NASA Technical Memorandum 107538

Scaling Methods for Simulating Aircraft

In-Flight Icing Encounters

David N. Anderson

Lewis Research Center, Cleveland, Ohio

and

Gary A. Ruff

Drexel University, Philadelphia, Pennsylvania

Prepared for the

Second International Symposium on Scale Modeling

sponsored by the International Scale Modeling Committee

Lexington, Kentucky, June 23-27, 1997

National Aeronautics and

Space Administration

Lewis Research Center

October 1997

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SCALING METHODS FOR SIMULATING AIRCRAFT IN-FLIGHT ICING

ENCOUNTERS

David N. Anderson

NASA Lewis Research Center

Cleveland OH 44135

and

Gary A. Ruff*

Mechanical Engineering and Mechanics Department

Drexel University

Philadelphia PA 19104

ABSTRACT

This paper discusses scaling methods which permit the use of subscale models in

icing wind tunnels to simulate natural flight in icing. Natural icing conditions exist

when air temperatures are below freezing but cloud water droplets are super-cooled

liquid. Aircraft flying through such clouds are susceptible to the accretion of ice on

the leading edges of unprotected components such as wings, tailplane and engine

inlets. To establish the aerodynamic penalties of such ice accretion and to determine

what parts need to be protected from ice accretion (by heating, for example),

extensive flight and wind-tunnel testing is necessary for new aircraft and

components. Testing in icing tunnels is less expensive than flight testing, is safer,

and permits better control of the test conditions. However, because of limitations on

both model size and operating conditions in wind tunnels, it is often necessary to

perform tests with either size or test conditions scaled. This paper describes the

theoretical background to the development of icing scaling methods, discusses four

methods, and presents results of tests to validate them.

NOMENCLATURE

A¢

b

C

Cp, w

d

Ko

LWC

M

n

P

Accumulation parameter, dimensionless

Relative heat factor, dimensionless

Characteristic model length, cm

Specific heat of water, cal/g K

Water droplet median volume diameter, _tm

Modified droplet inertia parameter of Langmuir and Blodgett, dimensionless

Liquid-water content of cloud, g/m 3

Mach number, dimensionless

Freezing fraction of impinging water, dimensionless

Ambient static pressure, nt/m 2

*Summer Faculty Fellow at Lewis Research Center.

NASA TM-107538 1
Re

t

V

We

&

0

P_

Reynolds number, dimensionless

Ambient static temperature, °C

Free-stream airspeed, rn/s

Weber number, dimensionless

Water-energy transfer term, °C

Latent heat of freezing for water, cal/g

Air-energy transfer term, °C

Density of ice, g/m 3

Subscripts

R Reference or full size

S Scale

INTRODUCTION

Aircraft are susceptible to ice formations on engine inlets, tail planes and wings whenever

flight through clouds at below-freezing temperatures occurs. Suspended water droplets in

clouds are frequently super cooled; that is, the water exists as a liquid at a temperature

below freezing. Supercooled water striking aircraft surfaces freezes, and the resulting ice

accretions can have a significant and dangerous effect on the aerodynamic performance of

an aircraft. In particular, ice formations decrease the lift and increase the drag. Large

transport aircraft are protected against ice on critical components by directing hot air bled

from the engine compressor to keep those surfaces warm enough to vaporize water.

Some less critical surfaces may not be protected, and smaller aircraft often use

intermittent impulse methods to remove small amounts of ice repeatedly.

Aircraft and component manufacturers must thoroughly test new products to determine

the effect of icing on their performance. This testing is performed both during the design

process and for certification purposes. Hight testing is ultimately required but is

expensive and can only be done when atmospheric icing conditions exist. Icing wind

tunnels can simulate natural icing with water-spray and refrigeration systems and provide

control of cloud conditions, temperature and airspeed to permit safe, convenient and

relatively inexpensive testing. Some measurement of lift and drag changes can be made

in the icing tunnel, and ice shapes are often recorded. More precise aerodynamic-penalty

studies can be made in flight or in an aerodynamic tunnel by attaching a wood or

styrofoam reproduction of the ice shape to the leading edge of the airfoil.

