Mario Vargas

Glenn Research Center, Cleveland, Ohio

Alex Feo

Instituto Nacional de Técnica Aeroespacial, Madrid, Spain

Experimental Observations on the Deformation 

and Breakup of Water Droplets Near the 

Leading Edge of an Airfoil 

NASA/TM—2011-216946

January 2011

AIAA–2010–7670
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Mario Vargas

Glenn Research Center, Cleveland, Ohio

Alex Feo

Instituto Nacional de Técnica Aeroespacial, Madrid, Spain

Experimental Observations on the Deformation 

and Breakup of Water Droplets Near the 

Leading Edge of an Airfoil 

NASA/TM—2011-216946

January 2011

AIAA–2010–7670

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Atmospheric and Space Environments Conference

sponsored by the American Institute of Aeronautics and Astronautics

Toronto, Ontario, Canada, August 2–5, 2010
Acknowledgments

The authors would like to thank Mr. Chris Lynch and Mr. Quentin Schwinn for their outstanding high speed imaging work during 

the experiment. Thanks also to Mr. Yago Sánchez and Mr. Carlos Molina from ALAVA INGENIEROS for their generosity in 

allowing us to use the Photron camera during the experiment and for their support and expertise during the experiment. Thanks 

Mr. Miguel Guerra-Valles for his help during the experiment and for establishing the procedure to align the camera with the 

airfoil. Thanks to all rotating rig INTA personnel for their excellent support in the preparation work and during the execution of 

the test program. Special thanks to Mr. Suthyuvann Sor for his excellent engineering support and for upgrading the rotating rig

to its present state. Also thanks to Ms. Eva Jarillo for her dedication to the NASA/INTA cooperation and in the development and

calibration of the Monodisperse droplet generator used during the test program. Thanks to Dr. Andy Broeren for his help with 

the monosize droplet generator during the pre-test imaging work done at the Icing Branch Flow Laboratory. The present work is 

part of the NASA/INTA collaboration under a Space Act Agreement. It is funded under the NASA Integrated Resilient Aircraft 

Controls (IRAC) Project of the Aviation Safety Program. The authors would like to thank Dr. OA Guo, Mr. Gene Addy and the 

Project Offi ce for their support. 

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Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
This work presents the results of an experimental study on droplet deformation and 

breakup near the leading edge of an airfoil. The experiment was conducted in the rotating 

rig test cell at the Instituto Nacional de Técnica Aeroespacial (INTA) in Madrid, Spain. An 

airfoil model placed at the end of the rotating arm was moved at speeds of 50 to 90 m/sec. A 

monosize droplet generator was employed to produce droplets that were allowed to fall from 

above, perpendicular to the path of the airfoil at a given location. High speed imaging was 

employed to observe the interaction between the droplets and the airfoil. The high speed 

imaging allowed observation of droplet deformation and breakup as the droplet approached 

the airfoil near the stagnation line. A tracking software program was used to measure from 

the high speed movies the horizontal and vertical displacement of the droplet against time. 

The velocity, acceleration, Weber number, Bond number, Reynolds number, and the drag 

coefficients were calculated along the path of a given droplet from beginning of deformation 

to breakup and/or hitting the airfoil. Results are presented for droplets with a diameter of 

490 micrometers at airfoil speeds of 50, 60, 70, 80 and 90 m/sec. 

Nomenclature 

avi = Audio video interleave movie format 

V = Velocity, mph 

Ttotal = Total temperature, oF 

LWC = Cloud liquid water content, g/m3

MVD = Water droplet median volume diameter, μm 

DBKUP 002 = Designation for Airfoil used in the experiment 

SLD = Supercooled Large Droplets 

INTA = Instituto Nacional de Técnica Aeroespacial 

ITC = Imaging Technology Center at NASA Glenn Research Center 

LED = Light Emitting Diode 

Slip Velocity = Relative velocity between the droplet and the air: ( Vdroplet - Vair)

TSIT = Time-Sequence Imaging Technique 

Experimental Observations on the Deformation and Breakup of 

Water Droplets Near the Leading Edge of an Airfoil 

Mario Vargas 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Alex Feo 

Instituto Nacional de Técnica Aeroespacial 

Madrid, Spain

NASA/TM—2011-216946 1
I. Introduction 

 Aircraft manufacturers have reported in-flight observation of droplet breakup near the wing surfaces of large 

transport aircraft1. This observation is important for in-flight icing because if large droplets break up before 

impinging on aircraft surfaces, the smaller droplets that result may not impinge on the airfoil potentially affecting 

the ice accretion process. If droplet breakup is a factor in the ice accretion process, current ice accretion codes will 

need to be modified to account for the breakup phenomena. 

 A large body of research exists on droplet deformation and breakup. Those studies are related to nozzle spray 

systems, fuel injection, liquid propellants, aerosol atomization, mixture formation in internal combustion engines, 

ink jet printing and spray drying among others. The experimental configurations used in those studies are 

completely different from droplets impinging on an airfoil. Only the configurations used by Wierzba2, Kennedy and 

Roberts3

, Suzuki and Mitachi4 have some similarities although no airfoil was used in those studies. Wierzba studied 

the critical Weber numbers (Weber number at the time of droplet breakup) when droplets are released normal to an 

instantaneous air flow in a horizontal wind tunnel. Kennedy and Roberts studied the breakup of droplets subject to 

an accelerating flow in a vertical wind tunnel. Droplets were released at the inlet of the tunnel and accelerated 

toward the test section of the tunnel where observations were conducted. In the process, a relative gas-droplet 

velocity was generated and was one of the parameters varied but they did not study the effect of the change of the 

relative velocity with time on the critical Weber number or the breakup time of the droplets. Susuki and Mitachi 

studied the effect of a linearly increasing relative droplet gas velocity on the droplet breakup. In their configuration 

the droplets were released into the unsteady droplet-gas velocity flow. They found that the critical Weber number 

increased as the rate of relative droplet-gas velocity was increased at the injection location. Although the 

experiments by Wierzba, Kennedy and Roberts, Suzuki and Mitachi included a relative droplet-gas velocity, only 

Suzuki and Mitachi studied the effect of varying the relative velocity with time. In no case was an airfoil used as an 

experimental configuration. 

 In 2005 the Federal Aviation Administration (FAA) sponsored a computational study by Wichita State 

University (Tan, Papadakis and Sampath1) to assess the effects of aerodynamic forces on water droplets near the 

leading edge of an airfoil and the leading edges of the slat and flap elements of a high-lift airfoil. Two-dimensional 

numerical computations of droplet breakup were done using the TAB model in the commercial code Fluent. The 

TAB model used included only vibrational and bag models of breakup. The effect of chord size and droplet 

diameter was studied for a NACA 0012 geometry for chords of 3 feet and 20 feet and droplet sizes of 100, 500 and 

1000 micrometers. For the case of a 20-foot chord airfoil, droplet breakup was studied for a three element airfoil 

high lift system in a landing configuration. The study indicated that droplets may breakup in regions with severe 

pressure gradient. For the 3-foot chord single element airfoil the droplet breakup occurred aft of the leading edge. 

For the 20-foot chord single element airfoil the droplet breakup occurred near the stagnation region only. Large 

droplets were found to be more susceptible to breakup than smaller ones. They found that when droplet breakup 

occurred near the airfoil surface there was insufficient distance between the airfoil wall and the location where the 

droplet breakup was initiated for the droplets to achieve complete breakup before hitting the airfoil. The trajectory 

followed by droplets larger than 500 micrometers were “ballistic” in nature. The study pointed out the lack of 

experimental data in this area and recommended experimental tests to assess the effects on droplet breakup and 

breakup modes from the pressure gradient and the relative droplet-gas velocity near the leading edge of an airfoil. 

 In 2007 the National Aeronautics and Space Administration (NASA) and the Instituto Nacional de Técnica 

Aeroespacial (INTA) in Madrid, Spain, began an experimental research program to obtain droplet breakup data on 

an airfoil configuration. A droplet breakup rotating rig5 was designed and built at the INTA installations near 

Madrid. The first sets of experiments were conducted at low speeds (15-66 m/s) in the fall of 2008. Using the 

experience gained from the low speed experiment the test rig was modified to attain speeds up to 90 m/sec. 

 The present work reports the results of a droplet deformation and breakup experiment conducted in the spring of 

2010. The objective of the experiment was to use high speed imaging to observe the droplet deformation and 

breakup and to measure the important parameters as the droplet approaches an airfoil near the stagnation line. The 

experiment was conducted in the rotating rig test cell at the Instituto Nacional de Técnica Aeroespacial (INTA) in 

Madrid, Spain. An airfoil model placed at the end of the rotating arm was moved at speeds of 50 to 90 m/sec. A 

monosize droplet generator was employed to produce droplets from 100 to 500 micrometers that were allowed to 

fall from above perpendicular to the path of the model airfoil at a given location. High speed imaging was employed 

NASA/TM—2011-216946 2
to observe the interaction between the droplets and the airfoil, and droplet deformation and breakup. A tracking 

software program was used to measure from the high speed movies the droplet horizontal and vertical displacement 

against time. The horizontal displacement data was curve fitted to obtain the velocity and acceleration. The 

velocity and acceleration, together with experimental values of the air velocity at the locations of the droplet, were 

used to calculate the Weber number, Reynolds number, Bond number, and the drag coefficients along the path of the 

droplet from beginning of deformation to breakup and/or hitting the airfoil. Observations and measurements were 

conducted near the leading edge of an airfoil for velocities from 50 to 90 m/sec for a droplet size of 490 

micrometers. 

