An Improved Three-Dimensional Simulation of the Diurnally Varying Street-Canyon Flow

Abstract

The impact of diurnal variations of the heat fluxes from building and ground surfaces on the fluid flow and air temperature distribution in street canyons is numerically investigated using the PArallelized Large-eddy Simulation Model (PALM). Simulations are performed for a 3 by 5 array of buildings with canyon aspect ratio of one for two clear summer days that differ in atmospheric instability. A detailed building energy model with a three-dimensional raster-type geometry—Temperature of Urban Facets Indoor-Outdoor Building Energy Simulator (TUF-IOBES)—provides urban surface heat fluxes as thermal boundary conditions for PALM. In vertical cross-sections at the centre of the spanwise canyon the mechanical forcing and the horizontal streamwise thermal forcing at roof level outweigh the thermal forces from the heated surfaces inside the canyon in defining the general flow pattern throughout the day. This results in a dominant canyon vortex with a persistent speed, centered at a constant height. Compared to neutral simulations, non-uniform heating of the urban canyon surfaces significantly modifies the pressure field and turbulence statistics in street canyons. Strong horizontal pressure gradients were detected in streamwise and spanwise canyons throughout the day, and which motivate larger turbulent velocity fluctuations in the horizontal directions rather than in the vertical direction. Canyon-averaged turbulent kinetic energy in all non-neutral simulations exhibits a diurnal cycle following the insolation on the ground in both spanwise and streamwise canyons, and it is larger when the canopy bottom surface is paved with darker materials and the ground surface temperature is higher as a result. Compared to uniformly distributed thermal forcing on urban surfaces, the present analysis shows that realistic non-uniform thermal forcing can result in complex local airflow patterns, as evident, for example, from the location of the vortices in horizontal planes in the spanwise canyon. This study shows the importance of three-dimensional simulations with detailed thermal boundary conditions to explore the heat and mass transport in an urban area.

Appendix: Description of the DOE-2 Method (LBL 1994; Pedersen et al. 2001)

The DOE-2 method calculates the convective heat transfer coefficient ($h$) based on

$$\begin{aligned} h=h_n +R_\mathrm{f} \left( {h_\mathrm{glass} -h_n} \right) , \end{aligned}$$

(1)

for unstable flow,

$$\begin{aligned} h_n =9.482\root 3 \of {\left| {\Delta T} \right| }/(7.238-|\cos \phi |), \end{aligned}$$

(2)

and for stable flow,

$$\begin{aligned} h_n =1.81\root 3 \of {\left| {\Delta T} \right| }/(1.382+|\cos \phi |). \end{aligned}$$

(3)

Here $h_n$ (W m$^{-2}$ K$^{-1}$) is the natural convection coefficient that is calculated from Eqs. 2 or 3, $R_\mathrm{f}$ is the surface roughness multiplier, and $h_\mathrm{glass}$ (W m$^{-2}$ K$^{-1}$) is the convection coefficient for very smooth surfaces (e.g. glass). In Eqs. 2 and 3, $\Delta T$ is the temperature difference between the surface and air, and $\phi$ ($^{\circ }$) is the angle between the ground outward normal and the surface outward normal. Equations 2 and 3 are equivalent when the wall is vertical $(\cos \phi =0)$. The surface roughness multiplier ($R_\mathrm{f}$) is based on the ASHRAE graph of surface conductance (ASHRAE 1981), where $R_\mathrm{f}$ is normalized to glass ($R_\mathrm{f} =1)$ and ranges up to 2.17 for stucco. $R_\mathrm{f} = 1.13$ for clear pine is used herein.

Here, $h_\mathrm{glass}$ is based on,

$$\begin{aligned} h_\mathrm{glass} =\sqrt{h_n^2 +\left[ {aV_0^b} \right] ^{2}}, \end{aligned}$$

(4)

in which constants $a$ and $b$ depend on the orientation of the surface with respect to the wind direction. For windward surfaces $a = 2.38$ (W m$^{-2}$ K (m s$^{-1}$)$^{b}$) and $b = 0.89$ and for leeward surfaces $a = 2.86$ (W m$^{-2}$ K (m s$^{-1}$)$^{b}$) and $b =0.617$ (Yazdanian and Klems 1994); $V_0$ is the environmental wind speed.