Normal-hemispherical Reflectance Research Articles

Critical review and experimental validation of radiative transfer models for semitransparent media containing large gas bubbles

Many materials manufacturing, photobiochemical, and photoelectrochemical processes involve radiation transfer through foams and bubbly fluids. Controlling and optimizing these processes require accurate predictions of radiation transfer through semitransparent media. Previously developed models treated the heterogeneous media as homogeneous plane-parallel slabs with some effective radiation characteristics while radiation transfer was governed by the one-dimensional radiative transfer equation (RTE). Unfortunately, their accuracy and range of validity remains unclear for lack of comparison with one another or against the same set of experimental data. This study aims to critically review and assess the validity of these models both numerically and experimentally. First, predictions of the transmittance and reflectance of heterogeneous slabs containing large randomly distributed bubbles were compared with those obtained from Monte Carlo ray-tracing (MCRT) method based on geometric optics. A new hybrid model was proposed that predicts the effective scattering coefficient and asymmetry factor using the Lorenz–Mie theory and the effective absorption coefficient as the volume-weighted sum of the bubbles and medium absorption coefficients and solves the RTE using the Monte Carlo method. Its predictions showed excellent agreement with those by the MCRT method for a wide range of bubble volume fractions (0%–30%) as well as slab thicknesses (2–40 mm) and medium absorption coefficients (0.1–100 m−1). Second, microcomputed X-ray tomography scans were performed on a fused silica sample containing bubbles with mean radius of 480 μm to retrieve the exact locations, diameters, and total volume fraction of bubbles. Here also, predictions of the hybrid model using the retrieved data agreed well with experimental measurements of the spectral normal-hemispherical reflectance and transmittance of the sample for wavelengths between 0.4 and 3 μm when silica ranges from weakly absorbing to absorbing.

Field validation of isotropic analytical models for simulating fabric shades

Fabric roller shades are common shading materials used in commercial and residential buildings. Accurately characterizing and modeling shades helps practitioners select the appropriate product and its control strategy based on climate and occupants' priorities, such as visual comfort and view to outdoors. Previous studies established a generalized method for modeling complex fenestration systems using data-driven tabulated bidirectional scattering distribution functions. However, deploying such a method at scale to all fabric shading products on the market is too costly and time-consuming. Analytical models that are based on a limited set of measurements (e.g., normal-normal and normal-hemispherical visible transmittance and reflectance, and directional cut-off angles) can be used to model the wide variety of shading products on the market. This study evaluates the performance of two isotropic analytical models, Roos-Wienold and Modified-Kotey, for modeling fabric roller shades, with a focus on the model's ability to predict occupant visual comfort. The performance evaluation was conducted through laboratory and field measurements and simulations. The results showed that both models are sufficient for predicting vertical illuminance at seated eye-level. Roos-Wienold model was able to predict binary visual comfort classification (glare/no-glare) under a wide range of luminance conditions, while Modified-Kotey model did not perform as well under high-contrast low-adaptation conditions. Both models are insufficient in predicting visual comfort at a four-point scale (e.g., imperceptible, perceptible, disturbing, intolerable). The two isotropic models become less accurate when the fabric exhibits high anisotropy.

Temperature-controlled spectrophotometry: a simultaneous analysis of phase transition, thermal degradation and optical properties of semi-transparent composites from 20 °C to 450 °C.

So far, optical and effective radiative properties of polymer matrix based composites were investigated at temperatures well below their degradation temperature. At the same time, polymers exhibit temperature dependent physical properties and may undergo structural changes as their temperature raises. In this work, we employ the "Temperature-Controlled Spectrophotometry", a new method enabling to identify simultaneously phase transitions, thermal degradation and radiative properties of semi-transparent composites over a large temperature range. The method consists of measuring simultaneously the normal-normal and the normal-hemispherical transmittances and reflectances of the sample subjected to a laser irradiation with tuneable wavelength while the temperature is rised from room temperature up to 450 °C by means of a CO2 laser. Physical changes of the sample are identified from the temperature variation of normal-normal transmittance and specular reflectance measurements. Most of the results here are presented at a specific wavelength of 1070 nm but the proposed method is suitable over the semi-transparency spectral domain of the material by changing the wavelength of the probe laser. An inverse method for parameter identification based on normal-hemispherical measurements is employed to determine the transport effective radiative properties of the sample, namely the transport extinction coefficient and the transport scattering albedo from room temperature to 325 °C.

