [29] verified their computational studies on drag reduction in freight trains using wind tunnels. Zhang and Zhou [30] also compared different train models and found that longer, thinner noses with higher slenderness ratios reduce drag more effectively when the difference in the nose lengths is small.

The overarching objective of this research is to scrutinize the flow field around high-speed trains, specifically focusing on various nose shapes, and discern their impact on aerodynamic drag. The paper is organized as follows: starting with the model of the train and the definition of the angles for the parametric analysis in Section 2, the numerical model, grid generation, computational domain and boundary conditions are presented in Section 3. After the mesh convergence study and the far-field independence analysis in Section 4, the results and the effect of the design variables on the aerodynamic performance and flow features are presented in Section 5. The summary and outlook are given in Section 6.

2. Train Model

The train geometry is based on the Alstom AGV high-speed EMU for car dimensions and Jacob bogies configuration [31,32]. The CAD model is realized using SolidWorks 2022. The AGV uses 11 coaches in the version run by Italo-NTV, but it has been chosen to modelize only 3 coaches to optimize the train length (to still have room for a standard coach in between the extremities) and computation time. The train is symmetrical in both the lateral and longitudinal directions, with both end cars sharing the same nose shape in all configurations studied. The modelized bogies also share the same CAD model based on the AGV Jacob bogie dimensions [31].

Table 1. Geometric description.

Dimension	Value	SI Unit
Train Length	52.0	m
Leading Car	17.1	m
Middle Car	17.8	m
Car Height	3.277	m
Car Width	2.985	m
Frontal Area	9.773	m2

, Figure 1 and Figure 2 show the train dimensions:

The objective of this study is to analyze the influence of the nose shape on high-speed train aerodynamic performance; therefore, the train geometry is simplified to reduce interferences around bogies and cars separations, and no pantographs are modeled. All the nose fillets used are chosen with a 300 mm radius to have a realistic geometry. The design of the nose, including its angles and shape, is a critical factor in determining the aerodynamic drag of high-speed trains like the ETR500, ETR1000, and ETR700. Based on these models, three angles are chosen to describe the geometry and to include the duck nose configuration, as well as comparing geometries with different aerodynamic shapes. The parametrization of the nose consists of two angles $\alpha$ and $\beta$, with values changing between 15°, 30°, and 50°, giving a total of nine combinations. It is also chosen to set the length of both nose parts to be equal (therefore, the nose length changes depending on the two angles). In the second segment of the study, the angle $\gamma$ is introduced on the train, with the aim of examining the aerodynamic impact of an angle defined on another plane. This angle begins 3 m after the nose so that there is no influence from the bogie located just further back. Figure 3 shows the train nose parametrization.

3. Numerical Model

3.1. Numerical Setup

In this study, steady-state incompressible RANS simulations are performed, using the open-source toolbox OpenFOAM. It employs the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm to solve the continuity and momentum equations. The flow is initialized by means of potential equations, largely used to initialize the internal fields away from walls for viscous computations. Turbulence is modeled using $k-\omega -SST$ due to its higher performance in operating with separated flows and with strong adverse pressure gradients. Based on a uniform free-stream velocity of 60 m/s aligned with the longitudinal axis, and the train height H, the Reynolds number is ≈${10}^7$. Since the Mach number is approximately $0.175$, the airflow can be treated as an incompressible fluid for the solution. The Gauss scheme is used as a discretization scheme, adopting a second-order scheme for the dissipative term, a first-order scheme for the turbulence, and a first- to second-order scheme for the convective term as the interpolation schemes. Moreover, wall functions are used to avoid resolving the boundary layer, achieving a significant reduction in the mesh size and computational cost, ensuring that the first grid cell is $30<y^{+}<300$.

Finally, the drag coefficient $C_D$ is defined as follows:

$$C_D={\displaystyle \frac{D}{\frac{1}{2}\rho U_{\infty }^{2}S}}$$

(1)

where D is the aerodynamic drag force, $\rho$ is the air density, $U_{\infty }$ is the free-stream velocity, and S is the body frontal area.