Because of size limitations some components cannot be tested full size in an icing wind

tunnel; furthermore, every tunnel has some bounds on the ranges of test conditions

available for testing. For these reasons, it is desirable to establish reliable methods to

scale either model size or test conditions. Efforts to establish scaling methods for icing

tests began in the 1950's and continue to the present. In general, to test scaling methods

an ice shape is recorded for a reference, or full-size, condition, the scaling equations are

applied to find the appropriate scaled condition, and the scaled ice shape is recorded. The

NASA TM-107538 2
two ice shapes are then compared. If size has been scaled, the comparison is facilitated

by multiplying the coordinates of the scaled shape by the appropriate scaling factor.

Whether the two shapes are in agreement is frequently dependent on subjective judgment,

and the quality of agreement when the match isn't perfect has always been difficult to

define. In this paper, in addition to the conventional subjective ice-shape comparisons,

we also present a new approach to quantifying the ice shapes which permits more

objective comparisons. We give an overview of the theoretical basis for traditional

scaling methods, discuss briefly a Buckingham-x analysis, describe four scaling methods

and present results from a series of tests of these scaling methods.

DERIVATION OF SCALING EQUATIONS

The traditional approach to the development of scaling methods has been to attempt

similitude in the geometry, the flowfield, the trajectories of the water droplets, the water

catch, and the energy balance at the surface. Various scaling "laws" have been derived

[1,2,3,4,5] which provide similitude in some or all of these factors which affect ice

accretion. When ice accretes in the rime form, in which impinging water freezes on

impact, simple scaling methods which ignore the surface energy balance have been shown

to work successfully [6]. On the other hand, glaze-ice accretion, for which water does not

freeze immediately on impact, can only be scaled by methods which include the energy

balance. Recently, attempts to understand more about the physics of ice accretion have

shown that for glaze ice, surface phenomena can also have a significant effect on the final

ice shape [7,8]. In this section, we will address each of the similitude requirements which

have been satisfied by traditional methods.

Geometry The scaled and reference models must be geometrically similar over their

entire surfaces. It is assumed that as ice accretes, the scale ice shape will continue to be a

scaled representation of the reference ice shape. An alternate approach is currently being

studied for airfoils in which the leading-edge-region geometry is full-size while the

remainder of the scale airfoil is truncated [9, 10]. The design of the truncated airfoil is

such that the flowfield around it matches that of the reference airfoil. This method will

not be discussed in this paper.

Flowfieid The flowfield over the scale model must simulate that of the reference

case. This requirement is implicitly satisfied in the scaling equations by assuming that

velocity, pressure and temperature distributions over at least the leading-edge region of

the scale model match those for the reference.

Droplet Trajectory To insure that the mass of water reaching each part of the scaled

model is relatively the same as that reaching the same part of the reference model, both

the droplet trajectories and the local water catch have to be similar. The water catch will

be discussed in the next section.

NASA TM-107538 3
A completeanalysisof droplettrajectorysimilarityhasbeenpublishedin Ref. [5] and

[11]. Theseanalysesshow that the scalewater droplet size, ds, must relate to the

reference size, dR, according to Eq. (1):

ds (csl62(ps)'24(Vs) -'38

This expression is convenient to use and is generally accurate for the range of droplet

sizes of interest to aircraft icing (10 - 50 _tm). It was derived by approximating the Re

effect on the drag of a moving spherical water droplet by a linear expression. A

somewhat more accurate approach was used by Ruff [5]; he determined the scale droplet

size which satisfied equality of the modified inertia parameters, Ko,s = Ko.n. Langmuir

and Blodgett [ 12] defined the modified inertia parameter to include effects of both Re and

inertia of a spherical droplet. Either Eq. (1) or RufFs method can be easily programmed

for computer calculation of the required scale droplet size.

Water Catch The total amount of water which impacts the model surface is assumed to

freeze eventually. The quantity of ice accretion can then be described by the nondimensional accumulation parameter, Ac = LWC V "c I c Pi. To insure that the scale test

will accrete the same relative quantity of ice, the scale accumulation parameter is matched

to the reference. Thus,

For rime ice conditions, because water freezes immediately on impact, it is only necessary

to satisfy Eqs. (1) and (2), with LWCs chosen for convenience. For glaze ice, however,

similitude in energy balance is also required; this will be discussed next.

