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Thermal effects on vehicle emission dispersion in an urban street canyon
Transportation Research Part D 10 (2005) 197–212 www.elsevier.com/locate/trd
Thermal effects on vehicle emission dispersion in an urban street canyon Xiaomin Xie *, Zhen Huang, Jiasong Wang, Zheng Xie School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200030, PR China
Abstract The impact of the thermal effects on vehicle emission dispersion within street canyons is examined. The results show that heating from building wall surfaces and horizontal surfaces lead to strong buoyancy forces close to surfaces receiving direct solar radiation. This thermally induced flow is combined with mechanically induced flows formed in the canyon where there is no solar heating, and affects the transport of pollutants from the canyon to the layer aloft. The relative influence of each of these effects can be estimates by Gr/Re2. When the windward wall is warmer than the air, an upward buoyancy flux opposes the downward advection flux along the wall; if Gr/Re2 > 2, the flow structure is divided into two counter-rotating cells, and pollutants are accumulated on the windward side of the canyon. When the horizontal surface is heated, and Gr/Re2 > 4, the flow structure is divided into two counter-rotating cells by upward buoyancy flux. Pollutants are accumulated at the windward side of the canyon. When the leeward side is heated, the buoyancy flux adds to the upward advection flux along the wall strengthening the original vortex and pollutant effects of transport compared to the isothermal case. 2005 Elsevier Ltd. All rights reserved. Keywords: Thermal effects; Vehicle emission dispersion; Street canyon; Numerical simulation
*
Corresponding author. E-mail address: [email protected] (X. Xie).
1361-9209/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.trd.2005.01.002
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1. Introduction The growth in road traffic has led to major problems of air pollution caused by vehicular exhausts, and this is now one of the primary source of urban pollution despite significant improvements in fuel and engine technology. At the same time, more very large and high buildings are constructed in dense formations within city centers, and the effects of narrow and deep street canyons on the environment have become more noticeable. They can make it difficult for vehicle exhaust gases in street canyons to disperse with urban air quality being adversely affected. Several parameters dominate the pollutant dispersion process including ambient conditions (wind speed and direction), building geometry (height, width, roof shape), street dimensions (breadth, width), thermal stratification (solar insulation and orientation, building and street thermal capacitance), vehicular movement (size, number, frequency) (Karim and Matsuia, 1998), plume buoyancy etc. The aerodynamic effects, including building geometry and architecture as well as street canyon dimensions, have been extensively studied mainly using wind-tunnel experiments (Baker and Hargreaves, 2001; Meroney and Pavageau, 1996; Kastner-Klein and Plate, 1999; Kastner-Klein and Fedorovich, 2001), numerical models (Huang et al., 2000; Chan and Dong, 2002) and occasionally deploying full-scale experiments (Croxford, 1998; Berkowicz, 1996). Thermal effects result mainly from variations in the solar heating of street walls and ground during the day; the sun warms the air near the wall or above the ground causing strong upward movements of air (Louka and Vachon, 2001; Kim and Baik, 2001). Sini (1996) studied these effects numerically using a model cavity and demonstrated that wall temperatures influence the instreet flow and its vertical transport capabilities. The aim here is to evaluate the impact of thermal effects due to sunshine on the surfaces within the street canyon using numerical simulation with validation provided by the wind tunnel data (Uehara and Murakami, 2000).
2. Numerical simulations A two-dimensional computational domain is used with wind direction assumed to be perpendicular to the street canyon. The ratio of street canyon height and width is H/W = 1, and both sides of the buildings have a same height. The computational domain is 1100 m · 360 m, a typical computational grid with 332 · 83 grid points in the horizontal and vertical directions. The sketch of the calculation domain and grid mesh is depicted in Fig. 1. The grid chosen is finer close to building and ground and then expands further away. The expansion ratio in this non-uniform grid system is 1.2. Extensive tests of the independence of the meshes are carried out with increasing mesh numbers until further refinement is shown to be less significant. k–e turbulence model is used in an isolated street canyon and the CFD modeling is based on the numerical solution of the governing fluid flow and dispersion equations, which are derived from basic conservation and transport principles: the mass conservation (continuity) equation, the two momentum conservation (Navier–Stokes) equations in x,y, and the transport equation for pollution concentration (Wang and Huang, 2002; Tao, 1995). Buoyancy forces are added in momentum conservation adopting the Boussinesq approximation. It is assumed that the density and the other physical parameters do not change except for the density in the buoyancy forces term. The
X. Xie et al. / Transportation Research Part D 10 (2005) 197–212
5H
Inflow
199
Outflow
5H
5H
(a)
(b)
Fig. 1. The sketch of calculation domain and the grid mesh. (a) Sketch of the calculation domain. (b) Enlarged view of the grid.
turbulence production due to the buoyancy effect is included when the thermal effect in the street canyon is taken into consideration. The k equation adds a term that is the volumetric production rate by gravitational forces interacting with density gradients. With the Boussinesq approximation, the variations in density is expressed as variations in enthalpy, or in terms of the temperature. Continuity equation: oU i ¼0 oxi Momentum equation: oU i q qn 1 oP o oU i gi Uj ¼ þ t ui uj q oxi oxj oxj qn oxj
ð1Þ
ð2Þ
Pollutant concentration is calculated with the convective-diffusion equation for atmospheric: oðuj C i Þ o oC i ¼ K ð3Þ þ Si oxj oxj oxj Ci is the pollutant concentration, K is the diffusivity coefficient, Si is the pollutant source.
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Table 1 Coefficient of k–e equation Cl 0.09
rk 1.0
re 1.22
Ce1 1.44
K and e transport equations in the standard k–e turbulence model are: ok o tt ok ¼ P k e þ Gb U jk þ ot oxj rk oxj oe o tt oe e ¼ ½C e1 ðP k þ Gb Þ C e2 e U je þ ot oxj k re oxj
Ce2 1.92
ð4Þ
ð5Þ
Where Gb ¼ bgj uj h0 tt ¼ C l
k2 e
oU i oU i oU j P k ¼ tt þ oxj oxj oxi
ð6Þ ð7Þ ð8Þ
uj h0 is the turbulent heat flux, b is the thermal expansion coefficient. The constants for k–e turbulence model are summarized in Table 1. Density is a function of temperature for incompressible turbulent inert flow. When solar radiation heats the building walls or ground, the air density changes due to air temperature increases. The rate change in the air density due to an increase in temperature is estimated by: q qn ¼ bðh hn Þ; ð9Þ qn where b is the thermal expansion coefficient, qn and hn are the reference density and temperature. In this case, hn = 20 C, qn is the dry-air density at 1 atm. For example, for a wall temperature of 30 C the expansion coefficient of unite volume is calculated by: b¼
1 q qn
3:32 103 qn h hn
ð10Þ
CO is used as a representative automotive emission gas because it is relatively stable, easily measured and comes mainly from vehicle emissions. Initial concentrations are presented in dimensionless form 1. The vehicular emissions are considered as a line source located at the center of the street. The thermal stratification of the inflow is neutral, and the ambient air temperature at ground level is 20 C. Cases with and without solar radiation at different locations, such as heating at ground level, the leeward and windward sides of buildings are analyzed.1 1 All the calculations were performed using the PHOENICS code. The governing equations were discretized using a finite volume method and the SIMPLE algorithm was used to solve the equations.
