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Physica Scripta
PAPER
The influence of jet on aerodynamic noise in the
pantograph area at different sinking heights
To cite this article: Yangyang Cao
et al
2024
Phys. Scr.
99 105228
View the article online for updates and enhancements.
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Phys. Scr. 99 (2024)105228 https://doi.org/10.1088/1402-4896/ad7413
PAPER
The influence of jet on aerodynamic noise in the pantograph area at
different sinking heights
Yangyang Cao, Jiye Zhang , Jiawei Shi and Yuzhe Ma
State Key Laboratory of Rail Transit Vehicle System, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China
E-mail: jyzhang@swjtu.edu.cn
Keywords: pantograph, jet flow, cavity, aerodynamic noise control, noise prediction
Abstract
The influence mechanism of jet on aerodynamic noise control in the pantograph region at different
sinking heights was numerically studied using an Improved Delayed Detached Eddy Simulation
(IDDES)model and the Ffowcs Williams-Hawkings (FW-H)equation. Active flow control was
achieved by setting jet slots at the leading edge of the cavity to predict the noise generated by the jet
itself. The results showed that in the pantograph region with a sinking height of 500 mm, the shear
layer was lifted by the jet, which prevented high-speed turbulence caused by flow separation from
entering the cavity. Therefore, the model with jet control device reduced the overall far-field noise on
the side of the pantograph by 1.6 ∼3.9 dB. Through flow field analysis, for the pantograph region
where flow separation occurs in the front of the cavity, the jet needs to lift the shear layer enough to
cross the front of the pantograph and prevent flow separation, thereby reducing the aerodynamic
noise. For the pantograph region without flow separation in the front of the cavity, the jet may
introduce additional noise sources, deteriorating the aerodynamic noise in the pantograph region.
1. Introduction
High-speed railway, being regarded as an important symbol of railway modernization due to its many
advantages such as safety, speed, punctuality, comfort, and environmental protection, has developed rapidly
worldwide. With the continuous increase in train speed and the densification of railway networks, noise control
has become an important issue for the sustained prosperity and development of high-speed trains.
High-speed trains mainly suffer the wheel-rail noise and aerodynamic noise. The former is proportional to
the third power of the train’s speed, while the latter is to the sixth. It is generally believed that when a train’s speed
exceeds 300 km h
−1
, aerodynamic noise will surpass wheel-rail noise and become the dominant external
radiation noise [1–3].The pantograph, one of the main aerodynamic noise sources, is generally considered as the
strongest local noise of high-speed trains [4,5]. For the aerodynamic noise generated by the pantograph, Tan
et al [6]conducted a predictive analysis of the pantograph flow field and far-field noise using Large Eddy
Simulation (LES)and FW-H equation. The results showed that the sound energy in the bottom region of the
pantograph accounted for over 50% of the total energy. Zhao et al [7]found that dipole sources dominate in the
far-field radiation noise of pantograph, while quadrupole sources can be ignored, and the contribution of
aerodynamic noise at the pantograph base frame, balance arm, and upper and lower arm rods is higher than
other components. Zhang et al [8]used computational fluid dynamics (CFD)/FW-H acoustic analogy method
to predict the far-field aerodynamic noise of pantographs, and the results indicated that the main aerodynamic
noise of pantographs was generated from the panhead and the base frame. Lei et al [9]numerically predicted the
noise radiation of single-arm pantograph at 300 km h
−1
, and found that the aerodynamic noise of high-speed
pantograph was caused by vortex shedding. Sun et al [10]used detached eddy simulation (DES)to numerically
simulate high-speed pantographs. It can be seen from the results that there were larger vortices around the head
and base of the pantograph, which affected the fluctuating pressure on the pantograph and resulted in
aerodynamic noise. Shi et al [11]studied the suppression technology of aerodynamic noise for Faiveley CX-PG
RECEIVED
27 April 2024
REVISED
12 August 2024
ACCEPTED FOR PUBLICATION
27 August 2024
PUBLISHED
5 September 2024
© 2024 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.
pantograph using Delayed Detached Eddy Simulation (DDES)and FW-H equation. It was found that the
strongest radiated noise in the range above 500 Hz came from the head region of the pantograph. Meskine et al
[12]used the FW-H equation to predict and analyze the aerodynamic noise of pantographs based on both
permeable surface method and impermeable surface method. As can be seen from the results, both methods
matched well with the experimental results.
In addition to the noise generated by the pantograph itself, in the pantograph region with a cavity, the
interaction between the cavity and the pantograph also affects the aerodynamic noise in this region. Kim et al
[13]compared the flow characteristics and radiated noise in the pantograph regions with and without cavities.
The research results indicated that the cavity structure reduces the velocity of the fluid to the bottom of the
pantograph, which facilitates noise reduction. Yao et al [14]used Large Eddy Simulation (LES)and Acoustic
Finite Element Method (FEM)to analyze the aerodynamic noise characteristics of high-speed trains with
pantographs installed on different roof bases (flat surface and concave surface). The analysis showed that the
pantograph with a concave base outperformed the flat structure in terms of aerodynamic noise. In the reference
[15], Kim et al mentioned that due to the flow separation in the cavity, significant pressure fluctuations may
occur on the tail wall of the cavity, which may introduce additional noise sources.
Therefore, for the leading-edge flow of the cavity, Saddington et al [16]experimentally installed a spoiler at
the leading edge of the cavity at Mach 0.71 for the reduction of momentum exchange between the free flow and
the cavity, and noise reduction. Kim [17,18]studied two noise-reduction effects of pantograph cabins on high-
speed trains represented by rectangular cavities (round edges and chamfered edges). It can be seen from the
results that this method can be used to significantly reduce the unsteady flow above the cavity, thereby reducing
radiated noise. The above measures are not well adapted to changes in flow conditions due to their nature of
passive flow control, since geometric shapes or mechanical devices cannot be changed once determined or
installed. It is therefore meaningful, in this regard, to study the noise reduction control technology in the
pantograph area based on active flow control methods.