Temperature dependent radiative properties of semi-transparent fiberglass-epoxy composite materials from 20 °C to 200 °C

The radiative properties of polymer-reinforced composite materials such as laminates may change according to the temperature. The knowledge of the relationship between radiative properties and temperature becomes crucial when designing structural components subjected to thermal stresses, induced for example by a laser irradiation. This study deals with the analysis of the absorption and scattering properties of fiberglass-epoxy composites from room temperature to 200 °C. From the point of view of thermal radiation, the two-phase system (polymer matrix and fibers reinforcements) is treated as an equivalent homogeneous medium characterized by volumetric radiative properties, namely the absorption coefficient, the scattering coefficient, and the scattering phase function. The light interaction with the rough boundaries of the sample is modeled by boundary scattering coefficients. The aim is to determine these volumetric and boundary scattering properties as function of the temperature. We use a robust inverse method based on a Gauss-Newton algorithm to solve the nonlinear least squares problem. It minimizes the sum of the squared difference between the theoretical and experimental data of bidirectional and normal-hemispherical reflectances and transmittances. Scattering measurements are carried out using a visible and near-infrared spectrometer (400 to 2500 nm spectral range) equipped with a goniometric system and a heated sample holder. Theoretical results are retrieved by employing the Monte Carlo method for solving the Radiative Transfer Equation (RTE). We report that reflectance are insensitive to the temperature rise below 150 °C, and increase above this temperature up to 200 °C. Transmittances increase with temperature, reach a maximum around 105–125 °C near the glass transition temperature of the resin (assessed by a differential scanning calorimetry analysis), and decrease until 200 °C. Upon others, this study reveals that radiative properties are strongly temperature-dependent above 100 °C, first because of the dependence of the resin refractive index to the temperature, but also due to the onset of the polymer chemical degradation. The mismatch between the glass fibers and the polymer refractive indexes is at its lowest near the glass transition temperature of the resin, and explains the peak of transmittances and the trough on the extinction coefficient and the scattering albedo. The onset of the resin chemical degradation above 150 °C increases the absorption coefficient. The asymmetry parameter of the Henyey Greenstein phase function decrease notably from 0.94 to 0.3 above 150 °C, due to the enhancement of backscattered light within the sample.

Reversible sequin fabrics as variable emittance surfaces

This study demonstrates, for the first time, the use of reversible sequin fabrics as inexpensive, scalable, and durable variable emittance surfaces. First, the spectral normal-hemispherical reflectance's of commercially available gold/black and silver/black reversible sequin fabrics were measured at room temperature for wavelength between 0.25 and 20 μm. The surface roughness and material composition of the sequins were also characterized. The dynamic range of the total hemispherical emittance of the gold/black sequin fabric at room temperature was found to be 0.8, exceeding the performance of other variable emittance surfaces reported to date. The use of reversible sequin fabrics for thermal management was demonstrated experimentally by achieving different equilibrium temperatures of the fabric exposed to simulated solar radiation by simply adjusting the sequin pattern. The experimental measurements were in good agreement with a first order transient thermal model. Finally, thermal infrared images were taken of the sequin fabrics to illustrate their capabilities for thermal camouflage, illusion, and messaging.

Radiative behavior of low-porosity ceramics: II–Experimental and numerical study of porous alumina up to high temperatures

We compare two methods of characterizing the radiative behavior of 22% porous sintered alumina disks containing μm-sized pores on the 1 µm to 7 µm wavelength range up to very high temperatures. The first consists of direct spectroscopic measurements of the normal-hemispherical reflectance and transmittance at room temperature, as well as the normal emittance up to 1300 ∘C. The second is a two-step multi-scale numerical approach: the volume radiative properties and surface reflectivity are first determined from physical optics computations on tomography-reconstructed microstructures, then applied to the resolution of the radiative transfer equation on an equivalent homogeneous medium to obtain the spectral reflectance, transmittance, and emittance. Uncertainties in the numerical results, mainly due to microstructural variability, are quantified through sensitivity studies. The good agreement between the experimental and numerical results confirm the ability of our proposed numerical approach to give accurate predictions of the high-temperature radiative behavior of porous ceramics.

