taylor galerkin num. model for aq simulation near roadway tunnel portals-okamoto

8/3/2019 Taylor Galerkin Num. Model for AQ Simulation Near Roadway Tunnel Portals-Okamoto

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1010 VOLUME 37J O U R N A L O F A P P L I E D M E T E O R O L O G Y

1998 American Meteorological Society

Development and Application of a Three-Dimensional TaylorGalerkin NumericalModel for Air Quality Simulation near Roadway Tunnel Portals

SHINICHI OKAMOTO

Tokyo University of Information Sciences, Yatocho, Wakaba-ku Chiba, Japan

KAZUHIRO SAKAI

Japan Highway Public Corporation, Kasumigaseki, Tokyo, Japan

KOICHI MATSUMOTO

Research Institute of Japan Highway Public Corporation, Machida, Tokyo, Japan

KENJI HORIUCHI

Chiyoda Engineering Consultants Co. Ltd., Iidabashi, Tokyo, Japan

KEIZO KOBAYASHI

Japan Environment Management Association for Industry, Ueno, Tokyo, Japan

(Manuscript received 5 November 1996, in final form 23 July 1997)

ABSTRACT

Since highway traffic has become one of the major emission sources of air pollution, air pollution predictionnear roadway tunnel portals is a very important subject. Although many models have been suggested to predictpollutant concentrations near roadways, almost all models can be applied to only at-grade or cutoff straighthighways. Therefore, a numerical model applicable to the site near roadway tunnels in complex terrain has beendeveloped.

The first stage of this study is to make a database of air quality and meteorological conditions near roadway

tunnel portals. The second stage is a screening of several wind field models. The third stage is an evaluationof the numerical schemes for the advection equation, mainly carried out based on the results of the rotatingcone problem.

In this limited comparative study, the most accurate and high-speed computing scheme was the TaylorGalerkinscheme. Next, a three-dimensional model based on this scheme was developed by operator splitting of locallyone-dimensional calculations.

The final stage is a validation study of the proposed model. The composite model consists of a wind fieldmodel, a model for the jet stream from a tunnel portal, and a model for the diffusion and advection of pollutants.The calculated concentrations near a tunnel portal have been compared to air tracer experimental data for twoactual tunnels: the Ninomiya and the Hitachi Tunnels. Good evaluation scores were obtained for the NinomiyaTunnel. Since predictive performance for the Hitachi Tunnel was not sufficient, some additional refinements ofthe model may be necessary.

1. Introduction

Highway traffic has become one of the major emis-sion sources of air pollution, and especially automobileexhaust gas pollution near roadway tunnel portals cansometimes become a serious environmental problem.

Corresponding author address: Shinichi Okamoto, Tokyo Uni-versity of Information Sciences, 1200-2 Yatocho, Wakaba-ku, Chiba265-8501 Japan.E-mail: [email protected]

Therefore, air pollution prediction is a very important

subject, and many models have been proposed to predictpollutant concentrations near roadways. Although thesemodels can usually be applied to at-grade or cutoffstraight highways, they are usually not well applied totunnels that are located in an area of complex terrain.Well-known numerical models for complex terrain thathave been developed in the last decade, for example,by Tesche et al. (1987) and Uliazs (1993), are mainlyprepared for larger-scale areas than the objective areaconcerned here, namely, near a tunnel portal.

The first stage of this study is to carry out air tracer


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OCTOBER 1998 1011O K A M O T O E T A L .

field experiments in order to prepare a database. Thesecond stage is a screening of wind field models, andthe development of a suitable wind field model. Thethird stage is an evaluation study on the numerical meth-ods for the advection equation to incorporate the com-posite model and the development of the three-dimen-sional numerical model suitable to the air quality sim-ulation near a tunnel portal. The final stage is the val-idation study of the proposed numerical model.

The paper describes the development of a three-di-mensional model for air pollution simulation near road-way tunnel portals. The procedure and results with re-gard to the wind field model screening appear in Kimuraet al. (1996) and only a brief summary is written in thispaper. The matters concerning field experiments are out-lined in section 4.