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3. Results The heating from the wall surface or the ground makes the air temperature inside the street canyon higher than that of outside air. This leads to a strong buoyancy force close to the wall or the
Level 12 11 10 91 8 7 6 5 4 3 2 1
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c 1.0556E-03 9.1487E-04 7.7412E-04 6.3337E-04 5.6300E-04 4.9262E-04 4.2225E-04 3.5187E-04 2.8150E-04 2.1112E-04 1.4075E-04 7.0375E-05
94 3
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Concentration profile of no heating
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Streamline of no heating
Concentration profile of leeward heated
Streamline of leeward heated
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Concentration profile of floor heated
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5 6
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Streamline of floor heated
6 9
Streamline of windward heated
Concentration profile of windward heated
Fig. 2. Airflows and concentration profiles when the wind speed is 2 m/s (Dh = 10 C).
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ground receiving direct solar radiation that affects the flow structure and the pollutants dispersion in the canyon. Assuming that there is no sunlight shining on any solid surface or there is no difference in temperature between the walls and the air, then a clockwise vortex within the street canyon and higher concentration at leeward side of building has been found in previous studies. Level 12 11 10 9 8 7 6 5 4 3 2 1
1 2 3
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Streamline of no heating
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Concentration profile of no heating
1 4
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6
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c 1.3772E-03 1.1936E-03 1.0099E-03 8.2631E-04 7.3450E-04 6.4269E-04 5.5088E-04 4.5906E-04 3.6725E-04 2.7544E-04 1.8363E-04 9.1813E-05
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
79
54
Concentration profile of leeward heated c 3.8597E-03 3.3451E-03 2.3158E-03 1.8012E-03 1.5439E-03 1.2866E-03 1.0292E-03 7.7194E-04 6.3450E-04 5.1462E-04 4.1230E-04 2.5731E-04
1
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32
1 109
42
Level 12 11 10 9 8 7 6 5 4 3 2 1
1
Streamline of leeward heated
811
Concentration profile of floor heated
1 3
4
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6
1 4 7
c 1.3847E-02 1.2001E-02 1.0154E-02 8.3081E-03 6.4619E-03 4.6156E-03 2.7694E-03 1.8463E-03 9.2313E-04 4.5321E-04 2.8750E-04 1.2370E-04
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
1
Streamline of floor heated
3
Streamline of windward heated
c 2.1431E-03 1.8574E-03 1.5716E-03 1.2859E-03 1.1430E-03 1.0001E-03 8.5725E-04 7.1437E-04 5.7150E-04 4.2862E-04 2.8575E-04 1.4287E-04
5
Concentration profile of windward heated
Fig. 3. Airflows and concentration profiles when the wind speed is 1 m/s (Dh = 10 C).
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Considering the case of thermal radiation from the sun shining on specific locations that leads to a temperature difference of 10 C, Fig. 2. shows the airflows and concentration profiles when the wind speed is 2 m/s and the temperature difference is 10 C. When the sun shines on the leeward side of the building and the ground, the airflow structure and pollutant dispersion patterns are similar to that without solar radiation. Because the air close to the leeward side of the building is heated when the sun shines directly on this side of the building, the buoyancy flux adds to the upward advection flux along this wall, and the air will rise vertically and strengthen the original vortex and pollutant transport compared to the isothermal case. As a result the pollutant concentration decrease in the street canyon. In the case of heating the windward side of the building the situation is different. When the windward wall is warmer than the air, an upward buoyancy flux opposes the downward advection flux along the wall, and divides the flow structure into two counter-rotating cells; a clockwise top vortex and a reverse lower vortex within the canyon. As a result, pollutants are accumulated at the windward side of the building, and the pollutant concentrations in the canyon increase. If the wind speed decreases (Fig. 3), the airflow structure with the leeward side heating does not change, but the airflow structure with ground heating does. The upward buoyancy flux creates a distinctive effect on the main flow, and divides the flow structure into two counter-rotating cells. As the result, there is a higher concentration appears on the windward face than on the leeward face.
4. Influence of ground heating on street canyon flows A different airflow structure occurs when the wind speed is low. Fig. 4 shows that when the wind speed decreases further, the vortex near the leeward side combines with the upper vortex, and the new vortex is larger but the anticlockwise vortex closes to the windward side shrinks. In this case, two counter-rotating cells are parallel in street canyon, and the pollutant accumulates at the windward wall side. Fig. 5 shows the flow structure and the pollutant dispersion profile when the temperature difference between the street canyon bottom and the air (Dh) ranges from 0 C to 15 C. The upward buoyancy flux creates a distinctive effect on the main flow, thereby dividing the flow structure into
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5 1
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Streamline with Vin=0.5m/s
1
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c 4.0809E-03 3.5368E-03 2.9927E-03 2.4486E-03 1.9044E-03 1.3603E-03 1.0882E-03 8.1619E-04 5.4412E-04 3.2560E-04 2.7206E-04 1.3560E-04
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
4 5 7
Concentration profile with Vin=0.5m/s
Fig. 4. Airflows and concentration in different wind speed (floor heated) (Dh = 10 C, Vin = 0.5 m/s, 1.0 m/s (reference Fig. 1), 2 m/s (reference Fig. 2)).
X. Xie et al. / Transportation Research Part D 10 (2005) 197–212 c 4.3997E-03 3.8131E-03 3.2264E-03 2.6398E-03 2.0532E-03 1.7599E-03 1.4666E-03 1.1733E-03 8.7994E-04 7.5240E-04 5.8663E-04 2.9331E-04
41
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3
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7 5
8
2
65
Level 12 11 10 9 8 7 6 5 4 3 2 1
1
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4 11 10 7 9
Concentration profile with ∆θ = 5ºC
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2
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3
6 35
8 910
Streamline with ∆θ = 15ºC
7 1
c 3.2222E-03 2.7926E-03 2.3629E-03 1.9333E-03 1.5037E-03 1.2889E-03 1.0741E-03 8.5925E-04 6.4444E-04 4.2963E-04 3.1580E-04 2.1481E-04
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
1
Streamline with ∆θ = 5ºC
Concentration profile with ∆θ = 15ºC
Fig. 5. Airflows and concentration profiles in different temperature range (floor heated) (Vin = 1 m/s, Dh = 0 K, Dh = 5 C, Dh = 10 C (reference Fig. 1), Dh = 15 C).
