CFD prediction of turbulent flow under the influence of moving automobiles in street canyons

Naoko Konno*, Yuichi Tabata**, Aya Kikuchi*, Akashi Mochida*, Takashi Maruyama***, Aya Hagishima****, Jun Tanimoto****, Yoshiki Kikuchi****

* Department of Architecture & Building Science, Graduate School of Engineering, Tohoku University, Japan ** Technical Research Institute, Obayashi Corporation, Japan

*** Disaster Prevention Research Institute, Kyoto University, Japan **** Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Japan

Abstract A series of wind tunnel experiments with different densities of car roughness elements was carried out to measure wind velocities and drag forces caused by the roughness elements. Next, CFD predictions with the ‘Vehicle Canopy Model’ were carried out for the same targets as these in the wind tunnel tests. The model coefficient included in a ‘Vehicle Canopy Model’ proposed by the present authors was determined based on the comparison of CFD results with the experimental results. Key words: Moving automobiles, Vehicle Canopy Model, CFD, wind tunnel experiment, drag force 1. INTRODUCTION Recently, the present authors have proposed a ‘Vehicle Canopy Model’ describing the effects of moving

automobiles on wind environment and turbulent diffusion of air pollutants in urban street canyons. In our previous research, the basic concept and the mathematical expressions of ‘Vehicle Canopy Model’ were proposed and outlined. The examples of applications using this model were also given [Mochida et al. 2006, Mochida et al. 2008]. The aims of this study are to determine the model coefficients of the abovementioned model and to examine its

accuracy. A series of wind tunnel experiments with different densities of car-shaped roughness elements was carried out to measure wind velocities and drag forces caused by the roughness elements. By comparing the CFD results with wind tunnel data, the model coefficients were then optimized. 2. OUTLINE OF VEHICLE CANOPY MODEL [MOCHIDA ET AL.2008] The Vehicle Canopy Model proposed in our previous study was derived based on the k- model in which extra terms were added into the transport equations. Table 1 shows the basic equations of k- model incorporating the effects of objects which have sizes smaller than the computational mesh, such as trees, automobiles etc. Here, the effects of each individual moving automobiles were not directly modelled, instead, the total effects of all moving automobiles existed on the street were considered as a whole. The aerodynamic effects of moving

Table 1: k- model incorporating the effects of small scale objects

< f >: ensemble-averaged value of f, : spatial-average of ensemble-averaged value (< f >)G: the ratio of fluid volume against unit volume

[Transport of turbulent kinetic energy k]

[Transport of energy dissipation rate ]

[Transport of momentum]

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< f >: ensemble-averaged value of f, : spatial-average of ensemble-averaged value (< f >)G: the ratio of fluid volume against unit volume

[Transport of turbulent kinetic energy k]

[Transport of energy dissipation rate ]

[Transport of momentum]

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Table 2: Additional terms for vehicle canopy model

Cf-car : Drag coefficient of automobiles [-]ucari : Moving speed of automobiles [m/s]Acar : Average of 4-side area of the box where automobile

is fitted in without gaps [m2]Vfluid : Fluid volume within the vehicle canopy layer [m3] (cf. Fig. 3)L : Average circumference length of the box where automobile

is fitted in without gaps [m]C-car : Ratio of turbulence scale of automobiles [-]

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Cf-car : Drag coefficient of automobiles [-]ucari : Moving speed of automobiles [m/s]Acar : Average of 4-side area of the box where automobile

is fitted in without gaps [m2]Vfluid : Fluid volume within the vehicle canopy layer [m3] (cf. Fig. 3)L : Average circumference length of the box where automobile

is fitted in without gaps [m]C-car : Ratio of turbulence scale of automobiles [-]

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kk 2/3

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Corresponding Author: Naoko Konno ; Graduate School of Engineering, Tohoku University, E-mail: konno@sabine.pln.archi.tohoku.ac.jp

