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CHAPTER 4
DESIGN AND OPTIMIZATION OF THE CONCENTRATOR
This chapter deals with design and fabrication of the concentrator and its optimization with
regard to cost and capability to produce enough heat for distillation of required quantity of
drinking water for an average family in the rural areas. Details of different types of concentrators
have been presented in this chapter. The design of a concentrator depends on the amount of
water to be evaporated and the intensity and variation of solar radiations available over a day.
Optimization of the concentrator entails selection of proper material and the size and shape of the
concentrator.
4.1 Selection of Solar Collector
In order to evaporate large quantity of water in a short time, required temperature needs to be
attained at the area/location where absorber is kept. Non concentrating solar collectors like a flat
plate collector can achieve temperature in the range of 600C to 800C with 20% to 25% efficiency
(Subodh Kumar et al., 1995). In panel or curved surface collectors, some part of solar energy is
reflected on the pot and some reflected outside the pot which results in substantial loss of energy.
This is because the shape of the concentrator is not perfectly parabolic.
Maximum utilization of solar energy is achieved in concentrating collectors and in a short time
the required heat can be generated at the absorber. Reviews show that temperature achieved
using parabolic concentrators is in the range of 2000C to 2500C with 30% to 35% efficiency
(Suple and Thombre, 2013).
4.1.1 Solar energy harvesting devices
There are two main types of solar energy systems. The photovoltaic (PV) system converts solar
radiation directly into electricity, and the solar thermal system converts solar radiation into useful
heat. In solar thermal systems, solar collectors are used to harness energy from the sun. The solar
collector is a device that basically absorbs solar energy in the form of heat through a heat transfer
medium and converts it into useful energy. The heat energy collected can then be used for
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various applications like electric power generation, cooking and water desalination. Solar
collectors are classified as concentrating and non-concentrating solar collectors. The
concentrating solar collectors use reflectors to focus and concentrate the solar radiation onto an
absorber. The non-concentrating solar collectors do not focus the solar radiation but only use flat
surface absorbers to capture the solar energy. The non-concentrating collectors are characterized
with low efficiency as compared to concentrating solar collectors (Agboola, 2012).
Types of concentrator collectors include parabolic trough, linear fresnel, dish collectors and
heliostats. Figure 4.1 shows different types of parabolic concentrators.
(a) Parabolic trough (b) Linear Fresnel (c) Dish collectors (d) Heliostats
Figure 4.1 Types of Solar Collectors
a. Parabolic trough: Parabolic trough collector is a type of concentrating solar collector that
uses the mirrored surface of a linear parabolic concentrator to concentrate direct solar
radiation on to an absorber tube running along the line joining the foci of the parabolas.
Parabolic troughs are devices that are shaped like the letter ‘u’. The troughs concentrate
sunlight onto a receiver tube that is positioned along the focal line of the trough.
51
b. Linear fresnel: The linear fresnel collector system consists of a set of parallel array of
linear mirrors which concentrate light on to a fixed receiver mounted on a linear tower. The
system operates on the principle of Fresnel. The system is similar to parabolic trough but it
is not parabolic in shape. It is also similar to the heliostat system, but the receiver is a linear
tube mounted on a tower not very high above the collector.
c. Dish collector: A parabolic dish collector is a point-focus collector that tracks the sun and
concentrates its energy onto a receiver located at the focal point of the dish. All the incident
rays parallel to its axis get reflected at a point called focal point. The dish structure must
track fully the sun to reflect the beam onto the thermal receiver. The receiver absorbs the
solar energy and converts it to thermal energy. A parabolic dish collector is similar in
appearance to a large satellite dish but has mirror-like reflectors and an absorber at the focal
point.
d. Heliostats field: The heliostat field solar thermal plant consists of a central receiver known
as power tower which is surrounded by a large array of heliostats field collectors. The
heliostats are flat mirrors that track the sun and reflect the solar energy onto a central point
receiver. The energy is transferred to a fluid (water, air, liquid metal and molten salt have all
been used) which is then pumped to the required application (Agboola, 2012).
Dish collectors are of two types, Scheffler’s collector and parabolic dish concentrator. In
Scheffler’s system, a section of parabolic curve is used and the focal point is away from the dish
as shown in figure 4.2.
a) Scheffler’s concentrator b) Parabolic dish concentrator
Figure 4.2 Parabolic Dish Collectors
52
A parabolic dish system with automated tracking tracks the sun and concentrates the sun's rays
onto a receiver located at the focal point in front of the dish. In some systems, a heat engine,
such as a Sterling engine, is linked to the receiver to generate electricity. Parabolic dish systems
can reach a temperature of 10000C at the receiver and achieve high level of efficiency for
converting solar energy into electricity in a small-power capacity range.