2. Selection of numerical method for advectionequation

The numerical method for the advection equation maybe the most important factor in composite atmosphericmodels because an inappropriate descretization of theadvection terms can sometimes have a devastating effecton a numerical model and should be selected carefully.There are many review papers concerning the numericalmethods, such as Rood (1987), McRae et al. (1982),and Chock (1991), and it was decided to carry out anevaluation study to confirm their conclusions. The can-didate numerical methods chosen for this evaluationstudy are four methods as follows: simple upwind dif-ferencing method of second order, TaylorGalerkinmethod selected from the schemes of Galerkin-type fi-

nite element method, cubic spline method selected as arepresentative of semi-Lagrangian-type schemes, andparticle method because this is sometimes used for Mon-te Carlo simulation. The spectral and pseudospectralmethods were not chosen because of difficult corre-spondence with complicated boundary condition overcomplex terrain.

a. Description of methods

1) UPWIND DIFFERENCING METHOD

The upwind differencing is one of the most popularnumerical models, although it is largely concerned with

numerical diffusion. Its advantage is that it is very easyto understand and that it suits computer programs. Wehave chosen this method of the second-order accuracyfor the underlying evaluation study. The upwind dif-ferencing of a space derivative is shown in Eq. (1):

C 1 (3C 4C C ), (1)i i1 i2 x 2x

i

where C is concentration, x is a spatial coordinate, andx is a spatial increment.

2) TAYLORGALERKIN METHOD

Although the Galerkin finite element method using achapeau function is an attractive scheme for the dis-cretization of a space derivative, the combination withtime differencing makes the scheme unstable because

of computational pseudonegative diffusion. The PetrovGalerkin and TaylorGalerkin methods were developedto overcome these defects. The TaylorGalerkin methodwas proposed by Donea (1984) and Donea et al. (1987).Chock (1991) carried out an extensive evaluation studyfor the numerical methods and concluded that the Tay-lorGalerkin method is one of the best choices for solv-ing the advection equation.

The one-dimensional advection equation descretizedby TaylorGalerkin method is shown in Eq. (2):

2 n1 2 n1 2 n1(1 )C (4 2 )C (1 )Ci1 i i1

6t 3t2 n 1 3 2 F (u) F (u) C1 2 i12

[ ]x x

12t2 n 4(1 ) F (u) 6tF (u) C1 3 i2[ ]x

6t 3t2 n 1 3 2 F (u) F (u) C ,1 2 i12[ ]x x

(2)

where

ut .

x

1 u2 2F (u) t u .1 2 x

2 23 u 1 u u2F (u) tu t u 7 u .2 2 2 x 6 x x

22u 1 u uF (u) t u 3 2 x 2 x x

2 21 u u2 t u 7 u , (3)

2 6 x xwhere t is time, t is the time increment, and is theCourant number. Moreover, the wind derivatives in Eq.

(3) are approximated by first-order center differencing.

3) QUASI-LAGRANGIAN CUBIC SPLINE METHOD

In the field of air quality simulation, the quasi-La-grangian cubic spline method was introduced by Pepperet al. (1979). This method uses the following basic con-cept: the concentration of place x i at time (n 1)t isidentical to that of place xi1 at time nt. To estimatethe concentration of place x (xi1 x xi ), the fol-lowing interpolation scheme was used:


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FIG. 1. Rotational flow.

FIG. 2. Initial mass distribution.

n1C (x)

2 2(x x) (x x ) (x x ) (x x)i i1 i1 in n D Di1 i2 2x x

2(x x) [2(x x ) x ]i i1 n Ci1 3x

2(x x ) [2(x x) x ]i1 i n C , (4)i 3x

where Di is a spatial differential and can be obtainedby solving the following equation:

1 1 1 1D 2 D Di1 i i1[ ]x x x x

n n n nC C C Ci i1 i1 i 3 3 ,

2 2x x

where x

xi xi1 and x x i1 xi .

4) PARTICLE METHOD

The dispersion phenomena can be simulated by themovement and distribution of a large number of parti-cles, and the atmospheric turbulence is modeled by apseudorandom number generated by a computer. Thismethod is known as particle method or random-walkmethod.

In the underlying comparative study this method was

selected as a candidate to solve the advection and dif-fusion equations. However, to evaluate only the advec-tion term, the diffusion process was omitted and move-ment of a particle was expressed by using only the meanwind field. The initial number of particles was set pro-portionally to the initial concentration field.

b. Evaluation of methods

The computational performance of the numericalmethods for the advection equation can be measured by

the rotating cone problem. In this test, the initial con-centration field is represented by the cosine function,and its center is biased from the center of the circulatingflow field. The two-dimensional advection equation isshown below:

