Post-Processing of Phase Doppler Interferometry Data for Planar Spray Characteristics

Transcription

1 ILASS-Americas 25th Annual Conference on Liquid Atomization and Spray Systems, Pittsburgh, PA, May 213 Post-Processing of Phase Doppler Interferometry Data for Planar Spray Characteristics K. M. Bade and R. J. Schick Spray Analysis and Research Services Spraying Systems Company Wheaton, IL 6187 USA Abstract An investigation into methods used to generate general planar spray characteristics, such as mean drop size and velocity, from discrete measurement points is conducted. Two sprays are investigated, a full cone spray, and a multi-orifice spray. For each spray, an ecessive array of sample-point locations are acquired using a Phase Doppler Interferometer (PDI); thus, the data may be down-sampled to determine the minimum number of required sample points to calculate reliable mean planar spray values. For the hydraulic flat spray it is found that a small subset of measurements may yield accurate results, when 23 evenly spaced samples are used incorporating measurements along the and y aes. For the multi-orifice, air-atomized spray, the measurements do not benefit from measuring more than a single radial line of measurement points, and approimately 12 evenly spaced measurements along a single radial path through the spray-plume-center provide the best results. In order to generate meaningful average values, weighting methods are used. These methods are described and assessed for relative influence on the final calculations. The ability of the PDI to measure the local volume flu allows the results to be flu weighted to represent the volume distribution of the sprayed material. Furthermore, by acquiring discrete point measurements, each measurement is epected to represent a small area of the measurement plane of interest, which is then used to generate an area weighting function. The results of this investigation allow for the acquisition of a minimum number of discrete data points to be processed into reliable planar representations of the spray characteristics using area and volume flu weighting post-processing methods. Corresponding Author: Kyle.Bade@Spray.com

2 Introduction The characterization of industrial spray nozzles involves many types of testing instruments. This study investigates the necessary measurement locations, and post-processing methods, required to generate planar spray characterization statistics from arrays and subsets of point-measurements. Here, an Artium Technologies, Inc. Phase Doppler Interferometry (PDI) instrument is used to collect detailed point-measurements of drop size and velocity distributions. The implementation and accuracy of this system to measure these parameters for a spray was eplored and optimized in, for eample, the study by Bade and Schick [2]; equivalent methods are used in this study. Furthermore, the ability of the PDI instrument to measure local volume flu offers a attractive and suitable weighting parameter for averaging these resultant point statistics throughout a spray plume. Furthermore, discrete point-measurements are presumed to represent a small area of a spray plume s characteristics, thus, if this area is non-uniform, then an additional weighting parameter is necessary. The use of the local flu and representative area for weighted averaging purposes is investigated in this study. Significant effort has been made by many researchers to establish meaningful statistics to represent drop size and velocity statistics. For eample, the well recognized tet by Lefebvre [6] includes definitions for the Arithmetic Mean, Sauter Mean Diameter, and many other statistical values that can be generated from well resolved drop size distributions. These distributions may be collected at a point within a spray, or throughout the spray plume. Many methods and instruments, some of which are reviewed in various tets such as that by Tishkoff et al. [7], Dodge, et al. [5], and Albrecht, et al. [1], may collect these distributions; the authors have not found a concise demonstration of the combination of multiple point-measurements into single characteristic values. Planar spray characteristics may be directly collected, by techniques such as interferometric Particle Imaging(IPI, see Albrecht et al. [1]), but these methods often suffer from very limited ability to measure within a moderate to very dense spray plume. Furthermore, a great advantage of point measurement systems, beyond the ability to measure in moderate and dense sprays, is the ability to collect flu information. Through this information, regions of high flu can be treated as more influential to the planar statistics. This is not possible with imaging techniques which only provide instantaneous or ensemble (spatial) spray measurements. The current investigation aims to use the flu information, along with the point-measurements from a Phase Doppler Interferometer (PDI), to generate flu sensitive planar spray statistics. Furthermore, an investigation is carried out to eamine the minimum number of measurement points required to calculate accurate planar mean values, for two candidate sprays. Eperimental