Solar energy potential according to climatic and geometrical parameters of cities and buildings: A case-study from Tabriz City- Iran

Urban Climate 28 (2019) 100469

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Solar energy potential according to climatic and geometrical parameters of cities and buildings: A case-study from Tabriz CityIran

T

Mahmoud Ouria1 Department of Urban Design, Eastern Mediterranean University, Famagusta, Cyprus

ABS TRA CT

This paper focused on the solar energy utilization in cities and buildings as exemplified by Tabriz City in Iran. All the geographic and climatic factors have been considered to estimate the solar energy potential for Tabriz City using angstrom model in SPSS. Then, the solar energy potential in the Blue Mosque (BM) of Tabriz investigated in detail. Decisive parameters in solar energy evaluation such as geographic parameters, climatic factors, radiation types, and orientation techniques and geometry analysis of buildings, were considered based on Tabriz regarding Duffie Beckman and Stephenson's cousin methods. The method of Lagrange interpolation regarded to define the elements geometrical equations. The rate of irradiation solar energy was analyzed for domed, horizontal and vertical surfaces of the BM in Tabriz City using Ladybug for Rhino and MS Excel software programs. The results of this study showed that it is possible to domesticate noticeable rate of solar energy in a cloudy climate like Tabriz by appropriate orientation and geometry of building elements.

1. Introduction Regarding the goals of sustainable development, renewable energy is more highlighted to compare with nuclear energy and fossil sources considering their negative aspects on the environment, and the resources limitations in cities (Ouria and Sevinc, 2017). Following climate-neutral aspiration, implementing local renewable energy resources on buildings is a far-fetched aim because there is not available experience in this regard. Solar radiation is the most viable source for a precise assessment of energy conversion and design. The average incident irradiance is required to estimate the solar potential of buildings/cities locally (Shukla et al., 2015a). The solar energy potential of cities/buildings regarding their geographical, local and geometrical features needs to be measured accordingly (Jakhrani et al., 2012), (Boehmea et al., 2015). Economically and environmentally, solar energy is essential because it protects eco-system (Ouria and Sevinc, 2017). Also, it supports a healthy society (Ouria and Sevinc, 2016). This paper investigates that kind of factors which are the effective on solar energy consumption in historic buildings, in particular, the case study of Tabriz. The main purpose of this paper is the estimation of solar energy potential in buildings, especially in Tabriz City. The paper concentrates on the solar conditions of the BM. Statistical and quantitative methods and simulator have been used to analyze climate, orientation, opening, and geometry. The city and the BM have high and moderate density features, respectively, and were selected as case studies to compute their solar potential, climatic and geographic conditions. Mean average horizontal radiation modeled using Angstrom method in SPSS. The solar potential of Tabriz graphically and numerically modeled using quantitative and statistical methods in MS Excel and Ladybug for Grasshopper programs. The outputs of the analytical computations have been fed into Ladybug using SPSS, MS Excel and Elements converter. The value of sky density computed for the Gen Cumulative Sky model of Tabriz City

1

E-mail address: [email protected]. Architect & Urban Designer, Independent Researcher.

https://doi.org/10.1016/j.uclim.2019.100469 Received 2 December 2018; Received in revised form 4 April 2019; Accepted 17 April 2019 2212-0955/ © 2019 Published by Elsevier B.V.

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Fig. 1. Zenith, altitude, and azimuth.

inputted to compute yearly radiation in Ladybug following isotropic Eqs. (19), (22) and (23). Finally, this paper highlights the important role of building geometry in passive solar absorption.

2. Solar theory and geometry According to (Ouria M. and Sevinc, 2017), solar energy analysis processes include five essential steps:

• Evaluation of the solar radiation. • Evaluation of climatic factors. • Evaluation of geographic factors. • Evaluation of site/building/element geometry. • Evaluation of materials/context types and color. Solar irradiance is the total beam flux density descending on a surface which is perpendicular with the radiation angle (β) with respect to the horizontal plane (Paulescu et al., 2013), (Steinhilber et al., 2009). The sun rises and sets from different points in the sky (the horizon) at different times of the year. It moves across the sky along different paths. Measuring altitude and azimuth is essential in analyzing the sun's path. The angular distance above the horizon is altitude that measured to the horizon perpendicularly. The maximum value of altitude is 90° at the zenith that is the upper point. The angular distance evaluated along the horizon is azimuth which measured in a clockwise direction, as shown in Fig. 1. The number of degrees along the horizon corresponds to the compass direction (Paulescu et al., 2013) and (Jin You, 2017). There are three parameters to measuring solar radiation in sites: Direct Normal Irradiance (DNI), Diffuse Horizontal Irradiance

