Development of Sea Shell concentrator profile using computer aided ray tracing technique and study of

optical performance

Abubakar Siddique, Shovasis Kumar Biswas, Surajit Sinha, Animesh Pal, Rezaul Karim Mazumder University of Dhaka

siddique_du05@yahoo.com, shuvodu86@yahoo.com, sinhalitondu@yahoo.com, animesh_du09@yahoo.com, rkmeteulabd@yahoo.com

Abstract—A 2D Sea Shell concentrator with maximum half acceptance angle 36° and vertical solar swing + 36° to - 36° has been developed using computer aided ray tracing technique for bifacial solar cell and photothermal applications. Based on the analytical geometry of this profile, a Matlab program has been made to estimate the average number of reflected and direct ray on the particular zone of the absorber. By using the simulated result of this program, the effect of the variation of the angle of incidence on the total number of reflected rays, concentration ratio (CR), local concentration ratio distribution (LCR) of solar radiation on the flat horizontal absorber, average number of reflections (ANR) and efficiency of the concentrator have been determined within the limit of acceptance. From the simulated result it was observed that LCR distribution is more uniform from equinox to winter than of summer but optical concentration ratio at summer solstice has estimated maximum. In this paper we have also estimated that the maximum optical efficiency of Sea Shell concentrator is 85.5 % at winter solstice. From the study of the results of the comparison of LCR distributions over the absorber surface in various seasons, it is found more uniform than in summer.

Keywords- Sea Shell Concentrator, Bifacial Solar Cell, Ray Tracing, CR, LCR, ANR, Efficiency.

I. INTRODUCTION Solar concentrator is an important device to collect energy

from the sun for PV and thermal applications. Since 1970, many research have had been oriented to take advantages of the solar energy in a more efficient manner. Many types of concentrator have been proposed for obtaining the maximum amount of radiations for different field of applications [5]. In 1974 Winston proposed first basic idea of non-imaging concentrator where many types of concentrator with different configuration of collector were described [5]. In 1976 Ari Rabl described a comparison among different types of concentrators [1]. He described the purpose of some new concentrator including CPC with the second stage, Fresnel mirror, and Sea Shell concentrator for different demands of the applications [1]. In this research work we have analyzed the optical performance of a concentrator with seasonably variable concentration called Sea Shell concentrator which was first described by Rabl. He proposed a 2D model of Sea Shell concentrator with maximum half acceptance angle θmax = 36° so that it can accept solar radiation 6 to 7 hours per day. He

proposed such two designs of concentrator, one for maximum output in summer and another for maximum output in winter and such output can be varied by truncation [10]. Rabl also proposed an idea of using convection heat loss suppressing cavities in the Sea Shell concentrator which has no concentration capability since entrance and exit aperture of the cavity are equal.

We have made a mathematical model for Sea Shell concentrator to investigate the performance of it. We have made a simulation program by using Matlab to analyze some performance parameter such as average number of reflections (ANR), optical concentration ratio (CRo), and illumination distribution on flat absorber (LCR). In this work it is observed that with the variation of incident angle within the limit of maximum acceptance, ANR is also varied. Due to this variation of ANR, radiation distribution on the absorber is varied. It is also observed that with the change of ANR, the efficiency of the concentrator is varied from low value at summer solstice to high value at winter solstice. This work provides a computer aided Matlab program to analyze LCR distribution on the flat horizontal absorber. It is observed that near summer solstice it is highly nonuniform but for other angles of incidence LCR distribution is moderately uniform. We have also analyzed the effect of some parameter such as maximum half acceptance angle, height of the CPC, the absorber width on the maximum possible concentration ratio of the Sea Shell. Although this concentrator is well suited for thermal application as a solar energy collector to drive absorption air conditioner which needs a temperature of 100 °C or more, we have also proposed an idea the use of it in bifacial PV cell application. Since the front and back side of the absorber can be illuminated by using Sea Shell concentrator so, it will be useful for bifacial solar cell for improving maximum power output.

