Jen-Ching Tsao and David N. Anderson

Ohio Aerospace Institute, Cleveland, Ohio

Latest Developments in SLD Scaling

NASA/CR—2006-214127

February 2006

AIAA–2005–5187
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Jen-Ching Tsao and David N. Anderson

Ohio Aerospace Institute, Cleveland, Ohio

Latest Developments in SLD Scaling

NASA/CR—2006-214127

February 2006

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

AIAA–2005–5187

Prepared under Cooperative Agreements NCC3–884 and NCC3–938

Prepared for the

Fourth Theoretical Fluid Mechanics Meeting

sponsored by the American Institute of Aeronautics and Astronautics

Toronto, Ontario, Canada, June 6–9, 2005
Acknowledgments

The NASA Glenn Research Center Icing Branch contributed to the work reported here. The Icing Research Tunnel (IRT)

studies were supported under a grant from NASA Glenn Research Center to the Ohio Aerospace Institute. The authors

wish to thank Tom Bond, Chief of the NASA Glenn Icing Branch, for his support of these tests and the IRT personnel

for their continuing excellent technical support of the testing effort. Our thanks also go to Pete Tate, Vince Reich,

 Craig Rieker, and Gary Nosky for their assistance in the recording of photographic data.

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

Available electronically at http://gltrs.grc.nasa.gov

Level of Review: This material has been technically reviewed by NASA technical management OR expert reviewer(s).

This report contains preliminary findings,

subject to revision as analysis proceeds.
NASA/CR—2006-214127 1

Latest Developments in SLD Scaling 

Jen-Ching Tsao and David N. Anderson 

Ohio Aerospace Institute 

Brook Park, Ohio 44142 

Scaling methods have been shown previously to work well for super cooled large droplet (SLD) main ice shapes. 

However, feather sizes for some conditions have not been well represented by scale tests. To determine if there are 

fundamental differences between the development of feathers for appendix C and SLD conditions, this study used 

time-sequenced photographs, viewing along the span of the model during icing sprays. An airspeed of 100 kt, cloud 

water drop MVDs of 30 and 140 μm, and stagnation freezing fractions of 0.30 and 0.50 were tested in the NASA 

Glenn Icing Research Tunnel using an unswept 91-cm-chord NACA0012 airfoil model mounted at 0° AOA. The 

photos indicated that the feathers that developed in a distinct region downstream of the leading-edge ice determined 

the horn location and angle. The angle at which feathers grew from the surface were also measured; results are 

shown for an airspeed of 150 kt, an MVD of 30 μm, and stagnation freezing fractions of 0.30 to 0.60. Feather angles 

were found to depend strongly on the stagnation freezing fraction, and were independent of either chordwise 

position on the model or time into the spray. Feather angles also correlated well with horn angles. For these tests, 

there did not appear to be fundamental differences between the physics of SLD and appendix C icing; therefore, for 

these conditions similarity parameters used for appendix C scaling appear to be valid for SLD scaling as well. 

Further investigation into the cause for the large feather structures observed for some SLD conditions will continue.

Nomenclature 

Ac Accumulation parameter (Eq. (6)), dimensionless 

b Relative heat factor (Eq. (10)), dimensionless 

c Airfoil chord, cm 

cp Specific heat of air, cal/g K 

cp,ws Specific heat of water at the surface temperature, cal/g K 

d Cylinder radius or twice the leading-edge radius of airfoil, cm 

hc Convective heat-transfer coefficient, cal/s m2K 

hG Gas-phase mass-transfer coefficient, g /s m2

K Inertia parameter (Eq. (2)), dimensionless

K0 Modified inertia parameter (Eq. (1)), dimensionless 

LWC Cloud liquid-water content, g/m3

MVD Water droplet median volume diameter, μm 

n Local freezing fraction, dimensionless 

n0 Stagnation freezing fraction (Eq. (7)), dimensionless 

p Pressure, Nt/m2

pw Vapor pressure of water in atmosphere, Nt/m2

pww Vapor pressure of water at the icing surface, Nt/m2

r Recovery factor, dimensionless 

Re Reynolds number of model (Eq. (11)), dimensionless 

Reδ Reynolds number of water drop (Eq. (3)), dimensionless 

s Distance along airfoil surface measured from stagnation line, cm 

tf Freezing temperature, °C 

ts Surface temperature, °C 

t Air temperature, °C 

T Absolute air temperature, K 

V Air velocity, kt 

WeL Weber number based on model size and water properties (Eq. (12)), dimensionless 

α Angle between feather and chord line, deg 
NASA/CR—2006-214127 2

β0 Collection efficiency at stagnation line (Eq. (5)), dimensionless 

φ Droplet energy transfer parameter (Eq. (8)), °C 

λ Droplet range, m 

λStokes Droplet range if Stokes Law applies, m 

Λf Latent heat of freezing, cal/g 

Λv Latent heat of condensation, cal/g 

μ Air viscosity, g/m s 

θ Air energy transfer parameter (Eq. (9)), °C 

ρ Air density, g/m3

ρi Ice density, g/m3

ρw Liquid water density, g/m3

σw/a Surface tension of water over air, dyne/cm

τ Accretion time, min 

Subscripts 

R reference 

S scale 

st static 

tot total 

I. Introduction 

Scaling methods for SLD conditions have been under development for several years at NASA Glenn (refs. 1 

and 2). These studies established that good simulations of SLD main ice shapes can be achieved at appendix C conditions using existing scaling methods. These methods match scale and reference values of the parameters n0 and 

