Combining the detached eddy simulation (DES) method and Ffowcs Williams-Hawkings (FW-H) equation, the effect of bogie cavity end wall inclination on the flow field and aerodynamic noise in the bogie region is numerically studied. First, the simulation is conducted based on a simplified cavity-bogie model, including five cases with different inclination angles of the front and rear walls of the cavity. By comparing and analyzing the flow field and acoustic results of the five cases, the influence of the regularity and mechanism of the bogie cavity end wall inclination on the flow field and the aerodynamic noise of the bogie region are revealed. Then, the noise reduction strategy determined by the results of the simplified cavity-bogie model is applied to a three-car marshaling train model to verify its effectiveness when applied to the real train. The results reveal that the forward inclination of the cavity front wall enlarges the influence area of shear vortex structures formed at the leading edge of the cavity and intensifies the interaction between the vortex structures and the front wheelset, front motor, and front gearbox, resulting in the increase of the aerodynamic noise generated by the bogie itself. The backward inclination of the cavity rear wall is conducive to guiding the vortex structures flow out of the cavity and weakening the interaction between the shear vortex structures and the cavity rear wall, leading to the reduction of the aerodynamic noise generated by the bogie cavity. Inclining the rear end wall of the foremost bogie cavity of the head car is a feasible aerodynamic noise reduction measure for high-speed trains.

Over the past decades, the high-speed railway has developed rapidly in the world due to its advantages of high efficiency, energy conservation, environmental friendliness, and safety. Nowadays, the operation speed of high-speed trains in many countries can achieve 300 km/h and people are still making efforts for further improvement. For example, the “CR450 technology innovation project” carried out in China aims to further improve the train operation speed to 400 km/h. To achieve this goal, many technical challenges need to be addressed, especially problems related to train aerodynamics [

The aerodynamic noise control of high-speed trains can be boiled down to the control of the main aerodynamic noise sources. The bogie region, especially the first bogie of the head car, is one of the most important aerodynamic noise sources of high-speed trains [

In terms of aerodynamic noise control of the bogie region, adding side skirts is the most widely used measure. The side skirts eliminate the discontinuity of train side walls and also have certain sound insulation effects [

The aerodynamic noise in the bogie region is also closely related to the airflow beneath the train. In recent years, the management of the underbody flow of high-speed trains has also been a hotspot in studies on train aerodynamic performance optimization. Zhang et al. [

The presence of the bogie cavity makes the flow in the bogie region present certain cavity flow characteristics. Many experimental and numerical studies have shown that the shapes of the front and rear walls of the cavity are key factors that affect the pressure fluctuation inside the cavity [

In this paper, the detached eddy simulation (DES) method is employed in combination with Ffowcs Williams-Hawkings (FW-H) equation to investigate the effect of bogie cavity end wall inclination on flow field and aerodynamic noise in the bogie region. The numerical study is conducted on a simplified cavity-bogie model first, including five cases obtained by changing the inclination angles of the front and rear end walls of the cavity. The influence regularity and corresponding mechanism are revealed by comparing and analyzing the flow field and acoustic results of the five cases. After that, the noise reduction strategy determined based on the simulation results of the simplified cavity-bogie model is applied to a three-car marshalling train model to verify its effectiveness when applied to the real train. The relevant results contribute to a deeper understanding of the flow field and aerodynamic noise characteristics in the bogie region and could provide valuable reference for the aerodynamic noise control of high-speed trains.

