Tunnelling and

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Tunnelling and Underground Space Technology 22 (2007) 474–482

Underground SpaceTechnologyincorporating Trenchless

Technology Research

CFD simulation and optimization of the ventilation for subwayside-platform

Feng-Dong Yuan *, Shi-Jun You

School of Environment Science and Technology, Tianjin University, No. 72, Weijin Road, Nankai District, Tianjin 300072, China

Received 27 May 2006; received in revised form 23 September 2006; accepted 19 October 2006Available online 5 December 2006

Abstract

To obtain the velocity and temperature field of subway station and the optimized ventilation mode of subway side-platform station,this paper takes the evaluation and optimization of the ventilation for subway side-platform station as main line, builds three dimen-sional models of original and optimization design of the existed and rebuilt station. And using the two-equation turbulence model asits physics model, the thesis makes computational fluid dynamics (CFD) simulation to subway side-platform station with the boundaryconditions collected for simulation computation through field measurement. It is found that the two-equation turbulence model can beused to predict velocity field and temperature field at the station under some reasonable presumptions in the investigation and study. Atlast, an optimization ventilation mode of subway side-platform station was put forward.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Ventilation; CFD simulation; k-e model; Subway; Side-platform

1. Introduction

Computational fluid dynamics (CFD) software is com-monly used to simulate fluid flows, particularly in complexenvironments (Chow and Li, 1999; Zhang et al., 2006;Moureh and Flick, 2003). CFD is capable of simulating awide variety of fluid problems (Gan and Riffat, 2004;Somarathne et al., 2005; Papakonstantinou et al., 2000;Karimipanah and Awbi, 2002). CFD models can be realis-tically modeled without investing in more costly experi-mental method (Betta et al., 2004; Allocca et al., 2003;Moureh and Flick, 2003). So CFD is now a popular designtool for engineers from different disciplines for pursuing anoptimum design due to the high cost, complexity, and lim-ited information obtained from experimental methods (Liand Chow, 2003; Vardy et al., 2003; Katolidoy and Jicha,2003). Tunnel ventilation system design can be developedin depth from the predictions of various parameters, such

0886-7798/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.tust.2006.10.004

* Corresponding author. Tel.: +86 22 8740 1917; fax: +86 22 2789 2626.E-mail address: yuanfd@gmail.com (F.-D. Yuan).

as vehicle emission dispersion, visibility, air velocity, etc.(Li and Chow, 2003; Yau et al., 2003; Gehrke et al., 2003).

Earlier CFD simulations of tunnel ventilation systemmainly focus on emergency situation as fire condition(Modic, 2003; Carvel et al., 2001; Casale, 2003). Many sci-entists and research workers (Waterson and Lavedrine,2003; Sigl and Rieker, 2000; Gao et al., 2004; Tajaduraet al., 2006) have done much work on this. This paper stud-ied the performance of CFD simulation on subway envi-ronment control system which has not been studied byother paper or research report. It is essential to calculateand simulate the different designs before the constructionbegins, since the investment in subway’s construction ishuge and the subway should run up for a few decade years.The ventilation of subway is crucial that the passengersshould have fresh and high quality air (Lowndes et al.,2004; Luo and Roux, 2004). Then if emergency occurredthat the well-designed ventilation system can save manypeople’s life and belongings (Chow and Li, 1999; Modic,2003; Carvel et al., 2001). The characteristics of emergencysituation have been well investigated, but there have been

F.-D. Yuan, S.-J. You / Tunnelling and Underground Space Technology 22 (2007) 474–482 475

few studies in air distribution of side-platform in normalconditions.

The development of large capacity and high speed com-puter and computational fluid dynamics technology makesit possible to use CFD technology to predict the air distri-bution and optimize the design project of subway ventila-tion system. Based on the human-oriented designintention in subway ventilation system, this study simu-lated and analyzed the ventilation system of existent stationand original design of rebuilt stations of Tianjin subway inChina with the professional software AIRPAK, and thenfound the optimum ventilation project for the ventilationand structure of rebuilt stations.