WeL, the product β0Ac and maintain β0 within about 10 percent. Figure 1 gives some typical examples of such scaling. Figure 1(a) shows a good simulation of both main ice shape and feather region for a reference velocity of 100 kt 

with model size scaled from 91 to 27 cm and MVD from 195 to 30 μm. The important similarity parameters were 

matched within about 10 percent, although the difference in the scale and reference WeL was somewhat larger; apparently, these matches were adequate. In figure 1(b), a reference velocity of 150 kt was used with size scaled again 

from 91 to 27 cm and MVD from 195 to 30 μm. The main ice shapes matched fairly well, but the scale (appendix C) 

feathers failed to simulate the large formations recorded in the SLD test. In each of the examples in figure 1 the β0

for scale and reference differ by only about 4 to 6 percent. 

Due to the failure of scaling methods to produce adequate simulations of feather regions in some situations, a 

study of feather growth has been undertaken (ref. 3). An understanding of the physical phenomena behind feather 

development and the identification of possible new similarity parameters is important to the improvement of scaling 

methods for SLD as well as appendix C conditions for at least three reasons. First, the large feather formations observed in some prior SLD studies need to be simulated accurately in scale tests at appendix C conditions. Second, 

even if feather characteristics for more normal-sized feather growth were not of particular interest in scaling, ice 

shape tracings indicate that feather and horn angle may be related. Thus, the same phenomena that determine feather 

angle may also regulate horn angle. Third, the same phenomena and similarity parameters governing straight-wing 

feather growth probably also control swept-wing ice scallop formation.

A first step in identifying any new similarity parameters for inclusion in scaling methods is to understand what 

differences there might be between SLD and appendix C feathers. In reference 3 the feather region was studied 

through close-up photographs to identify characteristics of feather appearance that might help to determine if there 

are differences between appendix C and SLD regimes. The authors were unable to determine any differences in the 

structural appearance of feathers formed at the same freezing fraction under the two regimes. Some differences in 

SLD and appendix C feather angles were reported at a speed of 200 kt, but additional data are needed to confirm 

these results and to cover a wider range of conditions. 

This paper presents the latest results in the examination of feather formation. Icing tests were performed at a 

velocity of 100 kt during which a sequence of still pictures were taken from an overhead camera every 10 sec to 

record both leading-edge and feather ice development. Drop MVDs were 30 and 140 μm and the stagnation freezing 

fractions were 0.30 and 0.50 for these studies. Feather-angle measurements will also be shown for a velocity of 150 

kt, an MVD of 30 μm and stagnation freezing fractions from 0.30 to 0.60. All tests were performed in the NASA 

Glenn IRT using a full-span, 91-cm-chord NACA 0012 straight-wing airfoil model mounted at 0° AOA. 
NASA/CR—2006-214127 3

II. Similarity Parameters 

The similarity parameters used in this study were based on the work originally done by Ruff (ref. 4). Descriptions and derivations are also given in Anderson (refs. 5 and 6). 

The modified inertia parameter, K0, was defined by Langmuir and Blodgett (ref. 7): 

0

1 1

8 8 Stokes

K K⎛ ⎞ =+ − ⎜ ⎟ ⎝ ⎠

λ

λ (1)

In equation (1), K is the inertia parameter, 

2

18

w MVD V K

d = ρ

μ

 (2) 

where d is the cylinder radius or twice the leading-edge radius of curvature for airfoils. For the NACA 0012 airfoil 

model, a leading-edge radius of 0.0158c was used (see Abbott and von Doenhoff (ref. 8)), where c is the model 

chord. λ/λStokes is the droplet range parameter, defined as the ratio of actual droplet range to that if Stokes drag law 

for solid-spheres applied. It is a function only of the droplet Reynolds number, Reδ. 

 δ

V MVD ρ Re = μ

 (3) 

Langmuir and Blodgett’s tabulation of the range parameter was fit to the following expression for this study: 

( )

1

0.8388 0.001483 0.1847 δ

λ = λStokes Re Re δ + +

 (4) 

(a) VR, 100 kt. 

Date/Run c, 

cm 

tst, 

°C

V, 

kt 

MVD, 

μm 

LWC, 

g/m3

τ, 

min 

β0, 

% Ac β0Ac n0

Re, 

104

WeL, 

106

(a) 11-05-04/03 91.4 -18 100 195 1.46 11.0 96.2 1.87 1.80 0.49 12.1 1.18 

08-24-04/03 26.7 -9 200 30 0.50 4.6 90.1 1.84 1.66 0.53 6.4 1.37 

(b) 11-03-04/07 91.4 -17 149 195 1.00 10.7 96.8 1.86 1.80 0.50 17.7 2.61 

02-15-02/08 26.7 -15 276 35 0.64 2.7 93.0 1.89 1.76 0.50 8.5 2.61 

Figure 1.—Examples of scaling from SLD to appendix C conditions (ref. 3). NACA 0012 models; chord scaled 

from 91 to 27 cm; n0, 0.5. 

