Monte Carlo Ray-tracing Code Research Articles

Performance predictions of the SPARC x-ray crystal spectrometers for ion temperature and toroidal rotation measurements.

SPARC will be outfitted with three systems of x-ray crystal spectrometer arrays. Two of these are designed using cylindrically bent crystals to achieve high spectral-resolution for ion temperature and toroidal velocity measurements via imaging He-like Kr and Ne-like Xe. The last acts as a spectral survey system to monitor Ne-like W and nearby H- and He-like emission from Cr, Fe, Co, Ni, and Cu. Line radiation intensities are calculated using the Flexible Atomic Code for atomic data and ColRadPy for collisional-radiative modeling, then convoluted with a Voigt line shape. Free-free, free-bound, and two-photon continuum radiation is also included. The ToFu code is used to perform volume-of-sight integration to produce synthetic detector images. In addition, presented is cross-validation performed using the XICSRT Monte Carlo ray-tracing code. Ion temperature and toroidal velocity profiles are reconstructed using ToFu via tomographic inversion.

Identification of the spectral complex refractive index of pure silica micrometric fibers versus temperature

A new methodology was developed to identify the spectral complex refractive index of semi-transparent solid phases within heterogeneous media up to high temperatures. In this methodology, numerical samples are first generated from statistical information about the microstructure of a given material obtained by X-ray micro-tomography. The radiative properties of these numerical samples (reflectance, transmittance, and emittance) are then simulated with a Geometric Monte Carlo Ray Tracing code while the radiative properties of the real material are measured by Fourier Transform Infrared spectroscopy. The spectral complex refractive index is then extracted thanks to an optimization algorithm, by minimizing the discrepancies between the experimental and numerical radiative properties. This methodology was applied to a fibrous sample made of pure silica. The complex index was extracted at 295 K and 1010 K. In both cases, it enabled a good prediction of the radiative properties of the material and proved the relevance of performing calculations with characteristics identified at the local scale instead of the bulk ones.

Beam radiation penetration in particle beds for heat transfer modeling of a centrifugal solar particle receiver

This article describes a study of beam radiation striking particle beds of randomly packed, spherical particles. The current study is focused on concentrating solar power receivers which use solid particles as a heat transfer medium, but results are applicable to particle beds in various industries. The analyses are carried out using a purpose-built open-source Monte Carlo Ray Tracing code for beam radiation striking a group of particles. Particle beds with a uniform solid fraction and diffuse reflections are studied first, with the total bed absorptivity found for various combinations of the incidence angle, absorptivity, and solid fraction, culminating in an expression for the total bed absorptivity as a function of these independent variables. In addition, the transmitted fraction of incident rays as a function of distance into the bed is given in table format for many sets of these parameters. These results form the foundation of an algorithm developed to estimate the radiation absorption at different depths in the more challenging case where the solid fraction varies as a function of depth in the bed. This is particularly important for the “CentRec” solar receiver, where the solid fraction oscillates due to the thin particle film used in this device (only 4–10 particle diameters thick), as well as the dynamic nature of the particle film. The algorithm is implemented in a Discrete Element Method model for heat transfer in the CentRec receiver, and the algorithm is shown to have a high accuracy with a very low computational cost compared to a full Monte Carlo Ray Tracing simulation.

Solving the infrared reflections contribution by inversion of synthetic diagnostics: First results on WEST

Infrared (IR) diagnostics are used to measure plasma-facing components (PFC) surface temperature in fusion devices. However, the interpretation of such images is complex in all-reflective environments because of unknown emissivity and multiple reflections issues. In order to assess these challenges an iterative inversion method based on a fast photonic model, the radiosity method, has been developed. This method is applied to two different direct models based on different geometries, Sec-Tore and RADIOS, in order to estimate temperatures from experimental-like data simulated with a Monte Carlo ray-tracing code with diffuse reflective surfaces or specularly reflective surfaces. RADIOS allows retrieving temperature on colder targets (lower than 200°C) with errors of 33% and the peak temperatures with errors of 6%.