Methods Measurements were acquired for two nozzle types, a single orifice hydraulic spray, and a multiorifice air-atomized spray. The single orifice nozzle is a Spraying Systems Co. flat spray nozzle, model TPU655-TC which provides an attractive baseline case given that this nozzle was investigated in detail in a previous study by the authors [2]. The operating condition of the single orifice TPU nozzle was with a liquid pressure of. bar, resulting in a flow rate of 225 ml/min. The hydraulic flat spray nozzle provides a symmetric volume distribution as well as a simple spray plume shape as is shown the Laser Sheet Imaging (LSI) result of the average spray plume, provided in Figure 1. Additionally, Figure 1 includes an overlay of the 273 discrete measurement points used in the PDI testing. A multi-orifice, air-atomizing nozzle provided an additional, more comple, spray plume shape for further analysis of the optimal spray measurementpoint location subset for interrogation when generating overall spray statistics. Figure 2 provides an LSI result of the average spray plume at the operating condition used for this study; 2. bar water pressure and 2.67 bar air pressure, resulted in 136 ml/min water flow and 75.6 standard L/min air flow. For this study, the comple shape of the spray plume generated by a single orifice was of interest, Figure 2 includes an overlay of the 53 discrete measurement points array on the plume of interest. It is assumed that all si plumes will ehibit similar characteristics Figure 1: Laser Sheet Patternation average image of the TPU655-TC with overlaid PDI test points 2

3 Figure 2: Laser Sheet Patternation average image of the SU26B with overlaid PDI test points Laser Sheet Imaging (LSI) measurements were conducted for each nozzle in order to provide high spatial-resolution, y planar contours representative of the liquid distributions of each spray. These planar contours are provided for the single-orifice TPU and multi-orifice SU26B sprays in Figures 1 and 2, respectively, with contour lines drawn at 5% intervals of the maimum level. The relative light intensity I, in these ensemble averaged results is scattered according to Mie theory and is directly representative of the total surface area of the sprayed droplets. This isacombinationofthe count ofalldropletsand size of the droplets and is referred to as the relative concentration distribution. In the work by Bade, et al. [3], the TPU nozzle is rigorously investigated using both Mie and Laser Induced Fluorescence (LIF) methods, and it is found that the Mie scattered images are very nearly representative of the planar volume distribution of the spray plume. Furthermore, the multi-orifice spray investigated here is a an air-atomized spray, which provides a much more uniform droplet size range and would therefore be epected to provide a similar area-based concentration and volume-based concentration result. Under these considerations, the LSI results are used to select the locations and number of PDI test points in each spray with an attempt to acquire measurement points within each 5% step of the volume distribution. As demonstrated in figures 1 and 2, there is a measurement point within nearly every 5% contour line throughout each of the y planar spray plumes. The resolution of the LSI data for the TPU nozzle is.239mm/pielinandy, andforthesu26bnozzle the resolution is.559 mm/piel in and y. Finally, these LSI distributions of spray concentration will be used in this study to act as the local relative flu at each measurement point. This is done for two reasons; first, the LSI results provide a high-resolution representation of the relative flu through the y measurement plane for each spray. Secondly, due to the etremely large number of PDI measurements acquired in this study, some measurements did not resolve a reliable local volume flu measurement and thus the weighted averaging methods investigation would not be representative. The sources of these errors could have been addressed, but this was not feasible for this study where over 726 discrete measurements were collected; the errors responsible for the inaccurate volume flu will not effect the drop size or velocity measurements as described by Bade [2]. It is noteworthy that the majority of the local volume flu measurements collected with the PDI demonstrated very good accuracy. Phase Doppler Interferometry (PDI) measurements were acquired through the y plane of each spray plume, at the points shown in Figures 1 and 2, to provide droplet size and velocity, as well as local volume flu. For the TPU nozzle, measurements were acquired at 3mm increments in both and y; for the SU26B nozzle, measurements were acquired at every 3mm in and every 6mm in y. The accuracyofthe PDI measureddroplet sizeand velocityis rigorously investigated by Bade and Schick [2], and shown to be fairly insensitive to setup parameters when using the AIMS auto-setup feature. Bade and Schick also provide an etensive investigation of the volume flu measurements of the PDI throughout a sprayplume and the results arefound to be accurate to within approimately 2% when proper droplet trajectory