A solar concentrator works by reflecting solar radiation to a small area where heating pot is
located. The area at which the pot is kept is called focal area where as the heating pot is termed
as an absorber. The parabolic concentrator is supported on a stand which also incorporates a
support at the focus for the cooker. To collect the maximum amount of sun rays on to the cooker,
the parabolic concentrator should always be in line with the sun as shown in figure 4.3 and sun
rays should be incident perfectly normal to parabolic concentrator. Manual alignment of the
concentrator to the sun is required regularly (every 10-15 minutes) if there is no automatic
tracking mechanism.
Figure 4.3 Principle of Solar Concentrator
The drawback of Scheffler’s or trough system is that it requires continuous tracking using
electricity and also has high initial and maintenance costs (Kalogirou, 2011). Considering the
system which is to be used for a family, especially in rural areas, parabolic dish concentrator
with manual tracking seems to be a viable solution. Considering this a parabolic concentrator has
been selected as a heating source for water desalination system.
53
4.1.2 Energy requirement
The system is being designed to fulfill the daily requirements of drinking water of a rural family.
It is important to find the quantity of water that is required and consequently the amount of heat
energy required to evaporate the required quantity of water.
Review and analysis show that bare minimum water requirement for a person is 2 liters per day
(Courtesy- World Health Organization and Renal and Urology News). Considering a family of 4,
a system needs to be designed to evaporate 8 liters of water. Further, considering that solar
energy is available for nearly 7 hours a day. The system should be capable of evaporating the
required quantity of water in 7 hours. Energy needed to evaporate 8 kg of water in 7 hours of
time is calculated using equation 3.1.
Q 8 4187 (100 27) 8 2257 (1000) 815 W7 3600
× × − + × ×= =
× 4.1
The temperature of water at room temperature is taken to be 270C, specific heat is 4187 J/kg K
and latent heat 2257 kJ/kg.
The amount of energy required to heat the water is obtained from solar energy using a solar
concentrator. The solar radiations falling on the concentrator area will be reflected and focused at
focal area. While travelling from reflective surface, they pass through the medium and also heat
losses take place at the absorber. The net solar energy falling on to the surface, Qs in Watts, is
given by equation 4.2.
csQ = I × A W 4.2
Where, I is the total solar radiations in W/m2, and Ac is the area of the concentrator. Further, net
heat energy leaving the surface, QL is given by equation 4.3.
L sQ = Q ρ × W 4.3
Where, ρ is the reflectivity of the material of the concentrator. If ‘X’ amount of heat is falling on
to the surface, then only 30% to 35% heat is available at the focal area, then the net heat energy
available, Qn at the focal area is given by equation 4.4.
n L Q = 0.3 × Q W 4.4
Or it can be written in the following form.
( )cnQ = I A ρ 0.3× × × W 4.5
54
The above equation shows that the heat energy utilized at the absorber depends upon the solar
radiations, area of concentrator and reflectivity of material. The intensity of radiations depends
on climatic conditions and varies from place to place. Hence design and optimization of the
concentrator is based on reflectivity of material and size or area of the absorber. As the system is
to be used in rural areas, cost is considered to be a major factor. Different sizes of concentrators
ranging from 1.8 m diameter to 10 m diameter are available in the market. The size of the
concentrator should be such that it generates 815 Watts of energy. If the values of intensity of
radiations and reflectivity are found, then the diameter of the concentrator can be calculated.
4.2 Intensity of Solar Radiations
To design the concentrator it is necessary to find the amount of heat energy required at the focal
area. The heat energy input is largely dependent on intensity of available solar radiations. Solar
radiations are generally available in most parts of India for the period of eight months from
October to May. The values of solar radiations were calculated here using theoretical analysis.
The analysis was carried out at Symbiosis Institute of Technology which lies in time zone
[G.M.T + 5.30], latitude is 18.73 N and longitude is 73.72 E. To find the intensity of radiations,
the value of sunshine factor and zenith angle should be known. Equations 3.3 to 3.16 represent
the formulae to find these values (Spencer 1971). A sample calculation is shown for 15th April
2011.
On 15th April, the value of day angle n2 was calculated using equation 3.3.
( )2 12n dayangle n 1 1.790365π
= = − =
The value of time (t2) was then calculated using equation 3.4 as under, ( ) ( ) ( ) ( )
( )2 t 229.18 0.000075 0.001868cos 1.790 0.0320sin 1.7(
0
90 0.0146cos 2 1.79)
0.040849sin 2 .241.790
= × + − − ×
× = −×
After finding the equation of time, time offset t5 is calculated using equation 3.5.
