Monte Carlo Ray Tracing Program Research Articles

Design and optimization of transparent scattering solar concentrator based on SiO<sub>2</sub> aerogel

Scattering solar concentrators (SSCs), an important component of transparent/translucent photovoltaic devices, can concentrate large-area sunlight on small-area solar cells while allowing some sunlight to pass through the devices. However, owing to the lack of suitable scattering materials, there have been few reports on SSCs in recent years. In this study, we fabricated SiO<sub>2</sub> aerogel-based SSCs and tested their performances. The photoelectric performance was found to be moderate. Additionally, the results demonstrated excellent transmittance and color rendering index, which meet the lighting requirements of the windows. A Monte Carlo ray tracing program was developed to simulate an SSC and analyze the fate of all photons. We also analyzed the multiple scattering mechanism in SSCs that damages the photoelectric efficiency of a device via theoretical simulation. Finally, we proposed an anisotropic scattering device that can increase the primary scattering and suppress multiple scattering, resulting in excellent photoelectric efficiency.

Light scattering in a spatially-correlated particle field: Role of the radial distribution function

Radiative transfer through particle-laden media such as clouds can be impacted by variations in particle spatial distributions. Due to mixing and inertial effects of droplets suspended in the almost always turbulent atmosphere, cloud particles are often spatially-correlated. The correlations result in clusters and voids within the droplet field that, even when smaller than the photon mean free path, can lead to deviations from the exponential extinction law. Prior work has numerically investigated these departures from exponential attenuation in absorptive media; this work extends those results for a scattering medium. The problem is explored with a Monte Carlo Ray Tracing (MCRT) program capable of tracking light attenuation through both perfectly random (uncorrelated) and spatially correlated collections of scatterers and/or absorbers. The MCRT program is favorably compared to two-stream flux equations, and numerical exploration of the pure-absorption case is used to determine the sampling statistics necessary to characterize radiative transmission within the numerical simulation. Light transmission through fields of spatially-correlated, non-absorbing, scattering particles is explored. Particles are distributed following a Matérn Point Process, which allows cluster strength and size, as well as the usual variables of particle scattering cross section and number density to be varied. The results show that the degree of non-exponential attenuation is determined by the magnitude and shape of the radial distribution function, which describes correlations in discrete (non-continuous) particle distributions. Parametric studies revealed that the number of clusters and cluster radius, factors in the Matérn radial distribution function, impact direct, diffuse and backward radiative transfer. The Matérn RDF is shown to be consistent with a previous “cloudlet” approach, providing a bridge between the analytical cloudlet model and continuous correlation function approaches.

Comparative study of the optical and economic performance of etendue-conserving compact linear Fresnel reflector concepts

This paper presents a comparative performance investigation of three Compact linear Fresnel collectors; a flat collector, a sun-tracking etendue-conserving collector and an off-peak etendue-conserving collector. A Monte Carlo ray tracing program is used to simulate the fields. The resultant incident radiation on the receiver aperture is used to quantify the geometric intercept factor and optical efficiency of the field. Each field is then optimised for mirror width and the ratio between the mirrors targeting each receiver aperture. The three fields are then compared on the basis of performance. The off-peak etendue-conserving compact linear Fresnel field reaches a peak geometric intercept factor of 92%, while the sun-tracking etendue-conserving field and flat field had a peak geometric intercept factor of 83% and 79% respectively. A maximum total plant cost for the same Levelized Electricity Cost is presented to incorporate a cost comparison.

Faceted structure: a design for desired illumination and manufacture using 3D printing

A new optical component of transmissive faceted structure that allows the reshaping of collimated white light beam is depicted and realized. After being illuminated, each facet element in the structure can slightly tilt along its own axes to deflect the incident light. The calculation of the tilt angles is made by a numerical approach, which is the inverse solution of the analytical relationships between the two-dimensional tilt angles of the facet element and the local coordinates of the outgoing ray on the target plan. For a predefined illumination pattern on a fixed screen, the numerical computation of the 2D tilt angle matrix of the faceted structure is described. In the meantime, a Monte Carlo ray tracing program is created to calculate and verify the irradiance map, all compared with well-recognized commercial illumination software programs. Afterwards, the component is fabricated using an innovative additive technology, inspired by 3D printing and proposed by Luximprint.