An approach to determine radiative properties of solid struts of open-cell foams by pore scale identification from macro scale measurements

Open-cell foams consisting of interconnected struts are widely used in thermal applications such as volumetric solar receivers. The thermal performance of foams strongly relies on their radiative behaviors which intrinsically depends on the radiative properties of struts. This study proposed a feasible approach to determine the radiative properties of solid struts by a pore scale identification from a macro scale measurement. First, the normal-hemispherical transmittance and reflectance spectra of two nickel foams were measured by an experimental system. Second, a pore scale forward calculation was conducted by a combination of Monte Carlo Ray-tracing method and real foam structures obtained from micro-computed tomography technique. Last, an Adaptive Particle Swarm Optimization algorithm was adopted to retrieve the spectral reflectivity and specularity of nickel struts from the measured spectra. The results show that it is unreasonable to assume the reflection behavior of strut surface simply as either specular or diffused, and also, it is unreliable to assign the reflectivity of strut surface directly by Fresnel's law. Within the investigated wavebands 0.4–2.2 μm, the average reflectivity of nickel struts is 12% lower than that of a nickel mirror. The proportion of specular reflection at nickel strut surface is between 37%–52%, almost increasing with wavelengths.

A modified inverse method for determining spectral radiative properties of participating medium from normal-hemispherical transmittance and reflectance

This paper presents a modified inverse method for retrieving the spectral absorption and transport scattering coefficients of participating medium, the method combines (i) several analytical expressions obtained from the modified two-flux (TF) approximation, (ii) the Monte Carlo (MC) method for predicting normal-hemispherical transmittance Tnh and reflectance Rnh generally obtained from experiments, as well as (iii) an optimization method employing the genetic algorithm (GA). Three types of typical participating medium, the green glass, the low-iron glass, and the silica aerogel with known radiative properties taken form the literatures, were used to illustrate the accuracy and robustness of the modified method by retrieving the input properties from the inverse identification in which the Tnh and Rnh ‘experimental data’ were obtained from the MC predictions. The results show that the modified inverse method was able to retrieve accurately the absorption and transport scattering coefficients of participating medium.

A development to determine spectral radiative properties of semitransparent struts of open-cell ceramic foams: From macro-scale measurement to pore-scale simulation

The radiative properties of a ceramic strut cannot be strictly the same as that of a dense sintered ceramic bulk composed of the same material. This contribution develops an approach to determine the radiative properties of semitransparent ceramic struts of open-cell foams. First, a macro-scale measurement was conducted to obtain the normal-hemispherical transmittance and reflectance spectra of alumina foam slices. Second, a pore-scale forward model was established to predict the radiative behaviors of 3D digital porous structures obtained from micro-computed tomography technique. Last, an identification method was proposed to retrieve the radiative properties of semitransparent ceramic struts from the measured data. The results indicate that it is unreasonable to simply assume the radiative properties of alumina struts as that of corresponding dense bulks. Within the investigated wavebands 0.4–2.2 μm, the average extinction coefficient of alumina struts is 33.5% lower than that of dense bulks. The scattering albedo shows a slight difference between alumina struts and dense bulks. Besides, the retrieved extinction coefficients and scattering albedos of alumina struts are proposed as a function of wavelengths, which can be used in potential applications.

Pore scale simulation of spectral radiative properties of Voronoi open-cell carbon foams at high temperatures

