Impacts of Realistic Urban Heating, Part I: Spatial Variability of Mean Flow, Turbulent Exchange and Pollutant Dispersion

Abstract

As urbanization progresses, more realistic methods are required to analyze the urban microclimate. However, given the complexity and computational cost of numerical models, the effects of realistic representations should be evaluated to identify the level of detail required for an accurate analysis. We consider the realistic representation of surface heating in an idealized three-dimensional urban configuration, and evaluate the spatial variability of flow statistics (mean flow and turbulent fluxes) in urban streets. Large-eddy simulations coupled with an urban energy balance model are employed, and the heating distribution of urban surfaces is parametrized using sets of horizontal and vertical Richardson numbers, characterizing thermal stratification and heating orientation with respect to the wind direction. For all studied conditions, the thermal field is strongly affected by the orientation of heating with respect to the airflow. The modification of airflow by the horizontal heating is also pronounced for strongly unstable conditions. The formation of the canyon vortices is affected by the three-dimensional heating distribution in both spanwise and streamwise street canyons, such that the secondary vortex is seen adjacent to the windward wall. For the dispersion field, however, the overall heating of urban surfaces, and more importantly, the vertical temperature gradient, dominate the distribution of concentration and the removal of pollutants from the building canyon. Accordingly, the spatial variability of concentration is not significantly affected by the detailed heating distribution. The analysis is extended to assess the effects of three-dimensional surface heating on turbulent transfer. Quadrant analysis reveals that the differential heating also affects the dominance of ejection and sweep events and the efficiency of turbulent transfer (exuberance) within the street canyon and at the roof level, while the vertical variation of these parameters is less dependent on the detailed heating of urban facets.

Appendices

Appendix 1: Supplementary Information on Model Validation

The energy balance model (TUF-IOBES) by Yaghoobian and Kleissl (2012) was validated by comparing the change of modelled interior wall temperature in response to a step change in outside air temperature with an analytical solution as well as other models. The difference between the analytical solution and the TUF-IOBES model was less than 2.3% which was lower than other numerical models, including the 5% difference reported for the CBS-MASS model (Zmeureanu et al. 1987).

Fig. 12

Left: vertical profile of exuberance [$Exu=(S_1+S_3)/(S_2+S_4)$]. Right: joint probability density functions calculated for current LES results and compared with the DNS of Coceal et al. (2007a) for neutral conditions

The PALM model for unstable flow in the urban canopy was validated by Park et al. (2012) against the wind-tunnel measurements of Uehara et al. (2000). The agreement in the vertical profiles of the normalized streamwise horizontal velocity and temperature supported the validity of the temperature wall function in the PALM model. The normalized scalar concentration simulated using the PALM model was successfully validated against wind-tunnel data of Meroney et al. (1996) with $R^2=0.97$.

The coupling of the TUF-IOBES and PALM models was validated against data from the wind-tunnel experiment of Kovar-Panskus et al. (2002) for a two-dimensional street canyon with a heated windward wall, and also compared with the LES results of Cai (2012). Both numerical studies showed that based on mass conservation (downward mass flux into the canyon near the windward wall equals the upward mass flux out of the canyon near the leeward wall) the primary vortex should be shifted to the right which is different from the sketch provided by Kovar-Panskus et al. (2002) and rendered this portion of the experimental data questionable. The agreement with the Cai (2012) numerical simulation is encouraging.

Here, the quadrant analysis obtained by LES are compared with DNS of aligned arrays of cubes at $Re_\mathrm{H}=5800$ for a neutral case performed by Coceal et al. (2007a). The DNS data are gathered every 0.005 s at heights 0.5H and 1.5H for 100T, where $T=H/u_\tau$, and $u_\tau$ is the friction velocity. LES results are outputted at various locations every $3\,{\mathrm{s}}$ for a period of $8\,{\mathrm{h}}$, therefore the number of data points are similar for the comparison. Grid resolutions relative to H are similar with 32 and 30 grid points per H for DNS and LES runs, respectively. Figure 12 shows close agreement in the shape of the quadrants, the frequency of events, as well as the value of exuberance at heights 0.5H and 1.5H at the centre of the canyon.