Effect of the collector geometry in the concentrating photovoltaic thermal solar cell performance

The aim of this work is the redesign of the reflector geometry in hybrid concentrating collectors that are currently manufactured by SOLARUS Sunpower AB** to improve the energy efficiency of their solar collectors. The analysis is first accomplished using a numerical model that uses geometrical optics to study the interaction between the sunlight and a concentrating collector along the year. More complex physical models based on open-source and advanced object-oriented Monte Carlo ray tracing programs (SolTrace, Tonatiuh) have been used to study the relation between the collector annual performance and its geometry. On an annual performance basis, a comparative analysis between several solar collector geometries was effectuated to search for higher efficiencies but with controlled costs. Results show that efficiency is deeply influenced by reflector geometry details, collector tilt and location (latitude, longitude) of the solar panel installation and, mostly, by costumer demands. Undoubtedly, the methodology presented in this paper for the design of the solar collector represents an important tool to optimize the binomial cost/effectiveness photovoltaic performance in the energy conversion process. The results also indicate that some modified concentrating solar collectors are promising when evaluating the yearly averaged energy produced per unit area, leading to evident improvements in the performance when compared to the current standard solar concentrating SOLARUS systems. Increases of about 50% (from 0.123 kW/m2 to 0.1832 kW/m2) were obtained for the yearly average collected power per reflector area when decreasing the collector height in 3.5% (from 143 mm to 138 mm).

Theoretical simulation and analysis of large size BMP-LSC by 3D Monte Carlo ray tracing model**Project supported by the National Natural Science Foundation of China (Grant No. U1632273) and the Chinese Universities Scientific Fund (Grant No. CX3430000001).

Luminescent solar concentrators (LSC) can reduce the area of solar cells by collecting light from a large area and concentrating the captured light onto relatively small area photovoltaic (PV) cells, and thereby reducing the cost of PV electricity generation. LSCs with bottom-facing cells (BMP-LSC) can collect both direct light and indirect light, so further improving the efficiency of the PV cells. However, it is hard to analyze the effect of each parameter by experiment because there are too many parameters involved in the BMP-LSC. In this paper, all the physical processes of the light transmission and collection in the BMP-LSC were analyzed. A three-dimensional Monte Carlo ray tracing program was developed to study the transmission of photons in the LSC. A larger-size LSC was simulated, and the effects of dye concentration, the LSC thickness, the cell area, and the cell distance were systematically analyzed.

Spectral reflectance, transmittance, and angular scattering of materials for solar concentrators

The narrow-angle spectral specular reflectance and angular scattering of conventional and novel reflective materials for solar concentrators are measured over the wavelength range 300–2500nm at incidence angles ranging from 15° to 60° using a spectroscopic goniometry system. The solar-weighted specular reflectance at near normal incidence and an acceptance half-angle of 17.5mrad is 0.941 for back-silvered glass, 0.908–0.926 for silvered polymer films, 0.895 for aluminized polyester film, 0.939–0.954 for silvered aluminum sheets, and 0.860 for aluminized aluminum sheet. The angular scattering, quantified in terms of the standard deviation of a Gaussian distribution, is found to be negligible for aluminized polyester (<0.05mrad) and back-silvered glass (<0.07mrad), and noticeable for silvered polymer films (0.27–1.12mrad) and silvered aluminum sheets (0.12–1.66mrad). In addition, the spectral transmittance of semi-transparent materials suitable for protective covers is measured, yielding solar-weighted normal transmittance values of 0.913 and 0.946 for 100μm thin films of ETFE (ethylene-tetrafluoroethylene) and FEP (fluorinated ethylene propylene), respectively. The measured optical properties are incorporated in a Monte Carlo ray-tracing program and applied to analyze the optical performance of solar concentrators.

Analyzing luminescent solar concentrators with front-facing photovoltaic cells using weighted Monte Carlo ray tracing

Luminescent solar concentrators (LSC) collect ambient light from a broad range of angles and concentrate the captured light onto photovoltaic (PV) cells. LSCs with front-facing cells collect direct and indirect sunlight ensuring a gain factor greater than one. The flexible placement and percentage coverage of PV cells on the LSC panel allow for layout adjustments to be made in order to balance re-absorption losses and the level of light concentration desired. A weighted Monte Carlo ray tracing program was developed to study the transport of photons and loss mechanisms in the LSC to aid in design optimization. The program imports measured absorption/emission spectra of an organic luminescent dye (LR305), the transmission coefficient, and refractive index of acrylic as parameters that describe the system. Simulations suggest that for LR305, 8–10 cm of luminescent material surrounding the PV cell yields the highest increase in power gain per unit area of LSC added, thereby determining the ideal spacing between PV cells in the panel. For rectangular PV cells, results indicate that for each centimeter of PV cell width, an additional increase of 0.15 mm to the waveguide thickness is required to efficiently transport photon collected by the LSC to the PV cell with minimal loss.