Energy Balance The energy analysis on an unheated surface with water impingement

and freezing was performed by Messinger [13] and has been the basis of most scaling

methods since that time. Messinger's heat balance included the loss of heat from the

surface due to convection, ice sublimation, water evaporation, radiation, and sensible heat

required to warm impinging water to the freezing temperature. The gain of heat at the

surface is due to release of latent heat on freezing and the kinetic energy of incoming

water droplets. Ruff [5] added terms for the conduction of heat through the model surface

and for heat carried from the surface by runback water.

Messinger [13] and Tribus [14] defined two non-dimensional parameters in the energy

balance: the freezing fraction, n, is the fraction of water which freezes within an

impingement region; the relative heat factor, b, is the ratio of the total heat capacity of the

impinging water to the ability of the airflow to convect heat from the surface. Two other

parameters used are ¢, which is a grouping of the terms associated with droplet energy

transfer, and 0, which groups the air-energy transfer terms. When the energy balance is

written using these parameters, it becomes

NASA TM-107538 4
n=Cp'---z-w(_+ 0) f3)

Various scaling methods have selected one or more of the parameters n, _, 0, and b to

match between scale and reference values.

BUCKINGHAM-H ANALYSIS

The scaling parameters discussed in the preceding section result from a

phenomenological approach in that they are derived from a set of equations that describe

our current understanding of the ice-accretion process. Classical scaling by dimensional

analysis and application of the Buckingham-rt methodology has also been applied to icing

scaling. The premise behind this approach is that if the proper dimensionless parameters,

or x terms, can be identified, any one of the rt terms can be written as a function of the

remaining x terms. Only the parameters relevant to physical phenomena and their

dimensions must be specified. This approach is very attractive because it requires

minimal knowledge about the physics of icing, and we presently lack a full understanding

of all the physical processes involved in ice accretion.

This methodology was applied to icing scaling by Bilanin [7] who identified 23 variables

that play a role in the ice-accretion process. With 23 variables and 4 dimensions (length,

mass, time and temperature), there are 19 possible dimensionless parameters. Three of

the parameters are easily recognizable as the Mach, Reynolds and Weber numbers.

Others are related to the drop size, inter-droplet spacing and free-stream temperature.

Still others are ratios of the physical properties of water and ice which will, of course, be

matched automatically between scale and reference situations. It's possible to show that

all of the traditional icing similitude parameters discussed previously can be expressed as

functions of some of the x parameters. If all 19 of the x parameters for the scale test were

simultaneously matched to their respective reference, or full-size, values the ice accretion

should be rigorously scaled.

Unfortunately, not all r_ parameters can be simultaneously matched from scale to

reference conditions. For example, a constant M requires approximately that Vs = VR, a

constant Re requires that cs/cR = VRIVs and a constant We requires that cs/cR = (VRIVs) 2.

Except for the special case when cs = cR, these are inconsistent restrictions. Fortunately,

it may not be necessary to match all rr parameters to scale successfully; the methods

described in Refs. [1] - [6] were based on the traditional icing similitude parameters

which ignored many of the rt parameters, yet scaled the geometry of ice accretions fairly

accurately for some conditions. Although Bilanin's Buckingham-rt analysis has not

proved to be practical as a scaling method by itself, it has served to identify parameters

which may have been overlooked by the traditional methods. One such parameter is the

We which has now been incorporated into a new scaling method discussed below.

NASA TM-107538 5
SCALING METHODS

Icing scaling methods have matched the scale and reference values of a variety of the

terms discussed above to find the scale test conditions. The scaling methods will be

described next in terms of the parameters matched. A summary of the 4 scaling methods

and the similitude parameters which they satisfy is given in Table 1. This list of scaling

Table 1. Similitude Terms Satisfied by Four Scaling Methods.

Method Drop Drop Rel. Freez. Drop Air M Re We

Traj Catch Heat Fract. Engy Engy

Fact Trans Trans

LWC x time x x

Olsen x x x

Ruff (mod) x x x

Const-We x x x

X X

X

X

X X X

X X X

methods is not complete; in particular, the French method [3] will not be discussed here.

It was evaluated in Ref. [6] and has been used extensively in the ONERA icing tunnel at

Modane.

"LWC x time = constant" This is the simplest and oldest scaling "law." It applies

when the model size is not scaled and all parameters except the liquid-water content can

be matched to the desired test conditions. In this situation, the law states that the amount

of accreted ice for the scaled LWC will be the same as for the desired LWC if the product

of accretion time and LWC for the scaled test equals that for the desired, or reference,

encounter being simulated. This expression is derived from Eq. (2) with cs = cR and Vs =

VR. In addition, with Ps = PR, Eq. (1) gives ds = dR. This method requires that the static

temperatures also match; i.e., ts = tR. As a result, and because of the other matched

parameters, Cs = CR, OS= OR, Wes = WeR, Res = ReR and Ms = MR as well.

