An improved correlation for pressure drop in a tunnel under traffic jam using CFD

J. Wind Eng. Ind. Aerodyn. 143 (2015) 34–41

Contents lists available at ScienceDirect

Journal of Wind Engineeringand Industrial Aerodynamics

http://d0167-61

n CorrE-m

journal homepage: www.elsevier.com/locate/jweia

An improved correlation for pressure drop in a tunnel undertraffic jam using CFD

Esmaeel Eftekharian a, Omid Abouali a,n, Goodarz Ahmadi b

a School of Mechanical Engineering, Shiraz University, Mollasadra Street, Shiraz, Iranb Aeronautical & Mechanical Engineering Department, Clarkson University, Potsdam, NY, USA

a r t i c l e i n f o

Article history:Received 4 June 2014Received in revised form9 December 2014Accepted 20 April 2015Available online 28 May 2015

Keywords:CFDTraffic jamTunnelOne directionalPressure drop

x.doi.org/10.1016/j.jweia.2015.04.01305/& 2015 Elsevier Ltd. All rights reserved.

esponding author. Tel.: þ98 711 613 3034; faxail address: [email protected] (O. Abouali)

a b s t r a c t

Undoubtedly, an accurate estimation of pressure drop due to vehicles can contribute to correctly pre-dicting the number of jet fans which ultimately leads to choosing the optimum ventilation system in atunnel. The main objective of the present study is to improve the 1D (one-dimensional) model, whichcurrently is unable to consider the effects of combination of cars in traffic jam on the total drag force. TheCFD technique has been applied to model several tunnels in different lengths under severe traffic jamconditions; this way, the difference between pressure drop predicted by CFD simulation and 1D modelcan be investigated. The CFD simulation results were used to develop a new correlation for pressure dropdue to cars inside the tunnel as a function of tunnel average air velocity and tunnel length. Additionally,the differences between the pressure drop due to the cars predicted by the CFD and the 1D model fordifferent traffic conditions were investigated. It was shown that the existing 1D model underestimates oroverestimates the pressure drop depending on the traffic condition and the drag-area value used inanalysis. Finally, 1D model is modified by a simple equation for the pressure drop in a tunnel in congestedtraffic conditions using an equivalent friction factor resembling the stopped vehicles.

& 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Providing a safe breathing air in tunnels is one of the mostimportant issues in the design and operation of tunnels in urbanenvironment. In this regard, providing a correct estimation of dragforce related to the presence of vehicles inside the tunnel is ofcrucial importance. This information is important for prediction ofthe number of the ventilation jet fans required for a tunnel undertraffic jam. Jang and Chen (2002) have proposed an approachbased on the optimization techniques in order to determine thedrag coefficient of vehicles under transient condition in a roadtunnel. It was shown experimentally that the vehicle spacingaffects the drag coefficient of vehicles. That is the presence of avehicle in the upstream of another car affects the drag coefficientof both vehicles. It was also concluded that the combined dragcoefficient of a number of isolated vehicles can be lower than thatof combination of vehicles (Watkins and Vino, 2008). Drag coef-ficient of a single moving vehicle in a tunnel evaluated from theCFD simulation is in good agreement with that obtained from 1Dmodel. The drag result for two moving vehicles, however, is totallydifferent. It was shown that an increase in vehicle space or a

: þ98 711 628 7508..

decrease in vehicle velocity leads to an increase in drag coefficient(Wang et al., 2014). In curved tunnels, it was found that as theradius of curvature of the tunnel reduces, the drag coefficient of amoving vehicle as well as the traffic force induced in the tunnelrises (Wang et al., 2011).

Investigation of the airflow field as well as pollutant dispersioninside the tunnel under traffic jam condition is another issueattracting attention (Bari and Naser, 2005,, 2010). Bari and Naser(2010) investigated dispersion of CO, CO2 and O2 inside a tunnelwith a burning vehicle when the cars under traffic jam are emit-ting pollutants and the jet fans are running. They showed thatafter about 8 min, the level of pollution exceeds the permissiblelevel. They also analyzed the effectiveness of jet fan performancefor removing the pollution emitted by the vehicles under thesevere traffic jam condition, and also showed that the absence ofjet fans will pose a threat to the health of passengers and drivers.In the same vein, Eftekharian et al. (2014) investigated the per-formance of banana and traditional jet fans in traffic jam in anurban tunnel and they demonstrated that in traffic congestion,both types of jet fans almost induce an identical volume flow rateinto the tunnel; additionally, they carried out the impacts ofadverse wind on the tunnel volume flow rate and it was shownthat in this regard, the results predicted by CFD simulation have aremarkable difference with those of engineering design.

