Jen-Ching Tsao and David N. Anderson

Ohio Aerospace Institue, Brook Park, Ohio

Further Assessment of MVD Effects in SLD

Applications

NASA/CR—2006-214125

February 2006

AIAA–2005–0072
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Jen-Ching Tsao and David N. Anderson

Ohio Aerospace Institute, Brook Park, Ohio

Further Assessment of MVD Effects in SLD

Applications

NASA/CR—2006-214125

February 2006

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

AIAA–2005–0072

Prepared for the

43rd Aerospace Sciences Meeting and Exhibit

sponsored by the American Institute of Aeronautics and Astronautics

Reno, Nevada, January 10–13, 2005

Prepared under Cooperative Agreement NCC3–884 and NCC3–938
Acknowledgments

The NASA Glenn Research Center Icing Branch contributed to the work reported here. The IRT studies were supported under a

grant from NASA 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 excellent and committed technical support of

the testing effort. Our special thanks go to Gary Nosky and Craig Rieker for their assistance in the

photographic recording of 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—2006-214125 1

Further Assessment of MVD Effects in SLD Applications 

Jen-Ching Tsao and David N. Anderson 

Ohio Aerospace Institute 

Brook Park, Ohio 44142 

Abstract 

The study reported here is part of an effort to develop scaling methods for super cooled large droplet (SLD) 

conditions. Previously reported results showed that SLD main ice shapes can be simulated quite successfully by 

appendix C conditions using scaling methods developed for appendix C. However, when the velocity was higher 

than 100 kt, the feather size and density for SLD tests at MVDs well above 100 μm was not well represented by the 

scaled appendix C conditions. This paper reports additional results of a study of the feather region with the objective 

of identifying differences between SLD and appendix C feathers. Both the feather appearance and the angle at which 

feathers grow from the airfoil surface were recorded over a range of MVD from 20 to 190 μm for airspeeds of 100 

and 200 kt and stagnation freezing fractions of 0.3 to 1.0. Tests were performed in the NASA Glenn Icing Research 

Tunnel (IRT) using a 91-cm-chord NACA0012 airfoil model mounted at 0° AOA. Photographs are presented to 

illustrate details of feather appearance. Appearance was noticeably affected by the stagnation freezing fraction of the 

test, but not by velocity or MVD. The angle of feather growth relative to the chord line decreased with increasing 

stagnation freezing fraction. For a velocity of 100 kt, no significant effect of MVD on feather angle was apparent, 

but at 200 kt, feather angle tended to increase with MVD for glaze conditions, but not rime. This finding is based on 

limited data, and its significance with respect to icing physics has not been determined.

Nomenclature 

Ac Accumulation parameter, dimensionless 

b Relative heat factor, 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, dimensionless 

K0 Modified inertia parameter, dimensionless 

LWC Cloud liquid-water content, g/m3

MVD Water droplet median volume diameter, μm 

n Freezing fraction, dimensionless 

n0 Stagnation freezing fraction, 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, dimensionless 

Reδ Reynolds number of water drop, 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, dimensionless 

α Angle between feather and chord line, deg 
NASA/CR—2006-214125 2

β0 Collection efficiency at stagnation line, dimensionless 

φ Droplet energy transfer parameter, °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, °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 

st static 

tot total 

Introduction 

The study reported here is part of an effort to develop scaling methods for SLD conditions. Previously reported 

(refs. 1 and 2) results showed that SLD main ice shapes can be simulated quite successfully by appendix C 

conditions using scaling methods developed for appendix C. However, when the velocity was higher than about 

100 kt, the feather size and density for the SLD tests at MVDs greater than 100 μm was not well represented by the 

scaled appendix C conditions. This paper reports additional results of a study of the feather region with the objective 

of identifying differences between SLD and appendix C feathers. Feather appearance as well as the angle at which 

feathers grow from the airfoil surface were examined over a range of MVD from 20 to 190 μm for airspeeds of 100 

and 200 kt and stagnation freezing fractions of 0.3 to 1.0. Tests were performed in the NASA Glenn IRT using a 

91-cm-chord NACA0012 airfoil model mounted at 0° AOA. 

