Solar Performance of Elliptical Domes
Mashina, G.
BRC, Tajoura, Tripoli, Libya
Abstract: In regions with hot desert climates, the improvement of comfort by passive solar
techniques is a very important issue. In this study, variation of the direct solar radiation over
domed roofs was estimated and compared with standard horizontal flat roofing, using a new
computer model. A number of investigations have been carried out on elliptical domed shapes
with varying cross-section ratio CSR1 (height/width) and orientations to study their solar
performances. The comparison showed that the use of the domed roofs leads to a significant
improvement of indoor space in summer.
Key,words: Domed roof, Elliptical dome, Solar Performance, Curved Surface, Passive Solar
System
Introduction
Economic buildings can be built in such a way that the structural elements are designed and
oriented to take maximum advantage of the local climate [1]. Olgyay [2] and Fathy [3]
indicated that the curved roofs can reduce local radiant flux on a rounded surface. As a result,
the heat flowing into buildings will be reduced. Bahadori [4] mentioned that domed
geometrical structures with vents in their crowns increase natural ventilation through
buildings. As a result, the indoor air will not become humid and the mean radiant temperature
can be reduced. Gadi [5] reported that about 40% of domed roofs would be reduced from
direct solar radiation. According to Vector [6], at noontime, the dome’s performance is
always better than that of a horizontal surface.
The Geometrical Resemblance
Wang [7] mentioned that the continuous curved surfaces could be approximated using a finite
number of small flat planes. Elseragy [8] also explained that it is possible with an acceptable
result to undertake calculation of radiation incidence on a large number of infinitesimal tilted
planers that resembled the curved forms
In this study, the curved exposed surface has been divided into a number of small flat planers
called “elements” as shown in Fig.1, The element can be a horizontal, vertical, or tilted
surface; the slope angle for each element is different from the others, depending on the
surface curvature of the exposed surface. The solar irradiation on each element depends on its
specific orientation and tilt angle, and upon the other common parameters such as the time,
latitude, atmospheric conditions and ground reflectivity. The total solar radiation received by
the entire exposed surface can be estimated as the sum of the irradiation on the surfaces of all
elements.
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Figure 1: Elliptical dome surface
Calculation of Direct Solar Radiation
Several geometric calculations are needed to compute the direct solar radiation (DSR)
received by the dome surface: the slope, the area, and the azimuth angle for each grid cell. For
area calculation, a simple algorithm was developed to calculate the area of trapezium and
triangular elements. The tilt angle for each element on the dome surface is the angle between
the element surface and the horizontal plane. The surface azimuth angle for the domed form
can be defined with respect to the major axis, which is perpendicular on the cross section
form. The orientation of each element depends on the element angle and the deviation angle
of an element surface with respect to the x-axis may be determined by taking the changes of
the coordinates between nodes.
Validation of the Developed Program
The performance of the developed simulation program has been validated through comparing
its results with the results of three different proven available models, namely ESRA [9], SRSM
[10] and RadOnCol [11]. Two statistical indicators were used: root mean square error, RMSE
and mean absolute error, MAE. Comparison results for DSR intensity have illustrated as
shown in table 1. a good agreement in the summer and winter months
Table 1: Comparison results for DSR intensity in terms of MAE and RMSE
Seasons
MAE
RMSE
Rad
ERSA
SRSM
Rad
ERSA
Summer
1.56
-0.28
0.21
1.67
0.04
Winter
0.65
1.02
0.8
0.66
1.06
SRSM
0.376
0.846
Evaluation of the Elliptical Dome Form
The amount of DSR received by an elliptical domed (CSR2=depth/width ≠1) surface with
difference cross section ratios (CSR1=1,2,4) at latitude 30°N directed to a N-S orientation in
2
the summer season is 16.59 MJ / m for a CSR1 of 1, while the amount of DSR received by a
2
domed surface of CSR1=2 is 11.75 MJ / m . These values show approximately a 35.9% and a
54.4% reduction in the flux of solar radiation compared with the amount of DSR received by a
2
horizontal surface (25.9 MJ / m ). Meanwhile, for its counterpart season, the DSR received by
2
an elliptical domed (ED) surface varies from 10.86 to 10.26 MJ / m when changing the CSR1
from 1 to 2. This loss is from 2.5% to 7.9% with respect to that received by a horizontal
2
surface (11.14 MJ / m ).
2
For the W-E orientation, in the summer months, the DSR received by an ED varies from 18.09
2
to 14.20 MJ / m for a CSR1 equal to 1 and 2 respectively. The loss in the amount of DSR
received compared with that received by a horizontal surface is between 30.2% and 45.1%.