II. SOLAR CONCENTRATORS Solar concentrator is a device that allows the collection of sunlight from a large area and focusing it on a smaller receiver or exit. Concentrating collectors reduce the area of the receiver by reflecting (or refracting) the light incident on a large area (the collector aperture) onto an absorber of small area. With the reduced heat loss, concentrating collectors can operate at elevated temperatures and still provide significant

978-1-4799-0400-6/13/$31.00 ©2013 IEEE

Figure 1. Cross sectional view of conventional solar cell and a bifacial cell

[12].

quantities of useful thermal energy. Since reflective surfaces are usually less expensive than absorbing (receiver) surfaces so large amounts of inexpensive reflecting surface area can be placed in a field, concentrating the incident solar energy on smaller absorbing surfaces.

A. Concentrator for Bifacial Solar Cell A bifacial solar cell differs from a conventional solar cell in

that the back surface, as well as the front surface, has a current-collecting grid. Photons that are incident on the back of the cell can then be absorbed and produce carriers in the bulk of the cell, along with photons incident on the front. Fig. 1 shows the conventional and bifacial solar cell.

The examples of Sea Shell concentrator are shown in Fig. 2 which have an acceptance half angle θmax = 36° and they are truly stationary with a collection time of at least 7 hours per day [1]. Their concentration ratio is 1.7 at normal incidence, but varies from zero to 3.4. During summer concentration is minimum for Fig. 2(a) and maximum for Fig. 2(b). Again during winter concentration is maximum for Fig. 2(a) and minimum for Fig. 2(b). For this reason Fig. 2(a) is the best one for winter and Fig. 2(b) for summer. To get the power improvement from a bifacial solar module, the integration of it in concentrator is important. The installation technique of bifacial PV module in Sea Shell concentrator is shown in Fig. 3. In this integration it is seen that only direct solar radiation falls on the front side of the cell and reflected sunlight from a concentrator fall on the rear side of the bifacial cell. For such illumination distributions power output of the bifacial PV module is improved due to power contribution from rear side which acts as concentrated solar cell.

B. Optical Concentration Ratio Optical Concentration Ratio (CRo) can be defined as the

average value of irradiance (radiant flux, Ir) integrated over the receiver area (Ar), divided by the insolation incident on the collector aperture [14].

Figure 2. Stationary Sea Shell concentrator with variable concentration (a) for maximum output in winter and (b) for maximum output in summer.[1].

For 2D Sea Shell concentrator the ideal concentration ratio is given by [1]

where Ia = Insolation incident on aperture area and this CRo also can be defined as the proportion of incident rays within the collecting angles that emerges from the exit aperture [4].

C. Local Concentration Ratio For calculating the local concentration ratio (LCR)

distribution, absorber width is divided into particular zones of fixed length. LCR can be estimated for each incident angle. In the present work, we have used the following equation to estimate LCR distributions [4].

D. Average Number of Reflection The average number of reflections <N> is needed to assess

reflection losses and optical efficiency of the concentrator. The fraction of the radiation incident on the aperture which is transmitted to the absorber can be approximated by [1],

where ρ is the reflectivity of the mirror, typically 0.75 to 0.95. The equation of average number of reflections <N> can be written as [2]

where ψm indicates the rim angle for the concentrator.

E. Efficiency Optical efficiency (ηo) calculated by an approximation method proposed by Rabl [1]. These results were shown the variations of ηo as a function of the incident angle of solar radiation on the

IdAIA1

CR arrr

o ⎟⎠⎞

⎜⎝⎛

∫=

absorber on theray direct Only

absorber on theray reflected anddirect ofnumber TotalCRo =

aperture of zone equal on the raysincident ofNumber absorber theof zone particular on the rays ofNumber LCR =

