Jen-Ching Tsao

Ohio Aerospace Institute, Brook Park, Ohio

Sam Lee

ASRC Aerospace Corporation, Cleveland, Ohio

Evaluation of Icing Scaling on Swept NACA 0012 

Airfoil Models

NASA/CR—2012-217419

May 2012

11ICE-0005
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Jen-Ching Tsao

Ohio Aerospace Institute, Brook Park, Ohio

Sam Lee

ASRC Aerospace Corporation, Cleveland, Ohio

Evaluation of Icing Scaling on Swept NACA 0012 

Airfoil Models

NASA/CR—2012-217419

May 2012

11ICE-0005

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared under Contract NNC07BA13B

Prepared for the

International Conference on Aircraft and Engine Icing and Ground Deicing

sponsored by the SAE International

Chicago, Illinois, June 13–17, 2011
Acknowledgments

The authors acknowledge the support of the Integrated Resilient Aircraft Control project under Aviation Safety Program 

at NASA Glenn Research Center. The authors also wish to thank the NASA Glenn Icing Research Tunnel (IRT) personnel

for their excellent and committed technical support.

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Level of Review: This material has been technically reviewed by NASA expert reviewer(s).
NASA/CR—2012-217419 1 

Evaluation of Icing Scaling on Swept NACA 0012 Airfoil Models 

Jen-Ching Tsao 

Ohio Aerospace Institute 

Brook Park, Ohio 44142 

Sam Lee 

ASRC Aerospace Corporation 

Cleveland, Ohio 44135 

Abstract 

Icing scaling tests in the NASA Glenn Icing Research Tunnel (IRT) were performed on swept wing 

models using existing recommended scaling methods that were originally developed for straight wing. 

Some needed modifications (Ref. 1) on the stagnation-point local collection efficiency (i.e.,  calculation 

and the corresponding convective heat transfer coefficient for swept NACA 0012 airfoil models have been 

studied and reported in 2009, and the correlations will be used in the current study. The reference tests 

used a 91.4-cm chord, 152.4-cm span, adjustable sweep airfoil model of NACA 0012 profile at velocities 

of 100 and 150 knot and MVD of 44 and 93 m. Scale-to-reference model size ratio was 1:2.4. All tests 

were conducted at 0 angle of attack (AoA) and 45 sweep angle. Ice shape comparison results were 

presented for stagnation-point freezing fractions in the range of 0.4 to 1.0. Preliminary results showed that 

good scaling was achieved for the conditions test by using the modified scaling methods developed for 

swept wing icing. 

Introduction 

The results presented here are part of an effort to develop appropriate scaling methods for swept wing ice 

accretion. Previously, Anderson (Ref. 2) has completed a NASA report that gave a detailed technical review 

of recommended scaling methods for ice accretion on unprotected, unswept aerodynamic surfaces in 

Appendix C condition. Later, Anderson and Tsao (Ref. 3) have further supplemented the Appendix C studies 

of Reference 2 with recent data from both SLD and Appendix C tests. 

It was concluded from those two references that acceptable scaling results could be achieved by 

matching the Ac, n0, and WeL. With scale model size selected, by matching scale and reference values of 

WeL the scale velocity can be determined. By matching 0 the scale MVD can be found. Reference 2 also 

showed that the effects of temperature and LWC are not independent, but interact through the freezing 

fraction. Therefore, with scale LWC chosen, by matching n0 the scale temperature can be calculated. Finally, 

by matching Ac the scale time can be established. For the scale test, then, only temperature, velocity, MVD 

and time have to be calculated from the known (reference) values of the similarity parameters. 

For swept wing icing scaling, the observations from recent work (Refs. 4 to 7) on ice accretion 

formations on swept wings have suggested that although there are distinct morphological differences in 

ensuing ice shapes on unswept and swept wings, the fundamental physics of ice accretion appears to be the 

same. Thus all the similarity parameters recommended for unswept wing icing scaling should be applicable 

to swept wing icing application provided appropriate modifications to the local collection efficiency and the 

convective heat transfer coefficient in the freezing fraction expression at the stagnation line were made due to 

model sweep angle. 

