PLIF AND IMAGE CHEMILUMINESCENCE
4.9 CH 2 O PLIF Results
4.9.1 Reduced CH 2 O PLIF Data
CH2O PLIF experiments were performed for all nine defined drive frequencies. (The seven base drive frequencies plus the two supplemental drive frequencies.) The reduced CH2O data is presented in its entirety in appendix H. Figure 4-23 shows a sample CH2O PLIF image of the flame under steady-state conditions (no acoustic forcing). As before, the horizontal axis represents the radius from the centerline of the burner, and the vertical axis represents the height above the nozzle exit plane. The stagnation body height is at z = 21 mm, which is shown as the top line of the graph frame. Also, as before, the data has been mirrored across the centerline of the burner to complete the visual appearance. The intensity scale presented has been normalized around the maximum intensity in the image.
Examining the steady image presented in Figure 4-23, it quickly becomes apparent that using formaldehyde PLIF as an independent indicator of the global or spatially resolved heat release rate is an unwise choice. The reason is that formaldehyde has an indefinite lifetime at low temperatures when it is not surrounded by an active radical pool. This can be seen by the “wings”
appearing on either side of the flame in the image above. Here, CH2O has escaped the edge of the flame and has entered the cooler, air-dominated surroundings where it persists. This type of residual adds an unknown, variable (during unsteady conditions), and frequently large contribution to the PLIF signal that is not directly related to the heat release rate.
Figure 4-24 shows typical results for the corrected, phase resolved CH2O PLIF images.
The presented images are for the 55 Hz acoustic drive frequency experiment. Only 12 of the 24 generated images are displayed. The phase angles shown follow the same conventions as described previously.
Figure 4-23: CH2O PLIF image of experimental burner flame under steady conditions (no acoustic forcing). Collected data appears on the left, and is mirrored across the centerline for a visual representation of entire flame. φ = 0.85, VR = 4.0
As was done before, the intensities of the 24 images for each drive frequency case were fully integrated (including the r dependence) and then processed by FFT in order to generate the global combustion response and forced Rayleigh index for the nine acoustic drive frequencies. The results are shown in Table 4-4.
Drive Combustion Forced Rayleigh Frequency (Hz) Response, H(s) Index, Rf
Mag Phase
55 170 -41.9 127
75 125 131.6 -83.3
100 183 62.1 85.9
150 20.7 -51.6 12.8
220 6.72 1.5 6.72
240 27.6 -49.8 17.8
243 50.9 9.8 50.2
265 22.7 -28.0 20.0
375 57.0 75.8 14.0
Table 4-4: Global unsteady combustion responses as discerned using CH2O PLIF for all nine prescribed drive frequencies. Positive phases correspond to the heat release lagging the pressure.
Figure 4-24: Phase resolved CH2O PLIF images for acoustic forcing at 55 Hz. The horizontal axis is the radius (mm) from the centerline of the burner. The vertical axis is the distance (mm) above the nozzle exit plane. Phase angle θ = 0º corresponds to the rising-edge zero crossing of the local unsteady pressure. Data from experiment 709. Burner operating parameters are: φ = 0.85, VR = 4.0
Magnitude
Frequency (Hz)
100.0 1000.0
1.0E-2 1.0E-1 1.0E+0 1.0E+1 1.0E+2 1.0E+3
20.0
Phase (deg)
Frequency (Hz)
100.0 1000.0
-2160 -1800 -1440 -1080 -720 -360
20.0
Figure 4-25: Combustion response function - points computed from CH2O PLIF data (shown as crosshairs) superimposed on the curves computed from the bulk
chemiluminescence experiments. Phase data points were placed on the appropriate branch for closest proximity to the curve. Here, negative phases correspond to I’ lagging p’.
Figure 4-26: Forced Rayleigh index - points computed from CH2O PLIF data (shown as crosshairs) superimposed on the curves computed from the bulk chemiluminescence experiments.
100.0 1000.0
-2000.0 -1000.0 0.0 1000.0 2000.0
20.0 Forced Rayleigh Index (Rf)
Frequency (Hz)
These data points can then be plotted on the graphs for the global combustion response function and the global forced Rayleigh index that were generated by bulk chemiluminescence measurements for the relevant test condition in chapter 3. These are shown in Figures 4-25 and 4- 26.