The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan

automobiles were modelled based on the methodology of canopy model. Similarly to the tree canopy and building canopy models, the extra term “-Fi” added in the momentum equation gives the effect of moving automobiles on velocity change, while the other extra terms “+Fk” and “+F” were put in the transport equations of turbulent kinetic energy k and energy dissipation rate to simulate the effects of moving automobiles on the amount of increase in turbulent kinetic energy and energy dissipation rate respectively. Table 2 describes the expressions of these extra terms. The extra term of “-Fi” was defined as a function of wind velocity iu in the building canopy and tree canopy models [Hiraoka 1993, Maruyama 1993]. In modelling vehicle canopy, iu was replaced by the relative velocity between wind velocity and moving speed of automobiles [Mochida et al.2008]. G is defined as a ratio of fluid volume per test volume. Here, we assume an imaginary box where the automobile is filled in without gaps. Based on the proposed definitions of effective area and length scale of building canopy model by Maruyama [Maruyama 1995], Acar is defined as the average 4-side area of the box and L is defined as the average circumference length of the box[Mochida et al.2008]. 3. OUTLINE OF WIND TUNNEL EXPERIMENTS A series of wind tunnel measurements of wind velocity over vehicle canopy layer and the drag force caused by a group of the simplified car-shaped molds (Fig. 2(1)) and the miniature cars (Fig. 2(2)) were carried out under the conditions with different staggered array mold densities. The experiments were carried out in a low speed single-return wind tunnel at the Interdisciplinary Graduate School of Engineering Science, Kyushu University [Hagishima 2008] (Note1). Roughness volume density r(z) was defined as a volume of car-shaped mold against unit volume Vcar /Vunit (=1-G) and was given in the upper and lower parts separately (cf. Fig. 3).Drag forces and vertical profiles of wind velocities affected by four different staggered array car-shaped molds densities were measured (simplified car molds: r(z1): 7.7, 17.4, 30.9, 38.6[%], miniature cars: r(z1): 8.9, 20.1, 35.9, 44.8[%]).

1H

2H1H

0.5H

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1H

2H1H

0.5H

1H=2

2.3H

1.1H

1H1H=25mm2.3H

1.1H

1H1H=25mm

r(z1)

r(z2)

Vcar

Vunit

Vfluid

r(z2)

r(z1)r(z1)

r(z2)

Vcar

Vunit

Vfluid

r(z2)

r(z1)

10 20 30 40 50

1.0

2.0

3.0

4

8

12

CfCp

r[%]

：抵抗係数Cf

：モデル係数Cp

drag coefficient Cf(cf. Eq. (5) in Table 2)

model coefficient Cpincluded in F(cf. Eq.(7) in Table 2)

10 20 30 40 50

1.0

2.0

3.0

4

8

12

CfCp

r[%]

：抵抗係数Cf

：モデル係数Cp

drag coefficient Cf(cf. Eq. (5) in Table 2)

model coefficient Cpincluded in F(cf. Eq.(7) in Table 2)

(2) Miniature car

Fig. 2: Car-shaped molds Fig. 3: Roughness volume density r(z) Fig. 4: Variation of roughness parameters with r [Maruyama 1993, 1995] 4. CFD PREDICTION FOR THE SIMPLIFIED CAR-SHAPED MOLDS CFD predictions with the developed ‘Vehicle Canopy Model’ were carried out for the same target as those in the wind tunnel tests described in the previous section. Test cases of CFD prediction targeting at the simplified car-shaped molds (cf. Fig. 2(1)) are shown in Table 3. Maruyama developed a canopy model expressing the effects of small scale buildings whose sizes are smaller than the grid size of the computational mesh and also obtained a detailed database from a series of wind tunnel tests when determining the model coefficients. In this study, coefficient for drag term “-Fi ” of automobiles Cf-car and the model coefficients included in the extra term added to transport equation, C-car (cf. Table2) were determined based on the database for the building canopy model produced by Maruyama, as shown in Fig. 4 [Maruyama 1993, 1995], and the validity of this treatment was examined through a comparison between the results of measurements and CFD predictions. The moving speed of the vehicle was set at 0m/s and the standard k- model was used in these predictions. Details of the computational conditions can be found in our previous paper [Mochida et al.2008]. Drag forces of the cases with different roughness densities r are compared in Table 4. Here, the drag force was evaluated as the sum of the form drag caused by all car-shaped molds existed in the canopy layer dVGF1 and the shear stress at the ground surface dAw over the area of the ground surface corresponding to the area of float in the wind tunnel test (Note2). Drag coefficient Cd was estimated in the same way of wind tunnel experiments (Note 3). Table 4 shows drag coefficient Cd and two elements composing the drag force. The Cd values obtained by CFD prediction showed generally good agreement. Thus, it can be said that Maruyama model which was developed for reproducing the effects of building canopy can be sufficiently applied to the predictions for the simplified car-shaped molds case. Next, CFD predictions of flow over a group of the realistic car-shaped molds (cf. Fig. 2(2)) were carried out.