 

The present work is the first time that a systematic study of droplet deformation and breakup has been conducted 

for droplets approaching the leading edge of an airfoil and the first time that the important parameters and 

dimensionless numbers have been directly measured along the path of the droplets from initial deformation to 

breakup and/or hitting the airfoil. The results have provided critical information on how the droplet breakup occurs 

and experimental measurements of the critical parameters involved. The results have also provided a clear view of 

the next steps to be followed in the experimental program. 

II. Experimental Setup 

The experimental setup has four main elements: the rotating arm unit, the airfoil attached at the end of the arm, 

the monosize droplet generator and the high speed imaging system. Figure 1 shows the conceptual view of the 

experiment setup with all the elements except the high speed imaging system. Figure 2 shows the experimental 

setup components in the test cell before a run. 

A. Rotating Arm Unit 

The rotating arm unit consists of a 5 kW electric motor mounted on a support structure that rests on a solid base 

attached to the floor (Fig. 2). The support structure is attached to the base through four slip ring vibration dampers. 

The motor is placed inside the support structure with the axle perpendicular to the horizontal plane and in the 

direction of the ceiling. A rotating arm is attached to the axle of the motor. The length of the arm measured from 

the center of the axle to the airfoil model attached at the end is 2.37 meters (93.3 inches). For balancing, vibration 

control and additional strength, a system of struts is mounted on the axle and opposite the arm location (Fig. 2). 

Accelerometers on the arm and the axle are used to monitor the arm vibrations. The revolutions per minute of the 

arm are measured using a light emitting diode (LED) optical system. The LED is mounted on the supporting 

structure with its beam pointed at an angle toward the rotating axle. A small reflecting tape mounted on the rotating 

axle reflects the light in each revolution. The reflected light is picked up by a detector placed next to the LED. Each 

time that the detector registers the reflected light from the LED one revolution of the arm is counted. The control of 

the electric motor is located in the control room, a section of the test cell separated from the rotating rig by a safety 

glass window (Fig 2). The revolutions per minute of the arm can be adjusted to set the airfoil model at velocities 

from 0 to 90 m/sec at less than 1m/sec intervals. 

B. Airfoil Model 

The airfoil model mounted at the end of the rotating arm is a generic type of thick airfoil designated as DBKUP 

002 (Fig. 3). Table I list the coordinates of the airfoil. The airfoil was chosen for the experiment because it has a 

blunt shape geometry that simulates a scaled version of the type of leading edge shape found on large transport 

airfoils. The airfoil measures 0.35 meters (13.78 inches) in the spanwise direction, and has a chord length of 0.47 

meters (18.5 inches). 

C. Monosize Droplet Generator 

A TSI MDG-100 Monosize Droplet Generator is used to produce water droplets within a diameter range from 

100 μm to 500 μm. The droplet generator (Fig. 4) consists of a water pressure container, a flow control valve, a 

frequency generator and the vibration head. Air from a compressor pressurizes the tank and generates the water 

flow from the tank to the vibration head. A high precision flow rate control valve with a manometer allows fine 

adjustment of the flow rate before the water flow reaches the vibration head. At the vibration head the water is 

forced through a small orifice (100 μm in diameter) and a jet is formed. A disturbance in the form of a square wave 

at the appropriate frequency is introduced by activating a piezoelectric transducer controlled with a BK Precision 

model 4011A frequency generator. The jet is unstable at resonant frequencies and breaks into uniform droplets. For 

NASA/TM—2011-216946 3
a given orifice diameter, flow rate and excitation frequency the diameter of the droplets generated is given by the 

equation: 

Where Q is the water flow rate in cubic centimeters per minute; f is the frequency in kilohertz; and D is the 

diameter of the droplets in micrometers. Previous to the droplet breakup high speed test, the monosize droplet 

generator was calibrated6 against a Phase Doppler Particle Analyzer (PDPA) for orifices of 50 and 100 μm. During 

the experiment only the 100μm orifice was used. 

D. High Speed Imaging System 

The high speed imaging system consists of the high speed camera, the camera software, the lens system and the 

lightning (Fig. 5). The high speed camera used during the experiment was a Photron SA-5. The camera can capture 

images at rates from 1,000 to 1,000,000 frames per second (fps). During the experiment frames rates of 25,000, 

50,000, 65,100, 75,000, 100,000 and 150,000 fps were used with corresponding resolutions given in pixels for the 

horizontal and vertical directions: 512x512, 192x512, 246x320, 192x312, 192x264 and 128x184. As the frame rate 

is increased the resolution of the camera decreases. The camera has a maximum shutter speed of 1microsecond (μs) 

at frames rates below 775,000 fps. The camera software employed for capturing the high speed image sequences is 

Photron’s FASTCAM Viewer (PFV) and is part of the camera system. The same software was used for postprocessing the image sequences to generate the data movies for data analysis. During the experiment one lens 

configuration was used for two magnifications of the droplet deformation and/or breakup. The lens configuration 

consisted of a 200mm Micro Nikkor lens with a 2x doubler added between the camera and the 200mm lens to 

double the focal length of the microlens. The two magnifications were achieved by placing the camera at two 

different distances from the location where the droplets were falling at 0.24 meters (9.25 inches) along the span of 

the airfoil. For the first magnification the distance was 0.91 meters (36 inches) and for the second the distance was 

0.36 meters (14 inches). The lightning was designed to illuminate the droplets from behind to create a shadowgraph 

(black color of the droplets against a white-gray background). The light source was a 2000 watt Xenon light with a 

lens to focus the beam. 

III. Test Procedure and Test Matrix 

A. Test Procedure 

Before a test run, the high speed camera system needs to be aligned, so that the line of view of the lens is parallel 

with the direction along the span of the airfoil at the midpoint of the leading edge (stagnation line along the span). 

The rotating arm is set at the position, where the falling droplets from the monosize droplet generator will just graze 

the leading edge. The airfoil is held at the same location during the whole alignment process. The camera is placed 

at the distance required by the optics to obtain the needed magnification and such that the center of the lens depth of 

field is at the location where the falling droplets graze the airfoil leading edge. A rectangular steel beam (extending 

from the airfoil to the camera) is placed parallel to the span the airfoil (grazing it) and parallel to the side of the 

camera. This ensures that the direction of the lens is parallel to the direction of the airfoil span but displaced a 

known distance. The steel beam is removed and the camera and lens are moved to a position where the lens 

direction is aligned, grazing the leading edge along the span of the airfoil. The motion of the camera can be 

carefully controlled because the camera sits on a x-y positioning table. 

 The airfoil is moved from the alignment position and a ruler with the smallest subdivision of one millimeter is 

placed at the location where the droplets will graze the leading edge of the airfoil. The camera is focus on the ruler 

and the number of pixels per millimeter is recorded, since the number of pixels in the camera sensor and the field of 

view are known. This conversion is used during the data analysis to measure the droplet diameter. 

The monosize droplet generator controls are adjusted to produce the range of droplet sizes needed. The pressure 

and the frequency values are read from the calibration table obtained during the previous calibration of the system6













=

( )

min)/(

3/1

317)(

kHz f

cc

Q

μmD

NASA/TM—2011-216946 4
for the orifice being used in the generator (100 μm). Table 2 shows the calibration table used to setup the monosize 

droplet generator conditions. The pressure valve and the frequency generator are set at the corresponding values and 

the generator is started. 

The personnel withdraw to the control room, where they are able to observe the motion and operation of the 

rotating arm through the safety glass. The camera is controlled with software run on a laptop computer located in 

the control room (Fig. 4.) The software is used to start the camera and set the controlling parameters including the 

frame rate and the shutter speed. The software allows writing information that will be part of the camera frames. It 

is located on each frame above the recorded image. This information is helpful during the data analysis. During the 

experiment the following information was recorded on each frame: frame rate, time of recording, image resolution, 

frame number, lens configuration, date and time, arm velocity and target droplet size. 

The rotating arm is set in motion at the revolutions per minute (rpm) corresponding to the target velocity. When 

it reaches the target speed, the camera recording is started and maintained for three rotations. Once the recording is 

completed the rotating arm is brought to a stop. The high speed movie is analyzed with the camera software to 

determine the quality of the recording in each of the three passes of the airfoil. If the recording is deemed of good 

quality the experiment moves to the next test point and the process is repeated. 

B. Test Matrix 

Table 3 shows the test matrix for the experiment. The strategy followed was to setup the droplet generator for 

theoretical droplet diameters of 523, 415, 332, 191, 138 and 114 μm. At each droplet size test points were for airfoil 

velocities of 50, 60, 70, 80 and 90 meters per second. Frame rate values employed were: 25,000, 50,000, 65,100, 

75,000, 87,000, 100,000 and 150,000 fps with 75,000 fps being the most used because it was a middle point between 

a frame rate that allowed observation of the droplet breakup and a reasonable resolution of 192x312 pixels. Table 3 

shows the run number, the calibration point for the monosize droplet generator taken from Table 2, the theoretical 

droplet diameter, the airfoil velocity, the lens magnification, the camera resolution and the frame rate. Two camera 

magnifications were employed during the test. The larger magnification gave more detail but it only allows 

observation of the droplets over a very small distance. The smaller magnification allows to observe the droplet over 

a larger distance, from no interaction with the airfoil, to beginning of deformation, deformation and breakup or 

impact with the airfoil. 

