Gray Body Assumption Research Articles

On the temperature and emissivity of torrefied biomass and coal in group particle combustion

This laboratory study reports results on the group particle combustion of pulverized bituminous coal and various types of torrefied biomass. Combustion of particle streams in a drop tube furnace in air was concurrently monitored by a spectrometer and an electronic camera to obtain spectral emissivities and temperatures. As particle number density (PND) increased, biomass particles became more prone than coal to group combustion. Spectral emissivities increased with increasing PND from 0.2 to 0.4 for coal and from 0.1 to 0.3 for biomass, in the wavelength domain of λ = 600–1000 nm. Emissivities changed little with wavelength, giving credence to the gray body assumption. Particle cloud temperatures were in the range of 1650–1900 K, depending on PND, type of fuel, and location in the cloud; temperatures decreased with increasing PND. The radiative heat of the particle laden flames was predominantly attributed to burning chars in the flames and it increased with increasing PND.

Comparative radiative property measurements of single biomass and coal particles burning at high reactor temperatures

This research measured the emissivity, temperature and soot loading of pulverized bituminous coal and three types of renewable biomass. Combustion occurred in a laboratory-scale drop tube furnace (DTF), where the fuels experienced high heating rates and ignited and burned in two distinct phases: devolatilization accompanied by volatile matter combustion in envelope flames, and sequential combustion of the char residues. Multi-wavelength spectrometry was used to concurrently determine the emissivity and the temperature of burning particles at discrete points in their history. Three-wavelength pyrometry was used to obtain entire temperature-time histories, and high-speed photography was used to provide both visual observations of phenomena and to obtain two-dimensional temperature distributions. Results showed that soot in volatile matter flames of burning single particles of the bituminous coal and of the three types of torrefied biomass had spectral emissivities in the range of 0.03–0.10, in the wavelength domain of 600–1000 nm. Emissivities were nearly constant with wavelength, i.e., soot mantles in these flames radiated as graybodies. Spectral emissivities of the chars of the bituminous coal and the three types of torrefied biomass were in the range of 0.29–0.5 and varied with wavelength, i.e., they radiated as non-graybodies. The highest measured temperatures of soot in volatile flames for all fuels were between 2150 and 2360 K and maximum temperatures of chars were between 1700 and 2000 K, based on the three measurement techniques. The graybody assumption caused negligible (± 10 K) deviations in volatile matter flame temperatures; however, it caused significant deviations (± 20–100 K) in char temperatures. Envelope flame diameters of torrefied biomass particles were larger than those of coal. To the contrary, soot volume fractions in the envelope flames of coal particles were found to be higher than those in biomass particle flames. Finally, the soot volume fractions in the flames of these fuels were inversely proportional to particle size.

Development of Two-Color pyrometry for flame impingement on oxidized metal surfaces

Measuring the temperature on a metal surface exposed to flame impingement is valuable for studying heat transfer. In this study, a non-intrusive two-color pyrometry was developed. It utilized visible light cameras to measure the two-dimensional temperature distribution on different metal surfaces. The experiment involved measuring the temperature distribution of metals (stainless steel, titanium, molybdenum) ranging from 700 °C to 1200 °C under flame impingement conditions. Thermocouple measurements were used as a reference for accuracy and uncertainty assessment. Two monochrome visible-light cameras equipped with optical filters at wavelengths of 750 nm and 905 nm captured different signal intensities corresponding to relative radiation temperatures. Calibration using a black body furnace at multiple temperature points was performed to enhance measurement accuracy. The variation in correction factor was assessed for shutter speeds ranging from 0.01 s to 0.03 s. An uncertainty analysis accounted for factors such as the grey body assumption, monochromatic wavelength assumption, and thermal radiation sources, and the respective uncertainties for these factors were 4.72 %, 2.5 %, and 1.02 %. Despite the presence of severe oxidation layers on the surfaces being measured, the two-color pyrometer successfully detected surface temperatures within an acceptable margin of error; the maximum relative error between the pyrometer and thermocouples was less than 4 %. This paper presents a technique for measuring temperature that produces a two-dimensional temperature distribution. Additionally, this method mitigates the effects of changes in surface emissivity due to temperature or materials.

