©2023 International Society of Arboriculture Arboriculture & Urban Forestry 49(5): September 2023 251 Table 1. Material specifications and components used in this study (Lin et al. 2019). Material Thermal conductivity (W/m2/K) Specific heat capacity (J/kg/K) Density (kg/m3) Emissivity Absorptivity Thickness (m) Earth 1.3 1,000 1,400 0.9 0.68 0.35 Brick 0.8 900 2,000 0.9 0.8 0.15/0.15/.05 Earth with concrete 1.5 300 1,600 0.85 0.85 0.5/9.5 Ground shaded 1.3 1,000 1,400 0.93 0.15 10 Canopy foliage 0.173 2,310 700 0.983 0.75 Crown width Limestone 908 1.3 1,090 Not a surface material Insulation 1,200 0.03 50 Not a surface material terms of thermal conductivity, specific heat, density, emissivity, and absorptivity are shown in Table 1. Absorptivity refers to albedo values of particular materials. Regarding the selected material for the sur- face elements, earth with concrete material was imposed on the ground beneath the building while shaded ground refers to zone directly under the canopy zone. Modeling the Effects of Vegetation The vegetation effect on airflow in CFD simulations was modeled by employing the momentum (SUi), tur- bulent kinetic energy (Sk), and dissipation rate’s sink/ source terms (Sɛ) into transport equations through user-defined functions. These terms were computed by Green (1992), Liu et al. (1996), and Sanz (2003) and are given below. In these equations, tree characterizing parameters are the drag coefficient (cd,cfd) and leaf area density (LAD). The tuned value of this coefficient (cd,cfd) is 0.15 (Gromke et al. 2015; Toparlar et al. 2018). How- ever, the actual form drag coefficient is used based on the canopy shape of tree species. The used value of model coefficients βd is 5.0 and βp ranges from 0 to 1, and the empirical coefficient Cɛ4 and Cɛ5 is 0.9. LAD’s value is 3.0 m2/m3 (National Parks Board 2017) for common tree species (Guaiacum offinale, Azadirachta indica, and Peltophorum pterocarpum) present in the (4) (5) (6) ... . ............... .. . .......... . . ........ . ......... .. . ............... . ...... studied urban environment. Another species (Bauhinia × blakeana) with a LAD of 4.41 m2/m3 was also stud- ied to simulate the effect of dense foliage density. The density of air was ρ. Ui and U was the velocity of fluid in “i” direction and flow velocity, respectively. K was the turbulent kinetic energy. The vegetation effect on temperature was also modeled in this study by using a time-dependent energy source term (i.e., volumetric cooling power [Pc][W/m3]) to consider its unsteady behavior (Topar- lar et al. 2018). This was incorporated into the energy equation through a user-defined function (UDF), given as follows: (7) where and denoted the potential evapotranspi- ration and equivalent hourly evapotranspiration in m/h. Rh (MJ/m2/h) was the incoming hourly solar radiation per unit area. The latent heat of vaporization was λ and λwh in Wh/kg and Watt-hours terms. The density of water was ρ. The shading of the tree canopy was modeled with reduced absorptivity of the ground (Equation 8). (8) where αshaded and αopen referred to the ground surface solar absorptivity with and without trees below its can- opy. Shading factor (SF), responsible for the regula- tion of solar radiation absorbed and reflected from the tree canopy, had average value of 0.88 (Nowak 1996). Vegetation was modeled as a cuboid zone in CFD simulation due to complex discretization involved with tree canopy. This simplified domain results in .. . ............ ...... . ...... ... . ......... . ............ ....... . ....... . ....
September 2023
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