Ice-Accretion Scaling Using Water-Film

Thickness Parameters

NASA/CR—2003-211826

June 2003

AIAA–2002–0522

David N. Anderson

Ohio Aerospace Institute, Brook Park, Ohio

Alejandro Feo

Instituto Nacional de Technica Aerospacial, Madrid, Spain
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Ice-Accretion Scaling Using Water-Film

Thickness Parameters

NASA/CR—2003-211826

June 2003

National Aeronautics and

Space Administration

Glenn Research Center

Prepared under Cooperative Agreement NCC3–884

Prepared for the

40th Aerospace Sciences Meeting and Exhibit

sponsored by the American Institute of Aeronautics and Astronautics

Reno, Nevada, January 14–17, 2002

AIAA–2002–0522

David N. Anderson

Ohio Aerospace Institute, Brook Park, Ohio

Alejandro Feo

Instituto Nacional de Technica Aerospacial, Madrid, Spain
Acknowledgments

The INTA, NASA Glenn Research Center Icing Branch, and the FAA 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 Jim Riley of the FAA and Tom Bond of NASA for their

support of these tests and the IRT personnel for their excellent

and committed technical support.

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

This report contains preliminary

findings, subject to revision as

analysis proceeds.

The Aerospace Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

Available electronically at http://gltrs.grc.nasa.gov
NASA/CR2003-211826 1 

Abstract

Studies were performed at INTA in Spain to determine 

water-film thickness on a stagnation-point probe inserted in a simulated cloud. The measurements were 

correlated with non-dimensional parameters describing 

the flow and the cloud conditions. Icing scaling tests in 

the NASA Glenn Icing Research Tunnel were then 

conducted using the Ruff scaling method with the scale 

velocity found by matching scale and reference values 

of either the INTA non-dimensional water-film thickness or a Weber number based on that film thickness. 

For comparison, tests were also performed using the 

constant drop-size Weber number and the averagevelocity methods. The reference and scale models were 

both aluminum, 61-cm-span, NACA 0012 airfoil sections at 0°AOA. The reference had a 53-cm-chord and 

the scale, 27 cm (1⁄2 size). Both models were mounted 

vertically in the center of the IRT test section. Tests 

covered a freezing fraction range of 0.28 to 1.0. 

Rime ice (n = 1.0) tests showed the consistency of the 

IRT calibration over a range of velocities. At a freezing 

fraction of 0.76, there was no significant difference in 

the scale ice shapes produced by the different methods. 

For freezing fractions of 0.40, 0.52 and 0.61, somewhat 

better agreement with the reference horn angles was 

typically achieved with the average-velocity and constant-film thickness methods than when either of the 

two Weber numbers was matched to the reference 

value. At a freezing fraction of 0.28, the four methods 

were judged equal in providing simulations of the reference shape. 

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 diameter or twice the leading-edge 

radius of airfoil, cm 

h Water-film thickness, 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

M Mach number, dimensionless 

MVD Water droplet median volume diameter, μm 

n Freezing fraction, dimensionless 

p Static 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 droplet, dimensionless 

tf Freezing temperature, °C 

ts Surface temperature, °C 

tst Static temperature, °C 

V Air velocity, m/s 

We Weber number based on droplet size and water 

properties, dimensionless 

Wec Weber number based on model size and air 

properties, dimensionless 

Weh Weber number based on water-film thickness 

and water properties, dimensionless 

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 

ICE-ACCRETION SCALING USING WATER-FILM THICKNESS PARAMETERS 

David N. Anderson* 

Ohio Aerospace Institute 

Brook Park, Ohio 

Alejandro Feo†

Instituto Nacional de Technica Aeroespacial 

Madrid, Spain 

*Senior Research Associate, Member 

†

Chief, Experimental Aerodynamics 
NASA/CR2003-211826 2 

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 

Introduction

Since the 1940’s six similarity parameters have been 

identified1,2 that are important to icing scaling. They 

are the modified inertia parameter, K0, defined by Langmuir and Blodgett3

 to insure similarity in droplet trajectory, the accumulation parameter, Ac, to insure 

similarity in quantity of ice accreted, and four parameters derived from the energy balance: the freezing fraction, n, the water-energy transfer parameter, φ, the airenergy transfer parameter, θ and the relative heat factor, 

b. The parameters n, φ, θ and b were defined by Messinger4

 and Tribus5 and are not all needed for similarity 

of ice accretion. The AEDC or Ruff scaling method2

matches the scale and reference values of the similarity 

parameters K0, Ac, n, φ and θ. It is applicable to tunnels 

with the capability to simulate altitude. For tunnels 

without pressure control, a modified Ruff method has 

been used in which only the parameters K0, Ac, n and 

φ are used. θ can also be substituted for φ when this 

leads to more favorable scale test conditions. 

During glaze-ice accretion water does not freeze immediately in the zone of impingement. The characteristics 

of the resulting layer of liquid surface water are believed to influence the shape of the accreted ice to some 

extent and are the subject of a number of ongoing studies. Bilanin6

 and Bilanin and Anderson7 advocated 

adding another similarity parameter, the Weber number, 

to scaling requirements to address surface-water effects. 

Two forms of the Weber number that might be applied 

include that based on the droplet MVD and water properties (We) and one based on model size and air properties (Wec). A third Weber number was suggested by 

Kind8,9,10; this one was based on the thickness of the 

water film at the leading edge (Weh). 

Anderson and Ruff11 and Anderson12 reported the best 

scaling results for glaze ice were achieved when a compromise between constant We and constant Re was used 

with the modified Ruff method. This approach has 

been called the average-velocity method. A possible 

explanation for the success of this method comes from 

the dependence of surface-tension effects on both We

and Re. For example, studies of droplet-surface impact13 for non-icing applications found that splashing 

effects correlated with a K factor depending only on We

and Reδ. Other surface-tension effects such as waterfilm breakup and rivulet formation are also We and Re

dependent. 

