Particle effects on the emissivity and temperature of optically thick, mixed media retrieved by mid-IR emission spectroscopy

Passive diagnostics offer new ways of obtaining real-time data for the control and modeling of industrial furnaces. It has been proposed elsewhere that from the intensity profile between 3.8 and 4.7 μm one may derive the temperature of a gas-particle medium and the particle emissivity (ε_p) at 3.95 μm. This technique applies to large columns of combustion products with enough CO₂. The temperature is retrieved by finding the best fit between Planck's function and the intensity profile between 4.56 and 4.7 μm, which is that of a blackbody due to CO₂ saturation. Here we consider the effect of particles on the intensity profile and, therefore, on the retrieved temperature and particle emissivity. We derive an analytic approximation of the effective emissivity for an optically thick gas-particle mixture that includes emission and absorption due to particles and gases, along with isotropic particle scattering. The derivation follows the method of embedded invariance and has been used already for particle-only clouds. It yields a spectral solution that is applicable in other infrared regions where gas and particle optical thicknesses are large. A key parameter (χ) is the ratio of the gas absorption coefficient to the particle extinction coefficient. For χ=1 and ε_p=0.5, particle effects decrease the gas band profile by 5% from that of a blackbody. For χ<1 and ε_p<0.5, particle effects on the calculated temperature and particle emissivity are noticeable and particle effects should be considered. If χ is known, an iterative procedure may be used to calculate temperature and particle emissivity. We illustrate this procedure with data from a coal-fired boiler. Accounting for particle effects, temperatures were 4% higher (at about 1500 K) and particle emissivities 28% lower (for ε_p within 0.3-05) than without considering these effects.