the alleviation of the aerodynamic drag and wave effects of high-speed trains in very long tunnels

Journal of Wind Engineering

and Industrial Aerodynamics 89 (2001) 365–401

The alleviation of the aerodynamic drag and waveeffects of high-speed trains in very long tunnels

Arturo Barona, Michele Mossib, Stefano Sibillaa,*aDipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Campus Bovisa, Via La Masa 34,

20158 Milano, ItalybFluid Mechanics Laboratory, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland

Received 10 July 2000; accepted 8 September 2000

Abstract

The design of new high-speed railway lines requires longer and more numerous tunnelsections, where aerodynamic effects limit the maximum allowed train velocity for a given

tunnel cross-section area. These effects influence the train power requirement, the tractionenergy costs and the pressure wave amplitude: the knowledge of the unsteady aerodynamicfield around the train is therefore essential to the optimum choice of a tunnel configuration,and mainly of the cross-section diameter and of the presence and position of pressure relief

ducts. In this paper, the aerodynamic phenomena generated by a train traveling at high speedthrough a long tunnel of small cross-section are analyzed by means of quasi one-dimensionalnumerical simulations of the air flow induced by a train traveling at 120m=s in a tunnel

connecting two stations 60 km apart. Several tunnel configurations at high blockage ratio arediscussed, together with the positive and negative effects of pressure relief ducts and of partialair vacuum. Aerodynamic phenomena are evaluated in terms of drag, pressure wave amplitude

and shock wave onset on the train tail. Results suggest that configurations consisting of twintunnels connected by pressure relief ducts near stations and operated under partial vacuumshould be preferred. # 2001 Elsevier Science Ltd. All rights reserved.

Keywords: High-speed trains; Tunnel aerodynamics; Partial vacuum; Aerodynamic drag

*Corresponding author.

E-mail address: [email protected] (S. Sibilla).

0167-6105/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved.

PII: S 0 1 6 7 - 6 1 0 5 ( 0 0 ) 0 0 0 7 1 - 4

1. Introduction

The continuous increase in personal mobility has led to the development of newtransportation technologies and to the improvement of the existing systems. In therailway field, commercial speed has been increased and new high-speed railway andmagnetic levitation train (Maglev) lines built. These new lines need straighter tracksand thus require longer and more numerous tunnel sections in order to avoidobstacles and to reduce environmental impacts [1]. Examples include the tunnels tobe built through the Alps (the Lyon–Torino connection with a 54 km long tunnel [2]or the Swiss AlpTransit [3] project with about 120 km of tunnels), the high-speed linebetween Seoul and Pusan in South Korea, which is planned to have 75 tunnelscovering 44% of the 437 km of the total line (see for instance Ref. [1]), or the newMaglev Yamanashi test line in Japan, which has 82% of tunnels on 42.8 km [4].

The passage of a high-speed train in a tunnel causes aerodynamic problems whichdo not appear in open air: compression and expansion waves are generated when thetrain enters the tunnel, when its velocity changes and wherever the tunnel cross-section is varied. These pressure waves can cause relevant aerodynamic loads onvehicle and tunnel structures. Aerodynamic noise, forces and moments acting on thetrain, and especially the aerodynamic drag, grow due to the confinement of thesurrounding space; moreover, at the tunnel exit, micro-pressure waves and sonicboom can generate inconveniences to the nearby residents. These aerodynamicphenomena gain in complexity and importance as the train speed and the blockageratio (ratio of vehicle to free tunnel cross-section area) increase. However, tunnelsappear to be the only practicable solution for high-speed railway connections,notably in densely populated areas and in mountainous regions.

Aerodynamic drag can exceed 90% of the total drag for high-speed trainstraveling in tunnels, and remains still the major contribution even at low speed. Theentity of aerodynamic drag (see e.g. Refs. [5,6]) depends on several parameters suchas the blockage ratio, the tunnel network geometry and surface, the number ofpressure relief ducts, the train type and its speed, the presence of other trains, etc. Ifthis drag is underestimated during design, either the required operating speed cannotbe attained, or the air temperature resulting from the dissipated power can exceedsafety limits. Such negative effects can be minimized by reducing the blockage ratio,or by connecting the tunnel to the atmosphere, or to a second parallel tunnel.

The need to keep building costs relatively low implies the reduction of the tunneldiameter. If the train velocity is not diminished, this reduction enhances unsteadyaerodynamic problems: the amplitude of pressure waves grows and pressurizedvehicles could be required; the air flow velocity increases and unsteady compressibleeffects become dominant; moreover, the train drag rises, leading to extremely high-power requirements for high-speed motion, eventually limiting the maximum speedallowed by the power supply system. A solution that allows the tunnel diameter toremain small while reducing the effect of pressure waves and avoiding a rise inaerodynamic drag, can be envisaged in running high-speed trains in low-pressureclosed tunnels. Several projects have been developed up to now, some realistic andothers somewhat utopian.

A. Baron et al. / J. Wind Eng. Ind. Aerodyn. 89 (2001) 365–401366

The first idea including tunnels under partial vacuum was published as early asNovember 1909 in Scientific American [7], where a possible underground Maglev linebetween Boston, New York and Philadelphia was illustrated. At the end of the1960s, the tube vehicle system (TVS) Program of the Office of High-Speed GroundTransportation, US Department of Transportation [8], proposed different technol-ogies for transportation systems operating in tubes at speeds exceeding 130m=s.Tube vehicle systems were classified by their operating pressure environment,atmospheric or partially evacuated, and by their propulsion and suspension system.For instance, the electric motor-evacuated system (EMES) [9] consisted in a highblockage ratio system evacuated to a pressure in the order of 100–1000 Pa; thevehicles were electro-actively self-propelled by motors and had a suspension andguidance system provided by steel-rimmed wheels on steel rails. More recently, inAustralia the futuristic project high-speed tunnel vehicle (HSTV) [10] studiedvehicles propelled by a linear electric motor and using air film lubrication as alevitation technique. These vehicles would run at a cruise speed of 280m=s in smalltunnels under a partial vacuum of 100–200 Pa. An advanced project including partialvacuum is the Swissmetro project, consisting in a high-speed underground transportnetwork in Switzerland: this network would consist in high blockage ratio tunnels(about 0:4) under a partial vacuum of about 1=10 of the atmospheric pressure;proposed Maglev train speed would be higher than 100m=s (see Refs. [11,12] for ageneral description of the project and Ref. [13] for mechanical, aerodynamic andthermal aspects).

The first studies of train aerodynamics in tunnels were carried out in 1927 by vonTollmien [14], who searched for an analytical expression of train drag by usinga quasi-static incompressible model. In the 1960s and 1970s, a very significantcontribution to the subject was made by Japanese researchers (see e.g. Refs. [15–19]).In the following years, several experiments (in situ or in test facilities) and theoreticaland numerical simulations were developed, as overviewed for instance by Hammitt[20] or Pope [21] or, more recently by William-Louis [22], Bourquin [23] orMossi [24].

The present study concerns the analysis of aerodynamic phenomena in longtunnels at high-blockage ratio and under partial vacuum during the cruise of high-speed trains, with particular emphasis on the influence of the tunnel design on theaerodynamic drag. The detailed analysis of the unsteady aerodynamic phenomenarelated to the passage of the train through the tunnel is beyond the scope of the work(see e.g. Ref. [25]).

The approach described in the present work consists in a numerical analysis usinga quasi one-dimensional finite volume model of air flow and train motion in thetunnel [26], as briefly described in Section 2.

The model problem here considered is outlined in Section 3: it consists in a tunnelconnecting two stations which are 60 km apart, crossed by a high-speed trainrunning at a cruise speed of 120m=s. Blockage ratios up to 0.52 are considered.These values are much larger than the classical ones adopted in railway tunneldesign, which do not usually exceed 0.17 for high-speed trains (e.g. about 0.12 for theJapanese Maglev or the German ICE=V).

A. Baron et al. / J. Wind Eng. Ind. Aerodyn. 89 (2001) 365–401 367

In Section 4, two open tunnel configurations at atmospheric pressure and atdifferent blockage ratios are analyzed. The effect of pressure relief ducts is alsoconsidered.

In Section 5, several realistic configurations under partial vacuum are studied andcompared with open tunnel results; pressure and thermal loads on stations andtrains, as well as the effects of train schedule, are then discussed in Sections 6 and 7.

2. Physical and numerical models of the flow

The unsteady flow generated by trains traveling inside railway tunnels iscompressible, three-dimensional and turbulent in nature. Pressure, density andvelocity fields around the train are affected by the confining effects of the tunnel wallseven at steady state; moreover, unsteady phenomena develop whenever the relativemotion between train and tunnel imposes strongly unsteady boundary conditions tothe flow. This is the case when the train ends cross the tunnel portals, when trainpassing occurs in the same tunnel and, in general, whenever the tunnel sectionencounters a change or a connection with a different tunnel or atmosphere. In thesecircumstances, pressure waves are generated: these waves propagate at the localspeed of sound, interfere with each other and reflect within the tunnel in a complexway [27,28]. For example, the pressure wave pattern produced by a train entering atunnel and the propagation and reflection of a compression wave at an abruptchange of the tunnel section are sketched in Figs. 1 and 2, respectively.

