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For all experiments in the investigation of dual tracer fluorescence, the incident X-ray beam was set to 10.1 keV. This energy is low enough to enable significant attenuation in the liquid while also exciting both liquid and gas-phase x-ray fluorescence. To excite liquid fluorescence, 200 ppm of nickel sulfate hexahydrate (7.5 keV Kα, 8.3 keV Kβ) and 200 ppm of zinc sulfate heptahydrate (8.6 keV Kα, 9.6 keV Kβ) were dissolved in water. The liquid properties of the salt solutions were similar to water within the accuracy of the measurements of viscosity (∼1%) and surface tension (∼3%), using a falling ball rheometer and force tensiometer, respectively.

Previous investigations have shown that the use of two tracer species allow for correction of fluorescence reabsorption through the spray to an accuracy of approximately 5% by comparing

Figure 4.17: Example showing uncorrected spectrum for transverse locations across the scan at a location of 1.6 mm (x/D0 = 0.16)from the injector exit.

the ratio of detected fluorescence from the two species (Halls et al. (2015)). If the attenuation from the location of fluorescence signal generation to the detector is large, for example, then the lower energy fluorescence from nickel will be more highly attenuated than that from zinc.

Gas phase fluorescence of argon was collected simultaneously with the liquid phase fluores- cence. Argon also strongly absorbs x-rays, providing measurable contrast between argon and ambient air. In this manner, the gas-phase distribution can be measured by either directly us- ing the argon fluorescence signal (after correction for reabsorption) or by subtracting the liquid path length, measured using fluorescence, from the total liquid and gas-phase path lengths, measured using radiography. An example line plots of total liquid and gas-phase path lengths measured from radiographs are shown in Fig. 4.18a. Note that the units of extinction lengths are not quantitative, as they assume an absorption coefficient of 1.

To obtain a quantitative measurement of the equivalent path length (EPL) of argon at each transverse location, a multi-step post-processing procedure was performed to correct for reabsorption.

First, a cuvette study is performed where a correlation equation is determined between the absorption path length (thickness of the cuvette) and fluorescence yield at the detector for each liquid tracer at their concentration in water. By traversing the signal across the width of

(a) Total extinction lengths (b) Water extinction only

Figure 4.18: Example line plots showing (a) total extinction lengths from attenuation and (b) the extinction lengths of the water correlated from the measured fluorescence signal of the liquid tracers. Note units of extinction length are arbitrary.

the cuvette, the equation takes into account self reabsorption of the liquid and any potentially scattering effects. Additionally, by using two tracers, the differential absorption of the tracers allowed (due to different fluorescence wavelength) for the compensation of reabsorption of the photons from the liquid across the scan. These effects can be observed in raw fluorescences traces shown in 4.17.

Once the correlation equation is created, the measured fluorescence yield of the liquid tracers can be correlated to an expected liquid path length, shown in Fig. 4.18b. By subtracting the calculated liquid path length (from the liquid fluorescence) from the total attenuation (calculated from radiograph line scans and shown in Fig. 4.18a), the differential amount can be inferred to be the gas phase.

Once the measurements of each phase is known from the measurements in extinction lengths, the wavelength dependent attenuation coefficient and density can then be used to calculate the quantitative path lengths of each phase using the Beers Law. An example plot of this is shown in Fig. 4.19.

This technique has an advantage in cases where high liquid densities near the injector exit cause substantial trapping of argon fluorescence. This leads to significant signal reabsorption and producing high uncertainties in the argon EPL measurements. By contrast, the relatively more precise measurement of total-minus-liquid attenuation can be used for accurate measure- ments, even at locations with low argon fluorescence signals caused by low concentrations or

Figure 4.19: Example showing quantitative measures of path length for liquid and gas phases.

Figure 4.20: Example showing quantitative measures of path length for liquid and gas phases at axial locations of X = 6.0 mm (x/D0= 0.58) (top) and X = 14 mm (x/D0= 1.37) (bottom).

high levels of reabsorption An example plot demonstrating the technique is shown in Fig. 4.20. Based on the total transmission through the spray, as measured using radiography, the spray is radially symmetric to within approximately 1.4 %. This is also reflected in the liquid EPL profiles of Fig. 4.20, with peak values that are symmetric to within 0.1% and 2.5%, respectively, at 6 mm and 14 mm downstream. This is consistent with prior work on dual-tracer X-ray fluorescence reported in literature, Halls et al. (2015), implying that accurate absolute liquid EPL values can be obtained through calibration of the corrected liquid fluorescence signals measured without argon flowing. The argon EPL data showed slightly higher potential

Table 4.2: Flow constituents and measured Signal-to-noise.

Flow Constituents Signal to Noise

Argon 20

Liquid Tracer 260

Total 83

(a) Reg=14,700 (b) Reg=17,600

Figure 4.21: Example plots for a constant liquid flow rate of 27.76 g/s and a gas Reynolds number of (a)14,700 and (b) 17,600 at axial locations of X = 6.0 mm (x/D0 = 0.58) (top) and

X = 14 mm (x/D0 = 1.37) (bottom).

systematic errors, with peak values that are symmetric to within 1.6% and 5%, respectively at 6 mm and 14 mm downstream. The latter are consistent with dual-tracer liquid fluorescence attenuation corrections reported in prior work and represent systematic errors relative to the attenuation measurements used for calibration of fluorescence signals. The minimum precision of the EPL measurements is 4 µm, based on ratios of signal-to-background noise of 83, 260, and 20 for the total, water, and argon EPL data, respectively.

In the application of studying sprays, this technique facilitates the probing of information relative to liquid and gas phase distributions. To understand how the spray of interest evolves as a function of different flow condition, the technique was applied to a series of runs with differing gas Reynolds number, Reg, but with a constant liquid water flow rate, show in Fig.4.21.

By comparing the two flow conditions at identical spatial locations, for Reg=14,700, the near

injector region 6mm from the injector is shown to have a distinct decrease in argon path length as compared to the Reg=17,600 condition. This could suggest that for the higher Reynolds

number case, the gas is shown to force more liquid into the center of the flow as compared to the lower case where the gas can diffuse to the middle without fully atomizing the liquid flow.

Additional support for this theory can be found by examining the relative width of the liquid distributions. For the Reg=17,600 condition, the liquid distribution is shown to have a much

narrower distribution of approximate -3 to 3 mm. Considering that the injector exit diameter is approximately 10.3 mm across, this seems to suggest that as gas flow is increased, the gas pushes the liquid towards the center of the flow initially.

Further downstream at X = 14 mm, the liquid path length is shown to decrease and broaden its distribution, indicative of atomization and mixing. The gas-phase profile is also observed to broaden downstream for both conditions. Interestingly, for the Reg=14,700 condition, the gas

EPL is shown to broaden and decrease, indicating that the flow is expanding outward, but at a constant flow velocity. In contrast, for the Reg=17,600 condition, the distribution is shown to

broaden, but increase in EPL. This seems to suggest that in addition to mixing and atomizing the liquid flow, the gas flow is decelerating once it is in the quiescent atmosphere.