Mario Vargas

Glenn Research Center, Cleveland, Ohio

Suthyvann Sor and Adelaida Garcia Magarino

Instituto Nacional de Tecnica Aeroespacial, Madrid, Spain

Mechanism of Water Droplet Breakup

Near the Leading Edge of an Airfoil

NASA/TM—2012-217704

September 2012

AIAA–2012–3129
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Mario Vargas

Glenn Research Center, Cleveland, Ohio

Suthyvann Sor and Adelaida Garcia Magarino

Instituto Nacional de Tecnica Aeroespacial, Madrid, Spain

Mechanism of Water Droplet Breakup

Near the Leading Edge of an Airfoil

NASA/TM—2012-217704

September 2012

AIAA–2012–3129

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Atmospheric Space Environments Conference

sponsored by the American Institute of Aeronautics and Astronautics

New Orleans, Louisiana, June 25–28, 2012
Acknowledgments

The authors would like to thank Mr. Chris Lynch for his excellent imaging work during the experiment. Thanks to Dr. Alex Feo, 

Dr. Mark Potapczuk, and Dr. Peter Struk for reviewing the paper, and to Dr. Andy Broeren for his help with the monosize droplet

generator during the pre-test imaging work done at the NASA Icing Branch Flow Laboratory. Thanks also to Mr. Yago Sanchez 

and Mr. Carlos Molina from ALAVA INGENIEROS for their support and expertise during the experiment. Thanks to all rotating 

rig INTA personnel for their excellent support in the preparation work and during the execution of the test program. The present 

work is part of the NASA/INTA collaboration under a Space Act Agreement. It is funded by the Atmospheric Environment Safety 

Technologies (AEST) Project, Aviation Safety Program (AvSP). Special thanks to Dr. Ron Colantonio for his support of the effort.

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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2012-217704 1 

Mechanism of Water Droplet Breakup Near 

the Leading Edge of an Airfoil 

Mario Vargas

National Aeronautics and Space Administration 

Glenn Research Center 

Brook Park, Ohio 44135 

Suthyvann Sor and Adelaida Garcia Magarino 

Instituto Nacional de Tecnica Aeroespacial 

Madrid, Spain 

Abstract 

This work presents 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. The airfoil model was placed at the end of 

the rotating arm and a monosize droplet generator produced droplets that fell from above, perpendicular 

to the path of the airfoil. The interaction between the droplets and the airfoil was captured with high speed 

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

near the stagnation line. Image processing software was used to measure the position of the droplet 

centroid, equivalent diameter, perimeter, area, and the major and minor axes of an ellipse superimposed 

over the deforming droplet. The horizontal and vertical displacement of each droplet against time was 

also measured, and the velocity, acceleration, Weber number, Bond number, Reynolds number, and the 

drag coefficients were calculated along the path of the droplet to the beginning of breakup. Droplet 

deformation is defined and studied against main parameters. The high speed imaging allowed observation 

of the actual mechanism of breakup and identification of the sequence of configurations from the 

initiation of the breakup to the disintegration of the droplet. Results and comparisons are presented for 

droplets of diameters in the range of 500 to 1800 m, and airfoil velocities of 70 and 90 m/sec. 

Nomenclature 

avi Audio video interleave movie format 

Bo Bond number 

c Airfoil chord 

Cd Drag coefficient 

D Droplet diameter 

DBKUP Airfoil designation 

f Square wave frequency introduced by activating a piezoelectric transducer 

INTA Instituto Nacional de Técnica Aeroespacial 

LED Light Emitting Diode 

PIV Particle Image Velocimetry 

Q Water flow rate 

Re Reynolds number 

SLD  Supercooled Large Droplets 

V Velocity 

VSlip Slip Velocity, relative velocity between the droplet and the air: (Vdroplet - Vair)

We Weber number 
NASA/TM—2012-217704 2 

Introduction 

Supercooled Large Droplet (SLD) breakup near the leading edge of large transport airfoils may alter 

the mass flux of water reaching the leading edge and be a factor that needs to be accounted for in the 

prediction of ice accretion formation in icing codes. Studies of droplet breakup can provide experimental 

data on the main parameters of droplet deformation and the sequence of steps that lead to droplet 

disintegration. They can indicate the location where droplet breakup is initiated and the size and shape of 

the pieces that may be carried away by the airflow as the droplet goes through the breakup process and 

disintegrates or impacts the surface of the airfoil. They can also provide an understanding of the physics 

involved in the process of deformation and breakup. 

Previous studies (Refs. 1 and 2) measured the droplet horizontal and vertical displacement against 

time and calculated the velocity, acceleration, Weber number, Bond number, and Reynolds number along 

the path of the droplet as it approached the leading edge near the stagnation line. The studies also 

presented the sequence of droplet deformation that leads to the initiation of breakup. Those studies were 

carried out for an airfoil with a chord of 0.47 m and droplet diameters up to 500 m and allowed defining 

the beginning of the actual droplet breakup as the point along the path at which the thickness of the 

droplet reaches a minimum. The final sequence of the droplet breakup was observed but not all the details 

were captured. The studies indicated the need to continue the study of droplet deformation, to do a 

detailed observation of the droplet breakup from its initiation to total disintegration, to extend the testing 

to airfoils of different chord size and to increase the size of the droplets up to 1800 m. 

This paper provides the results of a droplet deformation and breakup experiment conducted in July of 

2011 in the rotating rig test cell at the Instituto Nacional de Técnica Aeroespacial (INTA) in Madrid, 

Spain. The experiment is part of an international agreement between NASA and INTA. The experiment 

was conducted on airfoils with chord lengths of 0.21, 0.47, and 0.71 m placed at the end of an arm 

rotating about a central axis at speeds from 50 to 90 m/sec. A monosize droplet generator was employed 

to produce droplets from 100 to 1800 m that were allowed to fall from above, perpendicular to the path 

of the model airfoil at a given location. A high speed imaging system was used to capture the droplet 

deformation and breakup as the droplets approached the leading edge of the airfoil along the stagnation 

line (Figs. 1 and 2). 

The overall objective of the experiment was to extend previous experimental results on droplet 

deformation to three airfoils of same geometry but different chord size, to increase the range of droplet 

diameters tested, and to obtain a more detailed observation of the actual mechanism of droplet 

deformation and breakup from its initiation to disintegration. For a given droplet, digital imaging 

processing was employed to measure the diameter, coordinates of the centroid, the area, the perimeter and 

the horizontal and vertical dimensions at each location of a droplet along its path. The droplet 

displacement against time was measured and the important parameters along the drop path were 

calculated. The high speed movies allowed observing the details of the droplet breakup sequence. The 

image processing data and the calculated parameters were used to study the droplet deformation. 

