Experimental Investigation of Viscous Liquid Jet Transitions

Transcription

1 ILASS Americas, 25 th Annual Conference on Liquid Atomization and Spray Systems, Pittsburgh, PA, May 2013 Experimental Investigation of Viscous Liquid Jet Transitions S. Ramalingam 1*, M. D. Cloeter 1, B. Smith 1, S. C. Garrick 2, W. Liu 2 1 Core R&D, Engineering and Process Sciences The Dow Chemical Company Freeport, TX USA 2 Department of Mechanical Engineering University of Minnesota, Twin cities Minneapolis, MN USA Abstract Spray and atomization have been extensively studied in the past due to their broad applications in agriculture, pharmaceutical synthesis, ink jet printing, fuel spray in engines and so on. Fundamental knowledge of atomization process is important in predicting and achieving desired spray characteristics. However, the process is still not well understood due to the underlying phenomena, including turbulent mixing, primary breakup, secondary breakup, and droplet coalescence, etc. To better understand the physics of liquid jet breakup, experimental investigation were carried out in laminar, transient, and turbulent flow regimes to gain a complete understanding towards the breakup behavior. Experiments were conducted using a 4.6 mm diameter cylindrical nozzle with 20 cp glycerin-water mixture and flow rates ranging from 1 gpm to 10 gpm. Experimental investigation covered jet Reynolds numbers between 900 and 9000 and liquid Weber numbers between 1200 and 120,000. Jet transitions are studied via imaging of the jet up to 45 nozzle diameters. As a result, we are able to observe surface dynamics during Rayleigh breakup and satellite droplet formation. In the atomization regime, breakup behavior and droplet size are compared under different flow rates. It is found that droplet size decreases as flow rate increases in atomization regime. Droplets were generated by both ligament breakup and sheet breakup in the atomization regime. The droplet sizes generated by the two mechanisms differ by an order magnitude. It was also interesting to note that the jet transition Weber numbers from first wind induced to second wind induced breakup and second wind induced breakup to atomization shifted to higher values for the viscous jets. * Corresponding author: skramalingam@dow.com

2 Introduction Spray is a collection of small, dispersed liquid droplets surrounded by gas, normally formed from atomization-- the process where bulk liquid column disintegrates into fine droplets[1]. Sprays have broad applications in agriculture, pharmaceutical synthesis, engines, ink jet printing and so on. For example, in agriculture, chemicals such as pesticides are sprayed onto crops. One of the main focuses on agricultural spray control is to maintain the droplet size distribution within a certain range such that the droplets are not too large for the purpose of maximizing contact area, but also not too small, which will lead to droplet drift problems and negatively impact other crops, animals, and humans[2]. In pharmaceutical synthesis, spray drying is frequently used to produce solid powders where a solution is dissolved in liquid solvent and sprayed into a furnace containing hot gas through a nozzle. Droplets generated in such a spray, evaporate quickly and form solid particles that are then collected. The spray drying involves more complicated process including atomization and evaporation, but similar to agricultural spray, the goal is to produce a monatomic droplet size distribution, since large droplets may not evaporate completely while small droplets might be easily damaged in structure in overheated furnaces [3, 4]. Fuel injection in engine has been studied for a long time. In the combustion engine, fuel is ejected from an atomizing nozzle and generates a spray with very fine droplets which evaporate into vapor and mix with air for combustion to happen. In fuel spray, the droplet size needs to be very small in order for the evaporation to be complete in a short time, especially in high speed engines. As listed above, it is necessary to study spray and find ways to control some kind of characteristics in any application. This requires a clear knowledge of spray process. Although sprays have been studied for long, they are still not well understood due to the highly unsteady and complicated interface dynamics. Theories on liquid jets are confined to prediction of Rayleigh breakup region, where the flow is laminar and the droplets are of the same order of magnitude of nozzle[5] [6, 7]. Experimental tools have experienced difficulties, especially on capturing such dense, three dimensional dispersed liquid droplets in gas medium[2]. The main challenge in the numerical study of atomization is to find an efficient way of modeling the complicated topological changes in the spray. Numerical tools developed in recent years, however, have the ability to model such complicated, turbulent, multiphase process involving interfacial changes. With the fast development of large supercomputers, the time required for computing is greatly reduced and the increased accuracy allows researchers to better predict such complex, large scale turbulent multiphase systems. While the numerical tools have been successfully used in modeling sprays, few researches have reported the comparison between numerical results and experimental results. Such comparison in both global (drop size distribution, spray angle, etc) and local dynamics (breakup mechanism) is important to validate the numerical tools so that the technique can be used with confidence in predicting the spray phenomenon. The motivation of this research is to utilize advanced experimental techniques to investigate the breakup of turbulent liquid jet. Liquid jet breakup has been investigated for a long time since Rayleigh first published a paper on capillary breakup of a round jet[5]. Round jet breakup is frequently studied due to its relative simplicity compared to asymmetric jets. Researchers have divided the liquid jet breakup process into four regimes, which are Rayleigh regime, first wind induced regime, second wind induced regime and atomization regime [1, 7]. In Rayleigh regime, the flow is laminar and axisymmetric. The jet undergoes Rayleigh instability caused by surface tension force, and perturbation with wavelength on the order of nozzle diameter grows on the interface of liquid jet, forming droplets with size slightly larger than the nozzle diameter. In first wind induced regime, the jet is still laminar, but no longer axisymmetric. Large droplets on the order of nozzle diameter are still pinched off from the jet. Linear stability theory works well for Rayleigh regime and first wind induced regime, being able to predict breakup length (the length of coherent core in the liquid jet) very well and agreeing with observations from experiments[7]. The first wind induced regime gains its asymmetric shape due to the increasing effect of aerodynamic force from ambient gas. In the second wind induced regime, aerodynamic effect starts to play a significant role and the flow is in transitional regime. Small droplets with sizes order of magnitude smaller than the nozzle diameter start to peel off from the jet. In atomization regime, the dominant force is the aerodynamic force and predominantly fine droplets are formed. Flow is fully turbulent in atomization regime. Second wind induced regime and atomization regime have few theoretical analysis due to highly nonlinear behavior. Second wind induced regime and atomization

