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II3-6

The question arises as to what would happen if the two-wavelength technique were applied to the absorption spectra resulting from a non-isothermal distribution of temperaturę. As an example, if the transmittance curve marked with a six in Figurę 22 (which corresponds to the 6th optical path in Figurę 20 and the distributions of temperaturę and OH number density of Figures 10 and 11) is analyzed using Figures 15, 16 and 17, the resulting temperaturę is 1860° K and the optical depth is 1.0 x 10¹⁷. These numbers can be compared to the average temperaturę along the optical path 1740° K and the actual optical depth of 9.0 x 10¹⁶ radicals/cm². When the two-wavelength technique is applied to the theoretical spectra resulting from the radial distributions of temperaturę and OH number density predicted to exist along the diameter at several other axial locations within the combustor, axial distributions of average temperaturę and OH number density can be determined. Figures 19 and 20 show the results of the two-wavelength technique as compared to the actual average temperatures and actual optical depths for three axial locations within the combustor when viewing is limited to optical paths traversing the diameter of the duet. Thus, it appears that the two wavelength technique can be used to obtain optical depths and average temperatures for optical paths along the diameters of an axisymmetric combustor flowfield.

In those instances where off-diameter optical scanning is possible, the two-wavelength technique can be used to obtain the actual radial temperaturę and number density distributions at a given axial location. The entire procedurę is too lengthy to discuss in detail here, but is discussed at length in Reference 9. Basically, the combustor flowfield is assumed to consist of several isothermal rings with corresponding constant OH number densities.

There may be as many rings as there are off-diameter optical seans. Figurę 20 shows a combustor cross section of 11.8 cm diameter which has been divided into six concentric rings with an equal number of optical paths. Numbers proportional to the areas scribed out by the intersection of the optical paths with the concentric rings are assumed equal to the optical path lengths through the various isothermal regions.

The temperaturę and optical depth of the outer isothermal region are determined first using the two-wavclength technique as described above. The OH number density of the outer ring is then determined by dividing by the path length. The second optical path passes through three isothermal regions of which the properties of the outer two are already known. The absorption spectra obtained from the second optical path is adjusted so that the effects of the outer two regions are taken into account or “added back in”, so to speak. The adjusted spectra is then evaluated according to the two-wave!ength technique just as in the case of the outer optical path. In a similar fashion, the spectra from the third and subscquent optical paths are adjusted to take into account the effects of the outer layers for which the properties have already been determined. As the calculations proceed from the outer optical path inward, the errors are additive to some extent so that the properties determined for the inner rings are less accurate than those of the outer rings. The outer rings, however, represent a higher percentage of the total amount of gas for a given cross section than the inner rings.

When the above procedurę was carried out for the six transmittance curves of Figurę 22, the results were as shown in Figures 10 and 11. The maximum number of rings which can be assumed depends on the amount of absorption. Experimentally, it is difficult to measure less than 10 percent absorption at any given wavelength. It is not necessary that a great deal of change occur in the transmittance from one optical path to the next, however, as witnessed by the results shown in Figures 10 and 11 from the 4th, 5th and 6th optical paths for which the transmittance curves are nearly identical.

The second sample diagnostic technique is similar to the isointensity technique used in high resolution spectro-scopy. Instead of finding two spectral lines of equal intensity, two wavelengths of equal transmittance are used to determine the temperaturę. For this second technique, different temperaturę conditions (T_R = 1400° K,

T_v = 2400° K) have been assumed for the narrow linę OH source lamp in an attempt to take into account the “hot” 1-1 vibrational band of the lamp used at ARL for the absorption work. Transmittance curves similar to those of Figurę 14 are given in Figurę 23 for these different source lamp temperatures. The principle on which the isotransmittance method is based is illustrated by the dotted linę denoted as B in Figurę 23. The dotted linę B represents the wavelengths at which the transmittance is equal to the transmittance at 3080°A. As the temperaturę inereases, the wavelength for which the transmittance is equal to that at 3080 A inereases. The temperaturę dependence of this isotransmittance wavelength is shown in Figurę 25 for temperatures ranging from 400 to 2800° K. In a similar fashion, the wavelengths for which the transmittance is equal to the transmittance at 3072 A are shown in Figurę 26 as a function of temperaturę. The isotransmittance wavelengths are weakly dependent on optical depth as can be seen in Figures 25 and 26. The optical depth can be determined, once the approximate temperaturę and minimum transmittance of the spectra are known, by using Figurę 24. In practice, several independent temperatures can be determined from Figures 25, 26 and others like them. The temperatures determined in this fashion are then averaged to reduce cxpcrimental error. The agreement between the individual temperatures before averaging is a good indication of the validity of the technique and the measurements. Experimental results for a supersonic diffusion flame using the isotransmittance technique appear in References 11 and 12.

The most straight-forward technique for analyzing experimental data involves direct comparison with theoretical spectra by the trial-and-error process. Such a procedurę was employed to determine the vibrational and rotational temperaturę of the narrow OH linę source used at ARL. The direct comparison method was also used in the present study for a case in which chemiluminescence was observed to occur. During a supersonic mixing and com-bustion test (References 11 and 12), emission and absorption spectra were obtained. Once the emission spectra had been properly subtracted from the transmittance spectra, a rotational temperaturę of 1310° K and an optical