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An-improved-model-of-traffic-force-based-

An improved model of traf?c force based on CFD in a curved

tunnel

Feng Wang a ,b ,?,Mingnian Wang c ,Qingyuan Wang a ,Dongping Zhao d

MOE key Laboratory of Energy Engineering Safety and Disaster Mechanics,College of Architecture and Environment,Sichuan University,Chengdu 610065,China b

State Key Laboratory of Coastal and Offshore Engineering,Dalian University of Technology,Dalian 116024,China c

School of Civil Engineering,Southwest Jiaotong University,Chengdu 610031,China d

Research Division of Science and Technology Engineering,China Railway Eryuan Engineering Group Co.Ltd,Chengdu 610031,China

a r t i c l e i n f o Article history:

Received 2April 2013

Received in revised form 17November 2013Accepted 26December 2013

Available online 20January 2014Keywords:Traf?c force

The effective drag coef?cient Vehicle space

Tunnel ventilation CFD

a b s t r a c t

In this work,a numerical study using 1D (one-dimensional)model and CFD (Computational Fluid Dynamics)is developed to analyse effects of vehicle space on the ventilation and the results from CFD are employed to improve the accuracy of the traf?c force model in a highway curved tunnel with a radius of 600m.The air speed from 1D model is compared to that from CFD for a single vehicle in the tunnel and a good agreement is concluded.The air speed from both 1D model and CFD for two vehicles is shown to increase signi?cantly with the increase of vehicle speed and the number in the tunnel.However,the effective piston effect coef?cient exhibits two opposite variations for the two models.The absence of the effect of vehicle space in 1D model is considered to be responsible for its unreasonable result.An understandable result from CFD is observed that the effective piston effect coef?cient increases with the increase of vehicle space and the decrease of vehicle speed.It is subsequently used to improve the traf?c force model.The effective drag coef?cient increases signi?cantly with the increase of vehicle space,especially in a shorter vehicle space.The effective drag coef?cient is concluded to be among 0.85–1.16for a large size vehicle in this study.

1.Introduction

In a road tunnel,an effective ventilation system is widely employed to prevent the harmful substances from affecting tunnel users and maintain good visibility.In short one-way tunnels,the piston effect induced by the moving vehicles,together with nature ventilation,is usually suf?cient to drive fresh air in and to push polluted air out of the tunnel (Bari and Naser,2005).In long one-way tunnels,the piston effect also plays an important role in keeping the amounts of toxic gases within safety limits.Accord-ingly,the piston effect is one of the key points for the design of ventilation in a road tunnel.As is well known that the piston effect increases with the improvement of vehicle speed and vehicle density,nevertheless the effect of vehicle space is ignored in tunnel ventilation system.Vehicle space is actually observed to vary in normal traf?c condition and traf?c jam condition.Much attention is consequently payed to the effect of vehicle space on the ventilation in this study.

Generally,the piston effect is treated as a traf?c force in the one-dimensional mathematical model as follows:

D p v tD p j tD p d àD p f àD p i ?q L

d v t e1T

D p v ?Nc dj

A c A t q

ev c àv t T2

e2T

where D p v is the traf?c force,D p j is the fan thrust,D p d is the pressure difference between the inlet and outlet portals,D p f is the wall friction,D p i is the local resistance caused by the ?ow separation at the inlet portal,v t is the mean air velocity in the tunnel,q is the air density,L is the length of the tunnel.

From Eq.(2),we can conclude that the traf?c force mainly depends on the type of vehicle and its speed,as well as the number of vehicles in a designed tunnel.In order to improve the accuracy of the prediction,some researches have been carried out on the traf?c force in 1D model and its three-dimensional details.Field test was carried out in the Fu-De tunnel by Jang and Chen (Jang and Chen,2000).Some data have been recorded including traf?c data,meteorologic parameters near the outlet,air speed,pressure,temperature,CO concentration,etc.in the tunnel.Afterwards,these data were used to analyse the accuracy of the 1D model.A reasonable result was concluded in their research.Jang and Chen subsequently adopted an optimization procedure to determine the averaged drag coef?cients of small-sized and large-sized vehicles,as well as another two aerodynamic coef?cients of the 1D model of road tunnel ventilation based on the measurements

?Corresponding author at:MOE key Laboratory of Energy Engineering Safety and Disaster Mechanics,College of Architecture and Environment,Sichuan University,Chengdu 610065,China.