Recent SLD-to-appendix C scaling studies in the IRT have shown that scaling methods developed for 

appendix C can also be applied to scale SLD drop sizes to appendix C conditions. Good simulation of the main ice 

shape can be achieved by matching scale and reference values of the parameters n0 and WeL, the product β0Ac and 

maintaining 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 are adequate. In figure 1(b), a reference 

velocity of 150 kt was used with size scaled only from 91 to 53 cm and MVD from 185 to 30 μm. Again, the main 

ice shapes matched fairly well, but the scale (appendix C) feathers failed to simulate the large formations recorded in 

the SLD test. For this example, the scale β0 was only about 85 percent of the reference value, although the other 

similarity parameters matched well. This result suggests either that the match of scale and reference β0 may need to 

be significantly better than this, or there are significant SLD effects that result in different feather formation 

mechanisms than occur in appendix C. If this latter situation proves to be the case, the physics of feather formation 

in SLD would need to be studied and incorporated into the appendix C scaling methods. In figure 1(c) a scaling 

comparison is shown for nearly the same scaling scenario as figure 1(b), but for which a better match of β0 was 

achieved. For this case, the scale feathers match the reference significantly better than the previous comparison. 

Finally, in figure 1(d), although the β0 for scale and reference differ by only about 4 percent, the appendix C (scale) 

test again failed to simulate the large feathers of the SLD (reference) test. 

From scaling results alone, then, we cannot make a definitive judgment whether SLD feather features result from 

physical phenomena present only in that regime of icing. In the work reported here, the feather region was studied in 

more detail through close-up photographs to identify characteristics of feather growth that might shed clues on 

differences between appendix C and SLD regimes. 
NASA/CR—2006-214125 3

(a) Model Chord Scaled from 91 to 27 cm; n0, 0.5. (b) Model Chord Scaled from 91 to 53 cm; n0, 0.3. 

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 

08-28-04/03 26.7 -9 200 30 0.50 4.6 90.1 1.84 1.66 0.53 6.4 1.37 

(b) 05-06-03/01 91.4 -10 150 185 0.87 12.3 96.6 1.87 1.80 0.30 16.8 2.64 

08-24-04/03 53.3 -7 199 30 0.50 10.8 83.5 2.16 1.80 0.29 12.5 2.73 

(c) Model Chord Scaled from 91 to 53 cm; n0, 0.5. (d) Model Chord Scaled from 91 to 27 cm; n0, 0.5. 

Date/Run c, 

cm 

tst, 

°C

V, 

kt 

MVD, 

μm 

LWC, 

g/m3

τ, 

min 

β0, 

% Ac β0Ac n0

Re, 

104

WeL, 

106

(c) 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 

10-15-02/05 53.3 -10 200 38 0.49 11.5 87.4 2.24 1.96 0.47 12.6 2.73 

(d) 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. 
NASA/CR—2006-214125 4

Similarity Parameters 

For completeness, the similarity parameters used in this study are defined here. They are based on the work 

originally done by Ruff (ref. 3) and discussed in more detail in Anderson (refs. 4 and 5). 

The modified inertia parameter, K0, was defined by Langmuir and Blodgett (ref. 6): 

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 = ρμ

 (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. 7), 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) 

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. 8) steady-state surface energy balance formulation, the stagnation freezing fraction is 

p ws ,

0

f

c

n

b

⎛ ⎞ = + ⎜ ⎟ ⎝ ⎠

θ φ Λ (7) 
NASA/CR—2006-214125 5

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. 9) 

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. 10) and others, but the differences in values are not significant. 

