Simulation of a Conical Solar Collector for Steam Generation Khaled MAHDI and Nadir BELLEL Energy Physics Laboratory, University of Mentouri Constantine, Algeria Abstract. In the world, impure water is a major health problem. More than one billion people lack access to safe drinking water. Diseases due to water are responsible for about 80% of diseases in developing countries. Conical solar collector usually consists of a conic form solar energy concentrator, which reflects solar energy into a cylindrical absorber. The absorber is a tube, painted with solar radiation absorbing material, located at the truncated cone, the concentration ratio ranges from 3.6 to 26, depending on the radius of the aperture of the conic solar energy concentrator. The average absorber temperature can reach a temperature up to 300 °C, depending on the concentration ratio, solar intensity, wind speed and other parameters. Hence, such collectors are an ideal device for power generation, water desalination applications and sterilization. Keywords: conical solar concentrator, rate heat, steam production. Nomenclature kinematic viscosity of air A surface, m2 Stefan Boltzmann Cst, 5.6710 8 W/m 2 K 4 T température, °C z zenith angle, C geometrical concentration ratio Exposant, Indices Q ratio heat, W 1 lateral surface of absorber I radiation flux, W/m2 2 top surface of absorber F Factor view 3 bottom surface of absorber J radiosity 4 aperture of cone t step time, s 5 mirror h s solar elevation, ° amb ambient h heat exchange coefficient, W/°Cm 2 g ground k thermal conductivity of air, W/°Cm f film R radius, m use useful, V 0 velocity of the wind, m/s abs absorber D’ dimensions of the side of a square loss loss whose area is equal to surfaceA 2 , m rad radiation Gr Grashof number conv convection Pr Prandtl number cond conduction m mass, kg w water z altitude, m N incident normal radiation Symboles grecs o extra-terrestrial Absorptivity 1−4 shape factor of surface 1 to surfaces 4 Reflectivity 1−5 shape factor of surface 1 to surfaces 5 Emissivity 1−g shape factor of surface 1 to ground Efficiency 1s shape factor of surface 1 to sky 1. Introduction Corresponding author. Tel.: + 213661301958; fax: +21331811278 E-mail address: [email protected]International Proceedings of Chemical, Biological and Environmental Engineering, Vol. 91 (2016) DOI: 10.7763/IPCBEE. 2016. V91. 1 1
Transcript
Simulation of a Conical Solar Collector for Steam Generation
Khaled MAHDI and Nadir BELLEL
Energy Physics Laboratory, University of Mentouri Constantine, Algeria
Abstract. In the world, impure water is a major health problem. More than one billion people lack access
to safe drinking water. Diseases due to water are responsible for about 80% of diseases in developing
countries. Conical solar collector usually consists of a conic form solar energy concentrator, which reflects
solar energy into a cylindrical absorber. The absorber is a tube, painted with solar radiation absorbing
material, located at the truncated cone, the concentration ratio ranges from 3.6 to 26, depending on the radius
of the aperture of the conic solar energy concentrator. The average absorber temperature can reach a
temperature up to 300 °C, depending on the concentration ratio, solar intensity, wind speed and other
parameters. Hence, such collectors are an ideal device for power generation, water desalination applications
and sterilization.
Keywords: conical solar concentrator, rate heat, steam production.
Nomenclature kinematic viscosity of air
A surface, m2 Stefan Boltzmann Cst, 5.67108
W/m2K
4
T température, °C z zenith angle,
C geometrical concentration ratio Exposant, Indices Q ratio heat, W 1 lateral surface of absorber
I radiation flux, W/m2 2 top surface of absorber
F Factor view 3 bottom surface of absorber
J radiosity 4 aperture of cone
t step time, s 5 mirror
hs solar elevation, ° amb ambient
h heat exchange coefficient, W/°Cm2 g ground
k thermal conductivity of air, W/°Cm f film
R radius, m use useful,
V0 velocity of the wind, m/s abs absorber
D’ dimensions of the side of a square loss loss
whose area is equal to surfaceA2, m rad radiation
Gr Grashof number conv convection
Pr Prandtl number cond conduction
m mass, kg w water
z altitude, m N incident normal radiation
Symboles grecs o extra-terrestrial
Absorptivity 1−4 shape factor of surface 1 to surfaces 4
Reflectivity 1−5 shape factor of surface 1 to surfaces 5
Emissivity 1−g shape factor of surface 1 to ground
International Proceedings of Chemical, Biological and Environmental Engineering, Vol. 91 (2016)
DOI: 10.7763/IPCBEE. 2016. V91. 1
1
Thermal solar collectors can be classified into three categories, Point collector (high temperature, order
of 1000°C or more), line collector (intermediate temperature, order of 300C or more) and plane collector
(low temperature, order of 100C or less) [1]-[3]. Point collectors usually consist of a parabolic mirror, which
concentrates the solar radiation into a small area (point), or it consists of many mirrors directing the solar
energy into a small region.
