periodic flow & pollutant removal of street canyon in ...

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

PERIODIC FLOW & POLLUTANT REMOVAL OF STREET CANYON IN WINDBUOYANCY-DRIVEN CONDITION USING THE URANS MODEL W.C. Cheng, Chun-Ho Liu and Dennis Y.C. Leung Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China

Abstract An URANS model with the renormalization group (RNG) k-ε turbulence model was constructed to look into the effects of unstable stratification on the periodic pollutant removal from street canyons. Four different levels of stratification (ground heating) were considered in which well developed periodic flow behaviors were observed. The street canyon ventilation & pollutant removal performance were also examined in details. The results confirmed that ground heating helps both street canyon ventilation & pollutant removal. Key words: pollutant removal, urban street canyon, wind-buoyancy-driven 1. INTRODUCTION In the last decade, vast amount of studies have been performed to characterize the street canyon ventilation & pollutant removal performance under different prevalent wind conditions & building configurations. Most of these studies focused on isothermal condition & comparatively less on the effects of thermal stratification (Li et al. 2006). In practice, stratification is unavoidable in diurnal cycle that plays a major role in the ventilation & pollutant removal mechanisms of street canyons. By solving the Reynolds-averaged Navier-Stokes (RANS) equations with the standard k-ε turbulence model, Sini et al. (1994) investigated the effects of different facade heating on the ventilation of street canyons of different building-height-to-street-width (aspect) ratios (h/b). It was found that the wind is largely influenced by the wall temperature. Later, Uehara et al. (2000) used a stratified wind tunnel to examine the flow patterns inside street canyons in both stable & unstable conditions. It was found that the flow is enhanced in unstable stratification but is weaken in stable stratification. Afterward, Kim & Baik (2001), Xie et al. (2006) & Cheng et al. (2009) used RANS models to reveal the detailed behaviors of street canyon ventilation & pollutant removal under various heating configurations & building geometries. Recently, Baik et al. (2007) & Kang et al. (2008) used unsteady-state RANS (URANS) models to study the transport of reactive pollutants in a ground-heated street canyon. Though their focus was chemistry of pollutants, oscillations in wind & temperature were observed. In this paper, an URANS model equipped with the renormalization group (RNG) k-ε turbulence model was constructed to look into the effects of unstable stratification on the pollutant removal. Four different levels of stratification were considered. Well developed periodic behaviors of flow variables were observed for the cases with ground heating. The street canyon ventilation & pollutant removal were also examined in details. The results confirmed that ground heating indeed helps both street canyon ventilation & pollutant removal. 2. CFD MODEL AND COMPUTATIONAL DOMAIN Incompressible URANS model equipped with the RNG k-ε turbulence model was used. The simulation was performed by the commercial code FLUENT (FLUENT 2009). The computational domain consists of 13 street canyons regularly aligned under the shear layer (Figure 1). The height of shear layer hf (= 6h) & height of street canyon h (= b = w) are used in the current study. Symmetry boundary condition is applied at the upper boundary to direct the flow parallel to the domain boundary. Wind profile, U(z) =U0[(zh)/hf]α where α (= 0.28) is the exponent, is applied at the domain inlet at Re = U0h/ν =12,000, where ν is the kinematic viscosity. No-slip boundary condition is used for all building roofs, facades & streets. A constant concentration (Φ0) of passive scalar is adopted on the street of the center street canyon to model traffic emission. In case with unstable stratifications, all the streets are raised to a fixed temperature (Θ0 +ΔΘ), where Θ0 is the ambient temperature of free-stream air. Simulations at various Richardson number Ri = -gh/U02×ΔΘ/Θ0 (= 0, -8.2, -12.3 & -16.3) were performed where g is the gravitation acceleration. More than two million triangular elements were used.

Figure 1. Computational domain.


3. RESULTS & DISCUSSIONS 3.1 ACH, PCH & Θ The formulations of air (ACH) & pollutant (PCH) exchange rates for steady-state RANS model were reported in Cheng et al. (2009). They were slightly modified for the current URANS study. ACH measures the flow rate of air being removed from the street canyon whose mathematical expression is given by

1 ⎡ 2k ⎛ ∂w ⎞ ⎤ w + ⎢ − 2ν t ⎜ (1) ⎟ ⎥ dx. 2 ∫Γroof 3 ⎝ ∂z ⎠ ⎦ ⎣ Here w is the vertical velocity component, k the turbulent kinetic energy (TKE), νt the turbulent kinematic viscosity & Γroof the roof of street canyon. Overlines represent Reynolds-averaged quantities. On the righthand side of Equation (1), the first ( ACH ) & second (ACH’) terms correspond to the contributions from Reynolds-averaged & fluctuating velocities, respectively. Due to continuity, the rates of air going in & moving out of the street canyon are the same that equals 1/2 of the mean vertical velocity integral along Γroof. ACH =