E. Eftekharian et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 34–41 35

Costantino et al. (2013) used Froude method to model reduced-scale road tunnel; modeling both actual and reduced-scale tunnelequipped with jet fans, they investigated the impacts of ceiling andfloor roughness height on the velocity field inside the tunnel whichcan be useful for the future experimental apparatus. Severalresearches have been done indicating a comparison between bananaand traditional jet fans; compared to the latter, the former hasseveral advantages: they need a lower thrust in the fire scenario andthey can provide a lower temperature near ceiling in a tunnel (Bettaet al., 2010; Musto and Rotondo, 2014). CFD simulations have shownthat the optimal pitch angle in order to reduce pressure loss in atunnel depends on the operating condition (existence or non-existence of traffic) (Betta et al., 2009). The aerodynamic behaviorand optimal deflect angle of jet fans for curved tunnels were alsoinvestigated (Wang et al., 2012,, 2010). Apart from numericalinvestigation of jet fans, there are some experimental studies con-cerning evaluating the performance of jet fans in wind tunnels.Identifying the optimum pitch angle of a jet fan in a wind tunnel inorder to minimize the pressure loss has been experimentallydetermined (Jacques and Wauters, 1999). In this regard, experi-mental results demonstrate that although moving jet fans towardthe ceiling increases the pressure drop in a significant length of thetunnel, it induces a higher volume flow rate because once a jet fan istraversed toward the wind tunnel centerline, the fluctuations andflow instability close to the tunnel walls start to emerge (Mutamaand Hall, 1996). Furthermore, Angelies et al. (1996) both experi-mentally and numerically investigated air flow pattern around atwo-dimensional car in order to compare velocity and pressuremeasurements with numerical simulation.

The presented literature survey shows the lack of informationconcerning the accurate estimation of pressure drop due to thecars under traffic congestions, which in turn is of importance forpredicting the number of jet fans required to provide a safe ven-tilation condition inside a tunnel. In the view of the fact that notevery design engineer has the capability of CFD simulation andeven if they have, it involves high computational cost and a greatdeal of time to prepare the model; in the present study a corre-lation is to be presented to rectify the 1D model (engineeringdesign formula) considering the impacts of combination of cars onthe tunnel pressure drop. Moreover, in this study it is tried toconsider aerodynamic details of the cars instead of modeling themas blocks, previously used to model cars by other researchers.

Fig. 1. A schematic view of the cars modeled: (a) the real car and (b) the carmodeled. The dimensions are in millimeter.

Fig. 2. The arrangement of cars in traffic jam in (a) top view and (b) isometric view.

2. Model description

A tunnel, 890 m long, in different traffic conditions as well asfive tunnels which are 200, 400, 600, 890 and 1200 m long intraffic jam condition was investigated in order to present a com-parison between the results of 1D model and those of CFD simu-lation. All tunnels modeled in this study are straight, three-laneand one-directional which have cross-section area of 94 m2. Alsothe maximum tunnel height and width are 8.1 m and 14.3 m,respectively. The cars in the tunnel were modeled in a way that thedistance between two consecutive cars becomes 1.13 m in thesevere traffic jam followed by 8.248 m, 20.97 m and 45.6 m inlighter traffic conditions, respectively. Cars are assumed to be thesame in shape and they are modeled as a typical personal car usedin Iran. Figs. 1 and 2 show a schematic view of the cars andarrangement of cars, respectively. To consider the effects of othermarginal obstacles like possible small traffic signs in the tunneland the lightening system as well as the roughness related to thetunnel walls, an equivalent roughness of 1 cm was considered forthe tunnel wall.

Also, a wind tunnel with the rectangular cross section area of600 m2 and 100 m long containing a car at 49.73 m distance from

the inlet was designed in order to numerically compute the dragarea, CdA, of the car.

In order to show that the drag area of cars, when the flowdirection is from back to front of them, is almost independent ofthe type of car, a car was modeled as blocks in the wind tunnel.Fig. 3 shows a schematic view of the block car dimensionallychosen based on the aerodynamic car used in this study.