The present work is a continuation and extension of previous research efforts to measure the 

important parameters involved in droplet deformation and breakup, to study the effect of airfoil size and 

to identify the mechanism of droplet breakup as droplets approach the leading edge of an airfoil along the 

stagnation line. The results will help in determining if icing codes need to be modified to account for 

droplet breakup when the size of the droplets is in the SLD regime. 

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. The setup was identical to 

the one used in previous experiments (Refs. 1 and 2). 
NASA/TM—2012-217704 3 

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 m (93.3 in.). 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 1 m/sec intervals. 

B. Airfoil Models 

Three airfoils were used during the experiment. They have the same geometry but different chord size. 

They are a generic type of thick airfoil designated as DBKUP 001, DBKUP 002, and DBKUP 003 (Fig. 3). 

Table 1 lists the coordinates of the airfoil. This type of airfoil geometry was chosen for the experiment 

because it is a blunt shape that simulates a scaled version of the type of leading edge shape found on large 

transport airfoils. The chord sizes of the airfoils are 0.21 m (8.3 in.), 0.47 m (18.5 in.) and 0.71 m (30.0 in.), 

respectively. The airfoil geometry was the same as that used in previous experiments (Ref. 1). 

C. Monosize Droplet Generator 

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

range from 100 to 500 m. The droplet generator (Figs. 2 and 3) consists of a distilled water container, an 

electric pump, a power supply to drive the electric pump, a flow control valve, a frequency generator and 

the vibration head. The electric water pump delivers the water flow from the container to the vibration 

head. The high precision flow rate control valve with a manometer allows fine adjustment of the flow rate 

before the water reaches the vibration head. At the vibration head the water is forced through a small 

orifice (100m 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 a given orifice diameter, flow rate and excitation frequency the diameter of the 

generated droplets is given by the equation: 

    (kHz)

(cc/min)

1 3

317 m f

Q /

D  

(1) 

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 μm. Prior to the droplet breakup high speed test, the monosize droplet 

generator was calibrated for orifices from 100 to 800 m. The TSI MDG-100 Monosize Droplet 

Generator was not originally designed for orifice sizes larger than 100 m but when tested with 

commercially available larger orifices it performed well and droplets sizes up to 1500 m could be 

generated. 
NASA/TM—2012-217704 4 

D. High Speed Imaging System 

The high speed imaging system consists of the high speed camera (Fig. 2), the camera software, the 

lens system and the lighting. The high speed camera used during the experiment was a Photron SA-5. The 

camera can capture images at rates from 1000 to 1,000,000 frames per second (fps). During the 

experiment frames rates of 50000, 75000, and 150000 fps were used with corresponding resolutions given 

in pixels for the horizontal and vertical directions: 192512, 192312, and 128184. As the frame rate is 

increased, the resolution of the camera decreases. The camera has a maximum shutter speed of 1 (s) 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 post-processing the image sequences to generate the data movies for data analysis and to 

select the frames at which the droplet tracking was to begin and end. 

During the experiment one lens configuration was used for two magnifications of the droplet 

deformation and/or breakup. The lens configuration consisted of a 200 mm Micro Nikkor lens with a 

2x doubler added between the camera and the 200 mm 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 m (9.25 in.) along the span of the airfoil. For the first 

magnification the distance was 0.91 m (36 in.) and for the second the distance was 0.36 m (14 in.). The 

lighting 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 W Xenon light with a lens to 

focus the beam. 

Test Procedure and Test Matrix 

A. Test Procedure 

Before a test run, the high speed camera system is aligned so that the line of sight of the lens is 

parallel to 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. The camera sits on a x-y positioning table that allows careful 

adjustments in either direction. A custom made adaptor, designed to hold a laser pointer so that the laser 

beam is aligned with the camera lens, is inserted into the camera lens housing. The camera position is 

adjusted so that the laser beam from the laser pointer is parallel to the span of the airfoil (grazing it). This 

ensures that the direction of the lens is parallel to the direction of the airfoil span. 

The airfoil is moved from the alignment position and a ruler with the smallest subdivision of 1 mm is 

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

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

operation of the rotating arm through a safety glass. The camera is controlled with software run on a 

laptop computer located in the control room. The software is used to start the camera and set the 

controlling parameters including frame rate and shutter speed, and allows writing information on each 

camera frame above the recorded image. The following information is recorded on each frame during the 

experiment: 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 rotational speed corresponding to the target velocity. When it 

reaches the target speed, the camera recording is started and maintained for three or more rotations 

depending on the amount of data wanted for a particular run. Once the recording is completed the rotating 
NASA/TM—2012-217704 5 

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 or more passes of the airfoil. If the droplets are in focus, the 

back light is uniform and the image area covers the horizontal displacement of the droplets, the 

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

B. Test Matrix 

The test matrix for the experiment was designed to setup the droplet generator for a chosen theoretical 

droplet diameter. At each droplet size, test points were set for airfoil velocities of 50, 60, 70, 80, and 90 m 

per second. Frame rate values employed were 25000, 50000, 65100, 75000, 87000, 100000, and 

150000 fps. A speed of 75000 fps was used most frequently because it was a middle point between a 

frame rate that allowed observation of the droplet breakup and a reasonable resolution of 192312 pixels. 

Two camera magnifications were employed during the test. The larger magnification gave more detail but 

only allowed observation of the droplets over a very small distance. The smaller magnification allowed 

observation of the droplet over a larger distance, from no interaction with the airfoil, to beginning of 

deformation, deformation and breakup or impact with the airfoil. 

Data Analysis and Results 

The high speed camera was employed to observe and record the droplet deformation and breakup as 

the airfoil approached the location of the droplet generator. At each condition a high speed movie of the 

interaction between the airfoil and the falling droplets was obtained for three or more passes of the airfoil. 

The movie was recorded in raw format and stored on a hard drive for post processing. Before post 

processing, each movie for a given run was split into “clips”. Each “clip” consisted of the movie for one 

pass of the airfoil. A total of 154 runs were conducted and the imaging data were split into 1128 movie 

clips. In each clip there is usually one or more droplets deforming and/or breaking up. A subset of the 

data was analyzed and is presented in this paper. 

A. Data Post Processing 

The camera software was used to generate the clips and to change them from raw format to avi. The 

change in format from raw to avi was done without using any compression to avoid altering the data. To 

post process the droplet data from the clips, a data analysis program was developed (Ref. 3). The program 

has a digital image processing part and a calculation part. It reads the movie in avi format and converts 

each frame from grayscale to binary for image segmentation and tracking. The program is initialized with 

the following input: file name of the video clip, camera resolution, frame rate of the movie, chord length 

of the airfoil tested, assigned number of the droplet being tracked, frame number where the tracking 

begins and frame number where the tracking ends. 

