MATHEMATICAL MODELING AND ANALYSIS OF COMPOUND … · 2018. 6. 30. · Mathematical Modeling and...

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International Journal of Mechanical Engineering and Technology (IJMET)

Volume 9, Issue 6, June 2018, pp. 113–121, Article ID: IJMET_09_06_014

Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=6

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

MATHEMATICAL MODELING AND ANALYSIS

OF COMPOUND PARABOLIC

CONCENTRATOR USING SOLTRACE

Supriya S More

Assistant Professor, Automobile Engineering Department, RIT, Sakharale.

Dr. G. Ravindranath

Principal, Sampoorn Institute of Technology & Research, Benglore.

Sagar E More

Director, Technical, Utopia Automation and Control, Satara

Dr. S.S. Thipase

Assistant Director, Automotive Research Association of India, Pune

ABSTRACT

Efficient conversion of Solar energy in to usable form is need of era. The solar

energy conversion in electrical or thermal form for its decentralized application

should be appreciated in Asian countries. Increase in gain of solar thermal system will

be credibility of efficient solar thermal absorber. Concentrator plays main role in

efficient thermal absorber. The present research has presented Mathematical

modeling and simulation of solar incident radiation on CPC with ray tracing

software. In this research work attempt has been made to design thermally efficient

optics. The medium concentration solar thermal absorber up to 5X have been

designed and simulated. The SolTrace ray tracing software shows pattern of flux

distribution on the receiver. The results are surprising. It shows uneven pattern of

distribution of solar incident radiation on receiver. Mathematical relations between

maximum and minimum flux with average flux has been built. SolTrace results have

been utilized to find position of this maximum and minimum flux distribution on the

receiver. Effect of change in flux distribution with change in aperture width has been

also evaluated by building different models in SolTrace software. These results will

help to develop heat receiver based on maximum heat extraction from maximum heat

receiving area on receiver. This will achieve maximum possible heat gain.

Development of sustainable model for medium temperature (up to 2000 C)

temperature application can be possible with this technology.

Key words: compound parabolic concentrator, flux distribution, Ray tracing, solar,

SolTrace

Supriya S More, Dr. G. Ravindranath, Sagar E More and Dr. S.S. Thipase


Cite this Article: Supriya S More, Dr. G. Ravindranath, Sagar E More and

Dr. S.S. Thipase, Mathematical Modeling and Analysis of Compound Parabolic

Concentrator using SolTrace, International Journal of Mechanical Engineering and

Technology 9(6), 2018, pp. 113–121.

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=6

1. INTRODUCTION AND LITERATURE REVIEW

Solar energy is one of the popular non-conventional energy sources available in the abundant

form in Asian countries. In spite of this, effective utilization of the solar irradiation falling on

the earth is challenging task. The solar irradiance varies with relative positions of sun and

earth. The total irradiance (direct and diffuse) encashment into a usable form of energy can be

possible with scientifically designed solar thermal systems. Carefully designed solar thermal

absorber based on practical consideration and validation of the design with suitable the

software will help to trap more useful energy.

Compound parabolic concentrators are called as non imaging concentrators, as the

concentration of all incident rays is at the receiver. Design of medium concentration

compound parabolic concentrator requires perfect aperture width and acceptance angle. The

height is an interesting parameter as truncation in height changes the concentration ratio. The

optimization of CPC will balance between concentration ratio and manufacturing cost (which

lowers with truncation).

The concentrator is one of the prime components of the solar thermal system. Jaaz and

Hasan [7] have used CPC for, photovoltaic solar collector [10]. Seth and Shah [1], designed

and developed CPC with medium concentration (2 to 100) and truncated height and analyzed

for thermal efficiency. Rahman, Isa and Goh [2], Bellos, Korees [4] had optimized the

design by truncation of CPC baring some affordable loss in concentration ratio at the same

time reduction in cost-effectively. Zheng, Yang [6], have presented Experimental and

Numerical Analysis of CPC, Tchinda[3] developed solar air heater with CPC. Osório and

Horta [15], compared various ray tracing and optical simulation software. The Optical

simulation of ray tracing software for the various application has been put forth by

Zhongyuan and Shengyan [5] and Sainath and Nitin [8], Deep and Dinesh [13],.The attempts

of heat recovery has been made and reviewed in some literature[9,11]. Further improvements

in the design of CPC with wings have been tried [12] for improving the efficiency of CPC.

The simulation software comparison has been done [14] in view of applicability and operating

ease.

The flux pattern distribution on the receiver should be a key factor in designing solar

thermal absorber. This could be dealt best with performing ray tracing of the concentrator.

Though some literature has addressed these issues using some ray tracing software, neither

mathematical modelling have been presented nor the use of SolTrace software has been

demonstrated for simulation in any of the literature. This research work has put forth

mathematical modelling of the compound solar concentrator. The design has been optimized

for medium concentration ratio to serve medium temperature applications. The analysis of

concentrator has been done using SolTrace ray tracing software. The result also supports the

experimental data.