(b) VR, 150 kt. 

x/c

-0.04 0.00 0.04 0.08 0.12 0.16

y/c

-0.08

-0.04

0.00

0.04

0.08

c = 27 cm; MVD = 30 m (08-28-04/03)

c = 91 cm; MVD = 195 m (11-05-04/03)

x/c

-0.04 0.00 0.04 0.08 0.12 0.16

c = 27 cm; MVD = 35 m (02-15-02/08)

c = 91 cm; MVD = 195 m (11-03-04/07)
NASA/CR—2006-214127 4

Of more practical interest than K0 is the collection efficiency at the stagnation point, β0, which was shown by 

Langmuir and Blodgett to be a function only of K0, 

.84

.84

1 1.40

8

1 1+1.40

8

0

0

0

K -

β

K -

⎛ ⎞ ⎜ ⎟ ⎝ ⎠ =

⎛ ⎞ ⎜ ⎟ ⎝ ⎠

 (5) 

The accumulation parameter is: 

c

i

LWCV A

d = τ

ρ

 (6) 

If all the water impinging on the leading edge freezes at that location and the leading-edge collection efficiency 

is 100 percent, Ac is a measure of the normalized thickness of ice that will accrete. 

The freezing fraction is defined as the ratio of the mass of water that freezes at a given location on the surface to 

the total mass of water that impinges the surface at that location. From Messinger’s (ref. 9) steady-state surface 

energy balance formulation, the stagnation freezing fraction is 

p ws ,

0

f

c

n

b

⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠

θ φ Λ (7) 

The individual terms in this expression are φ, the water energy transfer parameter, θ, the air energy transfer 

parameter, and b, the relative heat factor, introduced by Tribus, et al. (ref. 10) 

2

, 2 f st

p ws

V

φ t t

c =−− (8) 

2

2 1

.622

ww tot w

G st tot st s st v

p c tot ww

tot st

p pp

V h T Tp θ tt r Λ

c h p p

T T

⎛ ⎞ − ⎜ ⎟ ⎛ ⎞

= −− + ⎜ ⎟

⎝ ⎠ −

⎝ ⎠

 (9) 

0 , p ws

c

LWC V c

b

h

β = (10) 

Equation (9) given by Ruff includes compressibility effects. Simpler forms without compressibility have also 

been used by Charpin and Fasso (ref. 11) and others, but the differences in values are not significant. 

The Reynolds and Weber numbers of the model, Re, are based on the twice the nose radius of the airfoil: 

Vd Re = ρ

μ

 (11) 

2

/

w

L

w a

V d We = ρ

σ

 (12) 

III. Test Description 

A. Facility, Model and Procedures 

The icing tests were performed in the NASA Glenn Icing Research Tunnel (IRT). The IRT is a closed-loop, 

refrigerated, sea-level tunnel with a 1.8 by 2.7 m rectangular test section. The icing cloud is generated by operating 

10 spray bars, a configuration in use since 1998. 
NASA/CR—2006-214127 5

The IRT cloud calibrations for both appendix C and SLD conditions used for these tests was performed in the 

summer of 2004. The LWC and MVD measurements were made using methods reported previously (ref. 12). However, drop-sizing instruments have been updated from past calibration work. Thus, the definition of MVD for a particular cloud may differ from interpretations previously reported, particularly for the SLD regime. For example, for 

given spray-bar pressures, the latest calibration gives MVDs of 85 to 95 percent of those obtained in a 2002 calibration. The MVDs reported in this paper are based on an analysis of the MVD calibration data completed in 

November, 2004. 

The model was a 91.4-cm-chord fiberglass NACA 0012 airfoil mounted vertically on the tunnel turntable at 0° 

angle of attack and 0° sweep. It is shown in figure 2 installed in the IRT test section. It extended from floor to ceiling (183-cm span). Horizontal lines at the leading edge were drawn at the tunnel vertical center (model mid span) 

and ±2.5 cm from the center to locate ice-tracing templates. Vertical lines were also placed at increments of 2.5 cm 

(labeled in inches on the model), measured along the surface from the stagnation line. These marks helped to identify sites on the model for close-up photographs of feather structure details. Because of the quick-start capability of 

the IRT spray system, no shielding of the models was required during the initiation of the spray. 

A digital camera was mounted on the third floor of the IRT to view the model from above (i.e., along the span) 

through transparent windows on the ceiling of the test section. Portions of both the horn and feather region of the 

lower surface were in the camera view. The shutter and an independent flash were remotely operated with an automatic signal to take a sequence of still images every 10 sec throughout the spray. Spray durations were 14 to 28 min 

for these tests. The stills were later assembled into movies of the ice-accretion development. 

In preparing for a test, the temperature and airspeed in the test section and the air and water pressures on the 

spray manifolds were set. When these conditions had stabilized, the spray nozzle valves were opened to initiate the 

spray. The spray was timed for the required duration, then turned off. The fan was brought to a full stop and the researchers entered the test section to document the ice shape with hand tracings. Close-up photographs were also 

taken with a hand-held digital camera. 

To record the ice shapes, a thin slice was first melted 

through the ice normal to the model surface. A cardboard 

template was then placed into this slit and an outline of the 

ice shape traced by pencil, giving a two-dimensional cross 

section of the ice. Tracings were taken at the vertical center 

of the tunnel (91 cm from the floor) and at 2.5 cm above the 

center. The ice shapes so recorded were digitized using an 

automated line-following feature in SigmaScan Pro (ref. 13) 

software. Only tracings taken at the model midspan (tunnel 

vertical center) will be presented. 