(1) Simplified car mold

The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan

Table 3: Test cases of CFD predictions targeting at the simplified car molds roughness volume density r(z)[%]

fetch area vehicle canopy (cubic models ) (simplified car molds)

Cf-car C-car

lower 7.7 1.55 2.30 Case 1s-m 17.4 upper 3.9 1.10 1.60 lower 17.4 2.20 2.80 Case 2s-m 17.4 upper 8.7 1.70 2.20 lower 30.9 1.80 5.90 Case 3s-m 17.4 upper 15.5 2.10 2.50 lower 38.6 1.40 16.00 Case 4s-m 17.4 upper 19.3 2.20 2.80

Table 4: The drag force caused by the all simplified car-shaped molds in the canopy, the shear stress at the ground surface and drag coefficient Cd (Note 2, Note 3)

drag coefficient Cd [-]

Roughness volume

density r(z1)

drag caused by the all molds in the canopy layer dVGF1

[N]

shear stress

dAw [N]CFD experiment

Case1s-m 7.8 1.72×10-1 4.37×10-3 9.91×10-3 8.92×10-3

Case2s-m 17.4 2.00×10-1 6.27×10-4 1.11×10-2 1.05×10-2

Case3s-m 30.9 2.20×10-1 8.00×10-5 1.20×10-2 1.24×10-2

Case4s-m 38.6 2.20×10-1 5.64×10-5 1.20×10-2 1.20×10-2

5. CFD PREDICTION FOR THE REALISTIC CAR SHAPED MOLDS Test cases are shown in Table 5. In these predictions, coefficients for drag term “-Fi” of automobiles Cf-car were decreased compared with the values given by Maruyama. The drag forces of the stream-lined miniature cars obtained by the wind tunnel experiment were generally smaller than those of the simplified car-shaped molds composed of two cubic blocks. By comparing the result of drag forces and wind velocities measured in wind tunnel tests, Cf-car values for the miniature cars were estimated to be about 30% of the values given by the Maruyama model for building canopy. In this section, the validity of this treatment is examined through a comparison between the results of experiments and CFD predictions.

Table 5: Test cases of CFD predictions targeting at the miniature cars* roughness volume density r(z)[%]

fetch area vehicle canopy (cubic models ) (miniature cars)

Cf-car C-car

lower 8.9 1.60 (m) 2.25 (m) Case 1r-m 17.4 upper 4.5 1.19 (m) 1.67 (m) lower 35.9 1.50 (m) 12.25 (m) Case 3r-m 17.4 upper 18.0 2.13 (m) 2.47 (m) lower 8.9 0.48 (0.3m) 2.25 (m) Case 1r-0.3m 17.4 upper 4.5 0.36 (0.3m) 1.67 (m) lower 35.9 0.45 (0.3m) 12.25 (m) Case 3r-0.3m 17.4 upper 18.0 0.64 (0.3m) 2.47 (m)

*In the case numbers,”m”means the case where Cf-car values were given by Maruyama model [Maruyama 1993, 1995] and ”0.3m”means the cases where Cf-car values were set to the values given by Maruyama model×0.3

Fig. 5 shows the vertical profiles of mean wind velocities )(zu / Hu20 ,turbulent kinetic energies k(z)/ 2)( zu

and the drag coefficient Cd (Note 3). When Cf-car was decreased to 30% of the value given by the Maruyama model, wind velocity )(zu / Hu20 was increased and showed good agreement with wind tunnel test (Case3r-0.3m cf. Fig. 5(1)) and k(z)/ 2

)( zu was greatly decreased (cf. Fig. 5(2)). In Fig. 5(3), the results with the Cf-car value decreased to 30% of the value given by the Maruyama model showed generally good agreement with those of experiments.