For the pollutant emitted at ground level of the center street canyon, PCH is defined as the integral of pollutant flux normal to Γroof whose mathematical expression is

∂c dx, (2) ∂z where c is the pollutant concentration & Dt the turbulent diffusivity. Similar to ACH, the first term ( PCH ) inside the integral in Equation (2) corresponds to the pollutant flux by Reynolds-averaged wind field & the second term (PCH’) corresponds to the pollutant flux by turbulence. In addition to ACH & PCH, the average pollutant concentration Ω in the center street canyon is calculated to measure the overall air quality PCH = ∫

Γ roof

Ω= Here, V is the volume of the street canyon.

wc − Dt

1 cdx. V ∫V

(3)

3.2 Streamfunction & pollutant concentration contours Upon heating, a substantial modification in flow pattern is observed inside the street canyon. A secondary recirculation is initiated at the ground-level windward corner as a result of heating (Figure 2). It then pushes the primary recirculation up toward the leeward side. The primary recirculation thus crosses the canyon roof that ends up in better ventilation. The streamlines for the cases at Ri = -8.2, -12.3 & -16.3 exhibit similar shapes but the recirculatiing wind speed is found to increase with decreasing Ri. A decrease in the overall pollutant concentration inside the street canyon is also observed as Ri decreases (Figure 3). For increasing the wind speed inside the street canyon, the pollutant removal becomes more effective. Significant decreases in pollutant concentration are observed on the leeward side once heating is switched on. Although the secondary recirculation causes some trapping of pollutant on the windward side, the (overall) pollutant concentration inside the street canyon decreases at large.

Figure 2 Streamlines inside street canyons. Ri =: (a) 0, (b) -8.2, (c) -12.3 & (d) -16.3.

Figure 3 Pollutant concentration inside street canyons. Ri =: (a) 0, (b) -8.2, (c) -12.3 & (d) -16.3.


Figure 4 Temporal behavior of vertical velocity fluctuation at (-0.9h, h). Ri =: (a) 0, (b) -8.2, (c) -12.3 & (d) -16.3.

Figure 5 Temporal behavior of pollutant concentration fluctuation at (-0.9h, h). Ri =: (a) 0, (b) -8.2, (c) -12.3 & (d) -16.3.

3.3 Periodic behavior Once heating is switched on, periodic behaviors of flow & pollutant transport are found in the street canyon. The oscillation starts at the street level of street canyons where is kept at a higher temperature (Ө0+ΔӨ). The oscillating wind is carried by the primary recirculation from the ground level to the leeward side. As a result, a larger oscillating aptitude is observed on the leeward side than that on the windward side. The fluctuations of vertical velocity & pollutant concentration at point (-0.9h, h) (leeward side near the canyon roof) are shown, respectively, in Figures 4 & 5. The notation corresponds to temporal average. Consistent periodic behaviors are observed under unstable stratification at Ri = -8.2, -12.3 & -16.3. For w, the aptitude of oscillation is about 1% of the U0 for Ri = -8.2. As Ri decreases, the fluctuating aptitude also decreases. In addition, as Ri decrease from -8.2 to -16.3 (more unstable), the oscillating behaviors change from sinusoidal forms to more complex oscillating forms. For c, the general behavior is similar to its w counterpart. Its aptitude of oscillation is about 0.03% of Ф0 at Ri = -8.2. Decreasing Ri also leads to the aptitude decreases. Similar to the vertical velocity component, the oscillating behavior of c changes from a sinusoidal form to a more complex form as Ri decreases from -8.2 to -16.3. The unsteady nature of unstable stratification could be one of the reasons for the aforementioned oscillating behaviors at different Ri. As buoyancy increases, the level of unsteadiness increases, & therefore the oscillating behaviors become more complex (from one sinusoidal wave to linear combination of several sinusoidal waves). Eventually, a more complex oscillating behavior is observed for the case at lower Ri (more unstable). Moreover, URANS models the turbulence of all the length scales. The temporal behaviors of the flows & pollutant transport were not captured in details that is not comprehensive enough to explain the characteristic oscillations at different Ri. Additional work is currently being undertaken to look into this aspect. 3.4 ACH, PCH & Θ The values of ACH, PCH & Θ are calculated for all the cases considered. Both the ACH & ACH’ are found to increase with decreasing Ri (Figure 5). The magnitudes of ACH & ACH’ are observed to increase with nearly the same amount with decreasing Ri. These results are consistent with previous findings available in literature using steady-state RANS models (Xie at al. 2006, Cheng et al. 2009). For pollutant removal, the PCH is found to increase with decreasing Ri (Figure 5b). However, the PCH’ attains its maximum value at Ri ~ -10 & decreases thereafter with further decrease in Ri. The reason behind is that the PCH’ is estimated from the gradient of pollutant concentration. As shown in Figure 3, owing to the rising primary recirculation in unstable stratification, the vertical pollutant concentration gradient at the roof level decreases with decreasing Ri. Hence, PCH’ turns back to decrease when the unstable stratification exceeds certain values (Ri ~ -10 in the current configuration). Because PCH increases & PCH’ decreases with decreasing Ri, the total (dimensionless) PCH converges to a value of 9×10-4 when Ri is down to -16.3. A decrease in Ω is also observed as Ri decreases (Figure 5c) that is consistent with the discussion in Section 3.1. The results reported above are therefore collectively suggesting that unstable stratification improves air quality of street canyons at large.