The interstellar dust emission spectrum

Context. Most of the modelling of the interstellar dust infrared emission spectrum is done by assuming some variations around a single-temperature grey-body approximation. For example, the foreground modelling of Planck mission maps involves a single dust temperature, T, along a given line-of-sight with a single emissivity index, β. The two parameters are then fitted and therefore variable from one line-of-sight to the other. Aims. Our aim is to go beyond that modelling in an economical way. Methods. We model the dust spectrum with a temperature distribution around the mean value and show that only the second temperature moment matters. We advocate the use of the temperature logarithm as the proper variable. Results. If the interstellar medium is not too heterogeneous, there is a universal analytical spectrum, which is derived here, that goes beyond the grey-body assumption. We show how the cosmic microwave background radiatively interacts with the dust spectrum (a non-negligible corrective term at millimetre wavelengths). Finally, we construct a universal ladder of discrete temperatures, which gives a minimal and fast description of dust emission spectra as measured by photometric mapping instruments that lends itself to an almost linear fitting. This data modelling can include contributions from the cosmic infrared background fluctuations.

Radiometric Temperature Determination in Nongray Bridgmanite: Applications to Melting Curve and Post‐Perovskite Transition Boundary in the Lower Mantle

AbstractExperiments in laser‐heated diamond anvil cells (LH DACs) are conducted to assess phase diagrams of planetary materials at high pressure‐temperature (P‐T) conditions; thus, reliable determination of temperature in LH DAC experiments is essential. Radiometric temperature determination in LH DACs relies on the assumption of sample's wavelength‐independent optical properties (graybody assumption), which is not justified for major lower mantle materials. The result is that experimental phase diagrams contain systematic unconstrained errors. Here we estimate the systematic error in radiometric temperature of nongray polycrystalline bridgmanite (Bgm; Mg0.96Fe2+0.036Fe3+0.014Si0.99O3) in a LH DAC by modeling emission and absorption of thermal radiation in a sample with experimentally‐constrained optical properties. A comparison to experimental data validates the models and reveals that thermal spectra measured in LH DAC experiments record the interaction of radiation with the hot nongray sample. The graybody assumption in the experiments on translucent Bgm (light extinction coefficient, k < ∼250 cm‐1 at 500–900 nm) yields temperatures ∼5% higher than the maximum temperature in the sample heated to ∼1900 K. In contrast, the graybody temperature of dark Bgm (k > ∼1500 cm−1), such as that produced upon melt quenching in LH DACs, underestimates the maximum temperature by ∼10%. Our experimental results pose quantitative constraints on the effect of nongray optical properties on the uncertainty of radiometric temperature determination in Bgm in the LH DACs. Evaluating nongray temperature in the future would enable a revision of the Bgm to post‐perovskite phase transition and the high‐pressure melting curve of Bgm.

Radiometric Temperature Measurements in Nongray Ferropericlase With Pressure‐ Spin‐ and Temperature‐Dependent Optical Properties

AbstractAccurate temperature determination is central to measurements of physical and chemical properties in laser‐heated (LH) diamond anvil cells (DACs). Because the optical properties of samples at high pressure‐temperature (P‐T) conditions are generally unknown, virtually all LH DAC studies employ the graybody assumption (i.e., wavelength‐independent emissivity and absorptivity). Here we test the adequacy of this assumption for ferropericlase (13 mol.% Fe), the second most abundant mineral in the Earth's lower mantle. We model the wavelength‐dependent emission and absorption of thermal radiation in samples of variable geometry and with absorption coefficients experimentally constrained at lower mantle P and P‐T. The graybody assumption in LH DAC experiments on nongray ferropericlase contributes moderate systematic errors within ±200 K at 40, 75, and 135 GPa and T < 2300 K for all plausible sample geometries. However, at core‐mantle boundary P‐T conditions (135 GPa, 4000 K) the graybody assumption may underestimate the peak temperature in the DAC by up to 600 K in self‐insulated samples due to selective light attenuation in highly opaque ferropericlase. Our results allow insights into the apparent discrepancy between available ferropericlase melting studies and offer practical guidance for accurate measurements of its solidus in LH DACs. More generally, the results of this work demonstrate that reliable temperature measurements in LH DACs require that the optical and geometrical properties of the samples are established.

