nasa technical nasa tm x-3160

AND

NASA TECHNICAL NASA TM X-3160MEMORANDUM

I

-

(N ASA-TM-X- 3160) EXPERIMENTAL AND N75- 1560 1

THEORETICAL LOW SPEED AERODYNAMIC

CHARACTERISTICS OF THE NACA 65 SUB 1-213,

ALPHA EQUALS 0.50, AIRFOIL (NASA) 74 p HC Unclas

4.25 CSCL 01A H1/01 09062

EXPERIMENTAL AND THEORETICAL LOW-SPEED

AERODYNAMIC CHARACTERISTICS OF

THE NACA 651-213, a = 0.50, AIRFOIL

William D. Beasley and Robert J. McGhee

Langley Research Center

Hampton, Va. 23665

6 ATIONA ARONATIANDSPA ADMINISTRATION WASHINGTON D. FEBRUARY 91

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION " WASHINGTON, D. C. . FEBRUARY 1975

1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.

NASA TM X-31604. Title and Subtitle 5. Report Date

EXPERIMENTAL AND THEORETICAL LOW-SPEED February 1975AERODYNAMIC CHARACTERISTICS OF THE 6. Performing Organization CodeNACA 651-213, a = 0.50, AIRFOIL

7. Author(s) 8. Performing Organization Report No.

William D. Beasley and Robert J. McGhee L-9773

10. Work Unit No.

9. Performing Organization Name and Address 505-06-31-01NASA Langley Research Center 11. Contract or Grant No.Hampton, Va. 23665

13. Type of Report and Period Covered

12. Sponsoring Agency Name and Address Technical Memorandum

National Aeronautics and Space Administration 14. Sponsoring Agency Code

Washington, D.C. 20546

15. Supplementary Notes

16. Abstract

Low-speed wind-tunnel tests have been conducted to determine the two-dimensional

aerodynamic characteristics of the NACA 651-213, a = 0.50, airfoil. -The results were

compared with data from another low-speed wind tunnel and also with theoretical predic-

tions obtained by using a viscous subsonic method. The tests were conducted over a Mach

number range from 0.10 to 0.36. Reynolds numbers based on the airfoil chord varied from

about 3.0 x 106 to 23.0 x 106

17. Key Words (Suggested by Author(s)) 18. Distribution Statement

Low-speed airfoil data Unclassified - Unlimited

Reynolds number effects

Experimental-theoretical comparisonSTAR Category 01

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price*

Unclassified Unclassified 74 $4.25

For sale by the National Technical Information Service, Springfield, Virginia 22151

EXPERIMENTAL AND THEORETICAL

LOW-SPEED AERODYNAMIC CHARACTERISTICS OF THE

NACA 651-213, a = 0.50, AIRFOIL

By William D. Beasley and Robert J. McGhee

Langley Research Center

SUMMARY

An investigation was conducted in the Langley low-turbulence pressure tunnel

to determine the low-speed two-dimensional aerodynamic characteristics of the

NACA 651-213, a = 0.50, airfoil. The results are compared with data from another

low-speed wind tunnel and also with theoretical predictions obtained by using a subsonic

viscous method. The tests were conducted over a Mach number range from 0.10 to 0.36

and an angle-of-attack range from -100 to 200. Reynolds numbers, based on the airfoil

chord, were varied from about 3.0 x 106 to 23.0 x 106.

The results of the investigation showed that the maximum section lift coefficient

at a constant Mach number of 0.22 increased rapidly as Reynolds number increased

from about 3.0 x 106 to 9.0 x 106 and attained a value of about 1.7 at 9.0 x 106; further

increases in Reynolds number had only small effects on the maximum section lift coeffi-

cient. The stall was abrupt below Reynolds numbers of about 9.0 x 106 and gradual at

higher Reynolds numbers. The application of a narrow roughness strip near the leading

edge resulted in only small effects on the lift characteristics at a Reynolds number of

about 6.0 x 106, whereas extensive roughness wrapped around the leading edge forward

of 5-percent chord resulted in a decrease in maximum section lift coefficient of about

13 percent. Increasing the Mach number at a constant Reynolds number of about 6.0 x 106

was found to have large effects on the maximum section lift coefficient as a result of the

flow over the airfoil becoming supercritical and the maximum section lift coefficient

decreased about 30 percent when the Mach number was increased from 0.10 to 0.36. Sec-

tion lift and pitching-moment coefficients obtained at low Reynolds numbers for the smooth

airfoil were in good agreement with results from another low-speed wind tunnel; however,

there were differences in drag coefficients in the lift coefficient range where the laminar

bucket would be expected. Comparisons of experimental section lift coefficients, pitching-

moment coefficients, and chordwise pressure distributions with those calculated from a

viscous flow theoretical method were good as long as no boundary-layer flow separation

was present; however, the theoretically calculated drag coefficients were generally less

than the experimental drag coefficients.

