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 Authors : Abhishek Agarwal , Vineet Kumar Vashishtha, Dr. S.N. Mishra
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 Volume & Issue : Volume 01, Issue 05 (July 2012)
 Published (First Online): 02082012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
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Comparative Approach For The Optimization Of Tilt Angle To Receive Maximum Radiation
1Abhishek Agarwal , 2Vineet Kumar Vashishtha, 3Dr. S.N. Mishra
1 Department of Mechanical Engineering, KNITSultanpur, UP, India228118
3Asst. Professor., Department of Mechanical Engineering, I.I.T, U.P. ,India Ghaziabad201003
2Professor., Department of Mechanical Engineering, KNITSultanpur, UP, India228118
ABSTRACT
India is both densely populated and has high solar insolation, providing an ideal combination for solar power in India. As the angle between the sun and a fixed surface is continually changing, the power density on a fixed PV module is less than that of the incident sunlight. Since the flat plate solar collectors are placed at an angle to the horizontal, it is necessary to calculate the optimum tilt angle which maximizes the amount of collected energy. The best way to collect the maximum solar energy is by using solar tracking systems, and thus to maximize the collected beam radiation. In this paper a mathematical model was used for estimating the total (global) solar radiation on a tilted surface, and to determine the optimum tilt angle and orientation (surface azimuth angle) for the solar collector in India at four different locations on a monthly basis, as well as for a specific period. The results reveal that changing the tilt angle 12 times in a year (i.e. using the monthlyaveraged optimum tilt angle) maintains approximately the total amount of solar radiation near the maximum value that is found by changing the tilt angle daily to its optimum value. This achieves a yearly gain in solar radiation of 4.56% more than the case of a solar collector fixed on a horizontal surface.
Keywords: solar collector, optimum tilt angle, clearness index, solar radiation.

INTRODUCTION
The natural energy flows through the Earths ecosystem are immense, and the theoretical potential of what they can produce for human needs exceeds current energy consumption by many times. For example, solar power plants on one percent of the worlds desert area would generate the worlds entire electricity demand today [1].
unprecedented manner and mankind seeks for additional energy sources.
Energy sources are vital and essential ingredients for all human transactions and without them human activity of all kinds and aspects cannot be progressive. Population growth at the present average rate of 2% also exerts extra pressure on limited energy sources Renewable energy supplies 19 percent of global final energy consumption, counting traditional biomass, large hydropower, and renewable (small hydro, modern biomass, wind, solar, geothermal, and bio fuels). Of this 19 percent, traditional biomass, used primarily for cooking and heating, accounts for approximately 13 percent and is growing slowly or even declining in some regions as biomass is used more efficiently or is replaced by more modern energy forms. Hydropower represents 3.2 percent and is growing modestly but from a large base. Other renewable account for 2.6 percent and are growing very rapidly in developed countries and in some developing countries. The amount of solar energy received by the surface of the earth per minute is greater than the energy utilization by the entire population in one year. Solar energy is referred to as renewable and/or sustainable energy because it will be available as long as the sun continues to shine. Estimates for the life of the main stage of the sun are another 4 5 billion years. The energy from the sunshine, electromagnetic radiation, is referred to as insulation.
The sun is a sphere of intensely hot gaseous matter with a diameter of . In effect the sun is a continuous fusion reactor in which hydrogen is turned into helium. The suns total energy output is
In recent centuries the types and magnitudes of the
3.8 1020 MW which is equal to
63 MW m2 of the suns
energy requirements have increased in an surface. This energy radiates outwards in all directions.
Only a tiny fraction,
1.7 1014 kwof the total radiation
calculating the hourly solar irradiation components
emitted is intercepted by the earth [1].
The performance of a solar collector is highly influenced by its angle of tilt with the horizontal. This is due to the facts that tilt angle change the solar radiation reaching the surface of the collector, the tilt angle, defined as the angle of collectors with respect to horizontal, is a dominant parameter affecting the collectible radiation of a fixed collector. In general, the optimal tilt angle of a fixed collector is related to the local climatic condition, geographic latitude and the period of its use. Hence, different places will have different optimal tilt angles for a yearlyused solar collector.