Fig. 2. Global, direct and diffused radiation. 2

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(DHI) and Global Horizontal Irradiance (GHI) (Cogliani, 2014), (Shukla et al., 2015a; Shukla et al., 2015b). Direct Solar Radiation or Direct Normal Irradiance (DNI) is the quantity of received solar radiation per unit area (Fig. 2.). The area of the surface is perpendicular to the sunbeams hitting directly. DNI is the maximum rate of radiation that can be measured (Paulescu et al., 2013) and (Cogliani, 2014). Solar energy, as one of the most important possible alternative energy sources, is best understood by acquiring an accurate knowledge of solar energy radiation at a particular geographical location. It is to be carefully studied, in order to analysis/build solar buildings, and for estimating their performance and efficiency. From the analyses of the data of the Tabriz City the solar radiation model of angstrom is used:

n H = H0 ⎡a + b ⎛ ⎞ ⎤ ⎝ N ⎠⎦ ⎣

(1)

Where; H: is monthly average daily global radiation on the orizontal surface (MJ/m^2), H0 is monthly average daily extraterrestrial radiation on a horizontal surface (MJ/m^2 day). n is the monthly average daily maximum number of hours of possible sunshine. (a) and (b) are regression constants. n : is the monthly average daily number of hours of bright sunshine, N: is the monthly average daily maximum number of hours of possible sunshine and (h) is the noon solar altitude on the. 15th of the month (degrees). Isc: is the solar constant equal to 1367 Wm-2.

H0 =

24 360 n πωs ⎞ × ⎡csc φcosδ sin ωs + Isc ⎛1 + 0.033 cos sin φsinδ⎤ π 365 ⎠ ⎣ 180 ⎝ ⎦

(2)

Where,

ωs = cos−1 − tan δ. tan φ

(3)

And, the declination angle (δ) is the sun `s angular position at noon (solar noon) regarding the equator's plane. The temperature varies between −23.45° at the winter solstice and + 23.45° at solstice (summer) according to:

δ = 23.45. sin ⎡ ⎣

2π . (284 + d) ⎤ 365 ⎦

(4)

d: is the numerical day of the year (between 1 and 365). For other locations different from the equator, the latitude (φ) varies the zenith angle further.

N=

2 ωs 15

(5)

Root Means Square Error (RMSE) and Mean Bias Error (MBE) used to calculate the regression constant's performance as presented in Eq. (6) and (7). ∑ (Yc − Yo)

MBE =

∑ Yo

n

(6)

n

Where; Yc = Hcalc, shows the calculated amount of radiation. Yo = Hmeas shows the measured amount of radiation. n = no. of data i.e. no. of months. ∑ (Yc − Yo )2

MBE =

n ∑ (Yo )

(7)

n

It is required to analyze the azimuth and radiation angles while computing solar potential on vertical surfaces. Regarding the solar radiation on vertical surfaces, there is a direct relation between azimuth angle and solar energy on vertical surfaced while the relation between radiation angle and solar energy on vertical surfaces is reversed (Fig. 3). The solar radiation energy of vertical envelops should be analyzed separately. Radiation angle (altitude) (β) is the angle of the solar beams and its image on the horizontal line. Its rate changes affecting hours angle ((see Eq. (3))) and declination (δ) as follows;

β = arcSin (Sinφ . Sin δ + Cosφ . Cosδ. Cosω)

(8)

Azimuth (Z) refers to the radiation direct that shows an image of the radius of radiation on earth. South equals 180° and north is zero degrees for azimuth (Fig. 3). Coordinates of each surface depend on coordinates of other surfaces because the solar energy radiates on three-dimensional space. So, the azimuth angle depends on the local hour angle (ω) and radiation angle as follow; 3

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Fig. 3. Azimuth angles.

Z = sin−1 ⎡ ⎢ ⎣

cos δ. sin ω ⎤ cos β ⎥ ⎦

(9)

The intensity of the solar energy absorbed by each surface in Tabriz City modeled as presented below:

Ioh = Isc ⎛1 + 0.033 cos ⎝

360 (N ) ⎞ (C osθz ) 365 ⎠

(10)

Cos θz = (cos φcosδ sin ω + sin φsinδ ) ωsr =

cos−1 (−tanδ .

