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Research Papers

Inverse Design of Spectrally Selective Thickness Sensitive Pigmented Coatings for Solar Thermal Applications

[+] Author and Article Information
Refet A. Yalçın

Department of Mechanical Engineering,
Boğaziçi University,
Bebek 34342, Istanbul, Turkey

Hakan Ertürk

Department of Mechanical Engineering,
Boğaziçi University,
Bebek 34342, Istanbul, Turkey
e-mail: hakan.erturk@boun.edu.tr

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received August 2, 2017; final manuscript received December 11, 2017; published online February 27, 2018. Editor: Robert F. Boehm.

J. Sol. Energy Eng 140(3), 031006 (Feb 27, 2018) (10 pages) Paper No: SOL-17-1319; doi: 10.1115/1.4039276 History: Received August 02, 2017; Revised December 11, 2017

Inverse design of thickness sensitive spectrally selective pigmented coatings that are used in absorbers of solar thermal collectors is considered. The objective is to maximize collection efficiency by achieving high absorptance at solar wavelengths and low emittance at the infrared (IR) wavelengths to minimize heat loss. Radiative properties of these coatings depend on coating thickness, pigment size, concentration, and the optical properties of binder and pigment materials, and a unified radiative transfer model of the pigmented coatings is developed in order to understand the effect of these parameters on the properties. The unified model (UM) relies on Lorenz–Mie theory (LMT) for independent scattering regime in conjunction with extended Hartel theory (EHT) to incorporate the multiple scattering effects, T-matrix method (TMM) for dependent scattering, and effective medium theory (EMT) for very small particles. A simplified version of the UM (SUM) ignoring dependent scattering is also developed for improving computational efficiency. Through the solution of the radiative transfer equation by the four flux method (FFM), spectral properties are predicted. The developed model is used in conjunction with inverse design for estimating design variables yielding the desired spectral emittance of the ideal coating. The nonlinear inverse design problem is solved by optimization by using simulated annealing (SA) method that is capable of finding global minimum regardless of initial guess.

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Figures

Grahic Jump Location
Fig. 1

Pigment distribution [16] that is used to model dependent scattering

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Fig. 2

Sketch of the spectrally selective coating on a substrate

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Fig. 3

Spectral reflectance for different regimes of UM

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Fig. 4

Spectral reflectance versus wavelength for validation and verification studies

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Fig. 5

SA iterations and variation of net heat flux for (a) fv = 0.1, 0.2, 0.3 together, (b) fv = 0.1, (c) fv = 0.2, and (d) fv = 0.3

Grahic Jump Location
Fig. 6

Optimal spectral emittance of different materials at Ta = 373 K, Cf = 1

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Fig. 7

Comparison of spectral reflectance of the optimal pigmented coatings with carbon pigments for flat plate and two concentrating solar collectors

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Fig. 8

Variation of collection efficiency with thickness

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Fig. 9

Variation of collection efficiency with radius

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Fig. 10

Variation of collection efficiency with volume fraction

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