231QR of RTRI, Vol. 54, No. 4, Nov. 2013

Sanetoshi SAITOSenior Researcher,Laboratory Head,

Countermeasure for Reducing Micro-pressure Wave Emitted from Railway Tunnel by Installing Hood at the Exit of Tunnel

Tokuzo MIYACHI, Dr. Eng.Assistant Senior Researcher,

Heat and Air Flow Analysis Laboratory, Environmental Engineering Division

Masanobu IIDA, Dr. Eng. Director,

Environmental Engineering Division

Micro-pressure waves radiated from tunnel exit portals are one of major wayside envi-ronmental problems in high-speed railways, and have thus prompted many studies aimed at developing countermeasures to this phenomenon. This paper proposes a new method involv-ing the addition of a hood to tunnel exit portals to reduce micro-pressure waves. An inside partition divides the inside of the hood in two in the vicinity of the mouth, and one of the par-titioned sides is closed off. Confirmation was obtained that the hood is effective in reducing the magnitude of micro-pressure waves.

Keywords: micro-pressure wave, pressure wave, railway, tunnel

1. Introduction

Micro-pressure waves are a major wayside environ-mental problem for high-speed railways and increase greatly with train speed. Consequently, effective measures need to be developed as train running speeds increase. The magnitude of micro-pressure waves is proportional to the maximum pressure gradient of the compression wave arriving at the far end of the tunnel (tunnel exit portal) opposite to the portal through which the train enters [1, 2]. Micro-pressure waves can, therefore, be reduced by low-ering the maximum pressure gradient of the compression wave. Common measures such as tunnel entrance hoods and the optimization of the train nose shape are used to achieve this at a portal through which the train enters (tunnel entrance portal). The compression wave generated at a tunnel entrance portal steepens (i.e. the maximum of its gradient increases) as it propagates through slab-track tunnels. The larger the maximum of the gradient of the compression wave at the tunnel entrance portal is, by far the larger its increase becomes [3]. Consequently, decreasing this maximum pressure gradient at the tunnel entry portal is very effective for mitigating micro-pressure waves. However, as the speed of today’s high speed trains rises, so does the required length of the tunnel entrance hood resulting in some tunnel entrance hoods being over 40 m long. In turn, as tunnel entrance hoods become longer (e.g. over about 40 m for Shinkansen), the effect on reduc-ing micro-pressure waves fall, i.e. there is a ceiling on the effectiveness of this measure [4].

This paper therefore proposes, a new means to reduce micro-pressure waves at tunnel exit portals where radia-tion of the micro-pressure wave. The exit box, ‘silencer’ [5], method already achieves this to a certain extent, whereas the method proposed in this paper applies a different ap-proach which improves the measure against micro-pres-sure waves radiated from the tunnel branch portal which

has already proposed in the past [6]. The method involves a hood installed at the tunnel exit portal and with a partition which divides the inside of the hood into two parts in the vicinity of its mouth, and with the end of one part closed. This study predicted the reduction in the micro-pressure wave by acoustic analysis and which was verified by model experiments using a train model launcher.

2. Investigation of methods for reducing micro-pres-sure waves

2.1 Basic principle

As shown in Fig. 1, compression waves are generated by a train entering a tunnel and propagate toward the tunnel exit portal at the speed of sound. When the wave arrives at the tunnel exit portal, a part of its energy is radiated outside in the form of an impulse pressure wave (micro-pressure wave).

If the wavefront thickness of the compression wave and the distance of the measured point from the tunnel exit center are much longer than the radius of the tunnel (low-frequency and far-field approximations), the relation between the compression wave p(t) at the exit portal and the micro-pressure wave P(t) is expressed as the following equation [1, 2].

P t Aru t r c

tArc

p t r ct

( ) ( / ) ( / )= ∂ −∂

= ∂ −∂

2 2ρΩ Ω

(1)

where r is air density, A is the cross-sectional area of the tunnel portal, W is the solid angle around the tunnel exit, r is the distance of the measured point from the tunnel center, t is time, c is the speed of sound, and u is the air ve-locity inside the tunnel at the exit portal. As shown in (1), reducing the gradient of the compression wave decreases the micro-pressure wave; in order to attain it, tunnel en-