A pore scale model was established to investigate the high-temperature radiative properties of carbon foams with high porosity. Voronoi Tessellation for the random structure of carbon foams and Monte Carlo ray-tracing method was employed to simulate the apparent radiative behaviors and volumetric radiative properties. By compared with the measured data at room temperature in Ref. (Celzard et al., 2012), the numerical model was verified to possess a high precision, which the maximum deviation are 1.8% for normal absorptance, 0.3% for normal-hemispherical transmittance and 1.5% for normal-hemispherical reflectance, respectively. It is also acceptable for the simulated results of volumetric radiative properties. Based on the spectral radiative properties of carbon basic material found in Ref. (Touloukian and DeWitt, 1972), the spectral radiative properties of carbon foam sheets at high temperature between 1183 K and 2073 K were predicted. It was found that absorptance is dominant in the apparent radiative behaviors of carbon foams at high temperatures with a wavelength of 0.665 μm. Then, the bidirectional reflectance distribution function was numerically investigated. The results showed a backward scattering of the reflected energy at the foam sheet surface and reflected energy peaks are always located at around respective incident angles. For volumetric radiative properties at high temperatures, extinction coefficient ranged between 200 m−1 and 450 m−1, which had been verified with relation formula in an error of less than 1%. In addition, scattering albedo and scattering phase function were not only simulated but also compared with the empirical formulas, to some extent, agreed well with them.

Light transfer through semi-transparent glass panes supporting pendant droplets

This paper quantifies experimentally the effect of pendant droplets condensed on the back of semi-transparent glass panes on their normal-hemispherical transmittance and reflectance in the visible and near-infrared. To enable sample characterization and ensure repeatability, acrylic droplets were deposited on the back side of 3 mm-thick soda-lime silicate glass slabs with or without hydrophobic surface treatment including perfluorinated silane, perfluorinated silane-coated silica nanoparticle monolayer, or Teflon coatings. The droplet contact angle θc was varied between 26° and 76° and the projected surface area coverage reached up to 60%. For contact angle θc smaller than the critical angle θcr for total internal reflection at the droplet/air interface, the presence of droplets did not significantly affect the normal-hemispherical transmittance and reflectance. However, for droplet contact angle θcr ≤ θc < 90°, the normal-hemispherical transmittance decreased significantly with increasing droplet contact angle and/or surface area coverage while the normal-hemispherical reflectance increased. The measurements of the normal-hemispherical transmittance were in excellent agreement with numerical predictions obtained from Monte Carlo Ray Tracing method. These results further validate our previous numerical simulations and the different optical regimes identified. The results of this study can provide guidelines for the design and operation of energy efficient flat-plate solar collectors, outdoor photobioreactors, greenhouses, solar desalination systems, and other solar energy conversion systems.

Thermally-induced structural changes and optical properties degradation of fiber-loaded aerogel composites under thermal exposures

Fiber-loaded aerogel composites possess remarkable physical and chemical properties, making them extensively used in a variety of science and technology fields. Structural changes were usually taken place inside the aerogel composites under an elevated thermal environment. However, scarce research can be found on the resulted optical properties degradation provoked by thermal exposures, possibly due to technical limitations in the characterization method of aerogel composites. With this motivation, the thermally-induced microstructural changes in fiber-loaded aerogel composites were firstly characterized and discussed in this work by in-situ characterization techniques. For comparison of optical properties of samples under various levels of thermal exposures, an inverse measurement method was developed to characterize intrinsic optical properties of samples based on the measured and predicted normal-hemispherical transmittance and reflectance spectra. The intrinsic optical properties evolution was then correlated with the microstructural developments caused by high-temperature annealings for the samples. The provided information is indispensable for promoting fundamental insights on the underlying physical mechanisms of aerogel composites and provide guidelines for further design and optimization under thermal environments.

Experimental study of the radiative properties of hedgehog-like ZnO–Au composite particles

The hedgehog-like ZnO particles (HPs) and ZnO–Au composite particles (HP-Au) show great potential in the application of photocatalysis, due to their special nanostructure and unusual dispersion behavior in fluids. To improve the efficiency of photocatalysis, one needs to analyze and optimize the radiative transfer of nanofluids containing HPs and HP-Au. Therefore, knowledge of the radiative properties of HPs and HP-Au is of great significance. In this work, the radiative properties of HPs and HP-Au are experimentally measured in the visible spectral range, and the effect of the deposited Au nanoparticles on the radiative properties of HP-Au is investigated. The extinction cross section is obtained from the normal-normal transmittance of particle water suspensions by the improved transmission method. The absorption cross section and the asymmetry parameter are retrieved from the measured normal-hemispherical transmittance and reflectance. It is found that the extinction cross sections of HPs and HP-Au range from 9 to 11 µm2, and peak at the wavelengths of about 380 and 650 nm due to the strong scattering ability of the particles. The deposited Au nanoparticles decrease the extinction cross section of HP-Au notably in the spectral range from 500 to 800 nm. The absorption cross section of HP-Au is enhanced by Au nanoparticles, which can be more than two times that of HPs. The absorption cross section of HP-Au peaks at the wavelength of about 520 nm due to the localized plasmon resonance of Au nanoparticles, which can reach 2.2 µm2. The asymmetry parameters of both HPs and HP-Au increase rapidly with increasing wavelength in the spectral range from 400 to 600 nm, but for wavelength larger than 600 nm their asymmetry parameters are round 0.9 and show very small spectral variation. The deposited Au nanoparticles, however, tend to decrease the asymmetry parameter of HP-Au.