The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan

0 0.5 1.00.050.1

0.5

1

510

<u(z)>/<u20H>

Hei

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z/H

) experiment Case3r-m Case3r-0.3m

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0.5

1

510

<u(z)>/<u20H>

Hei

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z/H

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0 0.2 0.40.050.1

0.51

510

k(z)/<u(z)>2

Hei

ght (

z/H

)

Case3r-m Case3r-0.3m

0 0.2 0.40.050.1

0.51

510

k(z)/<u(z)>2

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ght (

z/H

)

Case3r-m Case3r-0.3m

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0 10 20 30 40 50

roughness volume density r (z1) [%]

drag

coe

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ent C

d [-

]

experimentCase*r-m (Maruyama model)Case*r-0.3m (Maruyama modelx0.3)

(1) Wind velocity (2) Turbulent kinetic energy (3) Drag coefficient Cd

Fig. 5: Comparison of mean wind velocities, turbulent kinetic energy and drag coefficient

6. CONCLUSIONS

1) A series of wind tunnel measurements of wind velocities and drag forces was carried out by using the simplified-car shaped molds composed of two cubic blocks and miniature cars with different roughness volume densities. The accuracy of ‘Vehicle Canopy Model’ proposed by the present authors for expressing the effects of automobiles on turbulent flowfield was examined by comparing its results with wind tunnel data.

2) It was found that the methodology of the building canopy model proposed by Maruyama could be sufficiently applied to the predictions for the simplified car-shaped molds cases. CFD results obtained using the values of the two model coefficients Cf-car and C-car given by the Maruyama model showed generally good agreement with experimental data for these cases.

3) On the other hand, it was estimated from the experimental data that Cf-car values for the stream-lined miniature cars were about 30% of the values given by the Maruyama model. The drag coefficients of the miniature cars predicted using the estimated Cf-car values showed very close agreement with those of experiments.

Notes

1. The inflow turbulent boundary layer was generated by using the roughness composed of staggered arrayed cubic blocks located at the windward side. The floor of wind tunnel has a square void, in which floating element with a base is attached. The total drag force acting upon a floating element was directly measured using a strain gauge. Details of the experimental device can be found in the present conference paper of Hagishima and Tanimoto (Hagishima and Tanimoto 2008). The vertical profiles of wind velocities were measured by the split film probes (Hagishima and Tanimoto 2009).

2. The shear stress at the ground surface w was evaluated as follows;

where, *u : friction velocity [m/s] pu : wind velocity at the first grid point adjacent to the ground surface at z=hp [m/s]

: Karman’s constant (=0.4[-]), z0: roughness length [m] (=1.0×10-8m) : air density [kg/m3]

3. The drag coefficient Cd was estimated by using Eq. (10).

where, F: drag force[N], : air density[kg/m3], A: area of float [m2]

Hu20: spatial average of time-averaged wind velocity at 20H [m/s], H: a height of mold (cf.Fig.2)

References

Hagishima, A., and J. Tanimoto (2008), “Wind tunnel experiment on drag force coefficient of urban-like roughness with height variation”, the forth international conference on Advances of Wind and Structures 08, 29-31 May 2008, Korea

Hagishima A, Tanimoto J, Nagayama K, Meno S, (2009), “Aerodynamic parameters of urban-like roughness with nonuniform heights”, Boundary-Layer Meteorology, (submitted)

Hiraoka, H. (1993), “Modelling of Turbulent Flows within Plant/Urban Canopies”, J. Wind Eng. Ind. Aerodyn., 46 & 47, 173-182. Maruyama, T. (1993), “Optimization of roughness parameters for staggered arrayed cubic blocks using experimental data”, Journal of Wind

Engineering and Industrial Aerodynamics, 46&47, 165-171. Maruyama, T. (1995), “Numerical Simulation of Wind Flow over Urban Area Part 1 Examination of simulation method by case study of a real urban

city”, J. Struct. Constr. Eng., AIJ, 474, 49-58 (in Japanese) Mochida, A., N. Hataya, T. Iwata, Y. Tabata, H. Yoshino and H. Watanabe (2006), “CFD analyses on outdoor thermal environment and air

pollutant diffusion in street canyons under the influences of moving automobiles”, the 6th International Conference on Urban Climate (ICUC6), Goteborg, Sweden, 196-199

Mochida, A., Y. Tabata, A. Hagishima, J. Tanimoto, T. Maruyama, A. Kikuchi, Y. Kikuchi (2008), “Development of CFD Model for Reproducing Aerodynamic Effects of Moving Automobiles in Street Canyon”, the 4th International Conference on Advances in Wind and Structures(AWAS'08), Jeju, Korea, 100-114

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The seventh International Conference on Urban Climate, 29 June - 3 July 2009, Yokohama, Japan