3.2. Grid Generation

The grids of the models are generated using the $snappyHexMesh$ utility, which is within OpenFOAM. This utility has been widely and successfully applied to aerodynamic numerical simulation of trains [33,34]. The meshes are dominated by hexahedral cells. To obtain more efficient use of computing resources, different refinement levels are applied to achieve a better transition of the mesh density from the domain surfaces (Level $0=1$ m) to that of the train as shown in Figure 4. Coarse-, medium-, and fine-refinement boxes corresponding to Level 1, 2, and 3, respectively, and Level 4 up to $0.8$ m from the train surface are generated, in order to ensure that the size of the boundary layer gradually transitions to the size of the main grid. As can be seen in Figure 4, ten prism layers are attached on the train surfaces, where a thickness growth factor of 1.3 is used, and the thickness of the layer furthest away from the wall is $30\%$ of the undistorted size of the cell outside layer. These prism layers guarantee a better capture of the near-wall flow structure.

3.3. Computational Domain and Boundary Conditions

The computational domain used in this paper is shown in Figure 5. H is the train equivalent height. The boundary of the calculation domain should be as far away from the body as possible to eliminate the interference of the calculation domain boundary on the flow field around the train. However, the computing domain should not be excessively large, to reduce the number of cells and improve the computing efficiency. The size of the domain comes from a far-field independence study, illustrated in Section 3. The distances from the head car nose to the upstream boundary and from the side boundary to the longitudinal center of the train body are 10 H. The inflow side is set as the velocity inlet boundary condition. Considering the full development of the wake flow, the exit boundary is set as the zero-pressure outlet. The distance from the downstream boundary to the tail car nose point is 40 H. The height of the calculation domain is 10 H. In order to simulate the actual running state of the train, the train is stationary, the ground is set to the moving wall boundary condition, the speed is given as the train speed, and the upper and the side surfaces are set to the slip wall boundary condition. As a consequence, on the train body, a no-slip boundary condition is applied. As steady 3D CFD simulations are performed on a semi-train endowed with a longitudinal plane of symmetry, only half of the actual fluid volume around the body is considered in order to reduce the time and resources required by each simulation; hence, a symmetry boundary condition is set.

4. Validation

4.1. Convergence and Mesh Independence Study

To check the convergence of a steady-state simulation, it is needed to ensure that the residual values of the conserved variables have been reduced to an acceptable value and that the main output of the simulation has reached a steady solution, namely, the behavior of the force coefficient starts showing periodicity or confined oscillations around a constant mean value.

The residuals in Figure 6a, representative of the percentage of the force imbalance, are computed using the $L^1-norm$ inside the CFD solver. Ux, Uy, and Uz are the residuals of the velocities in directions x, y, and z, and refer to the frame present in Figure 5. As can be seen in Figure 6b, all results presented later are obtained through averaging on a window among the last 1000 or 1500 iterations. Grid refinement strongly affects the number of cells and, hence, the computational cost of the simulation. The refinement is pursued by simply controlling the size of the furthest cell from the train surface (i.e., Level 0), keeping fixed the proportion between the boxes.

Table 2. Grid independence.

Number of Cells	${\mathit{C}}_{\mathit{D}}$	$\mathbf{\Delta }{\mathit{C}}_{\mathit{D}}[\%]$
2.0 × 106	0.2620	6.72
3.4 × 106	0.2444	0.04
5.4 × 106	0.2443	-

show a convergent behavior, with a variation of 0.04% between the last two grids. Therefore, the second-last grid is picked, ensuring that computational time is saved without losing accuracy.

4.2. Far-Field Independence

The purpose of the far-field independence study is to verify that the flow features do not depend on the size of the domain. The volume should be neither too small to avoid boundary effects, nor too large due to a useless memory storage.

The refinement boxes and the cells are kept constant in size in this analysis. Different domains are obtained by scaling downstream and upstream lengths of the same factor, and consequently we obtain the dimensions towards the up, right direction.

Table 3. Domain independence.

Domain [m]	${\mathit{C}}_{\mathit{D}}$	$\mathbf{\Delta }{\mathit{C}}_{\mathit{D}}[\%]$
150 × 18 × 18	0.2572	4.98
180 × 24 × 24	0.2444	0.82
216 × 30 × 30	0.2424	0.45
248 × 36 × 36	0.2413	-

shows that a far-field independent solution is achieved, yielding a drag coefficient variation of less than 1%. All the following simulations are performed with the green-highlighted one in Table 3.