Optical properties of oakwood in the near-infrared range of semi-transparency.

The spectral absorption and scattering properties of oakwood are retrieved from the measurements of both the normal-hemispherical reflectance and transmittance in the visible and near-infrared ranges of semi-transparency. We employ two alternative methods for the radiative transfer in wood samples: the modified two-flux approximation and the high-order discrete ordinate method. The modifications of both methods take into account the effect of total internal reflection at both surfaces of the wood samples. The analytical approximate solution of the first method gives very accurate results for the absorption coefficient, but the transport scattering coefficient of wood appeared to be systematically underestimated. Fortunately, this error is between 7% and 12%, and that is acceptable for the estimates. The oakwood samples of four different thicknesses were used in the experiments. The effect of the wood cell orientation appears to be insignificant and can be observed in the reflectance from optically thin samples only. There is a considerable decrease in the transport scattering coefficient of oakwood with the wavelength. This effect is explained by a predominant contribution of micron-sized longitudinal pores in oakwood. The latter is used to develop an approximate theoretical model of scattering based on the rigorous solution for arbitrary-oriented cylindrical pores. The model suggested is in good agreement with the experimental data.

Transmittance of semitransparent windows with absorbing cap-shaped droplets condensed on their backside

This study aims to investigate systematically light transfer through semitransparent windows with absorbing cap-shaped droplets condensed on their backside as encountered in greenhouses, solar desalination plants, photobioreactors and covered raceway ponds. The Monte Carlo ray-tracing method was used to predict the normal-hemispherical transmittance, reflectance, and normal absorptance accounting for reflection and refraction at the air/droplet, droplet/window, and window/air interfaces and absorption in both the droplets and the window. The droplets were monodisperse or polydisperse and arranged either in an ordered hexagonal pattern or randomly distributed on the backside with droplet contact angle θc ranging between 0 and 180° The normal-hemispherical transmittance was found to be independent of the spatial distribution of droplets. However, it decreased with increasing droplet diameter and polydispersity. The normal-hemispherical transmittance featured four distinct optical regimes for semitransparent window supporting nonabsorbing droplets. These optical regimes were defined based on contact angle and critical angle for internal reflection at the droplet/air interface. However, for strongly absorbing droplets, the normal-hemispherical transmittance (i) decreased monotonously with increasing contact angle for θc< 90° and (ii) remained constant and independent of droplet absorption index kd, droplet mean diameter dm, and contact angle θc for θc≥ 90° Analytical expressions for the normal-hemispherical transmittance were provided in the asymptotic cases when (1) the window was absorbing but the droplets were nonabsorbing with any contact angles θc, and (2) the droplets were strongly absorbing with contact angle θc> 90° Finally, the spectral normal-hemispherical transmittance of a 3mm-thick glass window supporting condensed water droplets for wavelength between 0.4 and 5 μm was predicted and discussed in light of the earlier parametric study and asymptotic behavior.

