Radiative properties of ordered and disordered porous ceria particle clouds under solar irradiation

Abstract

We study the radiative behavior of particle clouds consisting of two types of highly porous spherical ceria particles under direct solar irradiation—one with a templated three-dimensionally ordered macroporous (3DOM) structure and the other with pores randomly located within the structure. Individual radiative properties—the scattering efficiency factor, absorption efficiency factor, and the scattering phase function—of the randomly porous particles are numerically predicted in this work for comparison against existing 3DOM data. Clouds of monodisperse particles with a spatially uniform particle density are studied for each case. Solutions are compared to results based on individual particle scattering properties obtained from an effective medium theory combined with Mie theory results. It is found that the high degree of order in 3DOM particles does not significantly change the radiative properties of the cloud. However *something interesting*.

The emerging field of high-temperature solar thermochemistry holds tremendous promise to disrupt the conventional paths of producing fuels, energy-intensive commodity materials and generating dispatchable power. Direct solar irradiation is concentrated by mirrors, captured by a receiver, converted into high-temperature process heat, often exceeding \(\mathrm{1000K}\), and used to drive highly-endothermic processes for production of chemical fuels and materials including synthesis gas, carbon black, ammonia, lime, and metals (Bader in print)(Fletcher 2001)(Steinfeld 2003)(Kodama 2003). Production of the components of synthesis gas, \(\mathrm{H_{2}}\) and \(\mathrm{CO}\), can be achieved in a single thermal dissociation step (thermolysis) followed by a high-temperature gas separation. However, the excessively high temperatures required for such chemistry pose serious limitations for practical implementation. For example, the thermolysis of \(\mathrm{H_{2}O}\) and \(\mathrm{CO_{2}}\) require temperatures exceeding \(\mathrm{2500K}\) in order to obtain significant \(\mathrm{H_{2}}\) and \(\mathrm{CO}\) concentrations, respectively (Bader in print). Alternatively, thermochemical redox cycles can be employed, in which active materials undergo cyclic reduction and oxidation (redox) reactions, with the net effect of splitting \(\mathrm{H_{2}O}\) and \(\mathrm{CO_{2}}\). In addition to lowering process temperatures, the added process steps can be leveraged to eliminate energetically expensive gas-phase separation requirements. High-temperature solar thermochemical reactors are designed for maximum solar-to-chemical energy conversion efficiency, to minimise the required size of the optical concentrators, and thus to improve the economic viability of the process (Palumbo 2004). The rapid and efficient transfer of energy from a concentrated solar source to the redox material—i.e. the transfer of energy from photons to chemical bonds—is therefore a critical research aspect for efficient reactor design. To this end, we study here the performance of a class of porous particles of cerium dioxide redox materials under highly-concentrated, direct solar irradiation. We believe these materials to hold promise for efficient energy transfer for a number of reasons we outline here. More specifically, we will answer the questions: ”Why particles?”, ”Why ceria?”, and ”Why porous?” while outlining the relevant literature in the process.

Unlike bulk materials, particles can have an absorption efficiency (potentially much) greater than unity. Note that this may seem impossible given the fact that absorption efficiency must be equal to emissivity by Kirchoff’s law and that a blackbody—the perfect emitter—cannot have an emissivity greater than one. However, the idea of a perfect blackbody is restricted to surfaces with low curvature. Both Planck and Kirchoff were clear on this when deriving their famous laws (Bohren 1998). Thus, for a material to absorb very well relative to its size—the trait needed to achieve high energy densities within a particle with relatively little input—we look at materials with features on the scale of the wavelength of light. Perhaps the simplest conceivable geometry is the sphere as we consider here.

Ceria has received significant attention as a redox material because of its relatively fast reaction rates and ability to remain in a solid state throughout the redox process which relieves previous problems associated with ferrite-based oxides and volatile metal oxides such as \(\mathrm{ZnO}\) and \(\mathrm{SnO_{2}}\) (Chueh 2010) (Chueh 2010a). The demonstrated ability of ceria to be used as a redox active material and the availability of relevant data make it a very strong candidate to be optimized for high-efficiency thermochemical cycling. The spectral optical properties of ceria are well-known (Patsalas 2002) at room temperature in its stoichiometric form and the thermodynamic properties of non-stoichometric ceria are available allowing detailed modeling in pursuit of this goal. Indeed, researchers have already begun to explore the potential for ceria-particle-based solar thermochemical reactor designs using numerical modeling (Scheffe 2014) (Oles 2015) (Bader 2014a).