2. Ventilation system

Tianjin Metro, the secondly-built subway in China, willbe rebuilt to meet the demand of urban development andexpected to be available for Beijing 2008 Olympic Games.The existent subway has eight stations, with a total lengthof 7.335 km and a 0.972 km average interval. For sake ofsaving the cost of engineering, the existent subway will con-tinue to run and the stations will be rebuilt in the rebuildingLine 1 of Tianjin subway. Although different existent sta-tions of Tianjin Metro have different structures and geom-etries, the Southwest Station is the most typical one. So theSouthwest Station model was used to simulate and analyzein the study. Its geometry model is shown in Fig. 1.

2.1. The structure and original ventilation mode of existentstation

The subway has two run-lines. The structure of South-west Station is, length · width · height = 74.4 m(L) ·

Fig. 1. The location of test section an

18.7 m(W) · 4.4 m(H), which is a typical side-platformstation. Each side has only one passageway (length ·height = 6.4 m(L) · 2.9 m(H)). The middle of station isthe space for passengers to wait for the vehicle. The plat-form mechanical ventilation is realized with two jet open-ings located at each end of station and the supply air jetstowards train and track. There is no mechanical exhaustsystem at the station and air is removed mechanically bytunnel fans and naturally by the exits of the station.

2.2. The design structure and ventilation of rebuilt station

The predicted passenger flow volume increase greatlyand the dimension of the original station is too small, soin the rebuilding design, the structure of subway stationis changed to, (length · width · height = 132 m(L) ·17.438 m(W) · 4.65 m(H)), and each side has two passage-ways. The design volume flow of Southwest Station is400000 m3/h. For most existent stations, the platformheight is only 2.9 m, which is too low to set ceiling ducts.So in the original design, there are two grille vents at eachend of the platform to supply fresh air along the platformlength direction and two grille vents to jet air breadthwaystowards trains. The design velocity of each lengthwaysgrille vent is 5.54 m/s. For each breadthways vent, it is5.28 m/s. Under the platform, 80 grille vents of the samevelocity (4.62 m/s, 40 for each platform of the station)are responsible for exhaust.

3. CFD simulation and optimization

The application of CFD simulation in the indoor envi-ronment is based on conversation equations of energy,mass and momentum of incompressible air. The study

d the layout of measuring points.

476 F.-D. Yuan, S.-J. You / Tunnelling and Underground Space Technology 22 (2007) 474–482

adopted a turbulence energy model that is the two-equa-tion turbulence model advanced by Launder and Spalding.And it integrated the governing equation on the capitalcontrol volumes and discretized in the definite grids, at lastsimulated and computed with the AIRPAK software.

3.1. Preceding simplifications and presumptions

Because of mechanical ventilation and the existence oftrain-driven piston wind, the turbulence on platform istransient and complex. Unless some simplifications andpresumptions are made, the mathematics model of three-dimensional flow is not expressed and the result is diver-gent. While ensuring the reliability of the computationresults, some preceding simplifications and presumptionshave to be taken.

(1) The period of maximum air velocity is paid attentionto in the transient process. Apparently the maximumair velocity is reached at the period when train stopsat or starts away from the station (Yau et al., 2003;Gehrke et al., 2003), so the period the simulation con-cerns about the best period of time for simulation isfrom the point when at the section of ‘x = 0.0 m’(Fig. 1) and the air velocity begin to change underpiston-effect to the point when train totally stops atthe station (defined as a ‘pulling-in cycle’).

(2) Though the pulling-in cycle is a transient process, it issimplified to a steady process.

(3) Because the process is presumed to a steady process,the transient velocity of test sections, which wastested in Southwest Station in pulling-in cycle, is pre-sumed to the time-averaged velocity of test sections.