Modeling Hot Spot Experiments on Shocked Octahydro‐1,3,5,7‐Tetranitro‐1,3,5,7‐Tetrazocine

AbstractFor the first time, mesoscale simulations of shocked explosives are validated with hot spot temperature data. Following recent experiments, we simulate a 25 μm aluminum flyer impacting a powder bed of octahydro‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocine (HMX) with an initial speed of 1.4 to 3.6 km s−1. The powder bed has a density of 0.56 g cm3, or 29 % crystal density, and an average grain size of 4 m. Simulations are performed in the multi‐physics code, ALE3D. We employ a comprehensive HMX material model that accounts for the chemistry, unreacted and product equation‐of‐states (EOSs), elastic‐plastic response, as well as melting and melt viscosity. Simulations show compaction, reaction, and gas jetting during the initial stages of shock in the powder bed. Shock reflection at the glass window interface increases hot spot temperatures in HMX product gas in excess of 7000 K at higher impact speeds which is readily observable using pyrometry techniques. We extract a temperature histogram from simulations at discrete times, using it to calculate an effective emission spectrum and effective temperature, Teff, for comparison to data. Simple T‐ and T4‐based methods inadequately weight the higher temperature regions and result in a low Teff that is in poor agreement with data. However, calculating Teff based on Planck's Law with a gray body assumption demonstrates good agreement with hot spot temperature data. A modified Arrhenius model is fit to the normalized reaction rates predicted by mesoscale simulations and inferred temperatures range from 1544 K to 1779 K; these temperatures are approximately 4x lower than the peak hot spot temperatures but 2‐3x higher than the bulk shock temperatures. The agreement with experimental results validates our mesoscale simulations as useful tools for elucidating the role of hot spot mechanisms in the shock initiation of heterogeneous explosives.

The Heat Transfer Problem in a Rigid and Nonconvex Gray Body with Temperature Dependent Thermal Conductivity

This work studies coupled steady-state conduction-radiation heat transfer in a non-convex gray body when the thermal conductivity temperature-dependent. The gray-body assumption is an improvement with respect to the black body model, because in this model a portion of the incident radiant energy can be reflected from the body boundary. The problem is mathematically described by a nonlinear partial differential equation subjected to a nonlinear boundary condition involving a Fredholm operator which arises from the non-convexity of the body. In this problem the absolute temperature distribution is the unknown, as in the case of a black body. The Kirchhoff transformation is employed to linearize the partial differential equation, giving rise to new boundary conditions. The solution of the problem is constructed by a proposed iterative procedure, employing sequences that involve the temperature and the radiosity. The convergence is explicitly demonstrated. Besides, an error estimate, for each element, is presented. It is remarkable that the results obtained for black bodies are a particular case of this work. In other words, the results presented in reference [1] consists of a particular case of this paper, obtained when the emissivity is equal to one.