LITERATURE REVIEW
There are various devices for absorbing the solar radiation. The Sun rays are to be always focused onto the absorber plate. The collector has to be rotated by tracking system, but the tracking system is very costly so we cannot use this for every system economically. Due to this reason the solar collector is fixed either monthly, seasonally or yearly pattern, based on our requirements. Ahmad M. Jamil and Tiwari
G.N. [2] analyzed the theoretical aspects of choosing a tilt angle for the solar flatplate collectors used at ten different stations in the world and makes recommendations on how the collected energy can be increased by varying the tilt angle. For Indian stations, the calculations are based upon the measured values of monthly mean daily global and diffuse solar radiation on a horizontal surface. As explained in Bekker et al [3]. The orientation and tilt of the panels directly relates to the annual energy yield of the panels Mehleri E.D. et. al. [4] determined optimum tilt angle and orientation for solar photovoltaic arrays in order to maximize incident solar irradiance exposed on the array, for a specific period of time. The ratio of monthly average hourly diffuse radiation to monthly average hourly global radiation was correlated by Ulgen Koray and Hepbasli Arif [5] with the monthly average hourly clearness index in the form of the polynomial relationships for the city of Izmir in the western part of Turkey.
The values of the monthly average daily clearness index ranged from 0.41 to 0.66, averaged for the same period.
KorayUlgen [5] found that the optimum tilt angle changes between 0 (June) and 61 (December) throughout the year. In winter (December, January, and February) the tilt should be 55.7, in spring (March, April, and May) 18.3, in summer (June, July, and August) 4.3, and in autumn (September, October, and November) 43. Sakonidou E.P. et. al. [6] developed a mathematical model. The model starts by
(direct, diffuse, groundreflected) absorbed by the solar chimney of varying tilt and height for a given time (day of the year, hour) and place (latitude). Moghadam Hamid et. al. [7] estimated solar global radiation on a horizontal surface using a mathematical model and the results were compared.
Ibrahim D. [8] examined for selection of optimum tilt angle of Cyprus. For maximum radiation the results were calculated by varying tilt angle form 0Â° to 90Â° with the increment of 10Â°.
Tang R. and Tong W. [9] presented a mathematical procedure to compare the optimum tilt angles of collectors through monthly diffused radiation and actual monthly diffused radiations. The best orientation for solar collectors in Izmir was south facing.

PROBLEM IDENTIFICATION
Based on the literature survey it is sen that the incident solar radiations on a collector surface are greatest for an optimal tilt angle of the collector at a particular region which is also not constant throughout the year. To obtain maximum power output from the solar collector system it is desirable to tilt the collector to that tilt angle at which the incident solar radiations are maximum. If not monthly, the tilt angles of the collector surfaces can be changed four times in a year to their seasonal optimum tilt angles at which slightly less power is obtained than monthly optimal angles but large compared to yearly optimal tilt angle.

OBJECTIVE OF THE STUDY
The following objectives are covered under this study:

Daily and monthly Optimum slope angles.

Seasonal Optimum tilt angles.

Yearly optimum tilt angle.

To compare the different model.

To compare with the solar panel setup installed at Village Nandha, Bhiwani, Haryana
Joakim WidÃ©n [10] mentioned the models of solar radiation, daylight and solar cells as a chapter in his thesis. M.S.Alam [11] et.al. developed a mathematical model for simulation of solar radiation system by using dynamics methodology in their paper.