Finally, in a recent study at above-freezing temperatures, Feo and Urdiales14 measured the water-film 

thickness, h, for heavy-rain conditions. The nondimensional film thickness, h/d, was found to correlate 

with We and Reδ. The authors suggested that h/d might 

itself serve as an appropriate similarity parameter for 

scaling studies. Although spray characteristics for that 

study were very different from Appendix-C conditions, 

the heavy-rain h/d was evaluated as a similarity parameter in studies comparing how methods to select 

scale velocity affected ice shape.11,12 However, matching the scale and reference h/d of Feo and Urdiales gave 

scale ice shapes that were generally a poorer match of 

the reference than did other methods of finding scale 

velocity. Later, Feo15 measured the thickness of the 

water film for MVD and LWC conditions closer to those 

in an icing cloud and established that the new results 

correlated with LWC and Re. With the availability of 

this new correlation for h/d, the constant-water-film 

thickness method needed to be reevaluated. This 

evaluation was a goal of the present study, along with 

the evaluation of the constant-Weber-number based on 

this water-film thickness, Weh. 

In this investigation, ice accretion scaling for a model 

size reduction of 1⁄2 was evaluated. The Ruff method 

provided the scale test conditions tst, MVD, LWC and τ. 

The scale V was found by matching We, Weh or h/d to 

the respective reference value or by using the average-V

method. The study compared how well the scaled ice 

shapes agreed with the reference shapes to evaluate 

each of these methods of determining scale velocity. 

This paper will briefly describe the recent nearAppendix C water-film thickness studies at INTA as 

well as the scaling tests performed in the NASA Glenn 

Icing Research Tunnel (IRT). The reference model for 

the scaling tests was an aluminum 61-cm-span, 53-cmchord NACA 0012 airfoil at 0°AOA. The scale model 

was also an aluminum 61-cm-span model but with a 

chord of 27 cm. Both models were mounted vertically 

in the center of the IRT test section. Test conditions 

covered a range of freezing fractions from 0.28 to 1.0. 

Scaling Method

The basis of the scaling used in this study was the Ruff2

method. Ruff demonstrated that the best scaling occurred when the five similarity parameters, K0, Ac, n, φ

and θ, were used. The matching of each of these scale 

parameters to its respective reference value allows the 

solution for scale MVD, time, LWC, temperature and 

pressure. For tunnels without control of test-section 

pressure, either of the parameters φ or θ can be used to 

find scale temperature12, with the other parameter ignored. The choice of scale velocity is left to the user. 
NASA/CR2003-211826 3 

The modified inertia parameter, K0, was defined by 

Langmuir and Blodgett:3

0

1 1

8 8 Stokes

K K  =+ −    

λ

λ (1)

A match of scale and reference K0 insures similarity of 

droplet trajectories. In equation (1), λ/λStokes 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, Reδ and was tabulated by Langmuir 

and Blodgett. K is the inertia parameter, 

2

18

w MVD V K

d = ρμ

 (2) 

Here d is the diameter for cylindrical models or twice 

the leading-edge radius for airfoils. For the NACA 

0012, a leading-edge radius of 0.0158c was used, where 

c is the model chord. 

The accumulation parameter is: 

c

i

LWCV A

d = τ

ρ

 (3) 

A match of scale and reference Ac insures that the same 

quantity of ice, relative to airfoil size, is accreted for 

both. This matching assumes that the leading-edge 

collection efficiency, β0, for scale and reference situations are also equal. However, because β0 is a function 

only of K0, if K0 is matched, so too is β0. 

The freezing fraction, from Messinger’s4

 surface energy 

balance, can be written in the form, 

p ws ,

f

c

n

b

  = +    

θ φ Λ (4) 

Thus, a match of scale and reference n insures the overall energy balance will agree. 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.5

 These 

parameters are defined as 

2

, 2 f st

p ws

V

φ t t

c =−− (5) 

2

2

G ww w s st v

p c

rV hp p θ t t Λ

ch p

    − = −− +        

 (6) 

0 , p ws

c

LWC V c

b

h = β (7) 

Equation (6) gives the form of θ used by Charpin1

 and 

others. A somewhat more complex form was presented 

by Ruff,2

 and Ruff’s expression for θ was used in the 

calculations in this paper. The values from the two 

expressions are not significantly different, however. 

Four ways to determine scale velocity were evaluated 

as supplements to the Ruff method. They involved 

either the inclusion of one additional similarity parameter, or the calculation of scale velocity as the average of 

that required to match scale and reference We and that 

to match Re. The additional parameter was either We, 

Weh, or h/d. The We, Weh and Re are defined as 

2

/

w

w a

V MVD We = ρ

σ

 (8) 

2

/

w

h

w a

V h We = ρ

σ

 (9) 

Vd Re = ρ

μ

 (10) 

The Feo correlation for the parameter h/d will be given 

in the next section. 

INTA Water-Film-Thickness Measurements

The water-film-thickness experiments were performed 

by Feo15 in the INTA 2.8-by-1.7-m wind tunnel shown 

in figure 1. The water spray was generated using a single air-atomizing nozzle located in the open test section 

as seen in figure 1(a). The target probe was positioned 

at the entrance to the bell mouth. Three nozzles were 

used, Spraying Systems models SUJ 12 A, SUJ 12 and 

SUJ 22 B. These operated at different air and water 

pressures and therefore provided some check on the 

validity of the relationship between film-thickness and 

(a) Water Spray and Probe. Dimensions are in m. 