Yu et al [19]established a SAS model for active control based on the two-equation SST turbulence model,
and analyzed the suppression effect of jet flow on cavity noise. The research showed that the jet raised the shear
layer, and reduced the high pressure on the back wall of the cavity. Ukai et al [20]investigated the effects of
injecting jets at different positions upstream of the cavity, and found that the separation shock oscillation formed
by jet flow at the leading edge of a cavity was significant. Zhao et al [21]demonstrated that a planar jet can
effectively eliminate the aerodynamic noise caused by the radiation of a series of rods in crossflow, however,
current research on jets mainly focuses on controlling high Mach number cavity noise only, and the cavity does
not contain any other objects. There is still a lack of research on lower Mach and other objects inside the cavity.
Therefore, in this paper, this active flow control technology was applied to the pantograph region of high-speed
trains, revealing its impact mechanism on the flow field and aerodynamic noise in the pantograph region. The
related research is expected to provide new understanding and insights for the innovation of aerodynamic noise
control technology in the pantograph region of high-speed trains.
2. Numerical methods
2.1. IDDES model
To achieve high computational accuracy at reasonable cost, a suitable turbulence model is necessary to simulate
the turbulent flow field around the pantograph region, as well as the details of flow separation and shedding
vortices in the turbulent flow field. Large Eddy Simulation (LES)is not widely used due to its computational
efficiency though it can simulate pressure fluctuations on the surface of objects well. Detached Eddy Simulation
(DES)is a hybrid of Unsteady Reynolds Average Navier–Stokes (URANS)and Large Eddy Simulation (LES)
methods. In the near-wall region, URANS with the Spalart-Allmaras (S-A)model is used to represent the flow,
which is useful to relax the strong LES mesh constraints close to solid surfaces. Meanwhile LES with a single-
equation model for the Subgrid-scale (SGS)viscosity is used in separated flow regions dominated by large
turbulence scales. To solve the problem of grid-induced separation caused by this method, Spalart et al [22]
improved the DES method into Delayed Detached Eddy Simulation (DDES)which was later found by Shur et al
[23]to possibly lead to logarithmic-layer mismatch. Therefore they introduced a new subgrid length scale that is
related to grid spacing and the wall distance, namely the Improved Delayed Detached Eddy Simulation (IDDES)
which was used in this paper to simulate the flow field in the pantograph region based on SST k-w. For more
details and research on IDDES model, please refer to references [24,25].
2.2. FW-H equation
As an exact re-arrangement of the N-S equation, the FW-H equation is directly derived from the N-S equation. It
is very difficult to solve this equation directly, therefore it’s more practical to think about this equation based on
2
Phys. Scr. 99 (2024)105228 Y Cao et al
Light hill acoustic analogy, that is, to think of the right-hand side as the source term. At this point, the equation is
a typical wave equation. A wave operator is introduced on the left side of the equation, and the three terms at the
right side correspond to the monopole source, dipole source distributed on the surface of the object and
quadrupole source in the fluid space, respectively. Thus, the far-field sound pressure is obtained by
superimposing the contributions of monopole sources, dipole sources, and quadrupole sources, as shown in
equation (1).
¢=¢ +¢ +¢ptp tp tp txx x x,,, , 1
TLQ
() () () () ()
where ¢ptx,,
T()
¢ptx,
L
()
and ¢ptx,
Q()
respectively represent the sound pressure generated by the monopole
source, dipole source, and quadrupole source terms.
References [26–28]all indicate that the pantograph quadrupole source can be ignored under flow conditions
with low Mach number. In the reference, Zhao et al analyzed the quadrupole and dipole sources of the
pantograph at a speed of 400 km h
−1
. It was found that quadrupole sources were mainly distributed in the place
where the inflow is split, with the highest energy reaching 1 ×10
7
. Dipole sources are mainly distributed on the
surfaces of various rods and cavities, with the highest energy of 1 ×10
8
.
The research results [7]showed that, at a speed of 400 km h
−1
, the dipole source intensity in the
pantograph region is greater compared to that of quadrupole source. From the perspective of calculation
methods, in this paper, the FW-H equation was used to predict the noise in the pantograph region. Limited by
computing resources, we are unable to consider a quadrupole source for volume integration. Therefore, the
influence of quadrupole sources was ignored considering the relevant research results and current computing
resources.
The numerical simulation in this paper is made based on the wind tunnel model, and the pantograph region
is a stationary rigid object surface, so the monopole source term is 0, and only the noise contribution from the
dipole source needs to be considered. Farassat proposed a space-time integrated solution of the FW-H equation
for subsonic flow conditions suitable for numerical calculations [29]. The formula for the sound pressure
contributed by a dipole source is expressed as follows:
⎡
⎣
⎢⎤
⎦
⎥⎡
⎣
⎢⎤
⎦
⎥
⎡
⎣
⎢⎤
⎦
⎥
òò
ò
¢=
p- +p
-
-
+p
+-
-
⋅
⋅
pt c
L
rM SLL
rM S
c
LrMcMcM
rM S
x,1
41 d1
41 d
1
41 d2
Lr
rret
rM
rret
rr r
rret
0222
0
00
2
23
() () ()
()
() ()
r=+ -LPn uu v 3
iijj inn
() ()
ds=- -Ppp 4
ij ij ij
0
() ()
where
M
i
refers to the Mach number in the x
i
direction and
M
r
stands for the Mach number in the observer
direction, the subscript
r
et
of the integral term represents the evaluation of the relevant variable over time,
c
0
denotes the speed of sound,
r
refers to the distance from a source point to the observer, u
n
represents the fluid
velocity component normal to the surface,
v
n
stands for the surface velocity component normal to the surface,
P
ij
is the compressive stress tensor,
s
ij denotes the viscous stress tensor, and p
0
refers to the ambient pressure.