(4) The volume flow driven into the station by pulling-intrain is determined by such factors as BR (blockingratio, the ratio of train cross-section area to tunnelcross-section area), the length of the train and theresistance of station etc. For existent and new sta-tions, BRs are almost the same. Although the lengthof the latter train doubles that of the former whichmay increase the piston flow volume, the resistanceof latter is greater than that of the former whichmay counteract this increase. So it is presumed thatthe piston flow volume is same for both existentand new station and that the volume flow throughthe passenger exits is also same. Based on this pre-

Table 1Distributing temperature of enclosure

Test positions Station walls

Top Railway

1 2 3 1

Temperature (�C) when x = 12.8 m 24.8 24.6 24.8 23.8Temperature (�C) when x = 25.6 m 24.8 24.6 24.6 24Temperature (�C) when x = 38.4 m 24.8 25 24.8 24Temperature (�C) when x = 51.2 m 24.4 24.4 24.4 24.2

sumption, the results of the field measurements atthe existent station can be used as velocity boundaryconditions to predict velocity filed of new station.

3.2. Original conditions

To obtain the boundary conditions for computation andsimulation, such as the air velocity and temperature ofenclosure, measures were done by times at Southwest Sta-tion. All data are recorded during a complete pulling-incycle. The air velocities were measured by the multichannelanemonmaster hotwire anemoscope and infrared ther-mometer is used to measure the temperature of the wallsof the station which are taken as the constant temperaturethermal conditions in the simulation.

3.2.1. Temperatures of enclosure

Divide the platform into five segments and select sometypical test positions. The distributing temperature ofenclosure is shown in Table 1. It can be seen from Table1 that all temperatures of enclosure are between 23 �Cand 25 �C, there is little difference in all test positions,and the average temperature is 24 �C. So all temperaturesof subway station’s walls is 24 �C in CFD computationand simulation.

3.2.2. Time-averaged air velocity above the platform

Fig. 1 is the location of test section and the layout ofmeasuring points. The data measured include 12 transientvelocities in each section (A–H in Fig. 1), which were dealwith section’s time-averaged velocities in the period, 12point’s velocities of passageway, which is used to acquirethe average flow, and the velocities of each end of station,which is used to acquire the average piston flow volume.

Fig. 2 is the lengthways velocities measured of platformsections, Vmax is the maximum air velocity, Vmin is theminimum air velocity and Vave is the average air velocity.Fig. 2 shows that the maximum air velocity is at the pas-sageway. At the passageway the change of air velocity isabout 2.25 m/s, which is the maximum and indicates thatthe passageway is the position effected most by the pistonwind effect, and the air velocity of section D and E afterthe passageway is almost the same, which indicates thatthe piston wind can hardly effect the air velocity after thepassageway.

Platform

ground Lateral wall Ground

2 3 1 2 3 1 2 3

23.8 23.8 24.2 23.8 23.6 23.8 23.8 23.824 24 24.4 24 23.6 23.4 23.8 2424 24 24.4 23.8 23.6 23.6 23.2 23.624.2 24.2 24.2 24.2 23.4 23 23.4 23.4

Fig. 2. Measured lengthways velocities at platform sections.

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In addition, because of the movement of train, the veloc-ity cannot be measured in section U of Fig. 1, the air veloc-ity of section U was computed in CFD simulation.