C (uC) (C), (5)

t x y

where C is concentration, and u and are wind com-ponents for x and y directions, respectively. Chock andDunker (1983) and Chock (1985, 1991) have carriedout an extensive evaluation study for the numericalmethods, using the rotating cosine hill test in a 33 33 grid. Rotating cone testing was carried out to re-confirm the evaluation results given by Chock. The ex-perimental conditions shown in Figs. 1 and 2, includingthe initial concentration field and the wind field, were

the same as that of Chock (1991).Seibelt and Morariu (1991) used the deformationalflow field to test their semi-Lagrangian numerical ad-vection methods. Their purely deformational flow fieldis expressed as follows:

u x and y, (6)

where is a constant.In this case, the deformation F cannot be zero, even

though the divergence becomes zero:

F du/dx d/dy 2. (7)

In this flow field the calculated mass after n timeincrements can be analytically obtained. This analytical

result suggests that a continuous growth of the total massmay occur in the ordinary Lagrangian model in whichthe first-order difference of the spatial derivative of windis used.

To evaluate the numerical methods, this deforma-tional flow field was also used. The initial concentrationfield was set for a rectangular-shaped block of 8 8grid elements in the center of a 32 32 computationaldomain, which is the same as that of Siebert et al.(1991). The flow field for the former half computationalcycle is shown in Fig. 3, and the flow for the latter half


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FIG. 3. Deformational flow.

FIG. 4. Contour plots after two revolutions in rotational flow: (a) second-order upwind differencing (UD), (b)TaylorGalerkin (TG), (c)cubic spline (3S), and (d) particle method (PM).

cycle is in reversed direction. Therefore, the rectangularblock stretches along the y axis. After that, the flowbecomes reversed, stretches along the x axis, and returnsto the shape of initial conditions after one cycle of com-putation.

As for the rotating cone and deformational flow prob-lems, the two-dimensional equation shown in Eq. (5)was numerically solved by operator splitting (McRae etal. 1982). In the rotating cone problem, the maximumCourant number was set at 0.4. This scheme wasinappropriate (only for the upwind differencing) for 0.4, and so the Courant number was set at 0.2. The

number of particles used in the particle method was 500.The calculated concentration distributions of the rotat-ing cone after two revolutions are shown in Fig. 4. Theresults of the deformational flow problem after five cy-cles are shown in Fig. 5. Good performance was ob-tained for cubic spline and TaylorGalerkin methods.The upwind differencing method reveals the worst inthis comparison because the concentration field aftertwo revolutions reveals a quite different shape from theinitial condition. In the particle method, a little bias ofthe center position and some spikes were observed.These errors may have occurred because the first-orderdifferencing of time derivative was used, and the particlemoved along the tangential line of airflow at the positionof this particle. If a higher-order time difference isadopted, these error may be suppressed.

When TaylorGalerkin and spline methods were used,small ripples occurred behind the cosine hill, and somenegative values appeared. The adoption of a numericalfilter may be useful to suppress these ripples, and an

additional study seems necessary. As for nearly non-reactive tracers, this defect does not seem to be fatal.More detailed considerations are made in the evaluationof the composite model.

For the quantitative evaluation, the mass conservationratio R1 and the mass distribution ratio R 2 were calcu-lated as follows:

R C (t) C (0) (8) 1 ij ijand

2 2R C (t) C (0), (9) 2 ij ij


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FIG. 5. Contour plots after five cycles in deformational flow: (a), (b), (c), and (d) are the same methods as in Fig. 4.

FIG. 6. The mass conservation ratio and mass distribution ratio af-ter two revolutions.

where Cij (0) are initial concentrations and Cij (t) are con-centrations at the time of evaluation.

The evaluation scores for each numerical method areshown in Figs. 6 and 7, and the computational time isshown in Fig. 8. These scores suggest preference forthe use of the TaylorGalerkin method, which is com-parable with Chock (1991).

c. Example of TaylorGalerkin model: Comparisonwith Gaussian model

The TaylorGalerkin method turns out to be the mostattractive method in this limited comparative study.Therefore, this method was selected for the basic nu-merical scheme, and the three-dimensional compositemodel was produced by operator splitting based on thelocally one-dimensional TaylorGalerkin method for thediffusion and advection equation.

This model was initially applied to the most simplecase of the effluent diffusion from a tall stack wherethe wind and diffusion coefficients were constant. An


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FIG. 7. The mass conservation ratio and mass distribution ratio af-ter five cycles.

FIG. 8. The CPU time for the calculations of two revolutions andfive cycles.

analytical equation was derived that is identical to theGaussian plume equation:

C( x, y, z)

2Q uy exp 4K x4K K (x) yy z

2 2u(z H) u(z H) exp exp , [ ]4K x 4K xz z

(10)

where H is source height, and Q is source strength; Kyand Kz are diffusion coefficients in y and z directions,respectively.