2.1. Governing equations

A correct description of the flow requires the solution of the three-dimensionalunsteady equations of gas dynamics. However, experimental evidence shows that ifthe tunnel length is much larger than its hydraulic diameter, the propagation ofpressure disturbances takes place by means of approximately plane waves and theinstantaneous distribution of the fluid dynamic variables is nearly uniform in eachtunnel section, while intrinsically three-dimensional features are concentrated only inthe close vicinity of the train and tunnel ends and in those regions where the tunnelwalls have a complex shape, i.e., abrupt changes of the cross-section area, mutualconnections between tunnels, tunnel connections with the atmosphere [29–31].

As a consequence, the large-scale behavior of the flow in a train–tunnel system canbe reasonably predicted by using quasi one-dimensional models and computationallyefficient schemes. Quasi one-dimensional models are obtained by coupling a one-dimensional mean flow description with suitable corrective models, capable ofcapturing the local three-dimensional features of the flow in some peculiar regions ofthe flow field.

The unsteady one-dimensional flow of a viscous, compressible fluid is governed bythe Navier–Stokes equations, namely by a set of partial differential equations whichexpress the physical principles of conservation of mass, momentum and energy.


Fig. 1. Pressure waves generated by a train entering a tunnel and their reflection at an open tunnel end. (a)

Compression wave 1 produced at the train head entrance; (b) expansion wave 2 produced at the train tail

entrance; (c) reflection of waves 1 and 2 at the downstream open portal of the tunnel. Ut indicates train

speed, c indicates the speed of sound.

Fig. 2. Propagation and reflection of a compression wave at an abrupt enlargement (a) and reduction

(b) of the tunnel cross-section. Subscripts indicate incident (i), reflected (r) and transmitted (t) pressure

waves.


When written in integral conservative form, the governing equations read asfollows:

@

@t

Ztr dt�

IsrðVa � nÞ ds ¼ 0;

@

@t

Ztru dt�

IsruðVa � nÞ ds ¼

Ispn � i dsþQm þDm;

@

@t

ZtrE dt�

IsrEðVa � nÞ ds ¼

Ispn � Va dsþQh þDh; ð1Þ

where Va ¼ ui is the mean air velocity vector coincident with its component u alongthe tunnel direction, represented by the unit vector i; r is the air density, p is thepressure and t is a tunnel element bounded by a surface s having unit inward normalvector n. At airshafts or tunnel junctions, Va is replaced by Va ¼ ui þ vj, wherethe component v along the normal direction, represented by the unit vector j, isintroduced to take into account the secondary fluxes through the lateral surface ofthe control volume t.

Heat conduction terms are neglected in Eq. (1) and E stands for the total energyper unit mass:

E ¼ eþ 12 u

2; ð2Þ

where e is the internal energy per unit mass.Qm and Qh denote source terms for momentum and enthalpy, due to corrective

models for locally 3-D flow regions, as described in Sections 2.2–2.4. Bulk viscosityeffects are neglected in the numerical scheme while momentum and enthalpydissipations Dm and Dh associated with the viscous and turbulent stresses onthe solid walls are modeled through the experimental friction coefficients of the trainCf t and tunnel Cfg :

Dm ¼ �IsL

1

2rðCfgujuj þ Cftðu� utÞju� utjÞ dsL;

Dh ¼ �IsLCft

1

2rðu� utÞju� utjut dsL; ð3Þ

where ut is the train velocity and sL is the wall surface of the control volume t. Theeffects of unsteady friction (see Refs. [32] or [33]) are not taken into consideration.

The constitutive equations of ideal gas are finally used to define the thermo-dynamic state and balance the number of unknown quantities:

p ¼ rRT ; ð4Þ

e ¼ CvT ; ð5Þ

where T is air temperature and Cv the air specific heat at constant volume.The train motion is taken in account by substituting the control volume t in

Eq. (1) with the free volume tf obtained by subtracting from t the total volumeoccupied by all the trains present in the considered tunnel section. The flux terms in


Eq. (1) are consistently computed by considering only the free cross-section in thetunnel.

Eqs. (1) are valid for subsonic as well as supersonic flow regimes; their numericalintegration requires both space and time discretizations. A second-order spacediscretization is obtained by means of cell-centered non-overlapping finite volumescovering the whole computational domain; numerical stability is ensured by theaddition of second-order numerical dissipation terms based on the Lax–Friederichsscheme [34]. The main advantage of a conservative finite volume formulation over anapproach fully based on the method of characteristics is the ability to take intoaccount the presence of physical discontinuities in the solution without requiring theuse of shock-fitting techniques or the a priori knowledge of their position. In high-speed flows at high blockage ratios, where shock waves are likely to arise, a finitevolume formulation is thus the best choice for the numerical simulation.

Time integration is based on the explicit Runge–Kutta 5-stage method proposedby Jameson [35], with separate treatment of convective and dissipative terms; viscousterms (3) are integrated together with dissipation terms. The value of the time step Dtdepends on the length Dx of the control volume and on the local wave speed juj þ c,where c is the local speed of sound. This time-integration scheme allows, in principle,a maximum CFL number (i.e., the ratio ðjuj þ cÞDt=Dx) of 4 when applied to thelinear convection equation. However, the presence of non-linear convective termsand of source terms in Eq. (1) reduces this limit: the maximum value used in thepresent work is 2.7. The dissipative term here used leads to a diffusive error whichincreases when the CFL number is reduced. However, it has been verified that theintensity and propagation of pressure waves is not appreciably affected by this errorif a CFL number higher than 1.5 is used.

2.2. Discontinuities in the tunnel cross-section

A railway tunnel can exhibit discontinuities in its section area due either to asudden expansion or contraction of the tunnel itself or to a connection with adifferent tunnel or atmosphere. In both cases, not only wave reflection arises (asshown in Fig. 2), but the flow can hardly be assumed to remain one dimensional:related head losses have to be taken into account through suitable empiricalcoefficients [36].

The present quasi one-dimensional scheme has proven to be robust enough totreat sudden variations of the tunnel cross-section without introducing anyunphysical oscillation in the solution. Fig. 3 shows the computed relative amplitudesof reflected and transmitted waves, compared with the ones predicted by the acoustictheory [37].

A pressure wave propagating in a tunnel and reaching a connection with asecondary duct is partly reflected in the tunnel as a wave of opposite sign and partlytransmitted with same sign into both the downstream tunnel and the shaft (Fig. 4).Airshafts and tunnel junctions are simulated as connections between two one-dimensional grids. In the computational cell common to both grids, flow quantitiesare calculated by means of the one-dimensional system of Eqs. (1) with the addition


of the flux terms of mass, momentum and energy due to the presence of the shaftand associated to the normal velocity component v. Solutions obtained with thepresent scheme are compared in Fig. 5 with the ones of a validated two-dimensionalscheme [38].

2.3. Open tunnel portals

Fluid dynamic quantities at the open portals of a tunnel are computed by means ofthe characteristic equations of gas dynamics.

Conventional characteristic boundary conditions impose a pressure value attunnel ends equal to the atmospheric one and take into account viscous effectsthrough a pressure loss coefficient. However, they produce an instantaneousreflection of plane waves which is in contrast with experimental evidence [39].

Actual three-dimensional effects at the portals are responsible for both a time-delayed reflection and an attenuation of the amplitude of the reflected wave. This isdue to the fact that, when a pressure wave reaches a tunnel portal, pressuredisturbances generated at the portal edges propagate at the local speed of sound both

Fig. 3. Relative amplitudes of the transmitted ðpt=piÞ and reflected ðpr=piÞ waves at a discontinuity in the

tunnel section, as a function of the ratio between the downstream and upstream section areas. Symbols:

present method. Solid line: acoustic theory.

Fig. 4. Wave propagation and reflection at a tunnel junction. Compression wave ðpiÞ incoming from the

main tunnel, reflected ðprÞ and transmitted ðptÞ into the main tunnel itself and transmitted into the

secondary duct ðpsÞ.


outwards and towards the tunnel axis, so that the actual reflection of the plane waveonly takes place when these disturbances have traveled a distance approximatelyequal to the tunnel diameter (Fig. 6). For an incident step pressure wave havingamplitude Dp ¼ ðpstep � patmÞ, where patm is the atmospheric pressure, the time-dependent amplitude of the reflected wave prðtÞ can be determined through theexponential law:

prðtÞ ¼ patm þ Dp exp �catmt� toDg

� �; ð6Þ

where catm denotes the speed of sound at external atmospheric conditions, Dg is thetunnel diameter and to is the instant in which the plane wave reaches the tunnel end.