PAPER

232 QR of RTRI, Vol. 54, No. 4, Nov. 2013

trance hoods have been installed or train nose shapes have been optimized. On the other hand, reducing the cross-sectional area of tunnel portal A also decreases the micro-pressure wave, as shown in (1). However, if the portal cross section is reduced closing part of the opening off with a plate for example, the decrease in the micro-pressure wave is not proportional to the reduction in the cross section, due to the increase in air velocity u [6]. In order to reduce the micro-pressure wave from a side branch of a tunnel, a proposal was made to install a partition to close half the mouth of the tube, as shown in Fig.2. The desired effect was then verified through model experiments [6]. However, this measure is impossible to apply in practice because the cross section of the tunnel corresponds closely to the struc-ture gauge; such a partition would prevent the train from passing. This paper therefore proposes an alternative mea-sure, namely for the installation of a hood at the tunnel exit portal whose cross-sectional area is larger than that of the tunnel and is internally divided by a partition (the hood with the inside partition).

Fig. 1 Schematic of the radiation of the micro-pressure wave

Tunnel

TrainCompression wave

Micro-pressure wave

Fig. 2 Schematic illustration of the tube with the inside partition

Inside partition

Cover Compression wave p(t)

2.2 Prediction of the mitigation effect by acoustic analysis

To predict the reduction in the micro-pressure wave in the case of the hood with the inside partition, a set of equa-tions were derived to calculate the micro-pressure wave using the waveform of the compression wave arriving at the tunnel exit portal. The hood with the inside partition is illustrated schematically in Fig.3. It is assumed that the wavefront thickness lw of the compression wave is much larger than the diameter d of the cross section of the tunnel (low-frequency approximation, lw >> d) and that the parti-tion length is much longer than the wavefront thickness (l >> lw). The wave reflected at the opposite portal (tunnel entrance portal) is not considered, and thickness of the partition plate, the effect of viscosity and the steepening of the wave by non-linear effect during propagation inside the hood are ignored.

The compression wave propagated through the tun-nel is divided into two waves by the inside partition and the waves propagate through O-side and C-side as plane waves. Each wave is reflected both at the open end and the closed end, and goes back toward point O and point C. There, each reflected wave is divided into two waves. One is reflected back to the end again and the other is transmit-ted to the opposite end and point J. The wave arriving at

Fig. 3 Schematic illustration of the hood with the inside partition

Hood

Inside partition(1－σ)A h’ Lh

Tunnel

σAh’ JO

C

AAh'

L p(t)x lw

point J where the cross-sectional area changes discontinu-ously, is divided between a reflected wave toward the hood and a transmitted wave toward the opposite tunnel portal. As a result, the pressure waves reflected or transmitted at points O and C, and the wave reflected at point J arrive pe-riodically at the open end and the closed end. The pressure inside O-side and C-side at x (Lh>x>Lh-L) are given by the following equations respectively:

po x t po x t po x ti ii

( , ) ( , ) ( , )*= + =

∞

∑1

(2)

pc x t pc x t pc x ti ii

( , ) ( , ) ( , )*= + =

∞

∑1

(3)

The reflected waves at the open end poi* and at the closed

end pci* are given by the following equations, respectively,

under low-frequency approximation.

po x t po x t L xc

lci i

h E*( , ) , ( )= − − − −

2 2 (i ≧ 1) (4)

pc x t pc x t L xci ih*( , ) , ( )= − − −

2 (i ≧ 1) (5)

where Lh is the hood length and lE is the end-correction. Since the end-corrections at points C, O and J, are small, they are ignored.

The i-th waves poi and pci are given by the following equations respectively:

po x t R po x t x L Lc

T pc x t x L L

i o ih

c ih

( , ) , ( )

, (

*

*

= − − +

+ − − +

−

−

1

1

2

2 ))

, ,* *

c

T R po x t xc

T R pc x t xco J i c J i

+ −

+ −

− −1 12 2

(i ≧ 2) (6)

pc x t T po x t x L Lc

R pc x t x L L

i o ih

c ih

( , ) , ( )

, (

*

*

= − − +

+ − − +

−

−

1

1

2

2 ))

, ,* *

c

T R po x t xc

T R pc x t xco J i c J i

+ −

+ −

− −1 12 2

(i≧ 2) (7)

po x t pc x t T p t xcJ1 1( , ) ( , )= = −

− (8)

where R is the reflection coefficient, T is the transmission coefficient and the subscript of R and T indicate the reflec-tion or transmission point. For example, Ro is the reflection coefficient at point O of the wave propagating in the direc-tion of negative x and T-J is the transmission coefficient at point J of the wave propagating in the direction of positive x. For low frequency waves, these values are approximated

233QR of RTRI, Vol. 54, No. 4, Nov. 2013

using the following equations which employ the opening ratio s (the ratio of the cross-sectional area of the open end to that of the tunnel, as shown in Fig.3) and the hood cross-sectional area ratio s h’ (=Ah’/A, as shown in Fig.3) [7].

