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.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Kalogirou, S. A. , 2004, “ Solar Thermal Collectors and Applications,” Prog. Energy Combust. Sci., 30(3), pp. 231–295. [CrossRef]
Mar, H. Y. B. , Lin, J. H. , Zimmer, P. P. , Peterson, R. E. , and Gross, J. S. , 1975, “Optical Coatings for Flat Plate Solar Collectors,” ERDA, Minneapolis, MN, Report No. NSF-C-957.
Kennedy, C. E. , 2002, “Review of Mid to High Temperature Solar Selective Absorber Materials,” National Renewable Energy Laboratory, Golden, CO, Technical Report No. NREL/TP-520-31267.
Duffie, J. A. , and Beckman, W. A. , 2006, Solar Engineering of Thermal Processes, Wiley, Hoboken, NJ.
Peterson, R. E. , and Ramsey, J. W. , 1975, “ Thin Film Coatings in Solar Thermal Power Systems,” J. Vac. Sci. Technol., 12(1), pp. 174–181. [CrossRef]
Orel, B. , Radoczy, I. , and Orel, Z. C. , 1986, “ Organic Soot Pigmented Paint for Solar Panels: Formulation, Optical Properties and Industrial Application,” Sol. Wind Technol., 3(1), pp. 45–52. [CrossRef]
Gunde, M. K. , Logar, J. K. , Orel, Z. C. , and Orel, B. , 1996, “ Optimum Thickness Determination to Maximize the Spectral Selectivity of Black Pigmented Coatings for Solar Collectors,” Thin Solid Films, 277(1–2), pp. 185–191. [CrossRef]
Orel, Z. C. , and Gunde, M. K. , 2001, “ Spectrally Selective Paint Coatings: Preparation and Characterization,” Sol. Energy Mater. Sol. Cells, 68(3–4), pp. 337–353. [CrossRef]
Granqvist, C. G. , 1985, “ Spectrally Selective Coatings for Energy Efficiency and Solar Applications,” Phys. Scr., 32(4), pp. 401–407. [CrossRef]
Niklasson, G. A. , 2006, “ Modeling the Optical Properties of Nano-Particles,” SPIE Newsroom, 10(2.1200603), p. 182.
Vargas, W. E. , and Niklasson, G. A. , 1997, “ Applicability Conditions of the Kubelka–Munk Theory,” Appl. Opt., 36(22), pp. 5580–5586. [CrossRef] [PubMed]
Vargas, W. E. , and Niklasson, G. A. , 1997, “ Generalized Method for Evaluating Scattering Parameters Used in Radiative Transfer Models,” J. Opt. Soc. Am., 14(9), pp. 2243–2252. [CrossRef]
Maheu, B. , Letoulouzan, J. N. , and Gouesbet, G. , 1984, “ Four-Flux Models to Solve the Scattering Transfer Equation in Terms of Lorentz-Mie Parameters,” Appl. Opt., 23(19), pp. 3353–3362. [CrossRef] [PubMed]
Vargas, W. E. , 1998, “ Generalized Four-Flux Radiative Transfer Model,” Appl. Opt., 37(13), pp. 2615–2623. [CrossRef] [PubMed]
Howell, J. R. , Mengüç, M. P. , and Siegel, R. , 2015, Thermal Radiation Heat Transfer, 6th ed., CRC Press, Boca Raton, FL.
Vargas, W. E. , 2003, “ Optical Properties of Pigmented Coatings Taking Into Account Particle Interactions,” J. Quant. Spectrosc. Radiat. Transfer, 78(2), pp. 187–195. [CrossRef]
Vargas, W. E. , Lushiku, E. M. , Niklasson, G. A. , and Nilsson, T. M. J. , 1998, “ Light Scattering Coatings: Theory and Solar Applications,” Sol. Energy Mater. Sol. Cells, 54(1–4), pp. 343–350. [CrossRef]
Vargas, W. E. , and Niklasson, G. A. , 2001, “ Reflectance of Pigmented Polymer Coatings: Comparisons Between Measurements and Radiative Transfer Calculations,” Appl. Opt., 40(1), pp. 85–94. [CrossRef] [PubMed]
Vargas, W. E. , Greenwood, P. , Otterstedt, J. E. , and Niklasson, G. A. , 2000, “ Light Scattering in Pigmented Coatings: Experiments and Theory,” Sol. Energy, 68(6), pp. 553–561. [CrossRef]
Vargas, W. E. , 2000, “ Optimization of Diffuse Reflectance of Pigmented Coatings Taking Into Account Multiple Scattering,” J. Appl. Phys., 88(7), pp. 4079–4084. [CrossRef]
Baneshi, M. , Maruyama, S. , Nakai, H. , and Komiya, A. , 2009, “ A New Approach to Optimizing Pigmented Coatings Considering Both Thermal and Aestetic Effects,” J. Quant. Spectrosc. Radiat. Transfer, 110(3), pp. 192–204. [CrossRef]
Baneshi, M. , Maruyama, S. , and Komiya, A. , 2011, “ Comparison Between Aesthetic and Thermal Performances of Copper Oxide and Titanium Dioxide Nano-Particulate Coatings,” J. Quant. Spectrosc. Radiat. Transfer, 112(7), pp. 1197–1204. [CrossRef]
Gonome, H. , Baneshi, M. , Okajimac, J. , Komiyac, A. , and Maruyama, S. , 2014, “ Controlling the Radiative Properties of Cool Black-Color Coatings Pigmented With CuO Submicron Particles,” J. Quant. Spectrosc. Radiat. Transfer, 132, pp. 90–98. [CrossRef]
Yalcin, R. A. , and Erturk, H. , 2011, “ Optimization of Pigmented Coatings for Concentrating Solar Thermal Systems,” International Mechanical Engineering Congress and Exhibition, Denver, CO, Nov. 11–17, pp. 1703–1713.