Fig. 5. Wave propagation at a tunnel junction: relative amplitudes of the waves transmitted ðpt=piÞ andreflected ðpr=piÞ in the main duct and transmitted ðps=piÞ in the shaft, as a function of the ratio between the

main tunnel and shaft section areas ðAp=AsÞ. Symbols: present method. Solid line: two-dimensional

second-order scheme [38].

Fig. 6. Propagation and reflection of a pressure wave at tunnel portal: when an outgoing wave reaches the

portal, disturbances generated at the portal reach the tunnel axis in a finite time; this causes an attenuation

and a time lag of the reflected wave.


To improve one-dimensional modeling of the reflection process, any pressure wavereaching the tunnel portal is decomposed into a number of elementary step wavesreaching the boundary at a different time step and reflecting according to Eq. (6)(Fig. 7).

2.4. Train ends

One-dimensional models cannot exactly reproduce the strength of the nosecompression wave and of the tail expansion wave, because of the intrinsically three-dimensional pattern of the flow, associated with turbulent phenomena andrecirculation regions. Nevertheless, a realistic prediction of the pressure field canbe obtained, provided suitable correction coefficients Cd are introduced for thederivatives of the free cross-section distribution at the train nose and tail [40].

The source terms in Eq. (1) are defined as

Qm ¼IsCdp

@A

@xds;

Qh ¼ �IsCdutp

@A

@xds; ð7Þ

where Cd values for nose and tail are in general functions of the shape of the trainends, of the train velocity ut and of the blockage ratio b ¼ At=Ag between the traincross-section At and the tunnel cross-section Ag.

Fig. 7. Time history of boundary pressure in case of incident step wave (a) and time discretization of

general pressure wave into multiple step waves (b).


Both nose and tail are approximated with sinusoidal functions, in order to obtainsmooth gradients of the free cross-section distribution.

The value of the nose correction coefficient

Cdnðut; bÞ ¼ 1þ ðCs � 1Þ Dpðut; bÞDpðutexp ; bexpÞ

ð8Þ

depends on the constant shape coefficient Cs and on the intensity Dp of the pressurewave generated by the train nose during the entrance in the tunnel.

The shape coefficient Cs for the train under consideration can be deduced from acomparison between numerical simulations and experimental tests at fixed trainvelocity utexp and blockage ratio bexp. For high-speed streamlined trains, it canbe assumed Cs ’ 1 since no major separation occurs; in applications concerning non-streamlined trains, Cs can assume values between 1.015 and 1.04. Dp can becomputed according to [41]

Dp ¼ ð1=2ÞgM2ð1�CÞCþMð1�CÞ � gM2ð1� ð1=2ÞCÞ; C ¼ ð1� bÞ2; ð9Þ

where g is the ratio of specific heats and M ¼ ut=c is the Mach number of the train.Likewise, a correction coefficient Cdt is introduced in order to account for the

reduction in the strength of the expansion wave on the train tail. However, the tailcorrection coefficient is less sensitive to both b and speed, so that a constant value of0.98 for conventional trains and of 0.99–1 for streamlined trains can be adopted. Aseparated turbulent wake is always present downstream of the tail of any train (bothstreamlined and not). This wake produces a displacement thickness, resulting in areduction in the free cross-section, and in a pressure drop which must be taken intoaccount. According to the turbulent wake theory by Abramovich [42], at highReynolds numbers an extension of the tail length by about 10 hydraulic diameters ofthe train main cross-section produces the required smoothing of the streamwisepressure gradient.

2.5. Validation

A numerical code named tunnel nets and trains (TNT) has been developed, basedon the physical model and numerical method outlined in the previous paragraphs.The code reliability has been tested through comparison with analytical solutions forcompressible flows, such as shock tube or acoustic wave propagation in bifurcations(Figs. 3 and 5), and with published experimental measurements in railway tunnelsincluding section changes [43], ventilation shafts [44]) and train crossing in a widerange of thermodynamic and kinematic conditions [26].

A simulation of the flow induced by an Etr500 high-speed train in the Terranuovatunnel is here reported to confirm the reliability of the TNT prediction. Thecharacteristics of the tunnel are described in Ref. [45]; the Etr500 train hereconsidered is 276.5 m long, has a 10 m long nose; the turbulent wake behind the tailis 10 hydraulic diameters long; the cross section of the train is 10:94 m2, resulting in ablockage ratio of 0.158. A shape coefficient Cs ¼ 1:001 has been considered to


describe three-dimensional effects on the train nose, while a tail correction coefficientCdt ¼ 0:995 has been found to match the experimental results correctly.The comparison of the simulation with the measurements obtained by a pressureprobe located on the roof of the central wagon [45] is shown in Fig. 8: a generallygood agreement in the prediction of pressure wave intensities and location can beargued.

3. Model problem

The following sections discuss numerical results obtained on different under-ground high-speed railway networks connecting two stations 220m long which are60 km apart, as sketched in Fig. 9 and summarized in Tables 1 and 2. These differenttunnel networks include single-track tunnels either with or without connections withother parallel tunnels or atmosphere. The blockage ratio b is always 0.52, except forthe case of a single open tunnel at atmospheric pressure, considered as a referencecase, where b ¼ 0:13. The initial air temperature is fixed at 300K. The initial pressurelevel in the closed tunnel is 10 000 Pa, while in open tunnels it is equal tothe atmospheric pressure level of 101 300 Pa. In all cases, the tunnel walls havebeen considered adiabatic, with a friction coefficient Cfg ¼ 0:003 corresponding to amean wall roughness of 0.5mm. Pressure relief ducts, when present, are 25m long,

Fig. 8. Static pressure evolution on the central wagon of an Etr500 high-speed train travelling in the

Terranuova tunnel. Numerical simulation (}}), experiment [45] (– – –).


cylindrical with 3m diameter, and connect perpendicularly two main tunnelswith equal section. Their friction coefficient is 0.005, higher than that of the maintunnel, to take into account the fact that these short ducts are usually boredmanually.

Each train running on the rail link is Lt ¼ 200 m long, has 10m long sinusoidallyshaped nose and tail, and a circular cross-section At of 3.6 m diameter. Its frictioncoefficient is Cft ¼ 0:003. The aerodynamic design of the train geometry has beenconsidered ideal: a shape coefficient Cs ¼ 1 has therefore been introduced. On thetrain tail, the correction coefficient has been set to the experimentally determinedvalue Cdt ¼ 0:99, which is valid for high-speed trains.

Fig. 9. The different tunnel configurations analyzed (not to scale). Gray indicates the position of the end

stations.

Table 1

Single monodirectional tunnel configurations

Tunnel Tunnel End Tunnel Blockage Pressure

configuration length (km) conditions diameter (m) ratio level (Pa)

60-op-10 60 Open 10 0.13 101 300

60-op-5 60 Open 5 0.52 101 300

60-cl-5 60 Closed 5 0.52 10 000

70-cl-5 70 Closed 5 0.52 10 000


The train accelerates at 2 m=s2 for 60 s1 reaching its cruise speed of 120m=s,which is maintained constant until the distance from the arrival station reaches3.86 km. At this point, a constant deceleration of 2 m=s2 brings the train to rest in60 s (Fig. 10). The total time needed to cover the 60 200 m distance is therefore561.66 s.

Table 2

Double monodirectional tunnel configurations with pressure relief ducts

Tunnel Tunnel End Tunnel Blockage Number of Pressure

configuration length (km) conditions diameter (m) ratio connections level (Pa)

60-op-5-13 60 Open 5 0.52 13 101 300

60-cl-5-2 60 Closed 5 0.52 2 10 000

60-cl-5-2 2 60 Closed 5 0.52 4 10 000

60-cl-5-2 6 60 Closed 5 0.52 12 10 000

60-cl-5-13 60 Closed 5 0.52 13 10 000

Fig. 10. The time evolution of the train velocity utðtÞ and position xtðtÞ in the model problem. utðtÞ (}}),

xtðtÞ (......).

1 It must be noted that constant acceleration has been chosen for convenience, although it is surely

unrealistic for a classical high-speed train weighing about 2 t per linear meter. In fact, a 2 m=s2 acceleration

would actually require a mechanical power higher than 48MW, while the propulsion power of a high-

speed train (having a maximum speed of about 300 km=h) with two power units is usually limited to

approximately 7MW.


All the computations have been performed with a CFL number of 2.7, resulting inan average time step of 0.007 s; the computational grid consists of 20 000 volumes foreach main tunnel, non-uniformly spaced: control volumes in high gradient regions(around the train, at tunnel ends and interconnections, in secondary ducts) have atypical length of 1.2m, namely 1=3 of the train diameter.

4. Tunnel at atmospheric pressure

The basic configurations analyzed consist in a single cylindrical tunnel open atboth ends. Two different tunnel diameters have been tested: one of 10m, leading tob ¼ 0:13, a classical blockage ratio value for high-speed trains, and the other of only5m, leading to b ¼ 0:52. The former configuration will be referred to as 60-op-10,while the latter as 60-op-5 (see Table 1).