IV. Data Analysis 

A. Tracking a Single Droplet to obtain the Droplet Displacement against Time 

 The data analysis is performed using the software program Spotlight-87 that allows frame by frame study of the 

movies, zooming in and out on single frames, running the movies forward and backward, and tracking a single 

droplet in x-y directions. Before each movie is analyzed with Spotlight 8 the camera software is used to convert 

from the camera format to audio video interleave (avi) format without any compression to avoid modifying the data. 

Using Spotlight-8, a high speed movie corresponding to a set of experimental conditions is opened and the 

frames where the airfoil impacts the droplets are located. There are three of those frames per movie, because during 

the test, the camera is programmed to capture three rotations of the airfoil. In general several droplets can be 

observed impacting the airfoil and in some cases breaking up before impact. The movie is run backward and 

forward to study the behavior of the droplets before and during their interaction with the airfoil. A droplet is 

selected for study and the program is returned to the frame where the airfoil is about to hit the droplet. The droplet 

may be deforming or is in the process of breaking up. A copy of the frame is saved in the experimental notes and 

the droplet to be studied is labeled for future identification (Fig. 6). The movie is run backward to the frame where 

there is no indication of deformation or interaction of the droplet with the approaching airfoil and where the tracking 

is going to be initiated. 

Before tracking the droplet, its diameter is measured at or near the frame where the tracking is going to be 

started. Zooming-in on the droplet, the number of pixels that form the droplet are counted in the horizontal and 

vertical directions and averaged (Fig. 7). The conversion of number of pixels to millimeters is used to obtain the 

diameter of the droplet in metric units. The counting of the number of pixels can introduce an error in the 

measurement of ±1 pixel in cases where it is difficult to determine the boundary of the droplet shape. In the case of 

NASA/TM—2011-216946 5
droplets with a diameter of 490 μm, for which the results are discussed in Section V, the error in the measurement 

could be as high as 14% depending on how well defined is the shape of the droplet on the image used to measure the 

diameter. 

Tracking is initiated by zooming-in on the droplet and using the threshold option to create a white background 

against the black droplet image but adjusting the threshold to maintain the same droplet shape. The center of mass 

tracking capability in Spotlight-8 is selected and the droplet image is enclosed in a rectangle, or region of interest 

(Fig. 8). After zooming out to see the whole threshold image frame, the program tracks the motion of the droplet. 

After tracking on a given frame, the region of interest is repositioned on the centroid of the tracked object. The 

tracking is followed on the computer screen and terminated just after the airfoil strikes the droplet. The tracking 

data is saved as a text file with the centroid position of the droplet at each frame given in (x,y) coordinates with 

respect to the first tracking frame. In the output file the data is displayed in three columns: one for the x coordinate, 

one for the y coordinate and one for the frame number. At each row in the table, the (x,y) coordinate and the 

corresponding frame are listed. The data is then transferred to an Excel spreadsheet. In the Excel spreadsheet the x 

and y coordinates of the droplet are converted from pixels to metric units. Since the inverse of the camera frame 

rate gives the time separation between each frame, the time associated with each (x,y) displacement can be obtained 

after taking the first tracking frame as the starting time. The droplet displacement against time can be plotted (Figure 

9). It is the droplet displacement measured by an observer located on a frame of reference at rest with respect to the 

control room in the test cell. 

B. Effect of the Camera Resolution on the tracked Droplet Displacement against Time 

To capture the behavior of the droplets and especially droplet breakup, it is necessary to go to frame rates higher 

than 50,000 fps because breakup occurs very close to the leading edge and in a reduced time frame window. The 

higher the frame rate the more frames will be captured in that reduced time frame where breakup occurs. The 

downside of higher frame rates is lower resolution. For a given frame rate the camera can sustain a given maximum 

resolution and the higher the resolution, the lower the frame rate. It is a limitation in the current technology of high 

speed cameras and it is related to the time that it takes for the camera system to extract the information from the 

sensor. Table 4 lists the resolutions for the frame rates used during the experiment. A frame rate of 75,000 was 

found to be the best compromise between frame rate and resolution and it was the frame rate most used as can be 

seen in the test matrix (Table 3). The combination of the optical configuration (lens, doubler, magnification), the 

high camera frame rate, the corresponding low resolution and the droplet moving at low speed affects the tracking 

data in the following way: at a high frame rate the time between frames is a few microseconds and during that time a 

droplet moving at low speed will cover a distance that is shorter than the physical dimension of a pixel in the camera 

sensor. The tracking data will indicate that the droplet remained at the same location when it is actually in motion. 

This can be seen in Figure 9. At the lower times the droplet seems to remain at the same location for a period of 

time. As the droplet speed increases the effect decreases and the droplet appears to remain at the same location less 

and less. 

 As an example, for a camera frame rate of 75,000 fps the maximum resolution possible is 192x312 pixels. At 

this resolution, for the optical configuration used, a scale on the field of view indicates that there are 14.295 pixels 

per millimeter in the horizontal direction; therefore each pixel is 70 μm wide. At a frame rate of 75,000 fps each 

frame is separated by 13.33 μsec. A droplet moving across the field of view at a velocity of less than 

70μm/13.33μsec (5.24 meter per second) won’t transverse a pixel in 13.33 μsec and will be tracked as remaining in 

the same location. If the droplet were moving at 1 meter per second (equivalent to 1μm/μsec), it would take the 

droplet 70μsec to cover a distance equivalent to the width of a pixel and it would be recorded by the tracking 

program as remaining in the same location for 70μsec/13.333μsec or 5 camera frames. 

C. Calculation of the Horizontal Velocity and Acceleration of the Droplet against Time 

The horizontal velocity and acceleration of the droplet are calculated from the curve fit of the droplet 

displacement against time. The data points in the plot are curve-fit with a double five parameter exponential growth 

equation (Fig. 9). The first and second derivatives of the curve-fit equation give the droplet velocity and 

acceleration (Fig. 10 and Fig. 11). Those are the droplet horizontal velocity and acceleration against time measured 

by an observer located on a frame of reference at rest with respect to the test cell. 

NASA/TM—2011-216946 6
D. Change from the Frame of Reference at the Test Cell to the Frame of Reference at the Airfoil 

The horizontal displacement, velocity and acceleration were initially measured in a frame of reference at rest 

with respect to the test cell. It is more convenient to work in a frame of reference at rest on the airfoil. The frame of 

reference located on the airfoil is shown in Figure 12. The origin is located at the stagnation point on the leading 

edge. In a strict sense, a frame of coordinates at rest with respect to the airfoil is not an inertial frame because the 

airfoil is rotating, it is accelerated. Since the interaction between the droplets and the airfoil occurs at a distance less 

than or equal to the airfoil chord, that section of the airfoil path is nearly straight and the frame of reference at rest 

with respect to the airfoil is assumed as inertial during that part of its path. The Galilean transformation together 

with the airfoil velocity was used to convert the velocity and acceleration of the droplet from the frame of reference 

at the test cell to the frame of reference at the airfoil (Fig.13 and Fig. 14). 

E. Position of a Droplet with respect to the Frame of Reference at the Airfoil 

At a given location along the droplet path, the number of camera frames separating the droplet from the airfoil is 

equal to the frame number at which the airfoil hits the droplet minus the frame number at the given location of the 

droplet. Multiplying the number of frames separating the droplet and the airfoil by the time lapse between frames 

(1/frame rate) and by the airfoil speed gives the horizontal position of the droplet with respect to the frame of 

reference at the airfoil. Repeating the calculation for each droplet location gives the distance of the droplet along its 

horizontal path with respect to the leading edge of the airfoil. The main parameters in the experiment were 

calculated at each position of the droplet as it approaches the airfoil and with respect to the frame of reference 

located at rest on the airfoil. 

F. Air Velocity at a given Droplet Location 

For an airfoil with the same geometry as the DBKUP 0012 but scaled down 1/10 in size (0.047m chord), the air 

velocity along the horizontal line ending at the stagnation point on the leading edge was measured experimentally 

with a Laser Droplet Velocimeter (LDV) at the INTA 0.3mx0.2m wind tunnel. Figure 15 shows the results. The 

vertical axis in the plot records the air velocity divided by the free stream velocity (Vair/Vα). The horizontal axis 

records the distance with respect to the leading edge of the airfoil divided by the chord (x/c). The experimental data 

was curve-fit (Fig. 15) and the resulting equation was used to calculate the air velocity at any given droplet position 

along its path. To calculate the position of the droplet using the curve-fit equation the value of the free stream 

velocity is needed. For the frame of reference at rest with respect to the airfoil, the air free stream velocity is the 

same as the velocity of the airfoil with respect to the frame of reference at rest with respect to the test cell. 

G. Relative Velocity between the Droplet and the Air (Slip Velocity) 

Since at each droplet position along its path the horizontal velocity of the droplet and the velocity of the air are 

known, the relative velocity between the droplet and the air can be calculated. This velocity, Vair-Vdroplet, is called 

the "slip velocity". The Reynolds number, the Weber number and the drag coefficient can be calculated when the 

horizontal slip velocity at each location along the droplet path is known 

H. Calculation of the Reynolds Number, the Weber Number, the Bond Number and the Drag Coefficient 

The main parameters measured along the path of the droplet were the Reynolds number, the Weber number, the 

Bond Number and the Drag coefficient. All those parameters were measured with respect to the horizontal motion 

of the droplet. The droplets leave the monosize droplet generator and fall vertically at a constant speed between 7-

10 m/sec (measured during the experiment). There was no indication from the physical behavior of the droplet that 

the vertical velocity had an influence on the deformation of the droplet. The shape of the droplet during deformation 

corresponded to the response of the droplet to the horizontal velocity and acceleration. In all the measurements and 

calculations the vertical velocity was not considered. 