In a more recent study (Ref. 1) Tsao and Kreeger have shown a best curve fit correlation to calculate the 

0 on swept wings of NACA 0012 airfoil profile. Some experimental evaluations of 0 were also performed 

for the validation of such correlation. In the present study, a limited number of reference and scale ice shape 

comparisons obtained from NACA 0012 airfoil models at 45 sweep angle were made to assess the proposed 

scaling methods in swept wing icing conditions. 
NASA/CR—2012-217419 2 

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/sm2

K 

hf Water film thickness, cm 

hG Gas-phase mass-transfer coefficient, g/sm2

K Inertia parameter, dimensionless 

K0 Modified inertia parameter, dimensionless 

LWC Cloud liquid-water content, g/m3

MVD Water droplet median volume diameter, m 

n Local freezing fraction, dimensionless 

n0 Stagnation-point 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 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 

0 Stagnation-point collection efficiency, dimensionless 

 Droplet energy transfer parameter, °C 

 Droplet range, m 

Stokes Droplet range if Stokes Law applies, m 

 Sweep angle, degrees 

f Latent heat of freezing, cal/g 

v Latent heat of condensation, cal/g 

 Air viscosity, g/m s 

 Air energy transfer parameter, °C 

 Air density, g/m3

i Ice density, g/m3

w Liquid water density, g/m3

 Surface tension of water over air, dyne/cm

 Accretion time, min 
NASA/CR—2012-217419 3 

Subscripts: 

R reference 

S scale 

f water film 

st static 

tot total 

 at sweep 

Similarity Parameters 

The similarity parameters used in this study were based on the work originally done by Ruff (Ref. 8). 

The scaling method involved matching scale and reference values of the key similarity parameters, 0, Ac, 

n0, and WeL. The equations for the similarity parameters will be presented here without much discussion. 

Readers who are interested in the physical descriptions and detailed derivations of these parameters are 

referred to References 2 and 3 and the references given therein. 

To maintain the droplet trajectory similitude, Langmuir and Blodgett (Ref. 9) introduced the modified 

inertia parameter, K0, defined as 

0

Stokes

1 1

8 8

K K            

for K>0.125, to describe the inertia of droplets in an air stream flowing around a cylinder of radius d

positioned normal to the flow. In Equation (1), K is the inertia parameter, 

2 MVD . 18

w V K

d

  

 (2) 

Departing slightly from Langmuir and Blodgett in this study, d represents 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. 10)), where c is the airfoil chord. In Equation (1), /Stokes is the 

droplet range parameter, defined as the ratio of actual droplet range to that if Stokes drag law for solidspheres applied. It is a function only of the droplet Reynolds number, Re

δ

MVDρ Re

μ

V = (3) 

This study uses a curve fit to Langmuir and Blodgett’s tabulation of the range parameter as given in 

the following expression: 

  δ

λ 1

λStokes 0.8388 0.001483 Re 0.1847 Re δ

=  

 (4) 

of more practical interest than K0 is the collection efficiency at the stagnation point, 0, which was shown 

by Langmuir and Blodgett to be a function only of K0, 
NASA/CR—2012-217419 4 

.84

0

0 .84

0

1 1.40

8 β

1 1+1.40

8

K

K

       

      

 (5) 

It should be noted that the 0 shown in Equation (5) denotes the collection efficiency at the stagnation 

point for unswept NACA 0012 models. As for a NACA 0012 model at a given sweep angle 45), this 

study uses a curve fit from Reference 1 to calculate the collection efficiency along the stagnation line,0, , 

0, 0    cos  (6) 

Thus the droplet trajectory similarity is satisfied if K0,S = K0,R and S = R (so is (0,)S = (0,)R), and the 

scale drop size, i.e., scale MVD, is determined. 