considerations are used in the data collection methods. The influence of droplet trajectory and slit aperture alignment are investigated therein and found to be of great importance to the in-situ calculation of probe volume, and subsequent volume flu calculation. For the current investigations, a rotating slit aperture within the PDI receiver unit allowed for alignment of the droplet trajectory and slit aperture which provides a highly accurate volume flu measurement. An analysis of the droplet trajectory as viewed by the PDI receiver unit, and resulting slit aperture angle, is provided as Appendi A at the end of this paper. As noted above, some error was found in a portion of the 726 discrete measurements, and thus the LSI relative concentration will be used in place ifthe PDI flu measurementsin this study. In practice, volume flu measurements optimized for accuracy provide a more attractive source 3

4 of flu values as each measurement point for drop size and velocity also includes an in-situ volume flu measurement. An important note, the methods outlined in this paper may be applied without the need for LSI data, by using the PDI measured volume flu. Weighted averaging techniques provide a useful method for combining many individual spray measurement point results into meaningful overall statistical values. The methods to generate weighted average values which are representative of the planar spray plume characteristics follow typical mathematical processes(see, for eample, the tet by Bevington and Robinson []; for the purposes of this paper, the practical steps to conduct the volume flu and area weighting calculation will be described. First, the weight of each value must be determined according to each of the desired weighting parameters. Equations 1(a) and 1(b) demonstrates the method by which to calculate the relative weight of each weighting parameter, ω A,n and ω q,n at each of the measurement locations, n. Note that the weighted area represented by each point may be calculated using either the dimensional area, A n, or equivalently, the relative area ratio, A n, as defined below. When done correctly, the sum of any ω n set will be equal to 1.. Net, a total weight, ω T,n must be calculated which will combine the contributions from each weighting parameter, this is demonstrated in Equation 2, for the volume flu and area weighting parameters investigated here. ω A,n = A n Σ n A n ω q,n = q n Σ n q n (1a) (1b) Finally, the total weighting parameter, ω T,n, and the measured values at each point will be used to generated planar weighted average results. For a givenmeasuredvalueatlocationn, X n,theweighted average value may be calculated according to Equation 3. ω T,n = ω A,nω q,n Σ n (ω A,n ω q,n ) (2) X = Σ n (X n ω T,n ) (3) The weighted average value, X, may be calculated for any of the point-measurement values and will be calculated in this paper for the Sauter Mean Diameter, D 32 and aial velocity, v z, in the Planar Spray Results section. The remainder of this section will focus on the weighting parameters to be used in this study. The two accounting parameters are directly appropriate for planar spray plume weighted averages and will be described: i) the local volume flu at the location of the measurement, and ii) the area that each discrete point measurement is epected to represent. The implementation of the local flu as a weighted averaging parameter for the drop size and velocity results is a straightforward practice where each discrete measurement is given a relative weight in the overall average according to the flu of the sprayed fluid that passes through the measurement location. Net, area weighting accounts for the fact that each discrete measurement point does not necessarily represent the same area within the spray plume. An eample where this will have a large influence is in the implementation for results with a round spray plume in which uniformly spaced radial measurements are acquired along a single center-toedge line (N =1), as demonstrated in Figure 3(a). There, the center-point (point #1) is intended to represent the spray characteristics of a very small total area compared to, for eample, the outer-most point (point #) which represents a much larger area-ring. By including additional radial measurement lines (N), the relative area of each discrete area is reduced, but remains non-uniform as demonstrated in Figures 3(a-c). a) b) c) 2b Figure 3: Schematic eample of the area represented by a subset of discrete measurement locations ( ) for a round spray with N number of radial lines of measurement for a) N=1, b) N=2, and c) N= The area ratio between the points noted as 1- are provided in Table 1 for Figure 3a (N=1), 3b (N=2), and 3c (N=); where the schematics which include N number of radial measurement lines from the spray center. Equation provides an equation for calculating the relative area for a given discrete point, n steps from the center-point, with N total radial measurement lines, relative to the area of the central measurement point, A 1 when uniformly spaced measurement points are used. Naturally, the area of the center-point is always A 1 = A 1/A 1 =1.

