834707668

II3-5

Absorption calculations are shown in Figurę 7 for two different temperatures and optical depths of the absorbing gas. The slit width is .5 mm for which the corresponding spectra! half width is 5.22 A. The computation of the intensities of the OH absorption source was carried out using a vibrational temperaturę of 2400°K and a rotational temperaturę of 1400°K. The electronic temperaturę and optical depth were chosen so that the absolute intensities were equal to those obtained experimentally. The numerically determined spectra of Figurę 7 can be compared to similar experimental spectra shown in Figurę 8 which were obtained during a supersonic combustion experiment in which thermal choking occurred. The absorption source is shown before the onset of combustion in the upper left corner of Figurę 8. The absorption spectra obtained during supersonic and subsonic portions of the combustion experiment are shown in the upper right and lower right, respectively. During the transition from supersonic buming to subsonic buming (thermal choking), highly oscillatory spectra such as that shown in the lower left were occasionally observed.

The four basie modes of operation of the Computer program are illustrated below using the numerically predicted temperaturę and number density profiles² shown in Figures 10 and 11 for an axisymmetric duet and a slit width of 1.0 mm. The optical path was divided into 26 different isothermal layers to approximate these distri-butions.

The results of the simple emission and emission with self-absorption modes of the program for viewing along the diameter of the flowfield are shown in Figurę 12. As can be seen, the effects of self-absorption are strong even though the absolute intensity is quite Iow. The results of the absoption calculations of a discrete OH linę source are illustrated in Figurę 21 for the six optical paths shown in Figurę 20. The associated transmittances are shown in Figurę 22. The rotational and vibrational temperatures for the absorption source used in Figurę 22 were both assumed to be 1500° K. Due to the Iow intensities of the emission spectra shown in Figurę 12, the results of the fourth modę of the program, which includes the effects of emission with self-absorption in addition to the absorption of a discrete OH linę source, were of negligible difference to those of Figurę 21. It is often assumed in spectroscopic studies that the degree of absorption is independent of the absorption source. In other words, the transmittance l/I₀ is assumed to be the same regardless of the temperaturę of the absorption source. Figurę 13 shows the results of numcrical calculations in which two different test gases were specified in conjunction with three different absorption source lamp temperatures. The results show significant dependence on source lamp temperaturę for the region beyond 3110 A in which the 1-1 vibrational band is located (see Figurę 6). It can therefore be seen that the correct rotational and vibrational temperaturę of the source lamp must be known if accurate spectra are to be predicted.

Another assumption which is often madę is that the shape, but not the magnitude, of the transmittance curvcs are independent of optical depth. Figurę 14 shows the results of numerical calculations in which the transmittance of 16 test gases, using four different optical depths and four different temperatures, were determined for a given absorption source temperaturę. As can be seen from Figurę 14, the shapes of the transmittance curves for a given temperaturę definitely are dependent on the optical depth.

USE OF PROGRAM TO GENERATE DIAGNOSTIC TECHNIQUES

As pointed out in the Introduction, a generał diagnostic technique applicable to all cases can not be developed because the spectral half widths of a given spectrometer as well as the rotational and vibrational temperatures of the source lamp must be included in the development of the technique. It is the purpose of this section to give three examples of how the Computer program can be used to generate diagnostic techniques for use in specific cases.

The first technique which will be discussed is the two-wavelength technique which is similar to the two-Iine technique of high resolution spectroscopy. A numerical parametric study has been carried out for the absorption of radiation from a 1500° K equilibrium source through isothermal layers of gas with temperatures ranging between 1000 and 2400° K and optical depths between 1.0 x 10¹⁵ and 5.0 x 10¹⁷ radicals/cm². Figurę 14 shows the results of only a portion of the total number of cases considered. As can be seen from Figurę 14, the ratio I(X, L)/I(X, 0) is very nearly temperaturę independent at X = 3135 A. The degree of temperaturę independence at 3135 A is illustrated in Figurę 15 where the transmittance at 3135 A is plotted as a function of optical depth for various temperatures. Thus, by measuring the transmittance at X = 3135 A, it is possible to determine the optical depth regardless of the temperaturę. Alternately, the widest variations in transmittance as a function of temperaturę as observed in Figurę 14 occurs for wavelengths of 3090 A and 3160 A. The two-wavelength technique is based on determining the ratio of absorptivity at 3090 A or 3160 A to the absorptivity. at 3135 A. The absorptivity, defined as one minus the transmittance, is plotted as a function of optical depth for various temperatures in Figurę 16 for the 3090 A case. As might be expectcd, the normalized absorptivities shown in Figures 16 and 17 are nearly independent of the optical depth for the lower values of optical depth. By observing the transmittance curves of Figurę 14, it can be seen that, below an optical depth of 2.5 x 10¹⁶ radicals/cm², the absorptivity at 3160 A is too Iow to be measured accurately. Likewise, above 2.5 x 10¹⁶ radicals/cm² the absorptivity at 3090 A is not sensitive to increasingly higher optical depths. Thus, oncc the optical depth has been determined from Figurę 15, the temperaturę of an isothermal gas can be determined from either Figures 16 or 17.