PREDICTION OF AERODYNAMIC PENALTIES CAUSED BY

ICE FORMATIONS ON VARIOUS AIRFOILS

By Vernon H. Gray

Lewis Research Center

Cleveland, Ohio

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

For sale by the Office of Technical Services, Department of Commerce,

Washington, D.C. 20230 -- Price $0.50

ri1

PREDICTION OF AERODYNAMIC P_ALTIES CAUSED BY

ICE FORMATIONS ON VARIOUS AIRFOILS*

SUMMARY

An empirical equation is developed by which changes in drag coefficients due

to ice formations on an NACA 85A004 airfoil may be calculated from known icing

and flight conditions; this equation is then extended to include available data

for other airfoils with thickness ratios up to 15 percent. The correlation was

obtained primarily by use of ice heights and ice angles measured on the

4-percent-thick airfoil. The final equation, however, does not include the ice

measurements, but relates changes in drag coefficients due to ice with the fol-

lowing variables: icing time, airspeed, air temperature, liquid-water content,

cloud-droplet-impingement efficiencies, airfoil chord, angles of attack, and

leading-edge radius of curvature.

Changes in lift and pitching-moment coefficients due to ice on an NACA 0011

airfoil are also related to the corresponding changes in drag coefficients; addi-

tional data on lift and pitching-moment changes due to ice are limited to the

65A004 airfoil, for which complex trends preclude a general relation within the

scope of this report.

INTRODUCTION

In the decade of the 1950's, much information about airfoil icing character-

istics and the resultant aerodynamic penalties was acquired by the NACA. This

information was obtained for the following airfoils shown in figure l: 65AOOA,

65A009, 0011, 651-212 , and 652-015. These airfoils have thickness ratios of

percent (ref. 1), 9 percent (ref. 2), ii percent (ref. 3), 12 percent (ref. 4),

and 15 percent (unpublished data), respectively. In addition, a much larger

wealth of information concerning the cloud-droplet-impingement characteristics

for a variety of airfoils and body shapes has been published. Unfortunately, de-

spite these data, very little direct correlation has heretofore been shown be-

tween the aerodynamic penalties due to ice formations, the shape and location of

*The material contained herein was presented as a paper at the SAE National

Aeronautic Meeting, Los Angeles, California, October A, 1957, under the title

"Correlation of Airfoil Ice Formations and Their Aerodynamic Effects with

Impingement and Flight Conditions." It is now being published because of present

interest in icing protection for light aircraft (CAR-3) and helicopters.

ice formations, and the impingement conditions that produce the ice. Impingementcalculations do not quantitatively foretell the size or shape of ice that willform under given conditions, nor are the published aerodynamic penalties relatedto the actual ice size and shape except in a gross way. Furthermore, it is verydifficult to estimate aerodynamic penalties in icing conditions different fromthose specifically investigated for a particular airfoil.

A review of the aerodynamic data from these previous icing studies showedthat, to understand the effects of ice on airfoil characteristics, it would benecessary to study the exact ice shapes and sizes and to relate the aerodynamiceffect of the ice to the knowneffects produced by surface roughness, flowspoilers, leading-edge flaps, etc., which ice simulates. Such a study was accom-plished with icing data for the NACA65A00_airfoil section shownin figure i(ref. 5). In this study, a variety of ice shapes was accurately measuredand re-lated to the generating impingement and icing conditions. The changes in airfoildrag coefficients due to ice were then correlated with the ice shapes and, fi-nally, with impingement and flight conditions. The object of this report is todescribe this analysis of icing data for the 4-percent-thick airfoil and to ex-tend it to include all the airfoil sections for whic_ aerodynamic data in NACAicing tunnel conditions are available.