Figure 1. INTA Wind Tunnel. 
NASA/CR2003-211826 4 

cloud conditions. Correlations of the nozzle air and 

water pressures with cloud characteristics at the position of the film-measuring stagnation-point probe were 

obtained by testing with an OAP-200 probe to determine MVD and a water-collection probe to measure

LWC. The nozzle spray can be seen in figure 1(b). 

Sixteen tests were performed; the test conditions are 

given in table I. The OAP-200 instrument measured 

droplet sizes no smaller than 25 μm; thus, Appendix-C

MVD’s could not be accurately determined. It was insensitive to the sprays generated by the nozzles SUJ 12 

and SUJ 12 A, suggesting that MVD’s were below 

25 μm for these. In two cases, the pressures used with 

these nozzles corresponded with the manufacturer’s 

published tests, and these are reported in table I as 

MVD’s of 13 and 15 μm. Test MVD’s, then, covered a 

range from well under 25 to 160 μm. 

LWC’s for this study were higher than desired to simulate Appendix-C clouds, but it was hoped that correlations developed from these data could be extrapolated 

to Appendix-C conditions. The tests were made at ambient temperatures well above freezing, representing a 

freezing fraction of zero. 

A conductance sensor mounted flush in the front face of 

a cylindrical stagnation-point probe was used to determine water-film thickness. A cross-section sketch of 

the probe14 is shown in figure 2 with a water-film of 

thickness h indicated conceptually. The probe was located 2.5 m downstream from the water nozzle. A detailed description of the conductance sensor is given in 

Feo and Urdiales14 and Feo, Rogles and Urdiales.16

Table I lists the measured water-film thicknesses reported in reference 15. The uncertainty in these data is 

estimated to be ±20%. They have been nondimensionalized and plotted in figure 3. Note that 

Table I 

Film-Thickness Test Conditions and Results 

Nozzle V, 

m/s 

MVD, 

μm 

LWC, 

g/m3

h, 

μm 

SUJ 12 A 55 13 5.39 75 

SUJ 12 A 55 <25 4.84 62 

SUJ 12 A 30 <25 4.53 79 

SUJ 12 A 30 <25 6.69 108 

SUJ 12 A 20 <25 6.99 95 

SUJ 12 A 20 <25 5.17 89 

SUJ 12 55 15 5.25 60 

SUJ 12 55 <25 4.22 65 

SUJ 12 55 <25 2.65 55 

SUJ 12 30 <25 6.41 72 

SUJ 12 20 <25 7.79 106 

SUJ 12 20 <25 8.45 125 

SUJ 12 20 <25 4.97 103 

SUJ 22 B 55 160 10.67 106 

SUJ 22 B 30 160 9.00 118 

SUJ 22 B 20 88 14.54 154 

(b) Test section with spray. 

Figure 1. Concluded. 

Figure 2. Stagnation-Point Probe with Water Film. 

Figure 3. Film-Thickness Correlation. 
NASA/CR2003-211826 5 

because of the Re dependency, the slope of the line will 

be affected slightly by test ambient pressure and 

temperature. The best correlation of the experimental 

film thickness data was found to be 

1/2

1/4 /

w

LWC h d Re−   ∝     ρ

 (11) 

This expression shows no water surface-tension effects, 

indicating that for the spray conditions and the stagnation probe geometry used, droplet impacts, film breakup and rivulet formation are not important. However, 

measurements on the stagnation point on a cylinder or 

airfoil might show a different behavior. 

Figure 3 shows that data for all three nozzles 

correlated well with the right-hand side of 

equation (11). The proportionality constant 

that should appear on the right side of equation 

(11) is not known for icing conditions at this 

time. However, it must be some function of 

the freezing fraction, because at a freezing 

fraction of unity, there is no water film, while 

at a freezing fraction of zero, the thickness h

would apply. Furthermore, different constants 

may be required for Appendix-C conditions 

than for the LWC’s of this study. The form of 

equation (11) has been verified analytically by 

Rothmayer17 for the range of temperatures and 

spray conditions of the INTA tests. 

The INTA tests provided two similarity parameters: the non-dimensional water-film thickness, 

h/d, and the Weber number using this film thickness as 

the length scale, Weh, defined in equation (9). These 

parameters were evaluated for their use in scaling in the 

IRT scaling tests described next. 

IRT Scaling Test Description

The scaling tests were performed in the NASA Glenn 

IRT. The IRT is a closed-loop, refrigerated, sea level 

tunnel with a test section of 1.8 by 2.7 m. The tunnel 

loop is shown in figure 4(a). The IRT has 10 spray 

bars. In the summer of 2000, a complete cloud calibration18 for both the mod-1 and standard nozzles was 

completed following the installation of a new heat exchanger and other upgrades.19

The models used for these tests were NACA 0012 61-

cm-span aluminum airfoil sections with chords of 53.3 

and 26.7 cm. They were mounted vertically between 

splitter plates at the center of the IRT test section as 

shown typically in figure 4(b). Horizontal lines at the 

leading edge indicated tunnel center, ±2.5 cm and ±5 

cm from the center as guides for locating ice tracings. 

The mounting arrangement permitted rotation of the 

model for angle of attack changes, but all tests were run 

at 0° AOA. The IRT spray system has rapid-start capability; consequently, the model did not require shielding 

during spray initiation. 

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, and then turned off. The fan was brought to a 

full stop and the tunnel entered to record the ice shape. 

A heated ice knife with a cutout in the shape of the 

model was inserted into the leading edge of the ice to 

melt a thin slice down to the model surface. A card-

(a) NASA Glenn Icing Research Tunnel. Revised Loop with 

New Heat Exchanger Installed in 2000. 

(b) Model Installed in IRT Test Section. 