E-mail address:wf1982625@https://www.wendangku.net/doc/3f109345.html, (F.Wang).

dynamic traf?c and the traf?c-induced air speed (Jang 2002).They found that the averaged drag coef?cients the small-sized and the large-sized vehicles fell in the ranges 0.32–0.35and 0.36–0.4respectively when the averaged traf?c den-sity was below 8vehicles/lane/km,and 0.20and 0.24respectively when the averaged traf?c density was increased to 8–23vehicles/lane/km.Chen et al.(1998)used a 1/20scale model tunnel and model vehicles to study the effect of moving vehicles on a straight tunnel ventilation.Their results showed that the piston effect in the straight tunnel was not con?ned to the vicinity of the vehicle,and the ratio of the mean ?ow velocity to the vehicle speed was close to 1/3for normal traf?c conditions,but smaller than 1/3for most other traf?c conditions.Katolicky and Jicha developed a qua-si-steady approach based on a computational Eulerian–Lagrangian model to study the impact of traf?c dynamic on operational ventilation in a road tunnel (Katolicky and Jicha,2005).The results showed that the air?ow rate was dependent on traf?c rate,vehicle speed and length of the tunnel.But the air?ow rate induced by continually increasing traf?c rates would eventually approach a limit at some high traf?c rate,and the higher the speed of cars the stronger was the effect on the induced ?ow rate.Wang et https://www.wendangku.net/doc/3f109345.html,ed dynamic mesh method to investigate the piston effect by a moving vehicle in a series of tunnels with various radii (Wang et al.,2011).The traf?c force was derived from the pressure histories and was found to increase with the decrease of the radius of the tunnel.And the size of the vortex near the rear of vehicle ventilation and the traf?c force in curved tunnels cannot be derived from these researches.In addition,it cannot be concluded from the 1D ventilation model in the tunnel as well.The actual space between vehicles is observed to vary in road tunnels although the rigid regulations issued in the tunnel.Accordingly,CFD (Computational Fluid Dynamics)simulation due to its relatively low cost is employed to investigate effects of vehicle space on the tunnel ventilation in a curved tunnel with a radius of 600m,these detailed information are subsequently used to improve the traf?c force model in the curved tunnel ventilation.2.Model description 2.1.One-dimensional model

This research mainly focuses on the traf?c force in a highway curved tunnel.The governing equation of air speed in the tunnel can be expressed brie?y in this simulation as follows:

Fig.1.Schedule of vehicles.

Fig.2.Planar view of the simulation domain and boundary conditions.

Fig.3.Cross-section of the highway curved tunnel.

Table 1

Simulation cases.

Case No.of vehicles Vehicles speed (km/h)Vehicles space Case No.of vehicles Vehicles speed (km/h)Vehicles

space 1140–92602L

D p v àD p f àD p i ?q L

d v t dt

e3T

where D p f ?f q 2L D v 2t ,D p i ?k q 2v 2t ,D p v ?Nc dj A c A t q 2

ev c àv t T2c dj and A c are the effective drag coef?cient of vehicles and the frontal area of vehicles.v c and v t are the speed of vehicles and the mean air speed in the tunnel.A t is the cross-section area of the tunnel.q is the air density.f and k are the friction coef?cient of tunnel and the coef?-cient of entrance loss respectively.Consequently,0.02and 0.6are ?xed for f and k respectively in this study.4p v is dependent on the schedule of vehicles moving into the tunnel.N is the number

vehicles in the tunnel.Taking the case as shown in Fig.1for example,N is equal to 1for Fig.1(a)and (c),2for Fig.1(b).

As referred previously,the type of vehicle is one of the factors traf?c force model.The effect of vehicle type is usually expressed the effective drag coef?cient which is given by a ?xed value.However,this coef?cient is essentially dependent on both the type vehicle and the ?ow ?eld around vehicle in the tunnel,and thereby is strongly in?uenced by vehicle space.Consequently,much attention is payed to the effective drag coef?cient and expected to further improve the accuracy of the traf?c force model a curved road tunnel in this study.