Those mirrors are usually monitored electronically. This type of collector needs a sophisticated solar
tracking mechanism and usually applied in power generation, metal melting, hydrogen production, etc.
The second type of the collector is the line collector, which usually consists of a parabolic cylinder that
directs solar radiation into a tube (line), located at the focal length of the collector. The conical solar
concentrator, shown in Fig. 1, is one of the line focusing concentrators.
It can be used over a wide range of concentration ratios depending on the relative dimensions of the
conical mirror and the central axial absorber. During the late 19th and early 20th centuries, solar collectors
with conical concentrators were operated as steam generators for solar power generating units.
The conical solar concentrator possesses the further advantage of being simple to manufacture [1] and of
having high concentration efficiency. The present work is a theoretical study of the conical solar
concentrator under perfect tracking conditions.
The climatology data of Constantine the concentrator receives approximately 800W/m2 of direct incident
normal solar radiation (dependent upon time of year), which is concentrated and reflected to the receiver.
By concentrating the incoming radiation, the operating temperature of the system increases significantly
and subsequently increases the efficiency of the conversion. The absorber average temperature and the
different rate heat distribution along the absorber are determined. The meteorological effect (incident rays,
wind), geometrical concentration, and the dimensions of the mirror absorber assembly on the local and
integrated concentration ratios are investigated.
These values are so chosen as to span a wide range of concentration ratios. Although some values may
be of slight, or no, practical significance, they are necessary to present a complete picture.
2. Description of the Prototype
Fig. 2 illustrates a complete profile, conical concentrator with a vertex angle equal to 90°, and a
cylindrical axial receiver. Under the perfect-tracking assumption, the direct solar radiation is always incident
in a direction parallel to the axis of the cone. The incidence angle is the same at all points of the reflecting
surface and is equal to 45°. Thus, the total reflectivity is constant all over the mirror surface. The solar rays
are diverted, by reflection, through an angle, 45°, and redirected to fall orthogonal on the axial absorber.
Fig. 1. Conical solar concentrator [2].
Fig. 2. design of the collector showing the surfaces 1-5
[3]
A prototype of solar conical concentrator was designed and tested. The design was achieved with the aid
of a FORTRAN program as a simulator.
3. Theoretical Model
2
The energy absorbed is partly lost to the atmosphere by convection and radiation and the rest is used for
heating the fluid (water) in the absorber.
Neither the energy absorbed nor the heat lost by the absorber is uniform over its surface.
The conical concentrator has the following parameters (Table 1).
3.1. Evaluation of solar radiation The solar conical concentrator was theoretical tested under Constantine climatic condition for the 22
December and 21 June where computing started at 10:00 a.m. to 2:00 p.m.
Constantine is situated on a plateau at 640 m above sea level in the center of eastern Algeria (latitude
36.23° N, longitude 7.35° E). The climate of the region is continental characterized by temperature of 25–38
in summer and 2–12 °C in winter [1], [2]. Ground level radiation can be estimated using Hottel’s clear sky
model for urban visibility 5 km at Constantine Altitude of Constantine (z) = 640 m = 0.640 km. Constants ao,
a1, k in Hottel’s model can be calculated as follows:
Table 1: Values used in the theoretical model program A1(m
2) 3.1415e−1
A2(m2) 3.1415e−2
A3(m2) 3.1415e−2
A4(m2) 1.1309
A5(m2) 1.4721
L(m) 0.4
C A4/ A1=
1=2=5 0.95
a 0.7
g 0.9
5 0.8
g 0.2
(kg/m3) 1.26
(Pas) (0.0046 Tf + 1.7176) 1. e−5
k(W/m2°C) 7.57e−5 Tf + 0.0242
mw(kg) 3.
mabs(kg) 0.95
cp(J/kgK) 4190
cabs(J/kgK) 465
3.2. Geometric concentration ratio for designed collector Where terms are defined in the nomenclature,
Fig. 3. Boundary of the absorber system
The energy absorbed is partly lost to the atmosphere by convection and radiation and the rest is utilized
for heating the fluid (Water) in the absorber. Neither the energy absorbed nor the rate heat lost by the
absorber is uniform over its surface (Fig. 3).