5. Results and Discussion

5.1. Effect of the Design Variables $\alpha$ and $\beta$

Figure 7 shows the results of different configurations of the train nose shape. For a flat geometry, the drag coefficient becomes larger with the design variable $\alpha$, thus the increase in the train nose length decreases the $C_D$ values of the whole train. The train with $\alpha ={30}^{°},\beta ={30}^{°}$ has a $C_D$ smaller of $21.47\%$ with respect to $\alpha ={50}^{°},\beta ={50}^{°}$, and the train with $\alpha ={15}^{°},\beta ={15}^{°}$ has a $C_D$ smaller of $19.11\%$ with respect to the former one. Furthermore, low values of $\alpha$ provide greater sensitivity to the second design variable $\beta$; on the other hand, for high values of $\alpha$ the drag coefficient curve tends to flatten out due to high values of $\beta$. Basically, high values of $\alpha$ do not lead to a $C_D$ optimization, but for high values of $\beta$, even train configurations with low $\alpha$ can lead to very high drag coefficients. Finally, the lowest value of the drag coefficient is given by the largest train nose length, with a flat shape, providing a $C_D=0.2154$, while the second best value is given by the duck-nose shape ($\alpha ={15}^{°},\beta ={30}^{°}$), providing a $C_D=0.2470$. It can be seen that the curves converge after $\beta ={30}^{°}$, where the increase in $\beta$ on the duck nose prevails in terms of increasing the $C_D$ value of the train, and the reason is that the upper wall of the nose tends to be more vertical, causing a very high pressure drag.

The accumulated drag coefficients along the train centerline are shown in Figure 8. The longer the head car nose, the lower the peak intensity and the slope of the curve. Similar behavior can be expected from the combination of two angles; if the starting angle is large, the increase in the drag is faster, while if the starting angle is low, a significant generation of the drag occurs later. Then, there is a zone in which the flow is accelerating and the pressure decreases, resulting in a negative force; thus, the train is pulled upstream and the cumulative drag drops.

Along the main train body, the drag increases slowly due to the friction forces, and it features two small peaks due to the two inter-car gaps.

In the rear part of the train, when the flow encounters a large curvature of the tail, the increase in the drag is steeper than with a smoother variation of the geometry.

At the rear of the duck nose configuration (purple curve), the flow encounters first an abrupt variation in the geometry, and thus the curve features a steep increase in the drag, and second, a positive pressure zone that pushes the train upstream, resulting in a drag reduction. Optimizing the aerodynamic shape for drag reduction mainly comes from reducing the pressure drag of the train, and pressure drag mainly exists on the front cone and the tail cone.

5.2. Pressure Distribution

The drag difference is analyzed from the perspective of the pressure distribution. The pressure distribution on the head coach surface is shown in Figure 9, in terms of pressure coefficient $C_p$, defined by

$$C_p={\displaystyle \frac{p-p_{\infty }}{q_{\infty }}}$$

(2)

where p is the local static pressure, $p_{\infty }$ the free-stream static pressure, and $q_{\infty }$ the free-stream dynamic pressure. A large area of high pressure exists at the stagnation point, giving a backward push to the nose cone of the train coach, increasing the pressure drag. If the train nose length is shorter, the static pressure at the top is more negative, with a greater reduction in drag but starting from a higher value of cumulative drag. At the front of the optimal train, the high-pressure region is smaller than the corresponding high-pressure region of the other trains. The decrease in size of this high-pressure region reduces the drag. The train with the duck-nose configuration $\alpha ={15}^{°},\beta ={30}^{°}$ exhibits an additional high-pressure zone close to the windshield, increasing the $C_D$ value of $14.67\%$ with respect to the $\alpha ={15}^{°},\beta ={15}^{°}$ configuration.

Overall, the increase in the train nose length reduces the size of the high-pressure region in front, leading to a reduction in the drag.

While keeping fixed the first design variable $\alpha$, it is always better to decrease the second design variable $\beta$, resulting in a reduction in the drag.

Comparing the trains in Figure 9e,d, with the same $\alpha$ and $\beta$ values but switching the order, results in a lower drag for the configuration with a lower value of the first angle, namely, the duck nose shape. Similarly, the pressure distribution around the trailing cars yields to positive pressure areas that give a forward push, lowering the pressure drag. The greater the curvature of the geometry, i.e., the shorter the train nose length, the greater the upward flow acceleration and the lower the pressure, resulting in a faster increase in drag.

