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Experimental Investigation of Droplet Impact on Metal Surfaces in Reduced Ambient Pressure
Available online at www.sciencedirect.com
ScienceDirect Procedia Manufacturing 10 (2017) 730 – 736
45th SME North American Manufacturing Research Conference, NAMRC 45, LA, USA
Experimental investigation of droplet impact on metal surfaces in reduced ambient pressure B. R. Mitchell, T. E. Bate, J.C. Klewicki, Y. P. Korkolis, and B. L. Kinsey Mechanics, Materials and Manufacturing Research Group Department of Mechanical Engineering University of New Hampshire Durham, NH, USA
Abstract Impacting water droplets are capable of eroding steam turbine blades, high speed aircraft and even serve as a machining operation. In this latter process, high velocity (~100m/s) water droplets impact a solid surface under conditions in which the ambient air pressure is sub-atmospheric. The physics of this erosion mechanism is not completely understood. To begin to unravel these physics, we present results pertaining to the effects of ambient air pressure on the impact force of low velocity (1m/s) droplets. It is well known that droplet splash is suppressed when the ambient air pressure is reduced. The effects on the associated impact force are, however, unknown. In this article we examine the impact force of 3.5mm diameter, low velocity droplets in a reduced pressure environment. A 38x38x50cm vacuum chamber fitted with a unidirectional piezoelectric force sensor to measure the transient force of impacting droplets. Preliminary results in atmospheric air pressure reveal that the impulse of the droplets depends linearly on impact velocity while the average impact force depends quadratically on impact velocity. The results under reduced pressures are compared and discussed relative to the underlying physics. ©©2017 by Elsevier B.V. by This is an open access article under the CC BY-NC-ND license 2017Published The Authors. Published Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of 45th NAMRI/SME. Peer-review under responsibility of the organizing committee of the SME North American Manufacturing Research Conference Keywords: Water droplet; erosion, vacuum
1. Introduction The impact characteristics of a liquid droplet is becoming widespread in industry and academia, with considerable attention focused on the splashing mechanisms in coating flows (i.e. inkjet printing) [1-3]. The corresponding impact force induced by a droplet on metal surfaces is not as prevalent, but is, however, an ever growing concern. Under the right conditions, liquid droplets are capable of eroding steam turbine systems [4], and scouring supersonic aircraft flying through rain storms [5]. This droplet induced erosion process can be harnessed through a focused waterjet,
2351-9789 © 2017 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 45th SME North American Manufacturing Research Conference doi:10.1016/j.promfg.2017.07.067
B.R. Mitchell et al. / Procedia Manufacturing 10 (2017) 730 – 736
and used as a materials processing technique [6]. This technique, HIP-SWaD (High Impact Pressure Supersonic Water Droplets), is different from waterjet cutting as a train of water droplets are used to transport momentum to a workpiece rather than a continuous jet, see figure 1. Also, no abrasive medium is used, which produces an environmentally friendly process. In this process, a source of high pressure (>1,500 bar) forces water through an orifice creating a high velocity continuous jet (>600m/s) which breaks-up into discrete droplets due to surfacetension-induced instability, under the appropriate conditions [7]. See figure 1 (a). The high velocity droplets collide and exchange their momentum with a workpiece causing deformation and ultimate material failure. Figure 1 (b) shows deformed steel after being machined with high velocity water droplets, which were emitted from a high pressure jet at the University of New Hampshire [8]. The exploitation of this water droplet impact phenomenon in industrial applications as a means to deform and remove material does not currently exist. If the impact dynamics of water droplets can be understood and controlled, then industries would have the framework upon which they could employ this phenomenon in novel manufacturing equipment. Interestingly, this machining technique has been effective only in reduced-pressure environments. Droplets become an ineffective mist, due to atomization [9] which occurs when the ambient pressure is too high, relative to dd vacuum pressure (0.1 bar). Viscous drag imparted by the surrounding gas severely deforms and ruptures the droplets causing them to fragment into smaller droplets disabling the inertial mechanisms necessary for material failure upon impact. Apart from this atomization process, droplets that strike a material may splash, sending a crown-like liquid film Figure 1 – a) Schematic of water droplet formation before collision with vertically away from the material. Fundamentals workpiece, b) Scanning Electron Microscope (SEM) image of removed paint and deformed steel caused by high velocity (~600m/s) water droplets from a of droplet splash have been the focus of many focused jet, 6.4mm/s jet traverse speed, 8kPa ambient air pressure researchers in the field of ink-jet printing, since attenuation of the splash allows for smooth deposition of ink droplets producing a high-resolution printing process. One method of attenuating the splash is by reducing the pressure surrounding the droplet. First reported by Xu et al [10], the splash of a droplet vanished once the ambient air pressure was reduced below a critical threshold. They found that the lateral liquid jet, known as the lamella (see figure 2), adheres to the surface below this critical value. An important quantity governing the formation of a droplet’s lamella and its subsequent splash is characterized by the Weber number, We=ȡ92DıZKHUHȡ is the OLTXLG¶VGHQVLW\9LVWKHLPSDFWYHORFLW\'LVWKHGURSOHWGLDPHWHUDQGıWKHVXUIDFHWHQVLRQ)RUPDOO\WKH:HEHU number signifies the ratio of inertial pressure to capillary pressure. For low Weber numbers We<<1, capillary pressure dominates and preserves the spherical shape of the impacting droplet. This type of impact does not create a lamella, as the droplet’s surface tension is strong enough to withstand the inertia from the bulk fluid in the collapsing drop. However, when the Weber number is sufficiently large We>>1, surface tension cannot hold back the inertia and thus a lamella is formed. Figure 2 shows an axisymmetric schematic of a droplet with a lamella jetting radially away from the initial point of contact. When the droplet makes first contact with the solid, the fluid at the initial point of contact suddenly decelerates, as time progresses, more fluid accumulates around this point as the fluid’s momenta is diverted from the perpendicular (Z) to the parallel (r) direction(s) of the solid. The laterally moving fluid bulges the liquid-gas interface giving rise to a fast, annular liquid jet (lamella). The condition for which the lamella either slides parallel about the solid or is ejected vertically away, is dictated by the surrounding gas.