INTRODUCTION

Research on both advanced technology and conventional airfoils has received con-

siderable attention over the last several years at the Langley Research Center. Partic-

ular emphasis has been placed on obtaining data at high Reynolds numbers to study the

shock-wave boundary-layer interaction phenomena and to compare results measured in

various ground test facilities. The present investigation was conducted to obtain the

basic low-speed two-dimensional aerodynamic characteristics of the NACA 651-213 air-

foil over a broad range of Reynolds numbers. In addition, the experimental results have

been compared with theoretical data obtained by using a viscous subsonic prediction

method. The NACA 651-213 airfoil was selected to be representative of conventional

airfoils because of the existence of flight data and wind-tunnel data obtained in various

research facilities.

The investigation was performed in the Langley low-turbulence pressure tunnel

over a Mach number range from 0.10 to 0.36. The Reynolds number, based on airfoil

chord, varied from about 3.0 x 106 to 23.0 x 106. The geometrical angle of attack varied

from about -100 to 200. The operational characteristics and a new calibration of the

tunnel are presented in an appendix.

SYMBOLS

Values are given in both SI and the U.S. Customary Units. The measurements and

calculations were made in the U.S. Customary Units.

a mean-line designation

PL-PCp pressure coefficient,qo

Cp,critical critical pressure coefficient equivalent to a local Mach number of unity

c airfoil chord, cm (in.)

cc section chord-force coefficient,

CP d() - CP d)Forward(t/c)max Cp Aft(t/)ma

Cd section profile-drag coefficient, Wake d(h)

cd point drag coefficient, 2 \ 11 12 P" /2 q

2

cI section lift coefficient, Cn cos a - cc sin a

cm section pitching-moment coefficient about quarter-chord point

Cp (0.25 - ) d) - Cp 0.25 - d

c, section normal-force coefficient, s. C d() - pu.s. d()

h vertical distance in wake profile, cm (in.)

M free-stream Mach number

p static pressure, N/m 2 (lb/ft2)

q dynamic pressure, N/m 2 (lb/ft2 )

R Reynolds number based on free-stream conditions and airfoil chord

t airfoil thickness, cm (in.)

x airfoil abscissa (see fig. 1), cm (in.)

z airfoil ordinate (see fig. 1), cm (in.)

a geometric angle of attack, deg

p density, kg/m 3 (slugs/ft3)

Subscripts:

L local point on airfoil

max maximum

min minimum

1 tunnel station 1 chord length downstream of model

3

2 tunnel station downstream of model where static pressure is equal to free-

stream static pressure and total pressure is assumed equal to total

pressure at station 1

undisturbed stream conditions

Abbreviations:

1.s. lower surface

u.s. upper surface

MODEL, APPARATUS, AND PROCEDURE

Model

The development of the NACA 6 series airfoils is discussed in detail in reference 1.

The NACA 651-213, a = 0.50, section was obtained by linearly increasing the basic

thickness distribution of the NACA 651-012 airfoil and combining this thickness distri-

bution with the a = 0.50 mean camber line for a design lift coefficient of 0.20. The

nose radius was increased as the square of the thickness ratio. The airfoil section

shape is shown in figure 1, and table I presents the measured airfoil coordinates.

The airfoil model was machined from an aluminum billet and had a chord of

60.63 cm (23.87 in.) and a span of 91.44 cm (36 in.). The model was equipped with both

upper and lower surface midspan orifices located at the chord stations indicated in

table II. Grooves were machined in the surface of the aluminum model and pressure

tubing was routed in the grooves to desired orifice locations. The tubes were potted in

place with a plastic resin and orifices were drilled through the plastic into the tubing.

The plastic was then machined to reform to the original surface and the airfoil surface

was hand polished in the chordwise direction with number 400 silicon carbide paper to

provide a smooth aerodynamic finish.

Wind Tunnel

The Langley low-turbulence pressure tunnel (ref. 2) is a closed-throat, single-

return tunnel which can be operated at stagnation pressures from 1 to 10 atmospheres

with tunnel-empty test-section Mach numbers up to 0.42 and 0.22, respectively. The

maximum unit Reynolds number is about 49 x 106 per meter (15 x 106 per foot) at a

Mach number of about 0.22. The tunnel test section is 91.44 cm (3 ft) wide by

228.6 cm (7.5 ft) high. Operational characteristics and results of a new calibration of

the tunnel are included in the appendix.

4

Hydraulically powered circular plates provided positioning and attachment for the

two-dimensional model. The plates are 101.60 cm (40 in.) in diameter, rotate with the

airfoil, and are flush with the tunnel wall. The airfoil ends were attached to rectangular

model attachment plates (fig. 2) and the airfoil was mounted so that the center of rotation

of the circular plates was at 0.25c on the model chord line. The air gaps at the tunnel

walls between the rectangular plates and circular plates were sealed with flexible sliding

metal seals, shown in figure 2.

Wake Survey Rake

A fixed wake survey rake (fig. 3) at the model midspan was cantilever mounted

from the tunnel sidewall and located 1 chord length behind the trailing edge of the airfoil.

The wake rake utilized 91 total-pressure tubes, 0.1524 cm (0.060 in.) in diameter, and

five static-pressure tubes, 0.3175 cm (0.125 in.) in diameter. The total-pressure tubes

were flattened to 0.1016 cm (0.040 in.) for 0.6096 cm (0.24 in.) from the tip of the tube.