The Reynolds number of the model, Re, is based on the twice the nose radius of airfoil: 

Vd Re = ρ

μ

 (11) 

and the Weber number used here employs a model dimension along with water density: 

2

/

w

L

w a

V d We = ρ

σ

 (12) 

Test Description 

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. It uses 10 spray bars, a configuration in 

operation since 1998, to generate a cloud of super-cooled water droplets. 

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. 11). 

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 feather study used a fiberglass 1.8-m-span 91.4-cm-chord NACA 0012 airfoil section pictured in figure 2. 

Horizontal lines at the leading edge were drawn at the tunnel vertical center (model mid span) and ±2.5 cm from the 

center to position tracing templates. Vertical lines were located at increments of 2.5 cm, measured along the surface 

from stagnation. These lines helped to identify sites on the model for close-up photographs. The model was mounted 

vertically at 0°AOA for all tests. Because of the quick start capability of the IRT spray system, no shielding of the 

models was required during the initiation of the spray. 
NASA/CR—2006-214125 6

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 record the ice 

shape through hand tracings and photographs. Tracings were taken 

to establish the ice cross-sectional profile, although these will not 

be presented here. To record the ice shapes, a thin heated stainless 

plate with a cutout in the shape of the airfoil leading-edge region 

was inserted into the upstream face of the ice to melt a thin slice 

down to the model surface. A cardboard template was then placed 

into this gap and an outline of the ice shape traced. Tracings were 

taken at the vertical center of the tunnel (91 cm from the floor) and 

at 2.5 cm above the center. Feather details were photographed with 

a digital camera, and feather angle was determined from the 

images as described later. The results presented are from test 

entries in 2004. 

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 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. 

These uncertainties in the test parameters 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. 

Results 

Feather Appearance 

Feathers typically grew from a narrow base at the surface of the model and expanded outward with time, forming 

a relatively flat structure that was trapezoidal in profile. 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 a surprising 

number remained at the end of the spray time. Nearer the leading edge, feathers were at such a density that they 

grew together to form fairly large structures. When traced in profile, these growths often looked much like mainshape horns, and in some cases the feathers grew into the horns to become indistinguishable from them. 

The detailed appearance of feathers was strongly dependent on the stagnation freezing fraction. This is illustrated 

in figure 3, which gives close-up photographs of feathers formed at three freezing fractions. All photos have been 

reproduced at about the same scale, as indicated. All were from tests at a velocity of 200 kt with MVDs of about 

110 μm. Table I gives the test conditions for the results of figures 3 to 6. 

For figure 3(a), the stagnation freezing fraction was 0.34. The feather surface had a glaze appearance, consistent 

with the low rate of freezing at this condition. Freezing was slow enough to permit water to flow over the surface 

before solidification. Some small-scale hemispherical roughness elements could be seen on the otherwise smooth 

surface. Figure 3(b) shows feathers formed with n0 = 0.56. At this stagnation freezing fraction fine branches formed 

along the edges as water was unable to fill in the crevices before freezing. This branching structure was not 

fundamentally changed when the stagnation freezing fraction was increased to 1.0 (fig. 3(c)). 

Figure 2.—91.4-cm-chord model 

installed in IRT test section. 
NASA/CR—2006-214125 7

(a) n0, 0.34 (b) n0, 0.56

2.5 cm

9-8-04/1 (9630) 9-8-04/2 (9644)

(c) n0, 1.00. 

9-7-04/6 (9613)

