2017 2nd International Conference on Industrial Aerodynamics (ICIA 2017) ISBN: 978-1-60595-481-3

Numerical Simulation of Aerodynamic Drag of

Single High-Speed Train Passing

through a Tunnel

Yonggang Yang, Dongbao Ma and Yuangui Mei

ABSTRACT

Train aerodynamics problem must be solved with the development of high-speed

railway around the world, and the drag directly affects the maximum running speed

of high-speed train. This paper established the numerical calculation model for single

train passing through the tunnel with the real configuration of a domestic EMU with

eight carriages. The formation mechanism and variation characteristics of the drag

over time were analyzed. The drag value and the distribution characteristic of the

individual parts were studied at different times of the train passing through the tunnel.

The maximum and minimum drag values of the tunnel were compared with the drag

of the open air condition. Results indicate the Mach wave directly affected on the

pressure drag, the aerodynamic drag distribution of the whole train is changed over

time and the fluctuation range of the pressure drag is larger than the friction

resistance when the train passing through the tunnel. The maximum value and

minimum value of total drag when the train passes through the tunnel are 1.95 times

and 0.88 times of that in the open air. When the train is running in the open air, the

pressure drag and frictional drag accounted for 61% and 39% respectively of the total

aerodynamic drag.

1. INTRODUCTION

In recent years, the operational speed of the high-speed train has largely

improved, and the dynamic of the train has become the key technologies in high-

________________________

Gansu Province Engineering Laboratory of Rail Transit Mechanics Application, School of Mechanical Engineering, Lanzhou Jiaotong University, 88 West Anning Rd., Lanzhou, Gansu, China

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speed train’s improvement. The aerodynamic problem has significantly affects the

economy, environment, safety, and comfort. When the train passes through the

tunnel, the aerodynamic problem is more serious. The drag directly affects the

maximum running speed of high-speed train. A large number of studies on

aerodynamic characteristics by domestic and foreign scholars using the field test,

model test, numerical simulation and other methods have carried out in recent

years[1,2,3]

, but fewer studies on tunnel aerodynamic drag. The aerodynamic drag’s

fluctuation amplitude is compared of the single train passing through the tunnel and

in the open air [4]

. The reason for the aerodynamics’ fluctuation is explained and the

fluctuation characteristic of aerodynamic along the train length is showed [4]

. The

variation characteristics over time of the drag is shown for the train single passing

through the tunnel [5]

. The drag’s variation characteristics over time for the train

passing each other in the tunnel [6,7]

and the effect of block ratio and the speed on the

maximum drag [8]

are analyzed by using three-dimensional numerical simulation. A

calculating formula of piston wind velocity is established and it has provided

theoretical basis on the aerodynamic drag in tunnel with double shafts [9]

. The

formula of aerodynamic drag is established and the drag coefficient of different

tunnel sections is discussed [10]

. The formula of aerodynamic drag is established

when rain running in opposite and same direction in oversized railway tunnel and the

general law of such aerodynamic drag is proposed. However, the above-mentioned

paper did not conduct a systematic study on the forming mechanism, distribution

characteristics of the drag when the train passing through the tunnel.

In this paper, eight carriages EMU were used to study the influence of the Mach

wave on the pressure and frictional drag in the tunnel, the change of the train surface

pressure to the drag value and distribution over time. The maximum and the

minimum value for passing through the tunnel were compared to the value in the

open air.

2. NUMERICAL MODEL AND MESH GENERATION

2.1 Numerical model

(1) Basic assumption

1) When high-speed train running in the tunnel, the air flow in the tunnel is very

complex and the flow is in a turbulent state. So, three dimensions, unsteady,

compressible N-S equation, k SST turbulent model is used to simulate the train

passing through the tunnel.

2) Ignore the slope along tunnel direction and the rails, logging, shaft and

pedestrian channel and other structures of the tunnel, assume the tunnel line is a

straight line.

(2) Geometric model

1) Train geometric

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The variation characteristics of the drag over time are analyzed by using a

domestic EMU with eight carriages. Train configuration and geometric dimensions

are illustrated in Figure 1. Take the height of the train body top to the rail top as the

base size. The train length L=51.6H.