The static-pressure tubes each had four flush orifices drilled 900 apart and located 8 tube

diameters from the tip of the tube and in the measurement plane of the total-pressure

tubes.

Instrumentation

Measurements of the static pressures on the airfoil surfaces and the wake rake

pressures were made by an automatic pressure-scanning system utilizing variable-

capacitance-type precision transducers. Basic tunnel pressures were measured with

precision quartz manometers. Angle of attack was measured with a calibrated digital

shaft encoder operated by a pinion gear and rack attached to the circular plates. Data

were obtained by a high-speed data-acquisition system and recorded on magnetic tape.

TESTS AND METHODS

The airfoil was tested at Mach numbers from 0.10 to 0.36 over an angle-of-attack

range from about -100 to 200. Reynolds number based on the airfoil chord was varied

from about 3.0 x 106 to 23.0 x 106.

Most of the roughness data were obtained with standard NASA type strips located

at x/c = 0.05 on both upper and lower surfaces. The strips were 0.25 cm (0.10 in.)

wide over the airfoil span and the carborundum grains were sparsely spaced and attached

to the airfoil surface with clear lacquer. The roughness was sized according to refer-

ence 3 and the size required for each Reynolds number is listed in table III. A limited

comparison of roughness techniques was made for the selected test condition of

M = 0.15 and R = 5.9 x 106 by utilizing a sparse distribution of number 60 grains in

5

the forms of a strip and extensive roughness wrapped around the leading edge. The strips

were 0.25 cm (0.10 in.) wide and located at x/c = 0.04, whereas the wraparound extended

from the leading edge to x/c = 0.04 over both surfaces.

For several test runs oil was spread over the airfoil upper and lower surfaces to

determine whether any local flow separation was present. Tufts were attached to the

airfoil and tunnel sidewalls with plastic tape to determine stall patterns on both the air-

foil and adjacent tunnel sidewalls.

The static-pressure measurements at the airfoil surface were reduced to standard

pressure coefficients and machine integrated (based on the trapezoidal method) to obtain

section normal-force and chord-force coefficients and section pitching-moment coeffi-

cients about the quarter chord. Section profile-drag coefficient was computed from the

wake-rake total and static pressures by the method reported in reference 4 and machine

integrated by use of the trapezoidal method.

An estimate of the standard low-speed wind-tunnel boundary corrections (ref. 5)

amounted to about 2 percent of the measured coefficients and these corrections have not

been applied to the data.

PRESENTATION OF RESULTS

The results of this investigation are presented in the following figures:

Figure

Flow-visualization photographs for NACA 651-213 airfoil . ............ 4

Effect of Reynolds number on section characteristics. M = 0.22 . ........ 5

Variation of airfoil minimum upper surface pressure coefficient with

Reynolds number. M = 0.22; transition fixed at x/c = 0.05 . ......... 6

Effect of various grit sizes on section characteristics. M = 0.22;

R = 5.9 x 106 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 7

Effect of strip and wraparound roughness on section characteristics.

M =0.15; R = 5.9x 106; no. 60 grit ....................... 8

Variation of maximum lift coefficient with Reynolds number. M = 0.22 . . . . . 9

Variation of minimum drag coefficient with Reynolds number. M = 0.22 . . .. 10

Effect of Mach number on section characteristics and chordwise pressure

distributions. R = 5.9 x 106; transition fixed at x/c = 0.05 . ......... 11

Variation of maximum lift coefficient and airfoil minimum upper surface

pressure coefficient with Mach number. R = 5.9 x 106; transition

fixed at x/c = 0.05 .................... . ........... 12

Comparison of section characteristics for NACA 651-212 (a = 0.60) and

NACA 651-213 (a = 0.50) airfoils. Models smooth; M _5 0.22 . ........ 13

6

Figure

Comparison of experimental and theoretical chordwise pressure

distributions. M = 0.22; R = 5.9 x 106; model smooth . ............ 14

Comparison of experimental and theoretical section characteristics.

M = 0.22 ........... .. .......................... . 15

DISCUSSION OF RESULTS

Experimental Results

Wind-tunnel sidewall effects.- The stall characteristics, and hence cl,max, of any

airfoil are generally a function of Reynolds number, Mach number, and airfoil surface

conditions (roughness). In addition, the maximum lift of an airfoil may be limited in

wind tunnels by the interaction of the airfoil upper surface pressure gradients and the

airfoil boundary layer with the wind-tunnel sidewall boundary layer. This interaction

may induce sidewall boundary-layer separation and hence premature airfoil stall.

Detailed examination of the pressure data and tuft pictures obtained on the NACA 651-213

airfoil indicated no evidence of any wind-tunnel sidewall boundary-layer effects severe

enough to induce premature stall. Selected tuft pictures are shown in figure 4(a) to

illustrate the flow field on both the wind-tunnel sidewall and airfoil upper surface at

several Reynolds numbers. Flow-field disturbances were confined to a small region at

the airfoil sidewall intersection.