Meanwhile, the winter shows a loss of between 9.9% and 20%, since the variations in DSR
2
are from 10.04 and 8.91 MJ / m for the same values of CSR1 (1 and 2). The obtained
simulation results for ED solar performance at different orientations are represented in table 2.
Table 2: The percentage reductions in loss
Orientation
Season
Loss in of DSR (%)
CSR1=1
2
4
W-E
Summer
30.2
45.1
56.2
Winter
9.9
20
27.9
N-S
Summer
35.9
54.4
68.3
Winter
2.5
7.9
12.9
NE-SW
Summer
32.8
49.5
61.5
Winter
6.8
15
21.5
NW-SE
Summer
32.8
49.5
61.6
Winter
6.8
15
21.5
The results of the considered cases can indicate that a number of interesting points may be
summarised as follows:
1-
The curved surface in any orientation is more efficient than a flat surface during the
summer (all curved surfaces with different curvatures receive less DSR than the
horizontal). However, the domed form is not preferable in the winter.
2-
The curved surface in an N-S orientation is more efficient than the other orientations. It
receives less DSR in summer and a larger amount in winter.
3-
As the CSR1 increases, the curved surface becomes more efficient during summer time.
The solar performance of an ED surface with different curvatures can also be illustrated using
the radar graphs as seen in Fig.2. Eight orientations (N, NE, E, SE, S, SW, W, and NW) are
presented, one on each axis, and then connected with a line to form an octagon. Ticks on the
scale that run along the radial axes are arranged to begin in the centre with a zero value and
extended towards the outside.
Fig.2. shows the DSR intensity values received by the ED surfaces in the summer time, with
three different cross-section ratios (CSR1=1, 2, and 4). The highest DSR is received by the
dome with lowest CSR1 (the outer line), while the minimum DSR values were received by the
dome with the highest CSR1 (the inner octagon). The curved surface of a domed form when
its orientation is N-S is predicated to receive more DSR than any other direction. For this
reason, the summer radar graph shows a slightly unsymmetrical octagon. When the ED height
is short (CSR1 value is very close to zero), the impact of the orientation on the amount of
solar radiation received by the exposed surface is insignificant. In the winter, the radar graph
in Fig.2. shows that there is less effect of a cross-section ratio on the amount of the DSR
received compared with its effect in the summer.
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Figure 2: The received DSR on ED surfaces in summer and winter
The radar graph also illustrates that the domed form is predicated to receive more DSR when
its orientation is W-E than for any other orientation. This could be due to the fact that the two
sections of the dome form in the W-E orientation are directly facing the Sun in the early
morning and late afternoon. It is important to point out that, with reducing the cross-section
ratio, the octagon shape becomes more symmetrical (when CSR1=0 the shape becomes a
circle).
The simulation results show that the ED surface in any orientation is more efficient than that
of a flat surface during the summer. However, the domed form is not preferable in the winter.
The N-S orientation (short axis direction) is more efficient than the other orientations. It is
also clearly seen from the results that, as the cross-section ratio CSR1 increases the domed
surface becomes more efficient during summer time.
References
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review, Department of mechanical Engineering, National Institute of technology, Jamshedpur,
INDIA
[2] Olgyay, V., (1973). Design with Climate. Princeton University Press, Princeton
[3] Fathy H., (1986). Natural Energy and Vernacular Architecture. Chicago and London, the
University of Chicago Press
[4] Bahadori M. N., (1985). Haghighat, Passive Cooling in Hot Arid Regions in Developing
Countries by Employing Domed Roofs and Reducing the Temperature of Internal Surfaces,
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[5] Gadi M., (2000). A Novel Roof-integrated Cooling and Heating System, International
Journal of Ambient Energy, Vol. 21, No. 4, pp 203-212
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[7] Wang S., Boulard T., (2000). Measurement and Prediction of Solar Radiation Distribution
in Full-Scale Greenhouse Tunnels, Agronomie, Vol. 20, pp. 41-50
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[8] Eleseragy and Gadi, (2003). Computer Simulation of Solar Radiation Received by Flat
Roof in Hot-Arid Regions, Eighth International IBPSA Conference, Eindhoven, Netherlands.
[9] Rigollier, C., Bauer, O. Wald, L. (2000), On the Clear Sky Model of the ESRA-European
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[10] Exell R. H. B. (1999), Solar Radiation Simulation Model.,
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Technology Thonburi
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[11]
Gary,
(2009),
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www.builditsolar.com/Tools/RadOnCol/radoncol.htm
On
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Collector
of
Program,
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