The following are the definitions of the main parameters measured along the path of the droplet: 

 

 Reynolds Number 

 

 Weber Number 

airwater

airair droplet DVV

We

/

2

σ

ρ −

=

air

airair droplet DVV

μ

ρ −

Re =

NASA/TM—2011-216946 7
 

 

 

 Bond Number 

 

 

 Drag Coefficient 

where D is the droplet diameter, Vdroplet is the droplet velocity, Vair is the air velocity at the location of the 

droplet, (Vair – Vdroplet) is the slip velocity, ρair is the air density, μair is the air absolute viscosity, ρwater

 is the water 

density for the droplet, σwater/air is the water surface tension for the droplet. The Bond number was defined with 

respect to the droplet acceleration. 

Since the air and water droplet properties are known and the droplet diameter, the slip velocity and the droplet 

acceleration are measured or calculated along the path of the droplet, then the non-dimensional parameters can be 

calculated. The velocities and accelerations employed in the calculation of the parameters are for the horizontal 

direction. 

 Figures 16, 17, 18 and 19 show the Reynolds number, the Weber number, the Bond number and the drag 

coefficient for the case of a droplet with a diameter of 490 μm, when the airfoil speed is 90 m/sec, the camera 

frame rate 75,000 fps and the resolution 192x312 pixels. The horizontal displacement and acceleration presented in 

Figures 9,10,11,13 and 14 are for the same droplet. 

 

I. Forces acting on a Droplet as it approaches the Airfoil 

A brief comment is needed on the forces acting on a droplet approaching the airfoil. The forces acting on a 

droplet in a non-uniform flow field8 ignoring particle rotation, slip in the shear flow of a boundary layer and other 

effects are: the pressure gradient force, the virtual mass force, the viscous drag force, the Basset force and the force 

of gravity. When ρdroplet is about three orders of magnitude or greater than ρair (999.7 kg/m3 vs. 1.205 kg/m3) only 

the viscous drag force needs to be considered8,9,10,11

.

 This approximation was tested on a limited number of droplets 

by calculating the pressure gradient force, the virtual mass force, the viscous drag force and the Basset force. To 

calculate the viscous drag force, the drag coefficient is needed and in the case of the water droplet it changes along 

the path of the droplet (Fig. 19) because the droplet is deforming, in a decelerating process. To calculate the viscous 

drag force the droplet was assumed to be spherical and the classical curve of drag coefficient versus Reynolds 

number was used. Since the Reynolds number for the droplets was measured between 900 and 3000, the drag 

coefficient in that part of the curve could be approximated by 0.4612. Using this value gives a lower bound value for 

the Viscous Drag Force, since the drag coefficient for deforming droplets tends to larger values than for the 

spherical droplet case. In all the cases the lower bound value of the viscous drag force was an order of magnitude 

larger than the other forces confirming the validity of the approximation. In the measurement of the drag 

coefficients at each location of the droplet as it approaches the airfoil the approximation was used and the drag 

coefficient was obtained from the equation: 

 

( ) dt

D dV

o

droplet

airwater

water B

/

2

σ

ρ

=

dt

dV

VV

D

d

droplet

air droplet

air

water C 3 24

−

= ρ

ρ

( ) air droplet air droplet

droplet

d

air

droplet droplet

droplet

droplet VVVV

d

d C

dt

d Vd rrrr

r

≈ ρ − −

π

ρ

π

6 8

3 3

NASA/TM—2011-216946 8
V. Results 

At each velocity tested, the high speed movies were studied to determine the behavior of the droplets as they 

approached the airfoil. The frame by frame and zooming capability of the Spotlight 8 program allowed careful 

observation of how the droplets deform and in some case breakup. After those general observations were recorded, 

droplets with a 490 μm were selected at each airfoil velocity for tracking and calculation of the parameters. The 

parameters were calculated and compared to study the effect of the actual parameter and also the effect of velocity. 

The tracking and calculation of the parameters was done following the procedure described in the Data Analysis 

section IV. 

A. Droplet Deformation as it approaches the Airfoil 

Initially the droplets leave the monosize droplet generator and fall under the action of gravity at measured speeds 

between 7-10 m/sec (Fig 20). The largest droplets show oscillations as they fall. As the droplet gets closer to the 

airfoil its shape begins to distort and becomes flattened at the front side (the side closest to the airfoil) and bulging at 

the rear (Fig. 21). As the droplet gets closer and closer to the airfoil, the distortion changes and the droplet shape is 

thinner in the horizontal direction, more elongated in the vertical direction (Fig 21) and then begins showing a small 

bump in the middle on the side that is closest to the airfoil. The bump signals the beginning of a Bag-type breakup 

mechanism observed by previous studies in different configurations2,13. The initial formation and growth of the bag 

is the last stage observed before breakup (Fig 21and Fig 22). The smaller droplets generated with the monosize 

droplet generator were in the range of 100μm and the largest ones in the order of 560 μm. The smallest droplet 

showed the initial spheroid shape deformation only. The largest droplet showed all the deformation steps described 

above and in some cases they broke up. Figure 21 shows the typical sequence of deformation observed. The figure 

shows the droplet shape as it approaches the airfoil. Shown below each frame is the corresponding time, Weber 

Number and distance from the leading edge of the airfoil. Figure 22 shows the last stages of deformation; from the 

beginning of formation of the Bag mechanism of breakup to the actual breakup. The figure shows five frames each 

separated by 71.4 μsec. The original data movie had 15 frames each separated by 14.28 μsec and it lasted a total of 

214 μsec from initial formation of the bag type breakup to the breakup. 

All the observed droplet breakups occurred just before the droplet hit the airfoil. The breakup was observed to 

occur on some of the bigger droplets but not on all of them. The smaller droplets showed the initial stages of 

deformation but not breakup. For velocities of 50 m/sec and 60 m/sec no droplet breakup was observed. A limited 

number of droplets were observed to breakup at 70 m/sec. Nearly all the droplet breakups were observed at 80 and 

90 m/sec. 

B. Droplet Velocity and Acceleration as the Droplet approaches the Airfoil 

In all the tracked droplets, the velocity and acceleration follows the same pattern: the velocity of the droplet 

decreases exponentially (Fig. 13) as the acceleration acting in the opposite direction of the droplet motion 

(deceleration) increases (Fig. 14). As the droplet velocity decreases the air velocity also decreases (Fig. 15) but at a 

higher rate. A relative velocity between the droplet and the air (slip velocity) develops and increases as the droplet 

approaches the airfoil, reaching a maximum when the droplet is about to hit the airfoil (Fig. 23). The case presented 

in figures 13-15 and 23 are for a droplet of 490 μm in diameter. 

Although the droplet velocity decreases, the change in the velocity is not large with respect to the initial velocity 

of the droplet, but it occurs in a very short time and the acceleration acting on the droplet is very large. In the case 

of the droplet measurements shown in Figures 10, 11, 13 and 14 for a droplet of 490 μm, the velocity of the droplet 

decreases from 89 m/sec to 75 m/sec in 440 μsec or an average deceleration of 31,818 m/sec2. The last deceleration 

calculated before the droplet impacts the airfoil was 118,034 m/sec2

. 

C. Weber Number as the Droplet approaches the Airfoil 

The Weber number represents the ratio of the inertial forces to the surface tension forces. Applied to a droplet 

approaching the airfoil, it compares the magnitude of the forces trying to pull the droplet apart to the surface tension 

force trying to keep the drop together. The Weber number is proportional to the square of the slip velocity. As the 

droplet approaches the airfoil the slip velocity develops and increases therefore the Weber number also increases 

(Fig. 17). Physically, it means that the inertia forces that pull apart the droplet are growing larger than the surface 

tension forces that keep the droplet together. As the inertial forces grow larger than the surface tension forces, the 

droplet is distorted and in cases where the inertial forces overwhelm the surface tension forces, breakup occurs. In 

NASA/TM—2011-216946 9
all the cases where the droplet breaks up the value of the calculated Weber number was between 30 and 50. The 

observed mechanism of breakup was the Bag type in all cases. 

D. Reynolds and Bond Numbers as the Droplet approaches the Airfoil 

As the droplet approaches the airfoil, the Reynolds number increases (Fig 16) because it is proportional to the 

slip velocity and the slip velocity increases as the droplet approaches the airfoil. For all the droplets tracked, the 

calculated Reynolds number was in the range between 200 and 3000. In all cases where the Bond number was 

calculated it increased as the droplet approached the airfoil (Fig. 18) because the absolute value of the droplet 

acceleration was increasing. Bond numbers as high as 389 were calculated prior to the droplet hitting the airfoil or 

breaking up. 

E. Viscous Drag Force and Drag Coefficient as the Droplet approaches the Airfoil 

For velocities of 80 and 90 m/sec and droplets of 490 μm diameter, as the droplet approaches the airfoil the drag 

coefficient increases (Fig. 19). The higher value calculated occurred just before the droplet breaks up or impinges 

on the airfoil. Those values can be compared to the case of a disk. For a circular disk the expected value of the drag 

coefficient is 3.6 times higher than the one expected for the classical case of the spherical droplet in a uniform flow 

field. Since the Reynolds numbers measured for the droplets fell between 900 and 3000, the value for the spherical 

droplet in that range can be approximated to 0.46 therefore the expected value for a disk is 1.7 in a uniform flow. In 

all case, the higher values of the drag coefficient were larger than the values expected for a disk. The reason may be 

that although the droplet in the last stages of deformation resembles a disk shape, the droplet is not a solid body and 

it is deforming and being decelerated. At a velocity of 70 m/sec the drag coefficient initially increases and then 

slightly decreases. At velocities of 50 and 60 m/sec the drag coefficient decreases as the droplet approaches the 

airfoil. These results should not be taken as general statements because measurements on other droplets indicate 

that the drag coefficient tendency may be different for different droplets. The actual deformation of an individual 

droplet as it approaches the leading edge of the airfoil influences the drag coefficient. 