Reynolds number effects (model smooth; M = 0.22).- The angle of attack for zero

lift coefficient was unaffected by Reynolds number. (See fig. 5.) The lift-curve slope

(measured between a = +4o and a = -40 and uncorrected for wall boundary effects)

showed a modest increase as Reynolds number increased up to about R = 9.0 x 106

and attained a value of about 0.12 per degree. The maximum lift coefficient (fig. 9)

increased rapidly as Reynolds number increased from R = 3.0 x 106 to R = 9.0 x 106

and attained a value of about 1.7 at R = 9.0 x 106; further increases in Reynolds number

had only small effects on cl,max. The stall (fig. 5) was abrupt (generally, a laminar

leading-edge type) below Reynolds numbers of about R = 9.0 x 106 and gradual (turbu-

lent trailing-edge type) at higher Reynolds numbers. Oil-flow photographs obtained at

R = 3.0 x 106 (fig. 4(b)) illustrate a laminar bubble near the leading edge on the airfoil

upper surface. The Reynolds number range was obtained at a Mach number of 0.22, the

maximum Reynolds number capability of the wind tunnel, and figure 6 indicates that local

compressibility effects may have been present for Reynolds numbers larger than about

R= 6.0 106 (Cp,min approaches Cp,critical near el,max).

7

The pitching-moment data (fig. 5) were generally insensitive to Reynolds number

except near stall. Abrupt negative increments in cm (figs. 5(a) and 5(b)) occurred

near stall for Reynolds numbers less than about R = 9.0 x 106.

The "laminar bucket" near the design cl of 0.20 is illustrated at R = 3.0 x 106

in figure 5(a). Increasing the Reynolds number to R = 5.9 x 10 6 (fig. 5(b)), however,resulted in a less distinct bucket and above R = 9.0 x 106 the bucket was no longer

apparent. The elimination of the bucket would not be expected to occur until somewhat

higher Reynolds numbers as indicated by the 6-series airfoil data of reference 1. How-

ever, reference 1 reports that wind-tunnel tests of 6-series airfoils indicated that airfoil

surface conditions had a marked influence on maintaining laminar flow. The model sur-

face orifices for the NACA 651-213 airfoil of this test were located at the center span of

the model, which was also the span station where the profile drag measurements were

made, whereas the airfoil models used in reference 1 had no orifices. Surface roughness

effects may have resulted from the presence of the orifices despite the care taken during

installation. Variation of Cd,min with Reynolds number is shown in figure 10. The

increase in cd as a result of increasing the Reynolds number from R = 3.0 x 106 to

R = 9.0 x 106 for the model without fixed transition is largely the result of the forward

movement of the natural transition point on the airfoil. Above R = 9.0 x 106, the

decrease in Cd,mi n with increasing Reynolds number is associated with the decrease

in the growth rate of the turbulent boundary-layer thickness and corresponding reduction

in skin-friction drag.

Roughness effects.- The effects of applying a standard roughness at x/c = 0.05

are shown in figure 5 for various Reynolds numbers. Roughness had no measurable effect

on the lift and pitch data except near the angle of attack for maximum lift. Figure 9

indicates that below Reynolds numbers of about R = 9.0 x 106, a slightly higher value of

Cl,ma x was obtained with roughness. This favorable effect on Cl,ma x at the lower

Reynolds numbers is believed to be the result of a reduction of the extent of laminar

separation near the airfoil leading edge. Applying roughness resulted in the expected

increase in cd compared with the smooth model results (fig. 5) with essentially full-

chord turbulent flow obtained over the airfoil and the effects of Reynolds number on

Cd,min are shown in figure 10. Increasing the Reynolds number from R = 3.0 x 106

to R = 23.0 x 106 resulted in a decrease in Cd,min of about 0.0022. The effects on

the section characteristics of applying various grit sizes varying from number 60 to

number 180 are shown in figure 7 for R = 5.9 x 106. The largest value of cl,maxwas obtained by using number 120 grit, the recommended size for this Reynolds number.

(See table III.) Figure 7(b) indicates that grit number 180 was sufficient to cause

boundary-layer transition at this Reynolds number. Increasing the grit size generally

resulted in increases in cd at moderate lift coefficients. This result is to be expected

because of the thickening of the turbulent boundary layer.

8

A comparison of the section data obtained with a roughness strip and with exten-

sive roughness wrapped around the leading edge is shown in figure 8. A decrease in the

angle of attack for cl,max of about 20 and a decrease of about 13 percent in cl,max

is shown in figure 8(a) for the wraparound roughness. Comparison of the drag data

(fig. 8(b)) indicates small increases in cd near design lift and rather large increases

at the higher lift coefficients for the wraparound roughness. A comparison of the lift

data obtained with a narrow roughness strip at x/c = 0.05 (fig. 7(a)) and x/c = 0.04

(fig. 8(a)) at R : 6 x 106 indicates that the nature of the stall changed from abrupt to

gradual when the strip was positioned at the most forward chordwise location.

Mach number effects.- The effects of Mach number on the airfoil characteristics

at a Reynolds number of R = 5.9 x 106 with a NASA standard roughness are shown in

figures 11 and 12. The expected Prandtl-Glauert increase in lift-curve slope is indicated

by increasing the Mach number from 0.10 to 0.36. Large Mach number effects are indi-

cated on both the stall characteristics and cl,max above M = 0.22. Increasing the

Mach number from 0.10 to 0.36 resulted in the stall changing from abrupt to gradual,

the stall angle of attack decreased about 70, and cl,max decreased about 30 percent.

