Optimization of pigmented coatings for concentrating solar thermal applications

Abstract

Spectrally selective coatings are used in absorbers of solar collectors to maximize efficiency of solar thermal energy systems. Desired coating should have high absorptance at solar wavelengths and low emittance at the wavelengths where absorber emits heat. This study focuses on pigmented coatings that consist of a binder and uniformly distributed nano-particles known as pigments that exhibit the desired spectrally selective behavior. Radiative behavior of coatings depends on coating thickness, pigment size, concentration, and the optical properties of binder and pigment materials. In order to understand the effect of these parameters, a unified radiative model of the pigmented coatings is developed, Lorentz-Mie theory in conjunction with Hartel theory to incorporate the multiple scattering effects is used to predict radiation properties for independent scattering, T-Matrix method is used to incorporate the dependent scattering and effective medium theory is used to handle cases with very small pigments. Through the solution of the radiative transfer equation by the four flux method, spectral reflectance is predicted. Design of such a coating is formulated as an inverse problem of estimating design variables such as pigment size, concentration and material to yield the desired spectral emittance of the ideal coating. The nonlinear problem is solved by optimization applying two methods; the Quasi Newton method and Nelder Mead simplex algorithm. While both algorithms are capable of providing the same solution, the convergence of Quasi Newton method is found to be superior to that of Nelder Mead simplex algorithm.