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As the expanding lamella gains momentum its apparent contact DQJOH ș LQFUHDVHVGHYHORSLQJD Bulk of droplet wedge at the solid-liquid-gas interface [11, 12], see figure 2. The gas in this immediate region is Surrounding gas Z trapped, permitting a thin layer of air to develop under the advancing lamella [13]. (The surrounding gas is modelled as an inviscid fluid, Lamella in which the Reynolds number is sufficiently large Wedge (Re>>1) Re=VD/Ȟ, where Ȟ is the gas’s kinematic Initial point Region viscosity [14]). The thin layer of air acts as a of contact ș lubricant for the propagating lamella and r eliminates the viscous boundary layer the lamella would have if it were in contact with the solid Solid [15]. With respect to the front of the lamella, air on the top side travels at a higher velocity than on Figure 2 – Axisymmetric schematic of droplet lamella the bottom. It is well known, from inviscid flow theory, that faster moving regions of the flow correspond to areas of lower pressure, therefore a pressure difference exists across the lamella. The pressure difference imparts a vertical lift force onto the lamella, analogous to an air foil, providing the lamella with an upwards trajectory, known as a splash. A detailed analytical description of lamella propagation and its associated splash can be found in [16]. In the absence of a surrounding gas (or in the case of reduced pressure, below the critical pressure), the lamella has no substance to gain lift from, therefore no splashing exists in a vacuum (i.e., low pressure). Since the impact physics are altered in reduced pressure environments, whether the corresponding impact force is altered as well is unknown. Droplet impact force in atmospheric pressure has been characterized by the authors through an extensive numerical and experimental investigation [17]. Agreement was established between numerical and experimental results for the impact velocities considered, (1-3m/s). Droplet impulse was found to depend linearly on impact velocity, while the peak force depended quadratically on impact velocity. As a continuation to this prior research, the dependence of ambient air pressure on the droplet impact force is investigated. A 380x380x500mm vacuum chamber was constructed to create a low pressure environment to investigate the impact force of droplets in reduced ambient pressures. In this paper, the impact force of 3.5mm ethanol droplets traveling at 4m/s is measured with a piezoelectric force sensor. In order to promote splashing, ethanol was used in the experiment as opposed to water, which has a surface tension over 3 times that of ethanol (at room temperature 19°C). Water droplets require greater impact velocities to obtain a splash, which is undesirable since high velocities deform the droplets from a spherical shape (due to air drag) and cause variations in impact locations due to turbulence. Ethanol droplets, which mitigate these negative effects, are favored owing to their inherent ability to splash at low velocities (lower free fall drop heights). For comparison, the critical impact splash speed for a 3.5mm diameter water droplet is over 4m/s while the critical impact speed for an ethanol droplet of the same diameter is under 2m/s [16]. In the experiments presented in this paper, the ambient pressure surrounding the droplets is changed to produce conditions in which 1) the droplet splashes and spreads vertically away from the initial point of contact, and 2) the droplet spreads radially along the surface about the initial point of contact. A high-speed camera is used to record the droplets’ velocity and deformation upon impact. The primary investigation is to compare the impulse and forces associated with the two different impact phenomena. 2. Experimental setup All A vacuum chamber was used as the testing apparatus where the air pressure could be varied to within a fraction of a kilopascal. A Hamilton model 1001 gastight microliter syringe was used with a variety of needles to produce droplets with diameters from 2mm to 4.2mm, however only one droplet diameter was tested, 3.5mm. Ethanol (200 proof ethyl alcohol 64-17-5) manufactured by PHARMCO-AAPER, was used for all tests in a constant
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temperature environment (19°C). Ethanol’s density is 789kg/m^3, its surface tension is 0.022 N/m and its kinematic viscosity is 1.52 (10-6) m2/s. The droplets were released from the syringe 81cm above the force sensor to impact at a velocity of ~4m/s. While the high speed camera is used to record the droplets’ deformation upon impact, it also serves to determine the impact velocity and diameter of the droplets. The camera used was a Photron Fastcam SA4 high-speed camera with an in-house position-tracking software to determine the droplets’ impact velocity. All droplet impacts were filmed at 13500fps with an exposure time of 28ȝs. A Northstar 250Watt light was used to illuminate the droplets while a 60mm Nikkor lens with a 14mm extension tube was used to magnify the droplets. The position tracking software utilized a cross-correlation algorithm which determined the physical displacement of a droplet between two consecutive images. The physical displacement was then divided by the time between consecutive images to obtain the droplet’s velocity. The impact force of 5 trials were tested in atmospheric conditions, while 4 trials were tested in a partial vacuum condition (23.3kPa). The impact velocity of the atmospheric droplets was 3.95m/s, while the impact velocity of the partial vacuum droplets was 4.07m/s. The increase in velocity is attributed to the decreased in air drag of the droplets in partial vacuum. The force sensor used was a PCB model 209C11 piezoelectric force sensor with a calibrated sensitivity of 524.3 mV/N. The sensor measured unidirectional transient forces perpendicular to its 17.9mm diameter delrin plastic impact plate. A PCB model 482 signal conditioner and a Lecroy Wavesurfer 64MXs-B oscilloscope sampling at 1MHz were used for all experimental measurements. While an Edwards 30 E2M30 vacuum pump was used to reduce the pressure in the vacuum chamber, a MKS Series 902 Piezo Transducer was used to measure the ambient pressure inside the chamber. A schematic of the experimental setup is shown in figure 3a, with an image of the setup in figure 3b.