Figure 4. Facility and Model Description. 
NASA/CR2003-211826 6 

board template was placed into this gap and an outline 

of the ice accretion traced. Tracings were taken at the 

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

at 2.5 cm above the center. Ice shape differences between the two tracing locations were never significant, 

and only centerline shapes will be reported here. The 

tracings were digitized and the x-y coordinates for each 

ice shape recorded. When plots of ice-shapes were 

compared for different sized models, the coordinates 

were normalized by the model chord. 

Reference test conditions were chosen so that both reference and scale conditions would fall within the IRT 

operating envelope. The six cases selected all had the 

same V, MVD, LWC and τ but with temperatures varied 

to provide a range of freezing fractions from 0.28 to 

1.0. Scale conditions for 1⁄2-size scaling were determined as discussed above. It turned out that the constant-We and constant-Weh methods of finding scale 

velocity gave virtually the same scale test conditions, 

thus, there were only three distinct sets of scale conditions for each reference case. Nevertheless, tests for 

both the constant-We and constant-Weh methods were 

made so that repeatability could be evaluated. Results 

from three test entriesAugust 2000, November 2000 

and March 2001will be presented. Only a sampling 

of typical results will be shown. 

Uncertainty Analysis for IRT

Tunnel and cloud conditions were recorded every 1 sec 

over the duration of each test for the August and November 2000 entries. For the March 2001 tests the recording interval was 3 sec. Reported conditions are the 

time averages of these records. Estimates of the uncertainty in the reported average conditions were made by 

considering fluctuations of the values over time, possible instrument errors, uncertainties in tunnel calibration 

of MVD and LWC and differences in measurements 

from one location to another in the test section. 

Total temperature was measured as the average of the 

readings of 24 thermocouples located on the D-corner 

turning vanes. Including inherent uncertainty in the 

thermocouples themselves, it is estimated that the total 

uncertainty in temperature is on the order of ±0.5 °C. 

Test-section velocity was determined from the average 

total and average static pressures from 2 pitot-static 

probes, one located on the north wall and one on the 

south wall of the tunnel at the entrance to the test section. The maximum computed difference in velocities 

indicated by the two probes was ±0.25%. Pressures 

also fluctuated modestly with time such that the maximum variation in velocity over the spray duration was 

determined to be ±1.3 m/s at an average velocity of 40 

m/s and ±1 m/s for speeds higher than 40 m/s. 

The most significant contribution to LWC uncertainty is 

the calibration process, and scatter in the calibration 

data suggests this uncertainty is about ±10%. 

The largest contribution to drop-size uncertainty comes 

from the instrument used in calibration and was estimated from the observed randomness recorded during 

calibration. The net uncertainty in MVD is estimated at 

±12%. This uncertainty applies only to the particular 

instruments used (OAP and FSSP probes) in the IRT 

calibration and do not suggest a reference to any absolute value of MVD, because the absolute value is not 

known. 

These uncertainties in the test parameters produce the 

following approximate uncertainties in the similarity 

parameters for the tests reported here: 17% in K0, 2% 

in β0, 12% in Ac, 15% in n, 1 °C each in φ and θ, 2% in 

Re, 12% in We, 7% in Weh, and 6% in h/d. For the last 

two parameters, uncertainties are in the relative values 

calculated with the correlation of equation (11). 

Scaling Results

Figures 5 to 11 present the non-dimensional scale and 

reference ice shapes recorded using each method of 

finding scale velocity. Each figure represents a different reference case. Reference ice shapes are shown 

shaded, while the scale shapes are indicated by a solid 

line. The table below each figure gives the test conditions and similarity parameters for each pair of reference and scale tests. The conditions given are 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. The numbers in the last 

column in the table are not actual water-film thicknesses but rather the relative h/d. This value was calculated from the right-hand side of equation (11). 

Scaling RepeatabilityFigures 5 and 6

Figures 5 and 6 each compare two sets of reference and 

scale tests for half-size scaling. Two of these used the 

average-V method of determining scale velocity, and 

two used constant-We or constant-Weh. As noted 

above, these latter methods produce almost identical 

scale test conditions. The freezing fraction was 0.28 for 

the average-V tests (figs. 5(a) and (b)), which were performed in August and November 2000, and 0.52 for the 

constant-We and constant-Weh tests (figs. 6(a) and (b)), 

which were made in November 2000 and March 2001. 

In the August 2000 average-V tests, (fig. 5(a)) the scale 

ice shape closely matched the reference in terms of the 

main ice accretion size and shape as well as the feather 

structure aft of the main shape. When the same reference and scale test conditions were repeated in the 
NASA/CR2003-211826 7 

November 2000 entry (fig. 5(b)), the results showed 

significant differences between the reference and scale 

shapes. In particular, the scale shape appears to have 

been formed at a lower freezing fraction than the reference. Figures 5(a) and (b) illustrate how variable ice 

shapes can be for low freezing fraction conditions. At 

freezing fractions as low as 0.28, variations within the 

uncertainties in temperature or 

LWC from run to run can make a 

significant difference in ice shape. 

Large differences in shape are usually not seen when the freezing 

fraction is higher than about 0.3. 

Figure 6 shows some typical repeatability results for a nominal 

freezing fraction of 0.5. The reference ice shapes shown in figures 6(a) and (b) had consistent 

horn angles and ice quantity, as did 

the two scale shapes. The results from the November 

2000 (fig. 6(a)) and March 2001 (fig. 6(b)) test entries 

were sufficiently different, however, that the nondimensional reference shape in figure 6(a) was slightly 

larger than the scale, while the scale in figure 6(b) appeared to be slightly larger than the reference. These 

differences in quantities are consistent with the 

uncertainty in test parameters. 