ρτ N ><=

(1) Ψ cos1

)Ψ cos(12Ψsinln

)Ψcos(1

])Ψ cos(12[Ψsin31

12π

N

m

m1/2

m

m3/2

m1/2

m

+++

+

−

−−+>=<

θsin 2C maxideal,2D =

aperture’s plane of the concentrator. This method is based on the <N>, and ηo is given by [19]

where τ is the total transmittance of the transparent cover around the absorber, α is the absorptivity of the absorbing surface, ρ is the reflectivity of the reflecting surface. The parameter γ is defined as the factor of diffuse solar radiation which indicate fractions of total radiation collected by the concentrator [2], [19], [7] and which is given by

It is an approximate relation for the case of concentrating solar devices with a small CR where Gb, Gd and Gt are the beam, diffuse and total intensity of the incoming solar radiation on the aperture’s plane respectively [18].

III. 2D RAY TRACING MODEL Analytical geometry has been used to design a 2D model for Sea Shell concentrators and this model is used for analyzing the optical performance of it. The idea of this concentrator described by Rabl and he proposed a geometrical concept where Sea Shell concentrator is made of two geometrical \shapes [1]. This type of concentrator consists of two geometric portions one is parabolic reflecting surface and another is a circular cavity which is used to suppress convection heat loss from the absorber. Parabolic concentrating side wall reflects energy onto the absorber. Fig. 4 shows a flat plate collector with Sea Shell concentrator which gives maximum output in the summer and the equation of the parabolic portion in (x, y) coordinates system will be in the form,

where f is the focal length of the parabola. The equation of the circular portion will be,

where f is the radius of the circle and also the absorber length. The equation of the aperture (winter to summer solstice in Fig. 3) can be written as,

Figure 3. Installation of bifacial solar cell module in Sea Shell concentrator.

where θmax indicates the maximum half acceptance angle and H is the height of the concentrator. To obtain the theoretical ray tracing model we have subdivided the x coordinate values of the aperture and get an expression for x coordinates of the aperture [3].

where N is the total number of the incident rays and values of n from 1 to (N – 1). Now corresponding y coordinates will be,

By using the coordinates of aperture we get the incident ray equation as follows (see Fig. 4),

Coordinate values for direct rays on the absorber,

If the values of Xd (n) are in the range 0 ≤ Xd ≤ f, then it will fall on the absorber directly, otherwise it may contribute in consecutive reflections from parabolic portion or from circular cavity or may be lost from the concentrator depending on the values of θin. Equation of the 1st reflected rays from the circular portion of the Sea Shell concentrator is

where (xc1, yc1) are the points of intersection of incident rays at circular portion and the slope of the reflected rays are,

where the slope angles of the tangent at the point (xc1, yc1) by using (5)

where

Coordinate values for reflected rays from the circular portion of the concentrator to absorber is,

If equation satisfies this condition 0 ≤ Xca1 ≤ f, then it will be counted as 1st reflected rays (Fig. 4). Similarly, the equation of the 1st reflected rays from parabola is

Figure 4. Ray propagations in Sea Shell concentrator.

(2) γρταη No

><=

(3) G)CRGG(γ t1

db−+=

(4) f)(y f 4x2 +=

)H f (2N

1)(n(n)x

−−=

fHθ tanH f 2θ tan(n)x (n)y maxmax −++=

)θθ(cot (n)x (n)y )θθ(cot x y inmaxinmax ++++−=

0)n(Y and (n)x )θθ tan (n)y n)X dinmaxd =++= ((

)θθ90Ψ (2tan mc inmaxc1−−+=

0θcot f)(HH f 2θcoty (n)x maxmax =−++−

xmyxmy c1c1c1c1++=

(5) fy 222 =+x

)dxdy(tan 1Ψc−=

)y(xdxdyc1c1

−=

m)yxm(X c1c1c1c1ca1 −=

where (xp1, yp1) is the point of intersection at parabolic portion and the slope of the reflected rays are,

Similarly, slope angle of the tangent at parabolic portion is,

where

When the rays reach at the absorber then coordinate values will be,

If 0 ≤ Xpa1 ≤ f is true then it will be counted as 1st reflected rays, otherwise it will contribute in 2nd, 3rd etc. reflections or may be lost. In a similar way we have estimated 2nd and 3rd reflected rays.