a)
b)
syringe
vacuum chamber
oscilloscope
camera
Figure 3 – Experimental Setup; a) schematic, b) image (some items not shown)
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3. Results and discussion Figure 4 shows the stages of droplet deformation for the 3.5mm diameter ethanol droplets impacting at 4m/s in standard atmospheric pressure 101kPa (a), and in reduced ambient pressure 23.3kPa (b). The time between successive images is 370ȝs. In both cases, the initial droplet deformations tend to resemble truncates spheres with a thin liquid film spreading radially away from the initial point of contact. Interestingly, for the atmospheric case, the liquid film spreads vertically away from the surface, while in the reduced ambient pressure case, the thin film remains attached and flows parallel to the surface. The vertical crown-like splash, in figure 4a, is commonly referred to as a corona splash [18]. As the surrounding atmospheric pressure is reduced the onset of corona splashing is
a)
1mm
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Figure 4 - 3.5mm Ethanol droplet impact at 4m/s in atmospheric pressure (a) and in partial vacuum (23.3kPa) (b). Time between successive images is 370us.
B.R. Mitchell et al. / Procedia Manufacturing 10 (2017) 730 – 736
delayed. When the ambient pressure is reduced below a certain threshold no corona splash is observed. From prior experiments, the threshold pressure for a 3.4mm diameter ethanol droplet impacting at 4m/s was found to be around 40 +/-5 kPa [9]. With similar conditions as in [10], we also observe splash attenuation in reduced pressure, see figure 4. While the high speed camera recorded the droplets’ deformation upon impact, the piezoelectric force sensor measured the droplets’ impact force. Owing to the small impact force generated by a droplet impact, a very sensitive force sensor must be used. The significant noise superimposed onto the force-time curves in [17] was attributed to the use of an oversized force sensor. In the present study, a force sensor 5 times more sensitive was used to obtain clear, unambiguous force-time curves. Five and four trials were recorded in the atmospheric (101kPa) and partial vacuum (23.3kPa) tests, respectively. The trials were averaged for each respective pressure and are presented in figure 5. The atmospheric and partial vacuum trials are labeled in blue and red, respectively. The general characteristics of the droplets’ force-time curve is a fast rise time to a maxima, followed by a progressively longer period of decreasing impact force before leveling off. There exists a higher peak force for the partial vacuum tests than the atmospheric tests. This is attributed to the slightly higher impact velocity in the partial vacuum case. Since there is less air drag acting on the droplet as it is falling, the droplets in the partial vacuum impact at higher velocities. The force-time curves exhibit superimposed high frequency oscillations. Due to the inherent nature of impacts, longitudinal waves propagate throughout the measurement system when a dynamic load is applied. These waves are a characteristic of the measurement system’s natural frequency. The measurement system includes the impact plate, force sensor and the 4kg steel block attached to the bottom of the force sensor. If the droplets’ strike the impact plate off center they introduce a non-unidirectional applied force, which activate other modes of vibration. Experiments were carried out with this in mind however, some oscillations still exist. In order to attenuate these undesirable oscillations, the data is filtered with a FIR low pass filter with a cut off frequency of 10kHz, shown in figure 6. The filter successfully attenuated the high frequency noise, however there still exists some oscillations for the partial vacuum tests, most apparent around 1000ȝs. Different modes of oscillation were excited by hitting the force sensor off center for the partial vacuum case. In figure 4 it is apparent that the partial vacuum tests did not strike the droplet directly in the center of the force sensor, leading to additional oscillations. It was shown in [17], that droplet impulse scales linearly with impact velocity, however the dependency of impulse on ambient pressure was not investigated. The impulse of each of the curves in figure 6 was calculated by integrating the force-time curves along the domain of their time durations, which is the time the droplet exerts a positive normal force onto the force sensor. For both the atmospheric and partial vacuum trials, the time duration is roughly 1700ȝs. The impulse for the atmospheric and partial vacuum tests was found to be 67.7 and 72.7 ȝN-s respectively. Since both curves have roughly the same time duration, the higher impulse in the partial vacuum case is attributed to its higher peak force.