two counter-rotating cells, with the vortex near the leeward wall side is coupled with the vortex in the upper of the canyon. When the temperature difference increases the vortex near the windward side expands and the anticlockwise vortex close to the leeward side shrinks due to the increase in buoyancy force. As a result, the pollutant accumulates at the windward side but the concentration in the street canyon decreases with increasing temperature differences. In Fig. 6 vertical velocity and horizontal velocity near the surfaces as well as the concentration profile are shown. The maximum vertical velocity near the leeward side is observed at roof level when the bottom is heated. This is different from the case of no heating when the maximum vertical velocity was observed at the middle part of the wall. The vertical velocity becomes higher with increasing temperature difference, the value at the same height exceed the value for no heating when Dh > 10 C. The concentration on the leeward side corresponds to the temperature difference, high temperature difference corresponds to low concentration and low temperature difference corresponds to high concentration. Vertical velocity values near the windward side are positive when the bottom is heated because the vortex near the windward side is anticlockwise. The maximum value is at upper part of the wall, and the maximum point shifts up when temperature differences increase. The vertical velocity with no heating is negative, and is maximized at Z/H = 0.7; the absolute value is almost equal to the maximum value with Dh = 15 C. The vertical velocity at Dh = 5 C wakes a minimal value at the same height. The concentration on the windward side is minimal if there is no ground heating. If the wind is light, the flow structure in the street canyon consists of two parallel vortices when the ground is heated. Thus the horizontal velocity changes its direction near the leeward side, and
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Fig. 6. Velocity and concentration near the surface in different temperature range (floor heated) (Dh = 0 K, Dh = 5 C, Dh = 10 C, Dh = 15 C).
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the value is relatively small. When the ground is not heated, the absolute value of the horizontal velocity near the floor reaches a maximum at the center of the floor. The concentration profile is governed by the flow structure. The horizontal velocity is negative when there is no heating, thus pollution at floor level is higher near the leeward side than the windward side. If the ground is heated, the pollution near the leeward side is lower than at windward side, and the value decreases with increasing temperature differences.
5. Influence of windward heating on street canyon flows When the windward wall is warmer than the air, the buoyancy generated by the warm windward wall tends to oppose the re-circulation motion and an upward buoyancy flux opposes the downward advection flux along this wall. Fig. 7 shows the flows and concentration profiles in the street canyon with windward heating and different wind speeds. When the wind speed is Vin = 3 m/s, there is a single vortex in the canyon, and the pollutant concentration is low. The buoyancy generated by the warm windward wall has a marked influence on the vortex structure when the wind speed is Vin 6 2 m/s; the flow regime changes from a one-vortex structure to a multi-vortex structure. The upper vortex shrinks and is displaced with its centre shifting towards the leeward side of the canyon, the lower vortex expands and the vortex centre shifts upwards as the wind speed declines. The pollutant accumulates at the windward side when the flow regime changes to the multi-vortex structure. The
1
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1
57
8
c 7.7756E-04 6.7389E-04 5.7021E-04 4.6654E-04 4.1470E-04 3.6286E-04 3.1103E-04 2.5919E-04 2.0735E-04 1.5551E-04 1.0368E-04 5.1838E-05
Concentration profile with Vin=3m/s
2
1
2
1
3 13
4
1
3 6 712
5
c 1.6875E-02 1.4625E-02 1.2375E-02 1.0125E-02 7.8750E-03 5.6250E-03 3.3750E-03 2.2500E-03 1.1250E-03 4.5780E-04 1.3560E-04 9.8750E-05
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
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Streamline with Vin=3m/s
Streamline with Vin=0.5m/s
6 3
Level 12 11 10 9 8 7 6 5 4 3 2 1
10
8
Concentration profile with Vin=0.5m/s
Fig. 7. Airflows and concentration profiles in different wind speed (windward heated) (Dh = 10 C, Vin = 0.5 m/s, 1.0 m/s (reference Fig. 1), 2 m/s (reference Fig. 2), Vin = 3 m/s).
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pollutant in the street canyon is dense and is accumulated not only on the leeward side but also on the windward side when the wind speed is 0.5 m/s, because the lower vortex is very weak. The flow structure and the pollutant dispersion in a street canyon with different windward temperature ranges are shown in Fig. 8. For a temperature difference of Dh = 2 C, there are two small vortices at the corner of the canyon, and the vortex at the windward side is slightly larger than those on the leeward. Pollutant accumulations appear on both sides of the street. When the temperature difference increases the flow structure changes and there are two vortices; a clockwise top vortex and a reverse ground vortex within the canyon. Pollution is accumulated at the windward side of the building, and the concentration decreases as the temperature difference increases. When the temperature difference Dh = 5 C, the lower vortex in the street canyon become weak, it is difficult for the pollutant to disperse, and the pollutant concentration is high.
Level 12 11 10 9 8 7 6 5 4 3 2 1
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1
1
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3
Concentration profile with ∆θ =2ºC
1
3 42
3 4
5
c 2.4122E-02 2.0906E-02 1.4473E-02 1.2865E-02 9.6488E-03 6.4325E-03 4.8244E-03 2.5460E-03 1.6081E-03 8.4560E-04 4.5680E-04 2.3450E-04
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Level 12 11 10 9 8 7 6 5 4 3 2 1
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Streamline with ∆θ =2ºC
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79
Concentration profile with ∆θ = 5ºC
1 2
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c 5.8959E-03 4.3237E-03 3.9306E-03 3.1445E-03 2.3584E-03 1.9653E-03 1.5723E-03 7.8613E-04 3.9306E-04 1.8456E-04 9.3152E-05 4.5987E-05
1
Level 12 11 10 9 8 7 6 5 4 3 2 1
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Streamline with ∆θ = 5ºC
Streamline with ∆θ = 15ºC
c 2.0606E-02 1.7859E-02 1.5111E-02 1.2364E-02 9.6163E-03 6.8688E-03 4.1213E-03 2.7475E-03 1.3738E-03 8.6540E-04 4.1230E-04 2.0100E-04
Concentration profile with ∆θ = 15ºC
Fig. 8. Airflows and concentration profiles in different windward-wall heating (windward heated) (Vin = 1.0 m/s, Dh = 2 C, Dh = 5 C, Dh = 10 C (reference Fig. 1), Dh = 15 C).
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Fig. 9 shows the vertical velocity, the concentration near the building wall, the horizontal velocity and concentration profile near the street floor. The vertical velocity near the leeward side is positive for Z/H P 0.5 then changes sign, this is because the lower vortex is anticlockwise and
Fig. 9. Velocity and concentration near the surface in different temperature range (windward heated) (Vin = 1.0 m/s, Dh = 0 C, Dh = 5 C, Dh = 10 C, Dh = 15 C).