Thus, when comparing normalized 

scale and reference ice shapes it is 

important to consider test uncertainties and not expect precise 

matches. 

Rime (Case 460)Figure 7

For rime ice, the heat transfer rate 

is high enough that water freezes 

immediately on impact with the 

surface. Thus, for scaling analyses, heat transfer or surface water 

expressions are unnecessary, and 

Scaling 

Method Date/Run c, 

cm 

tst, 

°C 

V, 

m/s 

MVD,

μm 

LWC,

g/m3

τ, 

min K0

β0, 

% Ac n φ, °C 

θ, 

°C 

Re, 

104

We,

103 Weh

rel 

h/d

(a) Ref 8-8-00/1 53.3 -7 67 40 1.00 7.3 5.7 86 1.90 0.28 7 9 8.6 2.8 68 5.8

Avg V 8-10-00/6 26.7 -11 115 21 1.21 1.8 5.8 86 1.95 0.30 9 10 7.1 4.3 116 6.8

(b) Ref 11-13-00/2 53.3 -7 67 38 1.00 7.3 5.3 85 1.88 0.28 7 9 8.6 2.6 68 5.8

Avg V 11-16-00/2 26.7 -10 114 21 1.20 1.8 5.8 86 1.87 0.29 9 9 7.1 4.2 114 6.7

Figure 5. Ice Shape Repeatability at a Nominal Freezing Fraction of 0.3. 

Scaling 

Method Date/Run c, 

cm 

tst, 

°C 

V, 

m/s 

MVD,

μm 

LWC,

g/m3

τ, 

min K0

β0, 

% Ac n φ, °C 

θ, 

°C 

Re, 

104

We,

103 Weh

rel 

h/d

(a) Ref 11-13-00/5 53.3 -13 67 38 0.99 7.3 5.3 85 1.88 0.52 12 17 8.9 2.6 67 5.8

Const We 11-16-00/7 26.7 -13 88 23 1.14 2.4 5.7 86 1.89 0.51 12 16 5.7 2.8 69 6.9

(b) Ref 3-20-01/5 53.3 -13 67 40 1.00 7.3 5.7 86 1.89 0.52 12 17 8.8 2.8 67 5.8

Const Weh 3-22-01/7 26.7 -13 86 24 1.16 2.4 5.8 86 1.86 0.52 12 16 5.6 2.7 67 7.0

Figure 6. Ice Shape Repeatability at a Nominal Freezing Fraction of 0.5. 
NASA/CR2003-211826 8 

any method of choosing scale velocity should be 

equally valid. 

Although they serve no purpose in evaluating scaling 

methods, rime tests can be used to validate tunnel calibrations because the different methods of choosing 

scale velocity result in a range of scale velocity and 

LWC. While the scale test conditions are different from 

method to method, they should all produce the same 

rime shape and quantity. 

Figure 7 shows the comparison of scale and reference 

shapes for three methods of determining scale velocity: 

constant We, constant Weh and constant h/d. Remember 

that for rime ice h/d = 0, so the values in the h/d column 

in the table have no physical meaning. Nevertheless, 

scale velocities found by matching scale and reference 

relative h/d are valid for use even in rime studies. 

In figures 7(a) and (b) the scale ice shapes simulated the 

reference well with regard to both shape and quantity of 

ice accreted. Even the feather region was well 

matched. The test of the constant-h/d method 

(fig. 7(c)), produced scale accretions with the right 

shapes, but with smaller quantity than the reference. 

Since the uncertainty in LWC has been estimated to be 

±10%, differences in ice quantity from one test to another should be within about 20%. The differences 

observed in figure 7(c) appear to be of about this 

magnitude. 

Freezing Fraction of 0.76 (Case 461)Figure 8

For a freezing fraction of 0.76, only the constant-We

(fig. 8(a)), constant-Weh (fig. 8(b)) and constant-h/d

methods (fig. 8(c)) were tested. All three methods gave 

approximately the same quantity of scale ice and nearly 

the same shape. Feather growth aft of the leading edge 

was well simulated by all methods tested. 

Freezing Fraction of 0.52 (Case 463)Figure 9

Shape differences among the different methods are 

more evident when the freezing fraction is reduced sufficiently to produce glaze horns. Horns were evident in 

tests at a freezing fraction of 0.6. Scaling results at this 

freezing fraction were essentially the same as those at a 

freezing fraction of 0.52, shown in figure 9, with the 

average-V and constant-h/d methods providing scale 

shapes that were good simulations of the reference. 

For n = 0.52, all four methods of determining scale velocity were tested. Because, as noted above, the constant-We and constant-Weh methods produced virtually 

the same scale test conditions, only the constant-Weh

results are shown in figure 9(a) for comparison with the 

average-V (fig. 9(b)) and constant-h/d results (fig. 9(c)). 

Neither the constant-We nor the constant-Weh methods 

were able to simulate the glaze horn angle, although 

both produced the correct quantity of ice and reproduced well the feather size and density. 