F. Airfoil Velocity Effect for Droplets of 490μm Diameter 

At each airfoil velocity of 50, 60, 70, 80 and 90 m/sec, a droplet of 490μm diameter was selected for tracking 

and the Weber number was measured and compared. Figure 24 shows the Weber number against the distance from 

the leading edge of the airfoil. This is the Weber number measured in a frame of reference at rest with respect to the 

airfoil. At a given airfoil velocity (initial droplet velocity with respect to the frame of reference on the airfoil), the 

Weber number increases as the droplet approaches the airfoil leading edge, and the higher the velocity the larger the 

value of the Weber number. This should be expected since the higher the airfoil velocity, the larger the slip velocity 

that the droplet can experience and the larger the Weber number that the drop can reach. For velocities of 70, 80 

and 90 m/sec the droplet breaks up before hitting the airfoil. For the droplets at 50 and 60m/sec the droplet did not 

breakup before hitting the airfoil. 

In general, at a Weber number of 10 the droplets show the change of shape that indicates the beginning of 

deformation. In Figure 24 a horizontal line at a Weber number of 10 can considered as the boundary above where 

the droplets are beginning deformation for a given velocity. The graph shows that as the velocity increases, the 

deformation begins further away from the leading edge of the airfoil. For the droplets in Figure 24, the time that the 

droplet remains at a Weber number greater than 10 was calculated. It showed that the higher the airfoil velocity the 

longer the droplet remains at a Weber number larger than 10. The times for the airfoil velocities of 90, 80, 70, 60 

and 50 m/sec were 587, 547, 480, 280 and 160 μsec respectively. At a higher airfoil velocity (higher initial droplet 

velocity in the frame of reference at rest with respect to the airfoil), the droplet experiences higher Weber numbers 

for longer times. 

Figures 25, 26, 27, 28 and 29 show the effect of the airfoil velocity on the droplet velocity, acceleration, slip 

velocity, Reynolds number and Bond number. 

VI. Conclusions 

Experimental observation, measurement and calculation of the main parameters for droplets impinging on the 

leading edge of a DBKUP 002 airfoil was conducted with a specially designed rotating rig. The airfoil was mounted 

at the end of the rotating arm and water droplets from a monosize droplet generator were allowed to fall vertically at 

NASA/TM—2011-216946 10
a location on the airfoil path. The deformation and breakup of the droplets was captured using high speed imaging. 

The data movies were analyzed using a software package to determine the behavior of the droplets as they 

approached the airfoil and to measure the droplet horizontal and vertical displacement against time, and to calculate 

the velocity, acceleration, slip velocity, Weber number, Reynolds number, Bond number and drag coefficient at each 

point along the horizontal location of the droplet as it approached the leading edge of the airfoil. Measurements 

were conducted at five airfoil velocities: 50, 60, 70, 80 and 90 m/sec for droplets of 490 μm and the effect of the 

velocity were studied. 

The following are the main conclusions from the observation and measurements: 

• As droplets approach the airfoil they change shape and deform following a well defined pattern: the droplet 

falling under the action of gravity shows oscillations; as it approaches the airfoil it begins distorting in the 

horizontal direction by becoming flattened at the front (the side nearest the airfoil) and bulging at the rear; 

the distortion continues with the shape changing to elongated in the vertical direction and thin in the 

horizontal direction; as the droplet gets very close to the airfoil the elongated shape begins to show a bump 

(“bag”) in the middle of the front side and for some of the large droplets the bump or “bag” grows until the 

droplet breaks up. 

• The pattern of deformation of the droplets and breakup follows the Bag type observed and reported 

by other researchers in past studies with other experimental configurations and disturbance types. 

• All the observed droplet breakups occurred just before the droplet hit the airfoil. 

• The breakup was observed to occur on some of the bigger droplets but not all of them. The smaller droplets 

show the initial stages of deformation but not breakup. 

• For velocities of 50 m/sec and 60 m/sec no droplet breakup was observed. A limited number of droplets 

were observed to breakup at 70 m/sec. Nearly all the droplet breakups were observed at 80 and 90 m/sec. 

• Measurements showed that as the droplet approaches the airfoil, the velocity decreases exponentially and the 

droplet is decelerated. The difference between the droplet velocity and the air velocity at each location along 

the droplet horizontal path creates a slip velocity that also increases exponentially as the droplet approaches 

the leading edge of the airfoil. The viscous drag force is proportional to the square of the slip velocity and as 

the slip velocity develops and increases, the force will also increase and begin deforming the droplet. 

• Measurements indicated that the droplet deceleration increases exponentially as the droplet approaches the 

leading edge of the airfoil. The deceleration is very high because the decrease in velocity of the droplet 

occurs during a very short time. 

• Values of the Weber number and Bond number along the path of the droplet increase as the droplet 

approaches the airfoil. 

• Measurements on droplets of 490μm in diameter at each airfoil velocity of 50, 60, 70, 80 and 90 m/sec 

showed that at a higher airfoil velocity (higher initial droplet velocity in the frame of reference at rest with 

respect to the airfoil), the droplet experiences higher Weber numbers for longer times along its path which 

translates to higher inertia forces for longer times trying to pull the droplet apart against the surface tension 

force keeping the droplet together. 

• For droplets of 490 μm diameter and velocities of 90 and 80 m/sec the drag coefficient increases as the 

droplet approaches the airfoil. For a velocity of 70 m/sec the drag coefficient slightly increases. For 

velocities of 60 and 50 m/sec the drag coefficient slightly decreases. These trends of the drag coefficient 

cannot be generalized. Additional measurements of the drag coefficient in other droplets indicate that its 

tendency may be different for different droplets. The actual deformation of an individual droplet influences 

the drag coefficient as the droplet approaches the airfoil. 

NASA/TM—2011-216946 11
The experimental results presented in this paper are the first time that droplet deformation and breakup are 

studied and measured for droplets impinging on the leading edge of an airfoil. No previous experimental 

observations and measurements existed in this configuration. 

VII. Future Work 

Much progress has been achieved in understanding and measuring droplet deformation and breakup since the 

program was started in 2007 but additional work is needed to expand the current research results. Additional 

experimental work is needed in the following areas: 

1) Observation and measurement of droplet deformation and breakup on two geometrical scaled versions of 

the DBKUP 002 airfoil. One model scaled down to 1⁄2 size of the DBKUP 002 and another scaled up 2 

times the size. This additional research will allow us to learn how to scale the droplet deformation, breakup 

and measurements to larger transport airfoils. 

2) Repeat the experimental observations and measurements on two airfoils of the same size but different 

geometry than the DBKUP 002. These experiments will allow to determine the effect of airfoil geometry 

on the droplet deformation and breakup 

 

NASA/TM—2011-216946 12
References 

1

 Tan, J., Papadakis, M., and Sampaht, M. K., “Computational Study of Large Droplet Breakup in the Vicinity of an Airfoil”, 

DOT/FAA/AR-05/42, Final Report, October 2005.

2 Wierzba, A., “Deformation and Breakup of Liquid Drops in a Gas Stream at Nearly Critical Weber Numbers,” Experiments 

in Fluids 9, 1990, pp. 59-64. 

3

 Kennedy, J.B. and Roberts, J., “Rain Ingestion in a Gas Turbine Engine”, ILASS-Americas, Inst. of Liquid Atomization and 

Spray Systems, 4th Annual Conference, Hartford, CT, USA, 1990, pp. 154-186. 

4 Suzuki T. and Mitachi, K., “Experimental Study on Aerodynamic Breakup of Liquid Droplets in Time-Dependent Relative 

Velocity Fields”, 8

th Int. Conf. Liquid Atomization and Spray Systems, Pasadena, CA, July 2000. 

5 Feo, Alex., Vargas, M., and Sor, S., “Rotating Rig Development for Droplet Deformation/Breakup and Impact Experiments 

Induced by Aerodynamic Surfaces”, to be published in 2011. 

6 Jarillo, E. and Feo, A., “Estudio Mediante Técnica Láser PDPA de la Formación de Gotas en el Generador de Gotas 

Monodisperso Aerometrics MDG-100”, Instituto Nacional de Técnica Aeoroespacial (INTA) Document No. 

AE/TNO/4420/119/INTA/06, March 2006. 

7 Spotlight-8, Version 2005.09.12 by Robert B. Klimek and Ted W. Wright 

8 Rudinger, G.,”Flow of Solid Particle in Gases”, AGARD –AG-222, 1976 

9 Hinze, J. O., “Turbulence”, McGraw-Hill, New York, 1959 

10 Fuch, N. A.., “ The Mechanics of Aerosols”, McMillan, New York, 1964 

11Hjelmfelt, A. T.and Mockros, L. F., “Motion of Discrete Particles in a Turbulent Fluid”, Appl. Sciences Res.,Vol. 16, pp. 