3 regime are extremely sensitive to small disturbances and inflow condition. These make the atomization hardly predictable by theory. Thus, the atomization has always been investigated by developing correlations between the operating condition and some characteristics of the spray, such as mean droplet diameter and spray angle[1]. Weber number, Reynolds number and Ohnesorge number have been successfully used by researchers to determine the onset of four regimes in round jets through empirical models[7]. Reynolds number is defined based on liquid property, written as Weber number can be defined based on liquid property or gas property, written as where is liquid density. is gas density, is surface tension coefficient. is nozzle diameter. is jet velocity. is liquid dynamics viscosity. Weber number is frequently used to divide the flow regimes. Experimental investigations report that in Rayleigh regime, We l should be greater than 8, while We g should be lesser than 0.4. For the first wind induced regime, We g needs to be smaller than 13. Second wind induced regime requires We g to be between 13 and Atomization regime requires We g to be greater than Since the goal of this project is turbulent breakup, the simulations and experiments will be focused on second wind induced regime and atomization regime where fine droplets are formed. Experiment system As mentioned earlier, the second wind induced breakup is expected between We g 13 and 40. Experiment conditions are chosen such that the Reynolds number and liquid Weber number are less than 6000 and respectively. The chosen Reynolds number and Weber number ranges ensure that the experimental conditions are simple for fundamental analysis, realizable in the lab, and reproducible in numerical analysis. Glycerin-water mixture of 20 cp viscosity as the working liquid is sprayed through a ¼ nozzle using gear pump. The gear pump with a pulse dampener was capable of delivering flow rates in the range of 1-10 gpm. The experiments were conducted with 10 gal. batch of working liquid in a closed loop such that the sprayed liquid was fed back to the feed tank. The recycle ensured that a continuous spray was achievable and initial dynamics are eliminated in the analysis. In order to pump 20 cp water and glycerin solution up to 10 gallons per minute, a Baldor 2 hp DC motor equipped with a 1 inch Eco Gearchem Pump was used. Short running piping was used to ensure that pressure drop would not affect pump s performance. On the suction side of the pump, 1 inch hard pipe was used to deliver the 20 cp solution to the pump. No check valve was needed. A 14 gallon plastic drum was used to hold 10 gallons of solution. This served as a feed tank and catch tank for the spray nozzle. On the discharge side of the pump, a bypass was installed using a Tee with a valve and returned to the feed tank. Using ½ inch pipe allowed the pump to work at the upper end of the pump curve. This would ensure that the flow rates would be met. From the discharge Tee, the outlet flow ran through an OMEGE rotameter. From the rotameter to the 4.6 mm I.D. nozzle, both ½ and ¾ inch plastic pipe was used to reduce pressure drop. The flow rate was set by the pump rpm and fine tuned by the bypass valve. The 20 cp solution was generated by using >80% by volume of glycerin in water. The solution was mixed and the viscosity was measured to be cp. The experiment was conducted with glycerin water mixture within the temperature range of o C. As indicated in Error! Reference source not found., the generated mixture was cp at 20 o C. At that concentration, the mixture density was measured to be 1.16 g/cc and the surface tension was inferred from charts to be 63 mn/m. Table 1 Glycerin-water mixture properties Liquid viscosity (cp) Liquid density (kg/m 3 ) Surface tension (mn/m) Nozzle diameter (mm) For the mixture with above properties, the first induced to second wind induced breakup transition is expected to happen at a flow rate of 3.3 gpm and the second wind induce breakup to atomization transition is expected to happen at 5.6 gpm. These flow rates correspond to We g of 13 and 40 respectively. A