2.5 cm

TABLE I.—TEST CONDITIONS FOR FIGURES 3 TO 6 

ALL TESTS WITH 91.4-CM-CHORD NACA 0012 AIRFOIL 

Figure Date/Run tst, 

°C

V, 

kt 

MVD, 

μm 

LWC, 

g/m3 τ, 

min 

β0, 

% Ac β0Ac n0

3 (a) 09-08-04/01 -9 200 115 0.43 16.2 94.7 1.62 1.54 0.34 

 (b) 09-08-04/02 -14 200 115 0.43 16.2 94.7 1.62 1.54 0.56 

 (c) 09-07-04/06 -18 200 105 0.28 26.2 94.1 1.71 1.61 1.00 

4 (a) 11-05-04/02 -16 100 190 1.29 12.4 96.1 1.86 1.79 0.50 

 (b) 11-03-04/05 -15 200 185 0.58 13.7 97.0 1.85 1.79 0.50 

5 (a) 09-10-04/03 -9 100 20 1.00 27.9 55.5 3.25 1.80 0.50 

 (b) 11-05-04/02 -16 100 190 1.29 12.4 96.1 1.86 1.79 0.50 

6 (a) 09-07-04/04 -11 200 20 0.50 23.7 64.9 2.76 1.79 0.50 

 (b) 11-03-04/05 -15 200 185 0.58 13.7 97.0 1.85 1.79 0.50 

Figure 3.—Evaluating the effect of stagnation freezing fraction on feather appearance. 
NASA/CR—2006-214125 8

Figure 4 compares feathers produced with velocities of 100 kt (fig. 4(a)) and 200 kt (fig. 4(b)), both at a stagnation freezing fraction of 0.50. In both figures 4(a) and (b) the background shows feathers that have merged into the 

horn structures. Details of the foreground feathers, both large and small, show no obvious differences with velocity. 

Possible dissimilarities between feathers formed in appendix C and SLD conditions are explored in figures 5 and 6. 

Figure 5 compares feathers from a 20-Hm spray (fig. 5(a)) with those obtained with 190-Hm MVD (fig. 5(b)). 

For both tests, the velocity was 100 kt and the stagnation freezing fraction was 0.50. Of course, because the collection efficiency is much smaller at an MVD of 20 Hm than at 190 Hm, the feathers in figure 5(a) are also smaller than 

in figure 5(b). Those feathers that have not merged, however, have the same appearance other than the size. The 

delicate branches along the feather sides appears to be the same for both dropsizes. Not surprisingly, the larger, more 

densely populated feathers of the 190-Hm accretion have tended to grow together more often than those from the 

20-Hm MVD have. This tendency has to be attributed to the higher collection efficiency of the larger-drop spray 

rather than to any fundamental differences in the physics of SLD and appendix C accretions. 

(a) V, 100 kt. (b) V, 200 kt. 

Figure 4.—Evaluating the effect of velocity on feather appearance. MVD, 185 to 190 μm; n0, 0.50. 

11-5-04/2 (30676) 11-3-04/5 (30449)

2.5 cm

9-10-04/3 (9889) 11-5-04/2 (30676)

2.5 cm

(a) MVD, 20 μm. (b) MVD, 190 μm. 

Figure 5.—Evaluating the effect of MVD on feather appearance at V = 100 kt. n0, 0.50. 
NASA/CR—2006-214125 9

Figure 6 provides another comparison between appendix C and SLD feathers, but at a velocity of 200 kt. As in 

figure 5, the stagnation freezing fraction was 0.50. Aside from disparities attributable to collection efficiency, no 

differences in basic structure between the two cases could be identified. 

Feather Angle 

Because of the difficulty of identifying significant appearance features that could be explained by differences in 

the physics of feather formation between appendix C and SLD, more quantitative measurements were next attempted. It was reasoned that if the water contributing to feather growth came from different sources for the two 

cloud regimes, the feather angle might show that. For example, evidence exists (ref. 12) that splashing of water 

droplets occurs as larger drops impact either the iced surface or puddles of water on that surface. If the ejected droplets are re-entrained in the airstream to impinge farther aft, one might expect their trajectories to differ from those of 

droplets from the free stream. Consequently, the feather angle could vary along the chord for those SLD conditions 

where splashing is most prevalent, and SLD feathers might well display different feather angles from those formed 

during appendix C icing. 

The feather angle reported here is that formed between the feather and model chord line as defined in figure 7. 