3. CFD model
3.1. Geometry model
The research object of this paper is the CX-PG type active control pantograph installed on the CR400BF high-
speed train in China, which is a typical single-arm single-sliding plate pantograph, and the computational model
is in the scale of 1:1. Figure 1(c)shows the geometric model of the pantograph used for CFD simulation. It can be
seen from the figure that most of the geometric features of the pantograph are preserved and fixed in the
uncovered cavity on the roof through insulators. And a jet slot with a width of 15 mm is set at the leading edge of
the pantograph cavity, with the right end of the jet slot 50 mm away from the front wall of the cavity, as shown in
figure 1(d). To explore the influence of jet on the aerodynamic noise of pantographs at different sinking heights,
six calculation conditions were set up. The non-jet models were Base model 1, Base model 2, and Base model 3,
respectively, with heights h of 350 mm, 500 mm, and 650 mm. The corresponding jet models were Jet model 1,
Jet model 2, and Jet model 3. And the specific dimensions and related details of the pantograph region are shown
in figures 1(a),(b).
3
Phys. Scr. 99 (2024)105228 Y Cao et al
3.2. Computational domain and boundary conditions
The calculation domain is established for the flow field simulation of the pantograph model to conform to the
actual operation of high-speed trains as much as possible, as shown in figure 2. The dimensions of the calculation
domain along the x, y, and z directions are 35 m, 20 m, and 50 m, respectively. The size of the region is sufficient
to eliminate blocking effects in computational simulations and ensure the full development of the wake. The lack
of computing resources currently in the laboratory makes it difficult to meet the minimum time step and spatial
grid scale requirement for compressible model. As can be seen from the research results in reference [7], for the
pantograph at a speed of 400 Km h
−1
, the presence of local high-Mach numbers in individual components does
not have a significant impact on the results. Due to the above reasons, an incompressible model is still taken as
Figure 1. Pantograph region model.
4
Phys. Scr. 99 (2024)105228 Y Cao et al
the research content in this paper. The entrance of the computational domain is set as the velocity-inlet, with an
inflow velocity of 111.11 m s
−1
(400 km h
−1
). While the outlet of the computational domain is set as the
pressure-outlet, with a gauge pressure of 0. Set symmetrical boundaries on both sides and the top of the
computational domain. The bottom surface is set as a slip wall, and the slip velocity is consistent with the
velocity-inlet. And the other surfaces are set as non-slip walls. For the modeling of planar jets, the surface of the
jet outlet is set as the velocity-inlet, without modeling the interior of the jet slot. The research results in reference
[30]show that this modeling method has no impact on the jet trajectory. In terms of jet velocity, Zhao et al [21]
found that the shielding region formed by the jet can reduce the aerodynamic noise of objects in it. Therefore, to
ensure that the shielding region meets the requirements to the maximum extent, this situation where the jet
velocity is 111.11 m s
−1
is mainly studied in this paper.
3.3. Mesh strategy
The computational domain is discretized based on a hybrid mesh strategy of prism layer mesh and trimmed
volume mesh. The surface mesh size of the pantograph was controlled between 1–5 mm. To accurately simulate
the flow of the boundary layer on the pantograph surface, 15 layers of fine prism layer mesh with an initial height
of 0.01 mm and a growth rate of 1.2 were generated on the pantograph surface. To verify the effectiveness of the
boundary layer, a convergent steady-state solution was obtained through 4000 steps of RANS simulation, with
its Y+value shown in figure 3. The Y+values in the entire pantograph area are all less than 5, as clearly shown in
the figure. As concluded in reference [25], for Y+value less than 5, full Y+wall treatment (A wall treatment
method of STAR-CCM+)should be adopted in numerical simulation calculations for better numerical
calculation results. Meanwhile, multiple refinement zones have been established to locally refine the
Figure 2. Computational domain and boundary conditions of pantograph region.
Figure 3. Y+distribution around the pantograph region.
5
Phys. Scr. 99 (2024)105228 Y Cao et al
computational domain volume mesh, resulting in a final volume mesh number of approximately 100 million.
Refer to figure 4for the specific distribution of the mesh around the pantograph region.
3.4. Solver setup
The discrete flow control equation is solved by using segregate flow solver based on SIMPLE algorithm. The
convection term is discretized by using a mixed second-order upwind and bounded center difference scheme,
while the diffusion term is discretized by using a second-order scheme. The gradient calculation was conducted
based on the second-order hybrid Gaussian LSQ method [25], while the second-order implicit method was used
for time advancement with an acoustic simulation time step of 5 ×10
−5
s. The fluctuations of the flow field
within the target frequency range can be fully and accurately analyzed to ensure the stability of the solution.
Meanwhile, as can be seen from the calculation, the convective CFL number is about 0.926, which can fully
ensure the stability of the pantograph region in the simulation experiment [25]. Before flow field data collection,
the converged steady-state solution obtained through RANS simulation was used as the initial field to simulate
the unsteady flow field, which lasted for 4000 steps. After the full development of the transient flow field for
0.15 s, the FW-H solver started to calculate the far-field aerodynamic noise of the research object while solving
the flow field. The transient simulation in this phase lasted for another 0.21 s. Based on the sampling theorem
(=D
f
t
max
1
2), it is expected that up to 10000 Hz of noise components can be analyzed. In this paper, to maintain
high accuracy of noise capture, as each cycle contains 4 sampling points, it is expected that up to 5000 Hz of noise
components can be analyzed. Meanwhile, if the second-order difference scheme is used for flow field
calculations, make sure that the minimum wavelength contains at least 8 mesh to capture sufficiently small
vortices [31]. In this paper, the analysis showed that the highest frequency of aerodynamic noise in the
pantograph area was 5000 Hz, which corresponds to a wavelength of 68 mm. Therefore, the size of the surface
grid should be less than 8.5 mm to fulfill the corresponding grid size requirements.