These pronounced Mach number effects are a result of supercritical flow occurring on

the airfoil. Figure 12 indicates that above a Mach number of about M = 0.22, the flow

on the airfoil upper surface exceeded sonic velocities; that is, Cp,mi n exceeded

Cp,critical near Cl,ma x . Similar compressibility effects are discussed in detail

in reference 6.

The effects of Mach number on the chordwise pressure data at a = 120 are illus-

trated in figure 11(c). At subcritical flow conditions (M < 0.28), compressibility effects

on the chordwise pressure data are small. However, for supercritical flow conditions

(M _ 0.28), the chordwise pressure coefficient is significantly reduced and the extent of

trailing-edge separation on the upper surface is increased. The resulting loss in lift

coefficient (fig. 11(a)) is therefore attributed to the presence of local supersonic flow on

the airfoil upper surface near the leading edge at Mach numbers equal to or greater than

0.28.

Increasing the Mach number had no effect on cm up to about a = 80 (fig. 11(a));

however, at higher angles of attack a positive increment in cm occurred and the break

occurred earlier. The drag data (fig. 11(b)) also indicate large increases at high lift

coefficients due to Mach number effects.

Comparison with other airfoil data.- Comparisons of the section data obtained in

this test (model smooth) with data obtained in another low-speed wind tunnel on another

NACA 651-213 airfoil (ref. 7) and with data on the NACA 651-212 airfoil (ref. 1) are

shown in figure 13. Reasonable agreement in the lift and pitch data (fig. 13(a)) obtained

in the two wind tunnels is indicated for the two NACA 651-213 airfoils. The drag data

9

for the NACA 651-213 airfoil of reference 7 (fig. 13(a)) indicate the absence of the

"laminar bucket." Reference 7 attributes this result to model surface-roughness effects.

The data for the NACA 651-212 airfoil indicate about a 0.10 higher value of cl,maxat R = 3.0 x 106 (fig. 13(a)) and about a 0.15 lower value at R = 6.0 x 106 (fig. 13(b)),compared with the NACA 651-213 data. Comparison of the drag data between the

NACA 651-212 (ref. 1) and the present NACA 651-213 airfoil at R = 3.0 x 106 (fig. 13(a))

and at R = 6.0 x 106 (fig. 13(b)) indicates that the extent of laminar flow was considera-

bly less for the NACA 651-213 airfoil, especially at R = 6.0 x 106.

Pressure distributions.- The chordwise pressure data of figure 14 illustrate the

effects of angle of attack at a Reynolds number of R = 5.9 x 106 and a Mach number of

M = 0.22 for the smooth model. The data in figure 14(c) (a = 0.60; c l = 0.20) indicate

the favorable pressure gradients extending to about x/c = 0.50 on both surfaces of the

airfoil at design lift. These pressure distributions are typical of the NACA 6-series

airfoils designed to have long regions of laminar flow. Figure 14(d) shows the pressure

data (a = 2.10; cl = 0.40) near the limit of the low-drag or laminar-flow region. Some

upper surface trailing-edge separation is indicated by the change in pressure recovery

over the aft region of the airfoil at about a = 80. (See fig. 14(f).) The extent of the

separated region progressed forward with further ihcrease of angle of attack and the

relatively flat pressure distribution over the aft region at cl,max (fig. 14(h)) indicated

separation extended from about x/c = 0.65 to the trailing edge. The lift-curve slope

decreased as the chordwise extent of separation increased (fig. 5(b)) and became zero at

stall. The stall was of the abrupt trailing-edge type as indicated by figure 14(i) at

a = 16.20

Comparison of Experimental and Theoretical Data

Examples of the chordwise pressure distributions calculated by the viscous flow

method of reference 8 are compared with the experimental pressure data of the present

investigation in figure 14 for free transition (model smooth) at R = 5.9 x 106. The

agreement between experiment and theory is good over most of the airfoil chord, as long

as no boundary-layer flow separation is present. For example, figures 14(f) and 14(g)

illustrate the discrepancies between experiment and theory near the trailing edge of the

airfoil caused by boundary-layer separation.

Comparisons of the experimental lift and pitching-moment data with theory for

Reynolds numbers from 3.0 x 106 to 22.8 x 106 with free transition (model smooth) are

shown in figure 15. The theoretical method satisfactorily predicts the lift and pitching-

moment data for angles of attack where no significant boundary-layer flow separation is

present. For example, at R = 5.9 x 106 (fig. 15(b)), good agreement is shown up to

about a = 120. The discrepancy in c l and cm at the higher angles of attack is as

10

expected, since the theoretical method is only applicable for airfoils with attached

boundary layers. Figure 15(e) shows the same results for R = 5.9 x 106 with transition

fixed at 0. 0 5c.