As predicted, the formaldehyde data is in very poor agreement with the baseline bulk chemiluminescence data. Examining Figure 4-25, it can be seen that the global magnitudes for drive frequencies of 150 Hz and lower fall woefully short of the baseline values. For the cases where the drive frequency is 240 Hz or higher, the magnitudes overshoot the baseline data in a fashion similar to that seen in the previous cases. However, the CH2O data points for these frequencies are noticeably erratic and exhibit less of a trend than was seen in the previous data.
Phase data in Figure 4-25 also shows substantial disagreement with the chemiluminescence baseline. Phase errors are large and occur in both directions; the low frequency data points tend to lead the baseline while higher frequency points tend to lag the baseline. Errors nearing 180° are present which hint at the possibility that some errors may actually be larger than shown but the corresponding data points have had the fortune of being placed on the incorrect branch during plotting.
Figure 4-26 repeats the forced Rayleigh index plot generated from the baseline bulk chemiluminescence data. This time, the CH2O PLIF-generated forced Rayleigh index data points are displayed on the graph. Points representing 55 Hz and 150 Hz drive frequencies show large errors. The intervening points at 75 Hz and 100 Hz appear to be in fair agreement with the chemiluminescence data; however, this is merely a coincidence as incorrect magnitudes and phases have conspired together to produce nearly correct results. Data points at 240 Hz and higher have Forced Rayleigh Indices that are small, being comparable to the baseline; however, this (again) is not necessarily for the correct reasons.
The spatially resolved functions produced by using the CH2O PLIF data as an indicator of heat release are shown in the next two figures. Figure 4-27 presents the spatially resolved combustion response function plots for each drive frequency with the magnitude images appearing on the left and the phase images appearing on the right. These plots show a banded appearance (with two bands) similar to what was seen in the CH PLIF images. As with the previous case, vertically displaced bands are observed for locations at smaller radii (r < 10 mm). This is seen to be true throughout the drive frequency range. For drive frequencies of 150 Hz and lower, however, the bands in the CH2O data take on a “head and tail” appearance similar to what was seen in the OH PLIF data; for the upper bands, prominent lobes appear at larger radii. Indeed, these bands bear a striking resemblance to their counterparts seen in the OH PLIF images. The lower bands, on the other hand, display much smaller lobes which are typically nestled under and to the inside of their larger associates. Visual inspection of the images reveal that the features with the largest magnitudes appear in the 75 Hz plot versus the 55 Hz plot as was the case in the OH data.
While some commonality in features was noted between the CH2O PLIF images and the corresponding OH PLIF data, an interesting parallel is also seen in the phase behavior between the formaldehyde PLIF images and their counterparts in the CH PLIF data. In examining the right- hand plots in Figure 4-27, the phases seen in the “tail” portions of the formaldehyde PLIF data appear relatively constant in the horizontal regions as a path is traced along each band from small radius to large radius. Furthermore, the phases shown in these “tail” regions are virtually identical to those presented in the corresponding CH PLIF images. Focusing on the low frequency cases (150 Hz and lower), the phase of each “tail” in the upper bands transitions smoothly into their respective “heads,” similar to what was seen in the OH PLIF data; no phase discontinuities appear.
However, for the lower bands in these four cases, the phase transitions between the “tail” and
“head” can be steep, bordering on discontinuous. Despite these aggressive transitions, the variation in phase over the whole area of each “head” is typically less than one complete phase wrap.
Figure 4-27: Spatially resolved combustion response function produced from CH2O PLIF data. Magnitude plots appear in the left column while phase plots are shown on the right.
Note that positive phase values correspond to I’ lagging p’. The coordinate system origin is along the burner centerline at the nozzle exit plane. Data for all nine drive frequencies are shown. (See next two pages.)
Figure 4-27 (cont): Spatially resolved combustion response function produced from CH2O PLIF data. Magnitude plots appear in the left column while phase plots are shown on the right. Data for all nine drive frequencies are shown. (See previous and next page.) Note the change in magnitude scale versus the plots for 150 Hz and lower.
