RADIANT HEAT TRANSFER MODEL ON 3D-CAD BASED THERMAL ENVIRONMENT SIMULATOR AND ITS APPLICATIONS TO THE SUBSTANTIAL URBAN AREA 　- INFLUENCE OF SPATIAL GEOMETRY OF URBAN BLOCK ON EFFECTIVE

ALBEDO AND SENSIBE HEAT FLUX

Kazuaki Nakaohkubo*, Akira Hoyano**Tokyo Institute of Technology, Tokyo, Japan

AbstractIn this paper, in order to examine influence of spatial geometry of urban blocks on effective albedo and sensible heat flux, radiant heat transfer analysis on 3D-CAD based thermal environment simulator ,which was developed by authors group, was improved. The budget of solar radiation received at block surface, which take into consideration direct solar radiation, sky radiation, multipath, reflected solar radiation and specular reflected solar radiation, was computed. Then, The effective albedo and the sensible heat flux were computed by 3D-CAD based thermal environment simulator which was improved in this study. In order to examine influence of spatial geometry on effective albedo and sensible heat flux, effective albedo and sensible heat flux at was the substantial urban area in Japan.

Key words: Effective Albedo, Sensible heat flux, Radiant heat transfer model

1. INTRODUCTIONIn recent years, the heat island phenomenon is a serious problem during the summer. In order to mitigate the heat island phenomenon, it is important to design urban blocks considering the influence of building spatial geometry and material, on urban thermal environment.Estimating the solar energy absorbed by an urban block is of fundamental importance in order to simulate the alteration of urban thermal environment when developing urban blocks. Many researchers have studied a numerical model to analyze the effective albedo(e.g. AKIRA K et al., 2001). And the thermal design tool in outdoor spaces has been developed by author’s group (Takashi A et al., 2008) based on a heat balance simulation. This tool allows to simulate the surface temperature distribution of urban blocks and evaluate the sensible heat flux from all surface while taking into consideration the actual design of the urban areas, including the buildings, the landscape and surrounding vegetation. In our study, we propose a radiation scheme for the actual design of the urban blocks based on the heat balance simulation that was developed by author’s group. The sky radiance distribution and multiple reflected solar radiation were introduced in this scheme. Then, the effective albedo of simple urban blocks and substantial urban area was calculated.

Figure.1 The flow chart of this simulation

Heat balance calculation for each mesh

Making urban block model using 3D-CAD softwareSpatial geometry and material of building, tree, ground etc.

Transforming 3D-CAD model into "3D-Mesh model" for calculation

Solar radiation analysis for each mesh

Heat island potential (HIP) Effective albedo

Solar radiation

WC

DB

Atomspheric radiaton

Longwave radiation

Surface temperature

Spatial Component Database

Building: building menber,

material, sufrace

color etc.

Tree　　: species, solar

transmittance etc.

Ground: ground cover,

materials etc.

Radiation and Heat Transfer Calculation Model

Databaserooftop lawn, louver etc.

Material DatabasePhysical properties of

materials:

optical reflectance, solar

reflectance, volumetric specific

heat heat conductivity etc.

・ Direct solar radiaton

・ Sky solar radiaton

considering solar radiance

distoribution

・ Reflected multiple solar

radiaton

Input

Solver

Output*:WC DB means Weather Condition Data Base

*

Finally, we discuss the relationship between effective albedo and sensible heat flux, which was calculated by the heat balance simulation.

2. CALCULATION METHOD FOR RADIATION FLUX AND SENSBLE HEAT FLUX WITHIN THE URBAN CANOPY

Figure 1 shows the scheme of the effective albedo and the heat sensible flux calculation. Detailed account of this scheme is mentioned below.

2.1 Reproduction of building spatial geometry and material position in urban blocksIn order to evaluate the influence of building spatial geometry and material position on radiation flux and sensible heat flux, actual urban blocks were reproduced by the following steps:1. The target spatial geometry including buildings, materials used, positions and the surrounding landscape were

4259-G5-2, Nagatsuta-cho, Midori-ku, Yokohama, 226-8502, Japan

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

recreated by 3D-CAD.2. The CAD models created above were then transformed into a 3D- voxel mesh model that included the

calculation parameters required for radiative analysis and heat transfer analysis. The voxel mesh size was set at 0.2 m in order to reproduce detailed outdoor spatial geometry.