4 maximum of 10 gpm was achievable with the current experimental setup. Visual observation at various flow rates showed that the jet was axisymmetric until 5 gpm flow rate. Small droplets were observed to peel from the jet s surface above 5 gpm flow rate. This phenomenon is the indication of the onset of second wind induced breakup. Therefore, measurements were made at 1 gpm interval for flow rates between 1-5 gpm and 0.5 gpm interval for flow rates beyond 5 gpm. Due to vibrations generated by the gear pump, the fluctuations at high flow rate can be as high as 0.2 gpm in spite of the pulse dampener. At each flow rate, the liquid temperature and nozzle back pressure are measured. High speed images of the jet are captured using a Photron FASTCAM SA3 camera at 1000 frames per second rate. The images of the jet were face lit with couple of incandescent lights and captured on a white background. The camera shutter speed, set at Hz, ensures the capture of instantaneous air-liquid interface without distortion due to jet motion while allowing enough light for a bright image. The resolution of the camera is set at 1024x256 pixels for flow rates upto 5 gpm and 1024x512 pixels for 5 10 gpm with the longer dimension along the jet direction. The higher pixel count in the transverse direction is necessary to capture the wider, non-axisymmetric jet at higher flow rates. The width of the nozzle in the image is used as a scale to convert pixel size to length scale. Two sets of at least 1000 images were captured at each flow rate. The first set of images spanned 11 cm in the direction of flow and captured the jet dynamics in the first 10 cm from the nozzle. The second set of images also spanned 11 cm in the flow direction but captured the dynamics of the jet beginning 10 cm downstream of the nozzle. The two sets of images together enabled the study of jet dynamics upto 20 cm (equivalent to 45 nozzle diameters) downstream of the nozzle. The high speed images are used to study the breakup phenomena of the liquid spray. In the axial range covered, the jet is dense and only partially broken in the second wind induced and atomization regimes. Therefore, no attempt is made to quantitatively measure the spray drop sizes. However, few images capture the breakup phenomena along the jet surface clearly enough to make qualitative assessment on the drop sizes. Liquid jet in laminar regime Figure 1 shows Rayleigh breakup of the liquid jet at increasing flow rate. At 2 gpm, flow is laminar and axisymmetric. Droplets larger than the nozzle diameter are formed and pinched off from the tip of the jet. In the mean time, droplets much smaller than the nozzle diameter, called satellite droplets, are formed between large primary drops. As flow rate increases to 3 gpm, flow is still laminar and axisymmetric. However, the breakup length is longer than 2 gpm case. Diameter of droplet pinched off from the tip of the jet is slightly larger than nozzle diameter. As flow rate increases to 4 gpm and 5 gpm, breakup length becomes even longer and falls out of the camera range. This trend of breakup length agrees well with theory, which states that in Rayleigh breakup, the breakup length increases with increasing flow velocity. When comparing Figure 1 Laminar jet breakup at (a) 2 gpm. (b) 3 gpm. (c) 4 gpm. (d) 5 gpm. Corresponding Weg are 1.26, 5.05, 11.37, and respectively. (c) and (d), one can observe the perturbation developing on the interface of the liquid jet. The wave length of such perturbation is much longer than nozzle diameter, and has a magnitude that increases with jet velocity. Due to the nature of gear pump being used, it is possible that such long wave perturbation is caused by the periodic flow perturbation created by the pump. Thus, to capture the similar effect in numerical simulation, it is important to add the perturbation with the same frequency to the inlet flow. Figure 2 and Figure 3 show the time sequences of droplet formation at 1 gpm, 2 gpm respectively. Both cases are in Rayleigh breakup regime. During Rayleigh breakup, the flow undergoes Plateau-Rayleigh instability, and droplets with diameters larger than nozzle diameters are formed[7]. At 1 gpm, the primary droplet has a diameter of 8.25 mm. While at 2 gpm, the primary droplet formed has a larger diameter of 9.28mm.