4. Validation of the numerical methods and mesh strategy
4.1. Cavity case
Limited by research funding and experimental resources, flow field and aerodynamic noise data of a full-size
pantograph are unavailable through wind tunnel tests. In this paper, the research of Kim et al [13]and the
experiment of Plentovich et al [32]were referenced to validate the mesh strategy and numerical method in the
current work through ‘clean cavity’(the cavity does not contain other objects). The cavity has a length of
L
1
=366 mm, a width of W
1
=244 mm, and a depth of D
1
=61 mm. The corresponding length-depth ratio is
6:1, and the width-depth ratio is 4:1. The static pressure distribution at the bottom of the cavity was calculated at
the inflow velocity of 0.2 Mach. The simulated computational domain and boundary conditions are shown in
figure 5.
To validate the effect of mesh size on numerical simulation, three sets of meshes of different sizes were
obtained by changing the surface mesh size of the cavity and the volume mesh size in the refinement zone, as
Figure 4. Mesh distribution around the pantograph region.
6
Phys. Scr. 99 (2024)105228 Y Cao et al
shown in table 1. The number of volume grids is 3.5 million, 5.2million, and 8.3 million, respectively. The mesh
distribution near the cavity is shown in figure 6.
In terms of the pressure coefficient CP(
=
r
-
¥
¥
C
p
PP
12u
2
/
)at the bottom of the cavity, the comparison and
validation based on three sets of mesh calculations and the experimental results of Plentovich et al are shown in
figure 7. The pressure data is measured on the centerline at the bottom of the cavity. As can be seen from the
figure, in the front and middle of the cavity, the calculated values are in good agreement with the experimental
results. And the pressure coefficient shows a trend of uniform distribution approaching 0. While at the rear of
the cavity bottom, the pressure coefficient increases rapidly with the increase of d/L
1
(where d refers to the
distance from the measurement point to the front wall of the cavity). The simulation results are higher than the
experimental values, but showing the same trend as the latter. This situation has not been significantly improved
even if the mesh is further refined. This difference is more likely caused by the difference between the simulated
region and the actual testing environment. Overall, the distribution trend of pressure coefficient at the bottom of
the cavity is consistent between the simulation results and the experimental results, and the difference between
Figure 5. Computational domain and boundary conditions of cavity.
Figure 6. Layout of cavity grid refinement region.
Table 1. Cavity mesh parameters.
mesh1 mesh2 mesh3
Cavity surface 1.8 mm 1.5 mm 1.2 mm
Rregion1(R1)2.1 mm 1.8 mm 1.5 mm
Rregion1(R2)4.2 mm 3.6 mm 3 mm
Rregion1(R3)8.4 mm 7.2 mm 6 mm
Rregion1(R4)16.8 mm 14.4 mm 12 mm
7
Phys. Scr. 99 (2024)105228 Y Cao et al
the two is also within an acceptable range. Therefore, the mesh parameters used in current research for the flow
field simulation in the pantograph region are reasonable considering both computational accuracy and resource
consumption.
4.2. Pantograph case
To further verify the rationality of the grid size used in transient numerical simulation, the transient flow field of
the pantograph at an inflow velocity of 200 km h
−1
was calculated based on the wind tunnel test results of the
CS-PG pantograph in [33]. The calculation domain is shown in figure 8where the center of the pantograph is
15 m away from the velocity inlet and 35 m away from the pressure outlet. The boundary conditions and mesh
strategy are completely consistent with chapter 3.
To collect aerodynamic noise in numerical simulations, a series of measurement points were established.
The distance from the measuring point to the centerline of the pantograph is 7 m, that to the no-slip wall surface
is 3.5 m, and the distance between adjacent measuring points is 0.8 m. Therefore, 11 symmetrical measuring
points were established around the geometric center of the pantograph. Among them, the strength of sound is
defined by sound pressure level, which is defined as follows:
=SPL P P dB20 log 5
0
() ()/
where SPL represents the sound pressure level,
P
is the sound pressure, and
P
0stands for the reference sound
pressure.
The numerical simulation results were obtained based on the same solution setup as in chapter 3, as shown
in table 2. As can be seen, the simulated values are basically consistent with the experimental values. The error
Figure 7. Simulation and test results of the pressure coefficient at the bottom of cavity.
Figure 8. Computational domain and boundary conditions of pantograph.
8
Phys. Scr. 99 (2024)105228 Y Cao et al
between the two may be due to the environment and experimental conditions during the experiment. Overall,
the numerical simulation results meet the requirements, and the errors are within the allowable range.
Therefore, in this paper, the mesh strategy and calculation method showed high accuracy, and the mesh used in
the pantograph region also has high robustness.
5. Results and discussion
5.1. Noise sources
The fluctuation of surface pressure (Standard deviation of pressure)in the pantograph region is shown in
figure 9, which determines the effect of jet introduction on the strength and distribution of surface dipole
sources in this region. As can be seen from the figure, high amplitude pressure fluctuations were observed in all
base models at the panhead, base frame, insulators, upper and lower arm bars, and the rear surface of the cavity.
After the introduction of the jet, compared with the corresponding base model, in Jet model 1, the pressure
fluctuations on the surface of the pantograph base frame, insulators, lower arm bar, and the back of the cavity are
significantly increased. While in Jet model 2, the pressure fluctuations on the surface of the lower arm bar,
insulators, and the cavity are significantly suppressed, and those in the region of the base frame are significantly
enhanced. In Jet model 3, the pressure fluctuations in the lower arm and insulator surfaces are enhanced, and the
pressure fluctuations in the base frame region and the rear wall of the cavity are somewhat reduced. For all Jet
models, the introduction of jet has no significant effect on the pressure fluctuations at the upper arm and
panhead of the pantograph. As can be seen in figure 9, there is no meaningful change in the pressure amplitude at
Figure 9. Surface pressure fluctuation in the pantograph region.