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the upper one clockwise when there is heating. The absolute value of the vertical velocity increases, and the concentration near the wall decreases as the temperature difference increases. Although the vertical velocity near the leeward side is at a maximum, the concentration is maximized when there is no heating. The anticlockwise lower vortex in the street canyon extends to the top of the windward building, so the vertical velocity near the windward side is positive which differs from the no heating case. The vertical velocity near the windward side obviously increased when the temperature range increase, as a result the concentration decreases. The pollutant concentration near the windward side is the minimal when there is no heating in the wall. The pollutant dispersion near the floor is controlled by the characteristics of horizontal velocity. If there is no heating in the ground, the airflow in the canyon is strong and the horizontal velocity is large, so the concentration near the floor is less. Because the velocity is negative the concentration close to the windward side is higher than that close to the leeward side. The horizontal motion decreases when the windward wall is heated, but the horizontal velocity increase with the temperature difference increases. The pollutant concentration near the floor decreases when the temperature difference increases. When the temperature difference Dh = 5 C, there is no difference between the concentration close to leeward side and windward side, and the concentration is very high.
6. Discussion on the influence factor Eq. (11) is the dimensionless momentum equation with the added buoyancy force. The first term in the equation is the buoyancy force. hn and hw indicate the reference temperature and the wall temperature. From the momentum equation, it can be seen that the ratio between Gr and Re2 can be used to estimate the effect of the thermal radiation on the flow in the street canyon. If the parameter Gr/Re2 is 1, the motion in the canyon is induced by thermal and mechanical effects. If the parameter Gr/Re2 < 1, the motion in the canyon induced by thermal effects can be ignored. oU oU Gr h hn 1 o2 U þV ¼ 2
þ oX oY Re hw hn Re oY 2 2 Gr gbDhL3 u0 L gbDhL ¼ ¼ 2 2 m m u20 Re U
Gr gLðqn qÞ ¼ 2 qn u20 Re
ð11Þ
ð12Þ
ð13Þ
All Gr/Re2 values are listed in Table 2. If the street geometry is certain, the parameter Gr/Re2 is decided by the temperature difference Dh and the wind speed Vin. Low wind conditions and large temperature differences cause large thermal effects. The thermal effects are different when the sun warms the wall or ground of the street canyon even though the Gr/Re2 values are the same, and the airflow characteristic is different. When the windward wall is warmer than air, an upward
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Table 2 The airflow characteristic in street canyon for different Gr/Re2 Vin (m/s) 3 2 1 2 1 1 1 0.5
Dh (C) 10 5 2 10 5 10 15 10
Gr/Re2 1.1 1.22 1.96 2.44 4.9 9.8 14.6 39.04
Airflow characteristic Windward heated
Ground heated
Leeward heated
One single vortex One single vortex One single vortex Two counter-rotating Two counter-rotating Two counter-rotating Two counter-rotating Two counter-rotating
One single vortex One single vortex One single vortex One single vortex Two counter-rotating Two counter-rotating Two counter-rotating Two counter-rotating
One One One One One One One
vortex vortex vortex vortex vortex
vortex vortex vortex vortex
single single single single single single single
vortex vortex vortex vortex vortex vortex vortex
buoyancy flux opposes the downward advection flux along the wall; if Gr/Re2 > 2, the flow structure is divided into two counter-rotating cells. When the ground is heated, and Gr/Re2 > 4, the flow structure is divided into two counter-rotating cells by the upward buoyancy flux, and the vortex near the leeward side is coupled with the vortex higher up in the canyon. When the leeward side is heated, the flow structure along the street canyon changes little.
7. Validation with the wind-tunnel data To validate the model, the simulation results with H/W = 1, Vin = 3 m/s and Dh = 2 C are compared with the wind-tunnel results with a bulk Richardson number, Rb, of 0.21 used by (Uehara and Murakami, 2000). The bulk Richardson number is defined as Rb ¼
gLðhn hÞ hn u20
ð14Þ
Gr gLðqn qÞ ¼ qn u20 Re2
ð15Þ
The density of any part of the atmosphere is given almost exactly by the perfect gas law MP q¼ ð16Þ RT The air in the street canyon is considered uncompressible and M is the gas constant for the air, so the density is determined by T. ðhn hÞ ðqn qÞ ¼ hn qn Gr ¼ Rb Re2 If H = 30 m, Vin = 3 m/s and Dh = 2 C
ð17Þ ð18Þ Gr Re2
¼ Rb ¼ 0:22.
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Fig. 10. The vertical profiles of the normalized horizontal velocity at the center of a street canyon.
The vertical profiles of the normalized horizontal velocity at the center of a street canyon are compared (Fig. 10). Above the roof-level (Z/H > 1.2), the normalized horizontal velocity is larger in the numerical simulation than in the tests. It is related to the inflow boundary condition. In the numerical simulation, it is assumed that the profile of the horizontal velocity is constant at the inflow boundary. Another reason is that there is an isolated street canyon in the model. In spite of these differences, both profiles of horizontal velocity are similar to each other suggesting the numerical model may be used for simulating airflow and pollutant dispersion in an urban street canyon with the solar heating.
Acknowledgments This work was supported by the USA GM & China Scientific Research Foundation (Grant 40122201) and National Natural Science Foundation of China (Grant 50208011).
References Baker, C.J., Hargreaves, D.M., 2001. Wind tunnel evaluation of a vehicle pollution dispersion model. Journal of Wind Engineering and Industrial Aerodynamics 89, 187–200. Berkowicz, R., 1996. Using measurements of air pollution in streets for evaluation of urban air quality-meterological analysis and model calculations. The Science of the Total environment 189/190, 259–265. Chan, T.L., Dong, G., 2002. Validation of a two-dimensional pollutant dispersion model in an isolated street canyon. Atmospheric Environment 36, 861–872. Croxford, B., 1998. Siting considerations for urban pollution monitors. Atmospheric Environment 32, 1049–1057. Huang, Z., Xie, Z., Wu, Z.J., 2000. Study on dispersion of vehicle exhaust pollutant. In: Proceeding of Traffic and Environment for Communication between Taiwan and the Mainland.
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Karim, M.M., Matsuia, H., 1998. A mathematical model of wind flow, vehicle wake, and pollutant concentration in urban road microenvironments. Part I: model description. Transportation Research Part D 3, 81–92. Kastner-Klein, P., Fedorovich, E., 2001. A wind tunnel study of organized and turbulent air motions in street canyons. Journal of Wind Engineering and Industrial Aerodynamics 89, 849–861. Kastner-Klein, P., Plate, E.J., 1999. Wind-tunnel study of concentration fields in street canyons. Atmospheric Environment 33, 3973–3979. Kim, J.J., Baik, J.J., 2001. Urban street-canyon flows with bottom heating. Atmospheric Environment 35, 3395–3404. Louka, P., Vachon, G., 2001. Thermal effects on the airflow in a street canyon-nantes Õ99 experimental results and model simulation. The 3rd international conference on Urban Air Quality-Loutraki, pp. 19–23. Meroney, R.N., Pavageau, M., 1996. Study of line source characteristic for 2-D physical modeling of pollutant dispersion in street canyons. Journal of Wind Engineering and Industrial Aerodynamics 62, 37–56. Sini, J.F., 1996. Pollution dispersion and thermal effects in urban street canyon. Atmospheric Environment 30, 2659– 2677. Tao, W.Q., 1995. Numerical Heat Transfer. XiÕan Jaotong University. Uehara, K., Murakami, S., 2000. Wind tunnel experiments on how thermal stratification affects flow in and above urban street canyons. Atmospheric Environment 34, 1553–1562. Wang, J.S., Huang, Z., 2002. Prediction of atmospheric environment in urban street canyon by applying various versions of turbulence models. Journal of Shanghai Jiao Tong University 36, 1496–1499 (in Chinese).