5 Besides the increase of primary droplet size with increasing Weber number, another distinct feature is the formation of satellite droplets at 2 gpm. Satellite droplets are relatively small droplets formed between primary droplets in a liquid jet. While the primary droplet size is affected by the nozzle dimension, the formation of satellite droplets is a localized phenomenon and completely independent of the nozzle size. As observed in Figure 3, right before the first primary droplet pinches off, a very thin liquid filament connects between the primary droplet and the bulk jet. This thin filament breaks first near the primary droplet and contracts at the tip, bounces back towards upstream direction quickly due to surface tension force at the tip of the filament. The filament then breaks near the second primary droplet to be formed. After detaching from the bulk jet, the stretched filament recoils, oscillates between oblate and prolate spheroid shapes due to liquid inertia and damped by liquid viscosity, and finally forms a spherical satellite droplet. The same process is repeated when the second primary droplet gets pinched off from the bulk jet, and forms another satellite droplet in front of the third primary droplet. Thus, two satellite droplets can be observed both in front of and behind the second primary droplet. In contrast, satellite drops are not formed at 1 gpm. And there is no clear observable filament connecting the primary droplet and the bulk liquid. The primary droplet that is about to be pinched off from the tip of the jet has a much more spherical shape comparing to the 2 gpm case. Without such filament, satellite droplet cannot be formed during pinch-off of primary droplet. Instead, droplet is connected to bulk liquid through a very short neck right before pinch-off. After pinch-off, this neck bounces to integrate with the bulk liquid column. Liquid jet in transient and turbulent regime Error! Reference source not found. shows the liquid jet in transient and turbulent regime, with flow rate ranging from 6 gpm to 10 gpm. At 6 gpm, disturbances with shorter wavelength can be observed on the interface of the liquid jet, as well as the long wave length disturbances observed earlier in Rayleigh breakup regime. Breakup does not happen in the region captured by camera. At 7 gpm, disturbances with relatively shorter wavelength can be observed on the interface of the jet and grow significantly as flow goes downstream. As the magnitude of short wavelength disturbances grow, some of them develop into fingers pointing outwards from the jet interface. The jet, which is laminar as it emerges from the nozzle, becomes turbulent towards the end of the domain. At 7.5 gpm flow rate, the oscillations on the interface caused by short wave disturbances is even stronger, flow becomes more turbulent, and longer and thinner ligaments are formed. Towards the end of the domain, due to the velocity gradient existing between liquid column and gas medium, ligaments are elongated, and droplets with diameter much smaller than the nozzle diameter are pinched off from the tip of the ligaments. At 8 gpm, magnitude of the disturbances grows further and disturbances with higher frequencies than lower flow rate case can be observed. One noticeable feature from the figure is the liquid sheet formed downstream of the jet. The sheet is attached to the bulk liquid column of the jet and spreads in the cross stream direction. Several ligaments can be observed forming at the edge of the sheets. As flow rate increases to 8.5 gpm, more ligaments are formed, causing more droplets pinched off from the tip of the ligament. Sheet structure can still be observed, and the spray angle increases due to the wider spreading of jet in the radial direction. At 9 gpm, 9.5 gpm and 10 gpm, it can be observed that as flow rate increases, more and more droplets are formed and they spread wider in the radial direction. The axial distance from the nozzle, where the first droplet pinches off from the jet, decreases as flow rate increases. Smaller droplets appear to be generated with increasing flow rate. Very fine droplets are generated at the middle of the domain at the higher 10 gpm case. The fact that smaller interfacial structures or droplets are formed as flow rate (or Weber number) increases can be explained in analogous to the concept of smaller scale in turbulent flow with increasing Reynolds number. In turbulent flow, the smallest scale is the size of the smallest eddy. Larger eddies are unstable and will break into smaller eddies. These small eddies might further break into smaller ones. At certain size, the eddy becomes stable due to the balance between viscous and inertial forces. This smallest size is determined by Reynolds number, since Reynolds number characterizes the ratio of inertial force and viscous force. In interfacial flow dominated by Weber number, the larger interfacial structures are unstable and will breakup into droplets or secondary structures. Until a small enough surface is generated such that the surface tension force overcomes the inertial force, the unstable interface continues to break up to generate smaller and smaller droplets. Larger the Weber number, smaller the droplet size. In Figure 4, as flow rate