(11)

tanφ)

(12)

ω = 15(t − 12)

(13)

Ih = Ioh. kt

(14)

Ibh = Ih − Idh

(15)

kT < 0.35 ⎧ 1 − 0.249 kT , Idh = 1.557 − 1.84 kT , 0.35 < kT < 0.75 ⎨ Ih 0.177 kT , kT > 0.75 ⎩

(16)

KT = a + b cos ωs (t − 12) KT

(17)

a = 0.409–0.5016 sin(ω − 60 )

(18)

b = 0.6607–0.4767 sin(ω − 60 )

(19)

1 1 Iw = Rb . Ib + Id + Sg Ih 2 2

(20)

Rb =

cos θ cos θz

(21)

cos θ = (sin δ sin φ cos(s)) − (sinδ cos φ sin(s) cos(z‵)) + (cos δ cosφ cos(s ) cos ω) + (cosδsinφ sin(s ) cos(z‵) cosω) + cosδ sin(s ) sin(z‵) sin ω)

(22)

2

(Ioh) computed in (w/m .hr). The extra-terrestrial insolation computed for a specific angle of time (ω). Radians is used measuring the hour angle at sunrise (ωsr). (Isc) is the constant of the solar which assumed with (1367 W/m2), and declination angle has been shown with (δ). The direct solar beam irradiance on the Tabriz surfaces has been presented with (Idh). The diffuse sky irradiance (Ibh) on the surface calculated based on climatic conditions of Tabriz. The albedo(Sg) or surface reflectivity calculated (0.23) for Tabriz (Table 4.) (Rb) shows the irradiation ratio between vertical and horizontal surfaces which varies based on surface azimuth (z`), surface slope (s) and orientation at a given time for Tabriz. (Ih) refers to the solar irradiation on horizontal surfaces in Tabriz City (φ = 38) on day number of the year (N). There is a relation 4

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Table 1 Vertical solar incidence in different directions. Direct

Schema

Energy Formula

N

IN = − Ioh cos β cos z (25)

E

IE = Ioh cos β cos z (26)

S

IS = Ioh cos β cos z (27)

W

IW = − Ioh cos β cos z (28)

between (Ih) and diffused irradiation (Id), direct irradiation (Ib), and clearness index (KT). The atmospheric factors impacted the calculated values. The clearness index (KT), shows the important atmospheric factors on the insolation value at Tabriz. (KT), clarifies the stochastic parameter which changes by latitude, altitude, climatic conditions and solar time. Table 9. shows solar time, monthly sunny hours and clearness index of Tabriz City. The clearness index is estimated based on the monthly average daily number of hours of bright sunshine in Tabriz (Sb), and monthly average daily maximum number of hours of possible sunshine (Sp) as follows;

KT =

Sb Sp

(23)

Sp =

2 ωs 15

(24)

Based on horizontal incidence, (I) which is calculated for the latitude and climatic parameters of Tabriz. Regarding the radiation angles and azimuth, the relations of vertical incidence on different surfaces is presented in Table 1. The rate of solar energy on vertical incidence for different surfaces computed for a specific hour on a specific day of the year. Estimating the effective azimuth angle on each (E, S, W, N) surface is needed to calculate the mean monthly solar incidence on vertical surfaces separately. For this reason, the sun path diagram is considered to illustrate which surfaces are exposed on what time. The total hourly solar radiation on Southern, Eastern, Western and Northern envelops calculated by integrating contacted surfaces depended on azimuth as follows; Z2

∫Z1

I (β, z ). cosz. d z

(29)

Subsequently, the equations of Table 1 are represented in Table 2. It is essential to describe the schematic shapes of elements to define the mathematical equation of each effective surface. The calculation of elements defines its height diagram according to the horizontal dimension (x), which makes it possible to compute surface area. The method of Lagrange interpolation is used to calculate the elements equations.

h (x ) =

(X − x1) − (X − x3 ) (h2) (x2 − x1 )(x2 − x13 )

(34)

3. Methodology Solar buildings and cities should be designed based on urban design, building form/geometry, and solar energy principles. Also, studies have shown the importance of geographic and climatic factors in solar energy potential and absorption. Transmission of solar energy depends on environmental factors (Iqbal, 1983). Accordingly, environmental (natural) factors should also be analyzed to optimize environmental (man-made) elements during the design, regeneration and restoration process. The aim of this paper is the evaluation of the solar effects in buildings, especially for Tabriz City in Northwest Iran. The paper concentrated on the solar conditions of the Blue Mosque (BM) an important building of Islamic Azerbaijani architecture in Iran. Qualitative, qualitative and statistical methods were used to analyze the BM. Tabriz City has high-density features that selected as cases studies to estimate their solar radiation, climatic and geographic conditions. The solar energy potential of Tabriz modeled statistically and graphically using SPSS, MS Excel and Ladybug for Grasshopper. 5