149-161, 1966 

12Sabersky R. H., Acosta, A. J., and Hauptmann, E. G., “Fluid Flow”, 2nd Edition, McMillan Publishing Co., 1971 

13 Arcoumanis, C., Gavaises M.,French B.,“Effect of Fuel Injection Process on the Structure of Diesel Sprays,” SAE paper 

970799, 1997 

NASA/TM—2011-216946 13
Table 1. DBKUP 002 Airfoil Coordinates

X-Coordinate Y-Coordinate X-Coordinate Y-Coordinate

1.0000 0.0000 0.0000 0.0000 

0.9989 -0.0009 0.0011 0.0139 

0.9957 -0.0014 0.0043 0.0310 

0.9904 -0.0025 0.0096 0.0498 

0.9830 -0.0042 0.0170 0.0674 

0.9735 -0.0064 0.0265 0.0842 

0.9619 -0.0089 0.0381 0.1007 

0.9484 -0.0120 0.0516 0.1170 

0.9330 -0.0155 0.0670 0.1318 

0.9157 -0.0195 0.0843 0.1458 

0.8967 -0.0240 0.1033 0.1584 

0.8759 -0.0291 0.1241 0.1700 

0.8536 -0.0347 0.1465 0.1797 

0.8297 -0.0410 0.1703 0.1880 

0.8044 -0.0479 0.1956 0.1943 

0.7778 -0.0554 0.2222 0.1985 

0.7500 -0.0634 0.2500 0.2007 

0.7211 -0.0721 0.2789 0.2006 

0.6913 -0.0815 0.3087 0.1985 

0.6607 -0.0915 0.3393 0.1938 

0.6294 -0.1019 0.3706 0.1870 

0.5976 -0.1128 0.4025 0.1780 

0.5653 -0.1240 0.4347 0.1683 

0.5327 -0.1353 0.4673 0.1577 

0.5000 -0.1466 0.5000 0.1466 

0.4673 -0.1577 0.5327 0.1353 

0.4347 -0.1683 0.5653 0.1240 

0.4025 -0.1780 0.5976 0.1128 

0.3706 -0.1870 0.6294 0.1019 

0.3393 -0.1938 0.6607 0.0915 

0.3087 -0.1985 0.6913 0.0815 

0.2789 -0.2006 0.7211 0.0721 

0.2500 -0.2007 0.7500 0.0634 

0.2222 -0.1985 0.7778 0.0554 

0.1956 -0.1943 0.8044 0.0479 

0.1703 -0.1880 0.8297 0.0410 

0.1465 -0.1797 0.8536 0.0347 

0.1241 -0.1700 0.8759 0.0291 

0.1033 -0.1584 0.8967 0.0240 

0.0843 -0.1458 0.9157 0.0195 

0.0670 -0.1318 0.9330 0.0155 

0.0516 -0.1170 0.9484 0.0120 

0.0381 -0.1007 0.9619 0.0089 

0.0265 -0.0842 0.9735 0.0064 

0.0170 -0.0674 0.9830 0.0042 

0.0096 -0.0498 0.9904 0.0025 

0.0043 -0.0310 0.9957 0.0014 

0.0011 -0.0139 0.9989 0.0009 

0.0000 0.0000 1.0000 0.0000 

NASA/TM—2011-216946 14
Table 2. Calibration for Generation of Monosize Droplet Generator Conditions 

Monosize Droplet 

Generator 

theoretical 

Calibration 

Point 

Orifice 

μm 

Pressure 

bar 

Frequency 

kHz 

Discharge 

Q 

ml/h 

Discharge 

Q 

cc/min 

Droplet 

Diameter 

μm 

Droplet 

Vexit

m/sec 

Punto 1 50 0.7 4.15 78 1.3 215.29 11.03 

Punto 2 100 0.4 10.37 138 2.3 191.89 4.88 

Punto 3 50 1.0 20.00 90 1.5 133.68 12.73 

Punto 4 100 0.7 2.00 270 4.5 415.39 9.55 

Punto 5 100 0.7 3.90 270 4.5 332.49 9.55 

Punto 6 50 1.0 40.00 90 1.5 106.11 12.73 

Punto 7 50 1.0 100.00 90 1.5 78.18 12.73 

Punto 8 50 1.0 50.00 90 1.5 98.50 12.73 

Punto 9 50 1.0 60.00 90 1.5 92.69 12.73 

Punto 10 50 1.0 70.00 90 1.5 88.05 12.73 

Punto 11 100 0.7 1.00 270 4.5 523.36 9.55 

Punto 12 50 1.0 4.00 90 1.5 228.60 12.73 

Punto 13 50 1.0 1.00 90 1.5 362.87 12.73 

Punto 14 50 1.0 80.00 90 1.5 84.22 12.73 

Punto 15

F Rayleigh 50 1.0 56.60 90 1.5 94.51 12.73 

Punto 17 50 0.7 10.00 66 1.1 151.89 9.34 

Punto 18 50 0.8 2.00 72 1.2 267.37 10.19 

Punto 19 50 0.8 30.00 72 1.2 108.41 10.19 

Punto 20 50 0.9 5.00 78 1.3 202.33 11.03 

Punto 21 50 0.9 100.00 78 1.3 74.54 11.03 

Punto 22 100 0.6 15.00 246 4.1 205.73 8.70 

Punto 23 100 0.6 50.00 246 4.1 137.72 8.70 

Punto 24

F Rayleigh 100 0.7 20.70 270 4.5 190.61 9.55 

Punto 25 100 0.8 70.00 282 4.7 128.84 9.97 

Punto 26 100 0.8 100.00 282 4.7 114.40 9.97 

NASA/TM—2011-216946 15
Table 3. Test Matrix

Run 

Number 

Point from 

Calibration 

Table 1 

Orifice 

μm 

Droplet

Theoretical 

Diameter 

μm 

Airfoil 

Model 

Velocity 

m/sec 

Magnification 

Resolution 

H x V 

pixels 

Frame Rate 

Frames/sec 

012510.01 Punto 23 100 137.72 90 1 512 x 512 25,000 

012510.02 Punto 23 100 137.72 90 1 192 x 512 50,000 

012510.03 Punto 23 100 137.72 90 1 192 x 312 75,000 

012510.04 Punto 23 100 137.72 90 1 192 x 264 100,000 

012510.05 Punto 23 100 137.72 90 1 128 x 184 150,000 

012510.06 Punto 23 100 137.72 80 1 192 x 312 75,000 

012510.07 Punto 23 100 137.72 70 1 192 x 312 75,000 

012510.08 Punto 23 100 137.72 60 1 192 x 312 75,000 

012510.09 Punto 23 100 137.72 50 1 192 x 312 75,000 

012510.10 Punto 24 100 190.61 90 1 192 x 312 75,000 

012510.11 Punto 24 100 190.61 90 1 192 x 264 100,000 

012510.12 Punto 24 100 190.61 90 1 128 x 184 150,000 

012510.13 Punto 24 100 190.61 90 1 128 x 184 150,000 

012510.14 Punto 24 100 190.61 90 1 128 x 184 150,000 

012510.15 Punto 24 100 190.61 80 1 192 x 312 75,000 

012510.16 Punto 24 100 190.61 70 1 192 x 312 75,000 

012510.17 Punto 24 100 190.61 60 1 192 x 312 75,000 

012510.18 Punto 24 100 190.61 50 1 192 x 312 75,000 

012510.19 Punto 11 100 523.36 90 1 192 x 312 75,000 

012510.20 Punto 11 100 523.36 90 1 192 x 312 75,000 

012610.01 Punto 11 100 523.36 90 1 192 x 312 75,000 

012610.02 Punto 11 100 523.36 90 1 192 x 312 87,500 

012610.03 Punto 11 100 523.36 90 1 128 x 184 150,000 

012610.04 Punto 11 100 523.36 90 1 128 x 184 150,000 

012610.05 Punto 11 100 523.36 80 1 128 x 184 150,000 

012610.06 Punto 11 100 523.36 70 1 192 x 312 75,000 

012610.07 Punto 11 100 523.36 70 1 128 x 184 150,000 

012610.08 Punto 11 100 523.36 60 1 192 x 312 75,000 

012610.09 Punto 11 100 523.36 60 1 128 x 184 150,000 

012610.10 Punto 11 100 523.36 50 1 192 x 312 75,000 

012610.11 Punto 11 100 523.36 50 1 128 x 184 150,000 

NASA/TM—2011-216946 16
Table 3. Test Matrix (Continuation)