( ) ( )5 t – 0.24 – 4 73.72 60 5.50 = 34.88= +
The hour angle ω is calculated using equation 3.6.
o12 60 0 34.88 180 8.724
× + +ω = − =
Declination angle is calculated using equation, 3.7.
55
o 1n 23 360[284 ].45 9.i3 5
45s n6
δ+
= =
Monthly average of the hourly extra-terrestrial radiation on a horizontal surface Ho is calculated
using equation 3.8.
Ho= ( ) ( ) ( ) ( ) ( )1367 8.72 sin 18.73 sin 9.853 cos 18.73 cos 9.53 sin 824180
.72 π × +
× π ×
× 3603
1 0.65
033 cos 105 + × × = 1550 W/m2
Zenith angle is calculated using equation 3.9.
θ [ ]1cos cos(18.73)cos(9.45) sin(18.73)sin(9.45)cos(8.72)−= + = 9.530
Whereas, the day length is then obtained using equation 3.10.
[ ]1Da 2 cos tan(18.73) tan(9.53)1
y length5
−= − × = 12.45 hours.
The average sunshine time in April for Pune is 9.33 hours per day. The sunshine factor is
obtained using equation 3.11.
sunshine factor = 9.33 / 12.45 = 0.75
Using Sunshine factor and Ho, monthly average of the daily global radiation on a horizontal
surface, Hg is obtained using equation 3.12.
Hg=( 0.31 + 0.43 × sunshine factor)× 1036 = 980W/m2
Coefficients a, b and c are required to obtain value of the monthly average of the hourly global
radiation on a horizontal surface Ig . These are obtained using equation 3.13 to 3.15.
a = 0.409 + 0.5016sin 8.72*180 3π π −
= 0.0176
b = 0.409 + 0.5016sin 8.72*180 3π π −
=1.033
Using the value of a and b, c is calculated as ,
c = a + bcos(ω)= – 0.1245 + 1.168cos(8.72) = 1.0385
Finally, the value of Ig is calculated using equation 3.16.
Ig= 2979 879 1549
1336 1.0385 W / m=× ×
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MATLAB program was developed to find the average global radiations per day and per month.
The details of program are annexed at Annexure 1. Table 4.1 shows the theoretical value of
average daily radiations over a period of eight months.
Table 4.1 Average Radiations for Six Months
Day
Average radiations in W/m2
Oct Nov Dec Jan Feb March April May
1 798 710 629 658 725 794 872 884
2 796 705 628 659 729 797 870 891
3 793 702 626 660 732 800 868 898
4 791 699 625 661 735 803 868 903
5 788 697 623 662 737 806 867 906
6 786 693 621 664 739 809 868 909
7 784 690 620 665 741 811 868 911
8 781 686 619 667 743 814 870 911
9 779 683 617 668 744 816 871 911
10 776 680 616 670 745 819 873 920
11 774 677 614 672 746 821 875 925
12 771 673 613 674 747 823 877 935
13 769 670 611 676 748 825 880 940
14 767 667 610 678 749 826 883 945
15 764 664 608 680 750 828 879 960
16 762 660 607 683 751 830 881 978
17 759 657 605 685 752 831 884 978
18 757 654 604 687 754 832 891 950
19 755 651 603 690 756 834 896 930
20 752 647 601 692 758 835 899 910
21 749 644 600 695 760 836 901 904
22 747 641 598 698 763 838 903 899
23 744 637 597 700 767 840 905 884
24 741 634 595 703 771 841 907 882
57
Day Oct Nov Dec Jan Feb March Apr May
25 739 631 594 706 775 843 908 882
26 735 628 592 709 780 846 908 881
27 732 624 591 711 786 848 909 882
28 729 621 589 714 792 851 900 883
29 726 618 588 717 NA 855 890 888
30 723 629 586 720 NA 859 885 889
31 720 NA 585 723 NA 864 NA 894
Average 760 660 600 680 750 820 885 910
Figure 4.4 shows the comparison of monthly solar radiations. It is found that in the month of
November and December the solar radiations are low, where as in the month of April and May
the solar radiations are high.
Figure 4.4 Comparisons of Monthly Solar Radiations
The available solar input is measured using optical pyranometer shown in figure 4.5. The
experimental values obtained using the pyranometer are compared with the values calculated
using MATLAB programming. Readings were taken from 9.00 am to 4.00 pm for four months.
