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Show correction does not properly compensate for a dip in the spectrum at 943 n m that is due to absorption by the fiber optic cable. Table 2 presents the results of fitting instrument-corrected M W P emission spectra using different functions for the wavelength dependence of the emissivity. The results in Table 2 were obtained by combining three different data sets (comprising a total of 120 M W P emission spectra) of the end wall recorded from a single port (Port B, see below); other data sets gave analogous results. The data sets were fit individually and their combined results are presented in Table 2. The results are reported as average values for the three data sets and the standard deviation of their average values. The least squares fits yield temperatures in K; for convenient comparison with results by other techniques, the fit temperatures are reported in °C. The mean square error ( M S E ) can be used as an indication of the goodness of fit. It is seen that allowing for wavelength dependence reduces the M S E and that the more fitting parameters used, the lower the M S E . Based on an extensive study of the fitting results, we conclude that for the emissivity relations considered, e(X) = € 0 best represents the wavelength dependence of the emissivity of the furnace walls in the wavelength region between 700 and 900 nm. A total of 341 wavelength/intensity pairs were used to least squares fit data in spectral region of 700-750 n m and 775-900 nm. Fits to e(X) = €0 + e,A yield € 0 values that are very small and are statistically indistinguishable from zero. The temperatures obtained from fits to e(X) = €,A and also to e(A.) = e0 + e,A are typically on the order of 150°C higher than expected based on measurements by other DIAL systems (see Tables 1 and 4), and emissivities that are lower than expected. Thus, it is concluded that the temperatures and emissivities obtained from fits of e(X) = e,X and also to e(A) = e0 + €,X are unrealistic. The temperatures and emissivities obtained from fits of e(X) = e0 + e,A. + e2X2 are more reasonable, but the variation in the temperatures and emissivities obtained from data set to data set are significantly larger than for the other relationships tested. The e(X) are parabolic in the 700-900 n m region with significantly different wavelengths for the minimum of the parabola for different wall sections; this is not physically reasonable. Moreover, over the fitting range the m a x i m u m and minimum values of e(A.) differ only by about 0.02, which is comparable to our least squares fit uncertainty for emissivity. Fits of e(X) = exp(€0 + e,A,) yield temperatures that are unrealistically high (200°C or more greater than expected) and emissivities that are unrealistically low. Thus of the wavelength dependencies for emissivity that w e considered, the relationship that best describes the wavelength behavior of the wall emissivity is an emissivity that is independent of wavelength. Table 2. Summary of wavelength-dependence least squares fits for furnace wall.* 6(A) e0 €,A e0 + €,A e0 + €,A +e2X2 exp(e0 + e,X) T( C) 1134 ±7 1257 ± 8 1257 ± 8 1205 ±119 1334 ±75 Emissivity 0.75 ± 0.06 0.30 ± 0.02 0.30 ± 0.02 0.60 ± 0.34 0.21 ±0.08 MSE 537 ± 156 390 ±103 390 ± 103 242 ± 98 244 ±96 *€Q, €], and €2 are fitting parameters. MSE = mean square error. Emissivity = emissivity at 900 nm calculated from fitting parameters. Table 3 presents the temperatures and (wavelength-independent) emissivities obtained by recording MWP emission spectra of the furnace wall through selected ports. The measurements at Port B were performed by aiming the probe toward the end wall of the furnace; the different measurements at this location correspond to viewing different portions of the wall. The measurement at both ports were performed by positioning the M W P probe so that M W P had views of only the wall, unobstructed by the tubes. It should be noted that the wall emissivity at Port A is significandy different from that at Port B. The furnace is lined with two different materials: fire brick and fire wool. Fire brick is used in the vicinity of the burners, and the less expensive fire wool is used elsewhere in the furnace. The |