（a）Side view

（b）Front view （c）pantograph

Figure 1. Train configuration.

2) Tunnel geometric

The tunnel is using in this paper is defined by the “Design specification for high-

speed train” (TB10621-2009) of double track with the speed is 300,350km/h. The

cross-sectional area is 100m2 and the line spacing is 5m. Tunnel cross section shows

in Figure 2. The tunnel length is 660m.

2.2 Computational region

Figure 2. 300,350km/h double track Figure 3. Computational region for single car

tunnel profile. passing through the tunnel.

Computational region is shown as Figure 3. The tunnel length marked as tuL . In

Figure 3, D is the diameter of the tunnel, and 13.3mD .

H

0.83H

51.6H

Overset

10D

20D

23D

tuL

Freestream

Tunnel wall

Wall

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2.3 Mesh generation

The mesh around the train is refined as the flow around the train has a greater

impact on the aerodynamic. In order to capture the aerodynamic characteristics of the

different parts of the train more accurately, the bogie, pantograph, train bottom, head

and tail wake area are refined separately. In order to ensure the accuracy of the

frictional force of the train, the prism layer mesh is generated on the train surface and

ground. The reliable mesh is generated through the comparison between the

simulation and experimental results. Trim and prism layer mesh are used in the

simulation. The mesh around the train is illustrated in Figure 4.

Figure 4. Mesh around the train.

2.4 Numerical method

When the train passing through the tunnel, the air flow is restricted and the air is

compressed by the tunnel wall. Therefore, based on three-dimensional Reynolds

average Navier-Stokes equation of unsteady, compressible, viscous flow, and on

k-Omega SST turbulent, the aerodynamic force of high-speed train passing through

the tunnel are investigated by three-dimensional numerical simulation by using

overset mesh. For the scene of the train passing through the tunnel, the boundary of

train, tunnel boundary, the vertical boundary at the tunnel portal, subgrade, rail set as

nonslip wall and the tangential speed set to zero.

Calculate parameters: train speed is 350km/h; far field pressure is 101325Pa;

reference temperature set to 283K.

2.5 The define of aerodynamic force and pressure coefficients

According to CEN standard [13], the aerodynamic force and pressure coefficients

are defined as follows:

Drag coefficient: 20.5

xd

FC

v S (1)

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Pressure coefficient:

20.5P

P PC

v

(2)

where xF is the drag force, reference pressure P was considered to be 0 Pa; air

density, ρ, was considered to be 1.225 kg/m3; v is the velocity of wind or the train

running speed, the reference area, S , was considered to be 11.93 2m .

3. ALGORITHM VALIDATION

3.1 Mesh generation

In order to validate the mesh used in this study is reliable; the aerodynamic forces

were verified with the wind tunnel test’s data. The test has been performed on a 1:8

scaled model of the CRH380A high-speed train. The actual cross section of wind

tunnel is 8m 6m , as

Figure 5 shows. The numerical simulation results and wind tunnel test results are

shown in Table I. From Table I: The maximum error of the resistance coefficient is

10.74%. Therefore, the mesh employed in this study is suitable for achieving

accurate numerical results.

3.2 Overset mesh

In order to validate the overset mesh method used in this study is reliable, the

pressure is verified with the field test’s data of the Fenghuangtai tunnel. In the field

test, the train is eight carriages, the speed is 300km/h, and the tunnel length is 1168m.

The numerical simulation results and field test results are shown in Figure 6. As

shown in figure 6: the time history curves of pressure wave are agreed with each

other and the maximum difference of the pressure is 6.5%. Therefore, the simulation

method employed in this study is also suitable for achieving accurate numerical

results.

To sum up, we think that the mesh and simulation method employed in this study

were suitable for achieving accurate numerical results of single train passing through

the tunnel.