The calculated concentration fields based on the Tay-lorGalerkin model and the Gaussian model are shownin Fig. 9. The results show sufficient consistency be-tween these models.

3. Model overview

a. Model structure

The objective of the proposed composite model is tosimulate automobile exhaust gas diffusion from a tunnel

portal. The model consists of two major modules andthree submodules. The first major module is a wind fieldmodule for calculating the three-dimensional wind com-ponents over a complex terrain; it contains a tunnelsubmodule to simulate the jet stream from a tunnel por-tal. The second major module is a diffusion module tocalculate the concentration field of automobile exhaustgas from the tunnel portal; it contains two submodules:a meteorological preprocessing submodel to calculatethe diffusion coefficients and an emission submodulethat gives the emission rate for roadways.

The schematic diagram of this simulation model isshown in Fig. 10. Basic input data for this model con-cerns the terrain, meteorology, traffic, and tunnel con-figurations. The terrain data include the terrain elevationand land surface representation.

The NOx emission intensity for a roadway is estimatedby the emission submodule based on the traffic volumesfor each automobile type and traffic conditions, and de-tails for the estimation methods for NOx emissions areshown in Okamoto et al. (1990).

b. Wind field estimation

Only a brief summary of the comparative study forwind field models is presented here. The model namesand evaluation scores are shown in Table 1. For thiscomparative study, three companies have cooperated.Each company was supplied with terrain data and winddata at one point (the most representative anemometersite shown in Table 2) for two runs of the Ninomiyaexperiment. They submitted the calculated three-di-mensional wind components for all grid points. Thecalculated wind at 10 anemometer sites were extractedfrom the grid point data and compared with observeddata. The companies did not participate in the processto evaluate the wind field model.

Table 1 shows that some fluid dynamic models do

not reveal a good performance. The main reason maybe that the data supply was not satisfactory (some fluiddynamic models required more detail terrain informa-tion about outer computational domain), rather than thatthe models themselves were not sufficient.

According to the comparative study on the wind fieldmodels (Kimura et al. 1996), a mass consistent (MAS-CON) model has been selected for the wind field model.Since we could not find a perfectly fitting fluid dynamicmodel, and the difference of the predictive performancebetween the candidate models was not so large, we


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FIG. 9. Comparison of the calculated concentrations by Gaussian plume model and TaylorGalerkin 3D numerical model (H 50 m, Q 1 106 m3 s1 , u 3 m s1, Kx 0 m

2 s1, Ky 10 m2 s1, Kz 5 m

2 s1).

FIG. 10. The schematic diagram of the composite air quality simu-lation model near tunnel portals.

adopted the model with the least computational require-ments.

The MASCON wind field model was developed ac-cording to Dickerson (1978) and Sherman (1978). Al-though the wind field model developed here is three-dimensional and similar to Shermans MATHEW model,

the terrain-following coordinate system was employed.The first step is to obtain a guess field by using theweighted-average interpolation scheme from severalmeteorological points, in which the weight is propor-tional to the inverse of the square distance from the gridpoint to each measuring point, and the vertical extrap-

olation is made by using the power law of the windprofile (Turner 1994). There were 10 wind measurementpoints for each experimental site, and wind measuringwas carried out at height of 610 m above terrain.

The second step is to modify the guess field so as tosatisfy the continuity equation. The coordinate system(x, y, z) was converted to the terrain adjusted coordinate(, , ), and the continuity equation in this system isshown in Eq. (12):

x, y, and z h( x, y), (11)

where h(x, y) is the terrain elevation at the place (x, y),and

u h u h 0. (12)

In the variational wind field model, the airflowthrough the obstacles varies depending on the ratio ofthe coefficients 1/2 [the same notation was used asin Sherman (1978).] When the atmosphere is stable, theairflow does not climb over a ridge but tends to followthe same altitude. This situation is simulated by usinga larger 2 value. When 1 is equal to 2, this flow isequivalent to the potential flow. Ueyama et al. (1984)


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TABLE 1. Wind field models: model type and evaluation scores.

Model Model typeRelative

computing speed

Correlation (r)*

Run 8 Run 17

Spectrum NavierStokes eq., kmodelLeast square Galerkin method

2.5 0.72 0.78

Favor NavierStokes eq., viscocity coef Control volume Favor method

0.8 0.78 0.80

Stream NavierStokes eq., kmodelControl volume upwind differencing

2.1 0.89 0.84

K imu ra m ode l N onhyd ros ta tic Bous sin esqApproximation, MellorYamada level 2.5Matuno scheme differencing

50.4 0.85 0.73

Mascon Variational method 1.0 0.82 0.83

* r ( Vobs Vcal cos)/( Vobs Vcal); : angular difference between the observed and calculated wind directions.