Thermal effects on vehicle emission dispersion in an urban street canyon Xiaomin Xie *, Zhen Huang, Jiasong Wang, Zheng Xie School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200030, PR China
Abstract The impact of the thermal effects on vehicle emission dispersion within street canyons is examined. The results show that heating from building wall surfaces and horizontal surfaces lead to strong buoyancy forces close to surfaces receiving direct solar radiation. This thermally induced flow is combined with mechanically induced flows formed in the canyon where there is no solar heating, and affects the transport of pollutants from the canyon to the layer aloft. The relative influence of each of these effects can be estimates by Gr/Re2. When the windward wall is warmer than the air, an upward buoyancy flux opposes the downward advection flux along the wall; if Gr/Re2 > 2, the flow structure is divided into two counter-rotating cells, and pollutants are accumulated on the windward side of the canyon. When the horizontal surface is heated, and Gr/Re2 > 4, the flow structure is divided into two counter-rotating cells by upward buoyancy flux. Pollutants are accumulated at the windward side of the canyon. When the leeward side is heated, the buoyancy flux adds to the upward advection flux along the wall strengthening the original vortex and pollutant effects of transport compared to the isothermal case. 2005 Elsevier Ltd. All rights reserved. Keywords: Thermal effects; Vehicle emission dispersion; Street canyon; Numerical simulation
*
Corresponding author. E-mail address: [email protected] (X. Xie).
1361-9209/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.trd.2005.01.002
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1. Introduction The growth in road traffic has led to major problems of air pollution caused by vehicular exhausts, and this is now one of the primary source of urban pollution despite significant improvements in fuel and engine technology. At the same time, more very large and high buildings are constructed in dense formations within city centers, and the effects of narrow and deep street canyons on the environment have become more noticeable. They can make it difficult for vehicle exhaust gases in street canyons to disperse with urban air quality being adversely affected. Several parameters dominate the pollutant dispersion process including ambient conditions (wind speed and direction), building geometry (height, width, roof shape), street dimensions (breadth, width), thermal stratification (solar insulation and orientation, building and street thermal capacitance), vehicular movement (size, number, frequency) (Karim and Matsuia, 1998), plume buoyancy etc. The aerodynamic effects, including building geometry and architecture as well as street canyon dimensions, have been extensively studied mainly using wind-tunnel experiments (Baker and Hargreaves, 2001; Meroney and Pavageau, 1996; Kastner-Klein and Plate, 1999; Kastner-Klein and Fedorovich, 2001), numerical models (Huang et al., 2000; Chan and Dong, 2002) and occasionally deploying full-scale experiments (Croxford, 1998; Berkowicz, 1996). Thermal effects result mainly from variations in the solar heating of street walls and ground during the day; the sun warms the air near the wall or above the ground causing strong upward movements of air (Louka and Vachon, 2001; Kim and Baik, 2001). Sini (1996) studied these effects numerically using a model cavity and demonstrated that wall temperatures influence the instreet flow and its vertical transport capabilities. The aim here is to evaluate the impact of thermal effects due to sunshine on the surfaces within the street canyon using numerical simulation with validation provided by the wind tunnel data (Uehara and Murakami, 2000).
2. Numerical simulations A two-dimensional computational domain is used with wind direction assumed to be perpendicular to the street canyon. The ratio of street canyon height and width is H/W = 1, and both sides of the buildings have a same height. The computational domain is 1100 m · 360 m, a typical computational grid with 332 · 83 grid points in the horizontal and vertical directions. The sketch of the calculation domain and grid mesh is depicted in Fig. 1. The grid chosen is finer close to building and ground and then expands further away. The expansion ratio in this non-uniform grid system is 1.2. Extensive tests of the independence of the meshes are carried out with increasing mesh numbers until further refinement is shown to be less significant. k–e turbulence model is used in an isolated street canyon and the CFD modeling is based on the numerical solution of the governing fluid flow and dispersion equations, which are derived from basic conservation and transport principles: the mass conservation (continuity) equation, the two momentum conservation (Navier–Stokes) equations in x,y, and the transport equation for pollution concentration (Wang and Huang, 2002; Tao, 1995). Buoyancy forces are added in momentum conservation adopting the Boussinesq approximation. It is assumed that the density and the other physical parameters do not change except for the density in the buoyancy forces term. The
X. Xie et al. / Transportation Research Part D 10 (2005) 197–212
5H
Inflow
199
Outflow
5H
5H
(a)
(b)
Fig. 1. The sketch of calculation domain and the grid mesh. (a) Sketch of the calculation domain. (b) Enlarged view of the grid.
turbulence production due to the buoyancy effect is included when the thermal effect in the street canyon is taken into consideration. The k equation adds a term that is the volumetric production rate by gravitational forces interacting with density gradients. With the Boussinesq approximation, the variations in density is expressed as variations in enthalpy, or in terms of the temperature. Continuity equation: oU i ¼0 oxi Momentum equation: oU i q qn 1 oP o oU i gi Uj ¼ þ t ui uj q oxi oxj oxj qn oxj
ð1Þ
ð2Þ
Pollutant concentration is calculated with the convective-diffusion equation for atmospheric: oðuj C i Þ o oC i ¼ K ð3Þ þ Si oxj oxj oxj Ci is the pollutant concentration, K is the diffusivity coefficient, Si is the pollutant source.