( ) ( ) and
(
)
(
)
3
Where the radiosities J1 and J2 are given by [3], [4]:
( )( )
( )(
)
And
(
*√(( ) )
+)
Since surface two is always kept normal to the solar rays, then:
[ ( )]
[ ( )]
The emissivity of the atmospheric air is given by [5],
[ ( ) ]
Where Tamb, is in °C, when Tamb ambient temperature is changes between 25 and 38°C in summer and
between 2 and 12 °C in Winter, a: varies between 0.7 and 0.9.
Were The total rate heat loss is given by:
and the rate heat useful:
is transferred to the water in the cylinder, and is given by:
[ ( ) ( )
(
)
(
)]
dTabs(t)/dt is the rate of change in time of the instantaneous absorber temperature of the system [6].
( ) ( )
The temperature of the absorber Tabs rises rapidly from the room temperature and reaches a constant
value. At this value the heat losses are equal to energy absorbed and Tabs = T1.
The values of the heat transfer coefficients are highly dependent on the velocity of the wind blowing
with respect to the cylinder. The heat transfer coefficient h1 is given by [7].
(
)
Where k and v are to be evaluated at the film temperature Tf When the wind velocity is zero, the heat
transfer from the cylindrical receiver will be by free convection and will be given by [8]:
( )
Where:
And
4. Results and Discussion
The computer simulation for both the bare receiver and the solar oven type models were solved under
different meteorological conditions and for various cylindrical receiver radiuses. Sets of runs were conducted
using water as the working fluid. the starting time of simulation was 10:00 and the runs continued until water
reached the boiling temperature (100°C) until 14:00.
Fig. 4. Absorber temperature measured and calculated
0
20
40
60
80
100
120
140
10 10.5 11 11.5 12 12.5 13 13.5 14
Ab
sorb
er t
em
pera
ture (°C
)
Hours of the day
experimental theoretical
Steam production
4
The following Fig. 4 shows the evolution of the temperature of the absorber measured and calculated
according to the time the Rung-Kutta method of fourth order [9]. The two temperatures have the same allure.
The difference between the calculated and measured temperature [10] is due to the optical errors of the
concentrator, solar tracking system, focusing of the absorber, the wind speed varies during the experiment,
and especially the value of the solar illumination, which is therefore different theoretical value of the actual
value.
4.1. Hourly evolution of the temperature of the absorber We show in Fig. 5 and Fig. 6 a variation of solar radiation with the hours of the day under the perfect-
tracking assumption, the direct solar radiation is always incident in a direction parallel to the axis of the cone.
These radiations were calculated with coefficients of transmission according Hottel’s model.
Fig. 5. Hourly variation of direct normal solar radiation
(IN) and absorber temperature (Tabs) for 22 December
Fig. 6. Hourly variation of direct normal solar radiation
(IN) and absorber temperature (Tabs) for 21 June
We note that the solar power received at the cone opening with tracking system is higher compared to
the solar radiation direct received without tracking system. The tracking system allows solar radiation gain of
about 45% in winter and 10% in summer; this variation is due to the influence of the solar altitude. At the
beginning of the heating, at t = 10 local time, the temperature of the absorber is equal to ambient temperature,
after five minutes of heating, the temperature increases as a function of solar radiation concentrated in the
opening of the absorber, it reached 30 ° C in winter and 50 ° C in summer. It continues to increase as its
value becomes stationary [3], [4], in this case the absorber is in thermal equilibrium, that is to say that all the
surfaces of the absorber at the same temperature, if the influence wind persists the state of thermal
equilibrium is very difficult. The maximum ambient temperature is reached between 12:00 and 13:00 hours
when solar radiation is important.
We observe that the temperature of the absorber can reach the order of temperatures of 200°C in summer,
by against the winter heating reduces its value to 120°C, in winter and with the fall of solar radiation, the
temperature of the absorber decreases slowly after 14:00.
4.2. Hourly evolution heating time The following Fig. 7 and Fig. 8 shows the variation of the temperature of the absorber during these two
different days. The temperature increases over time in the four heating operations. After each cooling, the
temperature of the whole water-absorber becomes equal to the ambient temperature. There is a difference
between the temperature of the absorber in winter and in summer, due to the solar radiation intensity.In the
summer, we observed that the heating season does not greatly influence the temperature of the absorber. In
winter the receiver temperature depends on the heating period, it reaches high temperatures between 12:00
and 13:00. During this period, the solar radiation value is important, the choice of the period of the
experiment to minimize the heating time.