T R T

R R T

O O C

C Jh

hJ

h

= = − = −

= − = −+

=+−

s s s

sss s

, , ,

, ,'

' '

1 111

21

(9)

When considering the effect of the phase difference by the end-correction at the open end, (1) is modified as shown in the following [8].

P t Arc

ptt rc

ptt rc

lcE( ) = ∂

∂−

+ ∂∂

− −

W

2 (10)

Therefore, the micro-pressure wave radiated from the hood with the inside partition PO is expressed in the fol-lowing equation using the pressure wave arriving at the open end poi and the cross-sectional area of the open end sAh’.

PO t Arc

potL t r

cpotL t r

clc

h ih

ih

E( ) , ,'

= ∂∂

−

+ ∂∂

− −

σΩ

2

=

∞

∑i 1

(11)

As shown in (11), when the partition length L is long enough, the micro-pressure wave radiated from the hood with the inside partition is decreased to s (opening ratio) times as large as that from the hood without the inside partition (i.e. s =1.0 and i=1 in (11)). On the other hand, using (8), (10) and (11), the ratio of the micro-pressure wave to that from the tunnel exit portal without the hood is a=2ss h′/(s h′+1), which is larger than the opening ratio s .

3. Model scale experiments to verify the mitigation effect

3.1 Description of the experiment

Scaled model experiments using a train model launch-

er [9] were carried out to verify the effect of reducing the micro-pressure wave by the hood with the inside partition. Table 1 shows the specifications of the models and Fig. 4 is a schematic illustration of the hood. The ground effect is represented by mirror image method [10]. The model scale is about 1/120. The train model was projected at a speed of V=350 km/h or 400 km/h and the opening ratio s of the hood with the inside partition was set at 0.7 (Fig.4 (b)).

As shown in Table 1, the hood cross-sectional area ra-tio s h’ is 1.36 corresponding to the current standard size of tunnel entrance hoods. The hood length is 190 mm corre-sponding to 23 m on the real-scale. The cross section of the tunnel model, the hood model and the train model are all circular. A RION NL-32 microphone, located outside at a distance of 0.4 m from the center of the hood in the lateral direction, was used to measure the micro-pressure wave and three pressure transducers (Kulite XCS-190-5G) were installed inside the tunnel at distance of 1 m from the tun-nel exit portal (p0), and inside the hood at the center of the inside partition at both the closed side (p1) and at the open side (p2) (as shown in Fig.4). There were no openings on the side of the hood.

Fig. 4 Schematic illustration of hood models

Table 1 Model specifications

TrainDiameter 52 mm

Length 1000 mm

TunnelDiameter 125 mm

Length 12000 mm

Hood (unvented)Diameter 146 mm

Length 190 mm

The cross-sectional ratio train to tunnel 0.17

The cross-sectional ratio hood to tunnel 1.36

(a) Hood without the inside partition

p1

p2

p1

p2

(b) Hood with the inside partition

p195 mm

190 mm

p1L/2

L

234 QR of RTRI, Vol. 54, No. 4, Nov. 2013

3.2 Results of the experiment

Figure 5 shows the compression wave waveform on ar-rival at the hood. Although the waveform shown in Fig.5 is measured where L=0 mm, the waveforms in fact to do not rely on hood characteristics (e.g. length, opening ratio, etc.). Therefore, waveforms measured where L=50 mm and L=150 mm, are the same. As shown in Fig.5, the wavefront thickness lw (defined as the range where the gradient of the compression wave is over 5% of the maximum) is about 650 mm (1.9 ms) at a speed of 350 km/h and about 340 mm (1.0 ms) at 400 km/h.

Figure 6 shows the micro-pressure wave ratio with respect to the partition length L. The horizontal axis ex-presses the non-dimensional length based on the wave-front thickness lw at respective speeds. The vertical axis expresses the ratio to the micro-pressure wave radiated from the hood without the partition i.e. the present tunnel entrance hood whose opening ratio is equal to 1. The non-dimensional length expressed as 0 on the horizontal axis is an expression of the present tunnel entrance hood (open-ing ratio s =1) in Fig.6. Fig.6 also shows the result of the calculation using the measured waveform of p0 at 350 km/h (Fig.5) in (11). Fig.6 further demonstrates that the micro-pressure wave ratio decreases when L/lw increases and, at L/lw > 0.15, becomes constant at a value of 0.7～0.75 cor-responding to the opening ratio s . Moreover, Fig.6 shows that the result of the calculation by (11) agrees with that of the experiment.