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Table 1 Coefficient of k–e equation Cl 0.09
rk 1.0
re 1.22
Ce1 1.44
K and e transport equations in the standard k–e turbulence model are: ok o tt ok ¼ P k e þ Gb U jk þ ot oxj rk oxj oe o tt oe e ¼ ½C e1 ðP k þ Gb Þ C e2 e U je þ ot oxj k re oxj
Ce2 1.92
ð4Þ
ð5Þ
Where Gb ¼ bgj uj h0 tt ¼ C l
k2 e
oU i oU i oU j P k ¼ tt þ oxj oxj oxi
ð6Þ ð7Þ ð8Þ
uj h0 is the turbulent heat flux, b is the thermal expansion coefficient. The constants for k–e turbulence model are summarized in Table 1. Density is a function of temperature for incompressible turbulent inert flow. When solar radiation heats the building walls or ground, the air density changes due to air temperature increases. The rate change in the air density due to an increase in temperature is estimated by: q qn ¼ bðh hn Þ; ð9Þ qn where b is the thermal expansion coefficient, qn and hn are the reference density and temperature. In this case, hn = 20 C, qn is the dry-air density at 1 atm. For example, for a wall temperature of 30 C the expansion coefficient of unite volume is calculated by: b¼
1 q qn
3:32 103 qn h hn
ð10Þ
CO is used as a representative automotive emission gas because it is relatively stable, easily measured and comes mainly from vehicle emissions. Initial concentrations are presented in dimensionless form 1. The vehicular emissions are considered as a line source located at the center of the street. The thermal stratification of the inflow is neutral, and the ambient air temperature at ground level is 20 C. Cases with and without solar radiation at different locations, such as heating at ground level, the leeward and windward sides of buildings are analyzed.1 1 All the calculations were performed using the PHOENICS code. The governing equations were discretized using a finite volume method and the SIMPLE algorithm was used to solve the equations.
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3. Results The heating from the wall surface or the ground makes the air temperature inside the street canyon higher than that of outside air. This leads to a strong buoyancy force close to the wall or the
Level 12 11 10 91 8 7 6 5 4 3 2 1
1 4
3
1
2
6 2
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57 3
5
c 1.0556E-03 9.1487E-04 7.7412E-04 6.3337E-04 5.6300E-04 4.9262E-04 4.2225E-04 3.5187E-04 2.8150E-04 2.1112E-04 1.4075E-04 7.0375E-05
94 3
10 8
Concentration profile of no heating
1
1
3
2 1
6 7 4
10 835
8
c 9.2484E-04 8.0153E-04 6.7822E-04 5.5491E-04 4.9325E-04 4.3159E-04 3.6994E-04 3.0828E-04 2.4662E-04 1.8497E-04 1.2331E-04 6.1656E-05
5
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Streamline of no heating
Concentration profile of leeward heated
Streamline of leeward heated
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c 8.4497E-04 7.3231E-04 6.1964E-04 1 5.0698E-04 4.5065E-04 3.9432E-04 3.3799E-04 2.8166E-04 2.2532E-04 1.6899E-04 1.1266E-04 5.6331E-05
4
4
Concentration profile of floor heated
1 4
2
1
3
7
2
3
c 4.5684E-03 3.9593E-03 3.3502E-03 2.4365E-03 1.8274E-03 1.2183E-03 9.1369E-04 6.0913E-04 4.5620E-04 3.0456E-04 2.1450E-04 1.3240E-04
5 6
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3
Streamline of floor heated
6 9
Streamline of windward heated
Concentration profile of windward heated
Fig. 2. Airflows and concentration profiles when the wind speed is 2 m/s (Dh = 10 C).
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ground receiving direct solar radiation that affects the flow structure and the pollutants dispersion in the canyon. Assuming that there is no sunlight shining on any solid surface or there is no difference in temperature between the walls and the air, then a clockwise vortex within the street canyon and higher concentration at leeward side of building has been found in previous studies. Level 12 11 10 9 8 7 6 5 4 3 2 1
1 2 3
5
1
4
72
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4
6
1 2
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Streamline of no heating
65
Concentration profile of no heating
1 4
5
2 1
3
8
4
7 31
6
8
c 1.3772E-03 1.1936E-03 1.0099E-03 8.2631E-04 7.3450E-04 6.4269E-04 5.5088E-04 4.5906E-04 3.6725E-04 2.7544E-04 1.8363E-04 9.1813E-05
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
79
54
Concentration profile of leeward heated c 3.8597E-03 3.3451E-03 2.3158E-03 1.8012E-03 1.5439E-03 1.2866E-03 1.0292E-03 7.7194E-04 6.3450E-04 5.1462E-04 4.1230E-04 2.5731E-04
1
7
4
5
2 3
6
32
1 109
42
Level 12 11 10 9 8 7 6 5 4 3 2 1
1
Streamline of leeward heated
811
Concentration profile of floor heated
1 3
4
2
6
1 4 7
c 1.3847E-02 1.2001E-02 1.0154E-02 8.3081E-03 6.4619E-03 4.6156E-03 2.7694E-03 1.8463E-03 9.2313E-04 4.5321E-04 2.8750E-04 1.2370E-04
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
1
Streamline of floor heated
3
Streamline of windward heated
c 2.1431E-03 1.8574E-03 1.5716E-03 1.2859E-03 1.1430E-03 1.0001E-03 8.5725E-04 7.1437E-04 5.7150E-04 4.2862E-04 2.8575E-04 1.4287E-04
5
Concentration profile of windward heated
Fig. 3. Airflows and concentration profiles when the wind speed is 1 m/s (Dh = 10 C).
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Considering the case of thermal radiation from the sun shining on specific locations that leads to a temperature difference of 10 C, Fig. 2. shows the airflows and concentration profiles when the wind speed is 2 m/s and the temperature difference is 10 C. When the sun shines on the leeward side of the building and the ground, the airflow structure and pollutant dispersion patterns are similar to that without solar radiation. Because the air close to the leeward side of the building is heated when the sun shines directly on this side of the building, the buoyancy flux adds to the upward advection flux along this wall, and the air will rise vertically and strengthen the original vortex and pollutant transport compared to the isothermal case. As a result the pollutant concentration decrease in the street canyon. In the case of heating the windward side of the building the situation is different. When the windward wall is warmer than the air, an upward buoyancy flux opposes the downward advection flux along the wall, and divides the flow structure into two counter-rotating cells; a clockwise top vortex and a reverse lower vortex within the canyon. As a result, pollutants are accumulated at the windward side of the building, and the pollutant concentrations in the canyon increase. If the wind speed decreases (Fig. 3), the airflow structure with the leeward side heating does not change, but the airflow structure with ground heating does. The upward buoyancy flux creates a distinctive effect on the main flow, and divides the flow structure into two counter-rotating cells. As the result, there is a higher concentration appears on the windward face than on the leeward face.
4. Influence of ground heating on street canyon flows A different airflow structure occurs when the wind speed is low. Fig. 4 shows that when the wind speed decreases further, the vortex near the leeward side combines with the upper vortex, and the new vortex is larger but the anticlockwise vortex closes to the windward side shrinks. In this case, two counter-rotating cells are parallel in street canyon, and the pollutant accumulates at the windward wall side. Fig. 5 shows the flow structure and the pollutant dispersion profile when the temperature difference between the street canyon bottom and the air (Dh) ranges from 0 C to 15 C. The upward buoyancy flux creates a distinctive effect on the main flow, thereby dividing the flow structure into
2
1
23
3
5 1
6
4
8
Streamline with Vin=0.5m/s
1
4
362
c 4.0809E-03 3.5368E-03 2.9927E-03 2.4486E-03 1.9044E-03 1.3603E-03 1.0882E-03 8.1619E-04 5.4412E-04 3.2560E-04 2.7206E-04 1.3560E-04
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
4 5 7
Concentration profile with Vin=0.5m/s
Fig. 4. Airflows and concentration in different wind speed (floor heated) (Dh = 10 C, Vin = 0.5 m/s, 1.0 m/s (reference Fig. 1), 2 m/s (reference Fig. 2)).