3. Numerical approach

3.1. Governing equation

Fluent software 6.3.26 was used to solve the equations gov-erning the airflow, namely, continuity, balance of momentum,turbulence kinetic energy, and turbulence energy dissipation rateunder steady condition. The flow is assumed to be incompressibleand the standard k–ε turbulence model was used in the analysis.The governing equations are:

Continuity:

u 0 1∇⋅ = ( )

Balance of momentum:

p gu u u 2T2ρ μ μ ρ⋅∇ = − ∇ + ( + )∇ + ( )

Fig. 3. A schematic view of the block car modeled based on the aerodynamic car. The dimensions are in millimeter. The blue lines are representative of the car modeled asblocks. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

E. Eftekharian et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 34–4136

Turbulence kinetic energy:

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥k k pu

3

T

kkρ μ

μσ

ρε⋅∇ = ∇⋅ + ∇ + −( )

Turbulence energy dissipation rate:

⎡⎣⎢

⎛⎝⎜

⎞⎠⎟

⎤⎦⎥ C p k C ku / /

4

Tk1 2

2ρ ε μμσ

ε ε ρε⋅∇ = ∇⋅ + ∇ + −( )ε

C k / 5T2μ ρ ε= ( )μ

Here ρ and p are respectively the fluid density and pressure, u isthe Reynolds averaged velocity vector, g is the gravity acceleration,k is the turbulence kinetic energy, Tμ is the eddy viscosity,C C C, , , , k1 2 σ σμ ε , respectively, are 1.44, 1.92, 0.09, 1.30 and 1.00. pkand ε are, respectively, the turbulence energy production anddissipation rate. It should be noted that RANS modeling used forturbulence modeling in this study has its own shortcoming anduncertainties both in discretization and turbulence modelingaspects. Hence, any results presented in this study entail theuncertainties of RANS modeling. Recently, improvement in CFDhigh resolution methods and Large Eddy Simulation haveaddressed and resolved such uncertainties (Drikakis et al., 2009). Itis generally accepted that compared to RANS modeling, LES enjoysa higher level of precision; however, the computational costshould be taken into consideration as well and that for suchindustrial applications and CFD projects in relatively high Rey-nolds Numbers, requiring a high number of grids, if not impos-sible, it would be so time consuming and difficult to apply LESmodeling.

3.2. 1D model

Considering 1D model, the total pressure drop due to thetunnel and vehicles was computed using the following model:

p p p 6total tunnel vehiclesΔ = Δ + Δ ( )

p p p p 7tunnel friction entrance exitΔ = Δ + Δ + Δ ( )

p nC A

AU U U U

12 8vehicles

d Veh

TT Veh T VehρΔ =

( )( − ) −

( )

p fL

DU2 9friction

H

T2ρ

Δ =( )

p KU2 10entrance ent

T2ρ

Δ = ( )

p KU2 11exit exit

T2ρ

Δ = ( )

where pfrictionΔ is pressure drop due to interaction between theairflow and the tunnel walls, pentranceΔ and pexitΔ are, respectively,the pressure drop of the inlet and outlet portals, f is the frictionfactor, L is the tunnel length, DH is the hydraulic diameter, n is thenumber of vehicles, Cd and A are, respectively, the vehicle dragcoefficient and the vehicle cross section area, ρ is air density, andUT and UVeh are, respectively, the tunnel average air and vehiclevelocities. Moreover, when an adverse wind blows into the tunneloutlet portal, a pressure drop due to the adverse wind should beadded to the right-hand side of Eq. (7). This pressure drop is givenas

p V12 12wind wind wind

2ξ ρ= ( )

In which windξ is a coefficient that its value depends on the shapeand dimension of the tunnel outlet portal. ρ and Vwind are airdensity and wind velocity, respectively.

Additionally, the drag area for an isolated car in a wind tunnelis computed as

C AF

U12 13

dd

2ρ=

( )∞

where Cd is drag coefficient, A is the car cross section area, Fd isdrag force, ρ is air density and U∞ is air velocity at the carupstream.

3.3. Boundary conditions

The no slip stationary wall boundary condition was used for thetunnel walls and car body. A uniform velocity profile, ranging from1 to 7, was prescribed for tunnel inlet in each case. As for the windtunnel inlet boundary, a uniform velocity distribution of 4.4 m/swas prescribed at the inlet portal, while the pressure outletboundary condition with pgauge,outlet¼0 was used for tunnel outletin all cases simulated.