6 increases, one can observe smaller droplets forming, as well as more small scale disturbances in the flow. This is due to the fact that Weber number and Reynolds number are increased at the same time with increasing flow velocity. Figure 5 shows the droplet formation at downstream location starting at 27D nozzle from the nozzle outlet under different flow rates. The flow regime varies from second wind induced regime to atomization regime. At 7 gpm, droplets are formed by pinch-off from the tip of the ligaments due to surface tension force. Towards the end of the domain in this figure, it is interesting to observe that while the larger droplet is pinched off from the tip of ligament, two smaller droplets are formed at the same time. At 7.5 gpm and 8 gpm, more droplets are formed from the pinch-off effect of the ligaments. The liquid core does not have a cylindrical shape. Instead, the bulk liquid deforms, twists, and forms coherent structures. At 8.5 gpm, the bulk liquid column breaks at the middle of the domain, forming liquid sheets and filaments. Droplet distribution appears to have a more polarized distribution. Larger droplets as well as fine droplets are formed simultaneously. As the flow rate further increases to 9 gpm, 9.5 gpm and 10 gpm, there are more and more fine droplets formed and the flow is in atomization regime. The droplets are spreading wider in the radial direction with increasing Weber number. To further illustrate the droplet forming mechanisms in atomization regime, a time sequence of jet breakup at 9.5 gpm case is shown in Figure 6. Two distinct droplet forming mechanisms can be found in the figures. One is from the pinch-off and breakup of the ligaments caused by surface tension. At low flow rates, this is the only mechanism of drop formation. As Shinjo and Umemura[8] report, the pinch-off of ligament is dominated by the unsteady short wave instability mode developing along the ligaments. The droplet formed by this mechanism has a diameter on the order of magnitude of the ligament diameter. Another mechanism observed is the forming of very fine droplet from liquid sheet. In the first image of Figure 6, a thin sheet is formed in the white circled region. This sheet quickly breaks and burst into several fine droplets. A rough estimate of the droplet size shows that the droplet formed from the ligament is an order of magnitude larger than the droplets formed from burst of liquid sheet. Significant fraction of droplets seen in this regime is produced from such sheet bursts. Figure 7 shows a time sequence of jet breakup and illustrate how liquid sheets burst into droplets. The region pointed by the green arrow shows that a hole first occurs in the sheet, then the edge of the hole quickly contracts. Such contractions are caused by surface tension force at the edge of the hole. The hole then quickly increases in area. It can be clearly observed that after enlargement of the hole, the sheet contracts into filaments. In a sheet where multiple holes exist and develop, the sheet will quickly evolve into multiple connected filaments. From the region pointed by the red arrow, it can be observed that the filaments will be stretched and break into small droplets. Several droplets are formed simultaneously during the breakup of filament. A distinct difference between the breakages of filament and the breakup of ligaments is that the breakup of a single filament will normally form lots of small droplets at the same time, while a single ligament will normally form fewer droplets. An image-based estimation on the diameter of the largest droplet size formed is carried out. The largest droplet in each image is found manually and measured in pixel using image processing software. The length in pixel is then converted into physical length based on the recorded scale of the image. The value is meant to show conceptually how the droplet size changes with Weber number. Thus, only one representative image at each Weber number is processed, and the droplet size given is not statistical value. At 10 gpm, the size of largest droplet has decreased by 72% compared to the case where flow rate is 7 gpm. Although it is insightful to also look at other important characteristics of droplet size, such as the size of smallest droplet size and the droplet size distribution, these are difficult to be obtained from the current image due to the larger relative error from pixel measurement for smaller droplets. However, it is intuitive from the image that the larger the Weber number, the finer the smallest droplets, and the finest droplets are on the order of one pixel in diameter, which corresponds to roughly 120 microns. These findings suggest that with increasing Weber number, the peak of droplet size distribution curve will shift towards smaller drop size value. Conclusions Experimental investigations are carried out in this research, in order to help understand the physics of liquid jet atomization. Experiments are carried out in laminar, transient and turbulent flow regimes, and breakup regime ranges from Rayleigh breakup to

