Gray Body Assumption Research Articles

A steady-state measurement system for total hemispherical emissivity

A steady-state calorimetric technique was developed for measuring the total hemispherical emissivity of a conductive material. The system uses a thin strip of the conductive sample electrically heated by alternating current to high temperatures in a vacuum chamber. The emissivity was measured in a central region of the sample with an approximately uniform temperature distribution. Considering the influences of the gray body assumption, wire heat losses, effects of residual gas and conductive heat loss from the region to the rest of the strip, the emissivity was accurately determined by solving the inverse one-dimension steady-state heat transfer problem. The emissivities of various metal samples (nickel and 45# steel) were measured to verify the system accuracy. And the results were then analyzed to estimate the relative errors of emissivity arising from the gray body assumption, wire heat losses, effects of residual gas, non-uniform temperature distribution and the measurement uncertainty of emissivity. In the temperature range from 700 to 1300 K, the accuracy is acceptable for practical applications within the total measurement uncertainties of 1.1%. To increase the system applicability, some issues related to sample specifications, heating power control and temperature uniformity of sample test section were discussed. Thus, this system can provide accurate measurements of the total hemispherical emissivity of conductive samples at high temperatures.

High-speed digital color imaging pyrometry

Temperature measurements of high-explosive and combustion processes are difficult to obtain due to the speed and environment of the events. To overcome these challenges, we have characterized and calibrated a digital high-speed color camera that may be used to measure the temperature of such events. A two-color ratio method is used to calculate a temperature using the color filter array raw image data and a graybody assumption. If the raw image data are not available, temperatures may be calculated from the processed images or movies, depending on proper analysis of the digital color imaging pipeline. We analyze three transformations within the pipeline (demosaicing, white balance, and gamma correction) to determine their effect on the calculated temperature. Using this technique with a Phantom color camera, we have measured the temperature of exploded C-4 charges. The surface temperature of the resulting fireball was found to rapidly increase after detonation, and subsequently decayed to a constant value of approximately 1980 K.

A calibrated dual-wavelength infrared thermometry approach with non-greybody compensation for machining temperature measurements

We report the development of a new approach for determining temperatures using the dual-wavelength infrared thermometry technique, which does not presume greybody behaviour and compensates for the spectral dependence of emissivity. This approach is based on Planck's radiation equation and explicitly accounts for the wavelength-dependent response of the IR detector and the losses occurring due to each of the elements of the IR imaging system that affect the total radiant energy sensed in different spectral bands. A thorough calibration procedure is utilized to determine a compensation factor for the spectral dependence of emissivity, which is referred to as the non-greybody compensation factor (NGCF). Calibration and validation experiments are carried out on Aluminum 6061-T6 targets with two different surface roughnesses. Results show that this alloy does not exhibit greybody behaviour, even though the two spectral bands used were relatively close to each other, and that the spectral dependence of emissivity is influenced by the surface finish. It is found that non-greybody behaviour of low emissivity surfaces can lead to significant systematic error in dual-wavelength IR thermometry. The inclusion of the NGCF eliminates the systematic error caused by the invalidity of greybody assumption and thus improves the accuracy of the measurements. Non-greybody-compensated dual-wavelength thermography is used to measure the chip temperature along the tool–chip interface during orthogonal cutting of Al 6061-T6 and sample results at three different cutting speeds are presented.

A simple judgment method of gray property of flames based on spectral analysis and the two-color method for measurements of temperatures and emissivity

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 a 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 (200–1100nm). The wavelength range that meets the gray body assumption, in which the emissivity can be assumed to be 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 solidified gasoline and red phosphorus flames, and pulverized coal-fired flames in a commercial 420ton/h boiler furnace. The results show that the gasoline flame can be assumed to be a gray body in the range between 550 and 900nm, for the coal-fired flame the range is between 500 and 1000nm; while the red phosphorus flame cannot be assumed to be a gray body within the measurement wavelength range. The temperature and emissivity calculation results of coal-fired flames are found to be in reasonable agreement with results using other methods described in the literature. The wavelength interval in the two-color method to calculate temperature is also discussed.