3.4. Validation

The experimental wind tunnel data of Angelis et al. (1996) havebeen used in order to validate the present study; they experimen-tally investigated the flow field in a wind tunnel whose length,height and width are 2.8, 1.4 and 1.8 m, respectively. Modeling atwo-dimensional car (Fig. 4) by using CFD technique, they carriedout velocity and pressure distribution around it so as to comparewith experimental data. The car modeled is 0.295 m in length andthe maximum height of the car is around 0.08 m. A uniform velocityof 15 m/s was prescribed as the velocity inlet boundary condition at

Fig. 6. Comparison between the present numerical simulation results andexperimental and numerical data of Angelis et al. (1996) for the pressure coefficientdistribution on the upper surface of the car.

E. Eftekharian et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 34–41 37

0.295 m of car upstream and that outflow boundary condition wasused for the outlet boundary located in 1.3774 m car downstream.The distance between car body and the ground is also 0.0295 m. Inaddition, k–ϵ standard was selected as the turbulence model, thesame model used by Angelis et al. (1996) for numerical simulation.The simulation condition in the present study is the same as thatnumerically and experimentally investigated by Angelis et al.(1996). Fig. 5 compares u-velocity profile where x/L is 0.26 (L is thecar length which is 0.295 m). Moreover, Fig. 6 shows a comparisonbetween the present numerical simulation results and experimentaland numerical data of Angelis et al. (1996) for the pressure coeffi-cient distribution on the upper surface of the car. These figuresshow a general agreement between the results of the present workand those of Angelis et al. (1996).

3.5. Grid sensitivity

Multi-zone grid method was used for the grid generation.Unstructured mesh was applied to the car zone, a rectangular zonewith a height of 2.25 m above the tunnel floor containing cars(Fig. 7). For the other computational regions, structured mesh wasused. In order to show that the solution is independent of thenumber of grids, three different mesh sizes listed in Table 1 were

Fig. 4. A view of two dimensional car modeled by Angelis et al. (1996).

Fig. 5. Comparison between numerical simulation results and experimental data ofAngelis et al. (1996) for normalized velocity at x/L¼0.26 (L is the car length which is0.295 m).

examined for a 200 m tunnel under traffic jam conditions, with thetunnel average air velocity of 6 m/s. Table 1 shows that mesh (B) hasa marginal difference (around 0.7%) with the finest mesh (C), whilethe course mesh (A) shows relatively large deviations of about 7%with the other two fine meshes. For computational economy,therefore, mesh (B) was used in all subsequent simulations.

4. Results and discussions

4.1. Computational wind tunnel results

A computational model for simulating the airflow in a windtunnel was developed and used to predict the drag-area of anisolated car. The average airflow velocity of the tunnel in thesesimulations is 4.2 m/s, which is a typical velocity prescribed fortunnel inlet. Using Eq. (13), the drag-area for these simulations is1.341 m2, while the drag-area reported by PIARC2012 (World RoadAssociation, 2012) standard is 0.9 m2. It should be emphasized thatthe PIARC standard reported the drag-area value for the conditionthat the air flow is directed to the front section of the cars towardtheir back. However, considering the flow direction produced byjet fans during the traffic jam condition, the air is moving fromback to front of the cars in one-way tunnels.

Fig. 8 shows the computed static pressure and velocity mag-nitude contours around an isolated car in the wind tunnel. It isseen that there is a low pressure region in front of the vehicle(when the air direction is from back to front); thus, in tunnelswhere there are many cars, a car may be in the low pressure regiongenerated by the car in upstream. As a result, the value of 1.341 m2

for drag area of an isolated car may not be appropriate for com-bination of cars.

4.2. Comparison of CFD simulation and the 1D correlation for pres-sure drop in traffic jam

To compute the pressure drop due to vehicles inside the tunnel,1D idealized model proposes Eq. (8) which does not consider theeffects of interactions of the flow around the cars. That is, in the 1Didealized model, the pressure drop due to an isolated car is multi-plied by the number of cars for estimating the total pressure drop.

Fig. 7. Different views of mesh (B). (a) The grid at the tunnel cross section. (b) Top view at a horizontal section at the vehicle level. (c) The center plane side view.

Table 1Comparison of pressure drop for a 200 m tunnel with average air velocity of 6 m/sfor different computational meshes.