Scaling 

Method Date/Run c, 

cm 

tst, 

°C 

V, 

m/s 

MVD,

μm 

LWC,

g/m3

τ, 

min K0

β0, 

% Ac n φ, °C 

θ, 

°C 

Re, 

104

We,

103 Weh

rel 

h/d

(a) Ref 11-13-00/8 53.3 -27 67 38 0.99 7.3 5.3 85 1.88 1.0 26 34 9.8 2.6 65 5.6

Const We 11-16-00/15 26.7 -27 88 23 1.18 2.4 5.8 86 1.88 1.0 26 32 6.3 2.8 68 6.9

(b) Ref 3-21-01/4 53.3 -26 67 40 1.00 7.3 5.7 86 1.89 1.0 26 33 9.6 2.7 65 5.7

Const Weh 3-22-01/1 26.7 -26 86 24 1.20 2.4 5.8 86 1.91 1.0 26 32 6.1 2.7 66 7.0

(c) Ref 3-21-01/4 53.3 -26 67 40 1.00 7.3 5.7 86 1.89 1.0 26 33 9.6 2.7 65 5.7

Const h/d 3-22-01/2 26.7 -27 117 21 0.93 2.2 5.8 86 1.87 1.0 25 30 8.0 4.4 102 5.8

Figure 7. Rime Scaling (Case 460). 
NASA/CR2003-211826 9 

Scaling 

Method Date/Run c, 

cm 

tst, 

°C 

V, 

m/s 

MVD,

μm 

LWC,

g/m3

τ, 

min K0

β0, 

% Ac n φ, °C 

θ, 

°C 

Re, 

104

We,

103 Weh

rel 

h/d

(a) Ref 11-13-00/7 53.3 -27 67 38 0.97 7.3 5.4 85 1.88 1.0 26 34 9.8 2.6 65 5.6

Const We 11-16-00/13 26.7 -27 88 23 1.18 2.4 5.8 86 1.88 1.0 26 32 6.3 2.8 68 6.9

(b) Ref 3-20-01/9 53.3 -26 67 40 1.00 7.3 5.8 86 1.89 1.0 26 33 9.6 2.7 65 5.7

Const Weh 3-22-01/4 26.7 -26 86 24 1.20 2.4 5.9 86 1.91 1.0 26 32 6.1 2.7 66 7.0

(c) Ref 11-13-00/7 53.3 -26 67 40 1.00 7.3 5.8 86 1.89 1.0 26 33 9.6 2.7 65 5.7

Const h/d 11-16-00/12 26.7 -27 117 21 0.93 2.2 5.9 86 1.87 1.0 25 30 8.0 4.4 102 5.7

Figure 7. Scaling with n – 0.76 (Case 461). 

Scaling 

Method Date/Run c, 

cm 

tst, 

°C 

V, 

m/s 

MVD,

μm 

LWC,

g/m3

τ, 

min K0

β0, 

% Ac n φ, °C 

θ, 

°C 

Re, 

104

We,

103 Weh

rel 

h/d

(a) Ref 11-13-00/7 53.3 -19 67 38 0.99 7.3 5.3 85 1.88 0.77 18 24 9.3 2.6 66 5.7

Const We 11-16-00/13 26.7 -19 88 23 1.17 2.4 5.8 86 1.89 0.77 18 24 6.0 2.8 69 6.9

(b) Ref 3-20-01/9 53.3 -19 67 40 0.99 7.3 5.7 86 1.89 0.77 18 25 9.2 2.8 66 5.7

Const Weh 3-22-01/4 26.7 -20 86 24 1.18 2.4 5.8 86 1.90 0.78 19 24 5.8 2.7 67 7.0

(c) Ref 11-13-00/7 53.3 -19 67 38 0.99 7.3 5.3 85 1.88 0.77 18 24 9.3 2.6 66 5.7

Const h/d 11-16-00/12 26.7 -20 114 21 0.92 2.3 5.7 86 1.88 0.77 18 22 7.6 4.2 98 5.8

Figure 8. Scaling with n = 0.77 (Case 461). 

Scaling 

Method Date/Run c, 

cm 

tst, 

°C 

V, 

m/s 

MVD,

μm 

LWC,

g/m3

τ, 

min K0

β0, 

% Ac n φ, °C 

θ, 

°C 

Re, 

104

We,

103 Weh

rel 

h/d

(a) Ref 3-20-01/5 53.3 -13 67 40 1.00 7.3 5.7 86 1.89 0.52 12 17 8.8 2.8 67 5.8

Const Weh 3-22-01/7 26.7 -13 86 24 1.16 2.4 5.8 86 1.86 0.52 12 16 5.6 2.7 67 7.0

(b) Ref 11-13-00/5 53.3 -13 67 38 0.99 7.3 5.3 85 1.88 0.52 12 17 8.9 2.6 67 5.8

Avg V 11-16-00/8 26.7 -16 115 21 1.15 1.8 5.7 86 1.89 0.52 15 17 7.4 4.2 110 6.5

(c) Ref 11-13-00/5 53.3 -13 67 38 0.99 7.3 5.3 85 1.88 0.52 12 17 8.9 2.6 67 5.8

Const h/d 11-16-00/6 26.7 -14 110 21 0.91 2.4 5.7 86 1.88 0.52 12 14 7.0 4.0 92 5.8

Figure 9. Scaling with n = 0.5 (Case 463). 
NASA/CR2003-211826 10 

Figure 9(b) shows that again the average-V approach 

provided an excellent match of the horn angle while 

also producing the correct ice quantity and simulating 

the feather region of the reference. Within typical 

shape repeatability, the results for the constant-h/d

method shown in figure 9(d) were also a very close 

simulation of the reference shape. 

Freezing Fraction of 0.40 (Case 464)Figure 10

For this freezing fraction, only the constant-Weh, average-V and constant-h/d methods for determining scale 

velocity were evaluated. The best match of the reference shape and quantity occurred when scale velocity 

was found by the constant-h/d method (fig. 10(c)). The 

constant-Weh method (10(a)) gave only an approximate 

simulation of the reference shape, while the average-V

method (fig. 10(b)) produced a poor simulation. Since 

typically the average-V method produces successful 

scaling, the results of figure 10(b) need to be reexamined with additional tests before conclusions can be 

made. 