Table 2. Comparison between numerical simulation and experimental results. Units:dB(A).
Measure point 1234567891011
Experiment 79.7 80.4 80.1 80.4 80.4 80.7 80.6 80.3 79.9 80 80.2
Simulation 80.8 81.6 81.2 81.7 81.9 81.8 81.9 81.8 81.6 81.2 81.1
Error 1.1 1.2 1.1 1.3 1.5 1.1 1.3 1.5 1.7 1.2 0.9
9
Phys. Scr. 99 (2024)105228 Y Cao et al
these two locations, which indicates that the jet raising the shear layer has no impact on the flow of air in the
upper part of the pantograph.
5.2. Flow field analysis
To further explore the impact of introduced jets on the pressure fluctuations in the pantograph region, in this
section, the impact of introducing a jet into the pantograph region on the wake flow field of the pantograph is
further analyzed.
Figure 10 shows the instantaneous vorticity distribution around the pantograph region in the base model
and jet model at three different sinking heights. In the figure, three important vortex triggering sources are
confirmed in the pantograph region, namely, the panhead, knuckle, and base frame. In panhead section, there is
almost no effect on its vorticity after the introduce of the jet. Although the jet raises the shear layer, it affects the
middle and lower regions of the pantograph, but has no significant impact on the position of the panhead.
Therefore, the analysis of the flow field in the pantograph region is focused on the middle and lower part of the
pantograph region.
In Base model 1, the flow separation occurred at the leading edge of the cavity, and a portion of gas entered
the cavity from the front, and formed shedding vortex which interacted with the front of the cavity and the
insulator at the bottom of the pantograph before reattaching and moving downstream. Another part of the gas
formed shedding vortex after interacting with the pantograph base, which continued to move downstream and
interact with the lower arm bar and knuckle of the pantograph. Different from Base model 1, in Jet model 1, the
introduced jet raises the shear layer and intensifies the shedding vortex formed after the impact of gas on the base
frame, resulting in the increase of pressure fluctuations at the pantograph base frame and lower arm. At the same
time, the obstruction at the front of the pantograph prevented the high-speed shedding vortex formed by the jet
from crossing the base frame, instead, it moved towards the bottom of the base frame, causing the high-speed
shedding vortex to impact the front of the cavity. The shedding vortex reattached and moved downstream after
the impact. In the downstream, these shedding vortex structures interacted with the bottom insulator and cavity,
significantly enhancing their pressure fluctuations. The increase in pressure fluctuations in these sections can be
clearly seen in figure 9.
In Base model 2, the flow separation occurred at the leading edge of the cavity, and a portion of the gas
entered the cavity from the front and formed shedding vortex. These shedding vortex structures rolled up and
moved downstream after hitting the front of the cavity, and then interacted with the bottom insulator of the
pantograph and the cavity. The other portion of the gas formed shedding vortex by impacting the base frame,
which continued to move downstream and interact with the lower arm and knuckle. In Jet model 2, the jet did
Figure 10. Distribution of instantaneous vorticity around the pantograph region.
10
Phys. Scr. 99 (2024)105228 Y Cao et al
not make a movement towards the bottom of the base frame, instead, it impacted the front of the
pantograph base frame. After the impact, a small portion of the shedding vortex formed by the jet crossed the
base frame and continued to move downstream. Compared to Base Model 2, the impact of the associated vortex
structures on the pantograph region was significantly weakened, and the formed wake was also significantly
narrowed. Considering the results of the pressure fluctuations shown in figure 9, the pressure fluctuations in the
pantograph region in Jet model 2 are significantly reduced.
In Base model 3, due to the fact that the height of the base frame is already lower than the cavity, the gas did
not undergo flow separation at the leading edge of the cavity. Instead, it impacted the front of the base frame, and
a small portion of the shedding vortex structure formed after the impact, and continued to move downstream
across the base frame and interacted with the pantograph lower arm bar. In Jet model 3, the jet did not interact
with the front of the pantograph region, but crossed the entire base frame region and continued to move
downstream. In downstream, the high-speed shedding vortex formed by the jet interacted with the lower arm of
the pantograph. A portion of the shedding vortex formed after the interaction continued to move downstream,
resulting in increased pressure fluctuations at the knuckle. The other part of the shedding vortex moved towards
the bottom of the pantograph, and interacted with the bottom of the cavity and then re-attached and moved
towards the front of the cavity, causing a slight increase in pressure fluctuations at the front of the cavity and the
insulator. Based on the analysis shown in figure 9, in Base model 3, the pantograph base frame blocked a portion
of the incoming flow from direct impact with the lower arm of the pantograph and the knuckle. However, the
high-speed shedding vortex formed by Jet model 3 after the introduction of the jet avoided the obstruction of the
pantograph base frame, resulting in increased pressure fluctuations in the lower arm bar of the pantograph,
knuckle, insulators, and the front of the cavity. The increase in pressure fluctuations in these sections can be
clearly seen in figure 9.
Figure 11 shows the time averaged streamline of the wake in the pantograph region, which better describes
how the jet affects the main vortex structure in the wake of the pantograph region, and clarifies its mechanism of
action in affecting the aerodynamic noise in the pantograph region. In Base model 1, the incoming air
underwent aerodynamic separation at the leading edge of the cavity, and introduced a recirculation region at the
front of the cavity. The similar separation and recirculation have also been pointed out by Kim [13]and Noger
[34]. At present, a portion of the gas, after the separation of the front edge of the cavity, moved toward the
bottom of the pantograph, and impacted the insulators at the bottom of the pantograph and the bottom of the
cavity. After the impact, the fluid velocity decreased significantly, and the fluid continued to move downstream,
and then rolled up at the back of the cavity. In Jet model 1, the jet raised the shear layer, but the same flow
separation occurred caused by the front of the pantograph base frame. A portion of the high-speed incoming air
Figure 11. Time averaged streamline of wake in the pantograph region.