Mesh type Number of cells (million) Tunnel pressure drop

A 1.1 39.17B 4.4 42.46C 12.2 42.75

E. Eftekharian et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 34–4138

In the CFD simulations, a constant inlet velocity was imposedas the inlet boundary condition of the tunnel when there is onecar, several cars, or no car in the tunnel. The differences betweenthe cases with cars and with no cars correspond to the pressuredrop due to the presence of vehicles. These simulations wereperformed for five tunnels with different lengths and the samecross section area in severe traffic jam conditions. As noted before,for each case, 7 different mean velocities ranging from 1 to 7 m/swere applied as the boundary condition to the tunnel inlet. Theresults obtained from the CFD simulation were fit to a correlationfor the pressure drop given as

P a b L U L 200,

for severely congested traffic conditions 14

vehicle Tc

Td

T( ) ( )Δ = + ≥

( )

where the constant values of a, b, c, d are 0.22, 0.005, 0.96 and2.0 respectively. LT is tunnel length and UT is tunnel average airvelocity. This formula is proposed for tunnels under severelycongested traffic conditions with the air velocity ranging from 1 to7 m/s; the average of errors for this equation is 2.81 percent. The

non-dimensional pressure drop due to vehicles ⎜ ⎟⎛⎝

⎞⎠

P

U1 / 2

vehicle2ρ

Δ

( ) ∞can also

be represented generally as a function of and ReLD

T

H( ) (DH is tunnel

hydraulic diameter and Re is Reynolds Number); however, it canbe shown that the results are in the range of Reynolds Numberindependency. Yet, looking at constant values of c and d in Eq. (14),one can perceive that the pressure drop due to the vehicles

Pvehicles( )Δ in Eq. (14) has a close resemblance to that represented

for a fully developed flow in a duct⎛⎝⎜

⎞⎠⎟P f L

D

U

2H

T2

Δ =ρ

; thus it seems

that an equivalent friction factor fequivalent( ), to be used in Moody

diagram, can be derived representing the effects of vehicles as a

roughness in the tunnel. In other words, the pressure drop due tovehicles in a tunnel can be indicated as an equivalent pressuredrop in a tunnel devoid of vehicles with a specific friction factorindicative of the effects of vehicles. Thereby, with a little bit morebut reasonable approximation (with the average of errors equal to3.33 percent), the pressure drop due to the vehicles can berestated as

P fL

DU

f2

, 0.06315

vehicles vehiclesH

Tvehicles

2ρΔ = =

( )

where L is the tunnel length, DH is tunnel hydraulic diameter, ρ isair density and UT is tunnel average air velocity. This friction factorcorresponds to the relative roughness of 0.038 in Moody chart.This means that the effect of stopped cars, when the air flowdirection is from back to front of them, can be considered as aroughness to the tunnel walls. Using Eq. (15), design engineers areable to simply and accurately calculate the pressure drop in atunnel in a congested traffic condition and that Eq. (8) ofengineering design approach can be substituted with Eq. (15).This means that it is enough to add fvehicles to the Darcy’s frictionfactor of the empty tunnel to include the effects of the pressuredrop due to stopped vehicles. It is worth mentioning that althoughthe presented correlation is based on only one type of car modeledin this study, it is conjectured that this empirical equation may beapplicable to other kinds of personal cars. This is because the drag-area of most of these cars is close to each other when the air flowdirection is from the back to front of the cars. To support thisclaim, the drag area for the cars modeled as blocks, whosedimensions were shown in Fig. 3, in the wind tunnel was alsoinvestigated. The drag-area value for the block car is found to be1.41 m2 which is roughly 5% higher than the aerodynamic car.

It should be noted that the tunnel length LT( ) in Eq. (14) isrepresentative of the number of cars; Eq. (16) represents relationbetween the number of cars in each lane of the tunnel and thetunnel length. Here LT is the tunnel length, N is the number of cars,LS is distance between two consecutive cars, LC is a car length andC is the summation of the distance between the nearest car to thetunnel inlet and tunnel outlet portal.

L N L NL C1 16T S C= ( − ) + + ( )

Based on PIARC standard, in severe traffic condition, there are165 cars per kilometer in each lane; consequently, the distancebetween two consecutive cars based on the cars modeled in this

Fig. 8. Contours of pressure and velocity magnitude around an aerodynamic car in the tunnel. (a) Pressure and (b) velocity. Flow direction is from the back to front of the car.

E. Eftekharian et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 34–41 39

study would be 1.67 m. Since the car length differs depending ontheir types, a value of 1.13 m for the distance between two con-secutive cars is assumed in this study. Similarly, Bari and Naser(2005) used 1 m distance between every two consecutive vehiclesin their model.

