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ICLASS 2009, 11th Triennial International Annual Conference on Liquid Atomization and Spray Systems, Vail, Colorado USA, July 2009
Refractive Index Measurements Using a
Dual-Mode Phase Doppler Anemometer
S. Kontin††, P. Loke†, R. Koch††, H-J. Bauer†† and P. E. Sojka†*
†School of Mechanical Engineering
West Lafayette, IN 47907 USA
††Institut für Thermische Strömungsmaschinen
D-76128 Karlsruhe GERMANY
A limitation of commercially available phase-Doppler analyzers (PDA) is their inability to make accurate diameter measurements in processes where the refractive indices of the particles being sampled are unknown. One example is evaporation of multi-component liquid drops. Since it is of interest to make simultaneous measurements of refractive index, particle diameter and velocities using a PDA, we have undertaken a program to do just that.
Several configurations of the PDA exist that could in principle perform all three measurements. Amongst these, a modified version of the dual-mode PDA is believed to be the most practical because of its commercial availability and ease of alignment. Refractive index and diameter measurements were therefore conducted by using the standard and planar phase differences supplied by a dual-mode PDA. Measurements were first performed for monodisperse drops with known refractive indices, and then for polydisperse sprays that also had known refractive indices. PDA reported mean refractive indices agreed with refractometer readings to within 1%. This motivated further experiments in a hot gas tunnel with a poly-disperse spray. Evaporation caused drop refractive index to be an unknown.
Hot gas tunnel data showed that droplet refractive index increases as droplet size decreases or as temperature increases. However, ambiguities existed for smaller droplets for two reasons, turbulent flow and Mie scattering effects, with both leading to a greater spread of measured refractive index. Turbulence leads to a variation in the degree of evaporation for drops with the same initial size. Surface waves are more important in these smaller droplets, which leads to a distortion of the PDA-received light signals.
Finally, measured droplet refractive indices can be used to determine droplet concentration for a given temperature. However, non-isothermal situations decrease accuracy because refractive index varies substantially with temperature. Droplet concentration estimation based on this technique is therefore expected to be most accurate for droplets that experience minimal impact of temperature on refractive index. To determine droplet concentration more reliably, droplet temperature would also have to be measured simultaneously.
A limitation of commercially available PDAs is their inability to make accurate diameter measurements when the refractive indices of the particles being sampled are unknown, for instance during evaporation of a multi-component drop. This limitation exists because PDAs require a constant refractive index when computing droplet size. Researchers are therefore motivated to extend the PDA technique to measure refractive indices while simultaneously measuring drop diameters and velocities, so that spray characterization can be extended to new areas.
Techniques to measure refractive indices using PDA have been reported (Benzon et al. (1994), Naqwi et al. (1991), Onofri et al .(1996), Brenn et al. (1997)), but have not been put into practice because of difficulties in implementation. Based on comparisons of these various techniques, it is believed that dual-mode PDA has the highest potential for providing accurate refractive index measurements while simultaneously collecting diameter and velocity data. This has yet to be demonstrated since past studies performed using dual-mode PDA went only so far as to compare measured refractive indices of monodisperse water droplets against refractometer data (Brenn et al., 1997). A quantitative evaluation of dual-mode PDA performance when measuring refractive indices of flowing particles was therefore performed to determine the limitations of the technique.
In principle, measuring the refractive index using any type of PDA is possible if two simultaneous phase difference measurements are obtained from two independent sets of detectors. This is because the phase differences are functions of the particle diameter dpart, the refractive index m, the wave number k, and the experiment geometrical parameters (the beam crossing half angle Θ, the scattering angle θ and the elevation angle Ψ). Since the setup geometry (Θ, θ, Ψ) and wave number (k) are specified by the user, this reduces the number of unknowns to two.
This is seen from Equations (1) and (2), which are applied to analyze the phase differences of a dual-mode PDA consisting of a standard PDA, denoted by subscript s, and a planar PDA, denoted by subscript pl.
The ratio of these analyzed phase differences, ΔΦ*, is independent of droplet diameter for fixed system geometry and illumination wavelengths so is solely a non-linear function of the refractive index m. As such, a table of ΔΦ* versus m can be generated for given input geometrical parameters (Θ, θ, Ψ). The corresponding refractive index m can then be determined for the dual-mode PDA-measured ΔΦ*.
There is a disadvantage to using one of the phase differences for refractive index calculations. This is the loss of the droplet sphericity check that is provided when the two phase differences are used to compare droplet diameters measured for both the meridional and equatorial axes. This loss may affect the refractive index measurement accuracy, because spherical particles are a prerequisite for PDA measurements. The following alternative approach was therefore developed to estimate drop sphericity.
The solution is to compute drop Weber numbers from PDA size and velocity data, and then compare them to a critical Weber number drawn from the work of Hsiang and Faeth (1995). For example, if deformation below 10% is defined to be a spherical drop, the limiting We is 1. Refractive index is not computed for drops with We > 1.