To ensure water-catch similarity, the accumulation parameter is introduced: 

LWC c

i

V A

d

  

 (7) 

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

efficiency is 100 percent, Ac directly becomes a measure of the normalized thickness of ice that will 

accrete. The scale accretion time can be found from Ac,S = Ac,R. When super-cooled water drops strike an 

aircraft surface, they may not freeze immediately on impact. The freezing fraction is the ratio of the 

amount of water that freezes in a specified region on the surface to the total amount of liquid water that 

reaches that region. Thus, local ice thickness depends on 0,Ac and freezing fraction. Because each local 

ice thickness around the model defines the overall shape of the ice, the freezing fraction obviously has a 

major influence on ice shape. The freezing fraction is influenced mainly by the ambient temperature, the 

LWC of the cloud and the aircraft velocity. 

The rate at which the water freezes on a surface depends on the magnitude of local heat transfer 

imbalance. For glaze ice, it is known that the fraction of water that freezes is less than unity, and the 

motion of unfrozen surface water can have an effect on the resulting ice shape. Therefore, it is important to 

maintain surface energy and surface-water dynamics similarities for glaze ice accretions. The freezing 

fraction is formally defined as the ratio of the amount of water that freezes at a given surface location to 

the total amount of water that impinges at that location. From Messinger’s (Ref. 11) steady-state surface 

energy balance analysis, the freezing fraction at the stagnation point can be written as 

,

0

p ws

f

c

n

b

          (8) 

The key terms in this formulation include  and which have dimensions of temperature and relate to the 

water drop energy transfer and air energy transfer, and b, the relative heat factor, which was first 

introduced by Tribus, et al. (Ref. 12) 

2

, 2 f st

p ws

V

t t

c

   (9) 
NASA/CR—2012-217419 5 

tot

2

st tot st

st

tot

tot

θ Λ

2 1

.622

ww w

G s v p c ww

st

p pp

V h T Tp tt r

c h p p

T T

      

    

  

 

 (10) 

LWC 0 , p ws

c

V c

b

h

  (11) 

Equation (10) from Ruff (Ref. 8) has included compressibility effects. Various incompressible forms 

of  have also been used by Charpin and Fasso (Ref. 13) and others; however, the differences are not 

significant mainly due to the fact that, for most icing conditions, the Mach number is relatively low. 

As for the sweep angle effect on the convective heat transfer along the stagnation line of a NACA 

0012 wing section, it was shown by Reshotko and Beckwith (Ref. 14) that for incompressible flow the 

ratio of swept to normal convective heat transfer coefficient became 

 

1

2 , cos c c h h    (12) 

It should be noted that the hc shown above represents the convective heat-transfer coefficient at the 

stagnation point for unswept NACA 0012 models and for brevity its expression can be found in 

Reference 2 for interested readers. Since for most icing conditions the Mach number is relatively low 

Equation (12) is used. Some experimental evaluations of this expression for calculating the freezing 

fraction on a swept wing were made in this study. 

In 1988 Bilanin (Ref. 15) presented a Buckingham- analysis in which he concluded that surfacewater phenomena had to be included in icing scaling methods. Olsen and Walker (Ref. 16) and Hansman, 

et al. (Refs. 17 to 19) studied surface effects and surface water during ice accretion, presenting additional 

evidence that these were important phenomena to consider in ice accretion. From the close-up photographs 

of these research studies, it was observed that for glaze ice accretion unfrozen water on the ice surface 

tended to coalesce to form beads. These beads sometimes were swept downstream and sometimes froze in 

place. Bilanin (Refs. 15 and 20) also argued that drop splashing on impact might affect the shape of the ice 

accreted. 

Hansman and Turnock (Ref. 17) found that when a surfactant was added to the icing spray water, the 

ice shape appearance and shape changed significantly, with the glaze horns moving toward the leading 

edge. Clearly, then, surface tension, and by implication, surface phenomena, have a significant role in the 

physics of ice accretion. 