Laser heating investigation of the high-temperature interaction between zirconium and UO2

The present work aims to improve accuracy of solid/liquid transition temperatures in Zr-rich corner of the U-Zr-O ternary system, where no experimental data are available in literature. A laser heating technique has been used to investigate three compositions close to the section Zr-UO2. A clear melting/solidification thermal arrest has been observed in the Zr-richer (86.4 at% Zr) composition. A double transition has been recorded for the compositions with higher uranium dioxide content (76.8 at% Zr and 65.5 at% Zr, respectively). Interestingly, the lowest temperatures at which the second thermal arrests occur in the latter two compositions are lower than the melting point retained for pure Zr (2125 K approximately). This suggests the presence, in this part of the phase diagram, of a minimum liquefaction point. Emissivity of the investigated samples has been obtained with a multi-wavelength pyrometer within the grey-body assumption: this is reasonable in a narrow wavelength range between the visible and the near infrared spectral domain. However, further investigation on the optical properties of this set of alloys might allow to reduce the uncertainty on the measured transition temperatures.

Flash Smelting Copper Concentrates Spectral Emission Measurements.

In this paper, we report on spectral features emitted by a reaction shaft occurring in flash smelting of copper concentrates containing sulfide copper minerals such as chalcopyrite (CuFeS2), bornite (Cu5FeS4) and pyrite (FeS2). Different combustion conditions are addressed, such as sulfur-copper ratio and oxygen excess. Temperature and spectral emissivity features are estimated for each case by using the two wavelength method and radiometric models. The most relevant results have shown an increasing intensity behavior for higher sulfur-copper ratios and oxygen contents, where emissivity is almost constant along the visible spectrum range for all cases, which validates the gray body assumption. CuO and FeO emission line features along the visible spectrum appear to be a sensing alternative for describing the combustion reactions.

Study of an improved two-colour method integrated with the emissivity ratio model and its application to air- and oxy-fuel flames in industrial furnaces

Inspired by the multi-wavelength method, the present work innovatively introduces an easier-to-describe emissivity ratio model to replace the customary grey body assumption, thus polishing the algorithm of the traditional two-colour method. The precision of this method was verified with a blackbody furnace, for which the relative errors were within ±1.50%. In situ experiments show that the air-coal flame in a stokerfeed boiler is significantly close to a grey body over the detected wavelength range of 600–1000 nm, except for the emission/absorption lines, and a nearly negligible disparity (25.58 K) is found between the temperature outcome of the improved method and that of the traditional method. The oxy-coke flame in a pilot-scale test facility, however, differs from a grey body to a certain degree within that range, resulting in the deviation of the temperature obtained by the traditional method from that obtained by the improved method by more than 190 K. Obviously, the traditional method is no longer valid in this case. Thus, the two-colour method is sensitive to emissivity variations of the target, and the grey body assumption incurs distinct restrictions on application of the traditional method, thereby highlighting the advantages of the improved method.

Measurement and theoretical prediction on the surface emittance of carbonized layer of silica/phenolic ablative material

As a typical fiber reinforced resin-based ablative material, silica/phenolic composite has important applications in the thermal protection of high-speed aircrafts. At high temperature, it can form a carbonized layer, whose surface emittance is directly related to its capacity of radiative heat dissipation. In this work, carbonization experiments of the silica/phenolic composite and pure phenolic resin were designed to obtain their corresponding carbonized samples. The spectral emittances in the wavelength range from 2.5 to 25 μm of the carbonized samples were measured by a Fourier transform infrared spectroscopy with a blackbody furnace and a sample heater at temperatures from 200 to 500 °C. The results showed that the spectral emittance of the carbonized ablative material is close to that of the carbonized phenolic resin. The spectral emittances of the two carbonized samples increase with temperature and almost do not change with wavelength, indicating that the carbonized samples have the nature of a grey body. A prediction model of the total emittance was constructed based on the grey body assumption and a geometric model extracted from structure characterization of the carbonized ablative material. The predicted total emittances and those obtained from the integration of the measured spectral results are all higher than 0.8, and the deviations are below 10%. Theoretical predictions of the model show that the total emittance of the carbonized ablative material increases with the increasing porosity (ϕ) and total emittance (εs) of the fiber bundle covered with carbonized phenolic resin. Both the experimental and theoretical results reveal that the high total emittance of the carbonized silica/phenolic ablative material can be mainly attributed to the high emittance of the carbonized phenolic resin.