After the ice tracings were obtained, the tracing template 

was removed and a thin plate on which was printed an orthogonal grid was placed in the mid-span slit. Photographs 

of feathers in several chord-wise locations on both sides of 

the model were taken with the hand-held camera looking 

spanwise along the airfoil surface with the grid in the background. The camera lens was placed as close to the model as 

possible to avoid distortion of the grid, although some distortion was inevitable. For each test three to five pictures 

were taken altogether, including photos of both the lower 

surface and upper surface feather regions. From these images, the feather angle was determined. 

The results presented are from IRT test entries in 

February 2005. 

B. Uncertainty Analysis 

Estimates of the uncertainty in the reported average conditions were made by considering inherent errors of instruments, temporal fluctuation and spatial variation of the 

instrument readings in the test section, and uncertainty in 

tunnel calibration of MVD and LWC. Recorded air temperature was believed to be accurate to ±0.5°C, and the 

uncertainty in air velocity was estimated to be ±1m/s. For 

Figure 2.—91.4-cm-chord, 183-cm-span fiberglass 

NACA 0012 airfoil models installed in IRT test

section.

02-11-05 40561
NASA/CR—2006-214127 6

appendix C conditions the net uncertainty in MVD was estimated at ±12 percent. For SLD conditions it may have 

been as much as ±20 percent. These uncertainties are not referenced to an absolute value of MVD, which is unknown. Repeatability and scatter in the LWC calibration data suggests the uncertainty is about ±12 percent for both 

appendix C and SLD conditions. 

The test-parameter uncertainties were used to estimate the following uncertainties in the similarity parameters 

for the appendix C tests: 9 percent in β0, 12 percent in Ac, 13 percent in n0, 3 percent in Re, and 5 percent in WeL. For 

the SLD tests the uncertainties were: 3 percent in β0, 12 percent in Ac, 11 percent in n0, 3 percent in Re, and 

5 percent in WeL. 

Feather-angle uncertainties were due primarily to subjective determination of the direction of growth of a 

feather. For very small feathers (e.g., early in a test or near the icing limit) the uncertainty may be as much as 10°, 

and for large feathers, only 5°. At the lowest stagnation freezing fraction tested (n0 = 0.30) glaze feathers were often 

not as well defined as those for higher freezing fractions, leading to further uncertainty of perhaps 5° to 10°. Independent analysis of a limited number of images by two researchers led to differences in average feather angle of 2° 

to 4°. It is estimated that additional errors of 5° to 10° could result from distortions of the grid used to calibrate the 

distances in an image. 

IV. Results 

A. Feather and Ice-Shape Development 

Photographs were taken every 10 sec with the overhead camera looking down along the span of the model. The 

view of this camera is shown in figure 3. The interpretations of ice development presented here are based on these 

photographs. Only glaze accretions will be discussed. 

Feathers typically developed from a narrow base at the surface of the model, growing wider in the spanwise 

direction with time. Thus, the resulting structure typically had a trapezoidal profile when viewed in the airflow 

direction, but had a relatively uniform thickness in the chordwise direction. The height of the individual feathers and 

the number of feathers diminished with distance from the leading edge, following the collection-efficiency decrease. 

Most feathers, particularly farther aft on the model, were very fragile, and sometimes little more than a touch was 

sufficient to break them loose. Feather shedding from time to time occurred during the ice accretion process, but 

only a relatively small number were lost from the final accretion for the conditions of these tests. Nearer the leading 

edge, feathers were at such a density that they grew together to form large structures. The main-shape horns were 

typically incorporated into these growths and indistinguishable from them. 

The non-reflective surface of the fiberglass model is apparent from the image of figure 3. This photo was taken 

at the beginning of a test just before the spray actually wetted the model. A sampling of the sequence of photos that 

followed that of figure 3 is shown in figure 4. The conditions for the test of figure 4 included a velocity of 100 kt, an 

MVD of 140 μm and a stagnation freezing fraction of 0.30. Complete details of test conditions for figures 4 to 9 are 

give in table I. 

The first frame in figure 4 was taken just 3 sec after that of figure 3. By this time, the model was wet from the 

spray, as evidenced by the red reflection from the tunnel floor that appeared in the leading-edge surface. Approximately 30 sec later (2nd frame), discrete feathers were visible about 2.5 to 5 in. aft of the stagnation. Thus, almost 

immediately, two separate areas of accretion became apparent: a leading-edge region in which the surface was covered with a film of water or ice, and a feather region characterized by discrete spikes of ice seeming to grow directly 

from the clean airfoil surface. 

 Figure 3.—Clean model before onset of spray. 
NASA/CR—2006-214127 7

Several studies (refs. 14, 15, and 16) using high-magnification photography over the last 20 years have led to a 

detailed description of the leading-edge region that was not examined in the present work. From these previous investigations, we know that for short accretion times, the leading-edge region can be subdivided into smooth and 

rough zones. The smooth zone extends aft from the stagnation line on both the lower and upper surfaces of the 

model, followed by transition to a rough zone. The rough zone is characterized by a distribution of small, hemispherical roughness elements over the surface (ref. 16). As accretion progresses the smooth-rough boundary moves 

 920 sec Centerline ice profile at end of spray. 

