Let us p = 2f - the focal parameter, Um is the opening (rim) angle, r1 is the radius of the concentrator, S1 is the area of the midsection of the concentrator, ρ is the radius vector of the extreme point of the concentrator, r2 is the maximum size of the focal spot, C is the average concentration. Then,
r1=p tg(Um/2) , S1=π r12, ρ=p/(1+cos(Um)), r2=ρ/cos(Um), S2= π (r2)2
and,
С=S1/S2=(r1/r2)2 =…=(sin(2Um)/2)2.
From last expression, we have for the maximum of C , Um = 450.
Thus, the optimal angle on the average concentration criterion is 45 deg.
I read somewhere that in solar engineering practice, taking into account technical and economic factors, the value 600 is used as the optimal opening (rim) angle of the solar concentrators.
I have no more information on this question.
I think this question where considered in some other works.
Please share who has materials on this question.
Thanks.
Maybe it is necessary to consider the dependence of the concentrator power on this angle?
Prof. @ Rasul Akbarov
You could Check the following paper, you might the answer of your question;
Zayed ME, Zhao J, Elsheikh AH, Li W, Abd Elaziz M. Optimal design parameters and performance optimization of thermodynamically balanced dish/Stirling concentrated solar power system using multi-objective particle swarm optimization. Applied Thermal Engineering. 2020:115539.
Link: https://www.sciencedirect.com/science/article/pii/S1359431120330210
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