680
690
700
710
720
730
740
750
760
770
780
0
20
40
60
80
100
120
140
10 10.5 11 11.5 12 12.5 13 13.5 14
Dir
ect
no
rm
al
sola
r r
ad
iati
on
(W
/m²)
Ab
sorb
er t
em
pera
ture (°
C)
Solar time (h)
Steam production
IN Tabs
Ta
880
885
890
895
900
905
910
0
50
100
150
200
250
10 10.5 11 11.5 12 12.5 13 13.5 14
Dir
ect
no
rm
al
sola
r r
ad
iati
on
(W
/m²)
Ab
sorb
er t
em
pera
ture (
°C)
Solar time (h)
Steam production
IN Tabs
Ta
5
Fig. 7. Hourly variation of absorber temperature (Tabs),
ambient temperature (Ta) and direct normal solar
radiation (IN) for 22 December
Fig. 8. Hourly variation of absorber temperature (Tabs),
ambient temperature (Ta) and direct normal solar
radiation (IN) for 21 June
4.3. Hourly evolution of the rates heats Exact evaluation of the rate heat is difficult. It depends highly on the velocity of the wind blowing with
respect to the cylinder. in the following Fig. 9 and Fig. 10, showing us the evolution of the rate heat loss and
useful and consumption during heating in the two different days. we find that the solar energy absorbed by
the absorber is less than the energy recieved by the opening of the cone. This variation is due to the reflection
losses of conical reflector and the absorption of cylindrical receiver (absorber).
Fig. 9. Hourly variation of loss (Qloss), useful (Quse) heat
and Efficiency () for 22 December
Fig. 10. Hourly variation of loss (Qloss), useful (Quse)
heat and Efficiency () for 21 June
When the temperature of the absorber increases, the receiver transfers the heat conduction through the
environment, radiation and convection [11], [12]. In addition, the difference between the temperature of the
absorber and the air is, the greater the rate heat loss from the absorber are large and the rate heat useful
decreases. Heating continues until reaching the thermal equilibrium state between the rate heat useful and
loss or at 10:25 in summer and at 14:15 in winter. In this point the temperature of equilibrium is reached.
The rate heat useful absorbed by the lateral external surface of the absorber; used to heat the water which is
inside the receiver and increases its temperature up to the boiling temperature. The value of the effective
power consumed by the opening of the absorber during the summer is greater than that of the winter.
4.4. Hourly evolution efficiency of the conical concentrator The green curves in Fig. 9 and Fig. 10 show the variation of the efficiency of the concentrator during the
heating. The efficiency is maximal at the beginning of heating where the temperature of the absorber is equal
to the ambient temperature. The absorber does not transfer heat to the ambient environment. When the
temperature increases, the efficiency decreases to become equal to zero at the point of thermal equilibrium.
680
690
700
710
720
730
740
750
760
770
780
0
20
40
60
80
100
120
10 10.5 11 11.5 12 12.5 13 13.5 14
Dir
ect
no
rm
al
sola
r r
ad
iati
on
(W
/m²)
Ab
sorb
er t
em
pera
ture (
°C)
Solar time (h)
IN
Steam production level
Tabs
Ta
880
885
890
895
900
905
910
0
20
40
60
80
100
120
140
160
180
10 10.5 11 11.5 12 12.5 13 13.5 14
Dir
ect
no
rm
al
sola
r r
ad
iati
on
(W
/m²)
Ab
sorb
er t
em
pera
ture (
°C)
Solar time (h)
Steam production level
IN
Tabs
Ta
-40
-30
-20
-10
0
10
20
30
40
50
60
70
-300
-200
-100
0
100
200
300
400
500
600
700
10 10.5 11 11.5 12 12.5 13 13.5 14
Eff
icie
ncy %
Hea
t (W
)
Solar time (h)
Thermal equilibirium point
Qloss
Quse
-60
-40
-20
0
20
40
60
80
-400
-200
0
200
400
600
800
1000
10 10.5 11 11.5 12 12.5 13 13.5 14
Eff
icie
ncy %
Hea
t (W
)
Solar time
Thermal equilibirium point
Qloss
Quse
6
After thermal equilibrium point, the efficiency becomes negative; the concentrator heats the environment
and is not used wisely. In this case, it is necessary to stop the water heating. [13], [14]. The winter heating
time is long compared to the summer because the summer equilibrium temperature is determined by 11:00
against winter it is 11:20.