In 2003 Anderson and Tsao (Ref. 21) had provided experimental evidence from past studies to show 

that a similarity parameter dependent on the ratio V x

c

y

/ z must be included in scaling methodology to 

account for surface-water dynamics effect in glaze ice accretions, although the powers x, y, and z are not 

yet determined. The length may not be chord itself but rather some physical characteristic L related to 

chord; for example, the water-film thickness. Likewise, the velocity could also be of the water-film that is 

related to V. Thus a Weber number based on L and V 

2

We w L

V L  

 (13) 

has been suggested as a potential additional similarity parameter to supplement Ruff’s basic scaling 

method. Studies by Bartlett (Refs. 22 and 23) and Oleskiw, et al., (Ref. 24) found no measurable effect of 

pressure on ice shape. These observations suggest that water density is a better choice than air density for 

Equation (13). In this study the WeL is based on the twice the nose radius of the airfoil: 
NASA/CR—2012-217419 6 

2

We w L

V d  

 (14) 

with the understanding that L d  . The scale velocity found from matching WeL,S = WeL,R is 

1/2

R

S R

S

d V V

d

      

 (15) 

Test Description 

Facility, Model, and Procedures 

The icing tests were performed in the NASA Glenn Icing Research Tunnel (IRT). The IRT is a closedloop, 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. The IRT cloud calibrations for 

both Appendix C and SLD conditions used for these tests were released in the January of 2010. The LWC 

and MVD measurements were made using methods reported previously (Ref. 25). The LWCs reported in 

this paper are based on an analysis of the LWC calibration data completed in April 2009 for both Standard 

and Mod-1 nozzles. In addition, since only a limited range of MVD-LWC combinations for speeds of 51, 

77, 103, and 129 m/s (100, 150, 200, and 250 kt) have been calibrated to date in the SLD regime, all SLD 

reference cases selected in this study were limited to these calibrated conditions. 

The aluminum test articles used in this study were NACA 0012 Adjustable Sweep Airfoil Models. The 

reference and scale airfoils have a 0.914 m (36 in.) and 0.381 m (15 in.) chord measured normal to the 

leading edge, and a 1.524 m (60 in.) and 0.609 m (24 in.) span, respectively. The reference model was 

mounted in the tunnel on the floor at 45 sweep angle position (left picture in Fig. 1). The scale model was 

mounted in the tunnel on a stand with a small extension that allows pivoting of the airfoil to sweep angle 

of 45 in the mid-span of the test section where the cloud uniformity is the best (right picture in 

Fig. 1). Blue horizontal lines at the leading edge were drawn on the surface of the airfoil at the tunnel 

vertical center to locate ice-tracing templates and to serve as a distance scale in some pictures. Because of 

the quick-start capability of the IRT spray system, no shielding of the models was required during the 

initiation of the spray. 

 

Figure 1.—Swept NACA 0012 airfoil models installed in IRT test section. 
NASA/CR—2012-217419 7 

To record the ice shapes, a thin slice was first melted through the ice normal to the model leading 

edge. 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 below the center. The ice shapes so recorded were digitized using an 

automated line-following feature in the image-analysis software, SigmaScan Pro (Ref. 26). The results 

presented in this study are from IRT test entry in April 15–16, 2010. Though the actual swept wing ice 

accretions could exhibit very complex three-dimensional ice shape features like scallops, the shape 

differences between the two tracing locations were never significant. Therefore only centerline shapes will 

be reported here. It should be noted that in general the IRT cloud uniformity, especially for LWC

distribution, in SLD regime is not as good as in Appendix C for any given air speed. 

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 1 m/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. 

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

parameters for the Appendix-C tests: 3 percent in 0, 12 percent in Ac, 13 percent in n0 and 2 percent in 

WeL. For the SLD tests the uncertainties were: 4 percent in 0, 12 percent in Ac, 12 percent in n0 and 

4 percent in WeL. 