Figure 7 shows the waveforms of the micro-pressure wave where L=150 mm (L/lw=0.23) for a micro-pressure wave ratio constant value of 0.7～0.75 and where L=50 mm (L/lw=0.08) when it is larger than the constant value. In ad-dition, Fig.7 also shows the waveforms predicted by (11)

Fig. 5 Measured waveform of the compression wave on arrival at the hood (p0)

Fig. 6 Variation of micro-pressure wave in relation to in-side partition length

0

2500

5000

7500

10000

0

1

2

3

4

Pres

sure

gra

dien

t (kP

a/s)

Pres

sure

(kP

a)

Time (ms)

V=350 km/h V=400 km/h

pressure gradient pressure

1.9 ms（650 mm）

1.0 ms（340 mm）

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6

Mic

ro-p

ress

ure

wav

e rat

io

Partition length L/lw

400km/h 350km/h calculation (350km/h)

σ=1.0without partition

Fig. 7 Waveform of the micro-pressure wave and the pressure wave inside the hood

-1

0

1

2

3

4

Pres

sure

(kPa

)

Time (ms)

P1 (Experiment) P2 (Experiment)

P1 (Calculation) P2 (Calculation)

-10

0

10

20

30

40

50

Mic

ro-p

ress

ure

wav

e (P

a)

Time (ms)

Experiment Calculation

-1

0

1

2

3

4

Pres

sure

(kPa

)

Time (ms)

P1 (Experiment) P2 (Experiment)

P1 (Calculation) P2 (Calculation)

-10

0

10

20

30

40

50

Mic

ro-p

ress

ure

wav

e (P

a)

Time (ms)

Experiment Calculation

(a) Partition length L=50 m (L/lw=0.08)

(b) Partition length L=150 m (L/lw=0.23)

1.0 1.0

1.0 1.0

235QR of RTRI, Vol. 54, No. 4, Nov. 2013

using the measured waveform of p0 (Fig.5). The waveforms of the micro-pressure wave and those of the pressure inside the hood obtained by experiment and through calculation agreed more or less. This indicates that it is possible to pre-dict the micro-pressure waveform radiated from the hood if the compression waveform on arrival at the hood can be obtained. The hood in the experiments was unvented. Consequently, if a hood is vented, calculated results may at some measurement points disagree with experimental results.

The micro-pressure wave is divided into two parts when the micro-pressure wave ratio is at a constant value (Fig.7 (b)), whereas the second part overlaps with the first part when there is no convergence effect (Fig.7 (a)). Al-though the partition length needs to be longer than lw/2 to divide the micro-pressure wave completely into two parts, according experimental results a length of between lw/7 to lw/6 would also be effective, i.e. a reduction in the micro-pressure wave corresponding to the opening ratio can be achieved with a partition length of less than lw/2 (Fig.6). The reason for this is that so long as the overlap between the first part and second part of the wave does not occur close to their respective peaks, even if their extremities do overlap, it will not affect the maximum of the micro-pres-sure wave.

The optimum partition length to achieve maximum micro-pressure wave mitigation was estimated by on-site measurement in a tunnel of 9.7 km in length [11]. Since the measured wavefront thickness of the compression wave at the tunnel exit portal was about 60 m, the necessary length was predicted to be half that value i.e. about 30 m. From the above however, it is inferred that the maximum mitigation effect could also be achieved with partition shorter than 30 m, though this would depend on the wave-form of the compression wave.

4. Discussions

In section, the micro-pressure wave ratio radiated from the hood with the inside partition is considered when it is installed at the exit portal of an actual Shinkansen tunnel. In double-tracked Shinkansen tunnels, trains run in both directions and therefore, in most cases the tunnel entrance hoods are installed at both ends of the tunnel. Therefore, the micro-pressure wave ratio is defined as the ratio of the micro-pressure wave radiated from the hood with the in-side partition in relation to that from the hood without the inside partition (i.e. the tunnel entrance hood).