The viscous-flow theoretical method of reference 8 was developed to calculate the

surface pressures for viscous, subsonic flows on airfoils composed of one or more

elements. An evaluation of the airfoil profile drag was not in the scope of the technical

effort. However, an approximate calculation of drag coefficient was included which

consisted of the integration of the airfoil pressure drag and the addition of skin-friction

drag based on flat-plate calculations. Reference 9 indicated that the resulting drag

coefficients were greatly in excess of the measured values. An attempt to improve the

agreement between experimental and theoretical drag coefficients was made by modifying

the pressure drag integration procedure and doubling the chord Reynolds number. Com-

parison of the modified drag coefficients with experiment in figure 15, however, indicates

that for either free or fixed transition, the theory now generally underpredicts the drag

coefficients. Further improvement in the theoretical drag prediction is therefore needed

even when no boundary-layer separation occurs.

SUMMARY OF RESULTS

Low-speed wind-tunnel tests have been conducted to determine the two-dimensional

aerodynamic characteristics of the NACA 651-213, a = 0.50, airfoil section. The results

have been compared with data from another low-speed wind tunnel and also with theoret-

ical predictions obtained from a subsonic viscous-flow method. The tests were con-

ducted over a Mach number range from 0.10 to 0.36. Reynolds number, based on the

airfoil chord, was varied from about 3.0 x 106 to 23.0 x 106. The following results

were determined from this investigation:

1. Maximum section lift coefficients at a constant Mach number of 0.22 increased

rapidly with Reynolds number from about 3.0 x 10 6 to 9.0 x 106 and attained a value of

about 1.7.

2. Stall was abrupt below a Reynolds number of about 9.0 x 106 and changed to

gradual at higher Reynolds numbers.

3. The application of a narrow roughness strip near the leading edge at a Reynolds

number of about 6.0 x 106 resulted in small effects on lift whereas extensive roughness

around the leading edge resulted in a decrease in the maximum section lift coefficient of

about 13 percent.

4. Increasing Mach number at a constant Reynolds number of about 6.0 x 106 showed

large effects on the maximum section lift coefficient as a result of the flow over the

11

airfoil becoming supercritical. The maximum section lift coefficient decreased about30 percent for an increase in Mach number from 0.10 to 0.36.

5. Section lift and pitching-moment coefficients at low Reynolds numbers for thesmooth airfoil were in good agreement with results from another low-speed wind tunnel.However, there were differences in the drag coefficients within the lift coefficient rangewhere the laminar bucket would be expected.

6. Comparisons of experimental section lift coefficients, pitching-moment coeffi-cients, and chordwise pressure distributions with those calculated from a viscous-flowtheoretical method were good as long as no boundary-layer flow separation was present;however, the theoretically calculated drag coefficients were less than the experimentaldrag coefficients.

Langley Research Center,National Aeronautics and Space Administration,

Hampton, Va., December 7, 1974.

12

APPENDIX

CALIBRATION OF THE LANGLEY LOW-TURBULENCE PRESSURE TUNNEL

A calibration of the Langley low-turbulence pressure tunnel has been performed

using a long survey probe alined with the longitudinal center line of the test section. The

nose of the probe contained a total-pressure tube and static-pressure orifices were

installed flush with the probe surface at fixed interval distances over the probe length.

These were used to measure the probe total-pressure and probe static-pressure distri-

bution of the airstream. A photograph of the probe is shown in figure 16 and a sketch of

the calibration arrangement, relative to the wind tunnel at various longitudinal stations

x cm (in.), is shown in figure 17. Also shown in figure 17 are the reference total-

pressure tubes on the floor of the wind tunnel and the tunnel sidewall reference static-

pressure orifices from which the tunnel test conditions are calculated.

Some typical Mach number distributions at various tunnel total pressures (that is,

Reynolds numbers) are shown in figure 18. The Mach number distributions show that

the flow is uniform with negligible deviations between x = -101.6 cm (-40 in.) and

x = 101.6 cm (40 in.). Figure 19(a) shows the results of the calibration in terms of a

calibration factor (C.F.) against average probe Mach number, and figure 19(b) shows the

present operational boundaries of the tunnel. The calibration factor is shown to vary by

less than 1 percent over the entire operational Mach number and Reynolds number range

of the tunnel, and no specific trends of variation of the calibration factor with either

Mach number or Reynolds number could be identified. The dashed line in figure 19(a)

indicates the root-mean-square value (rms value) of all the data (C.F. = 1.006), which

therefore is defined as the calibration factor for the tunnel. This calibration factor is

in good agreement with a previously used but unpublished value (1.005). The symbols

used in the calibration of the tunnel (see figs. 16 to 19) are as follows:

Pt,p- PC.F. calibration factor, , averaged from x = -30.48 cm (-12 in.)

Pt,ref ref

to x = 60.96 cm (24 in.)

M free-stream Mach number

Mav longitudinal average of probe Mach number between x = -30.48 cm (-12 in.)

and x = 60.96 cm (24 in.)

