Heating/melting of a fused silica particle by convection and radiation

The effect of internal absorption and emission of radiation on the heating/melting process of small fused silica particles is analyzed. The particle is considered to be semitransparent to radiation, and the radiative transfer theory is used to predict the local volumetric absorption/emission rate. The transient energy equation with conduction and radiation accounted for is solved to predict the temperature distribution in the particle and the solid–liquid interface position after the melting has started. The radiative transfer calculations are carried out on the spectral basis using published spectral optical property data for fused silica. Results of parametric calculations for different diameter particles, surroundings temperatures and external flow conditions are reported and discussed.     

Assessment of gas radiative property models in the presence of nongray particles

In this study, a radiation code based on the method of lines solution of the discrete ordinates method for the prediction of radiative heat transfer in nongray gaseous media is developed by incorporation of two different spectral gas radiative property models, banded spectral line-based weighted sum of gray gases (banded SLW) and gray wide band (GWB) approximation in the presence of nongray absorbing–emitting–scattering particles. The aim is to introduce an accurate and CPU efficient spectral gas radiation model, which is compatible with spectral fuel/ash particle property models. Input data required for the radiation code and its validation are provided from two combustion tests previously performed in a 300 kWt atmospheric bubbling fluidized bed combustor test rig burning low calorific value Turkish lignite with high volatile matter/fixed carbon (VM/FC) ratio in its own ash. The agreement between wall heat fluxes and source term predictions obtained by global and banded SLW models reveal that global SLW model can be converted to an accurate wide band gas model (banded SLW) which can directly be coupled with spectral particle radiation. Furthermore, assessment of GWB approximation by benchmarking its predictions against banded SLW model shows that GWB gives reasonable agreement with a higher CPU efficiency when the particle absorption coefficient is at least in the same order of magnitude with the gas absorption coefficient.     

Comparative spectral characteristics of solar radiation relative to air mass values

The results of the studies of the spectral characteristics of terrestrial solar radiation carried out based on the calculation model for an index dependence of spectral air mass transmission coefficients relative to the standard solar radiation АМ-1.5 are presented for different air mass values. Spectral transmission coefficients for standard air mass АМ-1.5 relative to extraterrestrial solar radiation AM-0 are obtained by comparing the respective spectral intensities from the published literature. During the theoretical calculations, the limiting value of the air mass (for the solar disk near the horizon) is taken to be large by a factor of 36 than for air mass AM-1.     

The Fresnel lens concept for solar control of buildings

Fresnel lenses are optical devices for solar radiation concentration and are of lower volume and weight, smaller focal length and lower cost, compared to the thick ordinary lenses. The advantage to separate the direct from the diffuse solar radiation makes Fresnel lenses suitable for illumination control of building interior space, providing light of suitable intensity level and without sharp contrasts. In this paper, the Fresnel lens concept is suggested for solar control of the buildings to keep the illumination and the interior temperature at the comfort level. Laboratory scale experimental results are presented, giving an idea about the application of this new optical system. The collection of 60–80% of the transmitted solar radiation through the Fresnel lenses on linear absorbers leaves the rest amount to be distributed in the interior space for the illumination and thermal building needs. In low intensity solar radiation, the absorber can be out of focus, leaving all light to come in the interior space and to keep the illumination at an acceptable level. The Fresnel lenses can be combined with thermal, photovoltaic, or hybrid type photovoltaic/thermal absorbers to collect and extract the concentrated solar radiation in the form of heat, electricity or both. By using thermal absorbers and for low operating temperature, efficiency of about 50% can be achieved, while considering photovoltaics, satisfactory electrical output can be obtained. Regarding the effect of the suggested system to building space cooling, the results showed a satisfactory temperature reduction, exceeding 10 °C for cold water circulation through the absorber.     