The frame numbers where the tracking begins and ends are selected from the movie clip with help of 

the camera software. The assigned number of the tracked droplet is obtained from the frame where the 

tracking begins. The program identifies the droplets in a given frame by numbering them from left to 

right. In each frame the digital image processing part of the program calculates and/or records the 

following parameters for the droplet being tracked: frame number, time with respect to the tracking 

frame, time with respect to the first frame of the movie, x coordinate of the centroid, y coordinate of the 

centroid, area, perimeter, major and minor axes of an ellipse superimposed on the droplet, equivalent 

diameter based on the measured area, equivalent diameter based on the volume for an oblate spheroid 

using the major and minor axes of the superimposed ellipse and calculated assuming the droplet is an 

oblate spheroid asymmetric about the major axis on the plane of observation, symmetric about the minor 

axis on the plane of observation and rotationally symmetric about the axis pointing in the direction that 

the droplet is moving toward the airfoil (Ref. 4). 
NASA/TM—2012-217704 6 

The diameter based in the volume of the oblate spheroid was used in all calculations. As long as the 

droplet remains an oblate spheroid with the symmetries mentioned above, this diameter should remain 

constant since the volume of the droplet does not change (Fig. 4). The diameter based on the area of the 

droplet cross section varies since the area is the cross section of a three-dimensional body changing in 

shape. In all the calculations presented in this paper that involve the diameter of the droplet, the diameter 

used was the one based on the volume of the oblate spheroid (Ref. 4): 

d  b  a

2 (2) 

where b is the height of the droplet and a the width. 

The calculation part of the program uses the parameters measured in the image processing part to 

calculate the following parameters with respect to time: horizontal and vertical displacement, velocity of 

the droplet with respect to the airfoil (frame of reference at rest with respect to the airfoil with the origin 

at the stagnation point), position of the droplet with respect to the airfoil, slip velocity, acceleration, 

Weber number, Reynolds number, Bond number and the drag coefficient. For the calculation of the slip 

velocity at a given location, the velocity of the air at that location is needed. The value of the velocity at a 

given location with respect to the airfoil and along the stagnation line was obtained using a correlation for 

air velocity from Particle Image Velocimetry (PIV) measurements conducted in the test cell (Ref. 5) for 

each of the three airfoil geometries tested. 

A droplet is a three-dimensional object. The tracking and measurements are made on a twodimensional profile of the droplet. In some instances this does not affect the data and conclusions. In 

other instances the three dimensionality of the droplet is important and will affect the results. If this is the 

case for the data presented, the effect of the droplet three-dimensionality on the results will be stated and 

explained. 

B. Data from Digital Image Processing 

The digital image processing part of the program allows study of the droplet deformation against 

time. Data from Run 072011.14C droplet #1 is presented in Figures 5 to 10. The size of the droplet is 

1062 μm, the chord of the airfoil is 0.710 m and the velocity of the airfoil is 90 m/sec. The movie clip has 

a single droplet that was tracked from frame 20 to frame 210. The droplet is initially nearly spherical 

(Fig. 5(a)) and as it approaches the airfoil it deforms into an asymmetric oblate spheroid (Fig. 5(b)) with a 

slight forward inclination with respect to the vertical axis. The inclination is small but noticeable. In 

describing the oblate spheroid, the two axes of the spheroid will be treated as being approximately in the 

direction of the horizontal and vertical axis. The oblate spheroid is asymmetric about the vertical axis, 

symmetric about the horizontal axis in the plane of observation, and assumed rotationally symmetric 

about the axis pointing in the direction of motion (horizontal axis). The front part of the spheroid is 

initially rounded but slowly becomes flatter as the droplet approaches the airfoil. The process continues 

until the droplet no longer can sustain the stretching shape against the aerodynamic forces and begins the 

actual breakup process. The breakup process is discussed in detail in section F. 

Figure 6 shows the horizontal displacement of the droplet against time with respect to a frame of 

reference at rest with respect to the test cell. It is a plot of the centroid x-coordinate against time. The 

displacement of the droplet increases exponentially. This can be explained as follows, in a frame of 

reference at rest with respect to the test cell: as the airfoil approaches the droplet, the velocity of the air 

increases exponentially around the droplet. The droplet is dragged in that direction but its inertia prevents 

it from following the air velocity and a difference between the velocity of the air and the velocity of the 

droplet develops (slip velocity) that displaces the droplet and generates aerodynamic forces that deform it. 

This process can also be explained from a frame of reference at rest with respect to the airfoil. In this 

frame of reference, when the droplet is far from the airfoil, the droplet approaches the airfoil at the same 

velocity as the velocity of the air at that location. As the droplet gets closer to the airfoil, a difference 

between the velocity of the air and the droplet develops (slip velocity) because the air velocity decreases 
NASA/TM—2012-217704 7 

exponentially along the stagnation line (reaching zero at the stagnation point of the airfoil) and the inertia 

of the droplet prevents it from following the velocity of the air. The slip velocity increases as the velocity 

of the air decreases and the generated aerodynamic forces deform the droplet. It is the exponential 

decrease in the velocity that is reflected in the exponential horizontal displacement of the droplet against 

time. Since the velocity of the droplet at each time is the tangent to the curve, it will also show an 

exponential behavior as will the acceleration of the droplet against time. The exponential behavior of the 

velocity and acceleration propagates to the Weber, Reynolds, and Bond numbers. 

Figure 7 shows the vertical displacement of the droplet against time. It is a plot of the centroid 

y-coordinate against time. It increases linearly with time indicating a constant velocity for the droplet. The 

reason for the constant velocity is that the droplets are tracked close to the head of the droplet generator 

where the droplets are ejected at a constant velocity, 2 m/sec for the droplet data presented in Figure 7. 

Figure 4 shows the two diameters that were calculated against time. The data in blue (triangles) 

corresponds to the diameter of a circular surface with the same area as the area of the tracked droplet 

measured by the program. The program measures the area in pixels. The diameter is measured initially in 

pixels and converted to micrometers using the resolution value of 14.26 pixels per millimeter used during 

the whole experiment. The behavior of the diameter against time reflects the change in the area of the 

tracked droplet as it deforms. If the initial shape of the droplet is close to being spherical, the value of the 

diameter using a circular cross section gives a good approximation to the real value of the diameter of the 

three-dimensional spherical droplet. As the droplet deforms and changes its shape, because it is a threedimensional body the value of the cross sectional area does not remain constant and should not be used to 

calculate the diameter. However, the volume remains constant as the droplet deforms (assuming density 

remains constant) and can be used to calculate an equivalent diameter as long as the droplet shape 

corresponds to an oblate spheroid asymmetric with respect to the vertical axis, symmetric with respect to 

the horizontal axis and rotationally symmetric with respect to the axis along which it is moving towards 

the airfoil. The diameter based on the volume of the oblate spheroid is the red data (rectangles) presented 

in Figure 4. The diameter remains constant along the path providing indirect confirmation that the 

spheroid is rotationally symmetric about the horizontal axis and giving a more accurate measurement of 

the diameter needed for calculations. The digital imaging program uses the diameter based on the volume 

of the spheroid in all the calculations where the diameter is involved. During the final stages of the 

droplet trajectory, either the shape is departing from an oblate spheroid or the volume is changing 

somehow. Figure 4 suggests that the shape changes from an oblates spheroid somewhere between 

1500 and 2375 sec and then departs dramatically after 2375 sec. 