7 atomization. In Rayleigh breakup regime, it is observed that the breakup length increases with increasing flow rate. This trend agrees well with the breakup lengths reported in literature. Satellite droplets in Rayleigh breakup regime are formed at flow rates greater than 2 gpm for the current experimental conditions but not observed at lower flow rates. Further observations point out that the long and thin neck connecting the primary droplet and the bulk liquid column causes the formation of satellite drops. In turbulent regime, change of flow regimes with increasing flow rate is investigated. The flow undergoes transient and turbulent regimes for Re > 4000 and becomes more and more chaotic with increasing flow rate. Increasing number of droplets and ligaments are formed with increasing flow rate accompanied by the spreading of droplets in the radial direction. Smaller interfacial structures and droplets are produced with increasing flow rates and such phenomena are analogous to smaller eddy structures with increasing Reynolds number in a turbulent flow. Further investigations downstream of the jet show two distinct droplet forming mechanisms in atomization regime. Long and thin ligaments are formed at the surface of the jet and droplets are pinched off from the tip of these ligaments, forming relatively larger droplets. Liquid sheets are also produced in the jet, which evolve into long and thin connected filaments. These filaments break up into several finer droplets simultaneously. The fraction of droplets generated by thinning liquid sheet can be observed to increase with Weber number. An imagebased rough estimation of largest droplet size shows that the largest droplet size decreases with increasing flow rate. 5. Rayleigh, L., On the instability of jets. Proc. London Math. Soc., (1): p Sharp, D., An overview of Rayleigh-Taylor instability. Phys. D, (1-3): p Lin, S. and R. Reitz, Drop and spray formation from a liquid jet. Annu. Rev. Fluid Mech., (1): p Shinjo, J. and A. Umemura, Simulation of liquid jet primary breakup: Dynamics of ligaments and droplet formation. Int. J. Multiphase Flow, (7): p Reference 1. Dumouchel, C., On the experimental investigation on primary atomization of liquid streams. Exp. Fluids, (3): p Crossland, N. and S. Shires, Fate and biological effects of spray drift deposits in fresh water adjacent to agricultural land. Aquatic toxicology, (5-6): p Okuyama, K. and I. Wuled Lenggoro, Preparation of nanoparticles via spray route. Chem. Eng. Sci., (3-6): p Vehring, R., Pharmaceutical particle engineering via spray drying. Pharm. Res., (5): p

8 ILASS Americas, 25 th Annual Conference on Liquid Atomization and Spray Systems, Pittsburgh, PA, May 2013 Figure 1 Laminar jet breakup at (a) 2 gpm. (b) 3 gpm. (c) 4 gpm. (d) 5 gpm. Corresponding We g are 1.26, 5.05, 11.37, and respectively. Figure 2 Droplet formation in Rayleigh regime at 1 gpm (We g = 1.26) * Corresponding author: skramalingam@dow.com

9 Figure 3 Droplet formation in Rayleigh regime at is 2 gpm (We g = 5.05) Figure 4 Turbulent jet breakup at (a) 6 gpm. (b) 7 gpm. (c) 7.5 gpm. (d) 8 gpm. (e) 8.5 gpm. (f) 9 gpm. (g) 9.5 gpm. (h) 10 gpm. Corresponding We g ranges from

10 Figure 5 Droplet formation within transient and turbulent regime at (a) 7 gpm. (b) 7.5 gpm. (c) 8 gpm. (d) 8.5 gpm. (e) 9 gpm. (f) 9.5 gpm. (g) 10 gpm. Streamwise location of images starts at 27D nozzle from the nozzle outlet Figure 6 Two mechanisms of droplet formation in spray at 9.5 gpm Figure 7 Droplet formation through ligament and sheet breakup from liquid sheet at 9.5 gpm