This investigation w_s conducted in the NACALewis 6- by 9-foot icing tunnelover the following ranges of variables:

Airfoil thickness ratio, percent .................... 4 to iSAirfoil angle of attack, deg ...................... 0 to 12Air velocity, mph .......................... up to 280Air total temperature, oF ....................... 0 to 50Liquid-water content, g/cu m ................ 0.25 to 2.0Volumemedian droplet diameter, microns ................ 7 to 19Icing time, min ............................ up to 27Pressure altitude, ft .......................... <ZS00

Increases in cloud liquid-water content were accompaniedby increases in thedroplet size because of the tunnel spray-system design.

ANALYSISOFICE SHAPE

The correlation of the aerodynamic effects of ice with its size and shaperequired accurate measurementof these factors. The measurementswere madeac-cording to the following techniques. A typical photograph of the cross sectionof an ice formation at a 6° angle of attack is shorn in figure 2. After an icingrun, the ice on the airfoil was removedby a steam-heated ice scraper except fora narrow band in a chordwise plane normal to the surface. The camera wasposi-tioned near the airfoil leading edge and directed spanwise nearly parallel to theleading edge. A black i/4-inch-mesh wire grid was placed against the ice to pro-vide a scale of measurement,and a white wire of the screen was alined to be anextension of the airfoil chordline. A point plotting procedure was used with thephotographs to obtain two-dimensional cross sections of the various ice forma-tions (inset of fig. 2).

2

For purposes of analysis, all the cross sections of ice deposits on the _-percent-thick airfoil section were reduced to two significant dimensions, h ande, as shownin figure 5. Dimension h is the height of the edge of the icefirst reached in going from the upper to the lower surface. The angle @ ismeasuredbetween this ice edge and the extended chord line. The angle is posi-tive if the ice edge is above the chord line and negative if the ice edge fallsbelow the extended chord line.

Representation of ice formations by only these two dimensions ignores thepart of the ice on the lower surface of the airfoil. Generally, however, protu-berances on this region contribute very little drag to the airfoil, except near0° angle of attack. In contrast, flow spoilers near the leading edge and towardthe upper surface cause large drag increases.

It was found that the dimensions @ and h could each be empirically cor-related with the icing test conditions. The resulting correlation for ice angle@,measuredprimarily on the A-percent-thick airfoil, is shownin figure 4.(Symbols are defined in the appendix.) In the abscissa of figure 4 the angleis modified by a term that accounts for the airfoil geometric angle of attack atwhich the ice was formed _i" The ordinate is a parameter accounting for liquid-water content w, air total_ temperature t0_ and airfoil total droplet-impingement efficiency Em. Although considerable scatter of data points exists,the exponents and coefficients of the variables were each adjusted until an equaland minimumscattering of data about an average straight line was obtained.

A convenient scale for classifying the ice formations as rime or glaze iceis provided by figure 4. The point of demarcation between observed rime andglaze ice deposits lies approximately at a value of 52 on the abscissa scale.Ice formations that plot to the left of this point are progressively more rime-like and those to the right are progressively more glazelike. Thus, use of theice-angle scale in reporting icing conditions or ice types should be more differ-entiating than use of the general terms rime and glaze.

The ice height h was correlated in a manner similar to that for the anglee, and the result is shownin figure 5. The ice height h was found to va_ryap-proximately linearly with icing time T and air velocity VO. The term _m inthe icing parameter of figure 5 is the maximumlocal droplet-impingement effi-ciency for the airfoil and usually occurs very near the leading edge.

Although the correlations developed for e and h in figures _ and 5 werebased on data for a 6-foot-chord NACA65A00_airfoil, the relations agree remark-ably well with limited unpublished icing data obtained on cylinders and struts ofless than 1-inch chord size. Therefore, the correlations given for ice heightand angle should be valid for a considerable range of airfoil shapes and sizes.Thus, with h and e predictable, and provided airfoil impingement data areavailable for determining surface limits of impingement (e.g., see ref. 6), theaerodynamically significant features of an ice formation can be composedby cal-culation.