In these simple configurations, despite the similarities, the behavior of air flowaround the vehicle is governed by different phenomena. In the larger tunnel, thefriction effects along the train sides are dominant, while in the smaller one, due to thehigher blockage ratio, the near-field flow is governed essentially by compressibilityeffects.

In the larger tunnel the blockage effects are small: air velocity in the tunnel frameis almost zero ahead of the train; its increase along the nose and the annular space isjust 22m=s: the air flow remains subsonic everywhere and the maximum Machnumber at the end of the annular space is 0.41 (Fig. 11).

The higher blockage ratio leads instead to a more pronounced piston effect[46]: the air pushed ahead of the train causes a significant pressure increase infront of the train nose and creates a pressure decrease behind the tail (Fig. 12),while a reduced portion of the air flows around the vehicle. This piston effectresults in an upstream Mach number lower than the free-stream value of0.35 (Fig. 11). Around the train, the air flow accelerates along the train nose andthe annular space in a quite spectacular way (as in a supersonic Laval nozzle).At t ¼ 300 s, the flow reaches sonic conditions at the end of the annular space.The Mach number reaches 1.12, before a shock wave on the train tail brings theflow back to subsonic regime. As the train approaches the tunnel exit, the pressurelevel in front of the train decreases due to the open end (Fig. 13) and the air flowloses the choked condition. For instance at t ¼ 500, when the train is less than 4 kmfrom the tunnel exit, the Mach number at the end of the annular space decreasesto 0.8.

Pressure-wave evolution can be represented through the pressure variation in frontof the train nose (Fig. 14). Pressure initially increases in front of the train in the60-op-5 case owing to tunnel friction; it reaches its maximum at t ’ 266 s, when thecompression wave generated by the train during its acceleration reaches the trainnose after having been partially reflected at t ’ 173 s as an expansion wave atthe tunnel open end. In the 60-op-10 tunnel, viscous and compressibility effects areinstead negligible due to the large tunnel section and low air velocity; the pressurelevel in front of the train nose remains in this case approximately constant. When the


initial compression wave reaches the end portal, an air outflow is generated and thepiston effect is reduced. This reduction continues while approaching the arrivalstation. Finally, during the deceleration phase the nose pressure level decreasesrapidly due to the expansion wave generated by the train. This wave, reflected as a

Fig. 11. Mach number distribution past the train in the vehicle-fixed frame of reference at time t ¼ 300 s

for the 5 and 10m diameter open tunnels. 60-op-5 (}}), 60-op-10 (– – –).

Fig. 12. Pressure distribution past the train in the vehicle-fixed frame of reference at time t ¼ 300 s for the

5 and 10m diameter open tunnels. 60-op-5 (}}), 60-op-10 (– – –).


compression wave at the end portal, reaches the train at t ’ 517 s and generates asmall pressure increase.

As shown for instance in Fig. 12, the Dp between the train ends is reducedfrom about 90 000 Pa in the smaller tunnel case to a few thousand in the larger one.This difference appears clearly in the evolution of the total aerodynamic power

Fig. 13. Pressure difference distribution into both open tunnels: 60-op-5 (a) and 60-op-10 (b). t ¼ 100 s

(}}), t ¼ 200 s (– – –), t ¼ 300 s ð2 �2 �2�Þ, t ¼ 400 s ð2 � �2 � �2 � �Þ, t ¼ 500 s (......).


Wtot ¼ ðDp þDfrÞut plotted in Fig. 15, where pressure and friction drag arecomputed as

Dp ¼Z Lt

0

p@At

@xdx

and

Dfr ¼Z Lt

0

1

2rðu� utÞju� utjCftpt dx;

respectively, pt being the local perimeter of the train cross-section.As expected, pressure effects are small for the larger tunnel when compared

with viscous effects: drag evolution is therefore practically independent oftime during the cruise at constant speed. On the other hand, in the smaller tunnelcase, pressure drag is always dominant and represents more than 60% of the totalone. In both configurations, the ratio of pressure to friction drag is almost constantin time.

Table 3 summarizes the average aerodynamic power hWtoti on the wholetrip (from the departure to the arrival station), the average power �Wtot duringthe cruise at constant speed (i.e., without acceleration and deceleration phases)and the maximum aerodynamic power Wmax

tot . The percentage distribution ofpressure and friction contributions, which is the same for the three quantities, is alsoreported.

Fig. 14. Static pressure history 2 m before the high-speed train nose. Comparison of both open

configurations. The pressure level for the 60-op-5 configuration has been divided by 10. 60-op-5-rescaled

(}}), 60-op-10 (– – –).


The required power in the 60-op-5 case is a function of the distance from thetunnel exit: it initially increases due to the effect of tunnel friction on the pressurewave; afterwards, owing to the presence of the open end, it decreases even though thetrain speed is maintained constant. At t ¼ 266 s it reaches its maximum value, whichis 11% higher than the the average power during the cruise at constant speed. As aconsequence, air temperature in the 60-op-5 configuration can increase by severaldegrees and exceed safety limits.

These power values can be compared with the total aerodynamic power measuredfor the Transrapid 07, the high-speed German Maglev, or the ICE=V, the high-speedGerman train. In open air, a Transrapid 07 vehicle 52m long requires a power of

Fig. 15. Time evolution of total power WtotðtÞ, power due to pressure forces WpðtÞ and to friction forces

WfrðtÞ for tunnels having 5 and 10 m diameter. 60-op-5 (}}), 60-op-10 (– – –).

Table 3

Aerodynamic power for analyzed open tunnel configurationsa

Tunnel hWtoti �Wtot Wmaxtot Wp Wfr

configuration (MW) (MW) (MW) (%) (%)

60-op-10 8.7 10.3 10.6 14 86

60-op-5 60.0 69.7 77.7 67 33

60-op-5-13 43.0 50.2 68.5 63 37

aTotal power averaged on the whole trip hWtoti; total power averaged on the phase at constant speed�Wtot; maximum power Wmax

tot ; and percentage of power due to pressure Wp ¼ Dput and friction

Wfr ¼ Dfrut.


3.1 MW at 400 km=h to overcome aerodynamic drag.2 Supposing that pressure dragis 10% of the total one and that friction drag is a linear function of train length, thetotal power for a 200 m long Transrapid could be estimated in about 11 MW. Similarvalues can be obtained for an ICE=V (200 m long) traveling at 120 m=s, according tothe formula for open air drag proposed by Peters [47]. These results have the sameorder of magnitude as the value obtained for the 60-op-10 configuration, whereaerodynamic drag is possibly underestimated due to the very simple train geometryhere chosen.

The data reported in Table 3 show that reduction in the tunnel diameter by afactor 2, although leading to a decrease in building costs approximately proportionalto the tunnel diameter, also implies an increase of energy costs by a factor 7. Thisfact plays an important role in the choice of the tunnel diameter for high-speed lines.

Another relevant environmental issue raised by high-speed train aerodynamics intunnels is the high velocity of air flow at the tunnel exit. At the higher blockage ratiotested, wind in the arrival station reaches nearly 50 m=s, while at the lower oneit does not exceed 5 m=s. These values should be compared with the currentrequirements for passenger comfort in underground stations, which prescribe an airvelocity not higher than 5 m=s [48].

A significant reduction of the piston effect can be obtained by coupling the maintunnel with another parallel tunnel through an array of pressure relief ducts. Thepresence of a second tunnel is in general required by the need of a double-trackconnection between the end stations, all of the tunnels here analyzed being single-track. A recent application of pressure relief ducts aimed at the reduction ofaerodynamic drag can be found in the Channel tunnel, where two single-tracktunnels of 50 km are connected every 250m by transversal ducts of 2m diameter [49].However, high aerodynamic loads on trains passing the same shaft have beenobserved.

The adoption of relief ducts in the 60-op-10 configuration does not yield anyrelevant drag reduction, the blockage ratio being already sufficiently low. The effecton the 60-op-5 configuration is instead more important. The addition of 13 pressurerelief ducts of 3m diameter, one every 5 km (configuration 60-op-5-13), causesan average power decrease of 17MW; when ducts are placed every kilometer thisdecrease reaches 32MW. However, the required power, needed to overcomeaerodynamic forces at these blockage ratios and train velocities, remains too high fora realistic underground transportation system, due to energy consumption andthermal evolution. Moreover, induced air velocity in pressure relief ducts easilyexceeds 60 m=s, thus generating very high transversal aerodynamic loads.

These computational tests point out the important role played in long tunnels bythe blockage ratio and the train speed. They allow to conclude that, if the tunneldiameter must be kept small and the required power for 200m long trains has to bemaintained in the order of 10–15 MW at 120 m=s – i.e., the required power for very

2Transrapid 07, Thyssen Henschel, Neue Verkehrstechnologien, Anziger Strasse 1, D-8000

Munchen 80.


high-speed trains or Maglevs in open air – the aerodynamic constraints impose areduction either of the cruise velocity or of the pressure level inside the tunnel.

