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Research Papers

Geometric Optimization of Concentrating Solar Collectors using Monte Carlo Simulation

[+] Author and Article Information
A. J. Marston, M. R. Collins

Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canadakjdaun@mme.uwaterloo.ca

K. J. Daun1

Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canadakjdaun@mme.uwaterloo.ca

1

Corresponding author.

J. Sol. Energy Eng 132(4), 041002 (Aug 19, 2010) (9 pages) doi:10.1115/1.4001674 History: Received December 08, 2009; Revised March 23, 2010; Published August 19, 2010; Online August 19, 2010

This paper presents an optimization algorithm for designing linear concentrating solar collectors using stochastic programming. A Monte Carlo technique is used to quantify the performance of the collector design in terms of an objective function, which is then minimized using a modified Kiefer–Wolfowitz algorithm that uses sample size and step size controls. This process is more efficient than traditional “trial-and-error” methods and can be applied more generally than techniques based on geometric optics. The method is validated through application to the design of three different configurations of linear concentrating collector.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Simple parabolic collector design example

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Figure 2

View factor used to examine uncertainty analysis

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Figure 3

Uncertainty magnitudes as a function of the difference parameter, h

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Figure 4

Vector reflection

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Figure 5

Geometry for (a) the initial design, Φ0=[11,−4]T, and (b) the optimal design, Φ∗=[10,0]T for the parabolic concentrating collector problem

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Figure 6

CPU time for varying K

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Figure 7

Solution path for rapidly diminishing step size

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Figure 8

Solution path using quadratic interpolation

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Figure 9

Solution path using diminishing step size, Eq. 11

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Figure 10

Directional absorptance of the solar collector (20)

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Figure 11

Faceted surface concentrating collector

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Figure 12

Geometry for (a) initial design Φ0=[8,3,6]T and (b) optimal design Φ∗=[6.81,2.51,7.79]T for planar surface trough problem

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Figure 13

Asymmetrical concentrating collector geometry

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Figure 14

Geometry for (a) initial design Φ0=[−4,−4,0,−6,4,−4]T and (b) optimal design Φ∗=[−5.41,−1.78,1.14,−4.30,6.82,−3.97]T for asymmetrical collector problem

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