Olsen A variation on "LWC x time = constant" is the Olsen method [6, 14] in which,

again, only the LWC is to be scaled. As in the case of the "LWC x time = constant"

approach, matching the model size and test conditions other than LWC results in a match

of the We, Re and M as well. In this method, however, the scale static temperature does

not equal the reference temperature, but is found by matching the scale and reference

freezing fraction, n.

NASA TM-107538 6
Ruff The last two methods to be discussed are used when the scale model size is

different from the reference. The Ruff method was developed at the AEDC by Ruff

[5] and is sometimes known as the AEDC method. It was intended originally for use

in wind tunnels with altitude capability. The user first selects a scale model size and

test velocity. The static temperature for the scale test can then be found by matching

the water-energy transport term, _. The scale droplet size is determined by

matching the modified inertia parameter, Ko, which insures that the scale droplet

trajectories will be the same as the reference case. The scale static pressure is found

by matching the air-energy transport terms, 0. For tunnels which cannot control the

static pressure independently of velocity, a modified Ruff method has been used in

which the 0 terms are not matched. Next, the freezing fraction is matched to

establish the scale liquid-water content, and, finally, the icing encounter time is

found from matching the scale and reference accumulation parameters.

Constant-We The Buckingham-r_ analysis of Bilanin [7] showed that the Weber

number may be a significant icing scaling parameter. This method assumes that We

is of greater importance than either Re or M, as no attempt is made to match these

two parameters to the reference values. The user chooses the model size; all other

scale parameters are determined by similitude requirements. The 3 equations formed

by matching the Weber number, the modified inertia parameter, and the waterenergy transfer term are solved simultaneously to give the scale velocity, droplet size

and static temperature. The scale liquid-water content and icing time are then found

from matching the freezing fraction and accumulation parameter, respectively.

EXPERIMENTAL METHODS

Test Facility and Models Tests to validate scaling methods were performed in

the NASA Lewis Icing Research Tunnel (IRT) shown in Fig. 1. It is a closed-loop

tunnel with a test section 1.8 m high by 2.7 m wide. Temperature can be controlled

from -30°C to 4°C. The water spray system gives a range of liquid-water content

3800-kW Fan

Figure 1. NASA Lewis Icing Research Tunnel (IRT).

and water droplet

size which covers a

significant portion

of the FAA Part 25

Appendix C icing

envelope. Velocities of up to 160

m/s are possible.

Fig. 2 is a photo of

a 53.3-cm-chord,

1.8-m-span NACA

0012 airfoil

mounted vertically

NASA TM-107538 7
in the IRT test section for tests to

be reported here. This model had a

uniform chord over the full span

and was unswept. Test conditions

were selected to represent

reference cases, and the various

scaling methods applied to

determine the corresponding scale

test conditions. When the scale

tests involved a size change, an

NACA 0012 model with 26.7-cm

chord was used. Tests were run at

both reference and scale

conditions, two-dimensional cuts

through the resulting ice accretions

were made at the center of the

tunnel test section, and ice shapes

were recorded by tracing the ice

outline onto a cardboard template.

These tracings were then digitized

for computer storage. From these

Figure 2.53.3-cm-Chord NACA 0012 Airfoil computer files, the shapes were

installed in IRT. analyzed and compared.

Quantitative Analysis of Ice-Shape Features In general, evaluations of icing

scaling methods have relied on qualitative comparisons of the scale and reference ice

shapes. With this approach, the experience, judgement and objectivity of the

researcher determine to some extent whether a scaling method is acceptable. In

practice, what constitutes an acceptably scaled ice accretion actually depends on the

purpose of the test. In aerodynamic tests, it is most critical that the sub-scale

accretion have the same lift and drag coefficients as the full-scale. In other

applications, geometric parameters such as the width or mass of the accretion is most

important. In still others, the critical parameter may be the mass of ice shed. For

general evaluation of scaling methods, however, a comparison of ice shapes is most

appropriate. In this study,

Horn Angle Length both qualitative and

-_ _ quantitative comparisons of

";)t'- _ ice shapes will be made.