500550600650700750800850900950
1000
Rad
iatio
ns(W
/m2 )
Day
Oct Nov Dec Jan Feb March Apr May
58
Figure 4.5 Optical Pyranometer
Table 4.2 indicates the average values measured experimentally and theoretically for each month
with percentage error. It is observed that error in the measurement using a pyranometer is in the
range of 0.2% to 0.5%. Figure 4.6 shows the comparison between theoretical and experimental
values of solar radiations. It is observed that both the analysis show almost the same output. In
the subsequent design work, readings taken from optical pyranometer were utilized for the ease
of work without compromising the accuracy of design and subsequent analysis.
Table 4.2 Error in Measurement for Solar Radiations using Pyranometer
Month
Average radiations(W/m2)
Error (%)
Using(Theoretical)
MATLAB
Using Pyranometer (Experimental)
February 750 754 0.53
March 820 823 0.37
April 885 889 0.45
May 910 912 0.22
Average value of solar radiations, I for eight months was then calculated from table 4.2 and used
for further calculations.
59
Figure 4.6 Theoretical and Experimental Values of Solar Radiations
Substituting, the value of I in the equation 3.18, the equation changed to,
c815 = 750 × 0.3 × A × ρ
c3.66 = A ρ× 4.1
The above equation shows that, if the value of ρ reduces, value of Ac will increase. Higher the
value of reflectivity lesser will be the area of the concentrator. A good reflective material has a
higher cost but it reduces the cost of manufacturing. The cost of normal reflective material is low
but that increases the area, which increase the cost of manufacturing. Hence, the next step was to
find out a cost effective, durable high reflectivity material.
4.3 Selection of Reflective Material
Good reflective material reflects more solar radiations and reduces the time of tracking. The
material used for solar concentrators needs to have high reflectivity and spectral physical
properties to ensure long life of the system. Consideration must be given to the effect of
accumulation of dust and contamination, stability of reflective coating, environmental effects,
cleaning needs and cost. Metals that obey the drude model are suitable for solar thermal
applications since they have a high reflectance in the infrared region.
Among the drude metals, silver and aluminum are the best solar reflectors, with a weighted
hemispherical reflectance of approximately 86% and 92% respectively. Also the high solar
60
reflectance is to be maintained during the entire lifetime of the collector, which is around 20-30
years before irreversible degradation takes place (Brogren et al., 2004).
Glass mirrors are generally considered to be the baseline reflector material for solar, thermal and
electric applications. Glass mirrors have high specular reflectance, long lifetimes, and durability
in the field. Drawbacks of glass include weight, fragility, and expense. Relative to glass, polymer
mirrors have advantages of being flexible, lightweight, and less expensive, but they have lower
durability and shorter lifetimes than glass mirrors.
Aluminum is the most widely used non-ferrous metal. It has low cost, high reflectivity and
malleability. To maintain optical integrity of aluminum, it must be treated with a protective
coating. Anodized aluminum reflectors are available at low cost and can serve the purpose of the
reflector for this work. Aluminum coated optical mirrors have good reflectivity ( 78 - 92%) but
have comparatively high cost of Rs. 2475 to Rs. 5380 per sq.m at current market prices, and can
not be fitted on the designed frame due to more weight and poor malleability (Ouannene, 2009).
The system is designed for domestic purpose. Hence optimal material should have high
reflectivity, low cost and good durability. A thorough search of reflective materials available in
the market and used for solar applications was carried out. Four anodized aluminum materials
which had properties in the desired range were shortlisted for experimentation.
4.3.1 Reflectivity testing
Reflectivity testing was carried out with the objectives of selecting a suitable material which
strikes a tradeoff between reflectivity and cost. Four materials A, B, C, D were anodized
aluminum with extra bright surface and high reflectivity and had a tensile strength ranging
between 160 and 200 MPa and yield strength of 140-160 MPa. Table 4.3 shows details of
reflective materials.
Material A was procured from a company based in Germany that manufactures a variety of
aluminum grades. The cost of this sample was Rs.1720/- per sq.m. Sample B was taken from a
U.S company which is world's leading integrated aluminum products manufacturer. The cost of
this material was Rs.2260/- per sq.m. Sample C was taken from another Indian company which
is Asia's largest integrated primary producer of aluminum. The cost of this sample was Rs.1830/-61
per sq.m. Sample D was a basic aluminum sheet, taken from an Indian company which is a
manufacturer of aluminum sheets. The cost of this sample was Rs.1210/- per sq.m.