DES is the most widely used turbulence model in the prediction of aerodynamic noise generated by intricate geometry structures. DES is a kind of hybrid model. Its basic idea is to solve the boundary layer in near wall region by Reynolds Averaged Navier-Stokes (RANS) model, and to solve the large-scale vortex motion by large eddy simulation (LES) model in the separation region [

The FW-H equation is the theoretical description of sound generated by the interaction between moving objects and fluid, as depicted in

In the current study, the quadrupole source term is neglected, which is a classical assumption for low Mach number flow. Besides, the numerical simulation is based on wind tunnel mode, the train is a static rigid surface, so the monopole source term is also 0. That is, the far-field noise only includes the contribution of the dipole source term. By using the Green’s function in free space, the sound pressure at far field point

The simulation is first conducted on a simplified cavity-bogie model, which is 1:8 scaled with respect to the real bogie, as shown in

By adjusting the inclination angles of the front and rear end walls of the cavity, five schemes of the bogie cavities are established, as shown in

case0 | case1 | case2 | case3 | case4 | |
---|---|---|---|---|---|

_{1} |
0° | 30° | 0° | 45° | 0° |

_{2} |
0° | 0° | 30° | 0° | 45° |

The computational domain established for this simplified cavity-bogie model is shown in

The trimmed mesh is used to discrete the computational domain. The surface grid size of the bogie and cavity is controlled within 0.375–1.5 mm, and the maximum grid size of the domain is 192 mm. To simulate the flow in the near wall region accurately, 15 layers of fine prism layer mesh with an initial height of 0.01 mm and a stretching ratio of 1.2 are generated on the train surface. Several blocks are established for local refinement of the volume mesh. The volume grids with 1.5 mm size are adopted for the refinement of the bogie region. By modifying the surface grid size of the bogie components, three sets of meshes are generated for the mesh independence test, which are named as mesh1-mesh3 in turn. The total number of volume cells of them are 15 million, 22 million and 29 million, respectively.

The Mach number in the current simulation is less than 0.3, so the air is considered as a gas with constant density. The segregated flow solver based on the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm is adopted to solve the discretized flow governing equations. The convection term is discretized by a hybrid scheme of second-order upwind and central differencing [

The time-averaged and fluctuating value of the pressure coefficient _{p}

The simple bogie model proposed by Zhu [

The wind tunnel test in reference [

For

Based on

_{rms} in the bogie region. In all the cases, the highest (d_{rms} values appear at the lower and lateral surface of the bogie, the rear wall of the bogie cavity and the carbody surface that connects to the cavity rear wall. In case0, the dipole source intensity at the rear of the bogie is significantly higher than that at the front of the bogie. In case1 and case3, the (d_{rms} values on front wheelset, front traction motor and front gearbox exhibit a significant increase compared with that in case0, especially in case3, while the (d_{rms} values on the rear wall of the cavity are almost the same as that in case0. In case2 and case4, the (d_{rms} values at the front of the bogie are basically the same as that in case0, while the (d_{rms} values on the rear wall of the bogie cavity show a notable decrease and this decrease in case4 is much more obvious. In summary, the forward inclination of the front end wall of the bogie cavity increases the intensity of dipole sources at the front part of the bogie, while the inclination of the rear end wall of the bogie cavity could reduce the dipole source intensity on the cavity rear wall.

The pressure fluctuation on the solid surface is typically induced by the interaction between vortex structures and the solid wall. To analyze the influence mechanism of the bogie cavity end wall inclination on the intensity and distribution of dipole sources in the bogie region,

In case0, the shear layer could span the front components of the bogie, mainly interacting with the rear part of the bogie and the rear wall of the cavity. As a result, there are fewer vortex structures at the front of the cavity and the flow field there is relatively stable. In case1 and case3, the inclined front wall makes the position where the shear layer loses stability and rolls up move upstream, which enlarges the influence area of the shear vortices. In _{rms} values on the cavity rear wall are significantly reduced compared with that in case0.

The relationship between correlation area

For broadband noise, considering that the turbulent fluctuating pressure on the surface of the sound source propagates at convective velocity, thus

_{rms}.