CORREI_TIONBETWEENICE SHAPEANDDRAG

Changesin drag coefficients due to ice formations on the _-percent-thick

airfoil section were analyzed on the basis of the ice acting as a leading-edgeflap or spoiler. A correlation was obtained utilizing the relations developed infigures _ and 5 for _ and h, respectively. This correlation is shownin fig-ure 6. The abscissa of figure 6 is the ice angle _ as determined from theequation of the line given in figure 4. The ordinate of figure 6 is the changein drag coefficient caused by various ice formations corrected to a commonheightequal to I percent of chord f_ZdC/100h, where hCd is the change in the drag co-efficient from the clean airfoil value due to the addition of ice and c is theairfoil chord. As shown in the ordinate of figure 6_ the dimension h is deter-mined from the equation of the line given in figure 5; as a result, figure 6 nowexpresses the drag changes due to ice in terms that are either knownor calcula-ble in a design or flight performance study.

For clarity_ the data points are not shownin figure 6, but instead, themeancurves that describe the trends. Included in the data are several cases inwhich ice was formed at an angle of attack _i and the airfoil was then changedto an angle _, for which Cd was measured_and ACd was obtained from theclean airfoil drag coefficient at angle _. Thesedata alined themselves verywell with the balance of the data taken at fixed angles of attack and thus cor-roborated the usefulness of e in correlating ACd.

Strikingly evident in figure 6 are the reductions in drag coefficients withice on the airfoil at high angles of attack and low ice angles (rime icing).These drag reductions below the clean airfoil values are possible because of thehigh drag coefficients associated with flow separation from thin airfoils withsharp beading edges. The addition of rime ice at the higher angles of attack mayat times add bluntness to the airfoil and form a drooped leading edge that as-sists the flow over the airfoil nose and reduces the amount of flow separationfrom the upper surface. Under glaze icing conditions, however_ the ice acts asa flow spoiler and always increases the airfoil drag coefficients.

Changesin drag coefficients due to ice are shownin figure 6 for each ofthe geometric angles of attack investigated. An equation has been developed thatagrees with the 4-percent-thick airfoil data of figure 6 and that accounts forvariations in the angles of attack from 0° to 12° . This equation is as follows:

Tv°AC d _ 8.7×10 -5

c--w_m (32- to)0"31 _ + SIl + 2 sin_12_)

- 81 + 65.3I i i I]- 1.7 sin411_l

CL.I. 35 m i. 35_

(1)

The term in the first bracket of equation (i) accounts for the height to chord

ratio of the significant ice formation, and terms in the last bracket account forthe ice angle, the angle of attack, and the formation of ice at an angle of at-tack different from that under consideration. This last term vanishes when iceis formed at the samegeometric angle of attack as that being considered (_i =_)"In the sin 2 function in the last bracket of equation (i), the expression

543 V_ tn] - 81 is valid between the limits 0 and 180_ beyond theselimits, a value of zero should be used for the expression instead of a calculatednumber.

PREDICTIONOFDRAGCHANGESDUETO ICE ONVARIOUSAIRFOILS

Becauseequation (i) for approximating the drag-coefficient changes due toice on an NACA65A004airfoil was determined, it was desirable to attempt a simi-lar relation for other airfoils, although ice measurementswere available onlyfor the 4-percent-thick airfoil. Accordingly, all the applicable NACAicing dragdata from references 2 to 4 were inserted into equation (i) for trial, and im-pingement parameters were interpolated from data of reference 6. These icingdata are listed in table I. It _as found that an airfoil thickness trend ap-peared; to account for this trend, a factor r was introduced, which is the air-foil leading-edge radius of curvature in percent of chord. Also, in the absenceof more knowledge as to the effect of sweepon drag due to ice formations, the63A009airfoil (sweep angle, 36°) was regarded for correlation purposes as an un-swept two-dimensional Airfoil, except that impingement, chord length, and radiusof curvature were taken for the streamwise cross section of the airfoil.