Figure 5 – Averaged force-time curve
Figure 6 – Filtered force-time curve
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4. Conclusion The materials processing technique, HIP-SWaD, is a process by which a discrete train of droplets impact and erode metal surfaces. Due to droplet fragmentation and atomization, the process has been effective only in reduced ambient pressures. In this paper, we investigated the significance of the ambient pressure during droplet impact, using the droplet’s impulse and peak impact force as criteria to distinguish the ambient pressure’s effect. A 3.5mm ethanol droplet impacting at 4m/s in standard atmospheric pressure (101kPa) and reduced ambient pressure (23.3kPa) showed vivid differences. The droplet impacting in atmospheric pressure, splashed with a significant corona that later fragmented into a myriad of smaller droplets, while the droplet impacting in reduced ambient pressure remained attached and spread radially along the surface. Despite the prominent difference in splash, no major differences in impulse and peak force were observed. Acknowledgements Funding from the U.S. National Science Foundation (CMII-1462993) is gratefully acknowledged. References [1] R. Dean, D. Nelson, M. Brown, R. Couch, M. Blanchard, (2008), “Method and apparatus for forming high speed liquid”, US Patent No. 7,380,918 B2. [2] L. Rayleigh, (1879) “On the instability of jets.” Proceedings of the London Royal Society, 10, 4-13. [3] G. Amini, Y. Lv, A. Dolatabadi, M. Ihme, (2014). “Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis.” Physics of Fluids, 26, 114105. [4] J. Yang, W. Chien, M. King, W. Grosshandler (1997) “A simple piezoelectric droplet generator.” Experiments in Fluids, 23, 445-447. [5] S. Tomotika (1935), “On the instability of a cylindrical thread of viscous liquid surrounded by another viscous fluid.” Proceedings of the London Royal Society, 150, 322-337. [6] S. S. Cook (1928), “Erosion by water-hammer.” Proceedings of the London Royal Society, 119, 481-488. [7] F. P. Bowden and J. E. Field, (1964), “The brittle fracture of solids by liquid impact, by solid impact, and by shock.” Proceedings of the London Royal Society, 282, 331-352. [8] G. C. Gardner, (1963), “Events leading to erosion in the steam turbine.” Proceedings of the Institution of Mechanical Engineers, 178, 593601. [9] Y. C. Huang, F. G. Hammit, and W. J. Yang, (1973), “Hydrodynamic phenomena during high-speed collision between liquid droplet and rigid plate.” Journal of Fluids Engineering, 95, 276-292. [10] W. F. Adler, (1995), “Waterdrop impact modeling.” Wear, 186, 341-351. [11] K. K. Haller, Y. Ventikos, and D. Poulikakos, (2002), “Computational study of high-speed liquid droplet impact.” Journal of Applied Physics, 92, 2821-2828. [12] P. E. Schleusener and E. H. Kidder, (1960), “Energy of falling drops from medium pressure irrigation sprinkler.” Agricultural Engineering 41(2), 100-103. [13] R. S. Palmer, (1965), “Waterdrop impact forces.” Trans. ASAE, 8, 69-70. [14] S. E. Hinkle, (1989). “Water droplet kinetic energy and momentum measurement considerations.” Applied Engineering in Agriculture, 5, pp. 386-391. [15] A. C. Imeson, R. Vis and E. deWater, (1981), “The measurement of water drop impact forces with a piezo-electric transducer.” Catena, 8, 83-96. [16] A. S. Grinspan, & R. Gnanamoorthy, (2010) “Impact force of low velocity liquid droplets measured using piezoelectric PVDF film.” Colloids and Surfaces, A, 356, 162-168. [17] J. Li, B. Zhang, P. Guo, Q. Lv, (2014), “Impact force of a low speed water droplet colliding on a solid surface.” Journal of Applied Physics, 116, 214903. [18] R. Rioboo et al., (2002), “Time evolution of liquid drop impact onto solid, dry surfaces.” Experiments in Fluids, 33, pp. 112. [19] R. Gunn & G. D. Kinzer, (1949). “The terminal velocity of fall for water droplets in stagnant air.” Journal of Meteorology, 6, 243-248. [20] S. T. Thoroddsen & J. Sakakibara, (1998). “Evolution of the fingering pattern of an impacting drop.” Physics of Fluids, 10, 1359 [21] H. Ghadiri & D. Payne, (1977), “Raindrop impact stress and the breakdown of soil crumbs.” Journal of Soil Science, 28(2), 247-258. [22] M. A. Nearing, J.M. Bradford, & R. D. Holtz, (1986), “Measurement of force vs. time relations for waterdrop impact.” Journal of Soil Science, 50, 1532-1536. [23] Abaqus Analysis User’s Manual Version 6.13, Volume II, Providence, RI, 2014. [24] Sarrate, J., Huerta, A., & Donea, J. (2001). Arbitrary Lagrangian–Eulerian formulation for fluid–rigid body interaction. Computer Methods in Applied Mechanics and Engineering, 190(24), 3171-3188. [25] Nassiri, A., Chini, G., Vivek, A., Daehn, G., & Kinsey, B. (2015). Arbitrary Lagrangian–Eulerian finite element simulation and experimental investigation of wavy interfacial morphology during high velocity impact welding. Materials & Design, 88, 345-358. [26] WEN, Q., Guo, Y. B., & Todd, B. A. (2006). An adaptive FEA method to predict surface quality in hard machining. Journal of materials processing technology, 173 (1), 21-28.