Shock‐compressed MgSiO3 glass, enstatite, olivine, and quartz: Optical emission, temperatures, and melting

Optical emission of MgSiO3 glass, enstatite, olivine, and quartz under shock wave compression was investigated with optical pyrometry at discrete wavelengths ranging from visible to near infrared. We develop a new analysis of optical emission that does not require a gray body assumption. Instead, at each wavelength, the optical linear absorption coefficients (a) and blackbody spectral radiances (Lλb) of shocked and unshocked materials were obtained by nonlinear fitting to the time‐resolved radiance from the target assembly. The absorption spectra of unshocked samples corresponding to the measured values of a reproduce those from independent static optical spectroscopic measurements. The measured values of a (ranging from 7 to 56 mm−1) for shocked samples indicate that shock‐induced high‐pressure phases (including melt) can be regarded essentially as black bodies in the optical range investigated, although starting phases such as enstatite and olivine have band‐like spectra at ambient conditions. The effect of emission from the air gap at the driver sample interface on the recorded radiance can be resolved, but a and Lλb cannot be separated for this component of the signal. The shock velocity‐particle velocity relationships of these silicates derived from radiance history are in accord with previous investigations using independent techniques. Given the limited amount of shock wave data, possible high‐pressure melting curves of Mg‐perovskite and its assemblage with periclase are deduced; their melting temperatures near the core‐mantle boundary (CMB) being 6000 ± 500 K and 4000 ± 300 K, respectively. It is proposed that Mg‐perovskite melts with density increase at the CMB pressure.

Research on the validity of the steady-state calorimeter for measuring the total hemispherical emissivity of solids

Under practical experiment conditions the validity of the steady state calorimetric technique for measuring the total hemispherical emissivity of solid surfaces is analysed. The maximum theoretical error resulting from the grey body assumption is estimated. In order to avoid measurements of the surface temperature of nonmetallic samples, a new steady state calorimetric technique is developed. The effects of nonradiative heat losses and various geometric factors are also analysed in detail; their error formulae are exactly derived.

IRAS observations and local properties of interplanetary dust

Thermal emission from the interplanetary dust cloud has been confirmed by IRAS to be the most prominent component of the sky brightness in the 10–25 μm range. It is indeed a severe foreground for astronomical observations. It is also a major source of information on the local properties of the dust grains. Unlike the solar scattered light (zodiacal light), the thermal emission of the grains is isotropic; even more progress can therefore be expected from the inversion of IRAS integrated brightnesses. The pre-IRAS understanding of the interplanetary dust cloud is reviewed. Recent results obtained through inversion methods are presented. In the ecliptic near 1 AU, the heliocentric gradient of temperature is about −0.33, i.e. conflicts with a greybody assumption, while the gradient of albedo is about −0.7, i.e. conflicts with a homogeneous cloud assumption. Out of the ecliptic, the dust distribution is still open to dispute. It is however neither smooth (dust bands and trails, warped symmetry surface), nor homogeneous (location dependence of local polarization or albedo). Such results imply that the mixing ratios of the various interplanetary dust sources (comets, asteroids, β meteoroids) strongly depend upon location in the cloud.

On the temperature and reaction rate of burning pulverized fuels

A two-color pyrometer technique has been used to measure the temperature of burningpulverized fuel particles flowing in dilute suspension on the centerline of a laminar flow reactor. The transparent reactor is fed by a premixed flat flame fueled with CH 4 −H 2 −O 2 −N 2 mixtures, which permit widely variable post-flame temperatures and oxygen concentrations to be obtained. The two-color system employs an optical-electronic system which includes two monochromators to acquire light emission intensity at two wavelengths simultaneously from individual burning particles passing through a 1 mm square area on the centerline of the reactor. Planck's law and the gray body assumption (verified here by measurements) are used to compute particle temperatures, and the average temperature is then determined by averaging the values for some 500 individual particles. Particle temperatures have been determined for various gas temperatures over a range ofoxygen mole fractions from 0 to 0.2 for size-graded (90 μm mean diameter) samples of a petroleum coke and a flash pyrolysis char. Particle burning rates per unit external surface area were determined from the measured temperatures by a heat balance analysis. The functional variation in burning rate with temperature was then used to infer whether the burning rate was controlled by chemical rates (Zone I), the combined effects of chemistry and pore diffusion (Zone II), or bulk diffusion (Zone III). For the petroleum coke, both zone I and Zone II conditions were observed, and chemical rate coefficients for each zone were derived. For the char, Zone II and a transition to Zone III conditions were observed, and a chemical rate coefficient for Zone II was derived. Reaction orders and activation energies were in the range expected from previous oxidation studies, and the chemical rates for both samples were in good agreement with previous measurements by a different method in another laboratory. The results show that careful temperature measurements can provide a sensitive method for the determination of pulverized fuel burning rates.