Figures 8 and 9 show the minor and major axes of an ellipse superimposed on the deformed droplet 

against time. The angle of the ellipse (major axis of the ellipse with respect to horizontal axis) is not 

always 90°. It depends on the specific shape of the droplet that is being superimposed with the ellipse. 

The width of the droplet (when deforming) is taken as the value of the minor axis, while the height is 

taken as the value of the major axis of the ellipse. Figure 8 shows how the width of the droplet decreases 

with time to a minimum and then starts increasing while Figure 9 shows how the height increases at the 

same time. The moment at which the width of the droplet reaches a minimum is defined as the beginning

of the actual “breakup”. Previous to that point the droplet is by definition designated as “deforming”. The 

point at which the droplet width reaches its minimum value correlates with the time in an image sequence 

when the droplet no longer continues to stretch and begins moving away from an oblate spheroid shape 

(Fig. 5(f)). From the beginning of deformation to the point where the actual droplet breakup begins 

(minimum width), the droplet resembles an oblate spheroid, initially symmetric, then asymmetric with 

respect to the vertical axis. Up to this point the droplet is deforming. Once the minimum width is reached, 

the droplet shape begins to deviate from an oblate spheroid and the droplet breakup sequence begins. The 

height of the droplet tends to follow the opposite pattern: increasing during deformation of the droplet and 

decreasing during breakup. 

The data presented in Figures 4 to 9 is only for one droplet case. In general, the droplet cases 

analyzed for an airfoil with a 0.710 m chord moving at 90 m/sec follow the same pattern. Differences 

occur with very large droplets (>1200 m) because they oscillate when falling and change shape during 
NASA/TM—2012-217704 8 

longer times before the presence of the airfoil is felt and the typical pattern of deformation begins. In 

those cases, the deformation of the droplet departs from the typical case presented in Figures 4 to 9. 

Smaller droplets (<500 m) have larger surface tension forces and have greater resistance to the pull of 

the aerodynamic forces toward deformation and breakup. They deform less and exhibit only part of the 

typical deformation pattern. 

C. Calculated Data 

Once the horizontal displacement of the droplet is measured at each location along the path, the 

important parameters can be calculated: velocity, acceleration, slip velocity, Weber number, Reynolds 

number, Bond number, and drag coefficient. The calculation of these parameters has been presented in 

previous publications (Refs. 1 and 2). The same droplet data case used in section B, Run 072011.14C 

droplet #1, will be used in this section. 

Figure 10 shows the slip velocity, the air velocity and the droplet velocity against the distance along 

the stagnation line from the leading edge of the airfoil. The exponential behavior of the slip velocity is 

expected since the slip velocity is the difference between the velocity of the air and the velocity of the 

droplet as seen in a frame of reference at rest with respect to the airfoil. As the air velocity decreases 

exponentially toward zero at the stagnation point, a difference in the velocity of the air and the droplet 

(slip velocity) develops due to the inertia of the droplet, and aerodynamic forces produce drag on the 

droplet decelerating it and deforming it. The slip velocity increases all along the trajectory due to the 

continued exponential decrease of the air velocity. Since the slip velocity increases exponentially, the 

Weber number (which is proportional to the square of the slip velocity) and the Reynolds number (which 

is proportional to the slip velocity) will follow the same behavior. Figures 11 and 12 show the Weber 

number and the Reynolds numbers against the distance along the stagnation line from the leading edge of 

the airfoil. The same behavior is noticed for the acceleration of the droplet and the Bond number since the 

acceleration is the second derivative of the function representing displacement against time. 

The exponential increase in the Weber number has special significance since it is the ratio of the 

aerodynamic forces trying to deform the droplet against the surface tension forces opposing them and 

trying to hold the droplet together. As the Weber number increases exponentially, the droplet is subject to 

higher and higher forces that deform it and in some cases break it apart. Although the forces increase 

exponentially, the increase is gradual allowing the droplet to slowly deform over time and tolerate 

relatively high Weber numbers before beginning to break up. In this sense, studies done in a rotating arm 

experimental configuration are different from studies done in other configurations where a droplet or 

droplets are suddenly subject to high Weber numbers. This suggests that the results found here are more 

representative of breakup for an airfoil encountering droplets suspended in air than the results of 

experiments with droplets injected into a moving airstream. 

D. Errors Associated With the Data 

Errors in the data come from three main sources: measurement of the diameter, curve fitting and 

choice of threshold value during the conversion of images from grayscale to binary. The determination of 

the diameter from use of the oblate spheroid volume is a larger error than any of these during the final 

stages of the trajectory. For the example used here, the departure from the oblate spheroid volume after 

2375 m would alter the calculation of the equivalent diameter and thus change the determination of the 

non-dimensional parameters. 

The diameter of the droplets is used to study droplet deformation and to calculate the nondimensional numbers, so errors in its measurement propagate to the Weber, Reynolds and Bond numbers. 

The error in its measurement results from limitations in the resolution of the images. The resolution was 

confined to 14.26 pixels per millimeter due to the imaging setup. The measurement of the diameter in the 

images has an uncertainty of at least one pixel. For droplets of 500, 1000, and 1500 m the corresponding 
NASA/TM—2012-217704 9 

error is 14, 7, and 4.7 percent. For droplets of 250 m the error grows to 28 percent and becomes even 

larger for smaller drops. For this reason only droplets with diameters larger than 500 m were analyzed. 

Another source of error that affects the measurement of the slip velocity and the non-dimensional 

parameters is the curve fitting of the droplet horizontal displacement against time. The values of the 

velocity (tangent to the curve) and of the acceleration (tangent to the velocity against time curve) are 

sensitive to the choice of the curve fit for the experimental data. Since the horizontal displacement grows 

exponentially with time, an exponential curve fit works well. Exponential curve fitting can be done with a 

function of the form y = Aoexp[β*x] or a combination of exponentials y = yo + a*exp[bx] + c*exp[dx] + 

The fit of the curve can be controlled monitoring the statistical parameters but variations in the 

calculated velocity appear depending on how many exponentials are used and the initial guess used to 

calculate the coefficients (a, b, c, d,..). The curve fitting for the data presented in this paper was done with 

two exponentials: y = yo + a*exp[bx] + c*exp[dx]. 

The choice of the threshold value used for the conversion of grayscale to binary images is an 

additional source of error. A movie frame in grayscale is a two dimensional array of intensity values 

between 1 and 255, that were measured in the camera sensor physical pixels. To identify an object and 

track it from one frame to another, image segmentation needs to be done. To do image segmentation, the 

image needs to be converted from grayscale to binary. The conversion is done choosing a cutoff value 

between 1 and 255. This value is called the threshold value. If an element of the image array is above this 

value, its intensity is converted to 1, if it is below this value its intensity is converted to 0. In this way the 

two-dimensional array is converted to 0s and 1s, a binary image. The change from grayscale to binary 

selects the pixels in the movie frame corresponding to an object and, consequently affects the 

measurement of some parameters of that object such as area and diameter. 