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Table 2 Sum of the vertical solar incidence in different directions. Direction

Domain

Equation

Schematic Domain

North (N)

(0,90)U(270,360)

IN= ∫ z=0°90° − Ih cos β cos z. dz+∫ z=270°360° − Ih cos β cos z. dz (30)

West (W)

(180,360)

IW = ∫ z=180°360° − Ih cos β cos z. dz (31)

South (S)

(90,270)

IS = ∫ z=90°270°Ih cos β cos z. dz (32)

East (E)

(0,180)

IE = ∫ z=0°180°Ih cos β cos z. dz (33)

Fig. 4. Location of Case Study in the annual average global horizontal irradiance (GHI) map of Iran. 6

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Table 3 Geographical location of stations. Latitude (φ) (deg.)

Altitude (m)

Longitude (degree)

38°5′ (N)

1361 m

46°16’

3.1. Climatic and geographic analysis of Tabriz City Tabriz is located in the Northwest part of Iran (Fig. 4). The city is located 38°5′ north of the equator and 46°16′ east of Greenwich. Tabriz city has a great need for domesticating solar energy because of its climatic situation and geographical position. Its climate is classified as BSk by Köppen and Geiger (Kottek, 2006).), with harsh winters and hot dry summers. The city's altitude is 1361 m above sea level. Humidity is low in both summer and winter. The geographical location of stations is presented in Table 3. Dew point and dry bulb temperatures, and relative humidity of the city have been shown using Lady Bug in Rhino software in Fig. 5 respectively. The used parameters inputted in the analyses have been taken from the Energy Plus database. The average annual rainfall is 323 mm. The average monthly temperature is 11.6 °C in a cold climate. The differences between the warmest and coldest months is 41 °C, with at least four months below −3 °C. 3.2. Albedo analyses of Tabriz City by GIS data The land cover is important in the rate of solar energy reflection which requires detailed analysis of land cover types and their portions impacting urban heat islands (Ouria and Sevinc, 2017). Accordingly, the distribution of land cover/use in Tabriz City analyzed. Then, the albedo constant in Tabriz City was calculated based on the proportion of different materials colors, proportion and GIS data used in the urban land cover (Fig. 6.). Analyzing land cover type is crucial, especially in regions with limited physical extents (Qingqing et al., 2012; Ouria and Sevinc, 2017). To analyze the solar energy in an area, it's land cover and type of use are necessary parameters because they have different reactions to solar radiation. Fig. 7 presented the distribution of the land cover in Tabriz. According to the land cover data given in (Figs. 6–8), around 9869 ha of the city allocated for the urban areas, which includes 56% of the total areas. 600 ha for the forested area, which presents just 3% of the total covered area. Bare ground covers 785 ha or 5%, Open Land (Light Soil and Grass) 880.41 ha, presents 9%. Open Land (Military and airport facilities) shows 10% (1586 ha) of the total covers area. Albedo/reflectivity of different surfaces depends on two important parameters including the surface areas proportion and surface reflection ratios (Ouria and Sevinc, 2017). The rate of land areas was computed using GIS data for Tabriz City. So, Table 4, presented the reflectivity of different surfaces (Oke, 1973; Ahrens, 2006). It should be highlighted that the albedo coefficient (0.23) is calculated for the urban scale of the Tabriz region by evaluating the area of the cover types and their special coefficients. Accordingly, the microscale of environmental factors for each building should be focused on. The albedo rates in different districts of the city are different. Subsequently, the percentage of each type of cover has been given in Table 1. Although the reflectivity rate changes from 0.2 to 0.5, the lower rate of albedo in Tabriz (0.23) does help citizens feel that the urban spaces are more comfortable. 3.3. Monthly and hourly solar radiation of horizontal surfaces in Tabriz City Regression model studied to calculate the amount of radiation and coefficients of each model by SPSS software after quality control data contained in Tabriz station. There are some independent parameters such as; mean temperature, humidity, cloudiness, and sunshine which their correlation is shown in Table 5. According to the data in Table 5, sunshine has a maximum correlation of solar radiation. By the use of independent parameters of Table 5 implement, the (Enter Method) of the regression model of solar radiation has been used according to the climatic parameters of Tabriz. The coefficients and amount of entered variables in the model are presented in Table 6. Summary of indicators regression by entering Model is presented in Table 7. A linear relationship between the variables is asserted by a regression analysis of variance. Because The significance level is zero

Fig. 5. a-c. Climatic data of Tabriz. 7

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Fig. 6. Land use/cover in the state of Tabriz after 2016. 12000

10000 Urban (Stone and Metals with Modorate color and Density) Farm land

8000

Open Land (Military and airport facilities) 6000 Open Land (Light Soil and Grass) Bare Ground (light and wet) 4000 Scrub forest 2000

0

Fig. 7. Different areas of land use/cover in the state of Tabriz after 2016.