3.2.3. Boundary conditions of simulation

Through analyzing the boundary data measured at theSouthwest Station, the boundary conditions of the existent

Table 2Boundary condition of existent stations in CFD simulation

Sections Section G Section U(estimated)

Section H Passtop

Air velocity (m/s) 0.67 0.67 0.67 0.67Air flow (m3/s) 0.67 0.67 0.67 0.67

Table 3Boundary condition of rebuilt stations in CFD simulation

(a) Heat load

Persons Lamps (on the topof platform)

Advewall

Heatload

44 kW/person

13 W/m2 15 kW

(b) Air velocity

Supply air (lengthways)

Air velocity (m/s) 5.54

(c) Boundary conditions of air velocity

The entrance oftrain

The exit oftrain

Passside

Boundary conditionsof air velocity (m/s)

0.2–0.59 0.41 1.44

(d) Temperature

Train walls (expert for excluding topand bottom of train)

Ou(su

Temperature(�C)

27 27

station in CFD simulation is shown in Table 2. Addition-ally, the Tianjin Metro is out of run during the measuringtime, so the heat load is not typical and is difficult to bedetermined so that the distributing temperature was notsimulated in this study.

Referred to the feasibility research report of No. 3design institute of China’s ministry of railway and the mea-sured data in Southwest Station, the boundary conditionsof new station in CFD simulation of the existent stationis shown in Table 3.

3.3. Solution process

3.3.1. Method of solutionThe governing equations to calculate original variables,

such as velocity and temperature etc., can be shown(Moureh and Flick, 2003).

o

otðq/Þ þ divðq~u/Þ ¼ divðCgrad/Þ þ S ð1Þ

where / is common variable and denotes (u,v,w,T), ~u isvelocity vector, q is density, C is dissipation function, S isthe source item. u is air velocity of direction X, v and w

are air velocities of direction Y and Z, respectively, andT is air temperature.

Eq. (1) is integrated on the spatial control volumes, andthrough discretizing in the definite grids

sageway of the train-ping side:EXIT1

Passageway of the non-trainstopping side:EXIT2

The exit oftrain F

0.67 0.670.67 0.67

rtisement lamps (lateralof platform)

Heat emitted from train

/station 320 kW (acceleration) and 200 kW(heat from applying brake)

Supply air (breadthways) Under the platform vents

5.28 4.62

ageway of the train-stopping Passageway of the non-train-stoppingside

0.97

tdoor airmmer)

Supply air(summer)

Tunnelair

Enclosurewalls

27 25 24

Table 4Settlement of existent station ventilation CFD simulation

Variable Pressure Kinetic k e

Discretization Body force weighted Second order upwind Second order upwind Second order upwindRelaxation coefficient 0.3–1.0 0.3–1.0 0.3–1.0 0.3–1.0Solution Pressure AMGa Kinetic AMG k AMG e AMGCycle type V-type Flexible Flexible Flexible

a AMG is algebra multi-grid.

Table 5Settlement of new station ventilation CFD simulation

Variable Pressure Temperature Kinetic k e

Discretization Body force weighted Second order upwind First order upwind First order upwind First order upwindRelaxation coefficient 0.3–1.0 0.3–1.0 0.3–1.0 0.3–1.0 0.3–1.0Solution Pressure AMG Temperature AMG Kinetic AMG k AMG e AMGCycle type V-type Flexible Flexible Flexible Flexible

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ap/ ¼X

nb

anb/nb þ b ð2Þ

In Eq. (2), nb denotes neighbor grids; ap and anb are thecoefficients of / and /nb, respectively, b is the source item.

(2) Tables 4 and 5 shows solution, cycle type andconvergence criterion and relaxation coefficient in CFDsimulation of the existent station ventilation and the newstation.

3.4. Simulation and discussion

Used the boundary conditions measured in SouthwestStation, the air velocity of subway side-platform stationwas simulated in AIRPAK. Fig. 3 is the air velocity com-parison of simulation and measurement in section A–E,which shows that the two-equation model and the preced-ing simplifications are acceptable in predicting flow at thestation. Although the computed velocity at section C and

Fig. 3. Air velocity of section A–E simulation and measurement.

E is not equal to the values of the field measurement, whoseerror is about 0.1–0.2 m/s, the differences are acceptableand the overall variance trend of the velocity along theplatform tallies with the measurement. The simulationresult of air velocity of 1.7 m height above platform of exis-tent station can be seen in Fig. 4. Fig. 4 shows that themajority of piston winds pour out from the passagewayand the air velocity of the zone after the passageway islower, which is below 0.4 m/s. The maximum air velocityat 1.7 m height above platform is the passageway of thetrain-stopping side, which is about 1.89 m/s.