Assessing the use of an infrared spectrum hyperpixel array imager to measure temperature during additive and subtractive manufacturing.

Accurate non-contact temperature measurement is important to optimize manufacturing processes. This applies to both additive (3D printing) and subtractive (material removal by machining) manufacturing. Performing accurate single wavelength thermography suffers numerous challenges. A potential alternative is hyperpixel array hyperspectral imaging. Focusing on metals, this paper discusses issues involved such as unknown or changing emissivity, inaccurate greybody assumptions, motion blur, and size of source effects. The algorithm which converts measured thermal spectra to emissivity and temperature uses a customized multistep non-linear equation solver to determine the best-fit emission curve. Emissivity dependence on wavelength may be assumed uniform or have a relationship typical for metals. The custom software displays residuals for intensity, temperature, and emissivity to gauge the correctness of the greybody assumption. Initial results are shown from a laser powder-bed fusion additive process, as well as a machining process. In addition, the effects of motion blur are analyzed, which occurs in both additive and subtractive manufacturing processes. In a laser powder-bed fusion additive process, the scanning laser causes the melt pool to move rapidly, causing a motion blur-like effect. In machining, measuring temperature of the rapidly moving chip is a desirable goal to develop and validate simulations of the cutting process. A moving slit target is imaged to characterize how the measured temperature values are affected by motion of a measured target.

Fast calculating method for radiative heat shielding by polydisperse and anisotropic scattering water sprays

For the purpose of improving the calculation efficiency of shielding and attenuating thermal radiation in fire protection with polydisperse and anisotropic fine water sprays, a database of radiative properties of sprays covering the wavelength range of 1–20μm and droplets radius range of 1–300μm is constructed. Also a method of combining database calls for radiative properties acquisition and combined spectral radiation and gray body radiation model for solving radiative heat transfer equation is proposed, and is validated by comparing the dimensionless radiative heat flux obtained by the method and that obtained by Mie theory and spectral bands model. By accuracy and efficiency analysis, the database calls for getting radiative properties are found to be accurate and with high efficiency. The accuracy of Spectral-Grey model depends on the wavelength range of gray body assumption. Choosing reasonable gray body assumption bands according to the droplets sizes and loading will not only guarantee the calculation accuracy at an acceptable level, but also reduce the CPU time significantly.

Pulverized Coal-Fired Flame Temperature and Emissivity Measurement Based on Spectral Analysis and the Two-Color Method

A method for judging the gray property of flames based on spectral analysis and the two-color method for determining the temperature and emissivity of flame has been demonstrated. A calibrated spectrometer system was used for the data acquisition of the radiation intensity profile of a flame over a range of wavelengths (200 – 1100 nm). The wavelength range that meets the gray body assumption, in which the emissivity can be assumed as a constant, can be determined from the emissivity profile obtained by spectral analysis and the two-color method. Then the temperature and emissivity of the flame and their relative mean square deviations were calculated within that range. Experiments were conducted on pulverized coal-fired flames in a commercial 300MW boiler furnace. The results show that the coal-fired flame can be assumed as gray body between 500 nm and 1000 nm, and the temperature and emissivity calculation results of coal-fired flames are found to be in reasonable agreement with results using other methods from the literature.

The robustness of the two‐colour assumption in pyrometry of solidifying AISI D2 alloy droplets

A drop tube‐impulse atomization technique was used to produce D2 tool steel powders. Shadowgraph (Sizing Master Shadow from LaVision GmbH in Göttingen, Germany) was utilized to measure in‐situ velocity and droplet size. Simultaneously, the DPV‐2000 (Tecnar Automation Ltée, St. Hubert Quebec, Canada) was used to measure the radiant energy and droplet size of atomized droplets. These devices were mounted on a 3D translation stage which was designed, constructed and installed in the drop tube. The measurements were done at three different distances from the molten metal crucible, 4 cm, 18 cm and 28 cm. A thermal model of droplet cooling was coupled with the temperature of primary phase undercooling for D2 tool steel. The results from this model were used in order to find the emissivity behaviour of the droplets. It is shown that emissivity of the droplets is a function of size and temperature. It was concluded that the DPV‐2000 should be considered as a single color pyrometer since the gray body assumption for D2 tool steel falling droplets using DPV‐2000 during is invalid for the range of measurements taken.