2.2.Three-dimensional model

https://www.wendangku.net/doc/3f109345.html,erning equations

The computational ?uid dynamic software FLUENT is adopted to simulate the unsteady incompressible ?ow ?eld induced by vehicles in this study.A dynamic mesh method and the standard k–e turbulent model are employed as well (Launder and Spalding,1974).

The governing equations solved in Fluent for the present problem can be written as:Continuity equation:

@u i

?0e4T

Momentum equation:

@q u i t@q u i u j j ?à@p i t@j l @u i j t@u

j i t

@àq u 0i u 0

e5T

k equation:

@k tu j @k j ?1q @

l tl t r k

@k j tl t q @u i j t@u j i

@u i

àe

e6T

e equation:

Fig.4.Air speed histories from 1D model.

Fig.5.Air speed histories from CFD:(a)the inlet and (b)the outlet.

Table 2

The air speed.

Vehicle speed (km/h)

406080Air speed from 1D model (m/s)

0.620.93 1.24Air speed on the section near inlet (m/s)0.630.93 1.23Air speed on the section near outlet (m/s)

0.75

1.12

1.47

Space Technology 41(2014)120–126

standard set of constants are adopted for the k–e equations,C l =0.09;C 1=1.44;C 2=1.92;r k =1.0;r e =1.3.u 0i u 0j are turbulent

stresses and are modelled as:q u 0i u 0j ?l t e@u i

@x j

t@u

j @x i Tà23q k d ij .Pressure–velocity coupling is taken care of by the PISO algo-rithm in this research as recommended for transient calculations (Fluent Inc.,2005).Moreover PISO algorithm is also considered to be a suitable method for the highly skewed meshes (Moukalled and Darwish,2000;Karthikeyan and Samuel,2008).Additionally,the second order,upwind discretization are used for convective

terms and a central difference scheme is used for diffusion terms.

2.2.2.Boundary conditions and simulation details

A numerical model of the tunnel has been developed to investi-gate the piston effect (Fig.2).Because the computational region and the time increase signi?cantly with the increase of the tunnel length and the number of vehicles.A model tunnel with 200

Fig.6.Air speed histories for two vehicles from 1D model:(a)1L;(b)2L;(c)5L and (d)10L.

Table 3

Air speed and effective piston effect coef?cient.Model

Vehicle space

Air speed (m/s)g

40(km/h)

60(km/h)80(km/h)40(km/h)60(km/h)80(km/h)1D

1L 1.158 1.737 2.3150.9210.9330.9422L 1.157 1.735 2.3120.9200.9320.9405L 1.153 1.730 2.3000.9170.9290.93610L 1.148 1.722 2.2950.9130.9250.9343D

1L 0.910 1.345 1.7550.7240.7230.7142L 1.011 1.473 1.9350.8040.7910.7875L 1.024 1.496 1.9770.8140.8040.80410L

1.060

1.549

2.022

0.843

0.832

0.822

length,together with two vehicles is modelled and the outside re-gion of tunnel depends on the vehicle space.Eleven times of the width of the outside region to the tunnel diameter is built to pre-vent the impact of the wall boundary condition.The cross-section of the tunnel is approximately68.55m2with a hydraulic diameter of D t=https://www.wendangku.net/doc/3f109345.html,rge size vehicles of10.668?2.205?3.010m are modelled in this study(Fig.3).

The boundary conditions are speci?ed as follows.The non-slip wall boundary condition is applied on the solid wall of the tunnel and the outside wall of the tunnel and a value of8mm of wall roughness is applied on the tunnel wall.The surfaces of vehicles adopt the slip boundary condition where vehicle speed is imposed. At the entrance and exit,the pressure inlet and pressure outlet conditions are speci?ed respectively(Fig.2).A standard wall function approach is used for regions closed to the walls and the ?rst mesh point is located within the logarithmic region of the boundary layer.

Regular mesh is employed in this model.The size of0.4m is adopted longitudinally in the curved tunnel and1.5m is for the outside region.In the region of the lane of vehicles moving,mesh is re?ned considering the complicated?ow around the vehicle, and a typical value of0.25m on the cross-section is?xed as recommended in the previous study(Wang et al.,2011).Total cells are dependent on the vehicle space and the maximum number cell is approximate820,000.