MODELING OF GLOBAL RADIATION
Angstroms equation[20] is used to express the average radiation on a horizontal surface in terms of
constants 1,2 and the observed values of average length of solar days.
Fig.1 Solar Panel installed at MGICCDelhi Govt., AlipurBakauli, New Delhi
The constants 1,2 will be determined for this model based on actual old measurements and equating the data in the Angstroms equation given as follows:
Manes A, and Ianetz A. [1] presented energy radiates outwards in all directions. Only a tiny fraction, of the total radiation emitted is intercepted by the earth. The variation of the earthsun distance due to earths orbit causes variable extraterrestrial radiation. The dependence of extraterrestrial radiation on time of year is indicated by Duffie J.A. and Beckman W. A. [13]:
G=
The sunset hour angle for any day (n) of the year can be obtained as follows. The total daily irradiation on a horizontal plane, H, is the combination of two components: the direct (beam) irradiation and the diffuse irradiation from the sky.
Fig.2 Earth Sun Geometry 6 EARTHSUN GEOMETRY
The term Earth rotation refers to the spinning of our planet on its axis. At any one moment in time, one half of the Earth is in sunlight, while the other half is in darkness. The edge dividing the daylight from night is called the circle of illumination. The Earths rotation also creates the apparent movement of the Sun across the horizon.
Fig.3Sun Path for Village Nandha, Haryana along the year
The annual change in the relative position of the Earth's axis in relationship to the Sun causes the height of the Sun or solar altitude to vary in our skies. Solar altitude is normally measured from either the southern or northern point along the horizon and begins at zero degrees. Maximum solar altitude occurs when the Sun is directly overhead and has a value of 90Â°.
7 MODELS FOR CALCULATION OF CLEARNESS INDEX
The monthlyaverage clearness index is the ratio of the monthly average daily radiation on a horizontal surface (H) to the monthly average daily extraterrestrial radiation ( )
Chandel S.S. [12] gave a relation between mean daily sunshine duration n and the mean daily global solar radiation h as a function of latitude, altitude, maximum and minimum temp of a site.
Where, is the difference in maximum and minimum temperature, Ã˜ is the latitude of the site (Nandha is 28.8482), h is the latitude from the mean sea height. The altitude of Haryana varies between 700 to 3600 ft (200 meters to 1200 meters) above sea level, the monthly mean maximum and minimum temperature is taken from the Indian Meteorological Department
An empirical method for the estimation of the monthly average daily total radiation incident on a tilted surface was developed by Liu B.Y.H. and Jordan R.C. [15]. In their correlation, the diffuse to total radiation ratio for a horizontal Surface is expressed in terms of the monthly clearness index Kt with the following equation:
Collares P. and M. Rabl A. [14] expressed the same parameter by also considering the sunset hour angle:
Knowing the value of the clearness index; one can calculate the diffuse component, Hdiff as follows (Erbs D.G. et al.) [16].
For 81.4
Where as > 81.4Â°
Then, the direct daily component can be computed.
The total solar radiation on a tilted surface is made up of the direct or beam solar , diffuse
radiation , and ground reflected on a tilted surface
Liu, B.Y.H. and Jordan R. C. [15] and anisotropic Hay,
J.E. [17] ones. The daily beam radiation received on an inclined surface can be expressed as
where H and are the monthly mean daily global and diffuse radiation on a horizontal surface, and Rb is the ratio of the average daily beam radiation on a tilted surface to that on a horizontal surface. The daily ground reflected radiation can be written as
= H (1cos)/2
Liu, B.Y.H. and Jordan R. C. [15] have suggested that can be estimated by assuming that it has the value which would be obtained if there were no atmosphere. For surfaces in the northern hemisphere, sloped towards the equator, the equation for Rb is given as below Miguel A. et. al. [18] and is used in the present study.
Where
' is the sunset hour angle for the tilted surface for the mean day of the month. min means the smaller of the two terms in the bracket.
For surfaces in the southern hemisphere, sloped towards the equator, the equation for Rb is given as below Liu, B.Y.H. and Jordan R. C. [15].
Where
Optimum tilt angle curve along the year, in winter, the tilt angle approaches to 55Â°, while in summer it approaches to 8Â°. Assuming all previous angles are random variables, so the expected values for those variables as follows:
[ ] = [ ] [ ]Fig.4 Optimum Tilt angle Vs Days

DIFFUSE RADIATION MODELS
The methods for approximation the ratio of diffuse solar radiation on a tilted surface to that of a horizontal are classified as isotropic and anisotropic models. The isotropic models assume that the intensity of diffuse sky radiation is uniform over the sky dome. Hence, the diffuse radiation incident on a tilted surface depends on the fraction of the sky dome seen by it. The anisotropic models assume the anisotropy of the diffuse sky radiation in the circumsolar region (sky near the solar disc) plus and isotropically distributed diffuse component from the rest of the sky dome. The sky diffuse radiation can be expressed as
Where Rd is the ratio of the average daily diffuse radiation on a tilted surface to that on a horizontal surface.
The diffuse radiation models chosen for study were as follows Kamali G.H. [19].
9 ISOTROPIC MODELS