A method for correction of cosine errors in measurements of spectral UV irradiance

One of the sources contributing to the overall uncertainty of spectral UV radiation measurements is the cosine error of the spectroradiometer. It leads to measurement errors that depend on atmospheric conditions and on solar zenith angle, and thus time of the day and season. Though the foreoptics of modern instruments are designed such as to minimize cosine errors, there remain deviations from the ideal cosine response. We have worked out a method to further reduce that remaining cosine error in global spectral irradiance. This method was applied to spectra of global UV radiation taken with a Brewer spectroradiometer. The only additional input data needed to apply the method of cosine correction to spectral irradiance data are concurrent broad-band UV-B radiation measurements of diffuse and global radiation recorded with filter UV instruments, which are used to estimate the optical thickness referred to global UV radiation for the time when the spectral scan is taken. The method takes account of the variable conditions of cloudiness and turbidity. In the case of measurements taken with Brewer instrument No. 30, the cosine corrected global UV-B radiation was higher than the measured irradiance by 9–20%, and even its daily totals turned out to be higher than the uncorrected radiation by 13–18%. An estimate of the uncertainty of ±4 to ±8% was derived from a theoretical approach as well as from model calculations using a radiative transfer model.     

Enhancement of ground radiation in greenhouses by reflection of direct sunlight

Substantial gains in greenhouse ground illumination/irradiance were obtained with a reflecting wall that was positioned so as to reflect the incoming sunlight from the northern face of the greenhouse to its ground. The effect was particularly significant in winter when the sun was low throughout the day and most of the radiation passed through the greenhouse so that its ground radiant power was reduced.Four types of greenhouses with reflecting walls exhibiting increasing efficiencies of insolation were developed. A theory describing a several-fold enhancement of ground irradiance and radiant energy was developed. Effects of sky (diffuse) radiation on clear and cloudy days were also considered.An experimental model, as well as a full-scale greenhouse with a reflecting wall with provision for measuring ground illumination was constructed and exposed to the sun: Actual measurements were conducted over several days, supporting the theoretical calculations.     

Comparison of long-term flat-plate solar collector performance calculations based on averaged meteorological data

The use of averaged meterological data for collector performance calculations is studied. To this end, a steady state, two-dimensional, nodal, heat transfer analysis is developed for a flat-plate solar collector. The analysis accounts for the temperature gradients in the fluid flow and vertical directions in the collector, the physical and thermodynamic properties of the materials in the collector, the collector location, the orientation and dimensions of the collector, the number of cover plates and any thin film selective coatings on the cover plates or absorber. Also accounted for are the time dependent variations in the meteorological conditions, insolation, and collimated and diffuse solar irradiation. The spectral nature of radiation heat transfer in the collector is modeled by two spectral bands, solar and thermal, with 3.0 μm as the cutoff frequency between the solar and thermal bands of radiation. The results indicate that long term collector performance calculations based on averaged meteorological data will not correlate with calculations based on hourly data if the weather is highly variable. When the weather variations are mild, averaged data can give results very close to those based on hourly data.     

Spectral Monte Carlo models for nongray radiation analyses in inhomogeneous participating media

A spectral line-by-line (LBL) method is developed for photon Monte Carlo simulations of radiation in participating media. The performance of the proposed method is compared with that of the stochastic full-spectrum k-distribution (FSK) method in both homogeneous and inhomogeneous media, and in both traditional continuum media and media represented by stochastic particle fields, which are frequently encountered in combustion simulations. By using random-number relations, the LBL method does its own spectral reordering, in effect similar to the FSK reordering. Both LBL and FSK methods result in the same level of statistical errors for similar numbers of photon bundles. It is shown that the FSK approach is superior to the LBL approach in both memory and CPU efficiency in all test cases. However, the CPU efficiency is not prominent when spectral calculations are not the dominant source of overall CPU-time cost. Due to a lack of correlation of absorption coefficients in inhomogeneous media, the FSK approach may produce substantial errors, which are avoided by the LBL method. The LBL database can be constructed once and for all, while the FSK database has to be reconstructed every time the reference state changes. Thus, the LBL method is more suitable for quickly-evolving media.     

QUENCHING OF FLAT GLASS BY IMPINGING AIR JETS

Quenching of hot glass by impinging round air jets is analyzed. Understanding of the temperature distribution in glass is required for thermal tempering operations. In the analysis the spectral dependence of the absorption coefficient on wavelength is appropriately accounted for by solving the radiative transfer equation for the axisymmetric cylindrical geometry. Specularly reflecting boundaries are considered, and Fresnel's equations are used to predict the spectral directional reflection and transmission characteristics of the interfaces. The finite volume method is used to solve numerically the thermal energy equation. The numerical calculations have been carried out for combined forced convection and radiation cooling from the surfaces. Transient temperature distributions for parametric calculations are presented and discussed. Determination of the resulting stresses under given impingement and thermal conditions is also discussed.     