Table 4.3 Details of Reflective Materials
These four materials were tested for reflectivity at University of Pune. The testing was done
using JASCO UV-Vis-NIR spectrophotometer in the percentage reflectivity mode in the range of
400 µm to 2000 µm. The samples were gently cleaned with soap and water to remove any
depositions on surface. Precautions were taken not to scratch the surface and no chemical
solvents were used. The testing results are shown in figure 4.7.
The infrared rays having wavelength ranging from 750 µm to 1000 µm are suitable for heating
purposes (Harrison, 2001). On the basis of this wavelength range, material B had reflectivity up
to 90% which was the highest among all four materials. But the cost of this material was
comparatively higher (Rs.2260/- per sq.m). On the other hand, the reflectivity of Sample A was
88% and its cost was Rs. 1722/- per sq.m.
Company/Supplier Product Alloy Al (%) Hardness Tensile
Strength (MPa) Symbols
Alanod-westlake(Germany) MIRO 27 99.85 Hard 160 - 200 A
Alcoa aluminium (USA) 5XXX 93 Hard 160 - 200 B
Hindalco aluminium(India) Hammered tone 99.85 Hard 140 C
Local Supplier (India) Aluminium sheets - - - D
62
Figure 4.7 Graph Showing Reflectivity Testing
Table 4.4 indicates the cost and reflectivity of the sample materials. Considering the cost and its
reflectivity, sample A (MIRO 27) was selected as a suitable reflector material. Although its
reflectivity was a little less (88%) than the best (91%) yet the cost was quite low.
Table 4.4 Total Cost and Reflectivity Comparison
Anodized Sample
Reflectivity (%)
Cost ( Rs/m2)
Area of concentrator
(m2)
Total Cost (Rs.)
MIRO 27(Sample A) 88 1720 4.11 7100
5XXX Plate (Sample B) 91 2260 3.97 9000
Hindalco (Sample C) 82 1830 4.42 8000
Basic Sheet (Sample D) 78 1210 4.63 5610
Having selected the material for fabrication of the concentrator the next step was to determine
the minimum value of aperture area of the concentrator from equation 3.2.
cA 815 750 0.3 0.88= × × × Ac = 4.11 m2
The value of the diameter of the concentrator was calculated using equation 3.18.
63
d =4 4.11π× =2.30 m
Hence the concentrator of diameter of 2.3 m was selected for evaporation of 8 kg of water. As the
value of radiation increases, 8 liters of water can be evaporated in less than 7 hours or for the
same time it can evaporates more than 8 liters of water.
4.4 Tracing a Parabolic Curve
The shape of solar concentrator is normally taken in the form of a parabola. A parabola may be
defined as the focus of a point which moves in a plane so that ray’s incident on it will gather at a
fixed point. The fixed point is called its focus. If the equation of parabola is, x2 = 4 a y, the
parabola is symmetric about Y axis, as shown in figure 4.8 where, x is the ordinate, y is the
abscissa and a is the focal Point. In this work the concentrator has been designed as a parabola
with a diameter of 2.3 m. The basic sketch is shown in figure 4.8.
Projected Diameter (2 x)
Focus (a) Depth (y)
Parabolic Concentrator
Figure 4.8 Parabolic Shape
A diameter of 2.3 m of the parabolic concentrator is required for evaporation of 8 kg of water in
the specified time. Against the value of focus (a) for tracing the parabolic curve, different values
of radius (x) were assumed and the corresponding values of y were calculated. Focus is the area
where the pot containing water is kept for heating. In order to keep focal area inside the
concentrator and also easy to operate, the value of ‘a’ should not exceed the value of ‘y’
considering different combination of a, the value of y was calculated. Also by considering the
height criteria for placing the water at focal area, finally value of focal point was assumed to be
0.5 m.
Now for the equation x2 = 4ay, values of extreme points x were fixed from 1.15 m to 0.15 m
with successive reduction in each stage and the corresponding values of y were calculated. For
64
x as 1.15 m, and a as 0.5 m, the value of y was calculated as 0.66 m. Similarly, for different
values of x, the values of y were calculated and tabulated in table 4.5.
Table 4.5 Calculations of Various Values of y
Different Values of x
(m)
Values of y y =x2/4a
(m)
Different Values of x
(m)
Values of y y =x2/4a
(m)
1.15 0.66 -1.15 0.66
1.00 0.52 -1.00 0.52
0.875 0.38 -0.875 0.38 0.7 0.24 -0.70 0.24
0.575 0.16 -0.575 0.16
0.35 0.64 -0.35 0.64
0.150 0.010 -0.150 0.010 0 0 0 0
The curve was then traced by joining all the points as shown in figure 4.9.