Figure 4.—Ice accretion development for 140-μm MVD and n0 = 0.30. 02-11-05 Run 2. c, 91.4 cm; V, 100 kt; β0, 

94 percent; β0Ac, 1.80. 

Spray hits model. 30 sec 

105 sec 460 sec 
NASA/CR—2006-214127 8

upstream toward the stagnation. In figure 4, this narrowing of the smooth zone with time can be inferred from the 

shrinking of the width of the red reflection at the leading edge. 

An abrupt transition took place from the leading-edge region to the feather region. The location of this transition 

was determined when the local freezing fraction, increasing with distance from the stagnation, reached a value sufficiently high to permit rapid freezing. Because β decreases with distance, those feathers at the transition grew the 

fastest and became the largest in the feather region. Feathers were also more dense in this location and tended to 

merge together as they developed, forming a barrier. Unfrozen surface water moving aft in the leading-edge region 

was prevented from further motion both by the physical obstruction of the feather structures at the transition site as 

well as by the high rate of freezing there. Liquid water reaching this location would tend to flow into these merged 

feathers, to fill voids in the feathers, and then to freeze to contribute to the structure. In this way, the ice horns 

formed. 

Figure 5 illustrates some of these features for the test of figure 4. It is a photograph of a portion of the feather region on the upper surface of the model taken at the completion of the test using the hand-held digital camera. The 

leading edge of the model is to the right in this picture, 

and during the spray, flow was from right to left. The discrete nature of the feathers is apparent, as is the fact that 

between the feathers there is no frozen water on the surface. On the right of the photograph, the largest feathers 

can be seen. Beyond them and out of focus in the background is the aft plane of the upper-surface horn. On close 

inspection feather structures can be seen embedded into 

the downstream surface of the horn. 

Other than the interaction at the transition, the two regions appeared to continue to develop independently. At 

105 sec in figure 4 the feathers were just discernible, 

while the rough zone of the leading-edge region has 

spread forward nearly to the stagnation line. At 460 sec 

the largest feathers had reached a significant size, and in 

the leading-edge region the rough zone now extended all 

the way to the stagnation line. The frame at 920 sec was 

taken just after the spray ended. The largest feathers continued to grow up to this point, but smaller feathers further aft ceased to develop after about 460 sec, presumably 

because they were shielded from the spray once the larger 

feathers reached a certain size. The spanwise variation in 

the width of the leading-edge ice from horn to horn is due 

to IRT cloud non-uniformities in LWC. 

The two-dimensional profile of the final ice shape appears in the lower right panel of figure 4. The difference 

between the continuous-ice accretion within the leadingedge region and the discrete isolated structures of the 

feather region is again apparent. At the transition between 

the two regions, water has frozen over the upstream surfaces of the largest feathers to form a continuous spanwise 

horn structure on both the pressure and suction sides of 

the model. 

TABLE I.—TEST CONDITIONS FOR FIGURES 4 TO 9 

Figure Date/Run c, 

cm 

tst, 

°C 

V, 

kt 

MVD, 

μm 

LWC, 

g/m3

τ, 

min 

β0, 

% Ac β0Ac n0

4, 5 02-11-05/02 91.4 -9 100 140 1.17 14.0 94.4 1.91 1.80 0.30 

6, 7 02-11-05/05 91.4 -15 100 140 1.17 14.0 94.4 1.91 1.80 0.50 

8, 9 02-11-05/03 91.4 -9 100 30 0.80 28.0 68.9 2.61 1.80 0.50 

Figure 5.—Feather region and aft plane of horn on upper surface at the completion of the spray of figure 4. 

02-11-05 run 2. c, 91.4 cm; V, 100 kt; MVD, 140 μm; 

β0, 94 percent; β0Ac, 1.80; n0, 0.30. 

02-11-05/02 40581
NASA/CR—2006-214127 9

Figure 6 presents a series of photographs taken during an accretion with only temperature changed from the test 

shown in figure 4. This change resulted in an increase in the stagnation freezing fraction from 0.30 to 0.50. Although 

the collection efficiency was the same as for figure 4, the higher n0 for the case of figure 6 caused the location of the 

transition from the leading-edge to the feather region to move forward. Because transition occurs when the local 

freezing fraction is sufficiently high, this result is not surprising. Other than the narrower leading-edge region and 

wider feather region, the development of ice in the two regions appeared to progress much the same as it did in the 

Spray hits model. 30 sec 

90 sec 170 sec 

840 sec Centerline ice profile at end of spray. 

Figure 6.—Ice accretion development for 140-μm MVD and n0 = 0.50. 02-11-05 Run 5. c, 91.4 cm; V, 100 kt; 

β0, 94 percent; β0Ac, 1.80. 
NASA/CR—2006-214127 10

case of figure 4. Once again, the horn grew at the site of transition from continuous leading-edge ice to discrete 

feather growth. The last frame of the figure, at the lower right, shows the ice profile traced at the completion of the 

spray. 