Simple methods for identification of radiative properties of highly-porous ceria ceramics in the range of semi-transparency

PurposeThe aim of this paper is to present advanced experimental–numerical methods for identification of spectral absorption and scattering properties of highly porous ceria ceramics in the range of semi-transparency at room and elevated temperatures.Design/methodology/approachAt room temperature, a period of quasi-steady oscillations of the sample surface temperature generated in response to recurrent laser heating at fixed values of the maximum and minimum temperature of the irradiated surface is measured along with the normal-hemispherical reflectance. Radiative properties are then identified using a combined heat transfer model. At elevated temperatures, an analytical solution proposed in an earlier study for zirconia ceramics is used to retrieve spectral absorption coefficient of ceria ceramics from the measured normal emittance.Findings and Originality/valueThis method can be used to obtain small absorption coefficient of ceria ceramics at room temperature. The required measurements of both the normal-hemispherical reflectance and the period of quasi-steady oscillations of the irradiated surface temperature of the ceramics sample between fixed values of the maximum and minimum temperatures can be readily conducted using thermal laboratory equipment. Another method has been suggested for identification of the spectral absorption coefficient of ceria ceramics at elevated temperatures. This method is based on a relation between the measured normal emittance of an isothermal sample and the absorption coefficient.

Light transfer in agar immobilized microalgae cell cultures

This paper experimentally and theoretically investigates light transfer in agar-immobilized cell cultures. Certain biotechnological applications such as production of metabolites secreted by photosynthetic microorganisms require cells to be immobilized in biopolymers to minimize contamination and to facilitate metabolite recovery. In such applications, light absorption by cells is one of the most important parameters affecting cell growth or metabolite productivity. Modeling light transfer therein can aid design and optimize immobilized-cell reactors. In this study, Parachlorella kessleri cells with areal biomass concentrations ranging from 0.36 to 16.9 g/m2 were immobilized in 2.6 mm thick agar gels. The average absorption and scattering cross-sections as well as the scattering phase function of P. kessleri cells were measured. Then, the absorption and transport scattering coefficients of the agar gel were determined using an inverse method based on the modified two-flux approximation. The forward model was used to predict the normal-hemispherical transmittance and reflectance of the immobilized-cell films accounting for absorption and scattering by both microalgae and the agar gel. Good agreement was found between the measured and predicted normal-hemispherical transmittance and reflectance provided absorption and scattering by agar were taken into account. Moreover, good agreement was found between experimentally measured and predicted mean rate of photon absorption. Finally, optimal areal biomass concentration was determined to achieve complete absorption of the incident radiation.

Radiative transfer equation and direct simulation prediction of reflection and absorption by particle deposits

Two methods for computing the normal incidence absorptance and hemispherical reflectance from plane parallel layers of wavelength–sized spherical particles are presented. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a system of randomly–positioned spherical particles excited by an incident plane wave. The second method is based upon the scalar radiative transport equation (RTE) applied to a plane parallel medium. Comparisons are made using five values of particle refractive index, sphere size parameters ranging from 1 to 4, and particle volume concentrations ranging from 0.05 to 0.4. The results indicate that the multiple sphere T matrix method (MSTM) and RTE predictions of hemispherical reflectance and absorptance converge when particle volume fraction becomes small. At higher volume fractions the RTE can yield results for hemispherical reflectance that, depending on the particle size and refractive index, significantly depart from the exact predictions. On the other hand, RTE and MSTM predictions of absorptance have a much closer agreement which is largely independent of the sphere optical properties and volume concentration.

Near-infrared optical properties of a porous alumina ceramics produced by hydrothermal oxidation of aluminum

The measured spectral normal–hemispherical reflectance of an optically thick sample of porous alumina ceramics produced by hydrothermal oxidation of aluminum and subsequent high-temperature treatment of boehmite (or böhmite), AlO(OH), is used in a combination with the published data for absorption coefficient of alumina to retrieve the near-infrared optical properties of the alumina ceramics at both room and elevated temperatures. The spectral emissivity of porous alumina ceramics is also determined. An approximate model based on the Mie theory for single grains is suggested to estimate the transport scattering coefficient and the radiative conductivity of the material at high temperatures.

Optical indices and transport scattering coefficient of pyrolytic boron nitride: a natural thermal barrier coating for solar shields

Absorption and scattering properties of pyrolytic boron nitride (pBN) have been characterized by infrared spectroscopy. The strong dielectric anisotropy predicted by first principles calculations is confirmed by measurements performed on a highly oriented pBN sample. Optical properties of textured samples elaborated by chemical vapor deposition were identified from normal hemispherical reflectance and transmittance spectra by applying modified two-flux and four-flux transport models. It is also shown that coating carbon–carbon composites used to build solar shields with a pBN layer having an optimal thickness could improve the protection performance.