There are several methods that can be used to select the threshold value. For the digital imaging part 

of the data analysis program, Otsu’s method (Ref. 7) was used because it is consistent and well founded 

and is used in many commercially available programs. To evaluate the error of the thresholding method, a 

limited study was conducted with nineteen droplets. The droplet diameters were measured from their 

grayscale images using the camera software in a systematic way and compared to the values given by the 

Otsu method. The measurements were done for only the first tracking frame in each of the nineteen 

tracking movies. The effect of the threshold value is presented in Figure 13. An error of 13 percent was 

found in the measurement of the diameter when using the Otsu method, assuming that the values from the 

grayscale image have minimal error. The Otsu method was used for the binary conversion of grayscale 

images in all of the data presented in this paper. This error is independent of what happens to the droplets 

and other errors. It is always present in the image processing part in the conversion from grayscale to 

binary. 

E. Droplet Deformation 

The objective of the studies done on droplets approaching the leading edge of the airfoil along the 

stagnation line is to gain understanding on the physics of the process and to measure droplet deformation 

and breakup. The first studies (Refs. 1 and 2) focused on an initial understanding of how the droplets 

behaved as they approached the airfoil and measured the main parameters involved: horizontal 

displacement, velocity, acceleration, Weber number, Reynolds number, Bond number and drag 

coefficient. The focus of the present study is on droplet deformation, drag coefficient, and the sequence of 

the actual droplet breakup. Droplet deformation and drag coefficients will be discussed in this section, 

and droplet breakup in section F. 

As the droplets approach the airfoil and are subjected to the aerodynamic forces generated by the 

increasing slip velocity, their shape changes from spherical to oblate spheroid. The oblate spheroid is 

asymmetric with respect to the vertical axis, symmetric with respect to the horizontal axis and assumed 

rotationally symmetric about the axis pointing in the direction of motion of the droplet. This assumption 

is based on observations of the images and the similarity in the deformation shape of the droplets of 

different sizes at different times in their paths. Nevertheless it remains an assumption until we can obtain 
NASA/TM—2012-217704 10 

front images of the droplets to test its validity. Ideally, in a study of droplet deformation the whole shape 

of the droplet or the two-dimensional profile would be studied. But in the study of a complex system such 

as the shape of the droplet it is better to begin with the simplest possible representation of deformation 

and add complexity later. In this study, the ratio of the height (major axis b of the superimposed ellipse) 

of the deforming droplet to its width (minor axis of the superimposed ellipse) was chosen as the 

parameter to represent deformation. 

Droplet deformation = b/a = major axis of superimposed ellipse/minor axis of superimposed ellipse 

To study deformation, a subset of nineteen droplets was selected. The chosen droplets were nearly 

spherical at the start of tracking, and the diameters were near values of 500, 750, 1000, 1250, 1500 or 

1750 m. Table 2 shows the test conditions for the selected droplets. All of the selected droplets were for 

a 0.710 m chord airfoil moving at 90 m/sec. Droplets below 500 m were not selected because of the 

higher error involved in the measurement of the diameter as discussed in section D. 

The deformation against time, slip velocity, Weber number, Reynolds number and Bond numbers was 

studied. In general the droplet behavior was similar and is illustrated in Figures 14 to 20 for the case of a 

droplet with a diameter of 1431 m, Run 072611.15B.9 droplet #2. The deformation increases 

exponentially with time, the rate of change of the deformation (tangent to the curve) increasing along the 

whole curve (Fig. 14). The behavior of the deformation against the slip velocity, Reynolds number and 

Weber number is slightly different. These parameters are changing because they are based upon the slip 

velocity and the droplet diameter and these are changing. Initially the deformation follows an exponential 

behavior but then the curve becomes almost linear until droplet breakup begins. Initially the rate of 

change of the deformation (tangent to the curve) increases but then levels off and remains approximately 

constant. The deformation against the Weber number (We) is presented in Figure 15 and the curves for 

the slip velocity and the Reynolds number (Re) follow the same pattern. A plot of the deformation b/a 

against We*Re accentuates the part of the curve that is more linear but overall was found to be similar to 

the plot in Figure 15 and for that reason is not presented with the figures. In the case of the deformation 

against the Bond number (Fig. 16), the rate of change of the deformation decreases initially and then 

remains nearly constant until the breakup of the droplet begins. Since the slip velocity, the Weber 

number, the Reynolds number and the Bond number have an exponential behavior against time, it would 

be expected for the deformation to follow the same pattern. It does to an extent, but is less pronounced 

and part of the curve is almost linear. This seems to indicate that the shape of the droplet at a given 

position depends on additional parameters intrinsic to the droplet, for example internal circulation of the 

water inside the droplet that will create an additional internal pressure at the droplet surface and be 

another parameter that influences the shape of the droplet. 

The change in deformation with droplet diameter at a slip velocity of 60 m/sec is plotted in Figure 17. 

There is scatter in this data, even for droplets with diameters fairly close to each other and therefore with 

similar Weber and Reynolds numbers. The scatter in the data for droplets with the similar Weber and 

Reynolds numbers indicates that other parameters are important in the droplet deformation. In particular, 

if the droplets are subject to different accelerations, droplets of the same diameter have different 

deformation. In Figure 18(a) the Bond number is plotted against the diameter for the same droplets 

analyzed in Figure 17. For droplets with similar Bond number values, going back to Figure 17, it can be 

observed that there is minimal scatter. For droplets with different Bond numbers and in some cases very 

close values of the diameter, the data for those droplets shows scatter in Figure 17. In Figure 18(b) the 

deformation (b/a) scaled by the Bond number is plotted against droplet diameter. The scattering is less 

pronounced. The standard deviation for the data in Figures 17 is 1.34 while for the data in Figure 18(b) it 

is 0.4. Thus droplet deformation depends on several parameters: Weber number, Reynolds number, Bond 

number and possibly others, complicating comparisons between droplets. The plots of deformation versus 

diameter for slip velocities of 25 to 70 m/sec at 5 m/sec intervals are similar: less scattering of the data at 

the lower slip velocities, increasing as the slip velocity increases. 
NASA/TM—2012-217704 11 

As the droplet deforms, the flow field around the droplet changes and the drag that causes the 

deceleration of the droplet changes. The drag coefficient would be expected to increase monotonically 

with the deformation since the shape of the droplet changes to an asymmetric oblate spheroid of 

increasingly flatter and flatter shape (for example a disk exhibits higher drag coefficients than a solid 

sphere). In Figure 19 the drag coefficient for a droplet with a diameter of 1431 m, Run 072611.15B.9 

droplet #2, is plotted against deformation until droplet breakup begins. As expected the drag coefficient 

increases linearly with the deformation. In Figure 20 the drag coefficient is plotted against the Reynolds 

number. In the same plot the drag coefficient for a solid sphere is plotted for comparison. While the drag 

for a solid sphere remains at a value of 0.4 in the Reynolds number range of 2000 to 8000, the droplet 

drag coefficient initially is also 0.4 when the droplet is still spherical but then increases linearly as the 

droplet deforms from a sphere to an asymmetric spheroid flatter and flatter as the deformation (b/a) 

increases. 