5. Tunnel under partial vacuum

The introduction of partial vacuum in the tunnel network should yield aconsiderable reduction in the aerodynamic drag acting on the vehicle, even thoughthe tunnel must be closed at both ends. In fact, both pressure and viscous drags aredirectly proportional to the environmental pressure level.

In the present and following sections, some tunnel configurations under a partialvacuum of 10 000 Pa will be examined. The blockage ratio is maintained constantand equal to 0.52. The accent will be put on aerodynamic drag, air velocity aroundthe train and pressure distribution. The flow induced by a train traveling in a singletunnel will be analyzed first; the influence of pressure relief ducts will then be pointedout.

5.1. Single closed tunnel

The simplest tunnel configuration under partial vacuum consists in a single tunnelclosed at both ends and directly connecting two stations (60-cl-5, see Table 1 andFig. 9).

As expected, air flow evolution in this configuration is initially similar to the oneobtained in the open-end configuration 60-op-5 (see Fig. 16, where open tunnel

Fig. 16. Static pressure history 2 m before the high-speed train nose. Comparison of the different

configurations of tunnel networks under partial vacuum. Pressure level for the 60-op-5 configuration is

rescaled to 10 000 Pa. 60-op-5-rescaled (}}), 60-cl-5 (– – –), 70-cl-5 ð2 �2 �2�Þ, 60-cl-5-13

ð2 � �2 � �2 � �Þ, 60-cl-5-2 2 (– – –), 60-cl-5-2 (............).


results are divided by 10.13, thus rescaling them to the partial vacuum pressure); theeffects of the closed portal downstream of the arrival station are still not influent,while those of the closed portal upstream of the departure station are negligible. Theaerodynamic drag is one-tenth of the one observed previously in the openconfiguration, while the flow around the train is still choked, i.e., sonic conditionsoccur at the end of the annular space. Later, differences appear due to the closedportals. Actually, the tunnel wall at the end station reflects the compression wavegenerated during the train acceleration as a compression wave – unlike the open airportals which reflect it as an expansion wave. When the reflected wave reaches thetrain nose (t ’ 266 s), it leads to an increase of the pressure level in front of the train.Due to the piston effect, this increase is accentuated when the train approaches thearrival station, as shown in Fig. 16. The pressure level in front of the train nosecontinues to grow, at a lower rate, even during the initial part of the decelerationphase, until the expansion wave generated by the deceleration reaches the train, afterits reflection at the tunnel closed end.

With respect to the open-end case, the sharp pressure increase on the train nosecauses a steeper pressure gradient along the train (Fig. 17): the flow is still chokedwith sonic conditions at the end of the annular space, but the supersonic expansionon the tail becomes more intense. A stronger shock wave appears on the train tail,and the Mach number reaches the value of 1.7 before the deceleration phase.

As shown in Fig. 18, aerodynamic drag evolution resembles the pressure one: itincreases sharply for t0266 s until the beginning of the deceleration phase; itcontinues to increase at a lower rate for other 10 s and later it decreases.

Aerodynamic power reaches instead its maximum value at the end of the cruisephase (Table 4). This peak value can be compared with the one obtained in the open-end configuration 60-op-5 rescaled to 10 000 Pa: the closure of the end portals causesa 130% increase of the maximum aerodynamic power Wmax

tot , and a 50% increase ofthe average power hWtoti.

A reduction of the sharp increase of aerodynamic drag can be obtained by a tunnelprolongation behind both stations. These additional sections can either be part oflonger tunnels connecting other stations or short sections built on purpose. Aconfiguration with two additional 5 km prolongations, named 70-cl-5, has beentested. (Table 1 and Fig. 9.)

The displacement of the end walls delays the instants in which the compressionwave generated by the train departure and the expansion wave generated by the traindeceleration meet the train nose after reflection at the tunnel end (Fig. 16).Therefore, the pressure rise on the train nose is retarded by about 21 s, weakening thepiston effect, although an important pressure reduction appears only at t ’ 539 s.The peak value of the required power at the beginning of the deceleration phase isanyway reduced by 25%; the shock wave on the tail is also weaker, the maximumMach number not exceeding 1.55 (Fig. 17).

It must be noted that the presence of the prolongation causes the persistenceof a high-speed air flow in the end station after the arrival of the train for about200 s, resulting in undesired aerodynamic loads on the passenger boardingequipment.


In conclusion, compared with the open configuration at atmospheric pressure(60-op-5), the introduction of a 10 000 Pa partial vacuum in the tunnel leads to areduction of the peak level of the required power by a factor 4.4 when the tunnel

Fig. 17. Mach number (a) and temperature (b) distribution around the train in the vehicle frame

of reference. 60-op-5 – t ¼ 300 s (}}), 60-cl-5 – t ¼ 500 s (– – –), 70-cl-5 – t ¼ 500 s ð2 �2 �2�Þ, 60-cl-5-13 – t ¼ 200 s ð2 � �2 � �2 � �Þ, 60-cl-5-2 2 – t ¼ 500 s (– – –), 60-cl-5-2 – t ¼ 500 s (............).


Fig. 18. Comparison of total aerodynamic drag (a) and power (b) of the different configurations of tunnel

networks connecting two stations 60 km apart. Except the 60-op-10, all other configurations are under

partial vacuum. 60-op-10 (}}), 60-cl-5 (– – –), 70-cl-5 ð2 �2 �2�Þ, 60-cl-5-13 ð2 � �2 � �2 � �Þ, 60-cl-5-2 2 (– – –), 60-cl-5-2 (..........).


length is unchanged and by a factor 5.8 when the tunnel length is extended after thearrival station. However, this peak level is still 70% (30% in the 70-cl-5configuration) higher than the corresponding value in the 60-op-10 configuration.Despite the construction cost reduction, the operational costs and powerrequirements make these configurations unattractive.

5.2. Tunnel network with connections

As mentioned in Section 4 and successfully applied for the Channel tunnel [49],satisfactory results in terms of piston-effect reduction can be obtained by couplingthe main tunnel with another single-track parallel tunnel through an array ofpressure relief ducts. In the twin tunnels, trains move in opposite directions;therefore, the interaction between trains strongly influences the air flow. In thepresent section, the train motion is considered perfectly synchronized; the effect of adifferent train schedule will be analyzed in Section 7.

In the present study, the number of secondary ducts is kept as low as possible,compared with the benefits in aerodynamic drag reduction, to limit unwanted raisingof construction costs and to guarantee an easy isolation of both tunnels for safety ormaintenance. A configuration having one connection every 5 km between the paralleltunnels is considered representative of this compromise. The first connections aresituated just after the end of each station to reduce the high-pressure levels whichoccur in the arrival stations when the trains are approaching. The total number ofconnections is thus 13, each being 25m long and having a diameter of 3m; theytherefore represent only 0.16% of the tunnel network volume. This configurationwill be referred to as 60-cl-5-13.

The presence of pressure relief ducts allows the generation of an air flow in thesecond tunnel from the high-pressure regions in front of the train nose to the lowpressure regions behind the tail. This alleviates the piston effect, thus reducing thepressure drag and the required power, as can be observed in Table 4 and Fig. 18. The

Table 4

Aerodynamic power of all configurationsa

Tunnel hWtoti �Wtot Wmaxtot Wp Wfr

configuration (MW) (MW) (MW) (%) (%)

60-op-10 8.7 10.3 10.6 14 86

60-op-5-rescaled 5.9 6.9 7.7 67 33

60-cl-5 8.8 9.5 17.7 71 29

70-cl-5 8.1 9.0 13.5 71 29

60-cl-5-13 4.7 5.4 6.7 64 36

60-cl-5-2 6.6 7.5 8.3 68 32

60-cl-5-2 2 6.4 7.3 7.7 68 32

aTotal power averaged during the whole trip hWtoti; total power averaged during the phase at constant

speed �Wtot; maximum power Wmaxtot ; percentage of pressure Wp and friction Wfr contributions. Powers for

the 60-op-5 configuration have been rescaled to 10 000 Pa giving the 60-op-5-rescaled configuration.


improvement with respect to the 60-cl-5 case is therefore very important: the averagepower is reduced by a factor 1.9, the peak power by a factor 2.6, i.e., 63% ofthe maximum power required in the 60-op-10 configuration at atmospheric pressure.This peak value occurs at the last connection before the train crossing, instead ofoccurring at the beginning of the train deceleration phase. Of course, due to the trainsynchronization and the perfect symmetry between tunnels, the connection in themiddle of the tunnel has no effect on the flow.

Thanks to the reduction of the piston effect, the air flow around the train remainssubsonic at all times (Fig. 17): the maximum Mach number at the end of the annularspace does not exceed 0.9.

A major drawback of the 60-cl-5-13 configuration is the strong drag increment onthe train at each shaft crossing. These increments occur when the train head crosses ashaft, due to pressure and air velocity differences in the main tunnel on each side ofthe connection; this drag gradient is very high: in 1.3 s – which is about three quartersof the time needed by the whole train to pass the bifurcation point – the drag can riseby a value close to 10 kN. In a real case, where the train speed is not imposed asconstant, these drag fluctuations could result in unwanted sudden decelerationduring cruise.