A tool to minimize the need of Monte Carlo ray tracing code for 3D finite volume modelling of a standard parabolic trough collector receiver under a realistic solar flux profile

AbstractThe energy collection element of a parabolic trough collector includes a selective coated metallic receiver tube inside an evacuated glass tube. Perpendicularly incident sun light on the parabolic trough mirror aperture is concentrated on the receiver tube highly nonuniformly along its circular direction. This solar energy is collected as thermal energy circulating a suitable heat transfer fluid (HTF) through the tube. This conjugate heat transfer phenomenon under nonuniform heat flux boundary condition is computationally studied applying 3D finite volume (FV) modelling technique of computational fluid dynamics coupled with Monte Carlo ray tracing (MCRT) optical data. The MCRT model simulates the actual flux profile around the receiver tube. Apart from a FV model, this coupled study requires expertise in, and access to, a suitable MCRT code. A combination of polynomial correlations and user‐defined function (UDF) is introduced in this article in order to minimize the need of MCRT codes from subsequent FV modelling of the receiver tube of the Luz Solar 2 (LS2) collector. The correlations are developed from a verified 3D MCRT model, which is equivalent to the local irradiation data as a function of receiver circular location. The UDF includes two algorithms: one to develop solar flux profile from the correlations around the receiver, and the other to calculate heat loss from the receiver. Interpreting the UDF into ANSYS Fluent, a 3D FV model of the LS2 receiver is developed and validated with experimental results. The effectiveness of the UDF as an alternative to MCRT code is verified. The FV model is capable to investigate the heat transfer characteristics of the LS2 collector receiver at different solar irradiation level, optical properties of the collector components, glass tube conditions, HTFs, inserts or swirl generators, collector length, and internal diameter of the tube.

A Monte Carlo method to solve for radiative effective thermal conductivity for particle beds of various solid fractions and emissivities

A method is described to find the effective thermal conductivity due to radiation (krad) for groups of particles at packed and less than packed states. Unlike most previous studies, the method does not rely on the assumption of a unit cell or absorption and scattering coefficients to derive krad. In this method, radiation is modeled with a 3D Monte Carlo ray tracing code, steady state particle temperatures are found with a particle-particle heat exchange simulation, and krad is found with a comparison to heat conduction in an isotropic solid of the same geometry. This leads to the dimensionless Exchange Factor (FE), allowing krad to be calculated at any temperature and particle radius. The key result is a model for FE over the entire range of emissivities from 0.3 to 1 and solid fractions from 0.25 to the fully packed state of 0.64. FE results are compared to previous models, with agreement shown in some cases but a large disagreement found for low solid fractions. The krad results are combined with the Zehner and Schlünder model for solid and fluid conduction, providing an equation for the full effective thermal conductivity.

Numerical Characterization of a High Flux Solar Simulator Using Forward and Inverse Methods

Abstract The numerical characterization of a 10 kWe xenon arc high flux solar simulator is thoroughly presented and performed using two approaches: a forward Monte Carlo ray tracing (MCRT) method and an inverse ray tracing method. Experimental characterization was previously performed for the solar simulator using an indirect flux mapping technique, where the experimental heat flux distribution was obtained at the focal plane and additional 12 planes away from the simulator. For the first numerical characterization method, an in-house MCRT code was used to determine the shape of the xenon arc to best model the simulator. It was determined that an isotropic volumetric source consisting of a hemisphere of 1 mm radius that is attached to a cylinder of 1 mm in radius and 10 mm in length well described the experimental results obtained. The in-house code was then used to generate heat flux maps similar to that obtained experimentally and determine the intensity at the focal plane to be used by the inverse ray tracing method presented for its validation. For the inverse method, intensity interpolation schemes of zeroth and first-order were examined in addition to different solution strategies. It is shown that a first-order interpolation scheme unnecessary complicates the inverse problem, leading to larger errors. In addition, a new approach of constraining the formulated system of equations with an equality constraint that works by eliminating intensity values not tracing back to the ellipsoidal reflector is proposed. This new approach provided intensity values with reduced percentage errors.