/

Maximum _ Several characteristic

Width dimensions representative of

_ the overall shape of a typical

glaze ice accretion were

identified. As shown in Fig.

_-- Stagnation Thickness 3, these dimensions included

---- _ Maximum Thickness the thickness of the ice accretion at the stagnation Figure 3. Ice-Shape Characteristic Dimensions.

NASA TM-107538 8
point, the maximum thickness, the maximum width of the ice accretion, the

impingement width, horn length and horn angle. These characteristics were all

measured on the main ice shape. Downstream of the primary glaze ice shape is a

region in which rime feathers form. The features of these feathers vary considerably

from test to test and from one location to another on the model. Because of this

variability, the feather region is ignored in comparing ice shapes. Measurements of

the characteristic dimensions were made by hand for this study.

Ice-ShapeRepeatability To be judged acceptable, scaling methods must

produce ice shapes that are similar to the reference shape within the typical shape

variability from run to run. To establish this variability, several test conditions were

repeated and the shapes compared. In Fig. 4 (a) are shown results for tests made in

October, 1995, December, 1995 and June, 1996 at the same tunnel conditions. In

J

(a) t, -12°C; V, 67 m/s; d, 30 _tm;

LWC, 1 g/m3; z, 7.3 min.

(b) t, -9°C; V, 89 m/s; d, 40 I.tm;

LWC, .55 g/m3; z, 10.0 min.

Figure 4. Repeatability of Ice Shapes. 53.3-cm-Chord NACA 0012 Airfoil.

Fig. 4 (b) are results from tests in October, 1995 and December, 1995 at another set

of conditions. The reference shape (October, 1995 test) is shown with a solid line in

both parts of the figure. Although small differences in ice shape are apparent from

this qualitative comparison, the IRT generally gives fairly repeatable ice shapes.

In addition to this subjective evaluation, a quantitative assessment of ice-shape

repeatability was also made.

Table 2. Variability of Six Characteristic

Ice-Shape Dimensions.

Ice Feature Average Percent Difference

from Mean Dimension

FiB. 4 (a) Fi_. 4 (b)

Stag. Thickness 8.7 11.4

Max. Thickness 2.8 5.2

Max. Width 10.4 6.6

Horn Length 0.4 4.2

Horn Angle 7.7 23.1

ImI_in_e. Width 9.4 13.7

The six characteristic

dimensions of the ice-shapes in

Fig. 4 were measured and

averages for each dimension

obtained separately for Fig. 4

(a) and Fig. 4 (b). The

difference between each

dimension and the average

value of that dimension was

then obtained. Finally, the

absolute values of these

differences were averaged and

NASA TM-107538 9
reported as a percent of the mean dimension in Table 2. For these two icing

conditions, the maximum thickness and horn length had the best repeatability, while

the stagnation-zone thickness, maximum ice-shape width, horn angle and

impingement width were less repeatable. Unfortunately, some judgement is still

required to determine some of these measurements. The impingement width, which

is dependent on the droplet trajectory, is often particularly difficult to define, and

this uncertainty was reflected in the relatively poor repeatability of this dimension.

Fortunately, scaling of droplet trajectories and impingement limits has been verified

both computationally and experimentally using temperatures above freezing [ 11,17].

It's reasonable to expect that the characteristic dimensions of an ice shape can be

defined better as more repeat data are available. In Table 2, for most dimensions, the

average deviation from the mean dimension was less when based on three ice shapes

(data from shapes in Fig. 4 (a)) than when only two ice shapes were used (results for

Fig. 4 (b)). Table 2 also indicates that most ice-shape characteristic dimensions are

repeatable to about +10%, with horn angle somewhat more difficult to repeat.

Ability to reconstruct most ice dimensions to within +10% is thus a reasonable goal

for scaling methods with somewhat more relaxed expectations to reproduce horn

angle.

EVALUATION OF THE SCALING METHODS

Scaling Liquid-Water Content Reference and scale ice shapes are compared in

Fig. 5 for the "LWC x time = constant" rule (Fig. 5 (a)) and for the Olsen scaling

(a) Scaling Using "LWC x time = Constant". (b) Scaling Using Olsen Method.