Urban (Stone and Metals with Modorate color and Density)

5% 3%

Farm land

9%

Open Land (Military and airport facilities)

10%

Open Land (Light Soil and Grass)

56%

Bare Ground (light and wet)

17%

Scrub forest Fig. 8. The land cover portions of Tabriz after 2016.

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Table 4 Average albedo value of land covers in Tabriz City. Cover types

Covered area (ha)

Covered area(%)

Albedo coefficient

Albedo portion

Urban (stone and metals with medium density) Farmlands Open land (military and airport facilities) Open land (light soil and grass) Bare ground (light and dry) Scrub forest Average constant for Tabriz

9869 3070.77 1836.57 1586.862 786.4314 600.46 17,747.1939

56% 17% 10% 9% 5% 3% 100%

0.18 0.28 0.25 0.44 0.24 0.2 –

10.08% 4.76% 2.5% 3.96% 1.2% 0.06% 22.56%

Table 5 The correlation of climatic variables on the amount of solar radiation. Climatic elements Radiation

⁎⁎

Mean temperature

Pearson correlation 0.00 N

0.88 0.00 70

Relative humidity

⁎⁎

Cloudiness

⁎⁎

−0.82 0.00 70

−0.68 0.00 70

Sunshine

⁎⁎

Radiation

⁎⁎

0.92 Sig. (2-tailed) 70

1

Correlation is significant at the 0.01 level (2-tailed).

Table 6 Regression coefficients of variables in model of entering. Variable

Constant factor model Mean temperature Relative humidity Cloudiness Sunshine

Unstandardized coefficients

Standardized coefficients

Statistics

B

Std. error

Beta

T

−6906.58 250.53 −1.36 701.97 930.99

1023.49 208.76 8.11 57.68 55.52

– 1.5 −0.01 0.68 1.5

−6.74 1.2 −0.16 12.17 16.77

Significance level

0.00 0.23 0.86 0.87 0.00

Table 7 Summary of regression indicators by entering model. Model

R

R square

Adjusted R square

Std. the error of the estimate

Durbin-Watson

1

0.98

0.96

0.95

335.3

1.8

Model

Sum of squares

df

Mean square

F

Sig.

Regression Residual Total

182,388,698.9 7,307,831.39 189,696,530.33

4 66 70

30,398,116.49 112,428.17

270.37

0.00

Table 8 Regression analysis of variance.

which is less than alpha levels of 0.01 and 0.05 (Table. 8). Fig. 9 presents the monthly average global radiation on a horizontal surface measured by Tabriz station and estimated model. The components of the hourly solar radiation, such as diffuse radiation, global solar radiation and direct radiation in Tabriz, have been generated by the Ladybug for Grasshopper Program. In this model, the rate of each component calculated according to the solar azimuth annually as shown in Fig. 10. For example, in April, the minimum rate of direct normal radiation by 140 Wh/m2 in noticeable, while it reaches above 340 Wh/m2 in Jun after 09:00 am. Regarding global horizontal radiation, there is a noticeable amount of radiation between 09:00 am and 02:00 pm in a range from Jun to October. 3.4. Solar radiation components at ground level Table 9 shows monthly sunny hours, clearness index and solar times of Tabriz City according to Eqs. (22) and (23). Potentially, Tabriz City has 4369 sunlight hours, but 30% of this amount is wasted during hazy, cloudy and foggy days. There are only 3047 sunny hours. 9

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Fig. 9. Comparing the measured and modeled monthly mean solar radiation of horizontal surfaces in Tabriz City.

Fig. 10. Hourly horizontal radiation.

Table 9 Monthly sunny hours, solar time and clearness index of Tabriz City. Month

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Sb (hrs) Sp (hrs) Κt

5.4 9.8 0.55

5.9 10.5 0.56

6.7 11.7 0.57

7.8 13 0.6

10.3 13.75 0.74

12.7 14.2 0.89

12.7 14.11 0.9

11.6 13.5 0.9

10.6 12.5 0.84

4.2 11 0.38

6.4 10.1 0.63

5.9 9.5 0.62

According to Eq. (8), the solar altitude average is 52° on March 21 at solar noon, while it decreases to 28° on December 21 and rises to 78° on June 21. Fig. 11. shows altitude angles at solar noon on Tabriz (latitude 38) in monthly average degree. According to Eq. (9), the solar azimuth angle of Tabriz City is presented in Fig. 12 using Microsoft Excel. The values are calculated for the monthly mean. The solar azimuth angle at sunrise is 90° on March 21 at 6:00, while it decreases to 60° on June 21 and rises to Altitude Angle (Degree) 90 80 70 60 50 40 30 20 10 0 1

2

3

4

5

6

7

8

Fig. 11. Altitude angles at solar noon. 10

9

10

11

12

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Fig. 12. Azimuth angle of Tabriz City.