3. The calculation parameters(material properties, such as solar reflectance, volumetric specific heat and normal direction of the surface, etc.) were entered at each point in the 3D-voxel mesh (Figure 2).

2.2 Calculation metheod for short wave radiation fluxThe budget of solar radiation received by each 3D-voxel mesh was calculated as following procedures.(i) Direct solar radiationDirect solar radiation was simulated by a ray-tracing method. In this method, the ray-tracing starting mesh and the tracer extends upward to the solar position. Direct solar radiation was allotted to any mesh if the ray being traced was not blocked in the calculation area.

Data stored 3D-Voxel mesh

Figure.2 3D-Voxel Mesh

a)Normal directionb)Material property Solar reflectance Solar transmittance Heat conduction Volumetric specific heat

Fig.3 Establishment of tracing directions

][iφ ][iθ∆

i=1

i

i=m

Figure.4 Establishment of tracing directions

Figure.3 Schematic diagram of solar radiation calculation

m =

�N

π + 1

n[i] = π × (2 × i − 1)

φ[i] = cos−1(2 × i − 12 × m

)

∆θ[i] =2π

n[i]

: Total number of tracer

φ[i]

m

n[i]

Δθ[i] : Horizontal division angle for tracing (rad)

: Division number for horizontal angle (round off)

: Division number for elevation angle (round off)

: Elevation of the tracing for i division (rad)

N

Diffuse reflected solar radiation

Multiple reflected solar radiation (until the value

of recived reflected radiation on surface is less

than 5W/m2)

Specular reflected solar radiation

Sky solar radiation considering solar

radiance distributionDirect radiation

(ii) Sky solar radiationSky solar radiation was computed taking into account sky radiance distribution. In this study, sky radiance distribution was calculated by the All Sky Model-R (Norio I et al., 2004). The multi-tracing simulation calculated sky solar radiation from the mesh towards multiple hemispherical directions. The tracing direction is established in a way that allows the tracing density to have the same form factor (Figure 4, Formula (1)). Sky solar radiation was estimated by aggregating the sky radiance obtained at the upper boundary surface that the tracers could reach.(iii) Reflected solar radaition on building and ground

surfaceThe budget of reflected solar radiation simulated by this method included both specular reflection and isotropic diffuse reflection. Both of these reflection factors considered the multiple reflections. Specular reflective solar radiation was calculated in such a way that the tracing simulation that extends in the direction of the specular reflection was implemented, and the budget of solar radiation was allotted to any mesh that the tracing could reach. Diffuse reflective solar radiation was estimated based on the assumption of isotropic diffuse reflection, following Lambert's cosine law, and the budget of solar radiation that a mesh receives was calculated by performing the multi-tracing simulation toward the surrounding meshes. The method used for the multi-tracing simulation was the same as that used for the sky solar radiation estimation. In this tracing process, if a ray tracing hit a mesh that had a diffuse reflection surface, the budget of solar radiation of the mesh was obtained. This ray tracing method was implemented for multiple directions in order to estimate the total amount of the budget of solar radiation received from the surroundings.(iv) Effective albedoThe effective albedo of urban blocks is expressed by formula (2).

Effective albedo[−] = 1 −�

all surfacea(Id + Is + Ir)ds

�all surface

(Id + Is + Ir)ds

a : Solar absorptivity[-]Id: Budget of Direct solar radition [W/m2]Is: Budget of Sky solar radition [W/m2]Ir: Budget of Reflected solar radition [W/m2]s : Surface

(2)

(1)

2.3 Calculation metheod for sensible heat fluxThe surface temperature distribution of buildings and ground ,that was needed to calculate the sensible heat flux for urban blocks, was simulated by Asawa’s method (Takashi A et al., 2008). When calculating surface