Figure 7 is a close-up photograph of the feathers on the lower surface, taken with the hand-held camera after the 

spray had ended. During the spray, the flow was from left to right. Compared to the feathers in figure 5, those in 

figure 7 were characterized by fine branches that grew from the core. At the lower n0 of figure 5 water would have 

taken longer to freeze on the feather, tending to fill in any branches. Measurement of feather angle also revealed that 

the higher stagnation freezing fraction of figure 7 produced a smaller feather angle with respect to the chord line of 

the model compared with that of figure 5. Thus, feather appearance and angle were both dependent on the freezing 

fraction. 

A third photographic sequence showing ice development is given in figure 8. The velocity and stagnation freezing fraction for this icing encounter are the same as for that of figure 6. However, the MVD has been reduced from 

140 to 30 μm to investigate possible differences between SLD and appendix C accretions. No change in the way 

appendix C and SLD feathers cover the surface initially and subsequently develop can be seen from the photos, except that the lower collection efficiency for the appendix C case resulted in a feather region that did not extend as far 

aft as that of the SLD situation in figure 6. Due to the lower collection efficiency feathers did not grow as quickly 

for the appendix C encounter. 

The ice shape traced at the completion of the 30-μm test is shown in the last frame of figure 8. The profile is of a 

similar shape compared with the 140-μm test of figure 6, but both the horns and feathers were smaller. In order to 

compare tests with the same velocity but different drop size, it was not possible to scale the conditions of figures 6 

and 8. In particular, β0 could not be matched for the two tests. The differences in the profiles can be attributed to the 

reduced β0 for the encounter of figure 8 compared with the conditions of figure 6. For scaling, clearly it is important 

to try to match the scale-test β0 as closely to that determined by the reference conditions as possible. 

Figure 9 shows a portion of the lower surface feather region and the aft side of the lower horn as photographed in 

the test section with the hand-held camera after the test of figure 8. The flow is from left to right in this picture. At 

the left is the aft plane of the lower surface horn and some of the feathers can be seen imbedded into this surface. 

The discrete nature of the feathers farther aft is apparent. The delicate branches and narrow base of these feathers, 

formed with a 30-μm spray, were also seen with the 140-μm-spray feathers documented in figure 7. Fundamental 

differences between appendix C and SLD feathers were not evident. 

Figure 7.—Feather region and aft plane of horn on lower surface at the completion of the spray of figure 6. 02-11-05 

Run 5. c, 91.4 cm; V, 100 kt; MVD, 140 μm; β0, 94 percent; β0Ac, 1.80; n0, 0.50. 

02-11-05/05 40634
NASA/CR—2006-214127 11

 1381 sec Centerline ice profile at end of spray. 

Figure 8.—Ice accretion development for 30-μm MVD and n0 = 0.50. 02-11-05 Run 3. c, 91.4 cm; V, 100 kt; 

β0, 69 percent; β0Ac, 1.80. 

Spray hits model. 73 sec 

241 sec 881 sec 
NASA/CR—2006-214127 12

B. Feather Angle 

The angle at which the feathers grow relative to the chord line was introduced into the study of reference 3 as a 

quantitative characteristic to complement close-up photos of feather appearance. It was reasoned that if appendix C 

and SLD feathers showed markedly different angles, it might be logical to conclude that the processes controlling 

feather growth were also different. While some differences were seen between the two regimes, they were small 

enough to conclude, at least tentatively, that the physics of formation were probably fundamentally the same. Data 

were limited, however. 

Feather angles were measured again for the tests of this study to supplement the data of reference 3. The feather 

angle reported is that defined in figure 10 for both a lower-surface (fig. 10(a)) and an upper-surface feather 

(fig. 10(b)). In either case, angles were recorded as positive, and no distinction was made in reporting results to indicate which surface was analyzed. 

The angle was determined by photographing the feather region of the accretion against a background of a dimensioned orthogonal grid. Figure 11 is an example of such a photo taken in the test section with the hand-held camera 

at the completion of one of the sprays. Some of the photographs taken during the spray from the overhead camera 

were also used for angle measurements by digitally superimposing an orthogonal grid on the image. For images 

from both sources, the grid provided calibration information for both x and y dimensions. The angle was then found 

from the image using the angle-measuring capability of SigmaScan Pro software (ref. 13). The chordwise location of 

the feather root and its angle were both recorded for well-defined feathers in each photograph. The angle was found 

to be independent of distance from stagnation; therefore, only ensemble average angles will be reported. Angles 

measured from different photos from the same test showed no significant differences within the scatter of data, and 

data from all the photographs for a particular test were included in determining average values for that test. 

For each test condition, feather-angle data were obtained from the overhead pictures taken during the test for times 

of approximately 12 and 100 percent of the total spray time. In figure 12 sample results from these within-spray photos 

are compared with angles measured from the after-test pictures taken within the test section. These tests used an MVD 

of 30 Hm at a velocity of 150 kt. Within the uncertainty of the data the feather angle did not change with time as the ice 

accreted and feathers grew. Furthermore, angles measured from the two photo sources were consistent. Although the 

local collection efficiency at a feather site must increase as the feather grows, the results of figure 12 suggest that the 

mechanism of feather formation that determines angle does not change significantly, it at all, from the time feather 

Figure 9.—Lower surface horn aft plane and feather region at the completion of the spray 

of figure 8. 02-11-05 Run 3. c, 91.4 cm; V, 100 kt; MVD, 30 μm; β0, 69 percent;

β0Ac, 1.80; n0, 0.50. 