A further crucial problem connected with pressure relief ducts is the cross-flowgenerated by pressure differences between the tunnels: as shown in Fig. 19, this airflow can reach 60 m=s, resulting in a lateral force of several thousand Newtons actingon the train at each shaft crossing. This lateral load, already experienced in very long

Fig. 19. Mean air velocity in the middle of some pressure relief ducts in the 60-cl-5-13 configuration.

4th and 10th ducts (}}), 6th and 8th ducts (........), central duct (– – –).


tunnels – like the Channel one – can generate high structural loads and poseproblems for train control. These problems can be reduced if the shafts are designedso as to prevent direct impingement of the cross-flow on the train; however, shaftefficiency could be reduced.

The best way to reduce the impact of these connections on the train motion,without diminishing their effect, is to locate them where the train speed and theupstream pressure level are not high enough to increase the piston effect andto generate high-velocity air flow in the connecting ducts. If two ducts are placedalong the track 10m after each station while the other two 1000m inside the tunnel(configuration 60-cl-5-2 2), the train crosses the inner ducts at about 65 m=s. Dueto this reduced speed, the air flow induced through the ducts does not exceed 40 m=s.Moreover, the drag rise at the crossing of the inner ducts is eliminated. The requiredaerodynamic power (Table 4), although 35% higher on average than in the 60-cl-5-13 configuration, maintains an almost constant value for most of the train cruise(Fig. 18). This value is practically the same obtained in an infinite tunnel, whereboundary effects are absent. The total and average power are still 30% smaller thanthose required in the 60-op-10 configuration at atmospheric pressure.

The position of the two inner pressure relief ducts has been varied to determine itsbest value in terms of train drag and cross-flow velocity reduction. If these shafts arelocated 2500m inside the tunnel, where the train speed is about 100 m=s, their effecton aerodynamic drag is slightly increased: however, due to the higher train speedduring the crossing, the maximum air velocity in the ducts still exceeds 60 m=s. If theducts are brought closer to the station (500m), the maximum required powerincreases to 8.9MW, due to a stronger piston effect, and air velocity inside pressurerelief ducts reaches 50 m=s.

These negative effects can be reduced by extending the cross-section or the numberof connecting ducts near the stations. In configuration 60-cl-5-2, only the ductslocated 10m after the stations are maintained and their diameter is increased to 5m,leading to the same cross-section as the main tunnels. This configuration does notavoid an increase of aerodynamic drag before the deceleration phase up to 8MW,but permits a reduction of the maximum flow velocity in the connection duct to30 m=s.

The presence of more ducts near each station helps to control both the pistoneffect and the air velocity in the connections. For example, a configuration havingsix connections of 3m diameter between the main tunnels during the first 1000m(60-cl-5-2 6) allows the aerodynamic drag to remain practically constant and theair flow in secondary ducts not to exceed 20 m=s.

However, in the 60-cl-5-2 2 configurations with all of the tested positions of theinner shafts, as well as in the 60-cl-5-2 and 60-cl-5-2 6 configurations, the air flowaround the train is choked and a supersonic expansion at Mach numbers up to 1.1takes place along the tail (Fig. 17). The intensity of the resulting shock wave iscomparable to the one found in the flow in the open tunnel at high blockage ratio.

In conclusion, the presence of pressure relief ducts greatly reduces the piston effect,and therefore the aerodynamic drag, in closed configurations under partial vacuum.If the array of pressure relief ducts is kept close to the end stations, the flow velocity


through each connecting duct can be minimized. The aerodynamic drag in theseconfigurations under partial vacuum is much smaller than the one obtained atatmospheric pressure in a standard low-blockage ratio configuration: the decrease inmaximum drag can range from 20% to 40%. However, because of the presence ofconnections between tunnels, trains traveling in opposite tunnels can reciprocallyinteract, suffering, in some cases, of high unsteady aerodynamic loads.

6. Aerothermal loads under partial vacuum

The preliminary structural design of trains running in tunnel networks underpartial vacuum requires a proper evaluation of mechanical and thermal stressesconnected with the train motion. Moreover, pressure and temperature stresses in thetunnel network are also needed for the preliminary design of the tunnel structure aswell as of the station systems connected with train housing, tunnel pressurization andpassenger boarding.

On one hand, operation under partial vacuum requires a design based on aconstant pressure difference of 1 atm at most between passenger areas at atmosphericpressure – i.e., inside trains and stations – and the tunnel. In this case, pressure peaksdue to train motion do not appear to pose design constraints, as they contribute toreduce the pressure gradient across seals.

On the other hand, in high-speed and high-blockage ratio conditions, wherecompressibility effects become extremely important and shock wave formationsometimes occurs, temperature gradients can become extremely high and thermalstresses must be carefully evaluated, although the flow regions involved are generallysmall. The main problems are related to the effects on the tunnel equipment of astationary shock moving with the vehicle.

It must be noted that the energy equation is here solved in the hypothesis ofadiabatic walls in tunnels and stations, and heat generation by train equipments isneglected: temperature values here reported must therefore be intended as apreliminary and approximate indication of thermal loads on trains and stations.

6.1. Aerodynamic loads on trains

As mentioned in the previous section, closed tunnel ends lead to the reflection ofcompression waves, and eventually to a pressure rise on the train nose: in the 60-cl-5case (Fig. 16) the pressure on the train head is almost three times the initial value inthe empty pressurized tunnel, while the coupling of tunnels through shaftscontributes to reduce this increment.

The pressure rise on the nose is not counterbalanced by an equal pressure rise inthe train wake (Fig. 20): this unbalance leads to a strong expansion on the train tail,and, eventually, to supersonic conditions and shock wave formation (Fig. 17), apartfrom the 60-cl-5-13 case.

The compression due to the piston effect generated by the train leads to anincrease in the air temperature upstream of the train nose: the increment with respect


to the initial air temperature ranges from 30K (60-cl-5-2 2) to 80K (60-cl-5). Itshould be noted that these temperatures could be reduced if heat transfer is taken inaccount. The rapid expansion along the train brings to a strong reduction of the airtemperature (Fig. 17), which reaches a minimum after the supersonic expansion. Att ¼ 500 s, in single tunnel configurations, the air temperature can fall 60K below theinitial reference temperature. Such a reduction in air temperature requires additionalcare in the structural and thermal design of the vehicle. Only in the 60-cl-5-13 case,where supersonic conditions are never reached and a subsonic expansion occurs onthe tail, DT hardly reaches negative values.

6.2. Aerodynamic loads on stations

Pressure evolution in the departure and arrival stations is influenced in an oppositeway by the train motion.

The departure station is immediately reached by the expansion wave generated bythe train tail, and by its multiple reflections between the tunnel end and the trainitself (Fig. 21). This effect is mostly noticeable in the 60-cl-5 case, where a minimalpressure of 8 kPa is reached; this value corresponds to the highest (negative) pressureload for the vacuum sealing systems in the station. Later, the pressure in thedeparture station rises, due to the effect of the reflected initial compression waveand, in the double tunnel configurations, of the piston effect of the second train in

Fig. 20. Static pressure history in the high-speed train wake, 30 m downstream of the train tail.

Comparison of the different configurations of tunnel networks under partial vacuum. 60-op-10 (}}),

60-cl-5 (– – –), 70-cl-5 ð2 �2 �2�Þ, 60-cl-5-13 ð2 � �2 � �2 � �Þ, 60-cl-5-2 2 (– – –), 60-cl-5-2 (.........).


the adjacent tunnel. In either case, pressure never reaches significant values whencompared to pressure levels in the arrival station (Fig. 22), where the differencebetween single and double tunnel configurations is more evident.

In single tunnel cases, the flow field in the arrival station is obviously undisturbeduntil the arrival of the pressure wave generated by train departure. In double tunnelconfigurations, on the other hand, each arrival station is immediately reached by theexpansion wave which is generated by the tail of the train leaving the adjacentdeparture station and transmitted through the pressure relief ducts; due to theconnections between the stations and the train synchronization, aerodynamic loadsin departure and arrival stations are therefore very similar. Peak pressure values inthe arrival station reach the same order of magnitude of the corresponding peakvalues on the train head (Fig. 16); as these are reached at the end of the cruise phase,at 3.8 km before the station entrance, peak values in the station occur about 11 s afterthe beginning of train deceleration.

It must be noted that thermal effects in the arrival station can be of extremeimportance: in the 60-cl-5 configuration the estimated peak temperature inthe arrival station reaches 100K more than the undisturbed initial value (Fig. 23).Such a high temperature value requires a careful design of proper coolingsystems to guarantee operation of station systems. In the 60-cl-5-2 2, 60-cl-5-2 6 and 60-cl-5-13 configurations, the peak temperature increase is reduced to40K, with an obvious reduction in related design problems. These values should be

Fig. 21. Static pressure history in the middle of the departure station. Comparison between the different

configurations of tunnel networks. 60-op-10 (}}}), 60-cl-5 (– – –), 70-cl-5 ð2 �2 �2�Þ, 60-cl-5-13

ð2 � �2 � �2 � �Þ, 60-cl-5-2 2 (– – –), 60-cl-5-2 (.............).