The entropy of terrestrial solar radiation

Complete thermodynamic evaluation of energy conversion devices calls for energy and entropy balance equations. While the subject of radiation energy has been well taken care of, the same is not true for the entropy of radiation. This has become obvious from the discussion about the maximum work that can be drawn from solar radiation. This article collects and reflects the basic equations needed to calculate the radiation entropy, and it discusses the influence of the three major input functions on the entropy, namely the spectral and hemispherical distribution of radiation intensity, and its degree of polarization. Results of realistic calculations using atmospheric models are given in the last section in form of an energy-entropy diagram.     

Transient temperature and thermal stress profiles in semi-transparent particles under high-flux irradiation

Transient temperature and thermal stress profiles in semi-transparent spherical particles heated by concentrated solar radiation are studied by means of a theoretical model. The analysis of radiative–conductive interaction is based on the spectral radiation transfer model in a refracting and absorbing particle. The stress–strain state of the particle is described by the thermoelastic approach. An analytical self-similar solution for the particle temperature profiles and thermal stresses during the quasi-steady period of the particle heating is derived. It is shown that the circumferential tensile stress near the particle surface is a non-monotonic function of the particle radius. The range of physical parameters corresponding to the maximal tensile stress near the particle surface is determined. The model is applied to ZnO and CaCO₃ particles, which are used as reactants in industrially-relevant high-temperature processes. It is shown that tensile stresses in the selected types of particles exposed to concentrated solar radiation cannot lead to their mechanical destruction. At the same time, the considerable temperature difference and thermal stresses in non-isothermal particles can be an interesting issue in a detailed analysis of the thermal decomposition of semi-transparent particles.     

Application of the full spectrum correlated-k distribution approach to modeling non-gray radiation in combustion gases

The treatment of radiative transport through combustion gases is rendered extremely difficult by the strong spectral variation of the absorption coefficients of molecular gases. In the full spectrum correlated-k distribution (FSCK) approach, a transformation is invoked, whereby the radiative transfer equation (RTE) is transformed from wavenumber to non-dimensional Planck-weighted wavenumber space after reordering of the spectrum. The reordering results in a relatively smooth spectrum, allowing accurate spectral integration with very few quadrature points. The numerical procedures, required to use the FSCK model for full-scale combustion applications, have been outlined in this article. The FSCK model was first coupled with the Discrete Ordinates Method (DOM) for solution of the transformed RTE. The accuracy of the model was then examined for a variety of cases ranging from homogeneous one-dimensional media to inhomogeneous multi-dimensional media with simultaneous variations in both temperature and concentrations. Comparison with line-by-line calculations shows that the FSCK model is exact for homogeneous media, and that its accuracy in inhomogeneous media is limited by the accuracy of the scaling approximation. Several approaches for effective scaling of the absorption coefficient are examined. The model is finally used for radiation calculations in a full-scale combustor, with full coupling to fluid flow, heat transfer and multi-species chemistry. The computational savings resulting from use of the FSCK model is found to be more than four orders of magnitude when compared with line-by-line calculations.     

Zur Simulation der Globalstrahlung(On the Simulation of Global Radiation)

Die in Simulationsanlagen für die Globalstrahlung vorhandene spektrale Verteilung der Strahlung wird in der Praxis immer von der der Globalstrahlung abweichen. Wenn in solchen Anlagen die Bestrahlungsstärke auf den Wert der für Prüfzwecke vorgeschlagenen Globalbe-strahlungsstärke eingestellt wird, ergeben sich Wirkungen bei bestrahlten Objekten, die von denen bei Bestrahlung mit Globalstrahlung abweichen.

Für diese Tests ist daher die Bestrahlung so einzustellen, daβ die “wirksame” Bestrahlungs-stärke in der Anlage ebenso groβ ist, wie die “wirksame” Globalbestrahlungstärke. Diese “wirksamen” Bestrahlungsstärken hängen immer von der relativen spektralen Wirkungsfunktion (relative spektrale Empfindlichkeit) des bestrahlten Objektes ab.