Figure 4-27 (cont.): Spatially resolved combustion response function produced from CH2O PLIF data. Magnitude plots appear in the left column while phase plots are shown on the right. Data for all nine drive frequencies are shown. (See previous two pages.) Note the change in magnitude scale versus the plots for 150 Hz and lower.
Figure 4-28: Spatially resolved forced Rayleigh index produced from CH2O PLIF data. Data for all nine drive frequencies are shown. (See next page.) Note the difference between the magnitude legends for the lower four drive frequencies and the upper five drive frequencies.
Figure 4-28 (cont.): Spatially resolved forced Rayleigh index produced from CH2O PLIF data. Data for all nine drive frequencies are shown. (See previous page.) Note the difference between the magnitude legends for the lower four drive frequencies and the upper five drive frequencies.
For the higher drive frequency plots (220 Hz and greater), the similarities in both magnitude and phase between the CH2O PLIF data and the CH PLIF data are striking. Although the bands in the CH2O images appear slightly thicker than those seen in the CH PLIF images, the distributions of magnitude and phase between the two cases (for each specific drive frequency) are almost identical up to a radial coordinate of approximately 14 mm. Around this radial position, the bands of the CH PLIF images terminate while the bands in the CH2O PLIF continue for up to 3 more millimeters. It is this short area of extension that holds the greatest difference between the two data sets (CH and CH2O PLIF) displayed in the higher frequency regime combustion response function plots. In this extended region, the upper and lower bands in the formaldehyde PLIF generated images diverge slightly and begin taking on a speckled appearance as they dissipate.
Despite this, the progression of phase along these ends is smooth.
Figure 4-28 displays the frames corresponding to the CH2O PLIF spatially resolved forced Rayleigh index for each of the acoustic drive frequencies. Once again, the size of the features in these images is somewhat akin to what was seen in the associated OH PLIF plots, while the double- banded nature is similar to what was displayed in the corresponding CH PLIF images. As observed in the previous CH data, the portions of the bands nearer to the burner centerline run virtually parallel to each other and have opposite sign. Additionally, at all drive frequencies except 75 Hz, the upper band is damping (negative sign) while the lower band is driving (positive sign). For the 75 Hz case, these signs are reversed. In the 55 Hz and 75 Hz images, the region at the outer radii of the flame (r ≈ 10 to 20 mm) is dominated by activity generated by the shear layer structures reaching the reaction zone. The lower band is seen to terminate, allowing a bridge from the upper band to sneak through and form a lobe below the lower band. Beyond this gap, a large lobe forms to the right with a sign that is the same as the lower band. At a drive frequency of 100 Hz, the structure of the response becomes far more complicated. In this case, both bands terminate at approximately the same radial position (r ≈ 12 mm). Beyond this point a host of five lobes appear,
two larger in size and three being small. The largest of these lobes is positive in sign while its counterpart is negative. By visual estimation, it appears there is more area covered in yellow-red zones within the image than there is covered in blue zones. This is consistent with the positive global forced Rayleigh index computed earlier and shown in Table 4-4.
As the drive frequency passes 150 Hz, the spatially resolved forced Rayleigh index develops the alternating lobe pattern observed earlier in the corresponding CH PLIF data. As discussed earlier, this sequence of lobes is generated by a continuous progression of the phase (along the band lines) for multiple wraps. The pattern is roughly centered on the path line that defines the reaction zone. Eight lobes are visible in the 150 Hz acoustic drive case, although three of the blue (damping) zones are not completely independent, but instead show narrow connections to each other. The peak number of lobes is seen at a drive frequency of 220 Hz. Counting the two bands that run back to the burner centerline, the total number of visible lobes is ten. Beyond this frequency, the number of lobes begins to decrease and varying levels of diffuse streaks (driving and/or damping) are seen to the right of the edge of the flame. At 265 Hz, the alternations vanish indicating that, in this case, the phase is relatively constant moving along each band. At 375 Hz, a string of lobes reappears at the outer edge of the flame, while the response near the center (small radius) portion of the flame nearly vanishes due to the phase shift generated by the burner nozzle’s Helmholtz response.