Mp probe Mach number (computed from pp and Pt,p)

13

APPENDIX - Concluded

p probe static pressure, kN/m 2 (lb/in2 )

Pref tunnel sidewall static pressur'e, kN/m 2 (lb/in2 )

Ptp probe total pressure, kN/m 2 (lb/in2 )

Pt,ref tunnel total pressure, kN/m 2 (lb/in2

q dynamic pressure, kN/m 2 (lb/in2 )

R unit Reynolds number per m (per ft), based on stagnation temperature300 K (5400 R)

x longitudinal station, cm (in.); x = 0 coincides with axis through center of

rotation of sidewall circular plates

14

RE FERENCES

1. Abbott, Ira H.; Von Doenhoff, Albert E.; and Stivers, Louis S., Jr.: Summary of Air-

foil Data. NACA Rep. 824, 1945. (Supersedes NACA WR L-560.)

2. Von Doenhoff, Albert E.; and Abbott, Frank T., Jr.: The Langley Two-Dimensional

Low-Turbulence Pressure Tunnel. NACA TN 1283, 1947.

3. Braslow, Albert L.; and Knox, Eugene C.: Simplified Method for Determination of

Critical Height of Distributed Roughness Particles for Boundary-Layer Transition

at Mach Numbers From 0 to 5. NACA TN 4363, 1958.

4. Baals, Donald D.; and Mourhess, Mary J.: Numerical Evaluation of the Wake-Survey

Equations for Subsonic Flow Including the Effect of Energy Addition. NACA

WR L-5, 1945. (Formerly NACA ARR L5H27.)

5. Allen, H. Julian; and Vincenti, Walter G.: Wall Interference in a Two-Dimensional-

Flow Wind Tunnel, With Consideration of the Effect of Compressibility. NACA

Rep. 782, 1944. (Supersedes NACA WR A-63.)

6. Wootton, L. R.: The Effect of Compressibility on the Maximum Lift Coefficient of

Aerofoils at Subsonic Airspeeds. J. Roy. Aeronaut. Soc., vol. 71, July 1967,

pp. 476-486.

7. Englar, R. J.; and Ottensoser, J.: Calibration of Some Subsonic Wind Tunnel Inserts for

Two Dimensional Airfoil Experiments. TN-AL-275, Naval Ship Res. & Develop.

Center, Sept. 1972. (Available from DDC as AD 913 412L.)

8. Stevens, W. A.; Goradia, S. H.; and Braden, J. A.: Mathematical Model for Two-

Dimensional Multi-Component Airfoils in Viscous Flow. NASA CR-1843, 1971.

9. McGhee, Robert J.; and Beasley, William D.: Low-Speed Aerodynamic Characteristics

of a 17-Percent-Thick Airfoil Section Designed for General Aviation Applications.

NASA TN D-7428, 1973.

15

TABLE I.- NACA 651-213, a = 0.50, MEASURED AIRFOIL COORDINATES

c = 60.63 cm (23.87 in.)

Upper surface Lower surface

x/c z/c x/c z/c

0.00000 0.00000

.00014 .00297 0.00021 -0.00096

.00042 .00431 .00054 -. 00215

.00080 .00551 .00098 -. 00327

.00127 .00669 .00152 -.00431

.00132 .00775 .00214 -. 00533

.00285 -. 00626

.00244 .00880 .00362 -.00717

.00313 .00981 .00444 -.00797

.00386 .01074 .00530 -.00871

.00624 .01311 .00619 -.00943

.00884 -. 01114

.01111 .01656 .01403 -.01363

.02348 .02298 .02680 -.01788

.04840 .03281 .05214 -.02404

.07345 .04052 .07737 -.02868

.09858 .04703 .10252 -.03256

.14893 .05750 .15271 -.03858

.19939 .06550 .20279 -.04308

.24993 .07153 .25280 -.04640

.30052 .07604 .30275 -.04872

.35115 .07897 .35267 -.05016

.40182 .08031 .40254 -.05065

.45254 .07990 .45238 -.04999

.50339 .07749 .50207 -.04811

.55416 .07291 .55185 -.04504

.60462 .06665 .60193 -.04106

.65493 .05918 .65216 -.03625

.70513 .05066 .70251 -.03086

.75522 .04151 .75297 -.02504

.80526 .03201 .80347 -.01899

.85525 .02250 .85403 -.01298

.90527 .01329 .90456 -.00729

.95532 .00520 .95506 -.00250

.99999 .00015 1.0 -.00013

16

TABLE II.- AIRFOIL ORIFICE LOCATIONS

c = 60.63 cm (23.87 in.)]

Upper surface Lower surface

x/c z/c x/c z/c

0.0 0.0

.00281 .00933 0.00515 -0.00862

.00715 .01388

.01031 .01619 .01010 -. 01183

.01273 .01753

.01759 .02017

.02012 .02144 .02008 -.01588

.02520 .02378

.03009 .02589

.05024 .03344 .05045 -.02372

.07538 .04107

.10044 .04750 .10087 -.03235

.15078 .05786 .15130 -.03843

.20105 .06574 .20129 -. 04296

.25178 .07180 .25162 -.04636

.30180 .07615 .30189 -.04870

.35211 .07902 .35204 -.05016

.37729 .07987

.40264 .08032 .40231 -.05065

.42775 .08033

.45293 .07990 .45260 -.04999

.47781 .07898

.50319 .07752 .50304 -.04806

.52811 .07551

.54077 .07432

.55334 .07302 .55337 -.04497

.56607 .07159

.57843 .07009

.59116 .06848

.60342 .06685 .60374 -.04090

.62863 .06324

.65391 .05934 .65377 -.03609

.70407 .05087 .70375 -.03074

.75419 .04173 .75459 -.02485

.80482 .03210 .80490 -.01879

.85509 .02252 .85513 -.01286

.90484 .01336 .90504 -.00722

.95530 .00519 .95543 -.00248

17

TABLE III.- NOMINAL ROUGHNESS PARTICLE HEIGHTS

[Grit located at x/c = 0.05]

R Grit number Nominal particle height,cm (in.)