Figure 4.9 Parabolic Curve
0
100
200
300
400
500
600
700
-1500 -1000 -500 0 500 1000 1500
Series1
65
4.5 Fabrication of the Concentrator
For fabrication of the concentrator, firstly a parabolic frame was fabricated to suit the top
section. The material of the frame was mild steel flat and the diameter of the top section was
2300 mm. It was made in the workshop of Symbiosis Institute of Technology. Similarly, bottom
frame of radius 148 mm was also fabricated using the same material. The assembly of the
concentrator is shown in figure 4.10. Figure 4.11 shows the major parts of the concentrator.
4.5.1 Fabrication procedure
1. The top section frame was placed on the ground and from the center of this section a pole
of height 661.25 mm was placed. At the depth of 11 mm below the top portion of the
pole a jig was held for keeping the bottom frame in position. A C-shaped hook was
provided on the jig by welding. The bottom circular frame was then mounted on these
hooks from all the sides on the jig.
2. The supporting plate was first drawn on the card board by drawing the radius of all the
circular rings and joining the ends of radius on the card board. Then the desired shape of
supporting plate was achieved by hammering. Eight supporting plates were manufactured
in this manner.
3. Welding of the supporting plates was done from bottom frame to top of the section at
equal distance around the circular path using arc welding.
4. This assembly was then reversed and the sizes and shapes of the rest of the circular
frames were calculated from the general equation of parabola. These were then fabricated
and placed inside the assembly.
5. This circular section was adjusted on the respective heights. This is how all the plates of
the parabolic frame were fabricated.
6. Then the anodized aluminum reflector plates were placed on the parabolic frame in order
to direct the rays from sun to the focus of parabola. For that, the standard aluminum
material sheets of 4.2 1.28 m × 1.28 m were used from which trapezoidal shapes were cut
of the required size (160 mm × 40 mm). A total number of 48 trapezoidal sections were
cut.
66
1. Hollow shaft 2. Grill with cooker support
3. Grill 4. Side friction plate
5. Friction plate 6. Supporting arm
7. Center Bar 8. Aluminum plates
9. Supporting Plate 10. Wheel
Figure 4.10 Assembly of Parabolic Concentrator Showing Major Components
67
Figure 4.11 Component of the Concentrator
68
7. First, marking was done with the help of a marker, followed by cutting and drilling on
aluminum sheets.
8. The aluminum foils were placed on the main parabolic frame one by one and tide to each
circular frame by copper wire through 3 mm diameter holes. Then this parabolic dish
with aluminum reflector was welded to side friction bracket.
9. The two supporting arms with bottom support, of square cross section were fabricated
and metallic rods and side plates were welded to the supporting arms, as shown in figure
4.10.
10. The center bar with grill and parabolic dish with friction plate were passed through the
metallic rods and fitted with the side plate. The side plate was placed parallel to the
friction plate and was bolted as shown in figure 4.11.
11. The fabricated concentrator is as shown in the figure 4.12 was used for further study. In
order to ensure that the exact position of the sun is in line with concentrator, two small
rods or two bolts were fitted on either side of the projected area of the concentrator. If the
shadow of the bolts or rods lies at the base or it is invisible then the position of sun would
be in line with the concentrator. This can be done manually and then tracking can be
done by rotating the concentrator with the help of a handle fitted on the axis. Once the
parabolic concentrator is fabricated. The next step was to design and fabricate the
absorber.
Figure 4.12 Photographic View of Parabolic Concentrator
69
4.6 Experimental Analysis
Experiments were carried out to find the temperature attained by various quantities of water in
20 minutes. The absorber used was a black coated stainless steel cooker. A different quantity of
water was kept in the absorber each time and the temperature of water was measured after every
5 minutes. The results are tabulated in table 4.6.
Table 4.6 Water Temperature after 20 Minutes
The second test was conducted with 2 kg mass of oil for finding maximum temperature attained
by using parabolic concentrator. The observations are tabulated in table 4.7. The temperature of
the oil was measured at an interval of five minutes.
Table 4.7 Oil Temperature at 5 Minutes Interval
Sr.No. Time
(Hrs) Air Temperature
(0C ) Irradiance (W/m2 )
Temperature of Oil ( 0C )
1 11.30 37.7 792 39 2 11.35 38.2 808 105 3 11.40 38.5 821 160 4 11.45 39 818 197 5 11.50 39.1 812 226 6 11.55 38.9 829 242 7 12.00 38.5 862 245 8 12.05 38.7 843 252 9 12.10 39.1 849 256 10 12.15 38.8 856 260 11 12.20 38.7 860 264 12 12.25 38.8 856 262 13 12.30 39.2 877 263 14 12.35 39.4 879 264
Sr.No.