Fig. 9 compares the pressure drop computed based on CFDsimulation and that predicted by the proposed correlation in termsof tunnel length and its average air velocity. This figure showsalmost a linear change in pressure drop in the tunnel with varia-tion in tunnel length when it is in traffic jam condition.

Table 2 compares the results evaluated from 1D model, CFDsimulation and those of correlation for different tunnel lengths. Itshould be mentioned that the results related to 1D model arecomputed for both cases where CdA¼1.341 m2 and CdA¼0.9 m2.The drag area of 0.9 m2 is suggested by PIARC and it is commonlyused by engineers even for cars in traffic jam condition. But asnoted before, this value corresponds to the flow from front to theback of the car. The drag area of 1.341 m2 is computed from the

present simulation of the wind tunnel for flow from the back tofront, which is the real condition for the traffic jam situation inone-way tunnels.

Table 2 shows that 1D model based on the actual drag area(CdA¼1.341 m2) overestimates the pressure drop for all tunnellengths. This is because when the tunnel is under full traffic jamconditions, due to the recirculation zones produced in proximity ofthe cars, the airflow velocity around a car is lower than thataround an isolated car where the effects of other cars are notpresent. Table 2 also shows that the 1D model based on PIARCstandard (CdA¼0.9 m2) underestimates the pressure drop. More-over, Table 2 indicates that the longer the tunnel is, the more errorin 1D model appears. The underestimation of the pressure droppredicted by the 1D model leads to the reduction in the number ofjet fans predicted, which in turn will deteriorate the tunnel ven-tilation. For instance, for a 890 m long tunnel needing velocity of6 m/s to remove the pollutants, based on Table 2, one-dimensionalmodel predicts a pressure drop of around 101 Pa, while the

E. Eftekharian et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 34–4140

presented correlation represents approximately 125 Pa; if thedifference between the two estimates is multiplied by the tunnelcross section area, it implies that the 1D model underestimatesabout 2350 N in the thrust required to be provided by jet fans(which is the thrust of at least two ordinary jet fans).

0

50

100

150

200

250

0 200 400 600 800 1000 1200 1400

Pres

sure

dro

p

Tunnel Length

CFD(v=1)CFD(v=2)CFD(v=3)CFD(v=4)CFD(v=5)CFD(v=6)CFD(v=7)Correlation(v=1)Correlation(v=2)Correlation(v=3)Correlation(v=4)Correlation(v=5)Correlation(v=6)Correlation(v=7)

Fig. 9. Comparison of the pressure drop in a tunnel with congested traffic jampredicted by the CFD simulations with the proposed correlation given by Eq. (14)versus tunnel length for different velocities.

Table 2A comparison between the results achieved from engineering design, CFD simulation an

Tunnellength(m)

Tunnelaverage airvelocity

ΔpCFD ΔP correlation

(15)Correlation(15) error (%)

ΔP Correlation

(16)Co(16

200 1 0.90 1.03 14.59 0.78 12200 2 3.47 3.45 0.43 3.14 9200 3 7.96 7.50 5.71 7.08 11200 4 13.81 13.16 4.66 12.58 8200 5 21.57 20.44 5.19 19.66 8200 6 31.05 29.34 5.48 28.31 8200 7 42.30 39.86 5.77 38.54 8400 1 1.61 1.79 11.10 1.57 2400 2 6.42 6.51 1.56 6.29 1400 3 14.39 14.38 0.032 14.15 1400 4 25.68 25.40 1.10 25.17 2400 5 39.98 39.56 1.03 39.33 1400 6 57.58 56.87 1.22 56.63 1400 7 78.48 77.33 1.45 77.08 1600 1 2.35 2.54 8.43 2.36 0600 2 9.39 9.51 1.32 9.44 0600 3 21.04 21.12 0.40 21.24 0600 4 37.39 37.38 0.03 37.76 0600 5 58.57 58.28 0.48 59.00 0600 6 84.16 83.83 0.38 84.95 0600 7 114.61 114.03 0.50 115.63 0890 1 3.42 3.62 5.83 3.50 2890 2 13.73 13.73 0.51 14.02 2890 3 30.93 30.77 0.50 31.54 1890 4 55.00 54.54 0.84 56.07 1890 5 85.50 85.10 0.47 87.61 2890 6 127.04 124.44 3.61 126.15 0890 7 176.93 166.58 5.85 171.71 2