Optical features of linear Fresnel collectors with different secondary reflector technologies

This paper is devoted to the analysis of different secondary reflector designs for linear Fresnel collectors. A number of authors have proposed alternative shapes of secondary reflectors in order to enhance the efficiency and the flux intensity at the absorber tube. In this work the primary mirrors layout has been maintained constant for all designs. Thus, only secondary concentrators that do not require a change in the primary mirrors field have been studied. In order to carry out the study a validated Monte Carlo ray trace code has been used, where three optical properties are considered: annual optical efficiency, mean flux intensity and circumferential flux intensity homogeneity. The maximum efficiency reached by each technology, for given optical flux specifications, is obtained. Finally, the optical performance of linear Fresnel collectors with secondary reflector is compared with that of state-of-the-art parabolic trough collectors. It is concluded that the efficiency of Fresnel collectors is around 23% than that of parabolic troughs, although with mean flux intensities around 46% higher and circumferential flux intensities notably more homogeneous (top to bottom flux intensity ratios five times higher).

Design of an innovative linear Fresnel collector by means of optical performance optimization: A comparison with parabolic trough collectors for different latitudes

Different innovative linear Fresnel field designs are obtained for two locations of latitudes 37° N and 24° N. This designs are the result of the exergy efficiency optimization by means of a validated Monte Carlo Ray Trace code and analytic methods. From the results obtained it is concluded that, whereas for high latitude locations East-West orientation achieves higher efficiencies with lower cost, when the solar field is located in latitudes closer to the tropics NS orientation is a better solution. From the performance comparison between Fresnel and trough collectors it results that, although the latter always achieves higher exergy efficiencies, differences are importantly reduced for low latitudes.

A simple expression for the normal spectral emittance of open-cell foams composed of optically thick and smooth struts

A set of 96 open-cell foams with growing porosities (0.35–0.95) and growing pore nominal diameters (0.4–2.6mm) was artificially generated to firmly connect their normal spectral emittances to their textural features. This work is strictly focused on foams that are composed of opaque struts with optically smooth surfaces. To compute the normal spectral emittances, a Monte Carlo Ray Tracing code was carefully used through an indirect method based on Kirchhoff's laws. The Monte Carlo Ray Tracing code considers the complex refractive index of the solid phase constituting the struts foams. Particular attention is therefore paid to performing the calculation with absorption indices (0.5–8) that preserve the opacity of each strut. From a thorough analysis of the ray transport within all the foams, where the Representative Elementary Volumes used for computing the homogenized radiative properties were known beforehand, a general and simple law is established that connects the normal spectral emittance, on the one hand, and the open porosity and the complex index of refraction, on the other hand. In the field of the thermal conversion of solar energy, for example, the new law gives relevant insight on the radiative performance of highly porous foams that are virtually coated with materials that are known for possessing an undeniable spectral selectivity when they are shaped as dense samples.

Tuning the spectral emittance of α-SiC open-cell foams up to 1300 K with their macro porosity

A simple and robust analytical model is used to finely predict the spectral emittance under air up to 1300 K of α-SiC open-cell foams constituted of optically thick struts. The model integrates both the chemical composition and the macro-porosity and is valid only if foams have volumes higher than their Representative Elementary Volumes required for determining their emittance. Infrared emission spectroscopy carried out on a doped silicon carbide single crystal associated to homemade numerical tools based on 3D meshed images (Monte Carlo Ray Tracing code, foam generator) make possible to understand the exact role of the cell network in emittance. Finally, one can tune the spectral emittance of α-SiC foams up to 1300 K by simply changing their porosity.

Secondary Concentrators to Achieve High Flux Radiation With Metal Halide Solar Simulators

This paper presents assessments of the sensitivity of the performance of high flux solar simulators to the key variables of conical secondary concentrators for metal halide lamps, which offer complementary benefits compared with xenon arc lamps. The assessment is performed for both a single-lamp configuration and a seven-lamp array, each lamp close-coupled with its own elliptical reflector, and then aligned with a common conical secondary concentrator. The simulation of heat flux from both the single- and the seven-lamp systems was performed with the Monte Carlo ray-tracing code, which was validated with the experimental results from the single-lamp system. The calculated heat flux at the focal plane agrees with the measured peak flux to within 5% and to within 13% of the measured half width. Calculated results also show that the addition of the secondary concentrator to the single-lamp system can increase the peak flux by 294% and the average flux by up to 93% within a target of 100 mm in diameter, with a corresponding reduction in total power by 15%. The conical secondary concentrator is less effective for a seven-lamp system, increasing the peak and average fluxes by 87.3% and 100%, respectively, within 100 mm diameter focal plane, with a corresponding reduction in total power by 48%. The model was then used to assess the sensitivity of the geometry of the secondary concentrators for both the single- and seven-lamp systems. The results show that the average heat flux is sensitive to the surface reflectance of the secondary concentrator, with the average flux decreasing almost linearly with the surface reflectance. The presence of the secondary cone greatly reduces the sensitivity of the concentrated heat flux to misalignment of the tilting angle of the elliptical reflector relative to the arc.