Fig. 22. Static pressure history in the middle of the arrival station. Comparison between the different

configurations of tunnel networks. 60-op-10 (}}), 60-cl-5 (– – –), 70-cl-5 ð2 �2 �2�Þ, 60-cl-5-13

ð2 � �2 � �2 � �Þ, 60-cl-5-2 2 (– – –), 60-cl-5-2 (........).

Fig. 23. Temperature history in the middle of the arrival station. Comparison between the different

configurations of tunnel networks. 60-op-10 (}}), 60-cl-5 (– – –), 70-cl-5 ð2 �2 �2�Þ, 60-cl-5-13

ð2 � �2 � �2 � �Þ, 60-cl-5-2 2 (– – –), 60-cl-5-2 (..........).


considered as limit values, since heat transfer between air and rock should lead totheir reduction.

7. Effects of train schedule

Because no perfect synchronization can be guaranteed in real operationalconditions (a real train schedule can require either asymmetrical or single trainmovement, or even multiple train movement in the same tunnel), the efficiency of thechosen configurations out of strict design conditions must be examined.

In the 60-cl-5-13 configuration, the reduction of the piston effect is related more tothe influence of each train on itself, through the pressure relief ducts, than to thesymmetric movement of the second train in the adjacent tunnel. The non-synchronized train schedule has in this case a negligible effect on the validity ofthe results described in Section 5.

The effect of the train schedule is instead remarkable in the 60-cl-5-2 2 and 60-cl-5-2 6 configurations, where pressure relief ducts are located only close tothe end stations and all the drag-reduction is due to the mutual effect of onetrain on the other. Three different train schedules have been compared inconfiguration 60-cl-5-2 2: the synchronized case described in Section 5; a secondcase where one train moves alone; a third one where two trains travel in oppositedirections and the second train starts when the first train is at mid tunnel. In thesetests, inner ducts are placed 2500m inside the tunnel. Results in terms of requiredaerodynamic power are shown in Fig. 24 and global drag and power data aresummarized in Table 5.

When the train movement is synchronized, the power required by one train isreduced when the train is reached by the expansion wave generated during theacceleration of the other one. A train traveling alone in the tunnel network does notbenefit of this effect: this results in an additional required power reaching up to700 kW. The case with two non-synchronized trains shows different onset times forthe ‘‘expansion wave reduction’’ of the piston effect: the train which leaves firstexperiences only a minor power reduction after 370 s, 90 s after the departure of thesecond train. On the other hand, the second train leaves the station in stronglyfavorable pressure conditions induced by the first train, and benefits from theseconditions until it reaches the middle of the tunnel. The sum of the mean powersrequired by the two trains in the asymmetric case is slightly lower than the double ofthe power required by each train in the symmetric case, thus enabling us to concludethat, with an asymmetric train schedule, the power required by each train is neverhigher than the power required by a train moving alone in the network.

The effects due to multiple train movement in the same tunnel and direction havebeen analyzed on the 60-cl-5-2 2 and 60-cl-5-2 6 configurations. In bothconfigurations, three trains leave the station at an interval of 4min in the sametunnel, the other being used only for air propagation. Results on aerodynamic dragare shown in Fig. 25 and summarized in Table 6. One can observe that the presenceof 6 pressure relief ducts near the station diminishes the piston effect with respect to


the 60-cl-5-2 2 case: the intensity of the compression wave reflected by the closedend is small, because the intensity of the wave transmitted in the other tunnel ishigher. The peak power for the first and second train is attenuated; moreover, all thetrains now require the same maximum power. Shafts placed where the train speed islow have little influence when crossed. The configuration 60-cl-5-2 6 appearstherefore as the most interesting for a tunnel network where several trains move inthe same tunnel.

Fig. 24. Aerodynamic power needed by the high-speed train motion during the 60 km travel between

stations of the 60-cl-5-2 2 configuration. One train alone (}}}), two synchronized trains ð2 �2 �2�Þ,first non-synchronized train (........), second non-synchronized train ð2 � �2 � �2 � �Þ.

Table 5

Aerodynamic power with different train schedule for the 60-cl-5-2 2 configurationa

60-cl-5-2 2 configuration hWtoti �Wtot Wmaxtot Wp Wfr

(MW) (MW) (MW) (%) (%)

Two synchronized trains 6.3 7.3 7.5 68 32

One train alone 6.7 7.7 8.2 69 31

First non-synchronized train 6.6 7.6 8.1 69 31

Second non-synchronized train 5.4 6.4 8.2 65 35

aTotal power averaged during the whole trip hWtoti; total power averaged during the phase at constant

speed �Wtot; maximum power Wmaxtot ; percentage of pressure Wp and friction Wfr contributions.


8. Conclusion

The air flow induced by the passage of high-speed trains in tunnels has beenpredicted by a quasi one-dimensional numerical model in order to establish tunneldesign criteria for long-range underground high-speed railways.

The reduction of the diameter of these tunnels is desirable in order tolimit construction costs (which can be tentatively considered proportional to the

Fig. 25. Aerodynamic power needed by three high-speed trains moving in the same tunnel with 4min of

interval (the first train starts at t ¼ 0 s, the second one at t ¼ 240 s and the third one at t ¼ 480 s). 60-cl-5-

2 2 configuration (}}), 60-cl-5-2 6 configuration (.........).

Table 6

Aerodynamic power of different trains for the 60-cl-5-2 2 and 60-cl-5-2 6 configurationsa

Tunnel configuration Train hWtoti �Wtot Wmaxtot Wp Wfr

(MW) (MW) (MW) (%) (%)

60-cl-5-2 2 First 6.9 8.0 10.2 69 31

60-cl-5-2 2 Second 6.4 7.7 10.8 68 32

60-cl-5-2 2 Third 6.0 7.1 8.7 66 34

60-cl-5-2 6 First 6.4 7.5 8.1 68 32

60-cl-5-2 6 Second 5.9 7.1 8.4 67 33

60-cl-5-2 6 Third 5.8 6.8 7.9 66 34

aAll the trains are moving in the same tunnel at an interval of 4 min. Total power averaged during the

whole trip hWtoti; total power averaged during the phase at constant speed �Wtot; maximum power Wmaxtot ;

percentage of pressure Wp and friction Wfr contributions.


cross-section diameter itself). However, this reduction increases blockage ratios forgiven train geometries, thus leading to an unwanted rise of propulsion costs.

The realization of such tunnel connections under atmospheric conditions appearstherefore to be inconvenient due to the high requirements in terms of power supplyand to environmental impact at open ends. The construction of undergroundconnections under partial vacuum seems to be the most viable solution to theproblem. However, the effects of multiply reflected compression waves on tunnelclosed ends reduces strongly the advantages of partial vacuum in single closedtunnels.

In this framework, the best configuration for this long-range, high-blockage ratiotunnel network seems to consist in two coupled tunnels connected by a number ofpressure relief ducts. These connections allow both a reduction of the piston effectgenerated by the moving train and a positive mutual interaction of trains moving inopposite directions.

Side effects of these connections are not always desirable: sudden increasesin aerodynamic drag and strong lateral wind loads on the train can be generated.A solution to this problem can be found by placing pressure relief ducts onlyin proximity of the stations, where the high-speed train is in its accelera-ting=decelerating phase. The power required for train motion is, in this case, morethan 50% lower than in the single tunnel connection and more than 90% lower thanin a single tunnel connection at low blockage ratio and atmospheric conditions. Thisreduction holds and seems even to improve when the train motion in the tunnelnetwork is not synchronized.

The aerodynamic phenomena which characterize these design solutions lead to theincrease of air temperature in the arrival station, which even in the most favorableconditions can reach up to 40 K, and to the onset of supersonic regime on the traintail, involving the generation of a shock wave.

Acknowledgements

The authors are sincerely grateful to Dr. Stefania Gualdi for her valuable help andcomments during the revision of this manuscript, and to Dr. Mame William-Louisfor fruitful discussions on the comparison between finite volume methods and themethod of characteristics.

References

[1] V. Bourquin, M. Mossi, R. Gregoire, J.M. Rety, The importance of aerodynamics on the design of

high-speed transportation systems in tunnels: an illustration with the TGV and the Swissmetro,

World Congress on Railway Research E, Florence, 1997, pp. 507–513.

[2] J.Y. Taille, J. Brulard, J.M. Rety, P. Fauvel, Les recherches techniques pour l’etude de faisabilite du

tunnel de base de la liaison transalpine Lyon-Turin, Revue Generale des Chemins de Fer 197 (1995)

17–27.

[3] www.alptransit.ch (Internet homepage).