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

Table 1. Calculation condition

Table 2 Solar Reflectivity

Figure 5. Diurnal change of albedo by changing of building and ground reflectivity

Figure 6. Diurnal change of effctive albedo for different of sky

solar radiation models Figure 5. Simple urban

blocks

Figure 7. Diurnal change of effective albedo for diferent of windows

position

660.20 0.00

0.21

Case1-7Case1-8

Case1-1,3,5,7(dot line) :isotropic modelCase1-2,4,6,8(full line)

HB=60[m]

0.10

0.05

0.22 0.15

0.23

0.20

0.25

0.240.30

0.35

0.25 0.40

1212timetime

Effe

ctiv

e A

lbed

o [-]

Effe

ctiv

e A

lbed

o [-]

99 1515 77 1313 1010 1616 88 1414 1111 1717 1818

temperature, convective heat transfer was calculated under the assumption that there was no distribution of air temperature and wind velocity in the subject urban canopy.

3. SIMPLE STUDIES OF INFLUENCE OF SPATIAL GEOMETRY AND MATERIAL ON THE EFFECTIVE ALBEDO

As first step for investigating the influence of spatial geometry and material on the effective albedo, the two simple parametric studies were carried out. In first study, the influence of difference of sky solar radiation models (sky radiance distribution model and isotropic radiance model) on effective albedo was investigated. In this study, the influence of differing buildings height on the effective albedo was also examined because the difference of sky solar radiation model influence on the budget of sky solar radiation of building walls.Then, another parametric studies were carried out, differing the material position, which mean the difference of the windows position and direction.Table 1 shows the basic calculation condition for the following case studies. And Table 2 shows the solar reflectivity for these studies. Figure 5 shows the simple urban block using in these studies.

3.1 Influence of sky radiance distribution on the effective albedoFigure 6 shows the diurnal change of effective albedo for the eight calculations in the uniform urban block configuration. For all cases, as building height decreased, the effective albedo value increased. These results were same as the calculations of many researches (e.g. AKIRA K et al., 2001). Considering sky radiance distribution, as the solar altitude angle decreased, the value of the effective albedo was larger than that assuming isotropic sky solar radiation. Therefore, it is important to considering sky radiance distribution when the effective albedo for urban blocks which consist of tall buildings is calculated.

3.2 Influence of windows position on the effective albedoFour calculations were carried out, differing in the position and direction of windows. Figure 7 indicates the diurnal change of effective albedo for this study. The value of effective albedo for Case 3-1 was highest and that for Case3-4 was smallest. The value of effective albedo depended on the area of windows because the solar reflectance of glass was low. Moreover, the specular reflected solar radiation from the glass was almost received by the ground or other buildings without reaching to the sky. As the solar altitude angle decreased, the value of effective albedo for Case 3-2 was lowering, on the other hand, that for Case 3-3 was lowering as the solar altitude angle increased. As a result, the windows position also influences on the diurnal change of the effective albedo.

4. EFFECTIVE ALBEDO AND SENSIBLE HEAT FLUX FOR THE SUBSTANTIAL URBAN AREA

4.1. Effective albedo for Substantila urban blocksIn order to investigate the influence of spatial geometry and material positions of substantial urban blocks on effective albedo, eight calculations were carried out. Figure 8 shows the eight urban blocks which exist in Tokyo. The solar reflectance of building and ground was the same values in Section 3.Figure 9 shows the diurnal change of effective albedo for substantial urban blocks. The value of the effective albedo for the blocks, of which value of building average height was relatively-large (Block-6, Block-7, Block-8), was low. However, The building average height of Block-2, of whose value of effective albedo was lowest in

Latitude 35

Longitude 135

Date Aug. 5

Wall, Roof 0.3(diffuse)

Ground 0.3(diffuse)

glass 0.07(specular)

WB(=16m)WD=WB/2(=8m)

HB

DB=WB(=16m)

HB=16[m]Case1-1Case1-2

Case1-3Case1-4

HB=32[m] HB=48[m]Case1-5Case1-6 Case2-1

No windows

windows allocated on

south and north walls

windows allocated on

east and west walls

windows allocated on

all wallsCase2-3 Case2-4

Case2-2

:sky radiatnce distribution model

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

value of the effective albedo for Block-7 was smaller than almost other blocks, the value of HIP was smallest. This was because the area of low surface temperature of buildings and ground was large due to the area of windows and the deep canopy, which increased the area of shadow in the blocks. As a result, the relationship between effective albedo and HIP was not clear because the surface temperatrue changed by differences of budget of solar radiation ,which means the solar radiation was received or not, or material thermal properties.