11
Phys. Scr. 99 (2024)105228 Y Cao et al
moved towards the bottom of the cavity, and a recirculation region was introduced in the front of the cavity and
near the pantograph insulator. It can be seen from the trend of the streamline that the shear layer impacts the
pantograph insulators and the bottom of the cavity before rolling up. The tendency to roll upwards is more
pronounced compared to the case of Base model 1, indicating that the shear layer impacts the cavity and the
pantograph more violently, generating larger pressure fluctuations.
In Base model 2, the incoming air also underwent flow separation at the leading edge of the cavity. A portion
of the separated gas moved downward, and impacted the front of the cavity. At the same time, a recirculation
region was introduced in the front of the cavity and the front of the pantograph insulator. The impacted gas
continued to move downstream, and reattached and rolled up downstream of the cavity after impacting the
pantograph insulator. It can be seen from the trend of the streamline, the incoming air also impacted the rear
part of the cavity, generating significant pressure fluctuations. In Jet model 2, the introduced jet raised the height
of the shear layer, and therefore, the incoming air did not undergo flow separation due to the front of the
pantograph, instead, it moved downstream after crossing the entire pantograph and introducing a larger
recirculation region at the rear of the cavity. Compared to Base model 2, due to the lack of high-speed fluid
entering the bottom of the pantograph from the front of the cavity, the impact of air on the bottom of the
pantograph and the cavity was greatly reduced, including the pressure fluctuations caused by it.
In Base model 3, due to the fact that the height of the pantograph base frame is lower than the depth of the
cavity, the incoming air did not undergo flow separation at the leading edge of the cavity, indicating that there
was no high-speed air separated from the leading edge of the cavity and entering the cavity. Instead, it directly
crossed the pantograph base frame and formed a relatively flat recirculation region at the rear of the cavity after
interacting with the front of the pantograph. In Jet model 3, the jet raised the shear layer, so that its height
exceeded that of the pantograph base frame. It is worth noting that the raised shear layer caused the velocity of
the incoming air to increase. Therefore, its impact on the lower arm and knuckle will be greater, causing
significant pressure fluctuations here, and the speed of the recirculation region formed by the shear layer
crossing the pantograph is also higher compared to the case of Base model 3. Due to the high speed of flow in the
recirculation region, the impact on the pantograph insulator is greater. The fluid in the recirculation region
continued to move towards the front of the cavity after impacting the insulator. It can be seen from figure 11 that
the velocity at the front of the cavity of Jet model 3 is greater than that of Base model 3, resulting in greater impact
of the fluid on the front of the cavity, which creates a larger pressure fluctuation at the front of the cavity. Figure 9
shows that the pressure fluctuations at the lower arm, knuckle, insulator, and the front of the cavity in Jet model
3 have all increased.
As can be seen from figure 12, the distribution of turbulent kinetic energy in the pantograph region is under
various conditions. Compared to Base model 1, Jet model 1 significantly enhances the amplitude of turbulent
kinetic energy in the lower arm region of the pantograph and the rear of the cavity. The reason is that the high-
speed turbulence is formed after the jet raises the shear layer, and the flow separation occurs in the front of the
pantograph. One part of the high-speed turbulence is pushed to the lower arm bar of the pantograph, while the
other part enters the cavity from the front of the cavity, and interacts with the bottom surface of the cavity. Seen
from figure 9, the amplitude of pressure fluctuation in these sections is significantly increased compared to the
case of Base model 1.
Based on the comparison with Base model 2, it can be clearly seen that due to the introduction of the jet, Jet
model 2 did not undergo flow separation. This also indicates that the high-speed turbulence formed by the jet
which raised the shear layer did not enter the cavity from the leading edge of the cavity, and it is also mostly
canceled by the front of the pantograph. Therefore, the high-speed turbulence in the cavity region and the rear of
the pantograph has been significantly reduced compared to the case of Base model 2. This can also be
understood as the reason for the reduced amplitude of pressure fluctuations in the pantograph region, as shown
in figure 9.
Based on the analysis of Base model 3 and Jet model 3, it can be concluded that no flow separation occurs at
this sink height with or without the presence of the jet. In another word, there is no high-speed turbulence
entering the cavity from the front of the cavity at this sink height. Figure 12 shows that, in Jet model 3 the high-
speed turbulence crosses the front of the pantograph, and directly interacts with the lower arm bar of the
pantograph, which continues to move towards the rear of the cavity, and interact with the back of the cavity. In
Base model 3, the front structure of the pantograph has a certain blocking effect on high-speed turbulence, with
only a small portion of high-speed turbulence crossing the front of the pantograph, resulting in less strong effect
on the lower arm and knuckle of the pantograph. However, due to the lack of jet to raise the shear layer, this part
of the turbulence collided with the upper part of the rear wall of the cavity, as can be seen from figure 9, the
pressure fluctuation in this part is large in Base model 3. However, the pressure fluctuations in Jet model 3 model
are significant at the front of the cavity, lower arm, and knuckle.
Through the analysis of the flow field in the pantograph region, it can be concluded that, at the same speed,
due to the obstruction of the pantograph base frame, in Jet model 1 with shallow cavities, it is difficult for the jet
12
Phys. Scr. 99 (2024)105228 Y Cao et al
to raise the shear layer to the required height. It can cause the high-speed fluid formed by the shear layer to enter
the bottom of the cavity from the front edge of the cavity, and result in a significant increase in pressure
fluctuations in Jet model 1 compared to Base model 1. For Jet model 2 and Jet model 3 with deeper cavities, this
situation will not occur. The results indicate that jet can raise the shear layer to a sufficient height. In Jet model 2,
the introduction of jet effectively solves the problem of flow separation that occurs at the leading edge of the
cavity in Base model 2, resulting in a significant reduction in pressure fluctuations in the pantograph region.
