Radiation absorption by a particle curtain formed in a solar free falling particle receiver is investigated using a Eulerian-Eulerian granular two-phase model to solve the two-dimensional mass and momentum equations (CFD). The radiative transfer equation is subsequently solved by the Monte-Carlo (MC) ray-tracing technique using the CFD results to quantify the radiation intensity through the particle curtain. The CFD and MC results provide reliable opacity predictions and are validated with the experimental results available in literature. The particle curtain was found to absorb the solar radiation efficiently for smaller particles at high flowrates due to higher particle volume fraction and increased radiation extinction. However, at low mass-flowrates the absorption efficiency decreases for small and large particles.

A thermotropic material is modeled as an absorbing, thin slab containing anisotropic scattering, monodisperse, spherical particles. Monte Carlo ray tracing is used to solve the governing equation of radiative transfer. Predicted results are validated by comparison to the measured normal-hemispherical reflectance and transmittance of samples with various volume fraction and relative index of refraction. A parametric study elucidates the effects of particle size parameter, scattering albedo, and optical thickness on the normal-hemispherical transmittance, reflectance, and absorptance. The results are interpreted for a thermotropic material used for overheat protection of a polymer solar absorber. For the preferred particle size parameter of 2, the optical thickness should be less than 0.3 to ensure high transmittance in the clear state. To significantly reduce the transmittance and increase the reflectance in the translucent state, the optical thickness should be greater than 2.5 and the scattering albedo should be greater than 0.995. For optical thickness greater than 5, the reflectance is asymptotic and any further reduction in transmittance is through increased absorptance. A case study is used to illustrate how the parametric study can be used to guide the design of thermotropic materials. Low molecular weighted polyethylene in poly(methyl methacrylate) is identified as a potential thermotropic material. For this material and a particle radius of 200 nm, it is determined that the volume fraction and thickness should equal 10% and 1 mm, respectively.

In this paper, radiative characterization of a packed bed of novel three-dimensionally ordered macroporous (3DOM) ceria particles is performed in the spectral range relevant to solar thermochemical processes, 0.35–2.2μm. Normal–hemispherical transmittance and reflectance of three samples of various thicknesses are measured. Monte Carlo ray-tracing and discrete ordinate methods are employed to identify transport scattering albedo and transport extinction coefficient in the spectral range corresponding to weak absorption in the semi-transparency band of ceria. 3DOM ceria particles are characterized by weaker scattering in comparison to sintered ceria ceramics, and increased transparency in the near-infrared spectral range 0.7–2 μm. The ordered pore-morphology of the 3DOM ceria after thermochemical redox cycling between temperatures 1373 K and 1073 K is altered due to sintering of walls of the 3DOM structure. The absorption coefficient of the packed bed is found to be practically independent of morphology. Radiative characterization of 3DOM ceria ceramics before and after thermochemical cycling suggests that preserving the 3DOM structure can lead to scattering characteristics that permit longer attenuation path lengths of incident concentrated solar radiation in the material, as well as be favorable for confinement of the near-infrared radiation during thermochemical cycling leading to favorable thermochemical conditions for fuel production.

Methanol reforming to produce hydrogen is an excellent way to provide fuel for hydrogen-based fuel cells. Since methanol reforming is an endothermic process, requiring an energy input, it is possible to use this reaction as a way to store primary energy. In this paper, we propose that this reaction can be driven with a new type of solar collector which has high overall efficiency. The advantage of the proposed design is that it can achieve high temperatures (up to 250°C) without tracking thus reducing capital and running costs. A CPC (compound parabolic concentrator) collector was designed with a half angle of 27.4 degrees and a concentration ratio between 1.5–1.75 over the entire cone angle. Furthermore, due to the small size of the designed type of collector, it would be easy to manually orient it so that the axis is aligned east-west, which would allow it to concentrate all day. The fabricated collector shown later in this paper has the advantage of being portable with a thickness of just 70mm. In this design, we use a vacuum layer between the receiver and the frame to minimize the convective heat loss and to allow for thermal concentration. Selective surfaces, such as TiNO x , are employed in the receiver to absorb solar (short wavelength) radiation while minimizing emission of thermal (long wavelength) radiation. An optical analysis via ray tracing shows an optical efficiency of 80% to 85% in the range of half incident angle. Also, a prototype of the designed CPC collector is manufactured and shown in this paper.