LWCxtime Olsen Parameters for Both Methods

t t V d LWC "¢

°C °C m/s _tm g/m 3 min

Reference -12 -12 67 30 1.00 7.3

u Scaled to .8 Ref. LWC -12 -10 67 30 .80 9.1

...... Scaled to 1.4 Ref. LWC -12 -15 67 30 1.40 5.2

Figure 5. Scaling Liquid-Water Content. 53.3-cm-Chord NACA 0012 Airfoil.

method (Fig. 5 (b)). In each case, the reference test (solid line) was performed with

a liquid-water content of 1 g/m 3, and scale tests were made with LWC's of .8 and 1.4

NASA TM-107538 10
Table 3. Quantitative Evaluation of "LWC x time = Constant" and Olsen Scaling Methods. Reference

LWC, 1.0 g/m3; Scale LWC, .8 and 1.4 g/m 3.

Ice Feature Percent Difference from Reference

LWC x Time Olsen

.8 g/m 3 1.4 _/m 3 .8 _/m 3 1.4 g/m 3

Stag. Thickness 10.0 -20.0 0.0 5.0

Max. Thickness 5.7 - 17.1 0.0 -4.3

Max. Width -17.0 30.1 11.3 -1.9

Horn Length 0.0 4.6 -2.8 -0.9

Horn An_le -43.5 39.1 -4.4 0.0

g/m 3. In this test series,

both methods of scaling

produced an ice shape

which simulated the

reference shape fairly

well when the liquidwater content was

reduced to .8 g/m 3, but

the Olsen method gave

a superior match when

the scale LWC was

increased to 1.4 g/m 3.

The ice shapes shown in Fig. 5 were analyzed quantitatively, and the results are

reported in Table 3. Because of the difficulty in defining the impingement width,

this dimension will not be included. With the exception of the horn angle, the scaled

dimensions resulting from using the "LWC x time = constant" method were close to

being within the acceptable limit of +10% of the reference dimensions when the

liquid-water content was scaled from 1 to .8 g/m 3. However, for the 1.4-g/m 3

scaling case, this method produced an ice shape with dimensions significantly

different from the reference.

The Olsen method provided scaled shapes whose dimensions closely matched the

reference for both scaling cases. The match of the horn angle produced by the Olsen

method is particularly notable. The formation of horns depends on the dynamics of

liquid water on the surface of the ice accretion. The success of the Olsen method

over the "LWC x time = constant" method indicates that the freezing fraction,

matched to the reference value by the Olsen method, is of greater importance in

determining final ice shape than the air-energy or water-energy transport terms,

which are matched by the "LWC x time = constant" method.

Scaling Size Results of tests with size scaled to Y2 the reference value are shown in

Fig. 6. The solid line in each part of the figure represents the reference ice shape

which was the same for each scaled test. The dotted-line shape is the scaled result.

Both the Ruff and the constant-We methods gave liquid-water contents for the Y2-

scale conditions which were outside the range of the operating map for the IRT;

consequently, the LWC for the scale tests was selected to be 0.8 g/m 3, and Olsen

scaling was applied to maintain the same freezing fraction as the reference test.

Thus, both size scaling and LWC scaling were combined for this evaluation.

Because the IRT does not provide control over the test-section pressure, the

modified form of the Ruff method was used. The results in Fig. 6 (a) show that the

scale ice shape was of similar size to the reference although, qualitatively, the

stagnation thickness and horn location were slightly different. The ice tracings

shown in Fig. 6 (b) for the constant-We scaling conditions appear to match the

NASA TM-107538 I 1
(a) Scaling Using Ruff (Mod) Method.

Reference

...... Ruff Method

...... Constant-We Method

(b) Scaling Using Constant-We Method.

c t V d LWC z

cm °C m/s lxm g/m 3 min

53.3 - 12 67 30 1.00 7.3

26.7 -8 67 20 .80 4.6

26.7 -10 88 18 .80 3.5

Figure 6. Model Size Scaled to V2Original Chord. NACA 0012 Airfoils.

Table 4. Quantitative Evaluation of Modified

Ruff and Constant-We Methods for

V2-Size Scaling. Test Conditions

Given in Fig. 6.

Ice Feature Percent Difference from

Reference

Ruff (Mod) Const-We

Stag. 25.0 25.0

Thickness

Max. - 17.1 -5.7

Thickness

Max. Width -22.6 -18.9

Horn Length - 14.8 - 13.0

Horn An_le 52.2 39.1

major importance to icing physics.

reference shape slightly better.