Am Beispiel einer Simulationsanlage mit Xenon-Lampen für Tests an Si-Solarelementen werden die notwendigen Berechnungen vorgeführt.

Equipment for the use of solar radiation must be tested under defined conditions, where the absolute irradiance and its spectral distribution, and the solid angle of the incident radiation are of importance.

In praxis the spectral distribution of the incident radiation differs from the prescribed function. Then the effect of the radiation differs from that received by the prescribed radiation for equal irradiance.

For exact test results it is necessary to irradiate the equipment to be tested (solar cell, solar collectors) with an “effective” irradiance, which is equivalent to the effective prescribed irradiation. This effective irradiance depends on the spectral distribution of the radiation used for the test, the prescribed spectral distribution, the relative spectral responsivity of the test object and the prescribed absolute irradiance.

The necessary calculations for the effective irradiance are shown as an example for a test equipment with Xenon-lamps for Si-solar cells.     

Numerical simulation of the interaction between turbulence and radiation in reactive flows

The interaction between turbulence and radiation (TRI) in reactive flows has been demonstrated experimentally, theoretically and numerically, and results from the highly non-linear coupling between fluctuations of radiation intensity and fluctuations of temperature and chemical composition of the medium. The instantaneous and the time-averaged form of the radiative transfer equation (RTE) are presented, and the TRI effects resulting from time-averaging are discussed. Methods to account for TRI in practical calculations are surveyed, and works where such methods have been employed are reviewed. These include both decoupled and coupled fluid flow/radiative transfer calculations. It is shown that the solution of the RTE using instantaneous scalar data is the most accurate way to deal with TRI, but it is computationally prohibitive for coupled problems. Hence, this approach has been mainly used to calculate the radiation intensity along lines of sight. The generation of time series of instantaneous scalar data may be accomplished using stochastic or deterministic models, which are also surveyed. Coupled fluid flow/radiative transfer problems are generally solved using the time-averaged form of the RTE or the Monte Carlo method, and rely on the optically thin fluctuation approximation, which neglects the correlation between fluctuations of the absorption coefficient and fluctuations of the radiation intensity. Experimental data and numerical calculations demonstrate that turbulent fluctuations may significantly increase the mean spectral radiation intensity in both non-luminous and luminous flames. Turbulent fluctuations contribute to decrease the flame temperature below the level observed without fluctuations, particularly for optically thick flames. The net radiative power and the fraction of radiative heat loss increase due to TRI, particularly in the case of optically thin flames. Recent direct numerical simulations provide additional insight on the role of different correlations responsible for TRI, and on how they are influenced by the optical thickness of the medium.     

Benchmarking grey particle approximations against nongrey particle radiation in circulating fluidized bed combustors

Investigation of the effect of grey/nongrey particle property models on radiative heat fluxes and source terms is performed in the dilute zone of the lignite-fired 150?kW Middle East Technical University circulating fluidized bed combustor test rig. Predictive accuracy and computational economy of several grey particle models, geometric optics approximation (GOA) with average particle reflectivity (GOA2), GOA with Fresnel solution for particle reflectivity (GOA3), and Planck mean particle properties from spectral Mie solution are tested by benchmarking their predictions against spectrally banded solution of radiative transfer equation (RTE). Comparisons reveal that all grey models lead to accurate and CPU efficient radiative heat flux predictions. On the other hand, only GOA3 and Planck mean properties are in favorable agreement with the benchmark solution for both incident fluxes and source terms. These findings indicate that grey particle approximation with GOA3 is a more practical choice in solution of RTE as it eliminates the need for spectral calculations.     