TABLE 2. Test conditions.

Tunnel Expt. DayTime

(LST)

Wind*

W.D.W.V.

(m s1)

Stabil-ity of

atmos.

Tunneljet

stream(m s1)

Trafficvolume

(veh h1)

Largesize

vehiclemixture

ratio (%)

Vehicle speed

Smallsize

(km h1)

Largesize

(km h1) Co mm ent

NinomiyaTunnel(1994)

R11R12R13R14R15

1/261/261/271/281/28

14151617

7878

1112

WSWWSWNENENE

5.74.93.63.43.7

CDDDDD

5.55.25.35.14.8

10571305

9331207

846

13.310.516.710.622.2

8578867890

7572787482

R16R17R18R19R110

1/281/291/291/291/29

15161011111216171718

NENENEENENNE

3.83.54.92.02.6

DCDFF

4.84.64.24.24.2

1043870838835895

16.515.916.111.1

7.0

8892908893

7883807884

R111R112

R113R114R115

1/301/30

1/311/311/31

9101011

91010111112

WNWWNW

NEESE

3.83.1

1.21.22.0

BCBC

ABABB

4.34.1

4.84.94.8

763929

820965889

4.64.1

26.121.621.3

9588

958692

8580

837879

R116R117R118

1/311/311/31

121313141415

SESSESSE

2.62.12.2

ABBB

4.74.94.9

813934

1062

19.221.320.7

969586

868477

R119R120R121

1/311/312/1

151616171011

SWSWW

2.02.22.9

CFD

5.05.05.0

10841226

806

19.313.325.6

888094

767378

HitachiTunnel(1995)

R21R22R23R24R25

2/32/42/42/42/5

1617910

141516171011

SEWNWSEENNW

1.02.71.11.02.4

DDDDD

4.84.54.04.33.8

953711712929716

18.324.913.111.3

7.4

95110

9899

108

9597989598

R26R27R28

R29R210

2/52/62/6

2/72/7

141516171920

9101112

NNEESENE

WWNW

2.11.01.3

0.82.6

DDG

DB

4.14.94.2

5.64.8

670894479

795643

11.819.927.8

41.535.5

105103109

104105

968992

8488

R211R212R213R214R215

2/72/72/82/82/8

15161920

91010111617

NWEWNWWSW

3.81.02.52.71.1

DGDBD

4.84.55.45.24.9

803534814740914

21.520.641.040.820.9

105108110

9598

9093828590

Jet Fan**

R216R217R218

2/82/92/9

19206778

NENE

1.60.50.4

GGD

4.33.64.4

536244770

25.034.415.5

110114

95

888790

* The wind data shown here are obtained by the most representative wind measuring point on the top of the ridge.** The jet fan ventilation system was operated to examine the effect upon the tunnel jet stream.


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studied the relation between the calculated wind fieldand the ratio 1/2 in their variational model, and theyconcluded that the most appropriate value for the ratio1/2 in moderately complex terrain is 0.7 for stableand unstable conditions. Therefore, this value was cho-sen for all cases of the simulations at this stage. A de-tailed description of these procedures is given in Kimuraet al. (1996).

For the lowest layer on the roadway, the vehicle-induced wind plays an important roll compared to theambient wind. The model describing this effect is ex-plained together with the model for jet stream from atunnel portal. The coordinate system and grid spacingfor this MASCON model is equivalent to that of tracerconcentration calculation, and details are given in sec-tion 4.

c. Jet stream from a tunnel portal

The velocity of the jet steam at a tunnel portal canbeen calculated with a traffic piston equation:

L A nm2 21 U (V U ) , (13)e 0 t 0 D A rwhere

e : tunnel entrance loss coefficient,: tunnel wall friction loss coefficient,L: tunnel length (m),D: tunnel diameter (m),A r: tunnel cross sectional area (m

2),Vt: traffic speed in tunnel (m s

1 ),U0: velocity of jet stream at the portal (m s

1),

n: number of vehicles in tunnel, andA m: equivalent resistance area of the vehicles (m

2).