ScienceDirect Procedia Manufacturing 10 (2017) 730 – 736
45th SME North American Manufacturing Research Conference, NAMRC 45, LA, USA
Experimental investigation of droplet impact on metal surfaces in reduced ambient pressure B. R. Mitchell, T. E. Bate, J.C. Klewicki, Y. P. Korkolis, and B. L. Kinsey Mechanics, Materials and Manufacturing Research Group Department of Mechanical Engineering University of New Hampshire Durham, NH, USA
Abstract Impacting water droplets are capable of eroding steam turbine blades, high speed aircraft and even serve as a machining operation. In this latter process, high velocity (~100m/s) water droplets impact a solid surface under conditions in which the ambient air pressure is sub-atmospheric. The physics of this erosion mechanism is not completely understood. To begin to unravel these physics, we present results pertaining to the effects of ambient air pressure on the impact force of low velocity (1m/s) droplets. It is well known that droplet splash is suppressed when the ambient air pressure is reduced. The effects on the associated impact force are, however, unknown. In this article we examine the impact force of 3.5mm diameter, low velocity droplets in a reduced pressure environment. A 38x38x50cm vacuum chamber fitted with a unidirectional piezoelectric force sensor to measure the transient force of impacting droplets. Preliminary results in atmospheric air pressure reveal that the impulse of the droplets depends linearly on impact velocity while the average impact force depends quadratically on impact velocity. The results under reduced pressures are compared and discussed relative to the underlying physics. ©©2017 by Elsevier B.V. by This is an open access article under the CC BY-NC-ND license 2017Published The Authors. Published Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of 45th NAMRI/SME. Peer-review under responsibility of the organizing committee of the SME North American Manufacturing Research Conference Keywords: Water droplet; erosion, vacuum
1. Introduction The impact characteristics of a liquid droplet is becoming widespread in industry and academia, with considerable attention focused on the splashing mechanisms in coating flows (i.e. inkjet printing) [1-3]. The corresponding impact force induced by a droplet on metal surfaces is not as prevalent, but is, however, an ever growing concern. Under the right conditions, liquid droplets are capable of eroding steam turbine systems [4], and scouring supersonic aircraft flying through rain storms [5]. This droplet induced erosion process can be harnessed through a focused waterjet,
2351-9789 © 2017 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the 45th SME North American Manufacturing Research Conference doi:10.1016/j.promfg.2017.07.067
B.R. Mitchell et al. / Procedia Manufacturing 10 (2017) 730 – 736
and used as a materials processing technique [6]. This technique, HIP-SWaD (High Impact Pressure Supersonic Water Droplets), is different from waterjet cutting as a train of water droplets are used to transport momentum to a workpiece rather than a continuous jet, see figure 1. Also, no abrasive medium is used, which produces an environmentally friendly process. In this process, a source of high pressure (>1,500 bar) forces water through an orifice creating a high velocity continuous jet (>600m/s) which breaks-up into discrete droplets due to surfacetension-induced instability, under the appropriate conditions [7]. See figure 1 (a). The high velocity droplets collide and exchange their momentum with a workpiece causing deformation and ultimate material failure. Figure 1 (b) shows deformed steel after being machined with high velocity water droplets, which were emitted from a high pressure jet at the University of New Hampshire [8]. The exploitation of this water droplet impact phenomenon in industrial applications as a means to deform and remove material does not currently exist. If the impact dynamics of water droplets can be understood and controlled, then industries would have the framework upon which they could employ this phenomenon in novel manufacturing equipment. Interestingly, this machining technique has been effective only in reduced-pressure environments. Droplets become an ineffective mist, due to atomization [9] which occurs when the ambient pressure is too high, relative to dd vacuum pressure (0.1 bar). Viscous drag imparted by the surrounding gas severely deforms and ruptures the droplets causing them to fragment into smaller droplets disabling the inertial mechanisms necessary for material failure upon impact. Apart from this atomization process, droplets that strike a material may splash, sending a crown-like liquid film Figure 1 – a) Schematic of water droplet formation before collision with vertically away from the material. Fundamentals workpiece, b) Scanning Electron Microscope (SEM) image of removed paint and deformed steel caused by high velocity (~600m/s) water droplets from a of droplet splash have been the focus of many focused jet, 6.4mm/s jet traverse speed, 8kPa ambient air pressure researchers in the field of ink-jet printing, since attenuation of the splash allows for smooth deposition of ink droplets producing a high-resolution printing process. One method of attenuating the splash is by reducing the pressure surrounding the droplet. First reported by Xu et al [10], the splash of a droplet vanished once the ambient air pressure was reduced below a critical threshold. They found that the lateral liquid jet, known as the lamella (see figure 2), adheres to the surface below this critical value. An important quantity governing the formation of a droplet’s lamella and its subsequent splash is characterized by the Weber number, We=ȡ92DıZKHUHȡ is the OLTXLG¶VGHQVLW\9LVWKHLPSDFWYHORFLW\'LVWKHGURSOHWGLDPHWHUDQGıWKHVXUIDFHWHQVLRQ)RUPDOO\WKH:HEHU number signifies the ratio of inertial pressure to capillary pressure. For low Weber numbers We<<1, capillary pressure dominates and preserves the spherical shape of the impacting droplet. This type of impact does not create a lamella, as the droplet’s surface tension is strong enough to withstand the inertia from the bulk fluid in the collapsing drop. However, when the Weber number is sufficiently large We>>1, surface tension cannot hold back the inertia and thus a lamella is formed. Figure 2 shows an axisymmetric schematic of a droplet with a lamella jetting radially away from the initial point of contact. When the droplet makes first contact with the solid, the fluid at the initial point of contact suddenly decelerates, as time progresses, more fluid accumulates around this point as the fluid’s momenta is diverted from the perpendicular (Z) to the parallel (r) direction(s) of the solid. The laterally moving fluid bulges the liquid-gas interface giving rise to a fast, annular liquid jet (lamella). The condition for which the lamella either slides parallel about the solid or is ejected vertically away, is dictated by the surrounding gas.