Parabolic trough collector or linear Fresnel collector? A comparison of optical features including thermal quality based on commercial solutions

Parabolic trough collectors (PTCs) are still today the most mature technology in concentrating solar power. However, linear Fresnel collectors (LFCs) have been identified by many authors as a candidate to reduce the levelized cost of electricity, although with lower efficiencies. Within Fresnel technology, two possibilities appear for the receiver: multitube receiver and secondary reflector receiver. In the present work a developed Monte Carlo Ray Trace code is used in order to compare the energy effectiveness and flux intensity map at the receiver for different days of the year and different orientations in Almería, Spain, and in Aswan, Egypt. The optical annual energy and exergy efficiencies are also obtained for PTCs and LFCs, with multitube or secondary reflector receiver, where the concentration at each tube is used to weigh the exergy efficiency. It results that the maximum efficiency is obtained by PTCs, while the lowest one corresponds to LFCs with multitube receiver. Also, it is concluded that, while for PTCs NS orientation leads to clearly higher efficiencies, this is not the case for LFCs, where both orientations achieve similar efficiencies even when the solar field has been designed for NS orientation.

Concentric multilayer model of the arc in high intensity discharge lamps for solar simulators with experimental validation

High flux solar simulators, comprising high-intensity-discharge lamps coupled with elliptical reflectors, have been widely employed to study concentrated solar thermal energy systems in a controlled manner. However, little information is available of the influence of the assumptions about the properties of the arc on the accuracy of the prediction of the heat flux at the focal plane. This paper presents a concentric multilayer model of the arc that is developed to predict the spatial distribution of the heat flux at the focus. Measurements were performed of both the time-resolved and time-averaged spatial distribution of the discharge arc from a commercial metal halide lamp with a 23mm spacing between the two electrodes. The efficacy of various alternative simplified approaches to model the arc using a commercial Monte Carlo ray-tracing code were assessed, which include models of cylinder, monopole sphere, dipole-sphere and three types of compounds of these three shapes. These predictions were validated with measurements using a CCD camera and a heat flux gauge, which shows that the predicted profiles from the three compound models agree with the experimental results to similar extent, with no difference in the predicted maximum heat flux and within a difference of 11% for the predicted half-width.

Calculation of Optical Efficiency for the First Central-receiver Solar Concentrator System in Korea

In 2011, the first Korean central-receiver solar thermal plant of 200 kWe was developed as a government research project. Its solar field consists of 450 heliostats in the northern half to a 49 m tall tower, and each heliostat is made of 4 flat mirror facets with a 1 m2 reflecting area. In this paper, we present its optical efficiency calculated with a Monte Carlo ray-tracing code. The code enables to break down the optical efficiency into its six components, that is, cosine, air transmission, shadowing, reflectivity, blocking, and spillage, while taking into account the solar limb darkening without circumsolar radiation as well as reflector surface slope error. We carried out calculations at specific times on summer and winter solstices and autumn equinox. Negligible block efficiency demonstrates that the no-blocking heliostat field layout is well realized. The shadowing efficiency, which is due mainly to the tower rather than neighboring heliostats, is also insignificant except winter solstice. Net optical efficiency is best on autumn equinox but worst on summer solstice mainly because of the cosine efficiency.