A final equation was derived that represents the available icing drag dataof the referenced airfoils and that is consistent with equation (i) for the4-percent-thick airfoil:

TV0ACd _ 8.7xi0 -5 --C

w_m (32- to)0'3] _ + 6{i + 2.$2 r0"I sin412_)

i.3S _i i. 0.17r sin411_ll

(z)

Measured values of AC d from table I and reference 5 are plotted in figure 7against the values calculated by using equation (2). The order of agreement

shown in figure 7 appears quite satisfaetory_ considering the nature and diffi-

culty of obtaining aerodynamic; impingement; and meteorological data in icing

conditions.

S

ESTIMATIONOFLIFT ANDPITCHING-MOMENTCOEFFICIENTS

Unfortunately, changes in lift and pitching-moment coefficients due to iceformations are knownonly for NACA0011 (ref. 3) and 65A004 (ref. i) airfoils.In addition to these data, however, it should be possible to estimate changes inlift and momentcoefficients by utilizing relations in the published aerodynamiccharacteristics of airfoils with and without flaps, spoilers, protuberances, etc.

From the limited data available in icing conditions, it appears that changesin lift and momentcoefficients due to ice formations can be related to the con-current changes in drag coefficients for a thick, blunt airfoil such as the 0011airfoil, whereas no systematic relation is readily apparent for a thin, sharp-nosed airfoil such as the 65A004airfoil. The relations between changes in lift,moment,and drag coefficients due to ice on the 0011 airfoil are shownin fig-ure 8 as functions of geometric angle of attack (data of ref. 3). Well-established trends are evident in figure 8, wherein increases in drag coeffi-cients are accompaniedby similar increases in momentcoefficients and by de-creases in lift coefficients of generally larger magnitude. These trends aresimilar to the trends with the 65A004airfoil, but only up to angles of attack ofabout 3° . At higher angles of attack, changes in lift and momentcoefficientsdue to ice on the 4-percent-thick airfoil were erratic with respect to changes indrag coefficients, primarily because of the flow separation from the upper sur-face starting at an angle of attack of about 4° (ref. i).

EXAMPLEOFUSEOFCORRELATION

To illustrate how the preceding correlations maybe used to assess the mag-nitudes of aerodynamic penalties for various airfoils in icing conditions, thefollowing hypothetical icing encounters will be evaluated:

Flight and icing conditions

AirfoilChord, in.Angle of attack, a degAirspeed, mphPressure altitude, ftAir total temperature, OFLiquid-water content, g/cu mVolumemedian droplet diameter, micronsDuration in icing, minClean airfoil drag coefficient a

Icing encounter

A

65A004

96

2

500

8000

25

0.5

15

4

O. 0067

B

651-212240

2

300

8000

I0

0.5

15

7

O. 0088

aCorresponding to tunnel geometric angle of attack

(uncorrected).

From references 5 and 6 the following impingement parameters may be determined:

i

Parameter

Modified inertia parameter, K0

Maximum local droplet impingement

efficiency, _m

Total droplet impingement

efficiency, Em

Icing encounter

A B

0.0179 0.00515

0.67 O. 35

0.18 0. 033

Substitution of the preceding values in equation (2) yields the following:

Change in drag coefficientdue to ice

Change from clean airfoil drag

coefficient, percent increase

Icing encounter

A

0.0051

76

B

0.0008

9

If the airfoil angle of attack is increased in a maneuver in clear air up to

8° with the ice formations that accumulated during the preceding encounters at 2°

angle of attack remaining where they were formed, the following results are ob-

tained by use of equation (2):

Angle of attack at which ice

was formed, deg

Angle of attack during clear

air maneuver, deg

Change in drag coefficient

due to ice

Clean airfoil drag coefficient

(at8°)Change from clean airfoil drag

coefficient, percent increase

Icing encounter

A B

2 2

8 8

0.0127 0.0041

0.119 0.0127

10.7 Z2.3

The 651-212 airfoil of encounter B is similar in shape to an NACA 0011 air-

foil, so that the relations in figure 8 may be used to estimate %he changes in

lift and pitching-moment coefficients due to ice accumulated in icing encounter

B. These changes were determined from the corresponding changes in drag coeffi-

cients previously enumerated and the ratio factors shown in figure 8. The fol-

lowing results were obtained:

Changein lift coefficientChangein momentcoefficientClean airfoil lift coefficient

(typical)Clean airfoil momentcoefficient(typical)

Change from clean airfoil lift

coefficient, percent decrease

Change from clean airfoil moment

coefficient_ percent increase

(less negative)

Angle of attack, deg

-0. 0009

O. 000_

O. 55

-0. 055

0.26

!.i

-0.025

O. 005

1.02

-0.04

2.5

12.5

Changes in lift and pitching-moment coefficients due to ice formations on the

6SA00_ airfoil of encounter A are not obtainable from the present correlation,

but must be estimated from data of reference i and related aerodynamic studies

of leading-edge spoilers, flaps, etc.

The foregoing examples are typical of calculations that must be made for

several representative icing encounters to assess fully the flight penalties due

to ice and the need for ice-protection equipment.

CONCLUSIONS

It should be noted in conclusion that this correL_ion is a first-order ap-

proximation of the presently available aerodynamic and icing data for airfoils

exposed to icing conditions in the NACA icing tunnel. Several factors that were

thought to be secondary in importance were ignored in this analysis. The corre-

lation should be useful, however, in estimating the type and size of ice forma-

tions that would result from any specified icing encounter, in estimating the

aerodynamic penalties that would result from an encounter, and in making flight

performance studies in which icing effects must be evaluated.

Lewis Research Center

National Aeronautics and Space Administration

Cleveland, Ohio, October 25, 1985

8

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APPENDIX - SYM_0LS

airfoil section drag coefficient

change in section drag coefficient due to ice

change in section lift coefficient due to ice

change in section pitching-moment coefficient (about the quarter-chord

point) due to ice

airfoil chord length, in.

total droplet-impingement efficiency (see refs. 5 and 6)

height of ice, in. (see fig. 3)

modified inertia parameter (see refs. 5 and 6)

radius of curvature of airfoil leading edge, percent of chord

free-stream total air temperature, OF

free-stream velocity, mph, or knots x 1.15

liquid-water content of cloud, g/cu m

airfoil geometric angle of attack (uncorrected for tunnel walls), deg

airfoil geometric angle of attack at which ice deposit is formed (uncor-

rected for tunnel walls), deg

maximum local droplet-impingement efficiency (see refs. 5 and 6)

ice angle, deg (see fig. 3)

icing time, min

9

REFERENCES

i. Gray, Vernon H., and yon Glahn, UweH.: Aerodynamic Effects Causedby Icingof an Unswept NACA65A004Airfoil. NACATN 4155, 1958.

2. von Glahn, UweH., and Gray, Vernon H.: Effect of Ice Formations on SectionDrag of SweptNACA63A-009Airfoil with Partial-Span Leadlng-Edge Slat forVarious Modesof Thermal Ice Protection. NACARME53J30, 1954.

3. Bowden,DeanT.: Effect of Pneumatic De-Icers and Ice Formations on Aerody-namic Characteristics of an Airfoil. NACATN 356_, 1956.

4. Gray, Vernon H., and yon Glahn, UweH.: Effect of Ice and Frost Formationson Drag of NACA651-212 Airfoil for Various Modesof Thermal Ice Protection.NACATN 2962, 1953.

5. Gray, Vernon H.: Correlations Among Ice Measurements, Impingement Rates,

Icing Conditions and Drag Coefficients for an Unswept NACA 65A004 Airfoil.

NACA TN 4151, 1958.

6. Gelder, Thomas F., Smyers, William H., Jr._ and yon Glahn, Uwe H.: Experimen-

tal Droplet Impingement on Several Two-Dimensional Airfoils with Thickness

Ratios of 6 to 16 Percent. NACA TN 3839, 1956.

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NASA-Langley, 1964 E-2524 19