Materials and Methods
Evaluation of dual-mode PDA refractive index measurements involved three steps. The experiments were carried out using the facilities shown in Figure 1.
Figure 1. Experimental apparatus. Left: Monodisperse droplet stream. Middle: Polydisperse spray under ambient conditions. Right: Polydisperse spray under hot gas conditions.
The first facility was used for ambient environment experiments. Monodisperse droplets with a known refractive index were produced by a droplet generator. The droplet generator main components were a piezoelectric ceramic and an orifice plate. The piezoelectric was driven at a suitable frequency to produce uniformly spaced droplets.
Droplet images were recorded using a CCD-camera and monochromatic, diffuse backlight from a frequency doubled pulsed Nd:YAG laser, and were captured immediately before and after the PDA measurements. The camera exposure time, dictated by the laser pulse length, was 8 ns. Calibration of drop images came from the length per pixel for the size of a known tube (0.6 mm). A sample imagee is provided in Figure 2.
Figure 2. Sample monodisperse droplet image (200 µm).
Polydisperse drops of a spray with known refractive index were studied in the second phase. The were formed using a commercial pressure atomizer having a supply pressure of 5 bar and a liquid flow rate 3.2 kg/h.
The third test phase was intended to mimic more realistic conditions. A facility was customized to run experiments high temperature. PDA optical access was located 0.3 m from the point of injection. Experiments were conducted at air temperatures of 23, 100, and 250 °C. The atomizer form the ambient measurements was used again.
In all cases, phase differences were measured using a Dantec Dynamics dual-mode PDA and Dantec Dynamics BSA v4.1 software. The data were post-processed by a Matlab program that solved for refractive indices and diameters.
PDA refractive indices were compared with values obtained using an ABBE refractometer to sample drops collected from sprays. The ABBE instrument had a least count accuracy of five significant figures. Filtered water and urea-water solutions of various concentrations by mass were employed as sample liquids. Urea-water solutions were initially Ad-Blue (a commercially available 32.5% urea-water solution), with other concentrations obtained by either adding filtered water or dissolving urea into Ad-Blue. The resulting concentrations of the solutions were verified through measurements using the refractometer.
Experimental uncertainty arose mainly from uncertainty in the scattering angle. For the chosen scattering angle, a Kline and McClintock (1953) analysis showed that an uncertainty of 1o resulted in approximately 1% uncertainty in measured refractive index. This is significant since differences in refractive indices were of that order of magnitude. Scattering angle accuracy was improved to ~0.2o using a Bosch digital protractor/spirit level accurate to 0.1o.
Other sources of uncertainty included the elevation angles for the standard component of the dual-mode PDA, those for the planar component of the dual-mode PDA, and the beam crossing angle of the setup that would result from imperfections in the lenses and masks. All were less than 1%. The calculated refractive index was insensitive to a changes in these amounts--less than a 0.1% variation.
A criterion for good alignment was also necessary to obtain accurate measurements. Phase plots (scatter plots of standard PDA phase difference, ΔΦs, versus planar PDA phase difference, ΔΦpl) were used as a measure of alignment quality. In the monodisperse case, the PDA was considered well-aligned when phase plot data were clustered in a small region (signifying the presence of monodisperse droplets) whose apparent center lay on the geometrical optics solution line (signifying the presence of only one refractive index). See Figure 3. In the polydisperse case, the PDA was considered well-aligned when phase plot data were clustered in a continuous band (signifying the presence of a polydisperse spray) whose apparent axis lay on the geometrical solution line of constant phase shift ratio. See Figure 4. Stray points are phase difference pairs that do not appear to satisfy the alignment criteria. They represent noise, and were less than 5% of the data.
Figure 3. Sample monodisperse spray phase-difference data for a well-aligned system (BSA Flow Software output). U12 is ΔΦs and V12 is ΔΦpl.
Figure 4. Sample polydisperse spray phase difference data for a well-aligned system (BSA Flow Software output). U12 is ΔΦs and V12 is ΔΦpl.
Drop refractive indices were evaluated from Figure 3 and 4 type data using Matlab. For ambient condition tests, an arithmetic mean of the 2-π ambiguity corrected phase shift ratios was determined, and a single refractive index that described the entire droplet population was computed from it. The uncertainty of this refractive index was based on the uncertainty of the scattering angle.
Results and Discussion
Using this approach, refractive indices for a well-aligned monodisperse droplet stream were in agreement with refractometer measurements to within experimental uncertainty (<1%). Agreement between dual-PDA and refractometer values for polydisperse sprays was again within 1%. See Figure 5.
Some complications were present in these measurements. For instance, referring back to Figure 4, measured phase differences tend to have greater scatter for smaller droplets (below 30 μm) even under well-aligned conditions. This is because of more pronounced Mie scattering effects in smaller droplets. As a result, the individually measured refractive indices tended to oscillate significantly for small droplets. In the measurements performed here, the laser intensity was intentionally set to avoid the detection of small droplets.