Zhao, S. , and Wackelgard, E. , 2006, “ Optimization of Solar Absorbing Three-Layer Coatings,” Sol. Energy Mater. Sol. Cells, 90(3), pp. 243–261. [CrossRef]
Etherden, N. , Tesfamichael, T. , Niklasson, G. A. , and Wackelgård, E. , 2004, “ A Theoretical Feasibility Study of Pigments for Thickness-Sensitive Spectrally Selective Paints,” J. Phys. D: Appl. Phys., 37(7), pp. 1115–1122. [CrossRef]
Gonome, H. , Okajima, J. , Komiya, A. , and Maruyama, S. , 2014, “ Experimental Evaluation of Optimization Method for Developing Ultraviolet Barrier Coatings,” J. Quant. Spectrosc. Radiat. Transfer, 133, pp. 454–463. [CrossRef]
Howell, J. R. , Daun, K. J. , Erturk, H. , Gamba, M. , and Hosseini, S. M. , 2003, “ The Use of Inverse Methods for the Design and Control of Radiant Sources,” JSME Int. J., Ser. B, Fluid Therm. Eng., 46(4), pp. 470–478. [CrossRef]
Daun, K. J. , Erturk, H. , and Howell, J. R. , 2002, “ Inverse Methods for High Temperature Systems,” Arabian J. Sci. Eng., 27(2C), pp. 3–48.
Brewster, M. Q. , and Tien, C. L. , 1982, “ Radiative Transfer in Packed Fluidized Beds: Dependent Versus Independent Scattering,” ASME J. Heat Transfer, 104(4), pp. 573–579. [CrossRef]
Modest, M. F. , 2003, Radiative Heat Transfer, 2nd ed., Academic Press, Boston, MA.
Mackowski, D. W. , and Mishchenko, M. I. , 2011, “ A Multiple Sphere T-Matrix Fortran Code for Use on Parallel Computer Clusters,” J. Quant. Spectrosc. Radiat. Transfer, 112(13), pp. 2182–2192. [CrossRef]
ASTM, 2012, “Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37° Tilted Surface,” American Society for Testing and Materials, West Conshohocken, PA, Standard No. ASTM G-173-03.
Kunitomo, T. , Tsuboi, Y. , Iwashita, S. , and Shafey, H. M. , 1983, “ Theoretical Study on Spectrally Selective Paint Coatings,” Sol. World Congr., 3, pp. 1943–1947.
Tesfamichael, T. , Hoel, A. , Wäckelgård, E. , Niklasson, G. , Gunde, M. , and Orel, Z. , 2001, “ Optical Characterization and Modeling of Black Pigments Used in Thickness Sensitive Solar Selective Absorbing Paints,” Sol. Energy, 69(Suppl. 6), pp. 35–43. [CrossRef]
Sadovnikov, S. I. , Kozhevnikova, N. S. , and Rempel, A. A. , 2011, “ Stability and Recrystallization of Pbs Nanoparticles,” Inorg. Mater., 47(8), pp. 837–843. [CrossRef]
Gordon, J. , 2013, Solar Energy: The State of the Art: ISES Position Papers, Routledge, London, p. 121.
Meinecke, W. , 2000, “ Parabolic Trough Collectors,” Renewable Energy Systems And Desalination (Desalination and Water Resources, Vol. II), EOLSS pp. 315–377.
Avriel, M. , 2003, Nonlinear Programming Analysis and Methods, Dover Publications, Mineola, NY.
Kirkpatrick, S. , Gelatt, C. D. , and Vecchi, M. P. , 1983, “ Optimization by Simulated Annealing,” Science, 220(4598), pp. 671–680. [CrossRef] [PubMed]
Lahtinen, J. , Myllymaki, P. , Silander, T. , and Tirri, H. , 1996, “ Empirical Comparison of Stochastic Algorithms,” Second Nordic Workshop on Genetic Algorithms and Their Applications, Vaasa, Finland, Aug. 21–23, pp. 45–59.
Porter, J. M. , Larsen, M. E. , Barnes, J. W. , and Howell, J. R. , 2006, “ Metaheuristic Optimization of a Discrete Array of Radiant Heaters,” ASME J. Heat Transfer, 128(10), pp. 1031–1040. [CrossRef]
Bertsimas, D. , and Tsitsiklis, J. , 1993, “ Simulated Annealing,” Stat. Sci., 8(1), pp. 10–15. [CrossRef]
Laaksonen, K. , Li, S.-Y. , Puisto, S. R. , Rostedt, N. K. J. , Ala-Nissila, T. , Granqvist, C. G. , Nieminen, R. M. , and Niklasson, G. A. , 2014, “ Nanoparticles of TiO2 and VO2 in Dielectric Media: Conditions for Low Optical Scattering, and Comparison Between Effective Medium and Four-Flux Theories,” Sol. Energy Mater. Sol. Cells, 130, pp. 132–137. [CrossRef]


Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

Sketch of the spectrally selective coating on a substrate

Grahic Jump Location
Fig. 3

Spectral reflectance for different regimes of UM

Grahic Jump Location
Fig. 4

Spectral reflectance versus wavelength for validation and verification studies

Grahic Jump Location
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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

Variation of collection efficiency with thickness

Grahic Jump Location
Fig. 9

Variation of collection efficiency with radius

Grahic Jump Location
Fig. 10

Variation of collection efficiency with volume fraction




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In