Figure 7(a) shows a lower-surface feather angle and figure 7(b) an upper-surface angle. No differentiation was made 

between the lower-surface and the upper-surface feathers when measuring the angle; i.e., the lower-surface feather 

angle was not recorded as a negative angle. 

The angle was determined by photographing the feather region of the accretion against a background of a dimensioned grid. Figure 8 is an example of such a photo. The camera lens was placed as close to the model as possible 

for these photographs to avoid distortion of the grid, although some distortion is inevitable. For each test three to 

five pictures were taken altogether, with some of both the lower surface and upper surface feather regions. Angles 

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

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

were recorded from each photograph along with the corresponding chord-wise location. The angle was determined 

with image-measuring software after calibrating for the horizontal and vertical distance scales on the grid. 

9-7-04/4 (9551) 

11-3-04/5 (30449)

2.5 cm2 

 (a) MVD, 20 μm. (b) MVD, 185 μm. 

Figure 6.—Evaluating the effect of MVD on feather appearance at V = 200 kt. n0, 0.50. 
NASA/CR—2006-214125 10

Figure 8.—Ice photographed against a grid for

feather angle measurement. Horizontal lines are

parallel to chord line. The scale is marked in

inches, and the grid is square. This is the same 

ice shape for which the tracing appears in

figure 7. c, 91.4 cm; V, 200 kt; MVD, 115 μm; 

n0, 0.56. 

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

Figure 7.—Definition of feather angle. c, 36 in; V, 200 kt; MVD, 115 μm; n0, 0.56. 
NASA/CR—2006-214125 11

Figure 9(a) shows feather angles recorded for tests at a velocity of 100 kt and a stagnation freezing fraction of 

about 0.3. Tests at this condition were performed only with the 30- and 110-μm-MVD sprays. Aft of about 9 cm, the 

30-μm feathers were too small to measure the angle reliably, so only data for 110-μm feathers exists. The solid line 

is a linear regression fit through the 30-μm data (open circles). Although this fit suggests a slight decrease in angle 

with distance from the leading edge, the scatter in the data is large and the distance represented is relatively small. 

More data are needed at this condition before any trend can be defined with confidence. The 110-μm data has been 

fit with the dashed line, showing angle to be independent of distance. Because no significant effect of position can 

be deduced from either set of data, the ensemble averages of the feather angles for each drop size are reported in 

table II to represent these results. These average values will also be used in a later figure. 

(c) V, 100 kt; n0, 0.75 – 1.00. (d) V, 200 kt; n0, 0.5. 

Figure 9.—Effect of chordwise location on feather angle. 

(a) V, 100 kt; n0, 0.3. (b) V, 100 kt; n0, 0.5. 
NASA/CR—2006-214125 12

The 110-μm ensemble average angle in figure 9(a) is nearly 25 percent higher than the 30-μm average, although 

there is considerable overlap of angles from the two datasets. Additional data are needed to resolve whether there is 

perhaps a small effect of MVD on feather angle at this condition. 

Similar conditions are reported in figure 9(b), but for a stagnation freezing fraction increased to about 0.5. Data 

are shown for all three drop sizes. Angles are somewhat lower overall than for the stagnation freezing fraction of 

0.3, and no difference is apparent between the feather angles for the range of MVD from 30 to 190 μm. The data fit 

(solid line) to all the data shows no meaningful effect of chordwise distance on angle. 

The last 100-kt example (fig. 9(c)) is for a stagnation freezing fraction. of 0.75 to 1.0. Tests were made for 

30- μm MVD with fully rime conditions and for 190-μm at a stagnation freezing fraction of 0.75. At this latter n0, 

conditions over much of the accretion were fully rime; therefore, in the absence of rime data at 190 μm, this comparison should be valid. The solid line is a linear regression fit to both sets of data. As in the results for lower 

stagnation freezing fractions at this velocity, no effect of distance from the leading edge was apparent, so ensemble 

averages of the data are suitable representations of each set. Again, no difference between the appendix C and SLD 

feather angle was evident. 