Spatial and temporal coherence of thermal radiation in asymmetric Fabry–Perot resonance cavities

There has been an increased interest on the development of micro/nanostructures with desired radiative properties for energy conversion systems and radiative cooling devices. A detailed experimental study is reported on the spatial and temporal coherence of thermal radiation in asymmetric Fabry–Perot resonance cavities. The reflectance of the fabricated samples was measured for both polarizations using a Fourier-transform infrared spectrometer, at several incident angles in the near-infrared region, and a laser scatterometer at the wavelength of 891 nm. The spectral measurement demonstrates sharp reflectance dips, while narrow angular lobes are observed in the angle-resolved measurement. Experimental results suggest strong spectral and directional selectivity in thermal emission, which is related to the reflection by Kirchhoff’s law since the samples are opaque. Theoretical calculations with the fitting geometric parameters agree well with the measurement results. This easy-to-fabricate structure has potential applications in solar cells, thermophotovoltaic devices, and radiation emitters.     

Spectral response and IV-characterization of dye-sensitized nanocrystalline TiO2 solar cells

Dye-sensitized nanocrystalline TiO₂ solar cells (nc-DSCs) are based on a fundamentally different working principle than solar cells based on semiconductors. This could have implications for the characterization of nc-DSCs. In this study a comparison is made between two methods for determination of the spectral response of nc-DSCs. The standard method for determination of the spectral response according to the ASTM E1021-84 norm appears to be valid for the nc-DSC. The response of the solar cell to pulsed irradiation plays an important role in this determination, since pulsed illumination of the solar cell is involved. The response time of the nc-DSC is related to electron trapping in the TiO₂ and depends on illumination conditions and also on chemical composition of the cell. For this reason, prior to measurements of spectral response of nc-DSCs, the response time of the cell should be measured under the same illumination conditions that are applied during spectral response measurements.     

A model for the volumetric radiation characteristics of cellular ceramics

A unit cell based model for cellular ceramics was developed in conjunction with the discrete ordinates method for radiative transfer to predict theoretically the effective volumetric radiation characteristics of the cellular ceramics. Model input parameters include the porosity, pores per centimeter (PPC) and reflectivity of the solid material. Numerical calculations of the extinction coefficients and single scattering albedo are reported over the range of reflectivities from 0 to 1, porosities from 0.6 to 0.95 and PPC from 4 to 26. A comparison between model predictions and spectral emittance data for cellular ceramics reported in the literature shows agreement within 5 to 10% which is within experimental uncertainty.     

A simplified technique to compute spectral atmospheric radiation

The spectral distribution of longwave atmospheric radiation arriving at the earth's surface is composed of contributions from atmospheric layers which absorb and re-emit longwave radiation. A procedure to estimate this radiation requires, as input, the temperature and pressure variations with altitude and the distribution of absorbing gases in the atmosphere. Such detailed information about the atmosphere at a given location and time is rarely known. However, local variation of the amount of water vapor is generally known, and ozone undergoes known seasonal variations. These two gases along with carbon dioxide are the main emitters of longwave radiation in the atmosphere.A rigorous technique to compute spectral atmospheric radiation is used together with atmospheric data from a Standard Atmosphere to examine the variation of spectral emissivity with the amount of absorbing gases in the atmosphere. A simple spectral correlation is thereby developed which is then applied to the other Standard Atmospheres utilizing their water vapor amount as the only input. Results obtained from this correlation are compared with those obtained from detailed computations for each Standard Atmosphere. Good agreement is observed at all the wavelengths considered except in a 1 μm region wherein the differences are somewhat larger. It is demonstrated that for any geographic latitude and season the spectral longwave atmospheric radiation can be computed from a simple correlation using precipitable water vapor amount as the only input parameter.     

An Estimate of the Temperature of Semitransparent Oxide Particles in Thermal Spraying

A considerable temperature difference in semitransparent oxide particles due to intensive heating in plasma spraying makes it difficult to interpret the optical measurements of their temperature. The problem of determining the bulk temperature of such particles from the experimental data on the color temperature is analyzed by using a recently proposed approximate model for the radiation transfer inside a nonisothermal refracting spherical particle. The same approximation is also employed for developing an improved model of particle heating, taking into account the radiation-conduction interaction inside the particle. Calculations for Al 2 O 3 and ZrO 2 particles in a typical plasma jet show that the color temperature of oxide particles may be less than or greater than their bulk temperature, depending on the spectral absorption coefficient of particle substance. This temperature difference during the melting of particles may reach the value of 200-300 K. A procedure for in situ evaluation of the absorption coefficient by comparison of color and brightness temperatures of molten particles is proposed.