0 2 4 6 8 10 120

200

400

600

800

0 70 140 210-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5 B

0 3 6 9 12 15-3.0

-1.5

0.0

1.5

3.0

Figure 5. Wind tunnel test model. Figure 6. Data comparison between numerical simulation and

test (monitor point is at a distance of 200 m

from the tunnel entrance).

Δp/kP

a

t/s

Field test Numerical simulation

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TABLE I. DRAG COEFFICIENTS VALUE.

dC

Head car Middle car Tail car Whole car

Numerical simulation 0.1114 0.0873 0.1139 0.3036

Wind tunnel test 0.1248 0.0819 0.1194 0.3261

difference 10.74% 6.6% 4.61% 6.9%

4 RESULTS AND DISCUSSION

4.1. Pressure fluctuation when passing through the tunnel

Figure 7 shows the pressure distribution of the train surface for the train passed

through the tunnel. As figure (a) ~ (c) show, when the train running in the open air,

on the nose tip of head car there is a positive pressure region and is radiated to all

sides. When the head car enters the tunnel, the pressure in front of the head car

increased suddenly, and the area of the positive pressure zone increased rapidly. With

the train continue running into the tunnel, the positive pressure zone further increased.

As figured (d) ~ (e) shown, when the expansion wave passes through the train, the

pressure on the train surface has decreased, when the compression wave passes

through, the pressure has increased as the train running in the tunnel. As figure (f)

shows, when the train runs out the tunnel, the pressure of train surface back to the

pressure of the train running in the open air.

To sum up, when the train passing through the tunnel, the pressure on train

surface was changed over time, it eventually leads to the pressure drag changed over

time. Then the total drag was changed over time.

（a）running in the open air

（b） half of the train running into the tunnel

（c） whole train in the tunnel

（d）expansion wave through the train

（e）compression wave through the train

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x/m

（f）half of the train running out the tunnel

Figure 8. Pressure distribution of train surface when passing through the tunnel.

4.2. Characteristics of drag force when train passing through the tunnel

The pressure and drag force time history curves of the train passing through the

tunnel are shown in Figure 8. As shown in figure 7: Before the train head enter the

tunnel, the pressure and drag force are almost in a stable state. When the head enters

the tunnel, the air flow is restricted by the tunnel wall and the air in front of the car is

compressed. This caused the suddenly increases of pressure at the nose tip and the

pressure drag of the train, as moment ① in the figure (c).

0 2 4 6 8 10 120.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12-0.8

-0.4

0.0

0.4

0.8

1.2

0 2 4 6 8 10 120.20

0.25

0.30

0.35

0 2 4 6 8 10 120.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10 120

220

440

660

Figure 8. The pressure and drag force time history curves.

0.05 0.044 0.043

0.315

-0.336

0.078

0.365

-0.29

0.121

-0.6

-0.3

0.0

0.3

0.6

Δp/Pa

0.027 0.028 0.0290.066

0.536

0.268

0.093

0.563

0.297

0.0

0.4

0.8

0.25 0.27 0.320.390.29

0.94

0.640.56

1.25

0.0

0.5

1.0

1.5

Dra

g c

oef

fici

ent

Dra

g c

oef

fici

ent

Dra

g c

oef

fici

ent

Pre

ssure

coef

fici

ent

Dra

g c

oef

fici

ent

friction pressure total

drag drag drag

(a)

(b) pressure time history curve

(c) pressure force time history curve

Figure 9. Head car drag distribution.

(e) Total force time history curve

(d) Friction force time history curve

Moment 1 Moment2 Moment 3

Moment 2 Moment 1 Moment 3

Figure 10. Tail car drag distribution.

Figure 11. The comparison of drag between running

in the tunnel and pen air.

In open air Minimum value Maximum value

friction pressure total

friction pressure total

drag drag drag

drag drag drag

Dra

g c

oef

fici

ent

Dra

g c

oef

fici

ent

①

①

①

①

②

②

②

②

③

③

③

③

④

④

④

④

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As shown in figure (b) and (c): At moment ②, when the tail completely enter the

tunnel, the pressure at the nose tip and the pressure drag is still increasing. This is

because even the train was completely in the tunnel, the compressed air in front of

the car cannot be completely fill the space behind the vehicle or out of the tunnel in

time, leading to the air is further compressed, ultimately the pressure drag of head car

is further increasing. Until the expansion wave passes the head, the pressure on the

front is increasing, as the moment ④ in the figure (b).