5 A n = A n /A 1 = (r2 n r2 n 1 ) N r 2 1 () Note that in Equation, r n refers to the radius from the center of the spray plume to the measurement point, plus one-half of the point-to-point spacing. Table 1 demonstrates the relative area ratio for the arrangements up to N = as demonstrated in Figure 3; additional radial measurement lines would follow a similar pattern using Equation with greater N values. All points at the same distance front the spray center would receive the same area weight, i.e. in Figure 3(b), point #2b would receive the same area weight as point #2. The benefit of using the identified A n term is the removal of any need to calculate the actual area of of measurement point due to the systematic relative area resulting from uniformly spaced measurement locations. In practice, the area weighting may be conducted using either A n or A n. n N=1 N=2 N= Table1: Relativeareatothecenterpointarea,A n = A n /A 1, of each subsequent measurement location, n, for various numbers of radial measurement lines from the spray center, N It is worth noting that the idealized round spray patterns of Figure 3 can also be converted to noncircular oval patterns and the relative area of each subsequent ring follows the same area proportions. Thus, with a standard flat-spray pattern, as that given in Figure 1 for the TPU nozzle investigated here, a nominally oval spray pattern assumption provides a close representation of the relative area epected to be represented by radial subsets of measurement points. The influence of specific radial measurement line patterns is eplored in the Planar Spray Results section. For the multi-orifice spray, additional considerations must be taken regarding the more comple spray plume shape. The assumption will be made that each orifice produces an identical spray plume, thus, a tear-drop shaped single spray plume is to be investigated as demonstrated by the measurement point grid in Figure 2. For this non-aisymmetric spray plume shape, determining a spray center-point can be very subjective, therefore, a method is devised to use uniformly spaced measurement points to investigate a single plume of the multi-orifice spray with measurements beginning at the nozzle center (z-ais, =y=). Figure provides one eample of a subset of measurement points which may be used to generate the planar spray statistics and each points epected area of representation Figure : Schematic eample of the area represented by a subset of measurement locations ( ) for a teardrop shaped spray plume Figure demonstrates a possible PDI measurement line-from-center that would provide a subset of measurement points to attempt to capture the overall spray statistics, where the location of maimum volume flu is taken as the dividing line (location of the drawn vertical ais) for area weighted representation. This, and other, subsets of the array of PDI point-measurements (see Figure 2) will be used to generate overall planar spray statistics to determine a minimized subset of measurement points to collect accurate overall spray statistics for this spray. Point Measurement Results The results of the PDI measurement point-array testing for each nozzle are presented in this section; for brevity of this paper, the results will focus on the Sauter Mean Diameter, D 32 and Aial Velocity, v z, along with the the relative concentration results from the LSI planar data. For the single orifice spray, a total of 273 measurement points were collected with the PDI according to the layout demonstrated in Figure 1. Figure 5 provides the y planar results, at z=5 mm from the nozzle, for the TPU655 nozzle spray. The results for D 32 and v z in Figure 1 demonstrate that these quantities are notn-aisymmetric through the spray plume. Therefore, weighted averages based on the relative concentration, I, or volume flu distribution, q, will likely require multiple lines-from-center measurements. This is instructive because the nominally oval spray pattern may be interpreted to suggest that the spray characteristics would be epected to be somewhat aisymmetric. It is clear from Figures 5(a) and 5(b) that the D 32 5