The velocity of a jet stream from a tunnel portal wascalculated as follows. The first step is to calculate the jet stream at the portal. The second step is to calculatethe decrease of the jet velocity (x axis: direction alongthe roadway) from the portal. Next, the distribution ofthe jet velocity in the y-axis and z-axis directions iscalculated. This distribution is assumed to be Gaussianand shown in Eq. (14) as referred by Ueyama (1985):

U U0 exp(x) exp{y2 / } exp{z 2 / }, (14)2 22 2y z

where

U: flow velocity at location (x, y, z) (m s1),U0: flow velocity at portal (m s

1),: distance decrement coefficient,y : standard deviation of wind in horizontal direc-

tion (m), andz: standard deviation of wind in vertical direction

(m).

The distance decrement coefficient varies by am-bient wind direction, wind velocity, and traffic condi-tions; the values for this coefficient were determined

based on the experimental results (Ueyama 1985). Thefunctional forms of the y and x were estimated by theresults of a scale model experiment published in Takasoet al. (1978).

The decrease of the jet stream was empirically mod-eled based on the Mikkabi Tunnel experimental data.The most typical cases are shown in Fig. 11. The ex-ponential decay was observed up to the distance of fivetimes the portal diameter and approached the asymptoticvalues that may be the function of the ambient windspeed, direction, and traffic conditions. The asymptoticvalues are large for nearly calm conditions, and rela-tively small for perpendicular and strong wind condi-tions. Therefore, these asymptotic values are assumedto be 3 m s1 for the former case and 1 m s 1 for thelatter case. Farther away from the portal, the jet streamfrom the portal decreased and merged with the vehicle-induced wind in the open field, and these effects cannotbe clearly separated.

Based on these data, the portal jet Eq. (14) can beused up to the distance where the calculated velocity ofthe jet stream becomes equal to these asymptotic values.When the vehicles size is larger and driving speed isfaster, the traffic-induced wind speed on the road isstronger. The traffic-induced wind is equivalent to thisasymptotic value.

The jet stream velocity for the lower two grid pointsjust above the roadway was fixed and did not vary underMASCON calculation. However, as for the other gridpoints, the jet stream velocity was combined with theguess ambient wind field calculated by the inverse-square-distance weighted averaging method, and itsfield was modified to satisfy the continuity equation in

MASCON calculation.

d. Diffusion coefficients

The diffusion coefficient Ky is assumed to be a func-tion of Pasquills atmospheric stability and reveals thesame value throughout the covered area, and Kz is animportant parameter that has been set based on theboundary layer meteorological model.

The coefficient Ky has been calculated in Eq. (15),by using the diffusion parameter of the PasquillyGifford (PG) diagram. Since the objected area for cal-culation was within 100 to about 200 m from the emis-sion source, the value of was taken from the PGy

chart of 100-m downwind distance,Ky /2x,

2uy (15)

where the assumed value of wind speed u in Eq. (15)is 3 m s1 .

The estimation methods for the turbulent diffusioncoefficient Kz in the boundary layer have been proposedby many researchers and one of the most simple andreliable methods may be the one described in Shir andShieh (1974). The computational process can be sum-marized as follows: the stability parameter s proposed


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FIG. 11. Decrease of the velocity of jet stream form the tunnel portal; representative examplesfor Mikkabi tunnel experimental results.

by Shir and Shieh is calculated by incoming solar ra-diation and wind speed, or with sky cover and windspeed. The stability length L is computed with stabilityparameter s and surface roughness parameter z 0, wherez

0for each surface grid can be obtained by the terrain

database. The nondimensional wind shear m is com-puted with stability length L and height z. The mixingheight His computed with the integrated incoming solarradiation. The mixing length l is computed with the vonKarman constant kand the mixing height H. The frictionvelocity u* is computed from the von Karman constant,the natural wind speed u, and the integrated value mof the nondimensional wind shear m . Calculating nbased on stability length L and height z, the diffusivitycoefficient K is computed from friction velocity u* andmixing length l.

These procedures were developed according to thereference of Shir and Shieh (1974). The turbulent dif-

fusion on the roadway is heavily influenced by the ve-hicles. Therefore, the vehicle-induced diffusion coeffi-cient Kz0 was estimated based on the data published inEskridge et al. (1979). This value Kz0 is set 2.0 m

2 s1

for the lowest two levels of grid cells within the road-way.

e. Numerical scheme

The basic mathematics of the diffusion module con-sist of the three-dimensional advection and diffusion

equation on the terrain adjusted coordinate system. Ac-cording to the review on numerical methods by McRaeet al. (1982), the operator splitting method was used tosolve the three-dimensional equation. The concentration

at time level n

1 can be expressed byCn1 Ax Ay Az Az Ay Ax Cn1, (16)

where Ax and Ay are the horizontal advection and dif-fusion operators, respectively: Az is the vertical advec-tion, diffusion, source, and sink operator.