The simulation results indicate that it is applicable to usetwo-equation turbulence model to predict time-averagedflow and temperature distribution at subway station sothe veracity is reliable.

Fig. 5 is the simulation result, which is the originaldesign of air velocity at 1.7 m height above platform ofnew station. It is shown from Fig. 5 that at the train-ing-stopping side of platform the supply air does notreach the zone between the two exits, which is for thepassenger to wait for the train, and pour out from thepassageway because of the leakage of passageway. Theair velocity between two passageways, which is below0.4 m/s, is a little low so that the ‘Dead Zone’ is formed.The simulation also shows that the maximum velocityexists at the exits, which agrees with the references andexperience.

Fig. 6 is the temperature distribution at 1.7 m heightabove platform of the new station, which is used to simu-late for original design ventilation mode. It shows thatthe temperature distribution is imbalanced for the leakageof exits at the training-stop side of platform, and at eachend of platform, the temperature should be approximatelybetween 24 �C and 26 �C while the temperature is between32 �C and 34 �C because the heat away from the train cannot be cooled and removed by the cold supply air in time,even at the x = 61 m point, the temperature reaches above40 �C, which makes people feel uncomfortable.

The simulation result of temperature and air velocity oforiginal design at the lengthways center section is shown in

Fig. 4. Simulation result of air velocity at 1.7 m height above platform of existent station.

Fig. 5. Simulation result of air velocity at 1.7 m height above platform of new station (original design).

Fig. 6. Simulation result of temperature at 1.7 m height above platform of new station (original design).

F.-D. Yuan, S.-J. You / Tunnelling and Underground Space Technology 22 (2007) 474–482 479

Fig. 7, which shows that the distribution of temperatureand air velocity is not balanceable and the zone betweentwo exits is ‘Dead Zone’.

From the simulation of original design, the followingcan be seen:

(1) The ventilation mode that the feasibility researchreport design for the side-platform station of subwaymakes the distribution of temperature and air veloc-ity unbalanced, so the passengers will feel uncomfort-able at the middle of platform.

Fig. 7. Simulation result of temperature and air velocity at the lengthways center section (original design).

480 F.-D. Yuan, S.-J. You / Tunnelling and Underground Space Technology 22 (2007) 474–482

(2) The air velocity is too high at some position of plat-form and the passengers feel easily the change of airvelocity, whose scope is between 0.4 m/s and 2.5 m/s,and feel uncomfortable when they go to exits fromthe middle of platform.

(3) The efficiency of ventilation is not as good as expec-tation and the supply air from jet fans cannot reachthe middle of platform adequately and part of themwill flow away from the passageways.

Because of the unbalanced distribution of temperatureand air velocity, original design’s ventilation mode wasoptimized. The exhaust vents are as same as that of originalones. The flow of supplied air remains the same and underthe platform there are tubes of supplied fresh air. Alsothere are some vertical tubes fetched out by platform. Asa result, the air is supplied widthways and reasonably theflow of supplied air is delivered in balance, which elimi-nates the unbalanced distribution of temperature and airvelocity on the platform. On the other hand the breadth-ways supplied air prevents the heat brought by train fromdiffusing onto the platform, and the heat can be vented intime from the exhaust vents under the platform. At thesame time the fresh air from the breadthways vents passesthrough the passengers, takes away heat and humidity, andthe efficiency of ventilation is quite satisfactory.

To validate the optimization ventilation mode, the sim-ulation adopted the same boundary conditions and set up

Fig. 8. Simulation result of air velocity at 1.7 m height a

with original design’s CFD simulation. The simulationresults are showed in Figs. 8 and 9.