X. Xie et al. / Transportation Research Part D 10 (2005) 197–212 c 4.3997E-03 3.8131E-03 3.2264E-03 2.6398E-03 2.0532E-03 1.7599E-03 1.4666E-03 1.1733E-03 8.7994E-04 7.5240E-04 5.8663E-04 2.9331E-04
41
2
3
3
6
7 5
8
2
65
Level 12 11 10 9 8 7 6 5 4 3 2 1
1
204
4 11 10 7 9
Concentration profile with ∆θ = 5ºC
1
4
2
5
3
6 35
8 910
Streamline with ∆θ = 15ºC
7 1
c 3.2222E-03 2.7926E-03 2.3629E-03 1.9333E-03 1.5037E-03 1.2889E-03 1.0741E-03 8.5925E-04 6.4444E-04 4.2963E-04 3.1580E-04 2.1481E-04
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
1
Streamline with ∆θ = 5ºC
Concentration profile with ∆θ = 15ºC
Fig. 5. Airflows and concentration profiles in different temperature range (floor heated) (Vin = 1 m/s, Dh = 0 K, Dh = 5 C, Dh = 10 C (reference Fig. 1), Dh = 15 C).
two counter-rotating cells, with the vortex near the leeward wall side is coupled with the vortex in the upper of the canyon. When the temperature difference increases the vortex near the windward side expands and the anticlockwise vortex close to the leeward side shrinks due to the increase in buoyancy force. As a result, the pollutant accumulates at the windward side but the concentration in the street canyon decreases with increasing temperature differences. In Fig. 6 vertical velocity and horizontal velocity near the surfaces as well as the concentration profile are shown. The maximum vertical velocity near the leeward side is observed at roof level when the bottom is heated. This is different from the case of no heating when the maximum vertical velocity was observed at the middle part of the wall. The vertical velocity becomes higher with increasing temperature difference, the value at the same height exceed the value for no heating when Dh > 10 C. The concentration on the leeward side corresponds to the temperature difference, high temperature difference corresponds to low concentration and low temperature difference corresponds to high concentration. Vertical velocity values near the windward side are positive when the bottom is heated because the vortex near the windward side is anticlockwise. The maximum value is at upper part of the wall, and the maximum point shifts up when temperature differences increase. The vertical velocity with no heating is negative, and is maximized at Z/H = 0.7; the absolute value is almost equal to the maximum value with Dh = 15 C. The vertical velocity at Dh = 5 C wakes a minimal value at the same height. The concentration on the windward side is minimal if there is no ground heating. If the wind is light, the flow structure in the street canyon consists of two parallel vortices when the ground is heated. Thus the horizontal velocity changes its direction near the leeward side, and
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Fig. 6. Velocity and concentration near the surface in different temperature range (floor heated) (Dh = 0 K, Dh = 5 C, Dh = 10 C, Dh = 15 C).
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the value is relatively small. When the ground is not heated, the absolute value of the horizontal velocity near the floor reaches a maximum at the center of the floor. The concentration profile is governed by the flow structure. The horizontal velocity is negative when there is no heating, thus pollution at floor level is higher near the leeward side than the windward side. If the ground is heated, the pollution near the leeward side is lower than at windward side, and the value decreases with increasing temperature differences.
5. Influence of windward heating on street canyon flows When the windward wall is warmer than the air, the buoyancy generated by the warm windward wall tends to oppose the re-circulation motion and an upward buoyancy flux opposes the downward advection flux along this wall. Fig. 7 shows the flows and concentration profiles in the street canyon with windward heating and different wind speeds. When the wind speed is Vin = 3 m/s, there is a single vortex in the canyon, and the pollutant concentration is low. The buoyancy generated by the warm windward wall has a marked influence on the vortex structure when the wind speed is Vin 6 2 m/s; the flow regime changes from a one-vortex structure to a multi-vortex structure. The upper vortex shrinks and is displaced with its centre shifting towards the leeward side of the canyon, the lower vortex expands and the vortex centre shifts upwards as the wind speed declines. The pollutant accumulates at the windward side when the flow regime changes to the multi-vortex structure. The
1
4
14
5
62
2
3
1
1
57
8
c 7.7756E-04 6.7389E-04 5.7021E-04 4.6654E-04 4.1470E-04 3.6286E-04 3.1103E-04 2.5919E-04 2.0735E-04 1.5551E-04 1.0368E-04 5.1838E-05
Concentration profile with Vin=3m/s
2
1
2
1
3 13
4
1
3 6 712
5
c 1.6875E-02 1.4625E-02 1.2375E-02 1.0125E-02 7.8750E-03 5.6250E-03 3.3750E-03 2.2500E-03 1.1250E-03 4.5780E-04 1.3560E-04 9.8750E-05
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
2
Streamline with Vin=3m/s
Streamline with Vin=0.5m/s
6 3
Level 12 11 10 9 8 7 6 5 4 3 2 1
10
8
Concentration profile with Vin=0.5m/s
Fig. 7. Airflows and concentration profiles in different wind speed (windward heated) (Dh = 10 C, Vin = 0.5 m/s, 1.0 m/s (reference Fig. 1), 2 m/s (reference Fig. 2), Vin = 3 m/s).
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pollutant in the street canyon is dense and is accumulated not only on the leeward side but also on the windward side when the wind speed is 0.5 m/s, because the lower vortex is very weak. The flow structure and the pollutant dispersion in a street canyon with different windward temperature ranges are shown in Fig. 8. For a temperature difference of Dh = 2 C, there are two small vortices at the corner of the canyon, and the vortex at the windward side is slightly larger than those on the leeward. Pollutant accumulations appear on both sides of the street. When the temperature difference increases the flow structure changes and there are two vortices; a clockwise top vortex and a reverse ground vortex within the canyon. Pollution is accumulated at the windward side of the building, and the concentration decreases as the temperature difference increases. When the temperature difference Dh = 5 C, the lower vortex in the street canyon become weak, it is difficult for the pollutant to disperse, and the pollutant concentration is high.