The operators Ax, Ay, and Az were all formulated bythe locally one-dimensional TaylorGalerkin numericalmethod. The boundary conditions were as follows:

top of the boundary: C/z 0,terrain surface: KzC/z 0,outflow side boundary: C/x 0,inflow side boundary: C Cbackground, and

surface of the structureinside:

KnC/n 0, (n perpendic-ular to the surface).

The x axis was made consistent with the direction ofthe roadway at the portal. The horizontal grid size isvariable: 5 m for center 20 20 grid points and 30 mfor the most outer grids. The vertical grid size is smallnear the surface (z1 3 m) and large for higher al-titude, and the top elevation of the highest grid cell is200 m from the reference heights (origin of the coor-dinate system). The maximum number of the horizontal


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FIG. 12. The experimental sites: dots indicate the sampling points for air tracer, and rectangles indicate the anemometer sites (contour lineis 5-m interval in height). Computational grid system is also shown by only frame.

( x, y direction) and vertical (z direction) grid cells is51, 51, and 18, respectively.

The time increment t is set so as to maintain thenumerical scheme stable, that is, 0.250.5 s dependingon the Courant number. Since the area considered coversseveral hundred square meters, the stable concentration

may be obtained after the appropriate time integrationfrom the initial concentration field, usually 360 timeincrements (i.e., 180 s) under 13 m s1 wind conditions.This stable concentration is considered as an hour-av-erage concentration in this simulation.

4. Database for the validation

The basic idea of this simulation model is formulatedbased on the experimental data at the Mikkabi Tunnelof the Tomei Expressway. This experiment was con-ducted in 1980 and 1981, and its scale may be the largestof its kind as an extensive field experimental project forthe air pollution near tunnel portals (Ueyama 1985).

However, to validate the proposed model, an inde-pendent database that was not used for the developmentof the model is necessary. Therefore, we carried out twofield experimental programs to prepare a sufficient da-tabase. These programs consist of an air tracer experi-ment, meteorological observations, and measurement ofthe traffic conditions at experimental sites as shown inFig. 12. The first program was carried out at NinomiyaTunnel (L 445 m) on Odawara-Atsugi Road, whichhas a traffic volume of about 30 000 vehicles per day.The second site is the Hitachi Tunnel (L 2439 m) on

the Joban Expressway, with 24 000 vehicles per day.Both tunnels have two tubes and two traffic lanes pertube. The Hitachi Tunnel has a jet fan to promote ven-tilation and is operated only for the case that the levelof visibility or air quality in the tunnel decrease to apredetermined condition.

The air tracer experiments presented a most importantdatabase for this validation study. The tracer used wasSF 6 and released from the inside of the tunnel, about150 and 300 m from the portal. Duration of the tracerrelease was about 160 and 170 h for the Ninomiya andHitachi experimental sites, respectively. About 30 re-ceptor points were connected to two multichannel FPD(flame photometric detector) sulfur analyzers with a pre-cut filter for SO 2 gas. At these receptor points, air sam-pling and analysis were continuously carried outthroughout the duration of tracer release time. Thesereceptor points were mainly located along the highway.At the other receptor points, bag air samplers were op-erated during each hour. The sampled air was collected

in 12-L polyvinylidene chloride bags and analyzed byelectron capture gas chromatography. This samplingwas conducted for 21 and 18 times for each program,respectively, and meteorological and traffic conditionsduring these sampling are shown in Table 2.

About 10 meteorological sites were set around thetunnel portal, and the elevation height of the wind sensorwas 610 m. Six anemometers with a one-direction windcomponent were also set along the highway, just outsidethe left lane and inside the tunnel to measure the velocityof the jet stream from the portal. The vertical temper-


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FIG. 13. Comparison between the calculated and observed jet stream velocities at the portals ofthe Ninomiya and Hitachi Tunnels.

ature difference, insulation, and net radiation were alsomeasured. Video tape recording for the highway laneswas carried out to measure the traffic volume and trafficconditions.

For the Ninomiya Tunnel experiment, the wind datawere obtained by nine anemometers. The meteorolog-ical sites are shown in Fig. 12. However, for the HitachiTunnel experiment, eight anemometers are located with-in the area shown in Fig. 12 and two other anemometers

are outside this map; one is the top of the mountain andthe other is located on a farm at about 500 m distancefrom the portal.