The quantitative comparison of

the dimensions shown in Table 4

show that the constant-We method

provided agreement with the

reference shape which was only

slightly better than that for the

modified Ruff method for this

case. Because the constant-We

method places more restrictions

on the scaling conditions, it's not

surprising that it was fairly

successful; however, the fact that

the Ruff method, which ignores

We, was relatively successful

suggests that We may not be of

Clearly, there is opportunity for additional

improvement in icing scaling by better understanding the phenomena involved in the

ice-accretion process.

CONCLUDING REMARKS

This paper described the theoretical background leading to the development of four

icing scaling methods. The phenomenological basis for current scaling technology

was presented and compared to the classical approach using the Buckingham-_

NASA TM-107538 12
methodology.Teststo evaluatethesescalingmethodswereconductedin the Icing

ResearchTunnelat NASA LewisResearchCenter,andresultswerepresented.The

"LWC x time = constant"andOisenmethodscanbe usedto scaletest conditions

while theconstant-WeandmodifiedRuff methodsscaletestarticlesize. A method

to quantify the goodnessof the scale ice shapesbased on measuring six

characteristicdimensionswasproposed. Resultsfrom this quantitativeapproach

supplementedvisualcomparisonsperformedbyoverlayingtwo-dimensionaltracings

of theiceaccretion.Theconclusionsfromthisstudyaresummarizedbelow:

1. Quantitativeverificationof icing scalingmethodsis helpful in defining their

accuracyandincreasingconfidencein theiruse.

. When comparing the characteristic ice-shape dimensions from repeat conditions,

differences on the order of +10% can result if only two tests are compared.

Characteristics such as horn angle and impingement width are sometimes

difficult to define, resulting in large run-to-run deviations in these dimensions.

Improved definition of dimensions resulted from a greater number of samples.

. When liquid-water content was scaled using a full-size model, the Olsen method

produced better results than the "LWC x time = constant" method. The former

maintains the freezing fraction constant between reference and scaled conditions,

while the latter matches the water-energy-transfer and the air-energy-transfer

terms. This result suggests that the freezing fraction has a greater effect on ice

shape than the water- or air-energy-transfer terms.

. For scaling to V2 size at the conditions tested, the constant-We method produced a

slightly better match of ice shape than the modified Ruff method. Either of these

methods appeared to provide at least approximate scaling for 1/2-size models.

However, the relative success of the less-restrictive Ruff method suggests that

We may not be as important to ice-accretion physics as once thought. Additional

study of the parameters of most importance to the development of ice shapes is

needed to improve scaling methods further.

Several directions for future work are evident from these results. The quantitative

evaluation of ice accretion shapes appears to be a promising tool, but the observed

variation between any two repeat conditions showed that a large number of repeated

tests providing better statistics are required to perform more detailed evaluations of

icing scaling methods. Characteristics of the ice shape other than those discussed

here may also need to be considered for future quantitative evaluations. To improve

scaling methods, other parameters, such as Re, need to be examined to determine

their importance relative to We. Finally, parameters relevant to the dynamics of

liquid water on the surface of an ice accretion during the freezing process should be

identified and included in icing scaling methods.

NASA TM-107538 13
REFERENCES

[1]

[21

[31

[4]

[5]

[6]

[7]

[81

[9l

[10]

[11]

[12]

[13]

[14]

[15]

E.J. Sibley and R.E. Smith, Model Testing in an Icing Wind Tunnel, Report

LR10981, Lockheed Aircraft Corporation, California Division, (1955).

E.D. Dodson, Scale Model Analogy for Icing Tunnel Testing, Document no.

D6-7976, Boeing Airplane Company, Transport Division, (1962).

F. Charpin and G. Fasso, Icing Testing in the Large Modane Wind Tunnel

on Full Scale and Reduced Scale Models, L'Aeronautique et

l'Astronautique, no 38, (1972); English translation: NASA TM-75373.

M. Ingelman-Sundberg, O.K. Trunov, and A. Ivaniko, Methods for

Prediction of the Influence of Ice on Aircraft Flying Characteristics, Report

No. JR-l, Swedish-Soviet Working Group on Flight Safety, 6 th Meeting,

(1977).

G.A. Ruff, Analysis and Verification of the Icing Scaling Equations, AEDCTR-85-30, Arnold Engineering Development Center, Tullahoma TN (1986).