Level 12 11 10 9 8 7 6 5 4 3 2 1
2
1
1
2
4
12
3 3
3
Concentration profile with ∆θ =2ºC
1
3 42
3 4
5
c 2.4122E-02 2.0906E-02 1.4473E-02 1.2865E-02 9.6488E-03 6.4325E-03 4.8244E-03 2.5460E-03 1.6081E-03 8.4560E-04 4.5680E-04 2.3450E-04
2
Level 12 11 10 9 8 7 6 5 4 3 2 1
1
Streamline with ∆θ =2ºC
2
6
8 11 12
79
Concentration profile with ∆θ = 5ºC
1 2
3 4
2
5
3
1
2
3
4
1
6 10
2 7 8
c 5.8959E-03 4.3237E-03 3.9306E-03 3.1445E-03 2.3584E-03 1.9653E-03 1.5723E-03 7.8613E-04 3.9306E-04 1.8456E-04 9.3152E-05 4.5987E-05
1
Level 12 11 10 9 8 7 6 5 4 3 2 1
1
Streamline with ∆θ = 5ºC
Streamline with ∆θ = 15ºC
c 2.0606E-02 1.7859E-02 1.5111E-02 1.2364E-02 9.6163E-03 6.8688E-03 4.1213E-03 2.7475E-03 1.3738E-03 8.6540E-04 4.1230E-04 2.0100E-04
Concentration profile with ∆θ = 15ºC
Fig. 8. Airflows and concentration profiles in different windward-wall heating (windward heated) (Vin = 1.0 m/s, Dh = 2 C, Dh = 5 C, Dh = 10 C (reference Fig. 1), Dh = 15 C).
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Fig. 9 shows the vertical velocity, the concentration near the building wall, the horizontal velocity and concentration profile near the street floor. The vertical velocity near the leeward side is positive for Z/H P 0.5 then changes sign, this is because the lower vortex is anticlockwise and
Fig. 9. Velocity and concentration near the surface in different temperature range (windward heated) (Vin = 1.0 m/s, Dh = 0 C, Dh = 5 C, Dh = 10 C, Dh = 15 C).
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the upper one clockwise when there is heating. The absolute value of the vertical velocity increases, and the concentration near the wall decreases as the temperature difference increases. Although the vertical velocity near the leeward side is at a maximum, the concentration is maximized when there is no heating. The anticlockwise lower vortex in the street canyon extends to the top of the windward building, so the vertical velocity near the windward side is positive which differs from the no heating case. The vertical velocity near the windward side obviously increased when the temperature range increase, as a result the concentration decreases. The pollutant concentration near the windward side is the minimal when there is no heating in the wall. The pollutant dispersion near the floor is controlled by the characteristics of horizontal velocity. If there is no heating in the ground, the airflow in the canyon is strong and the horizontal velocity is large, so the concentration near the floor is less. Because the velocity is negative the concentration close to the windward side is higher than that close to the leeward side. The horizontal motion decreases when the windward wall is heated, but the horizontal velocity increase with the temperature difference increases. The pollutant concentration near the floor decreases when the temperature difference increases. When the temperature difference Dh = 5 C, there is no difference between the concentration close to leeward side and windward side, and the concentration is very high.
6. Discussion on the influence factor Eq. (11) is the dimensionless momentum equation with the added buoyancy force. The first term in the equation is the buoyancy force. hn and hw indicate the reference temperature and the wall temperature. From the momentum equation, it can be seen that the ratio between Gr and Re2 can be used to estimate the effect of the thermal radiation on the flow in the street canyon. If the parameter Gr/Re2 is 1, the motion in the canyon is induced by thermal and mechanical effects. If the parameter Gr/Re2 < 1, the motion in the canyon induced by thermal effects can be ignored. oU oU Gr h hn 1 o2 U þV ¼ 2
þ oX oY Re hw hn Re oY 2 2 Gr gbDhL3 u0 L gbDhL ¼ ¼ 2 2 m m u20 Re U
Gr gLðqn qÞ ¼ 2 qn u20 Re
ð11Þ
ð12Þ
ð13Þ
All Gr/Re2 values are listed in Table 2. If the street geometry is certain, the parameter Gr/Re2 is decided by the temperature difference Dh and the wind speed Vin. Low wind conditions and large temperature differences cause large thermal effects. The thermal effects are different when the sun warms the wall or ground of the street canyon even though the Gr/Re2 values are the same, and the airflow characteristic is different. When the windward wall is warmer than air, an upward
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Table 2 The airflow characteristic in street canyon for different Gr/Re2 Vin (m/s) 3 2 1 2 1 1 1 0.5
Dh (C) 10 5 2 10 5 10 15 10
Gr/Re2 1.1 1.22 1.96 2.44 4.9 9.8 14.6 39.04
Airflow characteristic Windward heated
Ground heated
Leeward heated
One single vortex One single vortex One single vortex Two counter-rotating Two counter-rotating Two counter-rotating Two counter-rotating Two counter-rotating
One single vortex One single vortex One single vortex One single vortex Two counter-rotating Two counter-rotating Two counter-rotating Two counter-rotating
One One One One One One One
vortex vortex vortex vortex vortex
vortex vortex vortex vortex
single single single single single single single
vortex vortex vortex vortex vortex vortex vortex
buoyancy flux opposes the downward advection flux along the wall; if Gr/Re2 > 2, the flow structure is divided into two counter-rotating cells. When the ground is heated, and Gr/Re2 > 4, the flow structure is divided into two counter-rotating cells by the upward buoyancy flux, and the vortex near the leeward side is coupled with the vortex higher up in the canyon. When the leeward side is heated, the flow structure along the street canyon changes little.
7. Validation with the wind-tunnel data To validate the model, the simulation results with H/W = 1, Vin = 3 m/s and Dh = 2 C are compared with the wind-tunnel results with a bulk Richardson number, Rb, of 0.21 used by (Uehara and Murakami, 2000). The bulk Richardson number is defined as Rb ¼
gLðhn hÞ hn u20
ð14Þ
Gr gLðqn qÞ ¼ qn u20 Re2
ð15Þ
The density of any part of the atmosphere is given almost exactly by the perfect gas law MP q¼ ð16Þ RT The air in the street canyon is considered uncompressible and M is the gas constant for the air, so the density is determined by T. ðhn hÞ ðqn qÞ ¼ hn qn Gr ¼ Rb Re2 If H = 30 m, Vin = 3 m/s and Dh = 2 C
ð17Þ ð18Þ Gr Re2
¼ Rb ¼ 0:22.
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Fig. 10. The vertical profiles of the normalized horizontal velocity at the center of a street canyon.
The vertical profiles of the normalized horizontal velocity at the center of a street canyon are compared (Fig. 10). Above the roof-level (Z/H > 1.2), the normalized horizontal velocity is larger in the numerical simulation than in the tests. It is related to the inflow boundary condition. In the numerical simulation, it is assumed that the profile of the horizontal velocity is constant at the inflow boundary. Another reason is that there is an isolated street canyon in the model. In spite of these differences, both profiles of horizontal velocity are similar to each other suggesting the numerical model may be used for simulating airflow and pollutant dispersion in an urban street canyon with the solar heating.
Acknowledgments This work was supported by the USA GM & China Scientific Research Foundation (Grant 40122201) and National Natural Science Foundation of China (Grant 50208011).
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