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Fig. 12. (continued)

120° on December 2. The annual solar radiation components, such as diffuse radiation, global solar radiation and direct radiation in Tabriz, were again generated by the Ladybug for Grasshopper Program. In this model, Sothern facades (a range from 91 to 179°) are exposed in maximum rate of energy by 400 kWh/m2, 500 kWh/m2 and 900 kWh/m2 for direct, defused and total radiation respectively, while Northern facades (a range from 181 to 89°) are exposed in minimum rate of energy by 250 kWh/m2, 450 kWh/m2 and 700 kWh/m2 for direct, defused and total radiation respectively (Fig. 13.).

3.5. BM The Blue-mosque (Göy Məsçit in Azerbaijani language) of Tabriz was built in order of Jahan-Shah (Turkish king from of QaraQoyunlular) in 1448 AC (Fig. 14.). Its architectural style in Azerbaijani architecture categorized in the architectural school of Tabriz I (Ouria, 2015). It is a masterwork of Azerbaijani-styles in Iran. It should be mentioned that the majority of masterworks in ancient Azerbaijan-Iran follow their climatic condition by implementing different techniques, elements, and materials. The BM is one of the unique vernacular monument that's form follows climatic and environmental factors and that is why it has been chosen to be investigated in this paper.

Fig. 13. Radiation analysis in Tabriz City. 12

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Fig. 14. BM. (Ouria et al., 2016)

3.5.1. Determining the geometric functions of domes The size of each element is estimated in field surveying. The form of the building consists of two cubes with (8.7 m) height. Also, there are thirteen domes on its roof. The similar domes are arranged into the same category. These domes are categorized in Fig. 15. According to the method of Lagrange interpolation (Eque 33), the equation of each class of domes in the BM defined to estimate the rate of heights h(x) in different points (x). The equation of elements defines its height range according to the horizontal dimension (x), which makes it possible to compute surface area. The results of the analyzed diagrams of classification plan are presented in Table 10.

3.5.2. The solar energy in the BM According to Stephenson's cosine method (Eqs. (24)–(32)), the solar energy of vertical surfaces is evaluated. In this process, all the geographic and climatic factors, such as altitude, latitude and reflectivity (Table 4.) and sky clearness (Table 9.), have been evaluated. Fig. 16, shows the solar energy on different surfaces of the BM in Tabriz City per hour.

Fig. 15. Classification plan. 13

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Table 10 Elements equations. Group

Equation of height

A1,E1

h (x ) = −

A2,E2

) + ( x) h (x ) = x ( − x) h (x ) = (− x ) + ( x ) h (x ) = (− x ) + ( x ) h (x ) =

A3,E3

(

11 2 (x 50 1 2 − x 4

3 − 25

B1,D1

5

23 20

⎡0,+ 2 ⎤ ⎣ ⎦

73 10

2

31 40

17 200

27 2 100

C3

[0, +7]

− 7x )

1 2 8

A4,C1, E4

Dx

h (x ) =

(

9 2

47 − x 2

+

36 ⎤ 5 ⎦

⎡0,+ ⎣

12 ⎤ 5 ⎦ 17

⎡0,+ 5 ⎤ ⎣ ⎦ [0,+19]

1 h (x ) = ⎜⎛− (x 2 − 19x ) 6 ⎝

C5

⎡0,+ ⎣

)

⎡− ⎣

137 137 ,+ ⎤ 20 20 ⎦

1300

1400

1300

1200 1200 1000

950

900

1000

720

700

800

650

600 300

400

200

200 200

150

0 Annual Radiation on different surfaces (kwh/m2) Northern Wall

EasternWall

Southern Wall

Western Wall

Dom (A1,E1)

Dom (A2,E2)

Dom (A3,E3)

Dom (E3)

Dom (B1)

Dom (D1)

Dom (A4,C1, E4)

Dom (C3)

Dom (C5)

Fig. 16. Annual radiation on different surfaces in the BM (Tabriz-Iran) (kwh/m2).