Freezing Fraction of 0.28 (Case 465)Figure 11

The warmest case tested was case 465, which had a 

freezing fraction of 0.28. Results for three of the four 

methods are given in figure 11. An idea of the variability of ice shapes accreted at freezing fractions this low 

can be seen from the results shown above in 

figures 5(a) and (b). Given the repeatability variations 

demonstrated by those two tests, it can be concluded 

that the constant-Weh (fig. 11(a)) scale test simulated 

the main ice shape acceptably well. The average-V

scale results in figure 11(b) do not appear to be a good 

simulation of the reference shape; however, figure 5(a) 

showed results from an earlier test entry for which the 

constant-V scaling simulation at this freezing fraction 

was excellent. The constant-h/d method (fig. 11(c)) 

simulated the main ice shape well, although the scale 

feathers appear to be larger than for the reference test. 

Additional tests at this freezing fraction are needed to 

better assess the constant-h/d method. The preliminary 

assessment is, however, that any of the methods can 

produce acceptable scaling simulation for n = 0.28. If 

scale simulations are needed at such low freezing fractions, it is recommended that, due to the variability of 

shapes, tests be repeated with more than one test entry. 

Summary

Measurements of the water-film thickness on a stagnation probe in cloud conditions simulating those of icing 

led to the non-dimensional thickness expression, 

1/2

1/ 4 /

w

LWC h d Re−   ∝     ρ

Scaling 

Method Date/Run c, 

cm 

tst, 

°C 

V, 

m/s 

MVD,

μm 

LWC,

g/m3

τ, 

min K0

β0, 

% Ac n φ, °C 

θ, 

°C 

Re, 

104

We,

103 Weh

rel 

h/d

(a) Ref 3-19-01/6 53.3 -10 67 40 1.00 7.3 5.7 86 1.88 0.40 9 13 8.7 2.7 67 5.8

Const Weh 3-22-01/8 26.7 -10 87 24 1.12 2.5 5.8 86 1.91 0.41 10 12 5.5 2.8 68 6.9

(b) Ref 11-13-00/4 53.3 -10 67 38 1.00 7.3 5.3 85 1.88 0.40 9 13 8.7 2.6 67 5.8

Avg V 11-16-00/5 26.7 -13 115 21 1.17 1.8 5.7 86 1.89 0.40 12 13 7.3 4.2 112 6.6

(c) Ref 11-13-00/4 53.3 -10 67 38 1.00 7.3 5.3 85 1.88 0.40 9 13 8.7 2.6 67 5.8

Const h/d 11-16-00/4 26.7 -11 107 22 0.90 2.6 5.8 86 1.89 0.40 9 11 6.7 3.8 87 5.9

Figure 10. Scaling with n = 0.40 (Case 464). 
NASA/CR2003-211826 11 

The expression on the right side of this proportionality 

was used as a relative h/d scaling parameter, and a Weber number based on this relative water-film height, 

Weh, was also used as a second scaling parameter to 

determine scale velocity to supplement the Ruff scaling 

method. Results from tests with either of these two 

parameters were compared with those from tests with 

constant We and average velocity, which have been 

discussed in previous papers. Scale test conditions 

found using the constant-We and constant-Weh methods 

were the same, within parameter uncertainty. 

Each of the methods typically provided a good simulation of the size and density of the feather growth behind 

the leading-edge shape for all cases. However, the 

comparison of the main ice shapes near the leading 

edge revealed some differences in how well the various 

methods scaled the ice. The differences depended on 

the freezing fraction. 

For rime ice (n = 1.0) there is no surface water and all 

methods of choosing scale velocity should produce the 

same ice shape. This was generally true, except that for 

the highest scale velocities, the relative quantity of 

scale ice was less than the reference. The deficit appeared to be within the ±10% uncertainty in the IRT 

LWC calibration, however. 

At a freezing fraction of 0.76, there was no significant 

difference in the scale ice shapes produced by the different methods. Scale accretions were somewhat 

smaller than the reference for all methods, but were 

within 10% of the reference size. For freezing fractions 

of 0.40, 0.52 and 0.61, all methods resulted in scale 

accretions closely matching the size of the reference, 

but somewhat better agreement with the reference horn 

angles was typically achieved with the average-V and 

constant-h/d methods than with the constant-We or constant-Weh. At a freezing fraction of 0.28, the four 

methods were judged equal in providing simulations of 

the reference shape within the ice-shape repeatability. 

At low freezing fractions, poorer repeatability has been 

observed than for higher freezing fractions. 

Conclusions of this study with regard to the constantWe and average-V methods of finding scale velocity 

agreed with those of reference 12, in which those two 

methods were also tested. The conformity of the average-V and constant-h/d methods is consistent with the 

presumption that both Re and We are important parameters in describing those water-film phenomena that affect ice accretion. 

Scaling 

Method Date/Run c, 

cm 

tst, 

°C 

V, 

m/s 

MVD,

μm 

LWC,

g/m3

τ, 

min K0

β0, 

% Ac n φ, °C 

θ, 

°C 

Re, 

104

We,

103 Weh

rel 

h/d

(a) Ref 3-20-01/1 53.3 -7 67 40 1.00 7.3 5.7 86 1.89 0.28 7 9 8.5 2.7 68 5.8

Const Weh 3-22-01/11 26.7 -8 88 23 1.06 2.6 5.8 86 1.90 0.29 7 8 5.5 2.8 68 6.7

(b) Ref 11-13-00/2 53.3 -7 67 38 1.00 7.3 5.3 85 1.88 0.28 7 9 8.6 2.6 68 5.8

Avg V 11-16-00/2 26.7 -10 114 21 1.20 1.8 5.8 86 1.87 0.29 9 9 7.1 4.2 114 6.7

(c) Ref 11-13-00/2 53.3 -7 67 38 1.00 7.3 5.3 85 1.88 0.28 7 9 8.6 2.6 68 5.8

Const h/d 11-16-00/1 26.7 -8 102 22 0.87 2.8 5.8 86 1.90 0.28 7 7 6.3 3.5 79 5.9

Figure 11. Scaling with n = 0.28 (Case 465). 
NASA/CR2003-211826 12 

References

1

 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. 