IV. RESULTS AND DISCUSSIONS To design a 2D Sea Shell concentrator we have selected the

length of the flat horizontal absorber is f = 2 meter which is also the radius of the circular cavity. To collect solar radiation at least 6 to 7 hours per day, we select maximum half acceptance angle θmax = 36° [1]. By considering these parameters the height of the concentrator has been calculated as follows,

By considering the total number of incident rays N = 1000 in this work, the aperture of the Sea Shell concentrator is divided into 1000 sections and on each section one sun ray is made incident.

A. Variation of Reflected Ray on the Absorber We have considered 1000 incident rays on the aperture in

our simulation program and also considered up to 3rd reflection since most of the energy after 3rd reflection is lost.

Figure 5. Change of number of reflected rays with angle of incidence.

It is seen from the Fig. 5, the number of reflected rays that reaches the absorber is maximum at summer solstice and decreases from summer to winter and zero at winter solstice. When the Sun at the equinox (day time and night time are equal) total number of reflected rays is 402 in which 1st reflected ray is 241, 2nd reflected ray is 102 and the 3rd reflected ray is 69. 3rd reflected rays contribute from θin = – 15° to θin = + 9°. When θin = – 36° all of the rays of the absorber edge are 1st reflected, since the rays are parallel to the axis of the parabola and for θin = + 36° no reflected rays are collected.

B. Variation of Optical Concentration Ratio Concentration ratio determines how many rays (reflected

and direct) reach to the absorber with respect to direct rays. From Fig. 6, it is observed that for θin = 0° (Equinox) to θin = – 35° (close to the summer solstice) CR varies from 2.6 to 35.6. The reason of large CR value at summer solstice is that more rays fall on the parabolic section of the concentrator. From θin = – 26° to – 20° the value of CR remain below 5 and change within 5 to 3.126. From θin = 19° to 25° CR values vary from 3 to 2. CR value 1 at winter solstice means that at this time no reflected rays from a concentrator fall on the absorber and only direct rays can fall on the absorber.

C. Local Irradiation Distribution When concentrators are not used then radiation on the flat

absorber becomes uniform along on its length. In the presence concentrator, radiation distribution over the length of the absorber becomes less uniform but radiation intensity becomes high. It is seen from the Fig. 7, that LCR distribution on the absorber is less uniform from equinox (θin = 0°) to summer season. It is also observed that for θin = 0° the uniformity of LCR distribution on the absorber is better than other angle of incidence in summer and concentration ratio varies around 2 to 2.5 along the 2 meter length of the absorber. In case of another incident angle for example θin = – 10°, – 20° and – 30°, nonuniformity of illumination distribution increases and concentration varies from almost 1 to 5. But the problem is that the peaks of concentration ratio appear at different positions on the absorber. It is also seen from Fig. 7 peaks of CR shift to the left side of the absorber for θin = 0° to – 30° since more light rays fall on the parabolic reflector from equinox to summer.

Figure 6. Variations of CR with θin from summer to winter solstice.

xmyxmy p1p1p1p1++=

m)yxm(X p1p1p1p1pa1 −=

)θθ90Ψ(2tan m inmaxpp1−−−=

meter 3.789)36(cot 2H 2 =°=

)dxdy(tanΨ 1p

−=

)2fx(dxdy p1−=

Figure 7. Radiation distributions along the length of the flat horizontal absorber from θin = 0° (Equinox) to – 30° (Summer).

Local irradiance distributions on the flat horizontal absorber have also observed from equinox to winter solstice and the result is somewhat different from equinox to summer solstice.