Although the micro-pressure wave is obtained by com-paring (10) and (11), for simplification, the end-correction is ignore in this chapter. The magnitude of the micro-pressure wave from the hood without the inside partition is given by the following equation which is derived from (1), (8) and (9), ignoring the end-correction.

P t Arc

ptt rc

h

h( ) =

+∂∂

−

2 21Ω σ

(12)

where the cross-sectional area of the hood without the in-side partition is expressed as Ah and its ratio to the tunnel is expressed as s h (=Ah/A) to distinguish it from hoods with the inside partition. In the same way, the magnitude of the

micro-pressure wave from the hood with the inside parti-tion is given by the following equation which is derived from (11), ignoring the end-correction.

PO t Arc

potL t r

ch i

hi

( ) ,'

= ∂∂

−

=

∞

∑21

σΩ

(13)

PO(t) is the sum of several waves as described in (6)～(8). However, because waves after the third wave (i ≥ 3) are multiplied by the second power of reflection or transmis-sion coefficient, they are smaller than the first and the sec-ond waves and are therefore negligible.

The first and the second waves are given by the follow-ing equations which are derived from (6)～(9) and (13).

PO t Arc

potL t r

cArc

ptt Lc

hh

h

h

h

112

2 21

( ) ,'

'

'

= ∂∂

−

=+

∂∂

−

σ

σσ

Ω

Ω−−

rc

(14)

PO t Arc

pot

L t rc

Arc

p

hh

h

h

222

2 212 1

( ) ,

( )

'

'

'

= ∂∂

−

=+

− ∂∂

σ

σσ

σ

Ω

Ω ttt Lc

Lc

rc

R ptt L

crc

h

jh

− − −

+ − ∂∂

− −

2

1 2 3( )σ

　(15)

Comparing the coefficient in (14) and in the first term of (15), shows that the second wave is larger than the first wave when s < 0.5. However, when s < 0.5, the cross-sectional area of the whole hood with the inside partition Ah′ must be made larger to a certain degree to obtain the cross-sectional area of the opening (=sAh′) required for the passage of the train. Moreover, the micro-pressure wave ratio does not lessen in proportion to the opening ratio. Therefore, the feasible opening ratio is probably 0.5 < s < 1. In this case, the magnitude of the micro-pressure wave ra-diated from the hood with the inside partition is defined by the first wave (calculated by (14)). Using (12) and (14), the micro-pressure wave ratio is given by the following equa-tion:

PO tP t

h

h

11 1

1 1( )( )

max

max'

=+

+s s

s

(16)

Equation (16) shows that the micro-pressure wave ra-tio is defined by the opening ratio s and the cross-sectional area ratio of the hood with the inside partition s h′. Figure 8 shows the correlation described in (16) when the cross-sectional area ratio of the hood without the inside partition s h is equal to 1.4 corresponding to the standard value of the tunnel entrance hood installed at actual Shinkansen tunnels. When the cross-sectional area of the hood with the inside partition is equal to that of the hood without the inside partition (s h′=s h=1.4), the micro-pressure wave ratio corresponds to the opening ratio. However, when the cross-sectional area of the hood with the inside partition is larger than that of the hood without the inside partition (s h′>s h), the micro-pressure wave ratio is larger than the open-ing ratio (i.e. the mitigation effect on the micro-pressure wave is reduced). The cross-sectional area of the opening (=sAh′=ss h′ A ) needs to be large to ensure that the train

236 QR of RTRI, Vol. 54, No. 4, Nov. 2013

can pass in order to be able to apply the hood in practice on a Shinkansen line.

For example, assuming a standard tunnel entrance hood is remodeled into one with a partition inside it, s h =s h′ = 1.4 is substituted in (17) and therefore, the micro-pres-sure wave ratio corresponds to the opening ratio, in which case s h′ = 1.4, and if the cross-sectional area of the opening of the hood with the inside partition corresponds to that of the tunnel (ss h′ = 1) which is required to ensure safe pass-ing of a train, s = 0.7. The micro-pressure wave ratio then equals the opening ratio, giving an expected mitigation ra-tio of about 30%. However, in this case, the cross-sectional area of the entrance for the opposite train, being nearly equal to that of the tunnel, is smaller than that of the hood without the inside partition. Therefore, in order to prevent the effect of the micro-pressure wave generated by the opposite running train, further measures must be taken, such as adding opening windows installed on the hood side surface[2,12] and having a larger opening cross-sectional area (ss h′ > 1).