Test Results 

Due to very limited IRT test time available for the scaling method evaluation, this study only used the 

IRT calibrated SLD drop sizes as reference conditions. These reference cases included MVDs of 44 and 

93 m, and airspeeds of 100 and 150 knot. A baseline condition of V = 100 knot and MVD = 44 m was 

chosen, and air temperature was varied to create a range of stagnation-point freezing fractions (n0). Scale 

conditions were then calculated by matching 0, n0, Ac, and WeL with selected scale LWC value for each of 

the reference case. For each figure, reference ice shape was shown shaded, while a solid line indicated the 

scale ice shape. The table below each figure gave the test conditions and similarity parameters for each 

pair of reference and scale tests. The conditions given were the average conditions recorded over the 

duration of each test, which can sometimes differ slightly from the planned set points. The parameters in 

the tables were calculated from these average conditions. 

V 100kt (16) 

For the baseline condition of MVD = 44 m, there were three sets of reference and scale ice shape 

comparison for scaling method evaluation. 

Stagnation-point freezing fraction of 0.41.—The first pair of ice shape comparison was shown in 

Figure 2, and it was for stagnation-point freezing fraction of 0.41. The scale ice shape did simulate the 

reference main ice shape and feather region reasonably well, even including smaller feathers farther aft on 

the surface. Further examining the front, side and close-up view of reference and scale ice shapes (Fig. 3), 

it was noted that the scale ice scallop tip structure was somewhat less pronounced than the reference ice. 

 
NASA/CR—2012-217419 8 

Stagnation-point freezing fraction of 0.57.—The second pair of ice shape comparison was made for 

stagnation-point freezing fraction of 0.57. In Figure 4, it was shown that the scale ice shape was able to 

duplicate the reference main ice shape and feather region quite well but the size of reference ice was 

clearly off and under-sized. This was believed to occur because the slits were not totally clear from ice and 

the cardboard template was not able to go all the way in as freely as it should be. Consequently the 

resulting ice shape tracing became undersized. This mishap could happen rather often if one did not take 

enough time to melt the ice completely prior to the tracing. Unfortunately there was not any simple means 

to recognize this problem until the ice shapes were digitized and compared. Further examining the front, 

side and close-up view of reference and scale ice shapes shown in Figure 5, it was noted that the scale ice 

scallop tip structure also simulated the reference ice scallop tip structure fairly well. 

Stagnation-point freezing fraction of 0.74.—The third pair of ice shape comparison was shown in 

Figure 6 for stagnation-point freezing fraction of 0.74. The scale ice shape duplicated the reference main ice 

shape and feather region very well, even including smaller feathers further aft on the surface. Further 

examining the front, side and close-up view of reference and scale ice shapes shown in Figure 7, it was noted 

that the scale ice scallop tip structure also simulated the reference ice scallop tip structure fairly well. 

Stagnation-point freezing fraction of 1.0.—Figure 8 showed the last pair of ice shape comparison for 

baseline condition at stagnation-point freezing fraction of 1.0, i.e., rime ice shapes. It was shown that the 

scale ice shape was able to simulate the overall reference rime ice shape features which included the main 

ice shape and feather region quite well except the scale ice shape size was larger than the reference ice 

because a similar tracing template problem shown earlier in n0 = 0.57 case has occurred again. Typically if 

the cloud’s LWC were off from what it should be from the scaling calculation, the resulting ice shape not 

only would have different size but also would have quite different ice shape features. The size mismatch 

observed in the figure was clearly not of this nature but an operational mishap. Further examining the 

front, side and close-up view of reference and scale ice shapes shown in Figure 9, it was noted that the 

scale rime ice structure also simulated the reference rime ice structure fairly well. 

 150kt V  (17) 

For this higher reference velocity, there were two sets of reference and scale ice shape comparison 

obtained for scaling method evaluation. One was for the baseline condition of MVD = 44 m and the other 

was for larger SLD drop, i.e., MVD = 93 m. 