Liu and Jordan model (1962) Rd= [3 + cos (2)] / 4

Tian et al. model (2001) Rd= 1 /4

Koronakis model (1986) Rd= 1/3 [2+ cos ]

Badescu model (2002) Rd= [3+ cos 2] /4

ANISOTROPIC MODELS


Hay model (1979)

Skartveit and Olseth model (1986)
Where

Reindl et al. model (1990)

Steven and Unsworth model (1980)



TOTAL RADIATION ON A TILTED
SURFACE, can thus be expressed as

SITE ANALYSIS
Historical data for the specific site at Stellenbosch suggests that the total energy received on a horizontal surface differs from January to June.
Jan
Feb
Mar
Apr
May
Jun
July
kWh/m2/d
3.41
4.31
5.45
6.68
7.43
7.17
5.68
Aug
Sep
Oct
Nov
Dec
Annual
5.29
5.55
5.30
4.23
3.36
5.32
Table 1 Horizontal Irradiation data for Nandha, Haryana
Fig.5 – Daily solar radiation for Village Nandha, Haryana horizontal
Fig.6.Daily Averaged Insolation Incident On A Horizontal SurfaceNandha, Haryana
Table.2 Horizontal Irradiation data for New Delhi
Month
Jan
Feb
Mar
Apr
May
Jun
July
kWh/m2/d
3.8
4.68
5.8
6.30
6.42
6.07
5.22
Aug
Sep
Oct
Nov
Dec
Annual
4.81
5.06
4.83
4.18
3.52
5.06
Fig.7 – Daily solar radiation for New Delhi – horizontal
Fig.8Daily Averaged Insolation Incident On A Horizontal SurfaceNew Delhi, India.