D.N. Anderson, Rime, Mixed- and Glaze-Ice Evaluations of Three Scaling

Laws, AIAA 94-0718, American Institute of Aeronautics and Astronautics,

Washington DC, and NASA TM 106461, NASA Lewis Research Center,

Cleveland OH, (1994).

A.J. Bilanin, Proposed Modifications to the Ice Accretion/Icing Scaling

Theory, AIAA-88-0203, American Institute of Aeronautics and Astronautics,

Washington DC, (1988).

A.J. Bilanin and D.N. Anderson, Ice Accretion with Varying Surface

Tension, AIAA-95-0538, American Institute of Aeronautics and Astronautics,

Washington DC, (1995).

F. Saeed, M.S. Selig and M.B. Bragg, A Design Procedure for Subscale

Airfoils with Full-Scale Leading Edges for Ice Accretion Testing, AIAA-96-

0635, American Institute of Aeronautics and Astronautics, Washington DC,

(1996).

F. Saeed, M.S. Selig and M.B. Bragg, A Hybrid Airfoil Design Method to

Simulate Full-Scale Ice Accretion Throughout a Given Ct Range, AIAA-96-

0635, American Institute of Aeronautics and Astronautics, Washington DC,

(1996).

M.B. Bragg, G.M. Gregorek and R.J. Shaw, An Analytical Approach to

Airfoil Icing, AIAA-81-0403, American Institute of Aeronautics and

Astronautics, Washington DC, (1981).

I. Langmuir and K.B. Blodgett, A Mathematical Investigation of Water

Droplet Trajectories, Technical Report No. 5418, Army Air Forces, (1946).

B.L. Messinger, Equilibrium Temperature of an Unheated Icing Surface as a

Function of Airspeed, J. Aeron. Sci., 20:29 (1953).

M. Tribus, G.B.W. Young and L.M.K. Boelter, Analysis of Heat Transfer

Over a Small Cylinder in Icing Conditions on Mount Washington, Trans

ASME, 70: 971, (1948).

W.A. Olsen, Jr., unpublished notes, NASA Lewis Research Center, (1989).

NASA TM-107538 14
[16] D.N. Anderson, Evaluation of Constant-Weber-Number Scaling for Icing

Tests, AIAA-96-0636, American Institute of Aeronautics and Astronautics,

Washington DC, and NASA TM 107141, NASA Lewis Research Center,

Cleveland OH, (1996).

[ 17] M.B. Bragg, A Similarity Analysis of the Droplet Trajectory Equations, AIAA

J., 20:12 (1982).

NASA TM-107538 15
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October 1997 Technical Memorandum

4. TffLEANDSUBTITLE

Scaling Methods for Simulating Aircraft In-Flight Icing Encounters

6. AUTHOR(S)

David N. Anderson and Gary A. Ruff

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

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NASA TM- 107538

11. SUPPLEMENTARY NOTES

Prepared for the Second International Symposium Scale Modeling sponsored by the International Scale Modeling Committee, Lexington, Kentucky, June 23-27, 1997. David N. Anderson, NASA Lewis Research Center, retired and Gary A. Ruff, Mechanical Engineering and Mechanics Department, Drexel University, Philadelphia, Pennsylvania 19104 and Summer Faculty Fellow at NASA Lewis

Research Center. Responsible person, Simon C. Chen, organization code 5840, (216) 433-3585.

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13. ABSTRACT (Maximum 200 words)

This paper discusses scaling methods which permit the use of subscale models in icing wind tunnels to simulate natural

flight in icing. Natural icing conditions exist when air temperatures are below freezing but cloud water droplets are supercooled liquid. Aircraft flying through such clouds are susceptible to the accretion of ice on the leading edges of unprotected components such as wings, tailplane and engine inlets. To establish the aerodynamic penalties of such ice accretion

and to determine what parts need to be protected from ice accretion (by heating, for example), extensive flight and windtunnel testing is necessary for new aircraft and components. Testing in icing tunnels is less expensive than flight testing, is

safer, and permits better control of the test conditions. However, because of limitations on both model size and operating

conditions in wind tunnels, it is often necessary to perform tests with either size or test conditions scaled. This paper

describes the theoretical background to the development of icing scaling methods, discusses four methods, and presents

results of tests to validate them.

14. SUBJECT TERMS

Icing; Scaling; Aircraft safety

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