5. CONCLUSIONSIn this paper, in order to investigate the influence of substantial urban blocks on the effective albedo, the a radiation scheme for the actual design of the urban areas was proposed. Then, the infl uence of spatial geometry and material position on the effective albedo were confi rmed through the simple parametric studies with using the radiation scheme. Carrying out the calculations of effective albedo and the sensible heat fl ux from the all surface for substantial urban blocks, the infl uence of spatial geometry and material posision in substantial urban block on the effective albedo and sensible fl ux was grasped. We did not fi nd the strong relationship between effective albedo and sensible heat fl ux.

6. REFERENCESAkira Kondo, Megumi Ueno, Akikazu Kaga, 2001. The Infl uence of urban canopy confi guration on urban albedo,

Boundary-Layer Meteorology, 100, 225-242Takashi Asawa, Akira Hoyano, Kazuaki Nakaohkubo, 2008. Thermal design tool for outdoor spaces on heat

balance simulation using a 3D-CAD system, Building and Environment, volum 43, Issue 12, 2112-2123Norio Igawa, Yasuko Koga, Tomoko Matsuzawa, Hiroshi Nakamura, 2004. Models of sky radiance distribution and

sky luminance distribution, Solar Energy, 77, 137-157

Figure 8 Substansial urban blocks

Figure 9. Diurnal change of effective albedo for substantial urban blocks

Figure 10. Diurnal change of Heat Island Potential

60.20

00

5

3 6 9 12 15 18 21

10

15

20

25

30

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.30

12time

time

Effe

ctiv

e A

lbed

o [-]

Hea

t isl

and

pote

ntia

l [℃

]

9 157 1310 168 1411 17 18

this calculation, was as same as that of Block-6. The characteristics of the low effective albedo blocks(Block-6, 7, 8) was that almost buildings standing in the blocks were the same height. On the other hand, the height of each building in Block-2, 4 is different. The value of the effective albedo for block-4 was not small enough to show the study of Section 3 although the value of a ratio between window area and surface area of building was large.

4.2. Relationship betweew effective albedo and sensible heat fl ux

In order to investigate the relationship between effective albedo and sensible heat fl ux from the all surface, the all surface temperature distributions were carried out using the heat balance simulation(Asawa, 2008). In this paper, as an index of sensible heat fl ux from all surface, Heat Island Potential(HIP) is used. HIP is expressed formula 3.

Block-1

AHB :Average Height of Buildings[m] GBC: Gross buildings coveage[-]Block-4

Block-7

Block-1 Block-5Block-2 Block-6Block-3 Block-7Block-4 Block-8Block-5

Block-8Block-6Block-2

Block-3

N

=

�allsurface

(Ts − Ta)ds

AHIP[℃ ]

Ts: Surface temperature[℃ ]Ta: Air temperature[℃ ]A : Area of target sit[m2]s : Surface

(3)

The summer weather conditions at Tokyo were used for this calculations. Substantial urban blocks using for this investigation were the same as Figure 8. Figure 10 shows the diurnal change of HIP. The value of HIP was very different due to spatial geometry and material in the urban blocks during the day. Although the

Block-1 Block-5

Block-2 Block-6

Block-3 Block-7

Block-4 Block-8

AHB=23.3GBC=0.63

AHB=26.4GBC=0.68

AHB=24.3GBC=0.36

AHB=26.0GBC=0.39

AHB=13.5GBC=0.77

AHB=15.2GBC=0.61

AHB=30.7GBC=0.27

AHB=27.3GBC=0.44

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