Prediction of the radiative properties of reconstructed alpha-SiC foams used for concentrated solar applications

ABSTRACTA SiC-based ceramic foam applied in solar thermal processes was characterized in detail in terms of its textural parameters and its radiative properties. Scanning electron microscopy and x-ray µ-tomography were first performed to investigate the 3D texture of the sample at several length scales. Infrared reflectance microscopy was also applied to probe the local optical responses on the struts constituting the foam. Based on the whole set of experimental data, a numerical tool (C++) was implemented to reconstruct virtual SiC foams. A Monte Carlo Ray Tracing code (iMorphRad, C++) was then used to compute the normal spectral emittance for the real SiC foam and for another reconstructed SiC foam with similar textural features. The two numerically determined emittances were then compared with previous infrared spectroscopy experimental measurements. This numerical procedure enables us to propose a methodology for the design of SiC foams with prescribed radiative properties.

Simulation of the Infrared Views of the Upper Port VIS/IR Imaging System of ITER

In the majority of nuclear fusion experiments equipped with carbonaceous plasma-facing components (PFCs), infrared (IR) imaging diagnostics are routinely used for monitoring the surface temperature of the PFCs exposed to high heat fluxes. However, future fusion machines, such as ITER, will be equipped with metallic PFCs. As a consequence, due to their low emissivity, the evaluation of the surface temperature will have to take into account the multiple reflections of the light coming from hot regions. In order to assess the total IR flux collected by the sensor located at the upper port VIS/IR system of ITER, realistic simulations of the IR views of the ITER tokamak have been developed using a Monte Carlo ray-tracing code (SPEOS CAA V5 Based). The simulation includes the thermal emission, the bremsstrahlung radiation, and the reflections thereof inside the real complex 3-D geometry (from CATIA) of the vessel. The IR simulated images in conditions of plasma operation are presented, and the contribution of the reflected flux for two divertor configurations (carbon fiber composite and tungsten) is analyzed. Finally, the achievable measurement accuracy on the surface temperature of the PFCs from the upper port VIS/IR imaging system is discussed.

Designing of an efficient multi-aperture, edge pumped thin-disk laser

In this article the operation of a composite Yb:YAG/YAG asymmetric hexagonal thin disk laser is optimized. This structure consists an Yb:YAG thin sheet as laser material and a diffusion bonded undoped material on top of thin sheet. Three diodes are placed outside the asymmetric hexagonal shape disk, and the emitting light is coupled via three lens ducts through its three edges and propagates through the disk along the zigzag path and repeatedly passes the gain medium, thus pump uniformity and absorption efficiency are improved. A Monte Carlo ray tracing code and Finite Element Analysis is utilized for calculation of absorbed pump density and volume temperature distribution and also thermal and mechanical stresses, respectively. Finally the output power is calculated. The triplet designing parameters, namely absorbed power efficiency, absorption uniformity and temperature distribution are optimized. Results show this edge-facet pumped geometry is a high efficient configuration for thin gain lasers.

Numerical Analysis of Heat Loss From a Parabolic Trough Absorber Tube With Active Vacuum System

In current designs of parabolic trough collectors for concentrating solar power plants, the absorber tube is manufactured in segments that are individually insulated with glass vacuum jackets. During the lifetime of a power plant, some segments lose vacuum and thereafter suffer from significant convective heat loss. An alternative to this design is to use a vacuum pump to actively maintain low pressure in a long section of absorber with a continuous vacuum jacket. A detailed thermal model of such a configuration is needed to inform design efforts for such a receiver. This paper describes a combined conduction, convection, and radiation heat transfer model for a receiver that includes the effects of nonuniform solar flux on the absorber tube and vacuum jacket as well as detailed analysis of conduction through the rarefied gas in the annular gap inside the vacuum jacket. The model is implemented in commercial CFD software coupled to a Monte Carlo ray-tracing code. The results of simulations performed for a two-dimensional cross-section of a receiver are reported for various conditions. The parameters for the model are chosen to match the current generation of parabolic trough receivers, and the simulation results correspond well with experimental measurements.

Soft X-ray fluorescence from particulate media: Numerical simulations

We introduce a Monte Carlo ray tracing code for soft X-ray fluorescence in particulate media. We use the code to investigate the observation geometry dependent effects on absolute fluorescence line intensities and relative line ratios due to the medium porosity, incident spectrum, and particle size distribution. In particular, we assess the differences between the results given by the simulations and by the analytical fundamental parameters equation of X-ray fluorescence.