5. Evaluation of model performance

a. Calculated velocity of the jet stream at the portal

The strength of the jet stream at the portal was es-timated by Eq. (13), in which the empirical parameters


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FIG. 14. Comparison of the surface concentration distributions (a) R1-1, Ninomiya; (b) R1-10, Ninomiya; (c) R2-1,Hitachi; and (d) R2-4, Hitachi [unit of concentration (ppb)].

were determined based on the Mikkabi Tunnel experi-

ment. Therefore, the validation for this tunnel portalmodel is necessary. The calculated velocity U0 at theportal was compared to the observed jet stream mea-sured by the one-directional anemometer located justinside the portal. The scatter diagrams for the Ninomiyaand Hitachi Tunnels are shown in Fig. 13. The resultfor the Hitachi Tunnel is not much different from thatof Ninomiya. This figure suggests that this tunnel portalmodel can present an appropriate jet stream velocity atthe portal, and this calculated value can be used in theair quality simulation.

b. Calculated concentration field

Air quality simulation near tunnel portals has beencarried out by using the meteorological and traffic con-dition data for Ninomiya and Hitachi experiments. Inthis simulation, the wind field was made by a MASCONvariational model using the complete set of availablewind data: 9 meteorological stations for Ninomiya and10 stations data for Hitachi.

Comparison of the observed and calculated surfaceconcentrations are shown in Figs. 14ad. These figuresshow the typical cases for Ninomiya and Hitachi data.


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FIG. 14. (Continued)

In run R1-1 the wind direction was parallel to the tunnelportal jet, and the contour lines of high concentrationwere stretched along the roadway. This tendency wasreproduced by this simulation. In run R1-10, the winddirection was perpendicular to the roadway. The contourlines for calculated and observed SF6 concentrationswere stretched to the south side of the roadway.

Comparisons for R2-1 and R2-4 of the Hitachi ex-periment are shown in Figs. 14c,d. For the cases of theHitachi experiment, the calculated concentration distri-butions were limited to a narrower area near the portal.

The reason for this discrepancy may be the underesti-mation of the wind near the surface, which is causedby the wind field model.

The portal of the Hitachi Tunnel is surrounded by asteep ridge, and the wind direction at the top of theridge sometimes differed with that of the base of thevalley. Although wind measuring points were locatedon both the ridge and valley bases, this situation wasnot sufficiently simulated by this MASCON model, andit may be a reason why evaluation scores for Hitachiare not as good as those for Ninomiya.


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FIG. 15. Scatter diagrams for the normalized SF6 concentrations.

c. Statistical scores

At the receptor points, the calculated concentrationswere compared to the observed values. As for the cal-culated concentrations, no significant negative values(below 0.01 ppb) were seen, even without the use ofnumerical filters. Scatter diagrams for hourly normal-ized SF6 concentrations are shown in Fig. 15. The sim-ulation model results reveal an overprediction for theNinomiya and Hitachi data. The correlation coefficientsof 1-h Ninomiya and Hitachi data were 0.904 and 0.485,

respectively. At the Ninomiya Tunnel, a better predictiveperformance was obtained than at the Hitachi Tunnel.The most important reason for this difference may bethat for the Ninomiya experiment, the MASCON var-iational wind field model works well because the terrainat the Ninomiya Tunnel is less steep than at the HitachiTunnel.

There are many plots of underestimation in the upper-left corner of the scatter diagram of the Hitachi Tunnel.These plots mainly correspond to the site vicinity to theportal. One of the reasons may be an underestimation

of the extent of the width of the jet stream for the HitachiTunnel. As for the other sites of the Hitachi experiment,the tendency of overestimation can be seen. This reasonmay be the deficiency of the wind field model in steeperterrain. The treatment of meandering during the aver-aging time of concentration may also be an importantreason. To predict the 1-h-average concentration, thefluctuation of wind direction during the 1-h periodshould be considered.

6. Conclusions

An air quality simulation model applicable to theroadway tunnel portals located in the complex terrainwas developed. This model is a kind of three-dimen-sional numerical model and uses the operator splittingmethod based on the TaylorGalerkin descretization.This numerical method was chosen by the limited eval-uation study for numerical methods. The three-dimen-

sional numerical model based on this TaylorGalerkinmethod presents good performance in computing speedand accuracy and is easy to use.

Some empirical parameters in each submodule weredetermined by data archives. Therefore, the validationstudy is very important in increasing the reliability ofthis simulation model. The predictive performance wasvalidated based on the Ninomiya and Hitachi Tunnelsexperimental data prepared separately for validationstudy. The results indicate that the proposed model canprovide the appropriate concentration distributions.However, since evaluation scores for the Hitachi ex-periment are not sufficient, more extensive evaluationand refinement of the model may be necessary.

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