There exists a general need to compare radiative fluxes from experimental radiometers with fluxes computed in Thermal/Fluid simulations. Unfortunately, typical numerical simulation suites lack the ability to predict fluxes to objects with small view angles thus preventing validation of simulation results. A new model has been developed that allows users to specify arbitrary view angles, orientations, and locations of multiple radiometers, and receive as the output, high-accuracy radiative fluxes to these radiometers. This virtual radiometer model incorporates a reverse monte-carlo ray tracing algorithm adapted to meet these user specifications and runs on both unstructured and structured meshes. Verification testing of the model demonstrated the expected order of convergence. Validation testing showed good agreement between calculated fluxes from the model and measured fluxes from radiometers used in propellant fires. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DEAC0494AL85000.

The M-1 radiation model is a thermal radiation transport model that is derived from a maximum entropy approximation to the radiative transport equation. It involves the solution of four hyperbolic equations for conservation of radiative energy. The M-1 model has similarities to the classical diffusion approximations (like P-1), but is able to better predict directed flux. Consequently, shadowing and long-range transport can be well resolved for a fraction of the cost of methods with exponentially increasing accuracy costs like the method of discrete ordinates and Monte Carlo ray-tracing. The M-1 method is mostly used historically in astronomical radiation transport, but has recently been shown to work for combustion applications of smaller scale. Past work has shown it to give good comparisons to fire problems with length scales of interest. Because of the potential for the model to predict radiation transport more cost-effectively, it is being examined for implementation as an option in our fire codes. We present the theory behind the model. The Eddington factor is used to partition directed and diffuse radiation. It is normally modeled since it is derived from a transcendental functional relationship. We analyze Eddington factor models presented in previous work, and present a new model that we show to be superior in most ways to all the previously presented models. Some 1-dimensional calculations are also shown that illustrate the potential accuracy and challenges with implementing the M-1 model. Such challenges include the specification of boundary conditions and the development of robust solver methods.

In the area of micro- and nano-scale radiation heat transfer, the radiant characteristics of rough surfaces have drawn increasing attention. In this paper, three-dimensional Gaussian random rough surfaces were created by the Monte Carlo simulation method. Ray tracing method combined with the Kirchhoff approximation was employed to analyze the shadowing effect of random surfaces with different roughness. The relative scattering intensity from rough surfaces was further investigated by the Fresnel law. The results indicated that the peak of the relative scattering intensity occurred at the anti-scattering angle and the scattering distributions were continuous. With increasing surface roughness, the height of the peak became lower, the width of distribution became wider, and the distribution range of the scattering angle and the azimuth of the reflection electromagnetic waves increased. Furthermore, the relative scattering intensity concentrated in the vicinity of the anti-scattering angle and the largest scattering intensity occurred in the specular direction. Taking into account of the effects of polarization state and wavelength of incidence waves, it was shown that the relative scattering intensity of s polarized incident wave was slightly larger than that of p polarization, while the relative scattering intensity became stronger as the wavelength increased.

In this work is described a hybrid numerical code aiming to retrieve the thermal radiative properties of opaque heterogeneous coatings. The code is based on the combination of a Monte Carlo Ray Tracing (MCRT) program and of the use of the Effective Medium Approximation (EMA). This hybrid code is able to takes account for the surface roughness, the internal porosity and the chemical composition of a given layer. The solid part of a coating is composed of a conducting oxide which contents excess oxygen (δ ∼ 0.1–0.2). Due to δ and to their thicknesses (> 2 μm), the coatings are opaque for the spectral range going from the far infrared range to the visible range. For each layers, their normal spectral emissivity have been measured by infrared spectrometry ( T ∼1000K). The comparison of the numerical spectra to the experimental ones permits the discussion of the effects of both the surface roughness, and the internal porosity on the emissivity spectra.

A two-dimensional axisymmetric ray tracing photon Monte Carlo radiative transfer solver is developed. Like all ray tracing Monte Carlo codes, the ray tracing is performed in 3-D, however, arrangements are made to take advantage of the 2-D nature of the problem, to minimize computational time. The solver is designed to be integrated into finite volume hypersonic flow solvers, and is able to resolve the complex spectral properties of such flows to line-by-line accuracy. The solver is then directly integrated into DPLR, a hypersonic flow solver, and closely coupled calculations are performed.