When the droplets were large (above 120 μm), PDA data are subject to the slit (or trajectory) effect. However, this can be corrected by careful alignment. When not aligned properly, measured phase difference pairs deviated from the geometrical optics solution in regions corresponding to larger diameters in the phase plots. For instance, the impact of a misalignment as small as 0.2 mm was considerable: it led to the observation of two dominant refractive indices. If this was observed, the measurement location was adjusted until phase data from large droplets lay approximately symmetrical about the geometrical solution line for the corresponding refractive index.
Based on these complications, the technique will only be reliable for a range of drop sizes, depending on the characteristics of the spray and settings of the PDA.
Figure 5. Comparison of refractive index measurements for well-aligned monodisperse droplet streams (top) and polydisperse sprays (bottom).
The presence of evaporation complicates the measurements because both the drop diameter and refractive index are unknown. Therefore, a geometrical optics solution for liquids of various refractive indices was compiled before measurements were attempted. See Figure 6. Dotted lines are for constant phase shift ratios at three refractive indices. The directions of increasing and decreasing droplet diameters along lines of constant refractive index, and the directions of increasing and decreasing refractive indices along curves of constant droplet diameters are indicated. The results demonstrate that the system has better resolution for larger droplets and smaller refractive indices.
Figure 6. Standard phase difference versus planar phase difference for three droplet diameters and three refractive indices.
The refractive index and droplet diameter for each individual drop were obtained for gas flow temperatures of 23, 100 and 250oC. Data for the 23 and 250oC cases are presented in Figure 7.
Figure 7. Droplet refractive index versus diameter for a 10% urea-water solution. The curves are fit lines. Left: no evaporation (23o C). Right: with evaporation (250o C).
Data scatter is attributed to: not all drops of a size class having the same residence time between the atomizer and measurement location, and limitations in the planar part of the dual-mode PDA. They are discussed below.
The turbulent flow in the hot gas tunnel will result in droplets having different residence times between the atomizer and the measurement location. Droplets with longer residence times will experience more evaporation than others of the same size having shorter residence times. This will lead to a spread in refractive index for a single diameter class. Additionally, the spread will be wider for smaller drops since there are more combinations of residence time and initial drop diameter that can lead to the same measured drop size. Such behavior is evident in Figure 7.
Albrecht et al. (2003) documented that fluctuations in the Mie scattering cross section as a function of diameter become important when particles are small. According to these authors, the existence of surface waves in small particles might distort phase measurements for the planar component of the dual-mode PDA, leading to more scatter in measured phase differences. Since a large percentage of small droplets are more likely to be affected by evaporation and turbulence, more scatter in the data was expected. This was also observed in Figure 7.
The trend lines added to the data in Figure 7 indicate that larger droplets have lower refractive indices than smaller ones, and that droplet refractive index increases with an increase in tunnel temperature, regardless of diameter. Both are expected for the following reasons.
As the gas temperature increases so does evaporation. Since only the solvent leaves the drop during evaporation, the urea concentration must increase. Since the refractive index is a monotonic function of urea concentration for a given temperature, it must also increase.
If it is assumed that each droplet obeys the d2-law of evaporation, the fractional rate of liquid loss increases as droplet size decreases. As a result, the urea concentration rises more rapidly for smaller drops than for larger drops, so smaller drops exhibit greater increases in the refractive index. This is more evident in Figure 8.
Figure 8. Refractive index versus droplet diameter from an evaporating 10% urea-water solution.
Measured droplet refractive indices are helpful in determining drop composition. However, as a caution, it’s important to note that the accuracy of concentration measurement can suffer in non-isothermal situations because refractive index varies between -0.0003 and -0.0004/ oC for many substances whose refractive index is below 1.63. This means that refractive index uncertainty due to temperature increase can be as high as 0.02 when droplet temperature change is on the order of 70 oC. This is more than 20% of change in refractive index for the 250oC. This suggests that the technique will be more accurate for droplets that experience a large change in refractive index during evaporation, or those whose evaporation temperatures do not differ significantly from their initial value. In all other cases the temperature of the droplet has to be considered. Kneer et al. (1993) devloped a model to determine the response of a PDA for evaporating binary fuel droplets. For given droplet temperature, applying the Kneer et al. (1993) model to improve the accuracy of measured concentration appears promising. As future work, one could adapt the model to evaporating urea-water droplets to analyze the combined effects of temperature and concentration distribution inside a droplet.
In summary, this technique yields realistic refractive measurements for some bi-component droplets such as a 10% urea-water solution, even under evaporating conditions, as long as the droplets are above 30 µm. For the case of 10% urea-water solution, measured refractive index is accurate to ±0.01.
Onofri F., Girasole T., Gréhan G., Gouesbet G., Brenn G., Domnick J., Xu T.H., Tropea C., Particle and Particle System Characterization 13:112-124 (1996).
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