Figure 9(d) shows feather angles for a velocity of 200 kt, MVDs of 30, 110, and 190 μm and a stagnation 

freezing fraction of 0.5. Unlike the data at 100 kt at a stagnation freezing fraction of 0.5 (fig. 9(b)), the angle was no 

longer independent of distance along the model. Linear regression fits showed a significant decrease of feather angle 

with distance for the 30-μm data, effectively no influence of distance on angle for 110 μm, and a small increase in 

angle with distance for 190-μm MVD. Because the angle decreased with stagnation freezing fraction for the 100-kt 

tests and we know the local freezing fraction increases with distance from the leading edge of the model, a decrease 

in angle with distance for the 30-μm data is not surprising. The lack of an effect of distance on the 110-μm data is 

consistent with the 100-kt results. While the apparent 190-μm data trend is surprising, the scatter in those angles 

may simply mask the correct trend. Thus, ensemble averages appear to be justified to summarize the 200-kt results 

at both 110- and 190-μm MVD. For convenience, an ensemble average value was also used to represent the 30-μm 

data in table II and in figure 10, below, as well. At distances greater than 5 cm from the leading edge angles increased with MVD, and the average angles reported in table II show this increase. The significance of this difference 

in angle between the appendix C tests and the SLD is not presently known: we neither understand the underlying 

physics causing the difference nor do we know how closely scale tests must simulate the correct SLD feather angle. 

TABLE II.—TEST CONDITIONS AND FEATHER ANGLES FOR FIGURES 9 AND 10 

ALL TESTS WITH 91.4-CM-CHORD NACA 0012 AIRFOIL 

Figure Date/Run tst, 

°C

V, 

kt 

MVD, 

μm 

LWC, 

g/m3 τ, 

min 

β0, 

% Ac β0Ac n0

avg. 

α, ° 

std. 

dev., ° 

9 (a), 10 09-09-04/03 -4 100 30 0.70 28.0 68.8 2.28 1.57 0.33 36.1 5.1 

 09-10-04/01 -9 100 110 0.98 14.4 92.9 1.64 1.52 0.33 44.5 6.5 

9 (b), 10 09-10-04/02 -9 100 30 0.70 28.0 68.9 2.29 1.58 0.56 29.2 4.5 

 09-10-04/04 -15 100 110 0.98 14.4 92.9 1.64 1.53 0.55 30.5 4.8 

 11-05-04/02 -16 100 190 1.29 12.4 96.1 1.86 1.79 0.50 30.8 3.9 

9 (c), 10 09-15-04/03 -19 100 30 0.70 28.0 69.0 2.29 1.58 1.00 14.1 4.9 

 11-05-04/06 -26 100 190 1.29 12.4 96.1 1.87 1.80 0.75 14.0 2.5 

9 (d), 10 09-07-04/05 -12 200 30 0.50 19.4 76.2 2.26 1.72 0.51 17.3 6.9 

 09-08-04/02 -14 200 110 0.43 16.2 94.7 1.62 1.54 0.56 32.8 5.0 

 11-03-04/04 -14 200 190 0.52 15.3 97.0 1.85 1.80 0.50 41.6 6.5 

10 09-07-04/03 -8 200 30 0.50 19.4 76.2 2.26 1.72 0.31 39.2 7.5 

 09-07-04/06 -18 200 105 0.28 26.2 94.1 1.71 1.61 1.00 16.7 3.6 

 09-08-04/01 -9 200 115 0.43 16.2 94.7 1.62 1.54 0.34 52.5 5.9 
NASA/CR—2006-214125 13

In figure 10, the ensemble averages of the feather angles are plotted against stagnation freezing fraction. The 

error bars on each point show the standard deviations. In addition to averages of the data given in figure 9, data are 

included in figure 10 for three conditions at 200 kt that were not shown in figure 9. These are for a stagnation 

freezing fraction of approximately 0.3 for MVDs of 30 and 110 μm and a rime case with an MVD of 110 μm. None 

of these sets of data showed an effect of distance on the feather angle. 