2. MODELLING OF COMPOUND PARABOLIC CONCENTRATOR

Concentrators are of different types like a flat plate, parabolic, dish type etc. Use of flat plate

concentrator is limited due to its low-temperature gain while dish type of concentrator

Mathematical Modeling and Analysis of Compound Parabolic Concentrator using SolTrace


requires more space. These factors eliminate the possibility of using this concentrator for a

standalone solar thermal system for medium temperature application. Use of parabolic

concentrator for medium temperature application is appreciated by many scientists. Even

though, compound parabolic concentrators are more popular for medium temperature

applications.

Compound parabolic concentrator profile is obtained from two simple parabolas.Fig.1

illustrates the terminology of Compound parabolic concentrator.

Figure 1 Terminology of CPC concentrator

The equation of Parabola is,

(1)

The full height of CPC

(

) (2)

The point on parabola C can be expressed in terms of co-ordinates,

X= b cos c and Y= b (1- sin c)/ 2

Height to aperture ratio is given by,

*

+ cos (3)

The two models have been designed as shown in fig 2.based on above formulas one with

receiver width 100 mm and another with 200mm. The acceptance angles for both is same i.e.

11.54 degree. The full height for the first model is 1469 mm and for a second it is2938 mm

which is truncated at 820 mm. The full height leads to more material and manufacturing cost,

so the parabola is truncated to optimize the design from concentration ratio and manufacturing

cost point of view. There seems a mere compromise in concentration ratio (up to 10% ) while

great reduction in cost(up to 40%),[2].



(a) … (b)

Figure 2 (a) Complete drawing of CPC concentrator,(b) Fabricated CPC.

3. SIMULATION OF CPC

SolTrace is ray tracing software. It is developed by National Renewable Energy Laboratory

which is part of United State Federal Energy Department. In SolTrace at first, the script file

has been developed. Then the sun parameters are entered in the software like position,

reflecting surfaces etc. Then it is analyzed for a specific number of rays. The images of

analysis are given in following diagrams. Fig.3 (a) shows ray tracing of model 1 with 100 mm

aperture width while Fig.3 (b) is of ray tracing diagram of model 2 with 200 mm aperture

width. Table 1 gives the numerical data of ray tracing for both the models. The following

diagrams show ray tracing assuming count of 10,000 ray incident on aperture area. The rays

striking at reflecting surfaces and concentrated at focal plane called receiver in the CPC.

(a) (b)

Figure 3 Ray Tracing diagrams with 0 0 incident angle. (a) Model 1(100 mm receiver) (b) Model 2

(200 mm receiver)



Table 1 Model 1 Result Analysis Parameters

Sr.No. Parameter Model 1 Model 2

1. Sun Ray Count 49446 69196

2. Direct Normal Irradiance 1000 1000

3. No of Plotted Rays 23157 23099

The same analysis can be done by writing script file in SolTrace Software instead of

developing a model and GUI based analysis.

It is interesting to know flux distribution on the receiver surface. The number of rays

striking at the specific position on the receiver will decide the concentration of heat energy at

that area which is counted as flux density. The CPC has been designed for 5X concentration.

This denoted the flux on the receiver should be 5000KW/m2. The following diagram shows

flux density of model 1 . The surface plot and contour plots are Shown in Fig.4 for Model 1

and Fig.5 for Model 2 . Table 2 shows the corresponding numerical data of flux distribution

graph for both models.

(a) (b)

Figure 4 Flux distribution over the receiver of Model 1 (a) contour plot (b) surface plot

(a) (b)

Figure 5 Flux distribution over receiver of Model 2 (a) contour plot (b) surface plot



Table 2.Model 1 Result Analysis Parameters

Sr.No. Parameter Model 1 Model 2

1. Sun Ray Count 49446 69196

2. Peak Flux in W/m2 10159 (+/- 14.14%) 8663.3 (+/- 4.81%)

3. Minimum Flux in W/m2 1015.9 2231

4. Average Flux in W/m2 5022.3(+/- 0.65%) 4999.84(+/- 0.20%)

5. Uniformity 0.4 0.36

Above results are surprising, till this moment researchers are assuming a uniform

distribution of the solar irradiance on the receiver. The result shows its non-uniform in nature

and flux density varies with the position of incident ray on the receiver after reflecting from

parabolic reflectors. The flux density varies in the range of 1015.9 W/m2 to 10,159 W/m

2 in

case of Model 1.While it ranges between 2231 W/m2 to 8663.3 W/m

2 in case of Model 2.