An unsteady solution is implemented to trace the evolution of the air speed in the tunnel.The1st Order Implicit formulation is used so that no stability criterion is needed in determining the time step.However,a computational time step is still adjusted to avoid the presence of negative volume for the upgrade of dynamic meshes,resulting in a typical time step of0.002s.The maximum simulation time reaches up to30s.Typically the number of itera-tions per time step is about25with the convergence criterion set to10à3.A similar model has been carried out for a single vehicle moving in a straight tunnel in a previous study and an accepted re-sult was concluded(Wang et al.,2011).Accordingly,the numerical method and turbulent model described above is considered to be appropriate for this study.

2.3.Simulation cases

The simulation cases are listed in Table1,where L is the length of the vehicle and10.668m was used here.The average air speed is measured near inlet and outlet of the tunnel as shown in Fig.2

. Fig.7.Air speed histories for two vehicles from CFD:(a)1L;(b)2L;(c)5L and(d)10L.

3.Results and discussion

https://www.wendangku.net/doc/3f109345.html,parison of air?ow induced by a vehicle

Initially,the air?ow induced by a single vehicle is simulated with both the 1D model and CFD under the same condition in the curved tunnel.The result of the air speed from the 1D model is subsequently compared to the CFD result.

Fig.4shows the air speed histories at various vehicle speeds in the curved tunnel from the 1D model.The effective drag coef?cient of vehicle is equal to 1.16for a single large size vehicle in the sim-ulation.A linear increase in air speed can be seen for various vehi-cle speeds and the maximal acceleration at 80km/h.Although the duration is the shortest,the air speed induced is the highest at 80km/h followed by 60km/h and 40km/h in the tunnel.

Fig.5shows the air speed histories on the sections near inlet and outlet of the tunnel from CFD.The air speed is found to show different performances on the two sections.The air speed near out-let keeps rising before the vehicle arrival,whereas the air speed near inlet decreases gradually after the leaving of the vehicle.When the vehicle moving through the measured section,the un-steady variation of air speed like a saw is observed.The increase of air speed is also observed with the increase of vehicle speed.The air speed in the tunnel at the moment of vehicle moving out of the tunnel is taken as the piston effect in order to understand its contribution to the ventilation.Table 2shows the value of air speed from the two models.It can be seen that the air speed could arrive to more than 1.2m/s when a vehicle moving through the curved tunnel at 80km/h,and more than 0.6m/s at 40km/h.The air speed from 1D model is shown a good agreement with that near inlet,but markedly lower than that near outlet from CFD.It is likely to be a result of the in?uence of vehicle wake on the air?ow near outlet.The results of air speed from 1D model and on the section near in-let from CFD are subsequently adopted to analyse effects of vehicle space on the ventilation.

3.2.Effects of vehicle space

Fig.6shows the air speed histories by two vehicles at various spaces from 1D model.The effective drag coef?cient of vehicles is 1.16as well.Three linear increasing segments of air speed are observed in Fig.6.The acceleration of air speed by two vehicles in the tunnel is greater than that by a vehicle.The duration of two vehicles being in the tunnel decreases with the increase of vehicle space.Special attention is payed to the value of air speed by vehicles with different spaces.The air speed is observed to

Fig.8.Velocity contours.

effective drag coef?cients.Vehicle space

The effective drag coef?cient c dj 40(km/h)

60(km/h)80(km/h)1L 0.880.870.852L 1.00.960.955L 1.010.980.9710L

1.06

1.03

1.0

Fig.9.The effective drag coef?cient variations.

greater in a shorter vehicle space at the same vehicle speed,as shown in Table3which is different from CFD results.

Careful examination to the1D model is therefore carried out. The traf?c force is mainly dependent on the number of vehicles and vehicle speed although the slight difference in air speed.The duration of two vehicles simultaneously in the tunnel increases with the decrease of vehicle space.Accordingly,the contribution of traf?c force to the air speed gets enhanced at a shorter vehicle space.Contrarily,the friction and the resistance increase with the increase of the total duration in a longer vehicle space.Whereas the effect of vehicle space on the piston effect is absent in this 1D model.Consequently,the longer of the vehicle space,the lower is the air speed.

