Size-velocity pdfs for Drop Fragments Formed via Multi-mode Breakup

Transcription

1 ILASS-Americas 29th Annual Conference on Liquid Atomization and Spray Systems, Atlanta, GA, May 2017 Size-velocity pdfs for Drop Fragments Formed via Multi-mode Breakup G. Sondgeroth,+ C.M.L. White,* W. Shang,+ L. Yao,+ J. Chen+, and Paul E. Sojka+ *School of Aeronautics and Astronautics +School of Mechanical Engineering all Maurice J. Zucrow Laboratories Purdue University West Lafayette, IN USA and D.R. Guildenbecher Sandia National Laboratories Albuquerque, NM Abstract Digital-inline holography (DIH) was used to measure size probability distribution functions, pdf(d), for fragments formed via multi-mode breakup. A MATLAB script was used to reconstruct drop fragmentation dynamics, from which fragment sizes, as well as velocities (and accelerations), can be extracted. Results, which demonstrate multi-modal fragment size distributions, are reported in terms of Weber and Ohnesorge numbers for the ranges 30<We<50 and 0.002<Oh<0.45. Physical explanations for the presence of the two-and three-peaked size distribution are presented. The data will be useful to those modeling sprays in gas turbine engines, pharmaceutical tablet coaters, and spray dryers.

2 ILASS-Americas 29th Annual Conference on Liquid Atomization and Spray Systems, Atlanta, GA, May 2017 Introduction and Literature Review Drop breakup occurs in many multi-phase flows. Analytical or numerical models of that breakup can be used to optimize procedures such as agricultural spray drift, pharmaceutical tablet coating, and engine efficiency and emissions. The advantage of modeling drop break up lies in prediction of the relative quantity of different sized drops so their effects on a larger system can be predicted and system performance optimized. The majority of drop breakup research has focused on Newtonian drops. Nicholls and Ranger (1969), Krzeczkowski (1980), Pilch and Erdman (1987), Wierzba and Takayama (1988), Hsiang and Faeth (1992, 1995), and Liu and Reitz (1997) are among those who identified the five modes of breakup for low Ohnesorge numbers (Oh < 0.1). These modes include vibration (We<11), bag (11< We< 35), multi-mode (35<We<80), sheet thinning (80<We<350), and catastrophic (We> 350). These findings are summarized in the review of Guildenbecher et al. (2009). In order to predict drop breakup, the aerodynamic fragmentation is often modeled by solving gas-phase dynamics over a fixed grid. This grid aids in tracking drop dynamics, which, when coupled with models for aerodynamic drag, drop deformation, and drop fragmentation, results in predictions for breakup. Earlier models were criticized because they were based on boundary layer effects. Current versions employ Kelvin-Helmholtz and Rayleigh-Taylor instabilities (Theofanous, 20101). Deciding which instability is dominant during different time intervals within the breakup event can t be completed because of insufficient experimental data for this dynamic process. Such information must have sufficient temporal and spatial resolution, as well as dynamic range, to capture both large- (initial drop, rim, or core) and small-scale (fragments) structures. Previous efforts on multi-mode regime breakup observed the formations of complex structures, but did not address them quantitatively. This was due to a lack of spatio-temporal resolving capacity of the available measuring techniques, which, as a result, greatly hindered drop breakup modeling. Consequentially, a comprehensive and fundamental characterization of Newtonian drop fragmentation and experimental datasets to support model development remain absent. The majority of experimental data acquired for the modeling of liquid drop breakup were collected by means of 2D high speed imaging and/or PDA. However, these measuring techniques are incapable of recording the 3D spatial distribution of particle sizes and velocities. Furthermore, 2D imaging techniques may result in erroneous detection if the object in question is out of focus. Digital in-line holography (DIH) overcomes these limitations, as it provides 3D, time-resolved information. The measuring technique has been applied to the characterization of multiphase droplets (Tian et al., 2010; Gopalan and Katz, 2010; Lebrun et. al. 2011; Gao et al., 2013) Guildenbecher et al., 2016). While in use, DIH has demonstrated the ability to measure the sizes and 3D locations of the droplets without knowing the refractive index of the liquid. For this study, DIH was used to measure the sizes of fragments formed during the bag, rim, and stamen stages of breakup. The data were used to create a pdf for each stage. These measurements are significant because they have the potential to promote the development of new techniques for the optimal design of atomization systems that use droplet breakup. For example, this research may lead to new designs of fuel injectors in gas turbine and other engines, by creating optimal conditions for control of fuel droplet sizes, which may eventually lead to more efficient energy production and lower pollution levels. It may also contribute to the design of agricultural spray atomizers that optimize the consumption of herbicides and pesticides while also reducing drift to surrounding areas. This research is therefore expected to not only improve the fundamental understanding of drop breakup, but also have a broad and positive impact on society. Experimental Apparatus The drop generator and air nozzle used to study fragmentation are described by Guildenbecher and Sojka (2011) and shown in Figure 1. The air nozzle produces a nearly uniform jet velocity profile (Guildenbecher, 2009), while the drop generator operates in the periodic dripping regime (Clift et al., 1978) and is positioned to release drops of 3 mm diameter above the centerline of the air jet at approximately three second intervals. A drop initial height of 11 cm was used. This provides a vertical drop velocity 1.5 m/s. During this study, DIH was used to investigate fragmentation of DI-water drops as a function of We. Weber number was controlled by varying the air jet velocity. The DIH experimental apparatus follows that of Guildenbecher et al. (2016) and consists of a Big Sky Laser Evergreen (m/n ) frequency doubled Nd:YAG laser that produces a double-pulse (each 90 nsec) train at 2 Hz. The Nd:YAG beam first enters a spatial filter (25 μm pinhole) and lens (125 mm focal length) that expands and collimates it to a diameter of 5.0 cm. The 5.0 cm beam then illuminates the breakup field before being recorded by a Phantom V2512 camera with pixel size 25x25 μm. Typical raw holograms, shadowgraphs, and reconstructed holograms are presented below. Data extraction from these images follows and is discussed in the next section.