4. EXPERIMENTAL EVALUATION

Experimental set up for the testing of the compound parabolic concentrator is as shown in

fig.6. The monochromatic light beam of diameter 0.5 mm is used to observe the

concentration of rays on the absorber. The light source is mounted on a linear slide with

position counter. The aperture width is 500 mm on which total 500 positions are observed

during experimentation which are 1 mm successive points on the aperture. The rays get

reflected from the surfaces of concentrator and incident on the absorber surface.

The said positions of the incident rays are recorded as observations. This all data is

collected in observation table. The observation table given below shows that there are many

points where no of rays incident are more than one. The total no of positions on aperture

width with linear sliding mechanism counter counts 500.

Figure 6 Experimental set up for Evaluation of Ray Distribution Pattern

At the same time, the numbers of points on the absorber are 100. It ensures 5 sun

compound parabolic concentrations. Table 3 shows observations during experimentation.



Table 3 Model 1 Observations of Experimental Exercise.

Absorber

Width

(mm)

No. of

Rays

Absorber

Width

(mm)

No. of

Rays

Absorber

Width

(mm)

No. of

Rays

Absorber

Width

(mm)

No. of

Rays

Absorber

Width

(mm)

No. of

Rays

-50 7 -30 2 -10 7 10 7 30 2

-49 7 -29 3 -9 7 11 6 31 3

-48 7 -28 2 -8 7 12 7 32 3

-47 8 -27 2 -7 8 13 6 33 3

-46 7 -26 1 -6 8 14 6 34 4

-45 7 -25 1 -5 8 15 5 35 4

-44 5 -24 1 -4 8 16 5 36 4

-43 4 -23 2 -3 8 17 5 37 4

-42 5 -22 2 -2 8 18 4 38 5

-41 4 -21 2 -1 9 19 3 39 4

-40 5 -20 2 0 9 20 2 40 5

-39 4 -19 3 1 9 21 2 41 5

-38 5 -18 4 2 8 22 1 42 5

-37 4 -17 5 3 8 23 2 43 4

-36 4 -16 5 4 8 24 1 44 5

-35 4 -15 5 5 8 25 1 45 7

-34 4 -14 6 6 8 26 1 46 7

-33 3 -13 6 7 8 27 2 47 8

-32 3 -12 7 8 7 28 2 48 7

-31 3 -11 6 9 7 29 3 49 7

50 8

Figure 7 Flux distribution along the receiver width based on experimental observations.

The result in Fig.7 shows that the ray concentration on the absorber is not constant. The

no of rays incident on the specific point on the absorber depends on the position of a point on

the absorber. The flux density varies as per band pattern. At centre and at the outer edges of

the absorber the flux density is maximum. There are total four flux band patterns whose

details are given in Table 4.

0

2

4

6

8

10

-50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50

No

of

Inci

de

nt

rays

Position Across Absorber Width in mm

Graph of Absorber width Vs No. of incident ray



Table 4 Various Flux bands on Receiver Width

Model

No.

Aperture

Width

(mm)

Absorber

Width

(mm)

Flux

band-1 (mm)

High Flux

Flux band-2

(mm)

Low flux

Flux band-3

(mm)

High Flux

Flux band-4

(mm)

Low flux

Flux

band-5 (mm)

High Flux

1 500 100 -50 to -35 -35 to -20 -20 to 20 20 to 35 35 to 50

2 1000 200 -100 to -70 -70 to -40 -40 to 40 40 to 70 70 to100

5. RESULT DISCUSSION

The Experimental results are matching with simulation results. The flux band patterning is

similar in both the models when tested experimentally and in SolTrace ray tracing software.

The pattern of flux distribution can be expressed in the form of following relations,

Width of Band 1= 0.125 X …….(4)

Width of Band 2= 0.15 X …….. (5)

Width of Band 3= 0.25 X …….. (6)

Width of Band 4= 0.15 X …….. (7)

Width of Band 5= 0.125 X …… (8)

Where X is absorber width

The data obtained as a result is much useful in designing heat receiver which is situated

below absorber. The high flux area should have high heat receiving mechanism than low flux

receiving area. The design of such type of thermal heat receiver will add value in the solar

thermal system.

6. CONCLUSIONS

The article put forth design and analysis of CPC for obtaining efficient optics for solar

thermal absorber design. The two models with different absorber width but same

concentration ratio has been analyzed in SolTrace ray tracing software. The software results

give an uneven pattern of flux distribution. The same results have been observed during

experimental work. The ray with an average irradiance of 1000W/m2 is considered as per

Indian standards. For 5 sun solar compound parabolic collector the flux density varies from

1500 W/m2 to 10000 W/m

2. There is a fixed pattern of flux distribution with five

distinguished bands of high and low flux density situated alternately. At the end, the average

density is 5000 W/m2 as expected during design. The major output of this work is an

evaluation of pattern of flux distribution on the absorber and the mathematical relations

obtained for flux distribution pattern. The same findings are useful in the design of efficient

heat receiver.

REFERENCES

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Part XXIII,pp3237 to3241.



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conference2016

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