Fig. 8 Mitigation effect of the micro-pressure wave by a hood with a inside partition

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

Rat

io o

f mic

ro-p

ress

ure

wav

e

Opening ratio σ

σh'=1.4

σh'=1.7

σh'=2.0

5. Conclusions

A proposal was made for a measure to mitigate micro-pressure waves, which are a major wayside environmental problem for high-speed railways, at the point of radiation. The effect of this measured was estimated through acoustic analysis and validated by model experiments. The conclu-sions are as follows:

(1) Micro-pressure waves can be decreased by install-ing hoods with the inside partition at the tunnel exit portal (point where the train leaves the tun-nel and the micro-pressure wave is radiated). The partition serves to divide the inside of the hood into two parts in the vicinity of the hood mouth, forming a type of ‘cul-de-sac’ on one side of the hood. Its mitigation ratio corresponds to the opening ratio. However, if the hood is vented, the mitigation rate may vary depending on the point being measured.

(2) In order to achieve a reduction in the micro-pres-sure wave which corresponds to the opening ratio, the length of the inside partition of the hood need only be half the length of the wavefront thickness of the compression wave when it arrives at the tunnel

exit portal (e.g. about 30m for Shinkansen tunnel). The maximum reduction could be achieved by a shorter partition though its length depends on the waveform of the compression wave.

(3) The waveform of the micro-pressure wave radiated from the hood with the inside partition can be pre-dicted by simple acoustic analysis.

References

[1] Yamamoto, A., “Micro-pressure wave radiated from a tunnel exit, ”Preprint of Physical Society of Japan, 4pH4, pp. 91-96, No.4, Spring, 1977 (in Japanese).

[2] Ozawa, S., “Reduction of micro-pressure wave radiated from tunnel exit by hood at tunnel entrance, ” Quar-terly Reports of RTRI, Vol.19, No. 2, 1978.

[3] Fukuda, T., Ozawa, S., Iida, M., Takasaki, T., Wak-abayashi, Y., “Distortion of the Compression Wave Propagating Through a Very Long Tunnel with Slab Tracks, ” Transactions of the Japan Societ of Mechani-cal Engineers, Vol.71, No.709, pp.2248-2255, 2005 (in Japanese).

[4] Ozawa, S., Maeda T., Matsumura T., Uchida K., Kaji-yama, H., Tanemoto, K., “Countermeasures to Reduce Micro-pressure Waves Radiating from Exits of Shink-ansen Tunnels, ” The 7th Int. Symp. on the Aerody-namics and Ventilation of Vehicle Tunnels, pp.253-266, 1991.

[5] Aoki, T., Matsuura, T., Matsuo, K., “Passive Control of Micro-Pressure Wave from High-Speed Railway Tun-nel, ” Journal of the Visualization Society of Japan, Vol.22, No.1, pp.309-312, 2002 (in Japanese).

[6] Saito, S., Miyachi, T., Iida, M., “Reduction of Micro-pressure Wave Emitted from Portal of Side Branch of High-speed Railway Tunnel, ” Quarterly Reports of RTRI, Vol.51, No. 3, pp.146-150, 2010.

[7] Lighthill, J., Waves in Fluids, Cambridge, UK, p.105, 1978.

[8] Miyachi, T., “A Theoretical Model on Micro-pressure Wave Emission Considering the Effect of Geography around a Tunnel Portal, ” RTRI Report, Vol. 24, No. 9, pp. 23-28, 2010 (in Japanese).

[9] Fukuda, T., Iida, M., “Model Experiments on Aerody-namics in Train-Tunnel System, ” Acoustical Science and Technology, Vol.63, No.9, pp.543-548, 2007 (in Japa-nese).

[10] Tanaka, Y., Iida, M., Kikuchi, K., “Method to Simulate Generation of Compression Wave Inside a Tunnel at Train Entry with a Simple Geometry Model, ” Trans-actions of the Japan Society of Mechanical Engineers, Vol.69, No.683, pp.1607-1614, 2003 (in Japanese).

[11] Saito, S., Miyachi, T., Iida M., Wakabayashi, Y., Kurita, T., “Propagation characteristics of compression wave in a long slab-tracked tunnel, ” Proceedings (2) of 2007 Meeting of the Japan Society of Mechanical Engineers, pp.267-268, 2007 (in Japanese).

[12] Howe, M., S., “The genetically optimized tunnel-en-trance hood, ” J. of Fluids and Structures 23, pp.1231-1250, 2007.