6 and v z ehibit increased values as the distance from the spray center is increased in. In contrast, D 32 and v z undergoamonotonicdecreaseasthe distance from center is increase in y. The results of the LSI testing are quite interesting in light of these characteristics, in Figure 5(c), the largest concentration of spray material is at the spray center (=y=) indicating that the droplet count must be highly correlatedtothedistancefromcenter(i.e. therearemany more droplets at the spray center than at the edges, with a gradual reduction in the droplet counts). This conclusion is confirmed by the PDI data acquisition rate which shows a similar relative distribution with the largest level at the spray center and a monotonic decrease as and y are increased, indicating a higher frequency of droplet passage through the measurement volume as the spray center. For the multi-orifice spray, a total of 53 measurement points were collected with the PDI according to the layout demonstrated in Figure 2 covering one of the si spray from the si eit orifices of the nozzle. Figure 6 provides the y planar results, at z=178 mm, from these tests with the SU26B nozzle spray. In Figure 6(a), the Sauter Mean Diameter is shown to increase near the spray edges. THis is typical of an air-atomized spray where the core of the spray plume tends to ehibit only small variations in drop size while at the edges, the liquid is influenced by the nozzle eit orifice walls and larger droplets can be generated. As epected, the velocity of the droplets tends to decrease near the spray edges. Furthermore, because the SU26B is a multiorifice nozzle, each eit orifice is set to a angle relative to the measurement plane and the droplets in the large region have traveled further from the nozzle. Also, the atomizing air which also acts to carry the droplets out of the nozzle body, has been further slowed by the longer path to the larger locations. Eamining Figure 6(c), the location of largest I, or local volume flu, q, will be selected as the spray center point for area-weighting analysis as demonstrated in Figure. In the measurements provided in Figures 1 and 2, the PDI measurements arrays can be seen to etend outside of the final contour line, which is indicative of 5% local concentration, or volume flu, of the spray. Therefore, by employing appropriate flu weighted averaging methods, the contribution to the overall spray statistics by acquiring additional PDI measurement points would be insignificant because there is essentially no spray outside of the PDI investigated region. The net section will eplore the effect of using all of the acquired measurement points, as well as specific subsets of the PDI measurement point arrays, to generate overall planar spray average results. Planar Spray Results An analysis of the measurement point locations necessary for sufficiently accurate spray statistics as well as the necessary weighted averaging (volume flu and area) considerations are calculated and analyzed here. Table 2 provides the results of many subsets of the PDI data used to generate weighted average planar spray mean values. In Table 2, simple diagrams demonstrate the subset of measurement points used for each analysis, note that the number of points in each diagram are not representative and are instead indicated by n and n y, for the number of locations employed in each case in the and y directions, respectively. Also, the number of lines from center, N, is included in the table. Smaller values of n and n y were achieved by downsampling the number of measurement points in each subset, i.e. systematically skipping points in order to simulate a reduced set of measurement points, or an increase in the uniform point spacing. The TPU655 results are provided first, followed by the SU26B spray plume results. In the first row for each nozzle, the result of using all measurement points to generate volume flu and area weighted average values is provided, these values act as the baseline overall values from which to compare the results of smaller subsets of data. For measurement made across only the -ais of the TPU spray plume, the D 32 weighted average is over-estimated by approimately 21-28% and the aial velocity is over-estimated by approimately 25%. Eamining Figure 5(a), this oversized D 32 result is due to the large drop size regions near the flat spray edges along the -ais; similarly, in Figure 5(b), the largest velocities are centered around the -ais