F. Droplet Breakup 

Droplet breakup begins when the value of the minor axis of the superimposed ellipse (width of the 

droplet) reaches a minimum. Up to this point the droplet has passed from a spherical shape to a nonsymmetric oblate spheroid. In this process the width of the droplet decreases as the oblate spheroid 

stretches in height and reaches a point where its shape begins to deviate from an oblate spheroid and no 

longer can sustain the air flow pressure and viscous forces and begins the process that will lead to the 

droplet disintegration. 

Analysis of the imaging data indicates that in all the cases where the droplets are larger than 500 m, 

the sequence of droplet breakup is similar and can be separated in distinct stages. Without a detailed 

knowledge of the forces acting on the droplet at the different stages of its breakup these observations are 

qualitative only. The imaging data does give a clear view of how the process occurs and its different 

stages. Figure 21 shows the sequence of a droplet breaking up beginning at the point where the droplet 

width has decreased to a minimum but is still showing the shape of an asymmetric oblate spheroid 

flattened in the front part and quite elongated (Fig. 21(a)). At the initiation of the breakup the droplet 

shape changes, the front flat part starts to develop a bulge while the back area becomes flatter 

(Figs. 21(b), (c)). The bulge at the front develops into what from the side looks like a “hat” shape 

(Fig. 21(d)). This shape continues to increase in size (Figs. 21(e), (f), (g)), then starts shearing at the sides 

(Fig. 21(h)) and continues to shear losing mass in the process (Figs. 21 (i), (j)) until it hits the airfoil or all 

the mass is lost. 

The images are a two-dimensional view of a three-dimensional process of droplet disintegration, but 

they convey the three dimensionality of the process and the first indication that there is rotational 

symmetry around the axis pointing in the direction of the motion of the droplet. Additional color images 

were taken of the droplet breakup process that give better views of the three dimensionality of the droplet 

breaking up and the loss of mass by shearing. Figure 22 shows droplets in the last stage of breakup. Part 

of the core of the original droplet is still visible and losing water by shearing. It is followed by a trail of 

the water that ends in a cloud of smaller droplets. During breakup the droplet initially has a radical change 

from an oblate spheroid to a “hat” shape and then begins losing its mass by a shearing process. This mass 

loss is in the form of a tail that trails the droplet and ends in a cloud of smaller droplets. There is a definite 

time scale for the process, determined by the shearing mechanism that causes the disintegration of the 

droplet. For the droplet breakup presented in Figure 21 is of the order of 120 m. 

G. Distance From Airfoil Leading Edge at Which Droplets Begin Breakup 

The distance at which the droplet begins its breakup (minimum value of the width of the droplet) was 

measured for droplets of different sizes for the 0.710 and 0.470 m chord-size airfoil models. The resultant 

data was completely scattered. Comparing the distance at which droplets begin breakup is not correct unless 

the droplets share the same history with respect to the parameters that determine their deformation and 
NASA/TM—2012-217704 12 

breakup. The only statement that can be made about the data is that for both airfoils all of the droplets began 

their breakup within a distance interval from 0.02c to 0.09c where c is the chord of the airfoil. For the large 

airfoil (chord = 0.710 m), the distance at which the droplets begin their breakup, non-dimensionalized 

against the chord of the airfoil, was plotted against the diameter of the droplets for velocities of 70 and 

90 m/sec (Fig. 23). There is scatter in the data but the results indicate that as the velocity is increased the 

droplets begin their breakup process further away from the leading edge of the airfoil. 

The results of the work presented here will help in the development of improved break-up models for 

ice accretion codes. The results also indicate the need for better understanding of the break-up process 

and the distance from the airfoil at which it occurs. 

Conclusions 

A subset of the data from the 2011 droplet breakup experiment conducted in the rotating rig test cell 

at the Instituto Nacional de Técnica Aeroespacial (INTA) in Madrid, Spain, was analyzed. The diameter 

of the droplets analyzed ranged from 500 to 1800 m. Three airfoils were tested with the data presented 

being mostly for the larger airfoil with a chord of 0.710 m. The airfoil velocities tested were 50, 60, 70, 

80, and 90 m/sec. Most of the data presented is for the 90 m/sec cases. From the analysis of the data the 

following conclusions can be stated about the results: 

 Droplet deformation and breakup follows a well defined pattern with some modifications for the 

small droplets (diameters close to 100 m) and very large droplets (diameters larger than 1500 m). 

The droplet is initially spherical and as the slip velocity increases it deforms into an oblate spheroid, 

symmetric with respect to the horizontal axis, asymmetric with respect to the vertical axis and 

rotationally symmetric with respect to the axis in the direction of motion of the droplet, in a frame of 

reference at rest with respect to the airfoil. During this part of the deformation the width of the droplet 

decreases and its height increases as the droplet becomes elongated while maintaining the oblate 

spheroid shape. The width reaches a minimum value where the deformation ends and the actual 

breakup begins. At this point the droplet changes from the elongated oblate spheroid with a rear bulge 

to a front bulge or protuberance with a shape resembling a “hat” that grows initially and then starts to 

lose mass by shearing. The mass loss by shearing continues around the droplet core and forms a tail 

behind the droplet followed by a cloud of small droplets. The very large droplets fall oscillating 

heavily and the oscillation and large inertia delay the onset of the typical deformation pattern 

although it is still there. 

 Images of the final stages of droplet breakup showed a cloud of water behind the core-tail of the 

original droplet as mass is lost through shearing. This indicates that at least some of the mass of the 

droplet ends up in a cloud of small droplets that may be carried away by the flow depending on their 

sizes and how far they are from the leading edge. 

 The width of the droplet, as measured with a data analysis digital image processing program, 

decreases as the droplet approaches the airfoil and reaches a minimum value at the initiation of the 

droplet breakup where it begins to increase. 

 The diameter of the droplets, based on the volume of the oblate spheroid, remained constant until the 

initiation of breakup providing additional evidence that the spheroid is rotationally symmetric around 

the axis pointing in the direction of the motion of the droplet with respect to the airfoil. 

 The exponential decrease of the air velocity generates the slip velocity of the droplet and propagates 

to the behavior of the other parameters against time. Consequently the droplet horizontal 

displacement, velocity, acceleration, slip velocity, Weber number, Reynolds number, Bond number 

and drag coefficient all display exponential behavior against time. 