Drop MVD of 44 m, stagnation-point freezing fraction of 0.5.—Figure 10 showed the reference and 

scale ice shape comparison for constant WeL method. The scale ice shape simulated the reference main ice 

shape and feather region well. It was noticed during the test that some large feathers neighboring the 

reference main ice were accidently melted away while making the tracing. As a result it made the reference 

ice shape appear to be a bit smaller than the scale ice shape. If one examined the front, side and close-up 

view of reference and scale ice shapes as shown in Figure 11, it was shown that the scale ice’s complete 

scallop tip structure did duplicate quite well the reference ice complete scallop tip structure. 

Drop MVD of 93 m, stagnation-point freezing fraction of 0.51.—Figure 12 showed the reference and 

scale ice shape comparison for this large drop size of 93 m at freezing fraction of 0.51. The scale ice 

shape also simulated the reference main ice shape and feather region well. If one further examined the 

front, side and close-up view of reference and scale ice shapes as shown in Figure 13, it was shown that the 

scale ice’s complete scallop tip structure did duplicate quite well the reference ice complete scallop tip 

structure. 
NASA/CR—2012-217419 9 

Date/Run c, 

cm 





ttot, 

°C 

V, 

kt 

MVD,

m 

LWC, 

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106

4-15-10/01 91.4 45 -4.4 100 45 0.57 19.9 56 1.31 0.73 0.41 1.17

4-16-10/01 38.1 45 -2.5 155 22 0.50 6.12 56 1.32 0.74 0.42 1.17

Figure 2.—Reference (shaded) and scale (solid line) ice shape comparison for VR = 100 kt, MVDR = 44 m; n0 = 0.41. 

 

 

Figure 3.—Front, side and close-up views of reference (U) and scale (L) ice 

shapes of Figure 2. 
NASA/CR—2012-217419 10 

Date/Run c, 

cm 





ttot, 

°C 

V, 

kt 

MVD,

m 

LWC, 

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106

4-15-10/03 91.4 45 -6.7 100 45 0.56 19.8 56 1.31 0.73 0.58 1.18

4-16-10/03 38.1 45 -4.1 154 22 0.50 6.1 56 1.32 0.73 0.58 1.17

Figure 4.—Reference (shaded) and scale (solid line) ice shape comparison for VR = 100 kt, MVDR = 44 m; n0 = 0.57. 

 

 

Figure 5.—Front, side and close-up views of reference (U) and scale (L) ice 

shapes of Figure 4. 
NASA/CR—2012-217419 11 

Date/Run c, 

cm 





ttot,

°C 

V, 

kt 

MVD,

m 

LWC, 

g/m3

, 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106

4-15-10/06 91.4 45 -8.9 100 45 0.56 19.8 56 1.31 0.73 0.74 1.18

4-16-10/05 38.1 45 -5.7 155 22 0.50 6.1 56 1.31 0.74 0.74 1.17

Figure 6.—Reference (shaded) and scale (solid line) ice shape comparison for VR = 100 kt, MVDR = 44 m; n0 = 0.74. 

 .. 

 

Figure 7.—Front, side and close-up views of reference (U) and scale (L) ice 

shapes of Figure 6. 
NASA/CR—2012-217419 12 

Date/Run c, 

cm 





ttot, 

°C 

V, 

kt 

MVD,

m 

LWC, 

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106

4-15-10/07 91.4 45 -12.6 100 45 0.56 19.8 56 1.29 0.72 1.0 1.16

4-16-10/07 38.1 45 -8.4 154 22 0.50 6.1 56 1.31 0.73 1.0 1.16

Figure 8.—Reference (shaded) and scale (solid line) ice shape comparison for VR = 100 kt, MVDR = 44 m; n0 = 1.0. 