By the effect of the air’s stickiness, the friction is increasing as the annular space

increasing which between in the train and the tunnel, the moment ①~② in the figure

(d). In the figure (d), the friction drag is also increasing after the tail completely

enters the tunnel. This is mainly because: before the expansion wave arrives at the

front of the train, the compressed air in front of the train was accumulated and the

pressure was increasing. By this, the air in front of the car flow to the wake was

increased and the speed is also increased gradually that through the annular space,

thus leading the friction drag to increase. The pressure on the front is increasing until

the expansion wave passes the head, as moment ④ in the figure (d), the air speed and

the friction drag is decreased.

4.3. Drag distribution characteristics

Taking the head and tail car’s drag as an example to analyze the variation

characteristics of drag distribution over time. The drag distribution at different times

of the carriages is shown in Figure 9 and Figure 10. In the figures, moment 1 is the

moment that half of the train running into the tunnel, moment 2 is the moment that

the train is in the middle of the tunnel, moment 3 is the moment that half of the train

running out the tunnel. In Figure 9, the pressure drag and total drag at moment 1 are

greater than other moments, the pressure drag and total drag become negative at

moments 2, and the friction drag is also changing over time. In Figure 10, the drag of

tail car is changing over time. Sum up Figure 9 and Figure 10, the drag distribution of

different parts is changing over time when single train passing through the tunnel.

4.4. The comparison of drag between running in the tunnel and pen air

In Figure 11, when the train is running in the open air, the pressure drag and

frictional drag accounted for 61% and 39% respectively of the total aerodynamic

drag. The tunnel has a great impact on the aerodynamic drag, especially the pressure

drag. The maximum value of total drag when the train passing through the tunnel are

1.95 times of that in the open air, the pressure drag and friction drag are 2.41 times

and 1.28 times at the same time, and the minimum value of total drag of it are 0.88

times of that in the open air, the pressure drag and friction drag are 0.74times and

1.08 times at the same time. From the Figure 11, when the train running in the tunnel,

the pressure drag and total drag sometime is less than the drag that in the open air and

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sometime it is greater. But the friction drag when the train is running in the tunnel is

always greater than that in the open air.

5 CONCLUSIONS

This paper has simulated and analyzed the scene of single train passing through

the tunnel, obtained the following conclusions:

(1) Through the comparison between the field test and the wind tunnel test dates,

verify the mesh and simulation method that used in this paper are reliable.

(2) When the train is running in the tunnel, The Mach wave directly affected on

the pressure drag. The pressure drag and total drag sometime is less than the drag that

in the open air and sometime it is greater. But the friction drag when the train is

running in the tunnel is always greater than that in the open air.

(3) When the train passes through the tunnel, the pressure on train surface

changes over time, it eventually leads to the pressure drag changes over time. Then

the total drag is changed over time. The drag value and distribution character of each

part is changed over time.

(4) When the train is running in the open air, the pressure drag and frictional drag

accounted for 61% and 39% respectively of the total aerodynamic drag.

(5) When the train is running in the tunnel, the maximum value of total drag is

1.95 times of that in the open air, the pressure drag and friction drag are 2.41times

and 1.28 times at the same time, and the minimum value of total drag are 0.88 times

of that in the open air, the pressure drag and friction drag are 0.74 times and 1.08

times at the same time. The tunnel effect on pressure drag is more greater than on

friction drag.

ACKNOWLEDGEMENTS

The authors would like to thank the computational resources provided by Gansu

Province Engineering Laboratory of Rail Transit Mechanics Application Institute of

High Speed Train Aerodynamics and the support provided by the National Key

Research and Development Program of China (2016YFB1200506-04) and China

Railway Corporation Science and Technology Research and Development Project

(YS2016T-16).

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