and thus provide an inappropriate representation of the total spray plume characteristics. For subsets including only measurements along the y-ais large errors in average D 32 and v z are also found due to these subsets not providing a representative account of the spray characteristics. In the final two subsets which were investigated, where measurements from both and y are used, the accuracy of the weighted average results is greatly increased and the percent error is greatly reduced. It is shown that errors as low as 5.1% in D 3 2 and 1.8% in v z can be achieved using subsets of only 23 measurement points, which is a significant reduction from the full dataset array of 273 points. Without the full-measurement-array itwouldbeimpossibletoassesstheaccuracyofthese 6

7 weighted average subset results. For the SU26B results, the greatest reduction in systematic error, and increase in accuracy, occurs by using measurement points along only the -ais. For these investigations, the y-ais for the subset investigations was taken as the location of highest volume flu along the -ais. These results show that there is no appreciable benefit from including measurement points off the -ais, so long as the weighting is conducted so that the center point is taken as the location of largest volume flu. In summary, errors of.3% and 6.% were found for D 3 2 and v z, respectively, when using 12 evenly spaced measurements starting at the nozzle ais. These eact error values did not systematically vary with the number of points, and thus it is epected that no appreciable gain is made with additional points. This represents a significant reduction from the total measurement array of 53 points. This result is likely due to the air-atomized nature of the SU26B nozzle which produces a somewhat uniform drop size planar spray plume and has a well distributed spray plume in terms of the volume. Conclusions The results of this study demonstrate that it is possible to generate accurate overall planar spray statistic from small sets of point measurements. The formulation of these individual points into planar statistics using volume flu and area weighting methods has been described and evaluated. The quantitative results of this study are nozzle and operating condition specific. However, the volume flu and area weighting methods are applicable to many spray applications. Furthermore, the evaluation of the effect of many different subsets of data should provide insight for future investigations regarding what type of point measurement array is necessary for accurate planar statistics. It is found that for a hydraulic flat spray with larger drops near the edges, a two ais measurement program is necessary in order to capture the spray statistics. It is also found that for an air-atomized, multi-orifice spray plume, it is only necessary to collect measurements along a single radial line. For each nozzle, the arrangement of the best results with the minimum number of measurement point is highlighted in gray in Table 2. In either case, the volume flu and area weighting methods must be applied in order to properly weight spray regions with either a large flu or large discrete area representation. Finally, determination of the perspective droplet trajectory angle is investigated when the PDI receiver is placed at an off-ais angle; as is typically the case. Calculation of the of the perspective angle based on the PDI receiver off-ais angle and radial spray location is discussed and resolved in order to allow for accurate volume flu measurement. Acknowledgements The authors would like to acknowledge and thank Krunal Patel, Ben Bridges, and Stephen O Donnell of Spraying Systems Co. for their efforts in acquiring the high spatial resolution PDI measurements as well as the LSI results used in this study. References [1] H.