Optical Depth Effects on Aluminum Oxide Spectral Emissivity

Abstract

Measurements of high-temperature spectral emissivities of aluminum oxide were made within a heterogeneous shock tube over the spectral range of 650-900 nm. The spectral emissivity of optically thin micrometer-scale alumina particles scaled approximately as λ −1.4 from 2800 to 3500 K. Results from optically thin clouds of nanoscale alumina showed that a λ −1.2 dependence, closer to the λ −1 predicted by the Rayleigh limit, is appropriate over the same spectral and temperature ranges. For temperatures below the melting point of alumina, the emissivity of nanoalumina shows a significant temperature dependence. The effect multiple scattering has on the apparent emissivity is studied, and it is determined to contribute to the discrepancy between the current and previous works. A Monte Carlo simulation showed qualitative agreement with the experimental work. It was found that, at small to moderate optical depths, scattering is responsible for a small change in the spectral distribution of particle emissivity. At large optical depths, absorption has a much stronger effect on the apparent spectral emissivity. It was determined that choice of optical depth can strongly affect the results of pyrometry measurements. Nomenclature C = fit parameter F = calibrated spectral signal I = radiant intensity, W∕sr · m 2 L = length scale, m or cm l = length scale, m or cm k = absorptive index n = fit parameter R = randomly generated number R 2 = coefficient of determination T = temperature, K z = model coordinate, cm or m ϵ = emissivity κ = absorption coefficient λ = wavelength, nm or μm σ = scattering coefficient τ = optical depth Subscripts abs = absorption value bb = blackbody value cal = calibration value exp = experimental value new = new value prev = previous value sca = scattering value κ = absorption value λ = spectral dependence σ = scattering value

On the Origin and Use of the Emissivity Approximations for Alumina Particles

“…The resulting expression, Equation (8), has the same dependence on wavelength as Equation (4). If the absorptive indexs cales inversely proportional to wavelength, Equation (9) shows that this analysis gives the same emissivity wavelength dependence as Equation (5). This result was also observedf or solid alumina particles [4,5].…”

“…Equations (6)(7)(8)(9) are valid when the complex index of refraction approaches one [14];h owever, some agreement with Mie theory can be seen for aw ider range of the refractive index [16].P lass [16] showed that for materials whose real refractive index is close to one, Equation (8) is ag ood approximation. However,a sn was increased to-wards 2, the approximation is only valid for x 1( for reference, aluminah as ar eal refractive index near 1.7 [4]).…”

“…Emissivityc alculations showed that larger particles approach ag ray body at smallera bsorptive indices thant he smaller particles. This result can be rationalized by considering the results of reference [9],w here the characteristic absorption length (based on the particle radiative properties) is comparable the characteristic physical length scale (i.e. particle diameteri nt his case).…”

“…Recently,t he spectral emissivity of high purity alumina particlesw as measured at elevated temperatures relevant to aluminum combustion [3,9].T hese studiesh ave shown that the assumptions mentioned above may not be accurate for certain conditions basedu pon opticald epth, temperature, or material [10].T his work focuses on providing […”

Depression of melting point for protective aluminum oxide films

“…The experimental emission curve is first calibrated to account for the instrument's spectral response prior to comparison with the black body curve. Figure 2 shows an example power law fit (ε∼ −2.94 ) for the relative wavelength dependence of the particles at 1521 K. It was previously shown that the wavelength dependence of the emissivity properties of nano-alumina particles is affected by the phase of the material [13]. A similar effect is expected for micron sized aluminum particles with nanometer thin oxide layers.…”