Porous materials offer numerous benefits over solid materials for such radiation-driven thermochemistry applications including higher surface to volume ratio and smaller diffusion distances for reactive species. Bulk 3DOM ceria structures have been previously studied reavealing faster reactions (Venstrom 2012) as well as better structural stability (Petkovich 2011) in comparison with sintered ceria structures. In the form of particles, porous materials offer the additional benefit of lower density leading to lower necessary carrier velocities when fluidized allowing for more flexible control of residence time within the reduction and oxidation zones. We are not aware of any full reactor numerical or experimental studies based on such materials. Radiative characterization of individual 3DOM ceria particles were considered in our previous work. The initial study suggests that particles made up of highly porous ceria have a higher absorption efficiency per volume, which should lead to faster heating and higher chemical conversion efficiency (Wheeler 2014). In a follow-up study a degree of radiative property tunability was shown to be attainable by varying the internal pore structure as well as the overall particle size (Randrianalisoa 2014). Larger pores were shown to lead to broadening and decay of the absorption efficiency factor peak, redshifting and decay of the scattering efficiency factor peak, and a trend away from isotropic scattering. Increases in particle size leads to similar effects (Randrianalisoa 2014). Since ceria naturally absorbs well only in the ultraviolet region, any redshifting of of absorption peaks should lead to significant improvements in solar-weighted absorption. A scattering peak near the maximum of the solar spectrum is highly desirable to reduce the concentration ratios of the direct irradiation needed to drive high-temperature redox processes. The importance of the ordered nature of 3DOM particles to scattering properties is unknown.

The work we present here is divided in two parts. First we study the effect of pore and particle size on scattering properties of highly porous (\(\approx 85\%\)) ceria particles with a random pore structure in the spectral range \(\mathrm{0.29-10\mu m}\) using electromagnetic theory. These results are then used to study the behavior of clouds of such particles under the single scattering approximation in the geometrical optics limit. Radiative properties of the cloud is compared against clouds of previously characterized ceria particles with the same porosity but a highly ordered pore structure. An effective medium theory along with Lorenz–Mie theory is used as an inexpensive alternative to the full electromagnetic characterization. Particle densities considered correspond to estimates of the densities achievable in the pneumatic transport regime of fluidization according to a well-known correlation.

**In this paper, we highlight the dramatic effect such tunability can have on the macroscopic behavior of a cloud of such particles undergoing thermal reduction.**

*On the construction of porous geometry*

For all particles we utilize the experimentally-determined complex index of refraction by Patsalas et. al. (Patsalas 2002).

*on the DDA* The discrete dipole approximation (DDA) was used to solve Maxwell’s equations. Details of the numerical method are summarized in (Randrianalisoa 2014) as well as in the review by Draine and Flatau (Draine 1994)

*on the chosen dipole spacing and numerical validation*

A summary of the simulation parameters can be found in Table \ref{tab:DDA_summary}

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1 | 2 | 3 | 4 | 5 |

We calculate the radiative properties of clouds made up of monodisperse, cold, uniformly distributed particles of three different types. Representations and descriptions of the three particle types can be found in Figure \ref{fig:problem_setup}(a)-(b). The radiative transfer equation (RTE) has been solved in one dimension using the Monte Carlo method to recover the cloud reflectivity, absorbtivity, and spatially dependent divergence of the radiative flux. Using the notation of (Modest 2013) the RTE is given by,

\begin{equation} I\\ \end{equation}The computational domain is represented in \ref{fig:problem_setup}(d). On the left-hand side, radiative flux is incident on the computational domain with incoming angles between -15 and 15 degrees and a spectral distribution corresponding to the emission from Xenon arc lamps. This situation was chosen to match the irradiance of the inner lamps of the recently constructed solar simulator described in (Bader 2014), (Levêque in press) resulting in a uniform power input of \(\approx 1000\) suns; future experimental studies are anticipated with this physical setup.

Cloud scattering calculations were validated a

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