Time Interval (min)
Final temperature of Water(0C) Heat utilized (Watts)
4 kg 6 kg 9 kg 4 kg 6 kg 9 kg 1 0-5 46 40 37 893.2 837.4 879.3 2 5-10 65 52 46 1071.9 1004.9 1130.5 3 10-15 83 65 54 993.7 1088.6 1004.9 4 15-20 94 73 60 614.1 669.9 753.7
Average Heat Utilized = 900 W
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4.7 Thermal Performance Test for Parabolic Concentrator and Absorber
Heating and cooling tests were conducted to evaluate overall heat loss factor F’UL and optical
efficiency Factor F′ηo. In the first stage, (heating test) a cooking pot with predefined amount of
water was mounted at the focus of the parabolic concentrator. The parabolic concentrator was
exposed to unobstructed solar radiations and was adjusted in a manner that the bright spot of the
concentrated solar radiations fall on the centre of the bottom of the cooking pot. Measurements
were made at an interval of at least 10 minutes and recorded till water reached a temperature of
900C to 950C.
In the second test (cooling test), as soon as the water temperature reached 950C, the concentrator
was shaded by an adequately sized umbrella, so as to ensure total blockage of solar radiations.
The readings of temperature were taken at five minutes interval till the water temperature
reached close to the ambient air temperature. For each set of the data points, the value of
[ln (tw-ta)] was calculated for the time intervals and a plot with this value on Y-axis and time on
X-axis was drawn. Different points of the plot were fitted to a least square linear regression
equation. The slope of the line equals to (-1/τ0), where τ0 was defined as the time-constant for
cooling. Substituting, known values of time-constant for cooling τ0 , area of the cooking pot
(Aabs), and total thermal capacity of the cooking pot (m cp) the values of F’UL and F′ηo were
calculated. The testing was done on various quantities of water at different days to find variation
in the value of F’UL and F′ηo. The instantaneous efficiency was calculated using equation 3.2.
4.7.1 Analysis with 8 kg of Water
The first test was conducted with 8 kg mass of water. The observations are tabulated in table 4.8.
Table 4.8 Readings Taken for 8 kg of Water during Heating Test
Time (Hrs) 13.00 13.05 13.10 13.15 13.20 13.25 13.30 13.35 13.40 I (W/m2)
864 868 862 865 870 871 872 871 870
Temp. of water.(0C) 30 45.90 51.00 66.60 71.00 81.50 89.00 92.10 95.10 ∆T/ I
- 0.0118 0.009 0.011 0.007 0.011 0.008 0.003 0.003
Inst. Efficiency η - 0.323 0.257 0.303 0.194 0.305 0.238 0.102 0.099
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The heating and cooling curves were plotted against time, and are shown in figure 4.13.
Figure 4.13 Heating and Cooling Curve for 8 kg of Water
Then the readings were taken for cooling curves and are shown in table 4.9
Table 4.9 Readings taken for 8 kg of Water during Cooling Test
Time (Hrs) 13.40 13.50 14.00 14.10 14.20 14.30
Temp.(0C)
95.10 90.19 87.79 77.96 69.88 63.533
ln(tw-ta) 4.048 3.955 3.908 3.688 3.462 3.246
Time (Hrs) 14.40 14.50 15.00 15.1 15.2 15.3
Temp.(0C)
58.49 54.49 51.32 47.796 45.099 43.19
ln(tw-ta) 3.020 2.803 2.595 2.282 1.96 1.648
From the semi-log cooling curve, slope m and τo were calculated.
m = (3.908-3.02)/40 = 0.022
τo = 1/m = 45.04 min Taking a span of 10 minutes, i.e. τas 10 and substituting these values, the value of F′UL and F′η0
were calculated using equation 3.19 and 3.20.
F′ UL = ( )
8 4.187 10000.4 45.04 60× ×× ×
= 31.04 W/m2K
F′η0 = 31.02 0.4 (53 35) (30 35) 0.804.11 0.1999 862 862
× − − − × × = 0.314 = 31.4 %
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Similarly the values of F′η0 were calculated after every 10 minutes interval and are given in table
4.10.
Table 4.10 Values of Optical Efficiency Factor for 8 kg of Water with Time
Time (Hrs) 13.10 13.20 13.30 13.40
F’ηo 0.314 0.39 0.43 0.28
4.7.2 Analysis with 7 kg of Water
The second test was conducted with 7 kg mass of water. The observations are tabulated in table
4.11.