 Uncertainties in the data result from the resolution of the imaging system, the curve fitting involved in 

the calculation of the velocity and acceleration and the method used to choose the threshold value for 

the conversion of the images from grayscale to binary prior to segmentation and tracking of a droplet. 
NASA/TM—2012-217704 13 

Uncertainties also come from the deviation of the droplet geometry from that of an oblate spheroid. 

The error from the resolution affects the measurement of the diameter of the droplets. The error from 

the curve fitting affects the calculation of the velocity acceleration and slip velocity. The threshold 

error affects the measurement of the diameter 

 Droplet deformation was defined as the ratio of the major and minor axis of an ellipse superimposed 

on the deforming droplet. Droplet deformation was studied for a sample of nineteen droplets with a 

range of diameters form 500 to 1800 m. For individual droplets, deformation was found to increase 

exponentially against time and nearly linearly against the Weber and Reynolds numbers. Against 

acceleration, the rate of change increased rapidly initially and then settled to an almost linear 

behavior. 

 The data used to study the behavior of the deformation against droplet diameter at constant slip 

velocities showed scattering that increased as the slip velocity increased. Although some scattering 

was anticipated since droplets of different diameters at same slip velocity have different Weber and 

Reynolds numbers, scattering was also present in droplets with closer diameter values. The scattering 

was due to the difference in individual acceleration of each droplet and possibly other intrinsic 

parameters to the droplet. As measured by the standard deviation of the samples, scattering could be 

decreased by plotting of the deformation scaled with the Bond number against the diameter of the 

droplets at same slip velocity. 

 The drag coefficient was found to increase linearly with deformation as the droplet deformed from a 

sphere to an oblate spheroid before the beginning of the actual breakup. The drag coefficient also 

increased linearly with the Reynolds number. 

 Data for the distance at which droplets breakup for different velocities and two airfoils showed high 

scattering but it was found that all droplets breakup within a distance interval of 0.02c to 0.09c. For 

the large airfoil (chord = 0.710) at an airfoil velocity of 90 m/sec the droplets broke up earlier (further 

away from the leading edge) than at a velocity of 70 m/sec. 

 Study of the deformation of individual droplets was possible and the overall behavior of the droplets 

was similar. Comparison between different droplets was very difficult because droplet deformation 

depends on several parameters: Weber number, Reynolds number, Bond number and possibly 

additional parameters intrinsic to the droplets. Varying one parameter at a time was not possible and 

no parameter was found to be more dominant with respect to the droplet deformation than the others. 

The results of the work presented here will help in the development of improved break-up models for 

ice accretion codes. The results also indicate the need for better understanding of the break-up process 

and the distance from the airfoil at which it occurs. 

References 

1. Vargas, M. and Feo, A., “Experimental Observations on the Deformation and Breakup of Water 

Droplets near the Leading Edge of an Airfoil,” NASA/TM—2011-216946, AIAA Paper 2010-7670, 

August 2010. 

2. Feo, A., Vargas, M., and Sor, S., “Rotating Rig Development for Droplet Deformation/Breakup and 

Impact Induced by Aerodynamic Surfaces,” SAE Technical Paper 2011-38-0087, 2011, 

doi:10.4271/2011-38-0087. 

3. Vargas, M., “NASA Glenn Matlab Computer Program for the Analysis of Droplet Deformation and 

Breakup,” (to be published). 

4. Sor, S., García-Magariño, A., “Diameter and Axisymmetry Measurements of a Water Droplet 

Impinging on an Airfoil,” INTA Document No. AE-1NO-4420-065, March 2012. 

5. Sor, S., Personal communication on PIV data obtained at the INTA’s Rotating Rig Facility 

6. Otsu, N., “A Threshold Selection Method From Gray-Level Histograms,” IEEE Transactions on 

Systems, Man, and Cybernetics, Vol. 9, No. 1, pp. 62-66, 1979. 
NASA/TM—2012-217704 14 

TABLE 1.—DBKUP 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—2012-217704 15 

TABLE 2.—TEST CONDITIONS FOR DROPLETS ANALYZED 

[Airfoil DBKUP 001—Chord size 0.710 m.] 

Run number Orifice, 

m 

Droplet theoretical 

diameter, 

m 

Airfoil 

model 

velocity, 

m/sec 

Magnification Resolution 

H x V 

pixels/pixels per mm 

Frame rate 

Frames/sec 

072011.11 200 400 80 1/1 192312/14.26 75,000 

072011.13A 200 400 90 1/1 192312/14.26 75,000 

072011.13B 200 400 90 1/1 192312/14.26 75,000 

072011.14B 200 400 90 1/1 192312/14.26 75,000 

072011.14C 200 400 90 1/1 192312/14.26 75,000 

072111.05 100 200 90 1/1 192312/14.26 75,000 

072611.15A 700 1400 90 1/1 192312/14.26 75,000 

072611.15B 700 1400 90 1/1 192312/14.26 75,000 

072611.16 500 1000 90 1/1 192312/14.26 75,000 

072611.18 400 800 90 1/1 256312/14.26 75,000 

Figure 1.—Conceptual view of the experiment. 
NASA/TM—2012-217704 16 

Figure 2.—Experiment set-up in the INTA test cell. 

Figure 3.—Close-up picture of airfoil (DBKUP 003, chord = 0.710 m), TSI droplet generator and the high 

speed camera. 
NASA/TM—2012-217704 17 

Figure 4.—Equivalent Diameter against time. Run 072011.14C 

droplet #1, droplet diameter = 1062 m, airfoil chord = 0.710 m, 

airfoil velocity = 90 m/sec. The red data (rectangles) correspond 

to the diameter based on the volume of the asymmetric oblate 

spheroid. The blue data (triangles) correspond to the diameter 

based on the circular area of the droplet cross section. In the 

calculations made for this paper only the diameter based on the 

volume of the asymmetric oblate spheroid was used. 

 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) 

Frame # 20 60 100 140 160 180 190 194 200 210 

Time, 

μsec 

253 787 1320 1853 2120 2387 2520 2573 2653 2787 

xdistance 

from 

airfoil, 

mm 

225 177 129 82 58 34 23 18 11 0 

Vslip, 

m/sec 

15.5 19.8 25.9 35.4 42.9 54.0 61.8 65.3 71.3 82.6 

We 4.21 6.90 11.77 21.99 32.20 51.36 67.05 75.07 89.42 119.95 

Re 1120 1433 1872 2559 3102 3911 4469 4728 5161 5977 

Bo 2.14 2.50 3.20 8.10 21.55 71.34 134.75 174.41 257.47 495.06 

Cd 0.68 0.48 0.36 0.49 0.89 1.85 2.75 3.10 3.84 5.50 

Figure 5.—Sequence of deformation and initiation of breakup. Run 072011.14C droplet #1, droplet diameter = 

1062 m, airfoil chord = 0.710 m, airfoil velocity = 90 m/sec. The sequence shows the corresponding values 

for several of the parameters at each stage of the droplet deformation. 
NASA/TM—2012-217704 18 

Figure 6.—Horizontal Displacement against time. Run 072011.14C 

droplet #1, droplet diameter = 1062 m, airfoil chord = 0.710 m, 

airfoil velocity = 90 m/sec. 