a)
b)
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As the expanding lamella gains momentum its apparent contact DQJOH ș LQFUHDVHVGHYHORSLQJD Bulk of droplet wedge at the solid-liquid-gas interface [11, 12], see figure 2. The gas in this immediate region is Surrounding gas Z trapped, permitting a thin layer of air to develop under the advancing lamella [13]. (The surrounding gas is modelled as an inviscid fluid, Lamella in which the Reynolds number is sufficiently large Wedge (Re>>1) Re=VD/Ȟ, where Ȟ is the gas’s kinematic Initial point Region viscosity [14]). The thin layer of air acts as a of contact ș lubricant for the propagating lamella and r eliminates the viscous boundary layer the lamella would have if it were in contact with the solid Solid [15]. With respect to the front of the lamella, air on the top side travels at a higher velocity than on Figure 2 – Axisymmetric schematic of droplet lamella the bottom. It is well known, from inviscid flow theory, that faster moving regions of the flow correspond to areas of lower pressure, therefore a pressure difference exists across the lamella. The pressure difference imparts a vertical lift force onto the lamella, analogous to an air foil, providing the lamella with an upwards trajectory, known as a splash. A detailed analytical description of lamella propagation and its associated splash can be found in [16]. In the absence of a surrounding gas (or in the case of reduced pressure, below the critical pressure), the lamella has no substance to gain lift from, therefore no splashing exists in a vacuum (i.e., low pressure). Since the impact physics are altered in reduced pressure environments, whether the corresponding impact force is altered as well is unknown. Droplet impact force in atmospheric pressure has been characterized by the authors through an extensive numerical and experimental investigation [17]. Agreement was established between numerical and experimental results for the impact velocities considered, (1-3m/s). Droplet impulse was found to depend linearly on impact velocity, while the peak force depended quadratically on impact velocity. As a continuation to this prior research, the dependence of ambient air pressure on the droplet impact force is investigated. A 380x380x500mm vacuum chamber was constructed to create a low pressure environment to investigate the impact force of droplets in reduced ambient pressures. In this paper, the impact force of 3.5mm ethanol droplets traveling at 4m/s is measured with a piezoelectric force sensor. In order to promote splashing, ethanol was used in the experiment as opposed to water, which has a surface tension over 3 times that of ethanol (at room temperature 19°C). Water droplets require greater impact velocities to obtain a splash, which is undesirable since high velocities deform the droplets from a spherical shape (due to air drag) and cause variations in impact locations due to turbulence. Ethanol droplets, which mitigate these negative effects, are favored owing to their inherent ability to splash at low velocities (lower free fall drop heights). For comparison, the critical impact splash speed for a 3.5mm diameter water droplet is over 4m/s while the critical impact speed for an ethanol droplet of the same diameter is under 2m/s [16]. In the experiments presented in this paper, the ambient pressure surrounding the droplets is changed to produce conditions in which 1) the droplet splashes and spreads vertically away from the initial point of contact, and 2) the droplet spreads radially along the surface about the initial point of contact. A high-speed camera is used to record the droplets’ velocity and deformation upon impact. The primary investigation is to compare the impulse and forces associated with the two different impact phenomena. 2. Experimental setup All A vacuum chamber was used as the testing apparatus where the air pressure could be varied to within a fraction of a kilopascal. A Hamilton model 1001 gastight microliter syringe was used with a variety of needles to produce droplets with diameters from 2mm to 4.2mm, however only one droplet diameter was tested, 3.5mm. Ethanol (200 proof ethyl alcohol 64-17-5) manufactured by PHARMCO-AAPER, was used for all tests in a constant
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temperature environment (19°C). Ethanol’s density is 789kg/m^3, its surface tension is 0.022 N/m and its kinematic viscosity is 1.52 (10-6) m2/s. The droplets were released from the syringe 81cm above the force sensor to impact at a velocity of ~4m/s. While the high speed camera is used to record the droplets’ deformation upon impact, it also serves to determine the impact velocity and diameter of the droplets. The camera used was a Photron Fastcam SA4 high-speed camera with an in-house position-tracking software to determine the droplets’ impact velocity. All droplet impacts were filmed at 13500fps with an exposure time of 28ȝs. A Northstar 250Watt light was used to illuminate the droplets while a 60mm Nikkor lens with a 14mm extension tube was used to magnify the droplets. The position tracking software utilized a cross-correlation algorithm which determined the physical displacement of a droplet between two consecutive images. The physical displacement was then divided by the time between consecutive images to obtain the droplet’s velocity. The impact force of 5 trials were tested in atmospheric conditions, while 4 trials were tested in a partial vacuum condition (23.3kPa). The impact velocity of the atmospheric droplets was 3.95m/s, while the impact velocity of the partial vacuum droplets was 4.07m/s. The increase in velocity is attributed to the decreased in air drag of the droplets in partial vacuum. The force sensor used was a PCB model 209C11 piezoelectric force sensor with a calibrated sensitivity of 524.3 mV/N. The sensor measured unidirectional transient forces perpendicular to its 17.9mm diameter delrin plastic impact plate. A PCB model 482 signal conditioner and a Lecroy Wavesurfer 64MXs-B oscilloscope sampling at 1MHz were used for all experimental measurements. While an Edwards 30 E2M30 vacuum pump was used to reduce the pressure in the vacuum chamber, a MKS Series 902 Piezo Transducer was used to measure the ambient pressure inside the chamber. A schematic of the experimental setup is shown in figure 3a, with an image of the setup in figure 3b.