However, in Jet model 3, Base model 3 no longer experiences flow separation at the leading edge of the cavity,
and the introduction of a jet at this point may cause additional noise.
Meanwhile, flow field analysis focused on the potential impact of jet introduction on aerodynamic noise in
the pantograph area, without further analysis of the interaction between the jet and the flow inside the cavity. In
figure 11, it can be clearly seen from Jet model 2 and Jet model 3 that the jet crosses the pantograph base frame,
without entering the cavity from the leading edge of the cavity. Therefore, the flow inside the cavity is similar to
that in an open cavity (L/D<10)[35]. The flow inside the open cavity is less disturbed by the shear layer above.
Therefore, the introduction of jets into jet models 2 and 3 mainly reduced the velocity of the flow inside the
cavity, while the impact of the jet itself on the flow inside the cavity is relatively weak. For more information on
the mechanism of interaction between jets and open cavities, please refer to references [19,36]. In Jet Model 1,
the jet entered the cavity from the leading edge, and interacted with the cavity and pantograph frame, resulting in
increased pressure pulsation of related components and reduction of noise.
5.3. Far-field noise
To analyze the far-field noise in the pantograph region, 33 measurement points at different heights were set at
the most important location for evaluating train noise (track side), as shown in figure 13. The pantograph region
was divided into three parts for noise radiation calculation, namely, the overall part (cavity and pantograph),
pantograph part, and cavity part. Figure 14 summarizes the noise reduction effects of these three parts at the
measurement points.
For the three parts, Jet model 1 and Jet model 3 showed no good noise reduction effect, and compared to the
Base model without jet installed, their aerodynamic noise was reduced significantly. This is consistent with the
results of the analysis in the previous section. In Jet model 2, the aerodynamic noise was reduced by about
1.5–3.9 dB at all measurement points in the overall section. In the pantograph section, the aerodynamic noise
was reduced by about 0.1–0.5 dB at most measurement points. In the cavity section, the aerodynamic noise at
the measurement point was reduced by about 4.5–7.5 dB, showing a significant noise reduction effect. To
further analyze the noise reduction effect of Jet model 2, figure 15 shows the spectral results of Base model 2 and
Jet model 2 models at B6 and A6, and the corresponding overall sound pressure level (OASPL)is shown in
Figure 12. Turbulent kinetic energy distribution in the wake of the pantograph region.
13
Phys. Scr. 99 (2024)105228 Y Cao et al
Figure 13. Location of side measurement points.
Figure 14. Noise reduction effect at lateral measurement points.
14
Phys. Scr. 99 (2024)105228 Y Cao et al
figure 16(a). Figure 16(b)illustrates the noise reduction effect in the form of one-third octave band. Seen from
figure 15, for both Base model 2 and Jet model 2, their spectral results at B6 and A6 are generally broadband. And
for the entire pantograph region, the noise below 500 Hz is mainly contributed by the cavity, while the noise
above 500 Hz mainly comes from the pantograph. As can be seen from the spectrum of Base model 2, the vortex
shedding frequency and the peak corresponding to its harmonic frequency are clearly visible, and dominate the
total noise. From the spectrum of Jet model 2, the introduction of the jet mainly mitigates the noise in the
Figure 15. Spectral results of B6 and A6.
Figure 16. OASPL results and noise reduction effect of Jet model 2 at B6 and A6.
15
Phys. Scr. 99 (2024)105228 Y Cao et al
frequency range associated with vortex shedding, and the suppression of the cavity is extremely pronounced,
with a noise reduction of about 7 dB realized in the cavity section. The pantograph section achieved a noise
reduction of approximately0.4 dB. Therefore, for the entire pantograph region, OASPL has decreased by
approximately 3.7 dB.
5.4. Estimation of the planar jet noise
Considering that with the addition of the planar jet, it generates certain level of noise itself, which may affect the
noise reduction effect in the pantograph region. It is therefore necessary to evaluate the level of noise generated
by the jet itself to confirm that the noise itself generated by the addition of the jet does not affect the noise
reduction effect on the pantograph region.
Munro and Ahuja conducted aerodynamic-acoustic experiments on planar jets with high spreading ratios
(no cross flow)[37,38]. Rectangular jets with widths h between 0.66 and 1.45 mm and lengths w between 17 and
76 cm were tested, and the aspect ratios of the jets ranged from 100 to 3000 (12 different cases). The jet velocity
was set within the range of 150–335 m s
−1
, the noise measurements of the jet were made at different observation
angles
q
,
and they found that the noise intensity of the jet with high aspect ratio satisfies the following
relationship:
r
rqµ-
-
IVL
aR M1cos 6
mjeq
m
c
282
00
52
5
() ()
where
p
refers to the acoustic pressure,
r0
stands for the average density of the environment,
rm
represents the
density of the mixing zone,
a0
is the environmental sound velocity,
L
eq
denotes the equivalent length scale, and
M
c
stands for the convective Mach number. Based on the experimental results, the convective Mach number is
approximated as
=
M
M0.36
cj
where
M
j
refers to the Mach number of the jet. The definition of equivalent
length
L
eq
is expressed as follows:
=Lhw 7
eq 34 14
()
//
It should be noted that the convective Mach number does not work at the viewing angle of 90°. Therefore,
the spectral levels were normalized according to equation (6), and compared with the normalized frequency to
obtain:
q=-
+
ffLMVlog 1 cos 8
eq c j
[( )] ()/
Oerlemans et al [39]combined equations (6)to (8)to give the normalized spectrum used to estimate the jet
noise. With
SPL
nor
m
and
f
nor
m
(the normalized level and frequency as read from the normalized spectrum), and
all other variables in metric units, the dimensional sound level SPL and frequency
f
are determined by the
following equations:
xq=+ - - + - +
gg-
SPL SPL R V h w M20log 10 log 20log 50log 1 cos 98.72 9
mj cnorm 1
() () ( ) ( ) ()
q=-
gg-
ffhwMVlog 1 cos 10
norm cj
1
[( )] ()/
where
x
=8,
g
=0.75.