From Fig. 9, it is observed that the LCR distribution for incident angle θin = 10° and θin = 20° is more uniform than θin = 0° but CR at particular zone of the absorber is lower. For θin = 10° LCR varies in between 1.25 and 2.55 along the length of the absorber and for θin = 20° LCR varies between 1 to 2.5 which are lower than the local irradiance variation for θin = 0° (1.5 to 4.1). From these results we can conclude that the uniformity of local irradiance is increased from equinox to winter solstice but concentration ratio is decreased. If we replace bifacial solar module instead of thermal collector as receiver then although we get lower CR benefit but there is less probability to generate hotspots (local heating) in the PV module.

D. Average Number of Reflection and Efficiency To calculate optical efficiency of Sea Shell concentrator at

first we have estimated factor for solar diffuse radiation γ by using (3).

Figure 8. Change of average number of reflections with angle of incidence and CRo.

Figure 9. Radiation distributions along the length of the flat horizontal absorber from θin = 0° (Equinox) to 20° (Winter).

Where total incoming solar radiation on aperture plane is Gt = 1000 W/m2 (AM 1.5) and diffuse Radiation Gd = 0.2 Gt [2], [18] and beam radiation Gb = 800 Wm-2 then γ = 0.858 for CR = 3.4. Now if ρ = 0.85 (Aluminized Mylar) [18], [2], α = 0.95 (Black chrome) [18] and τ = 0.90 then the theoretical estimation of efficiency η = 57.17 %. Since <N> is different for different incident angles [1], it is possible to assess exact <N> at any incident angle by using ray tracing simulation. From theoretical model by using (1), we have an estimated average number of reflections <N> = 1.54. From the simulation result we have observed the variation of <N> with the angle of incidence from summer to winter solstice. It is seen from the Fig. 8, that the value of <N> is maximum 1.26 during the summer (θin = – 35°) since the total number of reflections is maximum in summer. From summer to winter with the decrease of CR, <N> is decreased. At winter solstice <N> = 0 means no reflection occurs at all, only the direct rays fall on the absorber. The impact of changing <N> with CR on the ηo of the concentrator is also obtained by using (2). From Fig. 8, it is observed that <N> increases with the increase of CR. Due to this increase of <N>, the efficiency of the concentrator is decreased to 56 % at winter solstice. At winter solstice <N> = 0 and η = 86 % (maximum) when no reflection occurs.

Figure 10. Change of efficiency with optical concentration ratio (CRo).

We have also estimated seasonal variation of the efficiency of the Sea Shell concentrator i.e., changes of efficiency with the change of incident angle with the equinox. At equinox θin = 0° and η = 67.7 % and from equinox to summer solstice efficiency decreases due to the increase of CR and <N>. For example during the summer when θin = – 30° then η = 58 %. Similarly from the equinox to the winter solstice, due to the decrease of CR and <N> efficiency increases up to η = 86 % (Fig. 10). This concentrator has a seasonal change of efficiency and CR with large view of angle, which indicates that it will be more effective to deliver heat energy based on load demands for solar absorption air conditioner than other concentrator having fixed CR. The results of our work indicate that in the case of PV applications of the Sea Shell concentrator, optimization is important to get maximum power output since LCR is not so uniform.

V. CONCLUSION The optical performance of a new type of concentrator for

bifacial PV applications has been analyzed in this work. From the result of simulation we have observed that the total number of reflections including 1st, 2nd, and 3rd are increased from equinox to summer and decreased from equinox to winter. We have estimated the theoretical value of ANR is 1.54 but from simulation result it is 1.25 at summer solstice and decreases during winter. The dependency of optical efficiency on some parameters has been investigated according to (2). Efficiency variations from winter to summer (Fig. 10) indicates that if bifacial PV modules are integrated in a Sea Shell concentrator then maximum power output will be improved and analysis of maximum power output from bifacial module will be a scope for further research in this field. This model will give a good first approach for more complex mathematical model of different types of new concentrator. In this research we have used analytical geometry to generate a ray tracing model for 2D Sea Shell concentrator which will help to analyze the performance of 3D Sea Shell and this model can be the key tools for analyzing the optical performance of different kinds of optical systems.