5.3. Flow Field Analysis

Figure 10 shows the limiting streamlines superposed on the skin friction coefficient distribution on the train surface. The skin friction coefficient $C_f$ is defined by

$$C_f={\displaystyle \frac{{\tau }_w}{q_{\infty }}}$$

(3)

where ${\tau }_w$ is the local wall shear stress, and $q_{\infty }$ is the free-stream dynamic pressure.

Examining the level of surface friction, the green areas signify that the air is conforming to the contours of the train’s geometry, indicating a state of attached flow. At the stagnation point, the wall shear stress is lower. However, near the leading edges around the stagnation point, where an abrupt change in curvature occurs, the skin friction coefficient tends to be higher, as in the first part of the roof of the train. Close to the inter-car gaps, the skin friction coefficient tends to be lower, due to the separation of the airflow. After that, the flow tends to reattach again. The skin friction magnitude tends to be lower in the rear part, indicated by the blue zones, which means that the flow is no longer attached. The attachment node at the stagnation point is also clearly visible. Flow separation occurs at the top of the surface, where the separation line is generated by the rapid convergence of the limiting streamlines from the lateral surface and the leading head. The greater the nose length, the smaller the separation and, consequently, smaller longitudinal vortices are produced.

The limiting streamlines on the tail surface, as shown in Figure 11, are an aid to a better comprehension of the flow separation. The airflow separates when the limiting streamlines converge rapidly, resulting in a separating surface that enters the flow field. In the duck nose configuration, four foci and a saddle-point can be marked by the limiting streamlines, which represent the generation of the vortex sheet as shown in Figure 11d. As pointed out below, as the train nose length increases, the wake becomes narrower, as the distance between the two counter-rotating vortices is smaller.

The vortex structure is described by the iso-surfaces of constant Q, which has been used for describing the flow structure around trains and has been used widely in studies of the aerodynamic performance of trains [21,35]. Figure 12 shows that the vortices around the train increase and strengthen from the train head to the train tail. Vortices around the train with a short train nose are bigger and stronger than those with a long train nose. Furthermore, in the latter one, the flow stays more attached to the train surface thus the separation is lower, and also the width of the wake is lower, yielding a lower drag coefficient. Comparing Figure 12b,d, the roll-up of the vortex sheet starts from the lower and from the higher A-pillar, respectively.

Figure 13 shows the vortex structure around the train tail. The longer the train nose, the thinner the wake. The organized longitudinal vortices originate from the C-pillar on the train tail. In the configuration of $\alpha ={15}^{°},\beta ={15}^{°}$, the flow remains attached to the inclined part, due to the induced velocity. Duck nose configurations are expected to generate two pairs of longitudinal vortices from the rear of the train (one weaker than the other) and could be captured when the Q value decreases, as the Q-criterion is sensitive to the iso-surface threshold. If the threshold is too large, the weak vortices will be wiped out. If the threshold is too small, weak vortices may be captured, but strong vortices could be smeared and become vague [36].

Figure 14 shows the pressure distribution along a line at a position 2.5 m from the track centerline and at a height of 1.5 m above the ground. In the nose region, there is a positive pressure due to the flow stagnation point and a negative pressure caused by the flow acceleration around the train nose shape. The greater the curvature imparted to the flow, the more negative the pressure and the steeper the change. The pressure jump near the head of the train with the short nose ($\alpha ={50}^{°},\beta ={50}^{°}$) is greater than the configuration with the long nose ($\alpha ={15}^{°},\beta ={15}^{°}$), stating that the airflow separation is strongly influenced by the shape of the train. Along the train body, a slightly negative pressure region and smaller pressure variations due to the spaces between the carriages occur, while at the rear, there is a negative to positive pressure transient but of a smaller magnitude than the nose transient.

5.4. Effect of the Design Variable $\gamma$

In order to show a clear and better dependence from the bluntness variable, it has been decided to work on flat trains ($\alpha$ = $\beta$), keeping the focus on the aerodynamic effect of $\gamma$ on the train without the coupled effect of $\alpha$ and $\beta$. All the previous results have been obtained considering a value of $\gamma =0^{°}$.