a)
b)
syringe
vacuum chamber
oscilloscope
camera
Figure 3 – Experimental Setup; a) schematic, b) image (some items not shown)
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3. Results and discussion Figure 4 shows the stages of droplet deformation for the 3.5mm diameter ethanol droplets impacting at 4m/s in standard atmospheric pressure 101kPa (a), and in reduced ambient pressure 23.3kPa (b). The time between successive images is 370ȝs. In both cases, the initial droplet deformations tend to resemble truncates spheres with a thin liquid film spreading radially away from the initial point of contact. Interestingly, for the atmospheric case, the liquid film spreads vertically away from the surface, while in the reduced ambient pressure case, the thin film remains attached and flows parallel to the surface. The vertical crown-like splash, in figure 4a, is commonly referred to as a corona splash [18]. As the surrounding atmospheric pressure is reduced the onset of corona splashing is
a)
1mm
b)
Figure 4 - 3.5mm Ethanol droplet impact at 4m/s in atmospheric pressure (a) and in partial vacuum (23.3kPa) (b). Time between successive images is 370us.
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delayed. When the ambient pressure is reduced below a certain threshold no corona splash is observed. From prior experiments, the threshold pressure for a 3.4mm diameter ethanol droplet impacting at 4m/s was found to be around 40 +/-5 kPa [9]. With similar conditions as in [10], we also observe splash attenuation in reduced pressure, see figure 4. While the high speed camera recorded the droplets’ deformation upon impact, the piezoelectric force sensor measured the droplets’ impact force. Owing to the small impact force generated by a droplet impact, a very sensitive force sensor must be used. The significant noise superimposed onto the force-time curves in [17] was attributed to the use of an oversized force sensor. In the present study, a force sensor 5 times more sensitive was used to obtain clear, unambiguous force-time curves. Five and four trials were recorded in the atmospheric (101kPa) and partial vacuum (23.3kPa) tests, respectively. The trials were averaged for each respective pressure and are presented in figure 5. The atmospheric and partial vacuum trials are labeled in blue and red, respectively. The general characteristics of the droplets’ force-time curve is a fast rise time to a maxima, followed by a progressively longer period of decreasing impact force before leveling off. There exists a higher peak force for the partial vacuum tests than the atmospheric tests. This is attributed to the slightly higher impact velocity in the partial vacuum case. Since there is less air drag acting on the droplet as it is falling, the droplets in the partial vacuum impact at higher velocities. The force-time curves exhibit superimposed high frequency oscillations. Due to the inherent nature of impacts, longitudinal waves propagate throughout the measurement system when a dynamic load is applied. These waves are a characteristic of the measurement system’s natural frequency. The measurement system includes the impact plate, force sensor and the 4kg steel block attached to the bottom of the force sensor. If the droplets’ strike the impact plate off center they introduce a non-unidirectional applied force, which activate other modes of vibration. Experiments were carried out with this in mind however, some oscillations still exist. In order to attenuate these undesirable oscillations, the data is filtered with a FIR low pass filter with a cut off frequency of 10kHz, shown in figure 6. The filter successfully attenuated the high frequency noise, however there still exists some oscillations for the partial vacuum tests, most apparent around 1000ȝs. Different modes of oscillation were excited by hitting the force sensor off center for the partial vacuum case. In figure 4 it is apparent that the partial vacuum tests did not strike the droplet directly in the center of the force sensor, leading to additional oscillations. It was shown in [17], that droplet impulse scales linearly with impact velocity, however the dependency of impulse on ambient pressure was not investigated. The impulse of each of the curves in figure 6 was calculated by integrating the force-time curves along the domain of their time durations, which is the time the droplet exerts a positive normal force onto the force sensor. For both the atmospheric and partial vacuum trials, the time duration is roughly 1700ȝs. The impulse for the atmospheric and partial vacuum tests was found to be 67.7 and 72.7 ȝN-s respectively. Since both curves have roughly the same time duration, the higher impulse in the partial vacuum case is attributed to its higher peak force.
