Effects of Roof-Edge Roughness on Air Temperature and Pollutant Concentration in Urban Canyons

Abstract

The influence of roof-edge roughness elements on airflow, heat transfer, and street-level pollutant transport inside and above a two-dimensional urban canyon is analyzed using an urban energy balance model coupled to a large-eddy simulation model. Simulations are performed for cold (early morning) and hot (mid afternoon) periods during the hottest month of the year (August) for the climate of Abu Dhabi, United Arab Emirates. The analysis suggests that early in the morning, and when the tallest roughness elements are implemented, the temperature above the street level increases on average by 0.5 K, while the pollutant concentration decreases by 2% of the street-level concentration. For the same conditions in mid afternoon, the temperature decreases conservatively by 1 K, while the pollutant concentration increases by 7% of the street-level concentration. As a passive or active architectural solution, the roof roughness element shows promise for improving thermal comfort and air quality in the canyon for specific times, but this should be further verified experimentally. The results also warrant a closer look at the effects of mid-range roughness elements in the urban morphology on atmospheric dynamics so as to improve parametrizations in mesoscale modelling.

Appendix 1: CFD Model Validation

A critical Reynolds number, based on the building height, of $Re_H=U_HH/\nu =4 \times 10^3$ has been suggested for a building model to be immersed within a deep boundary layer (Castro and Robins 1977), so it is necessary to reach and exceed this Reynolds number for simulations of interest to validate our model. Validation cases are run with $Re_H=U_HH/\nu =1.08 \times 10^4$ and a bulk Richardson number (using street-level and roof-level velocities and temperatures) of $Ri_b=gH(T_H-T_S)/(U_H^2T_{A})=-0.35$, and the cases include multiple numerical grids according to Table 3. The model domain is as in Fig. 3 but at a 1 / 100 scale to match wind-tunnel experiments of Uehara et al. (2000).

Table 3 Numerical grids for CFD validation cases

Fig. 16

Comparison of the LES model results with wind-tunnel experiments of Uehara et al. (2000) for a normalized velocity in the x direction ($\overline{u_x}/\overline{u_A}$) and b normalized temperature ($({\overline{T}}-T_A)/(T_S-T_A)$)

Table 4 Normalized mean-square error (NMSE) and fractional bias (FB) for both momentum (M) and energy (E) for comparing CFD validation cases to observations

These cases are compared to a wind-tunnel study (Uehara et al. 2000) of airflow over an array of blocks that are heated at the floor level (i.e. canyon street), and from this study a sub dataset with $Re_H=U_HH/\nu =9400$ and $Ri_b=gH(T_H-T_S)/(U_H^2T_A)=-0.21$ is used for comparison. Figure 16 shows the comparison between the LES model results and the wind-tunnel observations, where both observations and numerical model data are plotted on a vertical line in the centre of the canyon. A quantitative comparison between the wind-tunnel observations (O) and LES model (M) is also performed, using the normalized mean-square error (NMSE) and fractional bias (FB) (Hanna and Chang 2012) for both solutions: momentum (M), i.e. normalized velocity in the x direction, and energy (E), i.e. normalized temperature. These statistical metrics are quantified in Table 4 with NMSE and FB given as

$$\begin{aligned} \textit{NMSE}= & {} \frac{\sum _{i=1}^n \left( O_i-M_i\right) ^2}{\left( \sum _{i=1}^n O_i\right) \left( \sum _{i=1}^n M_i\right) }, \end{aligned}$$

(21)

$$\begin{aligned} \textit{FB}= & {} \frac{\sum _{i=1}^n O_i - \sum _{i=1}^nM_i}{0.5\left( \sum _{i=1}^n O_i + \sum _{i=1}^nM_i\right) }. \end{aligned}$$

(22)

It is confirmed that the mesh resolutions used are high enough so that the different resolutions do not affect the time-averaged solutions, and the model produces the experimental velocity and temperature fields reasonably well. The fractional bias for the momentum appears higher than expected, especially after comparing the model and observations in the figures, which is likely caused by division by a small number near zero where the momentum is close to zero at the centre of the main canyon vortex.

It must be noted that the concept of grid convergence is non-existent for LES models. In other words, a definition of a relative error may not necessarily approach zero or even reduce by further refining the numerical grid, which is the case for turbulence models that switch functions at a specific length scale. For example, the LES model essentially formulates and solves different sets of partial differential equations at above-grid and subgrid scales (Roache 1997). Even though grid convergence may not be verified in an LES model, a model must be run at different grid resolutions to ensure that the solution behaviour and a suitable definition of uncertainty (e.g. NMSE or FB) are bounded within a desired range.