RESULT AND DISCUSSION
The average winter value of H is 1.4858
W/m2day and its average summer value is 2.6843Ã— W/m2day
Fig.9 Monthly Average daily Extraterrestrial, Global, Direct and Diffuse solar radiation on horizontal surfaces at Village Nandha, Haryana
Fig.10Monthlyaverage daily solar radiation availability of tilted surface at Village Nandha, Haryana
Fig shows the beam radiation dominates throughout the year where the maximum beam radiation reaches in the month of May (2.3066 X 107 W/m2 day) whereas the least amount of beam radiation occurs in the month of December (1.1026 X 107 W/m2 day). The remaining city consider in the study is Delhi. Delhi shows somewhat similar trend as that of Village Nandha, Haryana. Fig. shows the average daily total solar radiation at Village Nandha, Haryana on a south
facing surface as the angle of tilt is varied from 0 to 90 in steps of 0.5Â°. It is clear from these graphs that a unique Opt exists for each month of the year for which the solar radiation is at a peak for the given month. The optimum angle of tilt of a flatplate collector in January is 60 and the total monthly solar radiation falling on the surface at this tilt is 2.4438Ã—107 W/m2day.The optimum tilt angle in June goes to a minimum of zero degree and the total monthly solar radiation at this angle is 2.6841Ã—107 W/m2 day. The optimum tilt angle then increases during the winter months and reaches a maximum of 62Â° in December which collects 2.5717Ã—107 W/m2day of solar energy monthly. The optimum angle of tilt of a flatplate collector in January is 44.5Â° and the total monthly solar radiation falling on the surface at this tilt is 3.3610Ã—107 W/m2day. The optimum tilt angle in May goes to a minimum of zero degree and the total monthly solar radiation at this angle is W/m2day.
The average daily total solar radiation at Delhi on a south facing surface as the angle of tilt is varied from 0Â° to 90Â° in steps of 0.5Â°. It is clear from these graphs that a unique opt exists for each month of the year for which the solar radiation is at a peak for the given month. The optimum tilt angle then increases during the winter months and reaches a maximum of 60Â° in December which collects 2.6844Ã—107 W/m2day of solar energy monthly. Table gives a list of opt for each month of the year at Village Nandha, Haryana using 2 isotropic models (Badescu model , Liu and Jordan model) and 2 anisotropic models (Reindl et al. model, Hay model) as mentioned previous. The optimum angle of tilt of a flatplate collector in January is 60Â° by Liu & Jordan model whereas Reindl model, Hay model, Badescu model indicate the optimum tilt angle as 61.5Â°, 61Â°, 60.5Â° resp. and the total monthly solar radiation falling on the surface at this tilt is 2.4438Ã—107 W/m2day by Liu & Jordan model whereas Reindl model, Hay model, Badescu model indicate the total monthly solar radiation falling on the surface at this tilt angle is 2.6367Ã—107 W/m2day, 2.6253Ã—107 W/m2day 2.4088Ã—107 W/m2day resp. The optimum tilt angle in June goes to a minimum of zero degree as indicated by all the models and the total monthly solar radiation at this angle is 2.6841Ã—107 W/m2day. Yearly average tilt was calculated by finding the average value of the tilt
angles for all months of the year. The yearly average tilt was found to be 30.61Â° for Village Nandha, Haryana. when the seasonal average angles are used, and when the yearly average angle is used throughout the year. When the monthly optimum tilt angle was used, the yearly collected solar energy was 2.500775 X
107 W/m2 day with the seasonally adjusted tilt angles, the yearly collected solar energy was 2.3669 X 107 W/m2 day. Finally, with the yearly average tilt angle, the yearly
Table:3 Optimum Tilt Angle opt for Each Month of the Year at Nandha, (Haryana)
Months
Liu & Jordan
Model
Reindl Model
Hay Model
Badescu Model
opt
Ht(opt)
107 W/m2day
107W/m2day
107W/m2day
107W/m2day
Dec
62
2.5717
63.5
2.7521
63
2.7437
62.5
2.5449
Jan
60
2.4438
61.5
2.6367
61
2.6253
60.5
2.4088
Feb
50
2.5391
53
2.6799
52
2.6710
50.5
2.5023
Mar
36
2.5746
38.5
2.6482
38
2.6438
35
2.5465
Apr
17.5
2.6801
18.5
2.6960
18
2.6954
16
2.6720
May
0
2.7839
0
2.7839
0
2.7839
0
2.7839
Jun
0
2.6841
0
2.6841
0
2.6841
0
2.6841
Jul
0
2.2942
0
2.2952
0
2.2941
0
2.2952
Aug
8
2.0969
9
2.1023
8.5
2.1021
6
2.0938
Sep
27.5
2.1374
28.5
2.1920
27.5
2.1874
22
2.1112
Oct
48.5
2.4989
48
2.6167
47.5
2.6095
44.5
2.4639
Nov
58
2.7239
59.5
2.8826
59
2.8755
58
2.6958
Average
30.61
2.5024
31.66
2.5808
31.20
2.5764
29.58
2.4835
Table 4 Optimum Tilt Angle opt for Each Month of the Year at Delhi
Months
Liu & Jordan
Model
Reindl Model
Hay Model
Badescu Model
opt
Ht(opt) 107 W/m2day
107W/m2day
107W/m2day
107W/m2day
Dec
60
2.6844
61
2.8476
59.5
2.8401
60
2.6575
Jan
57.5
2.5059
59.5
2.6870
59
2.6760
57.5
2.4692
Feb
48.5
2.5727
50.5
2.7011
50
2.6930
47.5
2.5362
Mar
34
2.6558
35.5
2.7145
35
2.7114
32.5
2.6327
Apr
14.5
2.7274
15
2.7380
15
2.7377
14
2.7220
May
0
2.7804
0
2.7804
0
2.7804
0
2.7804
Jun
0
2.5742
0
2.5742
0
2.5742
0
2.5742
Jul
0
2.1796
0
2.1796
0
2.1796
0
2.1796
Aug
5
1.9561
5.5
1.9582
6
1.9582
4
1.9548
Sep
21.5
2.0467
24.5
2.0890
24
2.0853
18
2.0253
Oct
43
2.5412
45
2.6456
44.5
2.6392
42
2.5081
Nov
55.5
2.7641
56.5
2.9143
56
2.9074
55.5
2.7344
Average
28.29
2.4990
29.41
2.5691
29.08
2.5652
27.58
2.4812
collected solar energy was 2.27168 X 107 W/m2 day. The seasonal optimum tilt angle for Delhi using different models out of which the Badescu model is very close to the data available in [14].
The optimum seasonally tilt angle is maximum in winter ie.57.33Â° and minimum i.e. 2.67Â° in summer by Liu and Jordan model. Optimum seasonally tilt angle is maximum in winter ie.57.83Â° and minimum i.e. approximately zero in summer by Badescu model. The optimum seasonally tilt angle is maximum in winter
ie.51.33Â° and minimum i.e. approximately zero in summer by Liu and Jordan model. Optimum seasonally tilt angle is maximum in winter ie.48.66Â° and minimum i.e. approximately zero in summer by Badescu model.
The optimum seasonally tilt angle is maximum in winter and minimum ie.0.33Â° in summer by Liu and Jordan model. Optimum seasonally tilt angle is maximum in winter and minimum ie.1.66Â° in summer by Badescu model. The daily variation of optimum slope has been extended to evaluate the yearly optimum tilt angle, (opt(y)) the yearly optimum tilt angle is a fixed value for any
Fig.11
Comparison of Monthly optimum tilt angle for Delhi
solar collector throughout the course of a year. It is for Nandha, Haryana and oriented towards the south. The amount of solar radiation received by the solar collector tilted at yearly optimum angle facing south was computed. Comparison of yearly optimum tilt angle for Village Nandha, Haryana using different models which is further compared from the working setup install at Nandha, Haryana shows that P.V panel at Village Nandha, Haryana is installing at the entire model shows that the yearly optimum tilt angle is close to but Badescu model shows very closeness to the setup install at Village Nandha, Haryana it underestimate the angle just by 0.43%.