High Precision Multicolorimetric Pyrometer With a Novel Photoelectric MOSFET

Colorimetric thermometry is a useful method for high temperature measurement. In this paper, a high precision multicolorimetric pyrometer is introduced. A multicolorimetric calculation without the gray body assumption is deduced. A novel photoelectric MOSFET with direct ac signal output is employed as the sensor, which works near the visible waveband and brings smaller uncertainty under the Wien approximation than the infrared radiation detectors. A dual-processor embedded signal process circuit is constructed, which ensures the pyrometer's portability as well as supports the accuracy of colorimetric calculation. Through the tests, the precision of the pyrometer is better than 30/00 in the temperature range 1323-1923 K.

Experimental confirmation of the MWIR and LWIR grey body assumption for vegetation fire flame emissivity

The temperature and emissivity of forest fire flames play a key role in understanding fire behaviour, modelling fire spread and calculating fire parameters by means of active fire thermal remote sensing. Essential to many of these is the often-made assumption that vegetation fire flames behave as grey bodies in the infrared (IR). Although the emissivity of flames and its relationship to flame depth has been measured experimentally using thermal imagers working in the long-wave IR (LWIR, 8–12µm), no published study has yet demonstrated relationships in the important mid-wave IR (MWIR, 3–5µm) spectral region, nor conclusively demonstrated that assumptions about grey body behaviour across these two important IR atmospheric windows fit well with reality. Our study explores these issues using measurements of boreal forest fuels burned with flame depths ranging from 0.2 to 4.2 m. Observations of two stable black body sources made through the differing flame depths were used to explore flame spectral emissivities and their relationship to flame depth. We found essentially the same relationship between flame emissivity and flame depth for both spectral regions, (extinction coefficient K=0.7 m–1), confirming that the grey body assumption for forest fire flames in the MWIR and LWIR atmospheric windows appears valid for the fire conditions encountered here.

Three improved methods for measuring spectral emissivity based on the FTIR spectrometer

To minimize the uncertainties related to the FTIR spectrometer, three improved methods were proposed to measure the spectral emissivity. For method 1 (M-1) and method 2 (M-2), an invented device was used to change the environment radiation which makes the ill conditioned equation solvable. Method 3 (M-3) is based on the gray body assumption, and an iterative procedure was applied to derive the temperature of samples, then the spectral emissivity can be retrieved based on this temperature and the FTIR measurements. In order to validate these methods, the emissivity derived from the measured temperature was used as a reference. The results indicate that for the samples with high emissivity, such as quartz plates and cardboard, three improved methods have comparable accuracy; while for the samples with low emissivity, such as rusty iron plate and aluminum plate, the M-3 is more reliable than the other two methods. M-1 and M-2 need to go through more procedures than M-3, and this may lead to some deviation from the reality. Overall, three improved methods greatly improved the spectral emissivity measurements with FTIR spectrometer.

Definition of brightness temperature and restoration of true temperature in laser cladding using infrared camera

Laser cladding is a surface engineering technique allowing depositing material of a different nature in the form of a powder or a wire on the surface of a metallic part.In this study, the laser cladding technique was used to deposit TiAl6V4 coating on TiAl6V4 substrate to study repairing of worn parts. An infrared camera was applied to measure radiation emission field that was transformed into brightness temperature after camera calibration by a black body. The emissivity value was found using known temperature of liquid–solid transition. True temperature profiles in cladded bead, temperature evolution at liquid–solid transition and cooling rates were found using gray body assumption.