In the study by Oerlemans et al [39], it was found that at jet velocities below 140 m s
−1
(M
j
=0.4), according
to the scale given in the reference [37,38], and the law of 8 powers of the jet velocity, the test results are not well
collapsing. Better results can be obtained if the law of 5 powers of jet velocity is used for normalization instead of
the law of 8 powers.
Therefore, noise estimation for the jet at a velocity of 140 m s
−1
is performed based on the results obtained
by Munro et al [37,38]and the normalized spectrum provided by Oerlemans et al [39]in combination with
equations (9)and (10). Then, the results were scaled by using the 5th power law of jet velocity to obtain a jet noise
spectrum at 111.11 m s
−1
. To simplify the calculations, only the observation angle of 90°is considered. Figure 17
shows the comparison between the noise spectra of Base model 2 and Jet model 2 at measurement points B6 and
C6 and the estimated jet noise spectra (displayed in the form of 1/3 octave band). As can be seen from the figure,
whether it is the Base model or the Jet model, the noise generated by the jet itself is much lower than that in the
pantograph region at the frequency below 2000 Hz. For frequency noise above 2000 Hz, the noise generated by
the jet itself is slightly greater. However, considering that high-frequency noise decays rapidly when measuring
far-field noise, its impact on far-field noise measurement is not significant. On the other hand, since only a 90°
observation angle was considered during estimation, it can be inferred from equation (9)that the actual
aerodynamic noise generated by the jet is lower than the estimation. Therefore, based on the overall results, the
noise generated by the jet itself will not affect the noise reduction effect.
16
Phys. Scr. 99 (2024)105228 Y Cao et al
6. Conclusions
This paper mainly explored the potential application of introducing a planar jet at the leading edge of the
pantograph cavity to control aerodynamic noise in the pantograph region of high-speed trains through
numerical research. Three different pantograph region models were established with sinking heights of 350 mm,
500 mm, and 650 mm, respectively, namely Base model 1, Base model 2, and Base model 3. On this basis, planar
jets are arranged at 50 mm away from the leading edge of the cavity, and the corresponding jet-
pantograph region models are called Jet model 1, Jet model 2, and Jet model 3, respectively. The jet velocity is set
to be the same as the incoming velocity during the simulation to provide enough momentum to lift the shear
layer. Based on the results, considering the plane jet, the dipole source intensity (pulsating pressure)on the
surface of the pantograph region in Jet model 2 is significantly reduced compared to the case of Base model 2,
especially at insulators, cavities and lower boom surfaces. And for measurement points on the side of the
pantograph, the overall sound pressure level is reduced by up to 4 dB, showing a significant noise reduction
effect. Meanwhile, the results of the far-field noise estimation of the jet itself show that the noise generated by the
jet itself does not affect the noise reduction. In Jet model 1 and Jet model 3, the dipole source intensity on the
surface of the pantograph region increases in different degree compared to the corresponding Base model, which
leads to a deterioration of the overall sound pressure level.
The analysis of the flow fields shows that the wake fields in both Base model and Jet model
pantograph regions are dominated by alternating vortex shedding. In the pantograph region with shallow
cavities (Base model 1 and Base model 2), the flow separation at the leading edge of the cavity mainly accounts for
the increase of the dipole source strength at the bottom of the pantograph and in the cavity. The comparative
analysis shows that the introduction of jet in Jet model 1 cannot solve the problem of flow separation. The reason
is that though the jet raises the shear layer, it is not enough to cross the base frame of the pantograph, instead,
flow separation occurs in the front of the pantograph, consequently, the high-speed turbulence enters the cavity
from the front of the pantograph, and interacts with the cavity and the pantograph to cause large pressure
pulsations. The introduction of the jet in Jet model 2 is a good solution to the problem of flow separation at the
leading edge of the cavity, which provides good noise reduction. For the pantograph region with a deeper cavity
(Base model 3), there is no flow separation at the leading edge of the cavity. If a jet is introduced (such as Jet
model 3), the high-speed turbulence formed by the elevated shear layer will impact the lower arm of the
pantograph, the knuckle, the insulators, and the front part of the cavity, introducing an additional noise source,
thus worsening the aerodynamic noise situation.
In summary, in the pantograph region where flow separation occurs at the leading edge of the cavity, the
introduced jet must raise the shear layer to cross the front of the pantograph, thereby preventing high-speed
turbulence from entering the cavity from the front of the pantograph to achieve noise reduction effect. On the
contrary, in the pantograph region where flow separation does not occur at the leading edge of the cavity, the
introduction of jet will introduce additional noise sources, leading to a reduction of aerodynamic noise in the
pantograph region. However, it should be noted that the current numerical results alone are not sufficient for
the investigators to fully understand the impact of the jet on the pantograph region. Therefore, further research
in this field is necessary in the future, especially to further describe the optimal jet velocity, position, and shape of
Figure 17. Comparison of spectral results of pantograph noise and jet noise.
17
Phys. Scr. 99 (2024)105228 Y Cao et al
the jet nozzle, and the effect of the jet on the pantograph region when the high-speed train is moving in the other
direction.
Acknowledgments
This work was supported by National Natural Science Foundation of China (12172308).
Data availability statement
The data cannot be made publicly available upon publication because no suitable repository exists for hosting
data in this field of study. The data that support the findings of this study are available upon reasonable request
from the authors.
Author contributions
Yangyang Cao:Conceptualization, Methodology, Data curation, Formal analysis, Writing - original draft. Jiye
Zhang: Funding acquisition, Supervision. Jiawei Shi:Writing - review & editing, Supervision. Yuzhe Ma:
Editing, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could
have appeared to influence the work reported in this paper.
ORCID iDs
Jiye Zhang https://orcid.org/0000-0003-2502-2444
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