Figure 10 shows clearly that the variable with the strongest effect on feather angle was stagnation freezing 

fraction. The two lines shown are the linear regression curve fits to the 30- and the 110-μm data, respectively. Data 

for both 100- and 200-kt velocities were included in these fits. Because of the scarcity of 190-μm results, no fit was 

made for this MVD. It appears that MVD may have a small effect on feather angle. From the data analyzed to date, 

no significant effect of velocity was apparent at most conditions. However, at 110 μm with a stagnation freezing 

fraction of 0.3, angles appeared to be about 20 percent higher for the 200-kt tests than for the 100-kt. For 0.5, two 

notable differences were seen between 100 and 200 kt. First, 30-μm tests at 100 kt produced feather angles 

independent of chordwise distance, while angles decreased with distance at 200 kt with the same MVD. As noted 

previously, the latter condition was the only one for which the data showed a significant effect of distance. Second, 

190-μm tests at 200 kt gave angles significantly higher than the 190-μm tests at 100 kt. The meaning of these 

observations is not understood, and additional data are needed to confirm the results reported here. 

Summary and Concluding Remarks 

Although the effect of MVD and velocity on feather characteristics has not been fully explored, the limited data 

analyzed to date permit some tentative conclusions to be made. It is not apparent from the close-up photographic 

records that SLD feather structure is fundamentally different from that of Appendix-C feathers. Feather appearance 

was primarily dependent on stagnation freezing fraction. Feather surfaces were relatively smooth at a stagnation 

freezing fraction of 0.3, while at stagnation freezing fractions of both 0.5 and 1.0 feathers consisted of fine branches 

growing up and away from the surface of the model. The change in surface structure appeared to be independent of 

either V or MVD. 

Quantitative measurements of feather angle also showed a major effect of stagnation freezing fraction. For a 

velocity of 200 kt and an MVD of 110 μm, for example, the average angle of feathers with respect to the chord line 

decreased from about 52° for n0 = 0.34 to 17° at n0 = 1.0. The effects of distance from the model leading edge, of 

velocity or of MVD were not as straightforward. At a velocity of 100 kt, the angle was dependent on neither distance 

nor MVD. However, at 200 kt, the angle increased as MVD increased, it decreased with distance for 30-μm drops, 

was independent of distance for 110-μm and appeared to increase modestly with distance for 190-μm. Additional 

data are needed to confirm these results and to examine drop-size effects at other conditions. 

The lack of a difference in feather appearance or angle between appendix C conditions and SLD for 100 kt 

suggests that any phenomena related to droplet distortion, breakup and splashing do not appear to affect the feather 

region of ice accretions at this speed. Previously published results showed that appendix C drop sizes could successfully simulate the main accretion of SLD encounters. That fact combined with the feather data presented here, indicates that for low velocities, appendix C scaling methods can be applied without modification to SLD 

conditions to scale both the main ice and the feather region. 

The situation at 200 kt is not so clear. Although the present results showed some influence of MVD on feather 

angle, there appeared to be no effect on appearance. In addition, for the SLD drop sizes studied to date, feather angle 

was uniform, or nearly so, with chordwise distance from the leading edge of the model. Because we do not yet understand either the physics of feather growth or the phenomena of drop distortion, breakup and splashing, we cannot 

completely appreciate how the latter might affect the former. It seems reasonable to speculate, however, that 

splashed drops if re-entrained in the airstream to re-impinge farther aft would produce feathers with a different angle 

than that of feathers produced by directly impinging drops in the cloud. Thus, local variations in feather angle along 

the model surface in the chordwise direction might have been a clue that there was some droplet distortion, breakup 

and/or splashing activity. Of course, the lack of angle variation with chordwise distance does not prove there is no 

significant amount of distortion, breakup or splashing incidents, but it does suggest that such activity can not play a 

significant part in the final ice accretion. Furthermore, we do not know if the magnitudes of the changes in feather 

angle with MVD reported here make any significant difference in the aerodynamic effects of ice accretion. Thus, the 

practical implication of the 200-kt results for scaling has to be left undetermined for now. 