3 Results and Discussions Data were collected at four different times during the breakup events. The first time was after the first bag fragmented and before another did. The second time was between the breakup of a second bag and when the rim fragmented. The third time was after the rim had broken up. For 30 We 40, the fourth and final time was after stamen breakup. However, for 45 We 50 the stamen formed a bag and rim of its own, which served in turn as a source of a second stamen and fourth time. The final time was after this stamen broke up. Figure 2 shows typical bag breakup data, in this case the first bag at We=40. pdf(d) has a single peak at a diameter of 100 m and then falls to zero by 600 m. These results were similar for all bag breakups at 30 We 50. Of particular interest was the observation that pdf(d) was the same for both the first and second bags, indicating that the bag breakup physics are independent of how many bags are formed and when they rupture. While the data for We=30 and We=35 are very similar, rim breakup at 40 We 50 yields a pdf(d) having different characteristics, as shown in Figure 4. There is a single maximum at a location similar to that for 30 We 35. This suggests a single dominant breakup mechanism. Figure 3. Fragment size pdf(d) for rim breakup at We=30. Figure 2. Fragment size pdf(d) for bag breakup at We=40. Figure 3 shows pdf(d) after the rim has broken up at We=30. Like the bag breakup phenomenon, pdf(d) has a peak at around 100 m, falls, then remains relatively constant for 200 d 300 m. A second pdf(d) peak occurs between 300 and m, suggesting a different mechanism is responsible for the second peak. Figure 4. Fragment size pdf(d) for rim breakup at We=45. Figure 5 shows a typical stamen breakup pdf(d) for 30 We 35. By this time, the bag and rim fragments had moved out of the field of view so only fragments from stamen breakup were present. This may be why there were several peaks in the pdf(d). Moreover, pdf(d) does