Run 

Number 

Point from 

Calibration 

Table 1 

Orifice 

μm 

Droplet

Theoretical 

Diameter 

μm 

Airfoil 

Model 

Velocity 

m/sec 

Magnification 

Resolution 

H x V 

pixels 

Frame Rate 

Frames/sec 

012710.01 Punto 4 100 415.39 90 1 192 x 312 75,000 

012710.02 Punto 4 100 415.39 80 1 192 x 312 75,000 

012710.03 Punto 4 100 415.39 70 1 192 x 312 75,000 

012710.04 Punto 4 100 415.39 60 1 192 x 312 75,000 

012710.05 Punto 4 100 415.39 50 1 192 x 312 75,000 

012710.06 Punto 4 100 415.39 90 1 192 x 312 75,000 

012710.07 Punto 4 100 415.39 80 1 192 x 312 75,000 

012710.08 Punto 4 100 415.39 70 1 192 x 312 75,000 

012710.09 Punto 4 100 415.39 60 1 192 x 312 75,000 

012710.10 Punto 4 100 415.39 50 1 192 x 312 75,000 

012710.11 Punto 4 100 415.39 90 1 128 x 184 150,000 

012710.12 Punto 4 100 415.39 80 1 128 x 184 150,000 

012710.13 Punto 4 100 415.39 70 1 128 x 184 150,000 

012710.14 Punto 4 100 415.39 60 1 128 x 184 150,000 

012710.15 Punto 4 100 415.39 50 1 128 x 184 150,000 

012710.16 Punto 5 100 332.49 90 1 192 x 312 75,000 

012710.17 Punto 5 100 332.49 80 1 192 x 312 75,000 

012710.18 Punto 5 100 332.49 70 1 192 x 312 75,000 

012710.19 Punto 5 100 332.49 60 1 192 x 312 75,000 

012710.20 Punto 5 100 332.49 50 1 192 x 312 75,000 

012810.01 Punto 5 100 332.49 90 1 128 x 184 150,000 

012810.02 Punto 5 100 332.49 90 1 128 x 184 150,000 

012810.03 Punto 5 100 332.49 80 1 128 x 184 150,000 

012810.04 Punto 5 100 332.49 70 1 128 x 184 150,000 

012810.05 Punto 5 100 332.49 60 1 128 x 184 150,000 

012810.06 Punto 5 100 332.49 50 1 128 x 184 150,000 

012810.07 Punto 5 100 332.49 66 1 256 x 320 65,100 

012810.07D Punto 5 100 332.49 66 1 256 x 320 65,100 

012810.08 Punto 11 100 523.36 90 1 192 x 400 70,000 

012810.09 Punto 11 100 523.36 90 1 192 x 400 70,000 

012810.10 Punto 11 100 523.36 90 1 192 x 400 70,000 

NASA/TM—2011-216946 17
Table 3. Test Matrix (Continuation)

Run 

Number 

Point from 

Calibration 

Table 1 

Orifice 

μm 

Droplet

Theoretical 

Diameter 

μm 

Airfoil 

Model 

Velocity 

m/sec 

Magnification 

Resolution 

H x V 

pixels 

Frame Rate 

Frames/sec 

012910.01 Punto 11 100 523.36 0 2 256 x 320 65,100 

012910.02 Punto 4 100 415.39 0 2 256 x 320 65,100 

012910.03 Punto 5 100 332.49 0 2 256 x 320 65,100 

012910.04 Punto 24 100 190.61 0 2 256 x 320 65,100 

012910.05 Punto 23 100 137.72 0 2 256 x 320 65,100 

012910.06 Punto 26 100 114.4 0 2 256 x 320 65,100 

012910.07 Punto 11 100 523.36 90 2 192 x 400 70,000 

012910.08 Punto 11 100 523.36 90 2 192 x 400 70,000 

012910.09 Punto 11 100 523.36 80 2 192 x 400 70,000 

012910.10 Punto 11 100 523.36 70 2 192 x 400 70,000 

012910.11 Punto 4 100 415.39 90 2 192 x 400 70,000 

012910.12 Punto 4 100 415.39 80 2 192 x 400 70,000 

012910.13 Punto 5 100 332.49 80 2 192 x 400 70,000 

012910.14 Punto 24 100 190.61 80 2 192 x 400 70,000 

012910.15 Punto 23 100 137.72 80 2 192 x 400 70,000 

012910.16 Punto 24 100 190.61 90 2 192 x 400 70,000 

012910.17 Punto 5 100 332.49 90 2 192 x 400 70,000 

012910.18 Punto 4 100 415.39 90 2 192 x 400 70,000 

012910.19 Punto 11 100 523.36 90 2 192 x 400 70,000 

NASA/TM—2011-216946 18
Table 4. Camera Frame Rates and Resolution used during the Experiment 

Frame Rate 

fps 

Maximum 

Resolution 

H x V 

pixels 

25,000 512 x 512 

50,000 192 x 512 

65,100 256 x 320 

75,000 192 x 312 

87,500 192 x 312 

100,000 192 x 264 

150,000 128 x 184 

NASA/TM—2011-216946 19
Figure 2. Experiment set-up in the INTA test cell. 

Rotating Arm Airfoil 

Motor 

Monosize 

Droplet 

Generator

High 

Speed 

Camera

Control 

Room

Struts 

 

air 

Water 

U

Airfoil

Figure 1. Conceptual View of the Experiment 

NASA/TM—2011-216946 20
 (a) (b) (c) 

Figure 3. DBKUP 002 Airfoil (a) Side view; (b) Front view of leading edge; (c) View from above 

Figure 4. TSI Monosize Droplet generator, frequency generator, flow rate control valve, 

water pressure tank, camera and lens system, computer used to operate the camera 

Monosize 

Droplet 

Generator 

Water 

Pressure 

Container 

Flow 

Rate 

Control 

Valve

Frequency 

Generator 

Computer 

with 

Software 

to operate 

the 

Photron 

Camera 

Camera and 

Lens 

System 

NASA/TM—2011-216946 21
 Figure 5. Close-up view of Photron SA-5 Camera with lens system. The camera is set atop 

an x-y positioning table. The monosize droplet generator can be observed above the airfoil 

Figure 6. Documentation frame where the airfoil is about to strike the droplets. Second 

droplet from the bottom of the data image is labeled “droplet #2” for identification, study and 

tracking purposes. The droplet is in the process of breaking up. Droplet diameter = 490 mμ, 

Airfoil speed = 90 m/sec, camera frame rate 75,000 fps, resolution 192x312 pixels, frame 7191

Image file: 01252010-19C_Frame_7191_600dpi.tif Droplet #2 

Droplet 2 

Airfoil 

shadow 

NASA/TM—2011-216946 22
Figure 8. Threshold image of a droplet enclosed in a rectangle in preparation for 

continuous tracking. Airfoil speed = 50 m/sec, camera frame rate 75,000 fps, resolution 

192x312 pixels, frame 2175, Image: 01252010-09_81-2098_600dpi_DropDiam.tif; 

Droplet #1 

Figure 7. Zoom-in on droplet image to measure the droplet diameter. Horizontal and vertical pixels are counted and 

averaged out. Airfoil speed = 70 m/sec, camera frame rate 75,000 fps, resolution 192x312 pixels, frame 2175, Image 

01272010-08B_Drop #2_5426_Droplet Diameter_600dpi.tif 

NASA/TM—2011-216946 23
Time, μs

0 50 100 150 200 250 300 350 400 450 500

Droplet

 Distance

μm

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

Figure 9. Horizontal displacement against time for 01252010-19C Droplet #2, Drop Diameter = 490 μm, 

Airfoil speed = 90 m/sec, Camera Frame Rate 75,000 fps, Resolution 192x312 pixels, Data from file: 

523-50to90.xls 

Time, μseconds

0 50 100 150 200 250 300 350 400 450

V

μm/μsec

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Figure 10. Horizontal velocity against time for 01252010-19C Droplet #2; Drop Diameter = 490 μm, 

Airfoil speed = 90 m/sec, Camera Frame Rate 75,000 fps, Resolution 192x312 pixels, Data from file:

523-50to90.xls 

NASA/TM—2011-216946 24
Time in μsec

0 50 100 150 200 250 300 350 400 450

Acceleration 

in

m/sec2

0

20000

40000

60000

80000

100000

120000

140000

Figure 11. Horizontal acceleration against time for 01252010-19C Droplet #2, Diameter = 490 μm 

Airfoil speed = 90 m/sec, camera frame rate 75,000 fps, resolution 192x312 pixels, Data from file: 

01252010-19C_DropletsData.xls 

Distance From Airfoil LE

millimeters

-50 -40 -30 -20 -10 0

0

10

20

30

40

50

Distance From Airfoil LE

millimeters

-50 -40 -30 -20 -10 0

0

10

20

30

40

50

Figure 12. Frame of reference at rest with respect to the airfoil. Origin of coordinate axes located at the stagnation point 

of the leading edge of the airfoil. Airfoil is not drawn to scale 

NASA/TM—2011-216946 25
Distance from the LE of the Airfoil

millimeters

-45 -40 -35 -30 -25 -20 -15 -10 -5 0

 Vdroplet

74

76

78

80

82

84

86

88

90

Figure 13. Droplet horizontal Velocity against Distance from the LE of the airfoil for 01252010-19C Droplet #2 

Drop Diameter = 490 μm, Airfoil speed = 90 m/sec, Camera Frame Rate 75,000 fps, resolution 192x312 pixels 

Data from file: 523-50to90.xls 

Distance from the LE of the Airfoil

millimeters

-45 -40 -35 -30 -25 -20 -15 -10 -5 0

Droplet 

Acceleration

m/sec2

-130000

-120000

-110000

-100000

-90000

-80000

-70000

-60000

-50000

-40000

-30000

-20000

-10000

0

Figure 14. Droplet horizontal Acceleration against distance from the LE of the airfoil for 01252010-19C Droplet #2, 

Diameter = 490 μm, Airfoil speed = 90 m/sec, Camera Frame Rate 75,000 fps, Resolution 192x312 pixels 

Data from file: 523-50to90.xls 

NASA/TM—2011-216946 26
x/chord

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0

Uair/Uα

0.0

0.2

0.4

0.6

0.8

1.0

Curve Fit Equation

f=a*(1-exp(b*x))+c*(1-exp(d*x))

a = 0.4201; b = 22.5663; c = 0.5532; d = 4.1106 

Figure 15. Experimental Uair/Uα vs. x/chord for DBKUP 002 airfoil geometry scaled down 1/10 in size, 0.047m chord 

Measurements conducted at the INTA 0.3m x 0.2m tunnel. Curve fit equation is shown. Uair is the air velocity 

measured with a Laser Doppler Velocimeter (LDV) at a given location along the horizontal streamline ending at the 

leading edge stagnation point. Uα is the free stream velocity. 