Figure 5 – Averaged force-time curve
Figure 6 – Filtered force-time curve
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4. Conclusion The materials processing technique, HIP-SWaD, is a process by which a discrete train of droplets impact and erode metal surfaces. Due to droplet fragmentation and atomization, the process has been effective only in reduced ambient pressures. In this paper, we investigated the significance of the ambient pressure during droplet impact, using the droplet’s impulse and peak impact force as criteria to distinguish the ambient pressure’s effect. A 3.5mm ethanol droplet impacting at 4m/s in standard atmospheric pressure (101kPa) and reduced ambient pressure (23.3kPa) showed vivid differences. The droplet impacting in atmospheric pressure, splashed with a significant corona that later fragmented into a myriad of smaller droplets, while the droplet impacting in reduced ambient pressure remained attached and spread radially along the surface. Despite the prominent difference in splash, no major differences in impulse and peak force were observed. Acknowledgements Funding from the U.S. National Science Foundation (CMII-1462993) is gratefully acknowledged. References [1] R. Dean, D. Nelson, M. Brown, R. Couch, M. Blanchard, (2008), “Method and apparatus for forming high speed liquid”, US Patent No. 7,380,918 B2. [2] L. Rayleigh, (1879) “On the instability of jets.” Proceedings of the London Royal Society, 10, 4-13. [3] G. Amini, Y. Lv, A. Dolatabadi, M. Ihme, (2014). “Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis.” Physics of Fluids, 26, 114105. [4] J. Yang, W. Chien, M. King, W. Grosshandler (1997) “A simple piezoelectric droplet generator.” Experiments in Fluids, 23, 445-447. [5] S. Tomotika (1935), “On the instability of a cylindrical thread of viscous liquid surrounded by another viscous fluid.” Proceedings of the London Royal Society, 150, 322-337. [6] S. S. Cook (1928), “Erosion by water-hammer.” Proceedings of the London Royal Society, 119, 481-488. [7] F. P. Bowden and J. E. Field, (1964), “The brittle fracture of solids by liquid impact, by solid impact, and by shock.” Proceedings of the London Royal Society, 282, 331-352. [8] G. C. Gardner, (1963), “Events leading to erosion in the steam turbine.” Proceedings of the Institution of Mechanical Engineers, 178, 593601. [9] Y. C. Huang, F. G. Hammit, and W. J. Yang, (1973), “Hydrodynamic phenomena during high-speed collision between liquid droplet and rigid plate.” Journal of Fluids Engineering, 95, 276-292. [10] W. F. Adler, (1995), “Waterdrop impact modeling.” Wear, 186, 341-351. [11] K. K. Haller, Y. Ventikos, and D. Poulikakos, (2002), “Computational study of high-speed liquid droplet impact.” Journal of Applied Physics, 92, 2821-2828. [12] P. E. Schleusener and E. H. Kidder, (1960), “Energy of falling drops from medium pressure irrigation sprinkler.” Agricultural Engineering 41(2), 100-103. [13] R. S. Palmer, (1965), “Waterdrop impact forces.” Trans. ASAE, 8, 69-70. [14] S. E. Hinkle, (1989). “Water droplet kinetic energy and momentum measurement considerations.” Applied Engineering in Agriculture, 5, pp. 386-391. [15] A. C. Imeson, R. Vis and E. deWater, (1981), “The measurement of water drop impact forces with a piezo-electric transducer.” Catena, 8, 83-96. [16] A. S. Grinspan, & R. Gnanamoorthy, (2010) “Impact force of low velocity liquid droplets measured using piezoelectric PVDF film.” Colloids and Surfaces, A, 356, 162-168. [17] J. Li, B. Zhang, P. Guo, Q. Lv, (2014), “Impact force of a low speed water droplet colliding on a solid surface.” Journal of Applied Physics, 116, 214903. [18] R. Rioboo et al., (2002), “Time evolution of liquid drop impact onto solid, dry surfaces.” Experiments in Fluids, 33, pp. 112. [19] R. Gunn & G. D. Kinzer, (1949). “The terminal velocity of fall for water droplets in stagnant air.” Journal of Meteorology, 6, 243-248. [20] S. T. Thoroddsen & J. Sakakibara, (1998). “Evolution of the fingering pattern of an impacting drop.” Physics of Fluids, 10, 1359 [21] H. Ghadiri & D. Payne, (1977), “Raindrop impact stress and the breakdown of soil crumbs.” Journal of Soil Science, 28(2), 247-258. [22] M. A. Nearing, J.M. Bradford, & R. D. Holtz, (1986), “Measurement of force vs. time relations for waterdrop impact.” Journal of Soil Science, 50, 1532-1536. [23] Abaqus Analysis User’s Manual Version 6.13, Volume II, Providence, RI, 2014. [24] Sarrate, J., Huerta, A., & Donea, J. (2001). Arbitrary Lagrangian–Eulerian formulation for fluid–rigid body interaction. Computer Methods in Applied Mechanics and Engineering, 190(24), 3171-3188. [25] Nassiri, A., Chini, G., Vivek, A., Daehn, G., & Kinsey, B. (2015). Arbitrary Lagrangian–Eulerian finite element simulation and experimental investigation of wavy interfacial morphology during high velocity impact welding. Materials & Design, 88, 345-358. [26] WEN, Q., Guo, Y. B., & Todd, B. A. (2006). An adaptive FEA method to predict surface quality in hard machining. Journal of materials processing technology, 173 (1), 21-28.