4 not go to zero until 1000 m, which is very large in comparison to the other breakup modes. Figure 5. Fragment size pdf(d) for stamen breakup at We=35. Data for stamen breakup at We=50 are shown in Figure 6; they are representative of behavior for 45 We 50. A single peak is observed suggesting a single breakup mechanism. Figure 6. Fragment size pdf(d) for stamen breakup at We= We 50 require data collection at an additional time due to the stamen forming its own bag before the final stamen breaks up. Figure 7 shows this pdf(d) at We=45. It is clearly multi-modal, with fragments up to 900 m, and is similar to bag breakup pdf(d)s discussed above. Figure 7. Fragment size pdf(d) for stamen rim breakup at We=45. Summary and Conclusions Drop breakup was investigated at 30 We 50 using DIH. Bag breakup yielded consistent results for the entire Weber number range with peaks near 100 m and maximum diameters of approximately 600 m. This was true for both the first and second bags, indicating a bag fragmentation mechanism which is independent of bag quantity. Rim breakup was bimodal for 30 We 35 but 40 We 50 had a single mechanism for breakup. Shadowgraph data support the conclusion that separate physical mechanisms are responsible for bag and rim breakup. Further investigation is required to determine the cause of rim breakup differing between the lower and higher Weber numbers. The quantity of bags, rims, and stamen formed increased with increasing Weber number. 45 We 50 had stamen breakup which resulted in further bags, rims, and stamen. The maximum non-zero pdf(d) value rose to about 1 mm. The final stamen breakup characteristics differed between 30 We 35 and 40 We 50. Probability distributions for stamen fragmentation with the lower We numbers included multiple peaks, while the upper We number range was mono-modal. Acknowledgements This work was supported by the Purdue University Provost Office, the Purdue University School of Mechanical Engineering. References Gao, J., D.R. Guildenbecher, P.L. Reu, V. Kulkarni, P.E. Sojka, and J. Chen, Quantitative 3D diagnostics of multiphase drop fragmentation vis digital inline holography, Optics Letters 38 (2013):

5 Gopalan, B. and Katz, J., Turbulent shearing of crude oil mixtures with dispersants generates long microthreads and microdroplets, Phys Rev Lett, 104, (2010). Guildenbecher, D.R., Lopez-Rivera, C, and Sojka, P.E., Secondary atomization, Experiments Fluids, 46, 371 (2009). Guildenbecher, D.R., and Sojka, P.E., Experimental investigation of aerodynamic fragmentation of liquid drops modified by electrostatic surface charge, Atomization Sprays, 21(2), (2011). Guildenbecher, D.R., M.A. Cooper, and P.E. Sojka, High-speed (20 khz) digital in-line holography for transient particle tracking and sizing in multiphase flows, Applied Optics 55(11) (2016). Hsiang, L.P., and Faeth, G.M., Near-limit drop deformation and secondary breakup, Int l J Multiphase Flow, 18(5), (1992). Hsiang, L.P., and Faeth, G.M., Drop deformation and breakup due to shock wave and steady disturbances, Int l J Multiphase Flow, 21(4), (1995). Krzeczkowski, S.A., Measurement of liquid droplet disintegration mechanisms, Int l J Multiphase Flow, 6(3), (1980). Lebrun, D., Allano, D., Mees, L., Walle, F., Corbin, F., Boucheron, R., and Frechou, D., Size measurements of bubbles in a cavitation tunnel by digital in-line holography, Applied Optics, 50(34), H1-H9 (2011). Liu, Z., and Reitz, R.D., An analysis of the distortion and breakup mechanisms of high speed liquid drops, Int l J Multiphase Flow, 23(4), (1997). Nicholls, J.A. and Ranger, A.A., Aerodynamic shattering of liquid drops, AIAA J 7(2), (1969). Pilch, M., and Erdman, C.A., Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop, Int l J Multiphase Flow, 13(6), (1987)). Theofanous, T.G., Aerobreakup of Newtonian and viscoelastic liquids, Ann Rev Fluid Mechanics, 43, (2011). Tian, L., Loomis, N., Dominguez-Caballero, J.A., and Barbastahis, G., Quantitative measurement of size and three-dimensional position of fast-moving bubbles in air-water mixture flows using digital holography, Applied Optics, 49(9), (2010). Wierzba, A., and Takayama, K., Experimental investigation of the aerodynamic breakup of liquid drops, AIAA J, 26(11), (1988).

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