Fig. 17. illustrates total radiation on the BM in critical days. In Jun, there is a dramatically increase which hits a peak at 28838 kwh/m2. It can be seen that the minimum rate of radiation is in Dec by 5511 kwh/m2. Fig. 17. 3.5.3. Solar potential in the BM The exact orientation of the BM toward South-North caused exposing in a high rate of radiation on southern envelope. Different azimuth angle causes varying rates of solar energy distribution on different faces or vertical surfaces. It is important to consider the energy behavior of exterior surfaces because it impacts energy costs, the period of energy demands and human activities. Therefore, the intensity of radiation is computed for all surfaces of the BM (Fig. 18.). Solar irradiation is calculated analytically for Tabriz City. 35000 30000

21-Jun, 28838

25000 20000

21-Sep, 19434 22-Mar, 15888

15000 10000 5000 0 11-Nov

01-Jan, 5600

31-Dec

19-Feb

21-Dec, 5511

10-Apr

30-May

19-Jul

07-Sep

Total Radiaon on the BM (kwh/m2)

Fig. 17. Total radiation on the BM (kwh/m2). 14

27-Oct

16-Dec

04-Feb

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Fig. 18. Classification plan.

The output of the analytical calculation has been fed as input to Ladybug. The data given in Tables 4 and 9 used the Gen Cumulative Sky model based on isotropic methods, which has been input to Ladybug to calculate yearly radiation. `` The result of the gendaymtx function. Use the selectSkyMtx component to select a desired sky matrix from this output for use in a radiation study, radition rose, or sky dome visualization`` (Rhino, 2019). The solar radiation rate is computed per square meter (kwh/m2). It has been computed according to the different radiation and azimuth angles of the Tabriz city on 38°N.

4. Results and summary A solar analysis of the BM in Tabriz City was conducted to analysis its passive solar energy potential. Climatic parameters, 15

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including a sky clearness coefficient, were calculated for Tabriz's sky using Duffie-Beckman and Stephenson's cosine methods. The absorbed solar energy of each surface was computed using numerical methods for the BM in Tabriz City. Calculations of solar energy absorption for each face were performed separately. 4.1. The results of climate analysis The average monthly temperature is 11.6 °C in a cold climate. Potentially, Tabriz has 4369 sunlight hours, but 30% of this amount is wasted during hazy, cloudy and foggy days. There are only 3047 sunny hours. 4.2. The results of albedo analysis The albedo rates in different districts of the city are different. Subsequently, the percentage of each type of cover measured. The albedo coefficient (0.23) is estimated for the urban scale of the Tabriz region by measuring the area of the cover types and their special coefficients. The reflectivity rate varies between 0.2 and 0.5, the lower rate of albedo in Tabriz (0.23) does help citizens feel that the urban spaces are more comfortable. 4.3. The results of orientation analysis The main aspects of the building orientated toward Southern aspect, which causes increased solar absorption in this façade. 4.4. The results of the opening analysis Regarding the severe condition of the city and prevalent wind direction, the openings are limited and there is no window in Northern façade. 4.5. The results of flat surfaces Analysis on average, vertical façades are exposed at a maximum rate from Southern aspect when the sun is low on December 21. In addition, horizontal surfaces receive maximum solar energy from the rooftop when the sun is high on June 21. lyth. 4.6. The results of domed surfaces Regarding geometrical benefits of domed surfaces in solar energy absorption rate, main domes of the BM (C3 & C5) absorb 44% more solar energy than Southern façade annually. Other domes which absorb less energy are impacted due to shadow and exposed surface area. Table 11 shows the results of surface area and shaded range of domes on the annual radiation rate. 4.7. Summary of the findings The results of this study are presented in a summarized form in Table 12. 5. Conclusion Tabriz City does not have an enormous potential to utilize solar energy, but the BM is able to produce a noticeable amount of passive solar energy because of its appropriate orientation and geometry. The solar altitude average is 52° on March 21 at solar noon, while it decreases to 28° on December 21 and reaches 78° on June 21. In December, the duration of sunlight hours is 5:45 on average, while this increases to 12:40 in July. The differences between the shortest and longest days is 6:55 h. Potentially, Potentially, Tabriz has 4369 sunlight hours, but 30% of this amount is wasted during hazy, cloudy and foggy days. There are only 3047 sunny hours remained. Total radiation on the BM computed for critical days. On Jun 21, there is a dramatic increase which hits a peak at 28838 kwh/m2. It can be seen that the minimum rate of radiation is in Dec21 by 5511 kWh/m2. Tabriz City's clearness index, the most important factor in diffusing direct beams, is 0.55 in January, and 0.90 in both Jul and August. Sky clearness influences diffused solar radiation. Therefore, global solar radiation on the city is influenced by both sky Table 11 Results of domed surfaces. Dom