CONCLUSIONS
In this study the solar radiation output of solar collector is investigated at various tilt between angles 0Â° to 90Â° for south facing to calculate daily and monthly optimum tilt angles, seasonal optimum tilt angles and yearly optimum tilt angle for different locations in India.
The beam radiation dominates throughout the year where the maximum beam radiation reaches in the month of May whereas the least amount of beam radiation occurs in the month of December at Village Nandha, Haryana. The optimum tilt angle in June goes to a minimum zero degree as indicated by all the models.

The optimum tilt angles increases during the winter months and reaches a maximum of 62Â° in December by Liu & Jordan model whereas Reindl model, Hay model, Badescu model indicate the optimum tilt angle as 63.5Â°, 63Â°, 62.5Â° resp.

When the monthly optimum tilt angles were used, the yearly collected solar radiation was W/m2day When the seasonal optimum tilt angles were used the yearly collected solar radiation was W/m2day Finally, when the yearly optimum tilt angle was used, the yearly collected solar radiation was W/m2day.

In winter, a panel fixed at the winter angle will be
relatively efficient, capturing 81 to 88 percent of the energy compared to optimum tracking. In the spring, summer, and autumn, the efficiency is lower (74 75% in spring/autumn, and 6874% in summer), because in these seasons the sun travels a larger area of the sky, and a fixed panel cant capture as much of it.
4. The proper tilt and azimuth angle choice is by far more important for photovoltaic systems design than solar thermal system design.
15 SCOPE FOR FUTURE WORK

The optimization tilt angle for other cities can be carried out for India and other location exterior of India.

For optimization of tilt angle, we can use isotropic models.

If your solar panels will have a fixed tilt angle, and you want to get the most energy over the whole year,
Fig.12 Solar panels installed at Village Nandha, Haryana at 30Â° tilt angle
A fixed angle is convenient, but notes that there are some disadvantages. As mentioned above, youll get less power than if you adjusted the angle.
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Author1 He is B.Tech. (Hons.) in Mechanical Engineering and pursuing M.Tech. in Thermal Engineering from KNIT, Sultanpur.
Author2 He is M.Tech. From NIT, Hamirpur and presently is Assistant Professor at Ideal Institute of Technology, Ghaziabad.
Author3 He is Professor and Head of Dept. of ME at KNIT, Sultanpur, having large research experience.