1200 1 4.61 4.74 2.90 4.72 21200 2 18.40 18.29 0.57 18.88 21200 3 41.35 40.88 1.12 42.48 21200 4 73.47 72.51 1.30 75.51 21200 5 114.80 113.17 1.40 117.99 21200 6 165.34 162.88 1.48 169.91 21200 7 225.20 221.62 1.58 231.26 2

4.3. Comparison between CFD simulation and 1D model for pre-dicting pressure drop in different traffic conditions

Table 3 shows the differences between pressure drops computedfrom the 1D model and those obtained from the CFD simulations ina tunnel 890 m in length under different traffic conditions at tunnelairflow velocity of 6 m/s. It is seen that the 1D model resultscomputed based on CdA¼1.341 m2, in lighter traffic conditions,underestimate the CFD simulation results; however, the trend isreversed under heavy traffic condition. When the drag area of0.9 m2 is assumed, at a time when distance between two con-secutive cars increases, (when the number of cars is 54 and 105) thepressure drop predicted by the 1D model is lower than that com-puted by CFD simulation. For somewhat heavier traffic condition,where the number of cars is 210, the 1D model leads to resultscomparable with the CFD results. But that is coincidental as the

d those of correlation (Eqs. 14 and 15) for different lengths and air flow velocities.

rrelation) error (%)

Δp1DCdA¼1.341 m2

Δp1DCdA¼0.9 m2

1D errorCdA¼1.341 m2

1D errorCdA¼0.9 m2

.41 0.90 0.61 0.0 32.22

.35 3.59 2.45 3.32 29.30

.01 8.07 5.52 1.43 30.59

.85 14.35 9.82 3.89 28.91

.81 22.41 15.34 3.94 28.87

.78 32.28 22.09 3.96 28.85

.88 43.93 30.06 3.85 28.93

.56 1.82 1.24 12.65 22.91

.90 7.27 4.98 13.41 22.39

.60 16.37 11.20 13.76 22.15

.00 29.10 19.91 13.30 22.47

.63 45.47 31.12 13.73 22.17

.64 65.47 44.81 13.71 22.19

.78 89.12 60.99 13.56 22.29

.37 2.74 1.88 16.58 20.22

.56 10.96 7.50 16.80 20.07

.94 24.67 16.88 17.25 19.77

.97 43.85 30.01 17.28 19.75

.73 68.52 46.89 16.99 19.94

.94 98.67 67.52 17.24 19.77

.89 134.31 91.91 17.18 19.81

.59 4.10 2.80 19.98 17.89

.09 16.39 11.22 19.41 18.29

.96 36.89 25.24 19.25 18.39

.94 65.58 44.88 19.22 18.41

.46 102.46 70.12 19.84 17.99

.70 147.55 100.97 16.14 20.52

.95 200.83 137.43 7.30 26.57

.38 5.53 3.79 20.02 17.87

.60 22.13 15.15 20.28 17.69

.72 49.80 34.08 20.43 17.59

.78 88.53 60.58 20.50 17.54

.78 138.33 94.66 20.50 17.54

.76 199.19 136.31 20.47 17.56

.69 271.12 185.53 20.39 17.61

Table 3Comparison of pressure drops computed from the 1D model with those of CFDsimulation for an 890 m long tunnel under different traffic conditions at tunnelaverage air velocity of 6 m/s.

Numberof cars

ΔpCFD Δp1DCdA¼1.341 m2

Δp1DCdA¼0.9 m2

1D error (%)CdA¼1.341 m2

1D error(%)CdA¼0.9 m2

54 25.43 16.59 11.35 34.72 55.33105 72.80 32.27 22.086 55.66 69.66210 41.56 64.55 44.17 55.32 6.28480 127.04 147.55 100.97 16.14 20.52

E. Eftekharian et al. / J. Wind Eng. Ind. Aerodyn. 143 (2015) 34–41 41

smaller drag area of 0.9 m2 tends to underestimate the pressuredrop, while the assumed velocity, which is the tunnel average airvelocity ( U∞ in Eq. (13)), is actually higher than the real situationtending to overestimate the pressure drop. As a result, the netestimate is reasonable. In full traffic jam condition, when thenumber of cars is 480, again the effects of underestimation in thedrag area outweigh the impacts of overestimation in the velocityprofile giving rise to a net underestimation of the pressure drop.