[4] www.rtri.or.jp=rd=maglev=html=english=yamanashi_testline_E.html (Internet homepage).

[5] A.E. Vardy, Aerodynamic drag on trains in tunnels, Part 1: synthesis and definitions, Proceedings of

the Institute of Mechanical Engineers, Part F, J. Rail Rapid Transit 210 (1) (1996) 29–38.

[6] A.E. Vardy, Aerodynamic drag on trains in tunnels, Part 2: prediction and validation, Proceedings of

the Institute of Mechanical Engineers, Part F, J. Rail Rapid Transit 210 (1) (1996) 39–49.

[7] The limit of rapid transit, Sci. Am. 101 (1909) 366.

[8] W.P. Trzaskoma, Tube vehicle system (TVS) technology review, Report PB 193 451, US Federal

Railroad Administration, Department of Transportation, Washington, 1970.

[9] Tube vehicle system (TVS) – definition, TRW Systems Report Number 06818-w454 RO-19, 4 October

1968.

[10] M. Kowalik, HSTV – high speed tunnel vehicle, RMIT Engineering Thesis, 1994.

[11] M. Jufer, SWISSMETRO – Preliminary Study, Ecole Polytechnique Federale de Lausanne, 1993.

[12] Ph. Pot, M. Jufer, Y. Trottet, Demande de concession, Troncon pilote Geneve-Lausanne, Swissmetro

SA, Geneva, 1997.

[13] V. Bourquin, M. Mossi, Rapport final – Etude principale – Groupe Mecanique, Rapport Swissmetro

EPFL 1.0111=1.6210=a, Lausanne, 1998.

[14] W. von Tollmien, Der Luftwiderstand und Druckverlauf bei der Fahrt von Zugen in einem Tunnel,

VDI-Zeitschrift 71 (6) (1927) 199–203.

[15] T. Hara, Aerodynamic force acting on a high speed train at tunnel entrance, Quarterly Report of

RTRI 1 (2) 1961.

[16] T. Hara, J. Okushi, Model tests on aerodynamical phenomena of a high speed train entering a tunnel,

Quarterly Report of RTRI 3 (4) (1962) 6–10.

[17] T. Hara, M. Kawaguti, G. Fukuchi, A. Yamamoto, Aerodynamics of high speed train, IRCA-UIC

High Speed Symposium, Vienna, Section I, 1968, pp. 1–26.

[18] A. Yamamoto, Aerodynamics of a train and tunnel, Proceedings of the First International

Conference on Vehicular Mechanics, Detroit, 1968, pp. 151–163.

[19] A. Yamamoto, Pressure variations, aerodynamic drag of train, and natural ventilation in Shinkansen

type tunnel, Quarterly Report of RTRI 15 (4) (1974) 207–214.

[20] A.G. Hammitt, The Aerodynamics of High Speed Ground Transportation, Western Periodicals

Company, North Hollywood, CA, 1973.

[21] C.W. Pope, Gas dynamics and thermodynamics of unsteady flow in a railway tunnel, Ph.D. Thesis,

the Milton Keynes Open University, 1986.

[22] M.J.-P. William-Louis, Etude aerodynamique de la propagation des ondes de pression lors de la

circulation des trains en tunnels simples ou ramifies, Ph.D. Thesis, Universite de Valenciennes et du

Hainaut-Cambresis, 1994.

[23] V. Bourquin, Problems of reduced-scale aerodynamic testing of high-speed vehicles in tunnels, Ph.D.

Thesis, Ecole Polytechnique Federale de Lausanne, 1999.

[24] M. Mossi, Simulation of benchmark and industrial unsteady compressible turbulent fluid flows,

Ph.D. Thesis, Ecole Polytechnique Federale de Lausanne, 1999.

[25] R. Gregoire, B. Eckl, A. Malfatti, TRANSAERO: a major European research programme on

transient aerodynamics for railway system optimisation, World Congress on Railway Research,

E, Florence, 1997, pp. 461–467.

[26] A. Baron, F. Losi, F. Orso, Simulazione numerica dei fenomeni aerodinamici prodotti da treni ad alta

velocita in tunnel di forma complessa, Ingegneria Ferroviaria 7 (1996) 3–19.

[27] D. Lancien, P. Caille, E. Parent de Curzon, M. Jutard, Aspects aerodynamiques de la circulation a

grande vitesse en tunnel, Revue Generale des Chemins de Fer 106 (1987) 5–22.

[28] E. Sockel, The tunnel entrance problem, Von Karman Institute 1972 Lecture Series, 1972, pp. 1–16.

[29] W.A. Woods, R.G. Gawthorpe, The train and tunnel – a large scale unsteady flow machine,

Proceedings of the Second International JSME Symposium on Fluid Machinery and Fluidic, Tokyo,

1972, pp. 249–258.

[30] W.A. Woods, C.W. Pope, On the range of validity of simplified one-dimensional theories for

calculating unsteady flows in railway tunnels, Proceedings of the Third International Symposium on

the Aerodynamics and Ventilation of Vehicle Tunnels, Sheffield, 1979, pp. 115–150.


[31] Kisielewicz, Validated computational aerodynamics for trains, J. Wind Eng. Ind. Aerodyn. 49 (1993)

449–458.

[32] M. Schultz, E. Sockel, The influence of unsteady friction on the propagation of pressure waves in

tunnels, Proceedings of the Sixth International Symposium on the Aerodynamics and Ventilation of

Vehicle Tunnels, 1988, pp. 123–135.

[33] A.E. Vardy, J.M. Brown, Transient, turbulent, smooth pipe friction, J. Hydr. Res. 33 (4) (1995) 435–

456.

[34] C. Hirsch, Numerical Computation of Internal and External Flows, Wiley, New York, 1988.

[35] A. Jameson, W. Schmidt, E. Turkel, Numerical simulation of the Euler equations by finite volume

methods using Runge–Kutta time stepping schemes, AIAA Paper 81-1259, AIAA Fifth Computa-

tional Fluid Dynamics Conference, 1981.

[36] I.E. Idelcik, Memento des Pertes de Charge, Eyrolles, Paris, 1969.

[37] L.E. Kinsler, A.R. Frey, A.B. Coppens, J.V. Sanders, Fundamentals of Acoustics, Wiley, New York,

1982.

[38] D. Ambrosi, Un metodo numerico per correnti instazionarie incomprimibili, Ph.D. Thesis,

Politecnico di Milano, 1993.

[39] M. Schultz, E. Sockel, Pressure transient in short tunnels, Proceedings of the Seventh International

Symposium on the Aerodynamics and Ventilation of Vehicle Tunnels, 1991, pp. 221–237.

[40] A. Baron, M. Arra, Transient flow prediction in railway tunnels, Conference of the Royal

Aeronautical Society on Vehicle Aerodynamics, Loughborough University of Technology, 1994,

pp. 15.1–15.12.

[41] W.A. Woods, C.W. Pope, Secondary aerodynamic effects in rail tunnels during vehicle entry,

Proceedings of the Second International Symposium on the Aerodynamics and Ventilation of Vehicle

Tunnels, Cambridge, 1976, pp. 71–86.

[42] G.N. Abramovich, The theory of turbulent jets, Massachussets Institute of Technology, 1963.

[43] H. Glocke, P. Pfretzschner, High speed tests with ICE=V passing through tunnels and the effect of

sealed coaches on passenger comfort, Proceedings of the Sixth International Symposium on the

Aerodynamics and Ventilation of Vehicle Tunnels, Durham, 1988, pp. 23–44.

[44] R.G. Gawthorpe, C.W. Pope, The measurement and interpretation of transient pressures generated

by trains in tunnels, Proceedings of the Second International Symposium on the Aerodynamics and

Ventilation of Vehicle Tunnels, Cambridge, 1976, pp. 35–54.

[45] G. Mancini, A. Malfatti, Full scale measurements on high speed train Etr 500 passing in open air and

in tunnels of Italian high speed line, Transient aerodynamics railway system optimisation,

TRANSAERO Symposium, Paris, 1999.

[46] M. Mossi, V. Bourquin, J.B. Vos, M. Deville, Simulation numerique de l’ecoulement d’air autour

d’un train evoluant a haute vitesse dans un tunnel, AAAF: 33eme colloque d’aerodynamique

appliquee, Poitiers, 1997.

[47] J.-L. Peters, Bestimmung des aerodinamischen Widerstandes des ICE=V im Tunnel und auf freier

Strecke durch Auslaufversuche, ETR 39, Heft 9, 559–564, 1990.

[48] D. Gabay, Un element de confort et de securite, La ventilation de la ligne Meteor, Revue Generale

des Chemins de Fer 6 (1996) 89–93.

[49] D.A. Henson, W.M.S. Bradbury, The aerodynamics of Channel tunnel trains, Proceedings of the

Seventh International Symposium on the Aerodynamics and Ventilation of Vehicle Tunnels, 1991,

pp. 927–956.


the alleviation of the aerodynamic drag and wave effects of high-speed trains in very long tunnels

Documents