A combined method of Reverse Monte-Carlo Ray-tracing (RMCRT) with Full-Spectrum k-distribution (FSK) for computing the radiative heat transfer is applied to an extreme non-homogeneous case (both temperature and gas mixture composition vary with positions) with absorbing, emitting media. Parameter Studies of the scaled FSK (FSSK) and correlated FSK (FSCK) methods for the case, such as g point resolution, mesh resolution, reference states and integration quadratures, are carried out. The results from the FSSK and FSCK are only affected by the chosen reference states, and are not sensitive to other parameters.

In this paper, efficient spectral modules and random number databases are developed for atomic and diatomic species for use in photon Monte Carlo (PMC) modeling of hypersonic nonequilibrium flow radiation. To model nonequilibrium flow conditions, the quasi steady state (QSS) assumption was used to generate electronic state populations of atomic and diatomic gas species in the databases. For atomic species (N and O), both bound-bound transitions and continuum radiation were included, and were separately databased as a function of electron temperature and number density as well as the ratio of atomic ion to neutral number density. For the radiating diatomic species of N 2 + , N 2 , O 2 , and NO, databases were generated for each electronic molecular electronic system. In each molecular electronic system, the ro-vibrational transition lines were separately databased for each electronic upper state population forming the electronic system. The spectral module for the PMC method was optimized toward computational efficiency for emission calculations, wavelength selections of photon bundles and absorption coefficient calculations in the ray tracing scheme.

The radiative characteristics of packed beds of ZnO particles, applied in the design of high-temperature solar thermochemical reactors, were investigated experimentally. ZnO samples of varying thickness were exposed to a continuous beam of near monochromatic thermal radiation in the 0.5–1 μm wavelength range. The overall transmitted fraction measured as a function of sample thickness s obeys an exponential trend exp(– As ), with the fit parameter A ranging from (4000 ± 100) m −1 at 555 nm to (2100 ± 100) m −1 at 1 μm. In the forward directions, the measured intensity distribution is approximately isotropic, whereas in the backward directions it is well approximated by a Henyey–Greenstein equation with asymmetry factor g ≈ − 0.4 at 555 nm and g ≈ − 0.1 at 1 μm. A Monte Carlo ray-tracing model of the experimental set-up is employed to extract the extinction coefficient and the scattering albedo for the case of non-grey absorbing-scattering medium.

Accurate prediction of radiative heat transfer plays a key role in many high temperature applications, such as combustion devices and fires. Among various simulation methods, the Monte-Carlo Ray-Tracing (MCRT) has the advantage of solving the radiative transfer equation (RTE) for real gas mixtures with almost no approximations; however, it has disadvantage of requiring a large computational effort. The MCRT method can be carried out with either the Forward MCRT or the Reverse MCRT, depending on the direction of ray tracing. The RMCRT method has advantages over the FMCRT method in that it uses less memory, and in a domain decomposition parallelization strategy, it can explicitly obtain solutions for the domain of interest without the need for the solution on the entire domain.

Beam guiding effects during laser drilling due to multiple specular reflections inside the hole are analyzed for the case of very short laser pulses (ns range). Specular reflections are valid for materials that retain a smooth surface during laser evaporation (small optical roughness compared to the laser wavelength). The problem is assumed to be 2D axisymmetric (unpolarized laser), with the hole geometry denned by nodal values connected through a cubic spline. The net radiative flux onto a surface node is determined through ray tracing methods. The resulting absorbed laser flux is combined with a simple quasi-one-dimensional conduction model (to assess the minor conduction losses) and an Arrhenius evaporation rate model, to predict hole development as a function of time through iteration. To stabilize this highly nonlinear and thus unstable problem (in numerical analysis as well as in experiments) the laser beam is diffused a small amount from the specular direction (to also account for the limitation that no beam can be focused down to a point), and by periodic slight smoothing of the irradiation levels. Results show that drilling rates are increased dramatically due to beam trapping for highly reflective materials, resulting in a more pointed hole profile.