 

 

Figure 9.—Front, side and close-up views of reference (U) and scale (L) ice 

shapes of Figure 8. 
NASA/CR—2012-217419 13 

Date/Run c, 

cm 





ttot, 

°C 

V, 

kt 

MVD,

m 

LWC, 

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106

4-15-10/02 91.4 45 -5.3 150 45 0.45 15.7 58 1.24 0.72 0.51 2.64

4-16-10/02 38.1 45 -3.2 231 21 0.50 3.9 58 1.25 0.73 0.50 2.62

Figure 10.—Reference (shaded) and scale (solid line) ice shape comparison for VR = 150 kt, MVDR = 44 m; n0 = 0.5. 

 

 

Figure 11.—Front, side and close-up views of reference (U) and scale (L) ice 

shapes of Figure 10. 
NASA/CR—2012-217419 14 

Date/Run c, 

cm 





ttot, 

°C 

V, 

kt 

MVD,

m 

LWC, 

g/m3 , 

min 

0, 

percent 

Ac 0Ac n0 WeL, 

106

4-15-10/05 91.4 45 -6.7 150 93 0.50 12.9 65 1.13 0.74 0.52 2.63

4-16-10/06 38.1 45 -6.5 232 44 0.75 2.3 65 1.12 0.73 0.51 2.63

Figure 12.—Reference (shaded) and scale (solid line) ice shape comparison for VR = 150 kt, MVDR = 93 m; n0 = 0.51. 

 

 

Figure 13.—Front, side and close-up views of reference (U) and scale (L) ice 

shapes of Figure 12. 
NASA/CR—2012-217419 15 

Summary/Conclusions 

Limited icing scaling tests were performed in the NASA Glenn Icing Research Tunnel to assess the 

modified scaling methods for swept wing icing application. The reference tests used a finite span 

91.4-cm-chord adjustable sweep airfoil model of NACA 0012 profile at velocities of 100 and 150 knot and 

MVD of 44 and 93 m. Scale-to-reference model size ratio was 1:2.4. All tests were conducted at 0 angle 

of attack (AoA) and 45 sweep angle. 

The preliminary result showed that good agreement of both size and shape of the main ice accretion 

and feather regions was observed. The present SLD reference tests were made with velocities of 100 and 

150 knot, and these observations may not be valid for higher velocities. Additional test is required to 

identify the range of test conditions, both Appendix C and SLD regime, in which the modified scaling 

methods for swept wing icing may not apply. 

Also it was evident from the ice shape comparison presented in this study that the traditional ice 

tracing method to document straight wing ice shapes was not sufficient to properly characterize the highly 

three dimensional ice shape features, e.g., the complete scallop tip, that are prevalent in swept wing ice 

accretion. Currently some effort is taken by NASA Icing Branch to develop a three-dimensional ice shape 

characterization method for swept wing icing. 

References 

1. Tsao, J.C. and Kreeger, R.E., “Experimental Evaluation of Stagnation Point Collection Efficiency of 

the NACA 0012 Swept Wing Tip,” AIAA–2009–4125 and NASA/TM—2010-216102, March 2010. 

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

3. Anderson, D.N and Tsao, J.C., “Ice Shape Scaling for Aircraft in SLD Conditions,” NASA/CR—

2008-215302 and DOT/FAA/AR-07/55, September 2008. 

4. Vargas, M., “Current Experimental Basis for Modeling Ice Accretions on Swept Wings,” 

AIAA–2005–5188, June 2005. 

5. Vargas, M. and Tsao, J.C., “Observations on the Growth of Roughness Elements into Icing 

Feathers,” AIAA–2007–0900, January 2007. 

6. Vargas, M., Tsao, J.C. and Rothmayer, A., “Review of Role of Icing Feathers in Ice Accretion 

Formation,” SAE-2007-01-3294, September 2007. 

7. Vargas, M. and Tsao, J.C., “Time-Sequence Observations of the Formation of Ice Accretions on 

Swept Wings,” AIAA–2008–0470, January 2008. 

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

(rev), March 1986. 