Distance from the airfoil LE to the droplet

millimeters

-45 -40 -35 -30 -25 -20 -15 -10 -5 0

Re

Reynolds

Number

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

Figure 16. Reynolds number based on the calculated horizontal slip velocity and the droplet diameter for 01252010-19C 

Droplet #2; Drop Diameter = 490 μm, Airfoil speed = 90 m/sec, Camera Frame Rate 75,000 fps, Resolution 192x312 

pixels. Data from file 523-50to90.xls 

NASA/TM—2011-216946 27
Distance from the airfoil LE to the droplet

millimeters

-45 -40 -35 -30 -25 -20 -15 -10 -5 0

We

Weber

Number 

0

5

10

15

20

25

30

35

40

45

50

Figure 17. Weber number based on the calculated horizontal slip velocity and the droplet diameter for 01252010-19C 

Droplet #2; Drop Diameter = 490 μm, Airfoil speed = 90 m/sec, Camera Frame Rate 75,000 fps, Resolution 192x312 

pixels 

Distance From Airfoil LE

millimeters

-45 -40 -35 -30 -25 -20 -15 -10 -5 0

Bo

Bond Number

0

50

100

150

200

250

300

350

400

450

Figure 18. Bond number based on the calculated horizontal acceleration of the droplet and the droplet diameter for 

01252010-19C Droplet #2; Drop Diameter = 490 μm, Airfoil speed = 90 m/sec, Camera Frame Rate 75,000 fps, Resolution 

192x312 pixels 

NASA/TM—2011-216946 28
Distance from the LE

millimeters

-45 -40 -35 -30 -25 -20 -15 -10 -5 0

Cd

Drag Coefficient

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Figure 19. Drag Coefficient based on the calculated horizontal slip velocity, the acceleration and the droplet diameter for 

01252010-19C Droplet #2; Drop Diameter = 490 μm, Airfoil speed = 90 m/sec, Camera Frame Rate 75,000 fps, Resolution 

192x312 pixels 

Time, μs

0 50 100 150 200 250 300 350 400 450 500

Droplet

 Distance

μm

0

500

1000

1500

2000

2500

3000

3500

4000

Figure 20. Vertical displacement against time for 01252010-19C Droplet #2; Drop Diameter = 490 μm, Airfoil speed = 90 

m/sec, Camera Frame Rate 75,000 fps, Resolution 192x312 pixels, Data from file: 523-50to90.xls 

Note: Origin of vertical axis located at the frame where the tracking of the droplet was initiated 

NASA/TM—2011-216946 29
Time: 0 μsec 13.3 μsec 80.0 μsec 146.7 μsec 213.3 μsec 280.0 μsec 

 

Distance: 81.4 mm -69.6 mm -63.6 mm -57.6 mm -51.6 mm -45.6 

 

 We: ~ 0 7.3 8.2 9.3 10.6 12.1 

Time: 346.7 μsec 413.3 μsec 480 μsec 546.7 μsec 613.3 μsec 680.0 μsec 

Distance: -39.6 mm -33.6 mm -27.6 -21.6 -15.6 mm -9.6 mm 

 

We: 14.0 16.4 19.3 23.2 28.2 34.9 

 

 

Time: 706.7 μsec 733.3 μsec 760.0 μsec 786.7 μsec 

Distance: -7.2 mm -4.8 mm -2.4 mm 0.0 mm 

 

We: 38.2 42.0 46.2 51.0 

 

Figure 21. Time sequence of a droplet approaching the airfoil showing the deformation along the path. Below each droplet, the 

time, the distance of the droplet from the leading edge of the airfoil and the Weber number are shown. 01252010-19C Droplet 

#3; Drop Diameter = 490 μm, Airfoil speed = 90 m/sec, Camera Frame Rate 75,000 fps, Resolution 192x312 pixels. Frames: 

140, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 202, 204, 206 and 208 

NASA/TM—2011-216946 30
246 μm 246 μm

 t = 0 μsec t = 57.1 μsec t = 85.7 μsec t = 114.3 μsec t = 142.9 μsec 

 15.5 mm 10.3 mm 7.7 mm 5.2 mm 2.6 mm 

Figure 22. Time sequence of the later stages of the droplet breakup. The “bag” type of breakup can be observed. The 

distance scale is shown on the first and last images (246μm). The time from the first frame to breakup is indicated below 

each image. The distance from the leading edge of the airfoil is indicated below the time. Movie 01292010-11D droplet #1; 

Airfoil speed = 90 m/sec, Camera Frame Rate 70,000 fps, Resolution 192x400 pixels 

Distance from LE of Airfoil at the location of the Droplet

millimeters

-45 -40 -35 -30 -25 -20 -15 -10 -5 0

Slip Velocity 

Absolute Value of 

(Vdroplet - Vair )

m/sec

0

10

20

30

40

50

60

70

80

90

100

Slip Velocity vs Distance 

Droplet Velocity vs. Distance

Air Velocity vs. Distancce

Figure 23. Droplet velocity, air velocity and slip velocity for 01252010-19C Droplet #2; Drop Diameter = 490 μm, Airfoil 

speed = 90 m/sec, Camera Frame Rate 75,000 fps, Resolution 192x312 pixels 

NASA/TM—2011-216946 31
-75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0

We

Weber Number

0

5

10

15

20

25

30

35

40

45

50

50 m/sec

60 m/sec

70 m/sec

80 m/sec

90 m/sec

Figure 24. Weber Number against distance from the leading edge of the airfoil for droplets of 490 μm at each 

velocity of 50 to 90 m/sec. Camera Frame Rate 75,000 fps, Resolution 192x312 pixels 

-75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0

Drop Velocity 

m/sec

40

45

50

55

60

65

70

75

80

85

90

95

100

50 m/sec

60 m/sec

70 m/sec 

80 m/sec 

90 m/sec

Figure 25. Drop velocities against distance from the leading edge of the airfoil for droplets of 490 μm at each 

velocity of 50 to 90 m/sec. Camera Frame Rate 75,000 fps, Resolution 192x312 pixels 

NASA/TM—2011-216946 32
Distance From the Leading Edge of the Airfoil

millimeters

-75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0

Droplet 

Acceleration

m/sec2

-80000

-70000

-60000

-50000

-40000

-30000

-20000

-10000

0

50 m/sec

60 m/sec

70 m/sec

80 m/sec

90 m/sec

Figure 26. Droplet acceleration against distance from the leading edge of the airfoil for droplets of 490 μm at each 

 velocity of 50 to 90 m/sec. The acceleration is in the opposite direction from the motion of the droplet (deceleration). 

Camera Frame Rate 75,000 fps, Resolution 192x312 pixels 

Distance from LE of Airfoil

millimeters

-75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0

Slip Velocity 

m/sec

0

10

20

30

40

50

60

70

80

90

100

50 m/sec

60 m/sec

70 m/sec

80 m/sec

90 m/sec

Figure 27. Slip velocity against distance from the leading edge of the airfoil for droplets of 490 μm at each 

velocity of 50 to 90 m/sec. Camera Frame Rate 75,000 fps, Resolution 192x312 pixels 

NASA/TM—2011-216946 33
Distance from LE of Airfoil

millimeters

-75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0

Re

Reynolds Number

0

500

1000

1500

2000

2500

3000

50 m/sec

60 m/sec

70 m/sec

80 m/sec

90 m/sec

Figure 28. Reynolds number against distance from the leading edge of the airfoil for droplets of 490 μm at each 

 velocity of 50 to 90 m/sec. Camera Frame Rate 75,000 fps, Resolution 192x312 pixels 

-75 -70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0

Bo

Bond Number

0

20

40

60

80

100

120

140

160

180

200

220

240

Distance from LE of Airfoil

millimeters

50 m/sec

60 m/sec

70 m/sec

80 m/sec

90 m/sec

Figure 29. Bond Number against distance from the leading edge of the airfoil for droplets of 490 μm at each 

 velocity of 50 to 90 m/sec. Camera Frame Rate 75,000 fps, Resolution 192x312 pixels 

NASA/TM—2011-216946 34
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4. TITLE AND SUBTITLE

Experimental Observations on the Deformation and Breakup of Water Droplets Near the 

Leading Edge of an Airfoil 

5a. CONTRACT NUMBER

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6. AUTHOR(S)

Vargas, Mario; Feo, Alex 

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WBS 457280.02.07.03.02 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

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John H. Glenn Research Center at Lewis Field 

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This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

This work presents the results of an experimental study on droplet deformation and breakup near the leading edge of an airfoil. The 

experiment was conducted in the rotating rig test cell at the Instituto Nacional de Técnica Aeroespacial (INTA) in Madrid, Spain. An airfoil 

model placed at the end of the rotating arm was moved at speeds of 50 to 90 m/sec. A monosize droplet generator was employed to produce 

droplets that were allowed to fall from above, perpendicular to the path of the airfoil at a given location. High speed imaging was employed 

to observe the interaction between the droplets and the airfoil. The high speed imaging allowed observation of droplet deformation and 

breakup as the droplet approached the airfoil near the stagnation line. A tracking software program was used to measure from the high speed 

movies the horizontal and vertical displacement of the droplet against time. The velocity, acceleration, Weber number, Bond number, 

Reynolds number, and the drag coefficients were calculated along the path of a given droplet from beginning of deformation to breakup 

and/or hitting the airfoil. Results are presented for droplets with a diameter of 490 micrometers at airfoil speeds of 50, 60, 70, 80 and 90 

m/sec. 

15. SUBJECT TERMS

Droplet breakup; Supercooled large droplet icing (SLD); Icing 

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