Fig. 8 is the air velocity distribution at 1.7 m heightabove platform of new station, which is simulated foroptimization design ventilation mode. It shows that thedistribution of air velocity is good enough and balanced.The breadthways supplied air makes the ‘Dead Zone’disappeared, and the maximum air velocity is onlyabout 1.67 m/s at 1.7 m height above platform of newstation, which makes it difficult for passengers to feelwindy.

Fig. 9 is the simulation result of temperature and airvelocity of original design at the lengthways center section,which shows that the ‘Dead Zone’ disappears at the length-ways center section. And the breadthways supplied air pre-vents the heat, which is from the air conditioningcondenser and the friction produced by train-stopping,from diffusing to the platform, so the temperature is aboutbelow 28 �C.

Compared with the ventilation mode in original design,the optimization ventilation mode has several advantagesas follows:

(1) The supply air is delivered to every zone in a balancedway and the distribution of temperature and airvelocity of side-platform is also balanced.

(2) The air velocity is balanced and the maximum is onlyabout 1.67 m/s.

bove platform of new station (optimization design).

Fig. 9. Simulation result of temperature and air velocity at the lengthways center section (optimization design).

F.-D. Yuan, S.-J. You / Tunnelling and Underground Space Technology 22 (2007) 474–482 481

(3) The supplied air removes the heat of platform betterand the whole platform’s temperature is lower thanthat of the original design, which can lower tempera-ture standard and can decrease the flow of supply airto save energy.

(4) The supplied air from breadthways vents also wellprevents the hot contaminated train-driven air fromspreading onto the platform, and on the other handthe fresh air from the breadthways vents passesthrough the passengers, takes away heat and humid-ity, collects and is exhausted by the under-platformvents.

(5) The ventilation efficiency is quite satisfactory.

4. Conclusions

The following can be concluded from this study:The air flow in platform of subway is a complex three-

dimensional transient turbulence. Simplification of the airflow to steady process and presumption of the transientvelocity to the time-averaged velocity are applicable to sim-ulate the distribution of temperature and air velocity ofsubway platform in the pulling-in cycle.

It is applicable to use two-equation turbulence model topredict time-averaged velocity and temperature distribu-tion at subway station. The simulation results are influ-enced greatly by the boundary conditions such asboundary velocity and temperature.

The optimization ventilation mode has more advantagesthan the original design’s. The breadthways ventilation issuggested when the height of platform is too low to haveceiling ducts. It makes the distribution of temperatureand air velocity balanced.

Before a design is accepted it is very necessary to evalu-ate and optimize it by such techniques as CFD, etc. It willhelp a lot to build a reliable, effective and economicalsystem.

Acknowledgement

This project was supported by the funding generated bythe Tianjin Municipal Science and Technology Commis-sion of China (Project No: 033112911).

References

Allocca, C., Chen, Q.Y., Glicksman, L.R., 2003. Design analysis of single-sided natural ventilation. Energy and Buildings 35, 785–795.

Betta, V., Cascetta, F., Labruna, P., Palombo, A., 2004. A numericalapproach for air velocity predictions in front of exhaust flange slotopenings. Building and Environment 39, 9–18.

Carvel, R.O., Beard, A.N., Jowitt, P.W., 2001. The influence of longitu-dinal ventilation systems on fires in tunnels. Tunnelling and Under-ground Space Technology 16, 3–21.

Casale, E., 2003. The automation of the aeraulic response in the case of afire in a tunnel-first concrete answers. In: Proceedings of Claiming theUnderground Space, pp. 185–191.

Chow, W.K., Li, J.S.M., 1999. Safety requirement and regulations reviewson ventilation and fire for tunnels in the Hong Kong SpecialAdministration Region. Tunnelling and Underground Space Technol-ogy 14, 13–21.

Gan, G.H., Riffat, S.B., 2004. CFD modelling of air flow and thermalperformance of an atrium integrated with photovoltaics. Building andEnvironment 39, 735–748.