Figure 7.—Vertical Displacement against time. Run 072011.14C 

droplet #1, droplet diameter = 1062 m, airfoil chord = 0.710 m, 

airfoil velocity = 90 m/sec. 
NASA/TM—2012-217704 19 

Figure 8.—Minor axis of ellipse superimposed on deformed droplet 

against time. Run 072011.14C droplet #1, droplet diameter = 

1062 m, airfoil chord = 0.710 m, airfoil velocity = 90 m/sec. 

Figure 9.—Major axis of ellipse superimposed on deformed droplet 

against time. Run 072011.14C droplet #1, droplet diameter = 

1062 m, airfoil chord = 0.710 m, airfoil velocity = 90 m/sec. 
NASA/TM—2012-217704 20 

Figure 10.—Drop velocity, air velocity and slip velocity against the 

distance from the airfoil leading edge along the stagnation line. 

Run 072011.14C droplet #1, droplet diameter = 1062 m, airfoil 

chord = 0.710 m, airfoil velocity = 90 m/sec. 

Figure 11.—Weber number against the distance from the leading 

edge of the airfoil along the stagnation line. Run 072011.14C 

droplet #1, droplet diameter = 1062 m, airfoil chord = 0.710 m, 

airfoil velocity = 90 m/sec. 
NASA/TM—2012-217704 21 

Figure 12.—Reynolds number against the distance from the leading 

edge of the airfoil along the stagnation line. Run 072011.14C 

droplet #1, droplet diameter = 1062 m, airfoil chord = 0.710 m, 

airfoil velocity = 90 m/sec. 

Figure 13.—Diameter of tracked droplet. Measurement of 

droplet diameter made manually from the grayscale image 

in the first tracking frame for nineteen drop tracking cases 

is plotted against the diameter of the same droplet 

measured with the digital image processing data analysis 

program after converting the image to binary using Otsu’s 

thresholding methodology. 
NASA/TM—2012-217704 22 

Figure 14.—Droplet deformation against time. Run 072611.15B.9 

droplet #2, droplet diameter = 1431 m, airfoil chord = 0.710 m, 

airfoil velocity = 90 m/sec. 

Figure 15.—Droplet deformation against Weber number. Run 

072611.15B.9 droplet #2, droplet diameter = 1431 m, airfoil 

chord = 0.710 m, airfoil velocity = 90 m/sec. 
NASA/TM—2012-217704 23 

Figure 16.—Droplet deformation against Bond Number. 

Run 072611.15B.9 droplet #2, droplet diameter = 

1431 m, airfoil chord = 0.710 m, airfoil velocity = 

90 m/sec. 

Figure 17.—Droplet deformation against droplet diameter, at 

constant slip velocity of 60 m/sec, airfoil chord = 0.710 m, 

airfoil velocity = 90 m/sec. 
NASA/TM—2012-217704 24 

Figure 18.—(a) Bond number against droplet diameter at constant 

slip velocity of 60 m/sec; (b) The deformation/Bond Number. 

Both plots for an airfoil chord = 0.710 m, airfoil velocity = 

90 m/sec. 
NASA/TM—2012-217704 25 

Figure 19.—Drag coefficient against deformation. Run 072011.14C 

droplet #1, droplet diameter = 1062 m, airfoil chord = 0.710 m, 

airfoil velocity = 90 m/sec. 

Figure 20.—Drag coefficient for the droplet against Reynolds 

number. For comparison, the drag coefficient for a solid 

sphere is plotted for the same range of Reynolds number. 

Run 072011.14C droplet #1, droplet diameter = 1062 m, 

airfoil chord = 0.710 m, airfoil velocity = 90 m/sec. 
NASA/TM—2012-217704 26 

 (a) (b) (c) (d) (e) 

Frame # 190 194 198 203 205 

Time 

(μsec) 2520 2573 2627 2653 2720 

x-distance 

from 

Airfoil 

(mm) 

32 28 23 17 15 

 (f) (g) (h) (i) (j) 

Frame # 207 209 212 215 218 

Time 

(μsec) 2747 2773 2813 2853 2893 

x-distance 

from 

Airfoil 

(mm) 

13 11 8 5 2 

Figure 21.—Sequence of deformation and breakup. Run 072011.14B.1 droplet #1, droplet diameter = 1032 m, 

airfoil chord = 0.710 m, airfoil velocity = 90 m/sec. Several parameters are shown for each stage in the droplet 

deformation. 
NASA/TM—2012-217704 27 

Figure 22.—Final stage of breakup for a droplet as it approaches the airfoil. The core of the droplet is followed by a 

tail of water that ends up in a cloud of smaller droplets. The sequence illustrates the shearing process that 

eventually consumes the droplet. 

Figure 23.—Distance that a droplet begins to breakup divided by the chord 

of the airfoil versus the diameter of the droplet for the airfoil with chord = 

0.710 m at two airfoil velocities: 70 m/sec (green data points) and 90 m/sec 

(red data points). 
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4. TITLE AND SUBTITLE

Mechanism of Water Droplet Breakup Near the Leading Edge of an Airfoil 

5a. CONTRACT NUMBER

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5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Vargas, Mario; Sor, Suthyvann; Magarino, Adelaida, Garcia 

5d. PROJECT NUMBER

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WBS 648987.02.02.03.10 

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National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

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14. ABSTRACT

This work presents 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 Tecnica Aeroespacial (INTA) in Madrid, Spain. The airfoil model was 

placed at the end of the rotating arm and a monosize droplet generator produced droplets that fell from above, perpendicular to the path of 

the airfoil. The interaction between the droplets and the airfoil was captured with high speed imaging and allowed observation of droplet 

deformation and breakup as the droplet approached the airfoil near the stagnation line. Image processing software was used to measure the 

position of the droplet centroid, equivalent diameter, perimeter, area, and the major and minor axes of an ellipse superimposed over the 

deforming droplet. The horizontal and vertical displacement of each droplet against time was also measured, and the velocity, acceleration, 

Weber number, Bond number, Reynolds number, and the drag coefficients were calculated along the path of the droplet to the beginning of 

breakup. Droplet deformation is defined and studied against main parameters. The high speed imaging allowed observation of the actual 

mechanism of breakup and identification of the sequence of configurations from the initiation of the breakup to the disintegration of the 

droplet. Results and comparisons are presented for droplets of diameters in the range of 500 to 1800 μm, and airfoil velocities of 70 and 90 

m/sec. 

15. SUBJECT TERMS

Icing; Engine icing 

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