-E. Albrecht, M. Borys, N. Damaschke, C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques, Springer-Verlag Berlin Heidelberg, 23. [2] K. M. Bade, R. J. Schick, Phase Doppler Interferometry Volume Flu Sensitivity to Parametric Settings and Droplet Trajectory, Atomization and Sprays, vol. 21, issue 7, pp , 211. [3] K. M. Bade, K. Cronce, R. J. Schick, Development of Low-Order Regression Models for Selected Flat Spray Characteristics, 12 th Triennial International Conference on Liquid Atomization and Spray Systems, Heidelberg, Germany, pp. 1-8, September 2-6, 212. [] P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, 3rd Ed., 23. [5] L.G. Dodge, D. J. Rhodes, R. D. Reitz, Drop- Size Measurement Techniques for Sprays: Comparison of Malvern Laser-Diffraction and Aerometrics Phase/Doppler, Applied Optics, vol. 26, no. 11, pp , [6] A. H. Lefebvre, Atomization and Sprays, Combustion: An International Series, Hemisphere Publishing Corporation, [7] J. M. Tishkoff, R. D. Ingebo, J. B. Kennedy (Eds.), Liquid Particle Size Measurement Techniques, American Society for Testing and Materials (ASTM) special technical publication 88,

8 (a) (b) D 32 (µm) v z (m/s) I (%) 1 (c) Figure 5: PDI point measurement results for the TPU655 single-orifice, hydraulic, flat spray for a) D 32, b) v z, and the LSI results for c) normalized spray concentration, I (a) (b) D 32 (µm) v z (m/s) I (%) (c) Figure 6: PDI point measurement results for the SU26B multi-orifice, air-atomizing spray for a) D 32, b) v z, and the LSI results for c) normalized spray concentration, I

9 Subset N total n total n y total n D 32 µm (% error) v z m/s (% error) y (baseline) 11. (baseline) (1.8) 11.1 (.9) (2.8) 11. (3.6) (8.6) 12.3 (11.8) y (21.7) 13.7 (2.5) (2.1) 13.9 (26.) (2.6) 13.8 (25.5) (26.3) 1.1 (28.2) y (25.9) 13.7 (2.5) (27.9) 13.9 (26.) (26.9) 13.8 (25.5) (27.6) 13.9 (26.) y (-11.5) 8.6 (-21.8) (-11.2) 8.8 (-2.) (-11.1) 8. (-23.6) (-1.1) 9.2 (-16.) y (-9.6) 8.9 (-19.1) (-1.) 9. (-18.2) (-9.3) 9.1 (-17.3) (-8.8) 9.5 (-13.6) y (5.1) 11.2 (1.8) (6.6) 11.8 (7.3) (6.9) 11.9 (8.2) (7.9) 12.7 (15.5) y (8.2) 11.3 (2.7) (8.9) 11. (3.6) (8.8) 11. (3.6) (9.) 11.7 (6.) y y y y (baseline) 3.77 (baseline) (-3.3) 3.87 (2.7) (-2.8) 3.82 (1.3) (-8.1).5 (7.) (-.6).5 (7.) (2.8) 3.8 (.8) (3.9) 3.73 (-1.1) (-.3).1 (6.) (-9.7) 3.81 (1.1) (-11.9) 3.85 (2.12) (-17.2).22 (11.9) (-19.7).6 (18.3) (6.1) 3.75 (-.5) (1.8) 3.8 (-7.7) (.7) 3.6 (-.5) (13.1) 3.32 (-11.9) Table 2: Weighted average results for overall y-planar spray characteristics using various subsets of the 2D PDI measurement points array as demonstrated by the included Subset diagrams 9

10 Appendi A: PDI Slit Aperture Angle In order to arrive at the correct slit aperture angle for accurate PDI volume flu measurement, the perspective angle of the droplet trajectory, as viewed from the PDI receiver, must be determined. Figure 7 provides a schematic of the change in droplet trajectory angle, β, perceived from the off-ais receiver location as the off-ais angle, θ r is changed. Note that the PDI receiver distance to the measurement location does not effect the perceived droplet trajectory angle. Spray Plume Nozzle β β r1 β p r β r2 p y r z = z p r = cos(θ r ) (6) Finally, the perspective -distance, p, and droplet trajectory angle, β p, perceived by the PDI receiver are represented by Equations 7 and 8, respectively, when y r = (i.e. the measurement point and PDI receiver are in the same y plane). Note that β p is the same for the near- and far-perspective locations due to the collapsed y-distance to maintain a purely z-plane droplet trajectory. p = r cos(θ r ) = cos 2 (θ r ) (7) β p = tan 1 ( p /z) = tan 1[ ] z cos2 (θ r ) (8) Thus, the slit aperture should be set to the proper perceived droplet trajectory angle, from the perspective of the off-ais PDI receiving unit, which is represented by β p. θ r = θ p = Receiver Location (off-ais angle, θ ) r Figure 7: Schematic to demonstrate the angle of the spray plume, or droplet trajectory, from the perspective of an off-ais receiver unit In Figure 7, the droplet trajectory angle relative to the eit orifice ais (z-ais) is represented by β, and may be calculated according to Equation 5. With the PDI receiver unit located at an off-ais angle, θ r, the perceived angle of a droplet s trajectory (demonstrated in Figure 7 for a droplet at the spray edge) is altered to β r1 or β r2, for a near or far point, due to the non-normal alignment of the receiver ais with the the z plane. As θ r is increased, the magnitude of r is reduced according to Equation 6 and results in a reduced droplet trajectory angle perceived by the PDI receiver. Note that for this analysis, it is assumed that the PDI receiver is located in the same y plane as the measurement point. β = tan 1 (/z) (5) 1