02-11-05/03 40594 
NASA/CR—2006-214127 13

growth begins until the spray is completed. The trend observed in reference 3, in which feather angle decreased with 

increasing stagnation freezing fraction, is also apparent in this figure. 

The horn angle was determined by averaging the horn upstream-surface angle and the horn aft-surface angle 

with respect to the chord line. These angles were measured from the ice-profile tracings. Figure 13 illustrates the 

resulting horn angle. Horn angles are compared in figure 14 with those feather angles that were recorded after the 

test. For this comparison, only the lower horn angle was used. The horn angle was always greater than the feather 

angle and showed the same decreasing trend with increasing stagnation freezing fraction. This result is consistent 

with the mechanism of horn formation postulated above, in which the location and angle of those feathers nearest 

the leading edge of the airfoil determine both horn location and angle. 

(a) Feather angle measured on lower surface. (b) Feather angle measured on upper surface. 

Figure 10.—Definition of feather angle. c, 36 in; V, 150 kt; MVD, 30 μm; n0, 0.30. 

x, cm

-4 -2 0 2 4 6 8 10 12 14 16

y, cm

-8

-6

-4

-2

0

2

4

6

8

α

x, cm

-4 -2 0 2 4 6 8 10 12 14 16

y, cm

-8

-6

-4

-2

0

2

4

6

8

α

Figure 11.—Feathers photographed against a grid for

angle measurement. Horizontal grid lines are parallel to

chord line. Major grid lines every 0.5 in. c, 91.4 cm; V, 

150 kt; MVD, 30 μm; n0, 0.40. 

02-14-05/02 040705

Figure 12.—Feather angle at multiple times into spray. 

c, 91.4 cm; V, 150 kt; MVD, 30 μm.

Stagnation Freezing Fraction, n0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Angle with chord line, deg

0

10

20

30

40

50

60

70

80

90

Source of Photo

Overhead, 12% Time

Overhead, 100% Time

Test Section, after Test
NASA/CR—2006-214127 14

V. Summary and Concluding Remarks 

Icing tests were performed using a 91-cm-chord NACA 0012 airfoil for both SLD and appendix C conditions 

with the objective of identifying differences in feather formation for the two icing regimes. All tests were for glaze 

conditions, with stagnation freezing fractions of 0.30 to 0.50. Images taken 10 sec apart during the spray showed 

two major, distinct regions of ice growth from the time the spray first impacted the model: the leading-edge region, 

in which a thin film forms over the surface, and the feather region, in which small discrete feathers appeared, apparently from direct-impingement of drops in the spray cloud. 

The feather region began some distance aft of the stagnation and extended to the impingement limit. The angle at 

which feathers grew relative to the chord line was found to be independent of time and position, but was a strong 

function of stagnation freezing fraction. Because the local collection efficiency decreases with distance from the 

stagnation line, feathers at the front of the feather region grew fastest and became the largest. Fairly soon into the 

spray, these upstream feathers grew together. The resulting structure would tend to form a barrier, preventing leading-edge-region surface water from flowing further aft. So blocked, this water would flow into and freeze onto the 

upstream face of the feather structure, producing glaze horns. This conclusion that feathers determine the location 

and angle of the horns in glaze icing encounters was substantiated by the fact that the horn angle was found to correlate with the feather angle. At some point, the larger upstream feathers captured cloud water droplets efficiently 

enough to shield the smaller downstream feathers from the cloud, and the latter ceased to grow. Analysis of photos 

and ice tracings taken at the completion of the spray showed that feather growth angle decreased with increasing 

stagnation freezing fraction. 

For the limited conditions of this study, there was no evidence of any difference in the fundamental formation 

mechanisms of either feather growth or horn formation between SLD and appendix C conditions. This conclusion is 

consistent with the findings of reference. However, SLD reference and appendix C scale tests performed in the past 

have shown that while the main ice shape could be matched nondimensionally, relatively larger feathers occurred for 

the SLD tests. Therefore, reasons for large feather formations other than unique physics of SLD icing need to be 

investigated. Potential causes of the feather-size differences for scaling tests include a mismatch of β0 for some scaling tests, differences in shedding of feathers at the disparate model sizes and velocities required for scaling, and dissimilarities in the cloud MVD distributions for SLD and appendix C conditions. Each of these causes has a different 

implication for scaling. If a better match of βo provides the feather agreement needed, the similarity parameters used 

in appendix C scaling methods can be used for SLD scaling as well. If feather shedding at the higher scale speeds 

explains the smaller relative feather sizes for scale models, new similarity parameters will be needed to include 

shedding analysis in the scaling methodology. If the IRT nozzles generate cloud drop-size distributions that are 

Figure 14.—Comparison of horn angles with final 

feather angles. c, 91.4 cm; V, 150 kt; MVD, 30 μm. 

Stagnation Freezing Fraction, n0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Angle with chord line, deg

0

10

20

30

40

50

60

70

80

90

Feather Angle

Horn Angle

x, cm

-4 -2 0 2 4 6 8 10 12 14 16

y, cm

-8

-6

-4

-2

0

2

4

6

8

Figure 13.—Definition of horn angle. c, 36 in; V, 

150 kt; MVD, 30 μm; n0, 0.30. 
NASA/CR—2006-214127 15

different for SLD and appendix C MVDs, ways to alter these distributions will need to be considered. Future 

research is being directed toward looking at each of these issues in order to resolve the feather-size issue and develop better SLD scaling methods. 