As depicted in

The simulation results of the simplified cavity-bogie model suggest that inclining the rear wall of the bogie cavity appears to be a promising measure for reducing aerodynamic noise in the bogie region. However, further confirmation is required to assess its effectiveness when applied to the foremost bogie region of a real train. On the one hand, the presence of the head streamlined surface and cowcatcher makes the incoming flow state of the foremost bogie region of the real train somewhat different from that of the simplified cavity-bogie model. On the other hand, additional validation is imperative to ascertain whether the two-way operation of the train will exert any influence on the efficacy of noise reduction. In this section, the aforementioned noise reduction strategy is applied to a three-car marshalling model to further substantiate its effectiveness. The model configurations are depicted in

The same mesh strategy as mesh2 in

_{rms}) of the two three-car marshalling models. As can be seen, the dipole source intensity in the foremost bogie region is much higher than that of other bogies. In the foremost bogie region of the optimized model, the intensity of dipole sources on the rear wall of the bogie cavity and the carbody surface connects to it exhibits a significant attenuation compared with that of the original model, which is similar to the simulation results of the simplified cavity-bogie models.

The far field noise generated by the bogies and cavities of the two three-car marshalling models are further calculated. The arrangement of the far field noise measurement points is shown in

As shown in

_{original}–OASPL_{optimized}) is also presented in

In general, the far field noise results of the three-car marshalling model further confirm the effectiveness of inclining the rear wall of the bogie cavity in aerodynamic noise reduction of the bogie region. This kind of effectiveness is reflected in the suppression of noise radiated by the bogie cavity, while having limited impact on the noise generated by the bogie itself. Considering that the measurement points located at the side of the bogie exhibit higher noise level and the noise at these positions is mainly contributed by the bogie itself, further investigation is imperative to explore measures to mitigate the aerodynamic noise generated by the bogie itself, as well as their integration with noise control measures for the bogie cavity, in order to achieve a comprehensive aerodynamic noise reduction in the bogie region.

In this paper, the influence regularity and mechanism of the bogie cavity end wall inclination on flow field and aerodynamic noise characteristics in the bogie region are numerically studied. The simulation is first conducted on a simplified cavity-bogie model, including five cases with different cavity end wall inclination angles. By comparing and analyzing the five cases’ flow field and acoustic results, a noise reduction strategy is determined and subsequently applied to the foremost bogie region of a three-car marshalling model to verify its effectiveness when applied to the real train. The results indicate that variations of the inclination angles of the bogie cavity’s front and rear end walls can significantly affect the aerodynamic noise in the bogie region and have different influence mechanisms. The inclined front wall makes the position where the shear layer rolls up move upstream and enlarges the influence area of the shear vortices, which intensifies the interaction between the shear vortex structures and the front wheelset, front motor, and front gearbox, thereby increasing the aerodynamic noise generated by the bogie itself. The inclined rear wall has certain flow guiding effects, making more vortex structures flow out of the cavity, which could effectively weaken the interaction between the vortex structures and the rear wall of the bogie cavity and reduce the aerodynamic noise generated by the bogie cavity over a wide frequency range. The far-field noise results of the three-car marshalling model further validate the efficacy of inclining the rear end wall in mitigating aerodynamic noise in the bogie region. This effectiveness is primarily observed in attenuating noise emitted by the bogie cavity while having a limited impact on the noise generated by the bogie itself. A noise reduction of 0.5 to 1.5 dB can be achieved in the main sound radiation direction of the bogie cavity. Considering that the measurement points located at the side of the bogie have higher noise level and the noise at these positions is mainly contributed by the bogie itself, further investigation is needed to explore measures to reduce the aerodynamic noise generated by the bogie itself, as well as their integration with noise control measures for the bogie cavity, in order to achieve a comprehensive aerodynamic noise reduction in the bogie region.

For the successful completion of this paper, the authors of this paper expresses their sincere gratitude to the research institutions where the participants work.

This work was supported by National Natural Science Foundation of China (12172308) and National Key Research and Development Program of China (2020YFA0710902).

The authors confirm contribution to the paper as follows: study conception and design: Jiawei Shi, Jiye Zhang; data collection: Jiawei Shi; analysis and interpretation of results: Jiawei Shi, Jiye Zhang; draft manuscript preparation: Jiawei Shi, Jiye Zhang. All authors reviewed the results and approved the final version of the manuscript.

Not applicable.

The authors declare that they have no conflicts of interest to report regarding the present study.