Gao, P.Z., Liu, S.L., Chow, W.K., Fong, N.K., 2004. Large eddysimulations for studying tunnel smoke ventilation. Tunnelling andUnderground Space Technology 19, 577–586.

Gehrke, P.J., Stacev, C.H.B., Agnew, N.D., 2003. Rail tunnel temperaturestratification and implications for train and tunnel ventilation design.In: Proceedings of 11th International Symposium on Aerodynamicsand Ventilation of Vehicle Tunnels, pp. 727–741.

Karimipanah, T., Awbi, H.B., 2002. Theoretical and experimentalinvestigation of impinging jet ventilation and comparison withwall displacement ventilation. Building and Environment 37, 1329–1342.

Katolidoy, J., Jicha, M., 2003. Eulerian-Lagrangian model for trafficdynamics and its impact on operational ventilation of road tunnel. In:Proceedings of 11th International Symposium on Aerodynamics andVentilation of Vehicle Tunnels, pp. 877–891.

Li, J.S.M., Chow, W.K., 2003. Numerical studies on performanceevaluation of tunnel ventilation safety systems. Tunnelling andUnderground Space Technology 18, 435–452.

Lowndes, Ian S., Crossley, Amanda J., Yang, Zhi Yuan, 2004. Theventilation and climate modeling of rapid development tunneldrivages. Tunnelling and Underground Space Technology 19, 139–150.

Luo, S., Roux, B., 2004. Modeling of the HESCO nozzle diffuser used inIEA Annex-20 experiment test room. Building and Environment 39,367–384.

Modic, J., 2003. Fire simulation in road tunnels. Tunnelling andUnderground Space Technology 18, 525–530.

Moureh, J., Flick, D., 2003. Wall air-jet characteristics and airflowpatterns within a slot ventilated enclosure. International Journal ofThermal Sciences 42, 703–711.

Papakonstantinou, K.A., Kiranoudis, C.T., Markatos, N.C., 2000.Computational analysis of thermal comfort: the case of the archae-ological museum of Athens. Applied Mathematical Modelling 24, 477–494.

482 F.-D. Yuan, S.-J. You / Tunnelling and Underground Space Technology 22 (2007) 474–482

Sigl, O., Rieker, K., 2000. NATM tunnelling in Singapore old alluvium-design assumptions and construction experience. In: InternationalConference on Tunnels and Underground Structures. pp. 205–212.

Somarathne, S., Seymour, M., Kolokotroni, M., 2005. Dynamic thermalCFD simulation of a typical office by efficient transient solutionmethods. Building and Environment 40, 887–896.

Tajadura, R.B., Carlos, S.M., Eduardo, B.M., 2006. Influence of the slopein the ventilation semi-transversal system of an urban tunnel.Tunnelling and Underground Space Technology 21, 21–28.

Vardy, A.E., Mori, E., Yokota, M., Nakahori, I., 2003. Model-basedpredictive control of road tunnel portal emissions. In: Proceedings ofClaiming the Underground Space, pp. 207–212.

Waterson, N.P., Lavedrine, J., 2003. Evaluation of a simplified model forthe design of ventilation systems in tunnel networks. In: Proceedings of11th International Symposium on Aerodynamics and Ventilation ofVehicle Tunnels, pp. 219–229.

Yau, R., Cheng, V., Lau, K.P., Lai, F., 2003. Design and analysis oftunnel ventilation system for the extension of an existing railwaytunnel in Hong Kong. In: Proceedings of 11th International Sympo-sium on Aerodynamics and Ventilation of Vehicle Tunnels, pp. 323–338.

Zhang, Lin, Feng, Jiang, Chow, T.T., Tsang, C.F., Lu, W.Z., 2006. CFDanalysis of ventilation effectiveness in a public transport interchange.Building and Environment 41, 254–261.