Subsequently,CFD is carried out and expected to improve our understanding of vehicle space and its effect on the piston effect as shown in Fig.7.It can be seen that the increase of vehicle speed would improve the piston effect signi?cantly and the air speed climbs up quickly when vehicle moving out of the tunnel as also observed in Fig.5.As the vehicle space decreases and vehicle speed increases,the duration among two vehicles through this measured section reduces correspondingly.The vehicle downstream conse-quently merges into the weak of the vehicle upstream too fast and the air speed measured is shown to be unsteady and oscillat-ing.The piston effect induced by two vehicle with various vehicle space and speed can also be found in Table3.

Table3shows the air speed and the effective piston effect.The effects of vehicle space and speed is expressed by the effective pis-ton effect coef?cient which is normalized by the air speed induced by a single vehicle from CFD results as follows.

g?v n

N v1e8T

where v n is the air speed induced by vehicles,v1is the air speed in-duced by a single vehicle in the tunnel.

The effective piston effect coef?cient from1D model is observed to improve with the increase of vehicle speed and the decrease of vehicle space.The absence of the effect of vehicle space in1D mod-el is considered to be responsible for this unreasonable results. Whereas the variation of air speed from CFD gives us an intelligible result.When two vehicles with10L space move through the curved tunnel at80km/h,the air speed is increased to more than2m/s.As the vehicle speed is reduced,the air speed drops down signi?cantly but the effective piston effect coef?cient rises up.With the increase of vehicle space,both the air speed and the effective piston effect coef?cient are found to grow up.The effective piston effect coef?-cient rises up rapidly at very short vehicle spaces and gradually at long vehicle spaces.The effect of vehicle space is consequently get-ting weakened with the increase of vehicle space.The velocity con-tours in Fig.8can further explain that the vehicle downstream drops into the high-speed wake in a short vehicle space,accord-ingly makes an increase in the loss of air?ow.Both of the air speed and the effective piston effect coef?cient from CFD are lower than those from1D model prominently.The effective piston effect coef-?cient is found among0.7to0.85in this study from CFD results.

3.3.The effective drag coef?cient

This section aims to improve the accuracy of the effective drag coef?cient of vehicles in1D model.The effective drag coef?cient is derived from Eq.(2)based on the air speed from CFD.The improved effective drag coef?cients are shown in Table4and in Fig.9.

It can be seen that the effective drag coef?cient increases signif-icantly with the increase of vehicle space,especially in a shorter vehicle space.Whereas this coef?cient decreases slightly with the growth of vehicle speed.All of these effective drag coef?cients are lower than1.16for a single vehicle in the curved tunnel.When the vehicle space rises up to more than10L space,the effective drag coef?cient would approach to that of a single vehicle.On the other hand,there will be a sharp decline in the effective drag coef?cient and the traf?c force for traf?c jam and shorter vehicle spaces in the curved tunnel.

4.Conclusions

A numerical simulation with1D model and CFD has been car-ried out to investigate the effects of vehicle space on the ventila-tion and the air speed from CFD has been employed to improve the accuracy of the traf?c force in1D model.The results show that the air speed in the curved tunnel is1.23m/s at vehicle speed of 80km/h and0.63m/s at40km/h for a single vehicle in the curved tunnel.The air speed from1D model shows a good agreement with that on the section near inlet from CFD for a single vehicle.When two vehicles moving through the tunnel,the air speed rises up signi?cantly.The air speed is also found to grow up with the in-crease of the vehicle speed for two vehicles in the curved tunnel. The effective piston effect coef?cient is observed to improve with the increase of vehicle speed and the decrease of vehicle space for1D model,and the opposite for CFD results.The absence of the effect of vehicle space in1D model is considered to be respon-sible for this unreasonable results.The results from CFD exhibit intelligible variations.CFD results are subsequently used to improve the effective drag coef?cient in traf?c force model.The effective drag coef?cient is found to increase signi?cantly with the increase of vehicle space and slightly increase as vehicles slow down.These effective drag coef?cients are lower than that for a single vehicle in the curved tunnel.Consequently these?ndings are expected to further improve the accuracy of the traf?c force in the1D model in the curved tunnel ventilation.

Acknowledgements

The authors gratefully acknowledge that the work reported in this paper was sponsored by the Natural Science Foundation of China through Grant Nos.10925211and51108287.

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