2

 Ruff, G.A., “Analysis and Verification of the Icing 

Scaling Equations,” AEDC–TR–85–30, vol. 1 (Rev), 

March 1986. 

3

 Langmuir, Irving and Blodgett, Katharine B.: “A 

Mathematical Investigation of Water Droplet Trajectories,” Army Air Forces Technical Report No. 5418, 

February 1946. 

4

 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. 

5

 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. 

6

 Bilanin, A.J., “Proposed Modifications to the Ice 

Accretion/Icing Scaling Theory,” AIAA Paper AIAA–

88–0203, January 1988. 

7

 Bilanin, Alan J. and Anderson, David N., “Ice Accretion with Varying Surface Tension,” AIAA–95–0538 

and NASA TM–106826, January 1995. 

8

 Kind, R.J., Dillon, T., Gaydos, J.A. and Oleskiw, M., 

“Evidence for the Importance of Scaling Viscous Effects in the Water Film in Glaze Icing Tests,” AIAA–

98–0196, January 1998. 

9

 Kind, Richard J., “Assessment of Importance of 

Water-Film Parameters for Scaling of Glaze Icing,” 

AIAA–2001–0835, January 2001. 

10 Kind, Richard J., “Experimental Assessment of a 

Water-Film-Thickness Weber Number for Scaling of 

Glaze Icing,” AIAA–2001–0836, January 2001. 

11 Anderson, David N. and Ruff, Gary A., “Evaluation 

of Methods to Select Scale Velocities in Icing Scaling 

Tests,” AIAA–99–0244, January 1999. 

12 Anderson, David N., “Effect of Velocity in Icing 

Scaling Tests,” AIAA–2000–0236, January 2000. 

13 Mundo, C., Sommerfeld, M. and Tropea, C., 

“Droplet-Wall Collisions: Experimental Studies of the 

Deformation and Breakup Process,” Int. J. Multiphase 

Flow, vol. 21, no. 2, 1995, pp. 151–173. 

14 Feo, A. and Urdiales, M., “Stagnation Point Probe in 

a Water Spray Immersed in an Airstream,” 

φAE/TNO/0452/003/INTA/95, Instituto Nacional de 

Técnica Aeroespacial, February 1995. 

15 Feo, A., “Icing Scaling with Surface Film Thickness 

Similarity for High LWC Conditions,” 

AE/PRO/4420/184/INTA/00, Instituto Nacional de 

Técnica Aeroespacial, October 2000. 

16 Feo, A., Rogles, F. and Urdiales, M., “The Measurement of Water Film Thickness on Airfoils in Heavy 

Rain Conditions Using Conductance Sensors,” AGARD 

CP–496, December 1991. 

17 Rothmayer, Alric, personal communication, May 

2001. 

18 Ide, Robert F. and Oldenburg, John R., “Icing Cloud 

Calibration of the NASA Glenn Icing Research Tunnel,” AIAA–2001–0234, January 2001. 

19 Irvine, Thomas B., Kevdzija, Susan L., Sheldon, 

David W. and Spera, David A., “Overview of the Icing 

and Flow Quality Improvements Program for the 

NASA Glenn Icing Research Tunnel,” AIAA–2001–

0229, January 2001. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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NASA CR—2003-211826

AIAA–2002–0522

E–13519

WU–708–20–13–00

NCC3–884

18

Ice-Accretion Scaling Using Water-Film Thickness Parameters

David N. Anderson and Alejandro Feo

Aircraft safety; Aircraft icing; Icing scaling

Unclassified -Unlimited

Subject Category: 02 Distribution: Nonstandard

Ohio Aerospace Institute

22800 Cedar Point Road

Brook Park, Ohio 44142

Prepared for the 40th Aerospace Sciences Meeting and Exhibit sponsored by the American Institute of Aeronautics and

Astronautics, Reno, Nevada, January 14–17, 2002. David N. Anderson, Ohio Aerospace Institute, Brook Park, Ohio;

Alejandro Feo, Instituto Nacional de Technica Aerospacial, Madrid, Spain. Project Manager, Thomas H. Bond,

Turbomachinery and Propulsion Systems Division, NASA Glenn Research Center, organization code 5840,

216–433–3900.

Studies were performed at INTA in Spain to determine water-film thickness on a stagnation-point probe inserted in a

simulated cloud. The measurements were correlated with non-dimensional parameters describing the flow and the cloud

conditions. Icing scaling tests in the NASA Glenn Icing Research Tunnel were then conducted using the Ruff scaling

method with the scale velocity found by matching scale and reference values of either the INTA non-dimensional waterfilm thickness or a Weber number based on that film thickness. For comparison, tests were also performed using the

constant drop-size Weber number and the average-velocity methods. The reference and scale models were both aluminum,

61-cm-span, NACA 0012 airfoil sections at 0°AOA. The reference had a 53-cm-chord and the scale, 27 cm (1/2 size). Both

models were mounted vertically in the center of the IRT test section. Tests covered a freezing fraction range of 0.28 to 1.0.

Rime ice (n = 1.0) tests showed the consistency of the IRT calibration over a range of velocities. At a freezing fraction of

0.76, there was no significant difference in the scale ice shapes produced by the different methods. For freezing fractions of

0.40, 0.52, and 0.61, somewhat better agreement with the reference horn angles was typically achieved with the averagevelocity and constant-film thickness methods than when either of the two Weber numbers was matched to the reference

value. At a freezing fraction of 0.28, the four methods were judged equal in providing simulations of the reference shape.