9. Langmuir, Irving and Blodgett, Katharine B. “A Mathematical Investigation of Water Droplet 

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

10. Abbott, Ira H. and von Doenhoff, Albert E., Theory of Wing Sections, Dover, New York, 1959, 

pp 114 and 321. 

11. 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. 

12. 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. 

13. 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. 

14. Reshotko, Eli and Beckwith, Ivan, “Compressible Laminar Boundary layer over a Yawed Infinite 

Cylinder with Heat Transfer and Arbitrary Prandtl Number,” NACA Rep. 1379, 1957. 
NASA/CR—2012-217419 16 

15. Bilanin, A.J., “Proposed Modifications to the Ice Accretion/Icing Scaling Theory,” AIAA-88-0203, 

January 1988. 

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

Ice Accretion on Aircraft Surfaces,” NASA TM 87184, 1986. 

17. Hansman, R. John, Jr. and Turnock, Stephen, R., “Investigation of Surface Water Behavior During 

Glaze Ice Accretion,” J. Aircraft, vol. 26 no. 2, February 1989, pp 140-147. 

18. Hansman, R. John, Jr. and Turnock, Stephen R., “Investigation of Microphysical Factors which 

Influence Surface Roughness During Glaze Ice Accretion,” 4th International Workshop on 

Atmospheric Icing of Structures, Paris, September 1988. 

19. Hansman, R.J., Breuer, K.S., Hazan, D., Reehorst, A. and Vargas, M., “Close-up Analysis of 

Aircraft Ice Accretion,” AIAA-93-0029, January 1993. 

20. Bilanin, Alan J. and Anderson, David N., “Ice Accretion with Varying Surface Tension,” AIAA-95-

0538 and NASA TM 106826, January 1995. 

21. Anderson, David N. and Tsao, J.C., “Additional Results of Ice-Accretion Scaling at SLD 

Conditions,” AIAA–2003–0390, January 2003 and NASA/CR—2005-213850, August 2005. 

22. Bartlett, C. Scott, “An Analytical Study of Icing Similitude for Aircraft Engine Testing,” 

DOT/FAA/CT-86/35 and AEDC-TR-86-26, October 1986. 

23. Bartlett, C. Scott, “Icing Scaling Considerations for Aircraft Engine Testing,” AIAA-88-0202, 

January 1988. 

24. Oleskiw, Myron M., De Gregorio, Fabrizio and Esposito, Biagio, “The Effect of Altitude on Icing 

Tunnel Airfoil Icing Simulation,” Proceedings of the FAA International Conference on Aircraft 

Inflight Icing, DOT/FAA/AR-96/81,II, August 1996, pp 511–520. 

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

Tunnel,” AIAA–2001–0234, January 2001. 

26. SigmaScan Pro, image-processing software, ver. 5.0, Systat Software, Inc., Point Richmond, CA. 
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Evaluation of Icing Scaling on Swept NACA 0012 Airfoil Models 

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14. ABSTRACT

Icing scaling tests in the NASA Glenn Icing Research Tunnel (IRT) were performed on swept wing models using existing recommended 

scaling methods that were originally developed for straight wing. Some needed modifications on the stagnation-point local collection 

efficiency (i.e., β0) calculation and the corresponding convective heat transfer coefficient for swept NACA 0012 airfoil models have been 

studied and reported in 2009, and the correlations will be used in the current study. The reference tests used a 91.4-cm chord, 152.4-cm 

span, adjustable sweep airfoil model of NACA 0012 profile at velocities of 100 and 150 knot and MVD of 44 and 93 mm. Scale-toreference model size ratio was 1:2.4. All tests were conducted at 0° angle of attack (AoA) and 45° sweep angle. Ice shape comparison 

results were presented for stagnation-point freezing fractions in the range of 0.4 to 1.0. Preliminary results showed that good scaling was 

achieved for the conditions test by using the modified scaling methods developed for swept wing icing.

15. SUBJECT TERMS

Icing; Scaling 

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