Appendix 2: Supplementary Information on Simulation Set-Up

This section describes the simulation set-up in more detail. Radiative and material properties of urban surfaces are shown in Table 2, which represents an example of a typical post-1980 building in a compact low-rise zone, with painted walls and roof, and asphalt/dry-soil street covers. The physical building set-up and thermal properties are chosen similar to Yaghoobian and Kleissl (2012) based on the construction materials that satisfy insulation requirements for non-residential buildings in ASHRAE 90.1-2004 (ASHRAE 2004). Buildings have square footprints of 21.3 $\times$ 21.3  m$^2$, and each wall of the buildings has a window centred on the wall with dimensions of $12.2(\mathrm{height})\times 15.2(\mathrm{width})\, \mathrm{m}^2$, resulting in a window fraction of 0.47. Total domain height is 7.4H, where H is the building height (18.3 m).

Table 2 Surface radiative and material properties

In the TUF-IOBES model, the outdoor surface energy balance consists of net longwave radiation, $L_{net}$, net shortwave radiation, $S_{net}$ (accounting for multiple reflections of direct solar radiation and shading), conduction, $Q_\mathrm{c}$, and convection, $Q_\mathrm{h}$, that are solved and enforced for each outdoor patch surface. Latent heat fluxes are assumed to be zero. Direct and diffuse horizontal solar radiation is based on the TMY3 forcing data. Downwelling longwave radiation from the sky is based on Browns sky model (1997) as implemented in the ASHRAE Toolkit (2001), where $L_{net}$ is a function of the air and dew point temperatures, cloud cover, and cloud height. The transient heat conduction is solved based on the z-transform method utilizing conduction transfer functions, and the diffusion equation by Hillel (1982) is solved to obtain a sinusoidal temperature boundary condition at the surface with a constant temperature boundary condition at soil depth. The surface convective heat fluxes are simulated based on the temperature differences between surfaces and canopy air, multiplied by a convective heat transfer coefficient based on an empirical model known as the DOE-2 method. Further information on the model, including fenestration model and forcing data can be found in Yaghoobian and Kleissl (2012) and Krayenhoff and Voogt (2007).

Appendix 3: Supplementary Analysis on the Three-Dimensional Flow Field

The effect of three-dimensional configuration and realistic surface heating in the streamwise canyon can be better understood by investigating the flow in the spanwise direction. In the absence of surface heating, several factors distinguish the roughness flow in three-dimensional aligned arrays compared to two-dimensional street canyons (Coceal et al. 2007a): (1) In the building canyon (BC, $z<H$), formation of two symmetric counter-rotating vortices is seen in the $x-y$ plane where the vortex size and its centre varies with height. (2) Due to the structure of counter-rotating vortices, the canyon vortex in the $x-z$ plane is smaller and the centre of the vortex is moved upward compared to the mid-height position in two-dimensional canyons (also shown in Fig. 5). (3) Due to the canopy-top shear layer, small eddies are shed off at the building edge into the streamwise canyon and above the building height.

The presence of surface heating further modifies the flow structure. For brevity, only the opposing condition is discussed here for different stability levels (Fig. 13). In the near-neutral case of $U_\mathrm{b}=3\,\mathrm{m}\,{\mathrm{s}}^{-1}$, the size of two counter-rotating vortices in the $x-y$ plane is as large as the canyon width, although their symmetry is influenced (indicated by the increased momentum entering the canyon from the south) by the temperature difference between north and south walls in the street canyon. In the highly unstable case, however, the two counter-rotating vortices in the $x-y$ plane shrink and occupy only half of the street-canyon region close to the leeward wall, and the vortex shed off at the building edge to the streamwise canyon is increased. This is due to the formation of the secondary vortex adjacent to the windward wall, and the increased velocity gradient at the edges of the building canyon. Additionally, the ground heating at the street canyon forces more flow in the building canyon, and enhances downward velocity in the $y-z$ plane for $U_\mathrm{b}=0.5\,{\mathrm{m}}\,{\mathrm{s}}^{-1}$. Subsequently, the region of low momentum above the building height is more pronounced for the opposing condition (not shown). Both temperature and concentration fields are modified by the flow structure in the building canyon and higher values are seen compared to the street canyon. $T^+$ and $C^+$ are more concentrated close to the ground and the leeward wall, and asymmetry due to differential heating in the street canyon is seen in the $x-y$ plane.

Fig. 13

Velocity vectors in the $x-y$ plane at different wind speeds ($U_\mathrm{b}=0.5$ and $3\,{\mathrm{m}}\, {\mathrm{s}}^{-1}$) for the opposing condition (OC case)