Figure 5 (a) against –Ri, (b) against –Ri (c) Θ against –Ri. {: Total or , : or , △:< ACH > or < PCH >. 4. CONCLUSION An unsteady-state model based on the Reynolds-averaged Navier-Stokes (URANS) equations & renormalization group (RNG) k-ε turbulence model was constructed to investigate the street canyon ventilation & pollutant removal, together with their periodic behaviors in unstable stratifications. Simulations at Ri = 0, -8.2, -12.3 & -16.3 were tested. It is found that, upon heating, a secondary recirculation is formed at the ground-level windward corner. The newly formed secondary recirculation pushes the primary recirculation upward to the leeward side. This intensified recirculation in the core implies better street canyon ventilation compared with the case in isothermal conditions. In addition, with heating on the street surface, a decrease in pollutant concentration is observed in most area of the street canyon which suggests that the overall air quality inside the street canyon is improved. Oscillating/periodic flow behavior is observed whenever heating is present in the street canyon. For both the vertical wind velocity & pollutant concentration, the aptitudes are found to decrease with decreasing Ri. As Ri decreases from 0 to -16.3, the flow changes from a stationary solution to oscillating with a simple sinusoidal form & eventually oscillation in a comparatively complex form. The change is believed to be caused by the unsteady-state nature of buoyancy which makes the originally steady-state problem to become more unstable with decreasing Ri. The formulations of air (ACH) & pollutant (PCH) exchange rates are applied in this paper to examine the street canyon ventilation behavior. Both the mean & turbulent components of ACH are found to increase as Ri decreases with nearly the same magnitude. For PCH, the mean component is also found to increase with decreasing Ri while the turbulent component initially increases then decreases as Ri decreases. This is due to the decrease of vertical pollutant concentration gradient as the primary recirculation rises up as a result of ground-level heating. A decrease in street canyon average pollutant concentration (Ω) is found with decreasing Ri which suggests the better air quality inside street canyons in unstable stratification. References Baik, J.J., Kang, Y.S., Kim, J.J., 2007. Modeling reactive pollutant dispersion in an urban street canyon, Atmos. Environ., 41, 934-949. Cheng, W.C., Liu, C.-H., Leung, D.Y.C. 2008. Computational formulation for the evaluation of street canyon ventilation and pollutant removal performance, Atmos. Environ., 42, 9041-9051. Cheng, W.C., Liu, C.-H., Leung, D.Y.C., 2009. On the correlation of air and pollutant exchange for street canyons in combined wind-buoyancy-driven flow, Atmos. Environ., in press. FLUENT 2009. http://www.fluent.com/. Kang, Y.S., Baik, J.J., Kim, J.J., 2008. Further studies of flow and reactive pollutant dispersion in a street canyon with bottom heating, Atmos. Environ., 42, 4964-4975. Kim, J.-J., Baik, J.-J., 2001. Urban street-canyon flows with bottom heating, Atmos. Environ., 35, 3395-3404. Li, X.-X., Liu, C.-H., Leung, D.Y.C., Lam, K.M., 2006. Recent progress in CFD modeling of wind field and pollutant transport in street canyons, Atmos. Environ., 40, 5640-5658. Sini, J.-F., Anquetin, S., Mestayer, P.G., 1996. Pollutant dispersion and thermal effects in urban street canyon, Atmos. Environ., 30, 2659-2677. Uehara, U., Murakami, S., Oikawa, S., Wakamatsu, S., 2000. Wind tunnel experiments on how thermal stratification affects flow in and above urban street canyons, Atmos. Environ., 34, 1553-1562. Xie, X., Liu, C.-H., Leung, D.Y.C., Leung, M.K.H., 2006. Characteristics of air exchange in a street canyon with ground heating, Atmos. Environ., 40, 6396-6409.