ACKNOWLEDGMENT We would like to express our deepest gratitude to Onirban

Islam, who has supported us throughout our work with his patience and knowledge.

REFERENCES [1] A. Rabl, “Comparison of Solar Concentrators”, Solar Energy, vol.18, pp.

93-111, 1976.

[2] M. Souliotis, Y. Tripanagnostopoulos, "Study of the distribution of the absorbed solar radiation on the performance of a CPC-type ICS water heater", Science Direct, Renewable Energy vol – 33, pp. 846–858, 2008.

[3] R. K. Mazumder, M. Hussain, "Comparative Studies on geometrical-optical performance of discrete mirror seasonally adjusted linear solar concentrator and continuous profile compound parabolic concentrator", Optica Applicata, Vol. XIX, No. 3, 1983.

[4] R. K. Mazumder, M. Hussain, "A comparative study of computer aided ray trace evolution of CPC and its derivatives", Bangladesh J. Sci. Res. 13 (2) : 139-147, 1995 (December).

[5] R. Winston, J. C. Minano, P. Benitez, "Non-imaging optics", Elsevier Academic Press , pp. (43-97) , 1974.

[6] J. H. Karp, E. J. Tremblay, J. E. Ford, "micro-optic solar concentration and next-generation prototypes", IEEE - Conference, 2010

[7] D. Y. Goswami, "Principles of Solar Engineering", 2nd Edition, chapter 3, Taylor & Francis, 2000.

[8] S. Senthilkumar, K. Perumal., P. S. S. Srinivasan, "Optical and thermal performance of a three-dimensional compound parabolic concentrator for spherical absorber", Sadhana Vol. 34, Part 3, pp. 369–380 , June 2009.

[9] J. Nilsson, "Optical Design and Characterization of Solar Concentrators for Photovoltaics" Lund University, Lund Institute of Technology, Sweden, Printed by KFS AB, Lund, 2005.

[10] A. Rabl, "Sea Shell Solar Collector", United States Patent, United States Energy Research and Development Administration, Washington. DC, July 8, 1975.

[11] A. Rabl, “Radiation Transfer Through Specular Passages”, Argonne National Laboratory Report SOL 75-03 (May 1975); Int. J. Heat and Mass Trans. 20^, 323 (1977).

[12] I. R. Edmonds," The performance of biracial solar cells in static solar concentrators " , Solar Energy Materials 21 (1990) 173-190, Elsevier Science Publishers B.V. (North-Holland), 1990.

[13] J. A. Duffie., and W. A. Beckman., “Solar Engineering of Thermal Processes”, Wiley Interscience, pp. 293–300, 2006.

[14] W. B. Stine, M. Geyer., “Power from the Sun” chapter 8, copyright 2001.

[15] V. Poulek., M. Libra., I. Persic., “Bifacial tracking concentrator TRAXLE”, Czech University of life Sciences Prague, Czech Republic, 2008.

[16] C. Honsberg, and S. Bowden, “A collection of resources for the photovoltaic educator”, http://www.pveducation.org, July, 2012.

[17] A. Rabl, “Optical and Thermal Properties of Compound Parabolic Concentrators”, Argonne National Laboratory Report SOL 75-01 (1975); Solar Energy, 18, 497 (1976).

[18] A. Rabl, J. O’Gallagher, R. Winston, “Design and test of non-evacuated solar collectors with compound parabolic concentrators”, Sol Energy,1980,25: 335-51.

[19] J. W. Allen, N. M. Levitz, A. Rabl, K. A. Reed, W. W. Schertz,G. Thodos, and R. Winston, "development and demonstration of compound parabolic concentrators for solar thermal power generation and heating and cooling applications", Solar Energy Group, argonne national laboratory, Progress Report for the Period July, December 1975.