(A1,E1)

(A2,E2)

(A3,E3)

(E3)

(B1)

(D1)

(A4,C1, E4)

(C3)

(C5)

Surface area Shaded range Annual radiation

Low Low 1000

High Low 1200

High Low 950

Low High 300

Low High 200

Low High 150

Low High 650

High Low 1300

High Low 1300

16

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Table 12 Summary of the findings. Issues effecting the solar energy

Good

Climate Albedo Orientation Opening Geometry

√ √ √ √

Poor

Comments

√

30% of this solar energy is wasted during hazy, cloudy and foggy days The lower rate of albedo caused feeling comfortable Exact orientation toward South-North caused absorbing high rate of energy on the southern envelope Limited opening without any window on Northern façade The proportion of two main domes without shading impact caused increasing absorption rate

clearness and buildings orientation and geometry. Orientation analysis shows good juxtaposing openings, walls and domes. However, some of the small domed elements have a shading problem, but it is not effective on total absorption. According to the energy modeling for Tabriz City using the Ladybug for Grasshopper in Rhino program, direct radiation is 400 Wh/m2, diffused horizontal radiation is 500 Wh/m2, and global horizontal radiation is 900 Wh/m2. On the other hand, Stephenson's cosine method for vertical surfaces modeling for Tabriz City shows a radiation rate for the BM of approximately 900 Wh/m2 from the south, 200 Wh/m2 from the North and 200 Wh/m2 from the East and West. Domed elements absorb 1300 Wh/m2. Conflict of interest None. References Ahrens, C.D., 2006. Meteorology Today: An Introduction to Weather, Climate and the Environment, 8th ed. Ky: Brooks/Cole, Florence. Boehmea, P., Berger, M., Tobias, M., 2015. Estimating the building based energy consumption as an anthropogenic contribution to urban heat islands. Sustain. Cities Soc. 19, 373. Cogliani, E., 2014. The role of the direct normal irradiance (DNI) forecasting in the operation of solar concentrating plants. Energy Procedia 49, 1614. Iqbal, M., 1983. Sun-earth astronomical relationships. Solar Radiation 1–28. Jakhrani, A., Othman, A., Samo, S., Kamboh, S., 2012. Estimation of incident solar radiation on the tilted surface by different empirical models. Int. J. Sci. Res. Publ. 2 (12), 1–6. Jin You, L., 2017. GEK 1506 Heavenly Mathematics: Sun and Architecture, S.L.: GEK 1506 Heavenly Mathematics. Kottek, M., 2006. World map of the Köppen-Geiger climate classification updated. Meteorol. Z. 259–260. Oke, T., 1973. City size and the urban heat island. Atmos. Environ. 7, 769–779. Ouria, M., 2015. Introduction to Architectural History of Azerbaijan, Akhtar. Tabriz 586. . (586 Ouria, M., Sevinc, H., 2016. The role of dams in drying up Lake Urmia and its environmental impacts on Azerbaijani districts of Iran. Saussurea 6 (1), 54–65. Ouria, M., Sevinc, H., 2017. Evaluation of the potential of solar energy utilization in Famagusta, Cyprus. Elsevier 37 (1), 189–202. Ouria, M., Akçay, A., Azami, A., 2016. Quantitative investigation on shaded area according to the geometry of blue-mosque domes in Tabriz-Iran. Int. J. Arch. Eng Urban Plan. 26 (1), 1–13 University of Teharan. Paulescu, E., Gravila, P., Badescu, V., 2013. Weather Modeling and Forecasting of PV Systems Operation, 1st ed. Springer-Verlag London, London. Qingqing, Z., et al., 2012. Spatial analysis of land use and land cover changes in the recent 30 years in the manas river basin. Procedia Environ. Sci. 12, 906–9016. Rhino, 2019. https://rhino.github.io/components/ladybug/genCumulativeSkyMtx.html. Shukla, K., Rangnekar, S., Sudhakar, K., 2015a. Mathematical modeling of solar radiation incident on the tilted surface for photovoltaic application at Bhopal, M.P., India. Int. J. Ambient. Energy 37 (6), 579–588. Shukla, K., Rangnekar, S., Sudhakar, K., 2015b. Comparative study of isotropic and anisotropic sky models to estimate solar radiation incident on the tilted surface: a case study for Bhopal, India. Energy Rep. 1, 96–103. Steinhilber, F., Beer, J., Frohlich, C., 2009. Total Solar Irradiance during the Holocene. American Geophysical Union, pp. 1.

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