Table 4.11 Readings taken for 7 kg of Water during Heating Test
Time (Hrs) 11.50 11.55 12.00 12.05 12.10 12.15 12.20 12.25 12.30
I (W/m2)
862 865 863 866 868 871 869 871 870
Temp. of water (0C) 29 48 54 67.50 78.34 83.00 90 92.7 95.64
∆T/ I
- 0.012 0.011 0.012 0.012 0.005 0.007 0.004 0.003
Efficiency η - 0.302 0.275 0.298 0.308 0.128 0.167 0.098 0.803
Then the readings were taken for cooling curves as shown in table 4.12. Heating and cooling
curves for these readings are shown in figure 4.14.
Table 4.12 Readings taken for 7 kg of Water during Cooling Test
Time (Hrs) 12.30 12.40 12.50 13.00 13.10 13.20
Temp.(0C)
95.64 88.50 78.50 70.60 64.60 59.00
ln(tw-ta) 4.085 3.945 3.7813 3.5243 3.3809 3.091
Time (Hrs) 13.30 13.40 13.50 14.00 14.10 14.20
Temp.(0C)
55.10 52.00 48.50 46.00 43.50 40.00
ln(tw-ta) 2.767 2.5672 2.3513 2.0794 1.8718 1.332
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Figure 4.14 Heating and Cooling Curve for 7 kg of Water
As done in case of experimentations with 8 kg of water, the values obtained from figure 4.14
were substituted in equation 3.20 and 3.21 the value of F′η0 and F′UL were calculated with τo
equal 40 minutes as under.
F′ UL = 7 4.187 1000
0.424 40.089 60× ×× ×
= 30.53W/m2 K
F′η0 = ( )54 3630.53 0.4 (30 36) 0.784.11 0.216 862 862
− × −− × ×
= 0.362 = 36.2%
Similarly the values of F′η0 were calculated after every 10 minutes interval and are given in table
4.13.
Table 4.13 Values of Optical Efficiency Factor for 7 kg of Water with Time
Time (Hrs) 12.00 12.10 12.20 12.30
F’ηo 0.36 0.43 0.32 0.25
4.7.3 Analysis with 5 kg of Water
The third test was conducted with 5 kg mass of water using the concentrator. Heating and
cooling curves were drawn similar to the previous cases from the readings as shown in figure
4.15.
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Figure 4.15 Heating and Cooling Curve for 5 kg of Water
Like previous cases, the values obtained from the tables and the graphs were substituted in
equation 3.20 and 3.21, and the value of F′η0 and F′UL were calculated with τo equal 30 minutes
as under.
F′ UL= 5 4.187 1000
0.4 30 60× ×
× ×= 29.07 W/m2 K
F′η0 = 29.07 0.424 (62 35) (30 35) 0.7254.15 0.2747 860 860
× − − − × × = 0.37 = 37 %
Similarly the values of F′η0 were calculated after every 10 minutes interval and are given in table 4.14.
Table 4.14 Values of Optical Efficiency Factor for 5 kg of Water with Time
Time (Hrs) 12.10 12.20 12.30
F’ηo 0.37 0.418 0.259
Figure 4.16 shows the variation of optical efficiency factor for different masses of water at
different times. The graphs drawn from tables 4.10, 4.13 and 4.14 show almost similar curves
with average value of F′η0 as 0.354.
Figure 4.16 Variation of Optical Efficiency Factor with respect to Times for 3 Cases 75
4.8 Optical Efficiency using Graphical Method
The optical efficiency obtained in the previous section was analysed in another way. The
difference between water temperature and ambient temperature ∆T was determined over an
interval of 5 minutes. The value of the instantaneous efficiency was calculated using equation
3.21. This analysis was carried out for two cases by taking values from tables 4.9 and 4.12 for 8
kg and 7 kg of water, respectively. The graphs were plotted as shown in figure 4.17.
Figure 4.17 Graph of Optical Efficiency for 2 Cases
The equation of line y = 0.358 - 0.028 x was compared with the equation 3.23 and the value of
optical efficiency obtained was 0.358 for 8 kg of water. Similarly, y = 0.369 - 0.036 x was
compared with the equation and the value of optical efficiency obtained was 0.369 for 7 kg of
water.
4.9 Concluding Remarks
The designed parabolic concentrator is found suitable for required heating. The maximum
temperature reached at the focal area was in the range of 2600C. The average amount of heat
generated by the concentrator was 900 W in good sunshine conditions. The optical efficiency of
the concentrator was calculated and found to be 35%. Proper selection of absorber helps to
improve the efficiency of the system and requires minimum tracking. The next chapter deals
with the design and optimization of the absorber.
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