4.5. Hourly influence of the intensity of the wind speed In Fig. 11, t = 10: 00 local time, the temperature of the absorber is equal to the ambient temperature. The
temperature decreases as a function of the intensity of the wind speed, it reaches a temperature of over 200 °
C for a low wind equal 2m / s and a temperature of over 150 ° C for a strong wind equals 12 m / s for the
same day.
Fig. 11. Hourly variation of absorber temperature (Tabs)
with speed wind for 21 June
Fig. 12. Hourly variation of absorber temperature (Tabs)
with different masse of water and geometrical
concentration for 21 June
4.6. Hourly influence of the absorber radius Fig. 12 above shows the influence of the radius of the absorber on the temperature of the absorber, the
decreasing of the radius cylindrical receiver causes increasing the geometric concentration which increases
the temperature of the absorber and decrease the side surface (heat exchange area) decreasing heat flux loss
to the environment outside.
5. Conclusion
In this paper we presented a theoretical model for the evolution of the temperature of the cylindrical
absorber that functions with energy provided to it by conical reflector. We also validated the model by
presenting a comparison of the model against experimental data [7]. Even though the model is simple it is
able to describe the physical phenomena. It can accurately reproduce the time of steam production, which is
when the phase transition begins in the thermodynamic system, even when we have a higher geometric
concentration combined with a lower irradiance (in Winter). Under the perfect-tracking assumption, the
direct solar radiation is always incident in a direction parallel to the axis of the cone. The times taken for
steam formation corresponding to different direct intensities, ambient temperatures, and different wind
speeds were also calculated theoretically. The results are shown in Fig. 4 and Fig. 5. The increase in wind
velocity increases the heating time.
The rate of rise of temperature can be increased by surrounding the cylindrical absorber by a glass tube
and evacuating the space. The use of a glass cylinder containing black fluid as a receiver is under
investigation. For such a receiver the convection and radiation losses will be appreciably small.
6. References
[1] J. A. Duffie and W. A. Beckman, Solar Energy Thermal Processes. Wiley, New York, 1991.
[2] M. M.Cobble, Analysis of a solar conical concentrator, Solar Energy 7,75, 1963.
0
50
100
150
200
250
10 10.5 11 11.5 12 12.5 13 13.5 14
Ab
sorb
er t
em
pera
ture (
°C)
Solar time (h)
2 m/s
4 m/s6 m/s8 m/s
10 m/s12 m/s
0
50
100
150
200
250
300
350
400
450
500
550
600
10 10.5 11 11.5 12 12.5 13 13.5 14
Ab
sorb
er t
em
pera
ture (°C
)
Solar time (h)
26 13.5 9.36
7.29 6 5.22
4.64 4.20 3.86
3.6
7
[3] M. N. Bahadori, Design of a solar autoclave, Solar Energy, 18, 489, 1976.
[4] Sparrow, E. M. (1973). Radiant interchange between surfaces separated by non absorbing and non emitting media,
in Handbook of Heat Transfer (Edited by W. M. Rohsenow and J. P. Hartnett), pp. 15-29 to 15-52, McGraw-Hill,
New York.
[5] D. Faiman, Solar thermal Collectors. Introduction to solar energy. Lecture 5 version 3 .1, 2003
[6] O. C. Jorgensen, Collector heat capacity effect on solar system performance, Solar Energy, Vol .29. No.2. pp 175-
176, Printed in Great Britain. 1982.
[7] S. S. Mathur, J. K. Sharma, Aman Dang And H. P. Garg, Design and development of a solar Conical concentrator,
Energy Research, John Wiley & Sons, Ltd, Vol. 6, 73-81, 1982.
[8] F.Kreith, Principles of Heat Transfer, IEP-A Dun Donnelley publisher, New York, 1976.
[9] N. Bellel, Study of two types of cylindrical absorber of a spherical concentrator, Energy Procedia, Vol. 6, pp 217-
227, 2011
[10] K. Mahdi, N. Bellel, Development of a Spherical Solar Collector with a cylindrical receiver, Energy Procedia,Vol.
52, pp 438 – 448, 2014
[11] K.Mahdi, N. Bellel, Estimation of Steam Production in a Receiver Under Solar Concentrating Radiation,
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