Figure 15 shows the drag coefficient of the trains with $\alpha ={15}^{°},\beta ={15}^{°}$ and with $\alpha ={30}^{°},\beta ={30}^{°}$ by varying the angle $\gamma$. The trend is that the higher the angle $\gamma$, the lower the drag coefficient. It can be noticed that with a short nose length, the slope of the curve is higher, and thus the advantages of bluntness are more visible, while with a long nose length, the benefits are less marked, with a flatter trend. Finally, the train that features the lowest drag is with $\alpha ={15}^{°},\beta ={15}^{°}$ and $\gamma ={20}^{°}$, and thus a long nose with pronounced sharpness, yielding a value of $C_D=0.1970$. However, it should be noted that a nose that is too long could reduce the space available for passengers and services, so bluntness could be a good design variable to improve the aerodynamic performance of high-speed trains.

The pressure distribution on the surface of the train head is depicted in Figure 16. Differences in the pressure distribution are observed at the nose tip, where a less blunt nose results in a small area of high pressure and therefore low drag. Thus a larger value of the design variable $\gamma$ produces a lower drag coefficient, as the nose is sharper and more aerodynamic.

Figure 17 shows the rear vortices’ behavior on $\alpha ={15}^{°},\beta ={15}^{°}$ and $\alpha ={30}^{°},\beta ={30}^{°}$ flat trains with a value of $\gamma ={10}^{°},{20}^{°}$ set on both configurations. Keeping $\gamma$ fixed, and thus increasing only $\alpha$, there is an expansion in terms of the vortex cross-section that induces greater aerodynamic resistance, as well as an increase in the divergence of the longitudinal counter-rotating vortices. On the other hand, keeping the inclination of the nose fixed and increasing the angle $\gamma$, the evolution is the opposite: the flow is able to detach itself from the train closer to the train longitudinal axis, resulting in a less wide wake.

6. Conclusions

The aerodynamic performance and flow fields for three-car trains with different nose shape were simulated without the yaw angle. The conclusions drawn from the obtained results are as follows:

• The parametric analysis of design variables $\alpha$ and $\beta$ indicates that increasing both angle values leads to an elevation in the drag coefficient $C_D$. When $\alpha$ is kept low, the drag coefficient experiences a more pronounced increase with a higher value of $\beta$. Conversely, at high $\alpha$ values, the growth in $C_D$ is more gradual with an increase in $\beta$. Trains configured with $\alpha ={50}^{°}$ exhibit the highest $C_D$ values, primarily due to a notable surge in pressure drag on the nose, attributed to the pronounced inclination of the leading head. The low angles of $\alpha$ and $\beta$ result in a minimum high-pressure region. Among the evaluated configurations, the train with the longest nose ($\alpha =\beta ={15}^{°}$) achieves the lowest $C_D$ at 0.2154. Interestingly, a duck-nose configuration emerges as a favorable compromise between drag reduction and nose length. For $\alpha ={15}^{°}$ and $\beta$ ranging from ${15}^{°}$ to ${30}^{°}$, this configuration features a $35\%$ shorter nose while experiencing a $14.67\%$ increase in $C_D$.
• From the flow field analysis, for streamlined shape body, a couple of counter-rotating vortices are generated from the train surface. Limiting streamlines coupled with the iso-surfaces of the Q-criterion are a good tool in order to understand the flow features around the train. The higher the nose length, the weaker and smaller the wake. For what concerns the pressure pulse, a longer nose produces a softer jump in terms of pressure difference. On the contrary, the steeper the head, the higher the pressure pulse, which is a constraining factor in terms of the surrounding infrastructures and train crossing.
• Examining the impact of the angle $\gamma$ from the analysis, results reveal that an elevation in the angle proves advantageous in the context of drag reduction. This is attributed to the minimization of the head high-pressure region and the generation of vortices resulting in a narrower wake. Considering the optimal nose configuration identified in the prior analysis, an angle $\gamma ={20}^{°}$ leads to a further drag reduction of $8.5\%$, culminating in the most favorable $C_D$ value of the study, which stands at 0.1970.

While this study provides valuable numerical insights into the effects of nose shape on drag reduction, experimental validation in a wind tunnel or through field tests would be beneficial. Such experiments could confirm the numerical results and provide additional data on real-world performance. Future research could explore novel nose shapes beyond those considered in this study. Investigating more complex geometries or hybrid designs might yield further improvements in drag reduction and overall aerodynamic efficiency.