5. Conclusions

In this study a series of computer simulation for airflows andpressure drops in tunnels under traffic jam condition was per-formed. The simulations for the pressure drops were comparedwith the simplified 1D model. The simulations results were alsoused to develop a new correlation for pressure drop as a functionof tunnel average air velocity and tunnel length under traffic jamconditions. It was shown that the available 1D model fails toaccurately predict the pressure drop due to combination of cars, asit does not account for the effects of low pressure area generatedin downstream of cars. It was also shown that the amount of trafficand the drag-area value used affect the differences betweenpressure drop predicted by the 1D model and the CFD simulations.Finally, as a simple way for using in engineering design and 1Dmodel, an equivalent friction factor for the stopped vehicles intunnels is presented (f¼0.063) which can be added to the Darcy'sfriction factor of the tunnel devoid of cars.

References

Angelis, W., Drikakis, D., Durst, F., Khier, W., 1996. Numerical and experimentalstudy of the flow over a two-dimensional car model. J. Wind Eng. Ind. Aerodyn.62, 57–79.

Bari, S., Naser, J., 2005. Simulation of smoke from a burning vehicle and pollutionlevels caused by traffic jam in a road tunnel. Tunn. Undergr. Space Technol.20, 281–290.

Bari, S., Naser, J., 2010. Simulation of airflow and pollution levels caused by severetraffic jam in a road tunnel. Tunn. Undergr. Space Technol. 25, 70–77.

Betta, V., Cascetta, F., Musto, M., Rotondo, G., 2009. Numerical study of the opti-mization of the pitch angle of an alternative jet fan in a longitudinal tunnelventilation system. Tunn. Undergr. Space Technol. 24, 164–172.

Betta, V., Cascetta, F., Musto, M., Rotondo, G., 2010. Fluid dynamic performances oftraditional and alternative jet fans in tunnel longitudinal ventilation systems.Tunn. Undergr. Space Technol. 25, 415–422.

Costantino, A., Musto, M., Rotondo, G., Zullo, A., 2013. Performance evaluation ofalternative tunnel longitudinal ventilation systems using two inclined jets. In:Proceedings of the 68th Conference of the Italian Thermal Machines Engi-neering Association, ATI2013.

Drikakis, D., Hahn, M., Mosedale, A., Thornber, E., 2009. Large eddy simulationusing high resolution and high order methods. Philos. Trans. R. Soc. A – Math.Phys. Eng. Sci. 367, 2985–2997.

Eftekharian, E., Dastan, A., Abouali, O., Meigolinedjad, J., Ahmadi, G., 2014. Anumerical investigation into the performance of two types of jet fans in ven-tilation of an urban tunnel under traffic jam condition. Tunn. Undergr. SpaceTechnol. 44, 56–67.

Jacques, E., Wauters, P., 1999. Improving the ventilation efficiency of jet fans inlongitudinally ventilated rectangular ducts. In: Proceedings of the U.S MineVentilation Symposium, pp. 503–510.

Jang, H., Chen, F., 2002. On the determination of the aerodynamic coefficients ofhighway tunnels. J. Wind Eng. Ind. Aerodyn. 90, 869–896.

Musto, M., Rotondo, G., 2014. Numerical comparison of performance betweentraditional and alternative jet fans in tiled tunnel in emergency ventilation.Tunn. Undergr. Space Technol. 42, 52–58.

Mutama, K.R., Hall, A.E., 1996. The experimental investigation of jet fan aero-dynamics using wind tunnel modeling. J. Fluids Eng. 118, 322–328.

Wang, F., Wang, M., Wang, Q., 2012. Numerical study of effects of deflected anglesof jet fans on the normal ventilation in a curved tunnel. Tunn. Undergr. SpaceTechnol. 31, 80–85.

Wang, F., Wang, M., He, S., Deng, Y., 2011. Computational study of effects of trafficforce on the ventilation in highway curved tunnels. Tunn. Undergr. SpaceTechnol. 26, 481–489.

Wang, F., Wang, M., Wang, Q., Zhao, D., 2014. An improved model of traffic forcebased on CFD in a curved tunnel. Tunn. Undergr. Space Technol. 41, 120–126.

Wang, F., Wang, M., He, S., Zhang, J., Deng, Y., 2010. Computational study of effectsof jet fans on the ventilation of a highway curved tunnel. Tunn. Undergr. SpaceTechnol. 25, 382–390.

Watkins, S., Vino, G., 2008. The effect of vehicle spacing on the aerodynamics of arepresentative car shape. J. Wind Eng. Ind. Aerodyn. 96, 1232–1239.

World Road Association, Road Tunnels, 2012. Vehicle emissions and air demand forventilation. PIARC Committee on Road Tunnels Operation (C4).