Inverse identification of intensity distributions from multiple flux maps in concentrating solar applications

Radiative flux measurements at the focal plane of solar concentrators are typically performed using digital cameras in conjunction with Lambertian targets. To accurately predict flux distributions on arbitrary receiver geometries directional information about the radiation is required. Currently, the directional characteristics of solar concentrating systems are predicted via ray tracing simulations. No direct experimental technique to determine intensities of concentrating solar systems is available. In the current paper, multiple parallel flux measurements at varying distances from the focal plane together with a linear inverse method and Tikhonov regularization are used to identify the directional and spatial intensity distribution at the solution plane. The directional binning feature of an in-house Monte Carlo ray tracing program is used to provide a reference solution. The method has been successfully applied to two-dimensional concentrators, namely parabolic troughs and elliptical troughs using forward Monte Carlo ray tracing simulations that provide the flux maps as well as consistent, associated intensity distribution for validation. In the two-dimensional case, intensity distributions obtained from the inverse method approach the Monte Carlo forward solution. In contrast, the method has not been successful for three dimensional and circular symmetric concentrator geometries.

PoDFluX: A new Monte Carlo ray-tracing model for powder diffraction and fluorescence

PoDFluX is a new Monte Carlo ray-tracing program that simulates from first principles x-ray powder diffraction from crystalline materials and x-ray fluorescence from materials with a defined elemental composition. This model has been written primarily for the optimization of miniaturized planetary x-ray diffraction instrumentation but wider applications are certainly possible. A particular strength of the model is the implementation of several variance-reduction techniques for the minimization of execution times. Comparisons of model output with experimental diffraction and fluorescence data show good quantitative agreement.

Temperature effect (300–1500 K) on the infrared photon transport inside an X-ray microtomographic reconstructed porous silica glass

A Monte Carlo Ray Tracing program has been developed to predict the thermal radiative properties of an X-ray microtomographic reconstructed silica glass containing gas bubbles, for a large domain of wavelength (1–25 μm) and for a large domain of temperature (300–1500 K). The main input of the program is the complex optical index of the corresponding homogeneous silica glass. Validity of the model is checked by comparing a simulated normal spectral emittance, obtained on the reconstructed glass, with the experimental one recorded at T = 1300 K .

Monte Carlo ray-tracing error analysis of a sagittal-focusing optical system as applied to synchrotron radiation

A Monte Carlo ray-tracing program was developed to analyze the geometrical defects and alignment errors on the shape of the x-ray beam image and focusing efficiency of a conical sagittal-focusing monochromator. The geometrical defects and alignment errors were represented with measurable and controllable parameters so that their effects can be analyzed quantitatively. The programmed analysis can be used as a guide to find the precision needed for an optimal sagittal-focusing optical system in terms of flux and focus for large horizontal divergences.

Flux Density Distribution in the Focal Region of a Solar Concentrator System

In high temperature solar energy applications highly concentrating optical systems, such as, e.g., parabolic dishes, achieve typical radiation flux densities &gt;2 MW/m2. In order to investigate thermo and photochemical reactions at temperatures &gt;1500 K and radiation flux densities &gt;2 MW/m2 a solar furnace was built at Paul Scherrer Institute (PSI). This furnace is a two-stage concentrator. The first stage is a prefocusing glass heliostat with a focal length of 100 m. The second stage is a highly concentrating parabolic dish with a focal length of 1.93 m. To design experiments to be carried out in the focal region of the parabolic dish, the radiation flux as well as its density distribution have to be known. This distribution is usually measured by radiometric methods. However, these methods are generally rather troublesome because of the high temperatures involved. In this paper we present a simple method to estimate the characteristic features of the radiation flux density distribution in the focal region of a concentrator system. It is well known from solar eclipses that the mean angular diameter of the moon is almost equal to that of the sun (9.1 mrad versus 9.3 mrad). Hence, the lunar disk is well suited to be used as a light source to investigate the flux distribution in a solar furnace. Compared to the sun the flux density is reduced by 4·105 and the flux density distribution can be inspected on a sheet of paper located in the plane of interest, e.g., the focal plane. This distribution was photographed and analyzed by means of an image processing system. The density distribution was also simulated using a Monte Carlo ray tracing program. Based on this comparison, and on further ray tracing computations, we show that the peak flux density decreases from 8.9 MW/m2 in December to values below 4 MW/m2 in June and the net radiation flux from 25 kW to 15 kW, respectively.

An internal cusp reflector for an evacuated tubular heat pipe solar thermal collector

This study involves the optical analysis of a slightly concentrating, symmetric cusp reflector inside a tubular glass envelope with a cylindrical heat pipe as the solar absorber. The basic design features of this non-tracking, evacuated, modular collector and the principles of heat removal are shown in Figs. 1 and 2. Differential equations of the cusp reflector optics, given the geometrical restrictions in Figs. 1 and 2, are derived, and solutions for the largest possible aperture inside a given diameter envelope and acceptance angle are presented. As an extension of the same study, the optical efficiency of a single collector tube has been simulated by means of a Monte Carlo Ray-Tracing Program. For a concentration ratio of 1.15, the flux distribution around the heat pipe is computed as a function of incidence angle. In addition, the impact of mirror defects and absorber misalignment on the optical performance are analyzed.