References 

1. Anderson, David N., “A Preliminary Study of Ice-Accretion Scaling for SLD Conditions,” AIAA–2002–0521, 

January 2002. 

2. Anderson, David N. and Tsao, J.C., “Additional Results of Ice-Accretion Scaling at SLD Conditions,” AIAA–

2003–0390, January 2003. 

3. Tsao, Jen-Ching and Anderson, David N., “Further Assessment of MVD Effects in SLD Applications,” AIAA–

2005–0072, January 2005. 

4. Ruff, G.A., “Analysis and Verification of the Icing Scaling Equations,” AEDC-TR-85-30, vol. 1 (rev), 

March 1986. 

5. Anderson, David N., “Manual of Scaling Methods,” NASA/CR—2004-212875, March 2004. 

6. Anderson, David N. and Tsao, J.C., “Overview of Icing Physics Relevant to Scaling,” FAA In-Flight 

Icing/Ground De-icing International Conference & Exhibition, SAE-2003-01-2130, June 16–20, 2003. 

7. Langmuir, Irving and Blodgett, Katharine B. “A Mathematical Investigation of Water Droplet Trajectories,” 

Army Air Forces Technical Report No. 5418, February 1946. 

8. Abbott, Ira H. and von Doenhoff, Albert E., Theory of Wing Sections, Dover, New York, 1959, pp. 114 and 321. 

9. Messinger, B.L., “Equilibrium Temperature of an Unheated Icing Surface as a Function of Airspeed,” J. Aeron. 

Sci., vol. 20 no. 1, January 1953, pp. 29–42. 

10. Tribus, Myron, Young, G.B.W. and Boelter, L.M.K., “Analysis of Heat Transfer Over a Small Cylinder in Icing 

Conditions on Mount Washington,” Trans. ASME, vol. 70, November 1948, pp. 971–976. 

11. Charpin, Francois and Fasso, Guy, “Essais de givrage dans la grande soufflerie de Modane sur maquettes a 

echelle grandeur et echelle reduite,” L’Aeronautique et l’Astronautique, no. 38, 1972, pp. 23–31. English translation published as “Icing Testing in the Large Modane Wind-Tunnel on Full-Scale and Reduced Scale Models,” NASA TM–75373, March 1979. 

12. Ide, Robert F. and Oldenburg, John R., “Icing Cloud Calibration of the NASA Glenn Icing Research Tunnel,” 

AIAA–2001–0234, January 2001. 

13. SigmaScan Pro, image-processing software, version 5.0, Systat Software, Inc., Point Richmond, CA. 

14. Olsen, W. and Walker, E., “Experimental Evidence for Modifying the Current Physical Model for Ice Accretion 

on Aircraft Structures,” NASA TM–87184, May 1986. 

15. Hansman, R. John, Jr., Reehorst, Andrew and Sims, James, “Analysis of Surface Roughness Generation in Aircraft Ice Accretion,” AIAA–92–0298, January 1992. 

16. Shin, Jaiwon, “Characterization of Surface Roughness Associated with Leading Edge Ice Accretion,” NASA 

TM–106459, January 1994 and J. Aircraft, vol. 33, no. 2, pp. 316–321, March–April 1996. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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21

Latest Developments in SLD Scaling

Jen-Ching Tsao and David N. Anderson

Icing physics; Scaling; SLD; LWC

Unclassified -Unlimited

Subject Category: 03

Ohio Aerospace Institute

22800 Cedar Point Road

Brook Park, Ohio 44142

Prepared for the Fourth Theoretical Fluid Mechanics Meeting sponsored by the American Institute of Aeronautics and

Astronautics, Toronto, Ontario, Canada, June 6–9, 2005. Project manager, Thomas H. Bond, Propulsion Systems

Division, Glenn Research Center, organization code RTI, 216–433–3900.

Scaling methods have been shown previously to work well for super cooled large droplet (SLD) main ice shapes. However,

feather sizes for some conditions have not been well represented by scale tests. To determine if there are fundamental

differences between the development of feathers for appendix C and SLD conditions, this study used time-sequenced

photographs, viewing along the span of the model during icing sprays. An airspeed of 100 kt, cloud water drop MVDs of 30

and 140 μm, and stagnation freezing fractions of 0.30 and 0.50 were tested in the NASA Glenn Icing Research Tunnel using

an unswept 91-cm-chord NACA0012 airfoil model mounted at 0° AOA. The photos indicated that the feathers that

developed in a distinct region downstream of the leading-edge ice determined the horn location and angle. The angle at

which feathers grew from the surface were also measured; results are shown for an airspeed of 150 kt, an MVD of 30 μm,

and stagnation freezing fractions of 0.30 to 0.60. Feather angles were found to depend strongly on the stagnation freezing

fraction, and were independent of either chordwise position on the model or time into the spray. Feather angles also

correlated well with horn angles. For these tests, there did not appear to be fundamental differences between the physics of

SLD and appendix C icing; therefore, for these conditions similarity parameters used for appendix C scaling appear to be

valid for SLD scaling as well. Further investigation into the cause for the large feather structures observed for some SLD

conditions will continue.