Scaling tests have not yet been performed to determine even if main ice shapes at 200-kt in SLD conditions can 

be adequately simulated with Appendix-C conditions and such tests would be helpful. Such tests are only possible to 
NASA/CR—2006-214125 14

a limited extent because of the high scale velocity required to match the appropriate similarity parameters when scaling SLD conditions at this speed. Scaling test results given in the Introduction at a reference velocity of 150 kt 

showed that SLD feathers are not always properly simulated in size by appendix C tests, even when the stagnation 

collection efficiency is nearly matched (fig. 1(d)). A possible explanation for this result is that the drop-size 

distributions in the SLD and appendix C clouds are sufficiently different that aft of the main ice accretion local collection efficiencies may be quite different even if β0 is matched. Drop distribution effects have not yet been studied. 

The implication of the results of this study to date is that either splashing phenomena have no significant effect 

on the appearance or shape of ice accretions at low velocities, or these phenomena are adequately described in the 

similarity parameters used for appendix C scaling methods. At higher velocities, although questions remain about 

the interpretation of results, much of the data also seems to suggest little or no effect of splashing phenomena on ice 

accretion. In summary, the data obtained so far do not show any significant fundamental ice shape features that are 

only attributable to unique SLD physics. 

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

March 1986. 

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

5. 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. 

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

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

7. Abbott, Ira H., and Von Doenhoff, Albert E., Theory of Wing Sections, Dover, New York, 1959, pp. 114 

and 321. 

Figure 10.—Effect of stagnation freezing fraction on feather angle. 
NASA/CR—2006-214125 15

8. 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. 

9. 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. 

10. 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. 

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

AIAA–2001–0234, January 2001. 

12. Papadakis, Michael, Rachman, Arief, Wong, See-Cheuk, Bidwell, Colin and Bencic, Timothy, “An Experimental Investigation of SLD Impingement on Airfoils and Simulated Ice Shapes,” SAE 2003–01–2129, June 2003. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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21

Further Assessment of MVD Effects in SLD Applications

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 43rd Aerospace Sciences Meeting and Exhibit sponsored by the American Institue of Aeronautics and

Astronautics, Reno, Nevada, January 10–13, 2005. Project manager, Thomas H. Bond, Propulsion Systems Division,

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

The study reported here is part of an effort to develop scaling methods for super cooled large droplet (SLD) conditions.

Previously reported results showed that SLD main ice shapes can be simulated quite successfully by appendix C conditions

using scaling methods developed for appendix C. However, when the velocity was higher than 100 kt, the feather size and

density for SLD tests at MVDs well above 100 μm was not well represented by the scaled appendix C conditions. This paper

reports additional results of a study of the feather region with the objective of identifying differences between SLD and

appendix C feathers. Both the feather appearance and the angle at which feathers grow from the airfoil surface were

recorded over a range of MVD from 20 to 190 μm for airspeeds of 100 and 200 kt and stagnation freezing fractions of 0.3

to 1.0. Tests were performed in the NASA Glenn Icing Research Tunnel (IRT) using a 91-cm-chord NACA0012 airfoil

model mounted at 0° AOA. Photographs are presented to illustrate details of feather appearance. Appearance was noticeably

affected by the stagnation freezing fraction of the test, but not by velocity or MVD. The angle of feather growth relative to

the chord line decreased with increasing stagnation freezing fraction. For a velocity of 100 kt, no significant effect of MVD

on feather angle was apparent, but at 200 kt, feather angle tended to increase with MVD for glaze conditions, but not rime.

This finding is based on limited data, and its significance with respect to icing physics has not been determined.