3.0 x 10 6 80 0.021 (0.0083)5.9 120 .012 ( .0049)9.0 180 .0089 ( .0035)

11.8 220 .0074 ( .0029)14.5 220 .0074 ( .0029)17.4 220 .0074 ( .0029)22.8 220 .0074 ( .0029)

18

Moment reference

z/c 0

- I

S0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0x/c

Figure I.- Section shape for NACA 651-213, a = 0.50, airfoil.

CD.

Tunnel side walls

Diam.= 1.68 c--

- -- .. . . ---_ 1.51c

Airflow A A

Circular plate

Metal seals - Airfoil positioningattachment

Top view Model attachmentplate

Seal detail "z"

-I _Zero incidence7 reference

Tunnel center line

c/4 c -

End view ,section A-A

Figure 2.- Airfoil mounted in wind tunnel. All dimensions are in terms

of airfoil chord c = 60.63 cm (23.87 in.).

20

o.126c .042c

Static-pressure probes

.042c--

.021c

(typ.)

Airflow 1 L.17c-1

.0052 c

(typ.)

Total-pressure probes

(tubes flattened)

,189c0 y p.

Figure 3.- Drawing of wake rake. All dimensions are in terms

of airfoil chord. c = 60.63 cm (23.87 in.).

21

a = 150; R=3.0 x 10 6 a =160; R =6.0x 106

Stall cmC,max

(a) Tufts. L-74-8543

Figure 4.- Flow-visualization photographs for NACA 651-213 airfoil. M = 0.22; model smooth.

a=17 0 ; R= 12.0 x 10 6 a = 160; R= 18.0 x 106

O Stall Stall

(a) Tufts. Concluded. L-74-8544

Figure 4.- Continued.

C-

= 50; R= 3.0 x 106. L-74-8545

(b) Oil flow.

Figure 4.- Concluded.

24

2.0 - ___

Roughnesso Off

1.

-. 4

1.2 A- A

:J-

.8C 4 iiiii !i --

-2

-12 -8 -4 0 4 8 12 16 20a,deg

(a) R 3.0 x 106

Figure 5.- Effect of Reynolds number on section characteristics. M = 0.22.

25

::-I::::I: _::25

o ' Off

[ On

.020

.012

Cd

.008

.004

-I.2 -. 8 -. 4 0 .4 .8 1.2 1.6 2.0

(a) R = 3.0 x 10 6 . Concluded.


2626

2.0 -- -. - - - -i

Roughness I0 Off

1.2 -:_: : i H\

rn

0-

-. 4

-. :i~iri i.....iiii. ... .i .: ......

-1.2

-1

-. 2-12 -8 -4 0 4 8 12 16 20

adeg

(b) R = 5.9 x 106


27

; -i

4;t , V"4 Houghness

0 Offo On

.020

.016

.012

cd

.008

.004

-1.2 -. 8 -. 4 0 .4 .8 1.2cl

(b) R = 5.9 x 10 6 . Concluded.


28

Roughnesso Off

1.6 i - 0 On

SL:

.8

0-

-. 8

-1 i.2 Ii

-

-12 -8 -4 0 4 8 12 16 20a,deg

(c) R 9.0 x 106


29

[ On

.020

.0 16

.012

cd

.008

.004

01.2 -. 8 -. 4 O .4 .8 1.2 1.6 2.0cCl

(c) R = 9.0 x 106 . Concluded.


30

2.0 .___ lllii .Roughness : __ - - -

1: 711 1 0 Offi ii ili :.6 : :!'i: :: o O ff :

a On

.2

. .. ... . . : ': ....... .. . .... ...

c 4 F4

- I:1

l , ; .2

0t I .I I

i i i:i :: . :::

-1 i ! iii : iii; 2 2 1 ij: jhi: -- --l-- : I: : :I : i : .


' ' E i l ' E F': . . .. . -

:i i!; i I'Eii:

*i iEi:'uh iH : : I'i iFh ' F

-12 -8 -4 0 4 8 12 16 20

o Off

.024 o On

.020

.016

cd .012

.008

.004

1.2 -. 8 -,4 0 .4 .8 1.2 1.6 2,0

(d) R = 11.8 x 106 . Concluded.


32

Roughness i ii

o Off1.6 o On

1.2

- .4 -,;:ii

-1.2

-. 4 ............ ,:: .'-! 7777 ,;i

i H:!:1 1:: l: lI* l: i iii1 1 .i!ii iiii 'I h

-12 -8 -4 0 4 8 12 16 20a,deg

(e) Rr 14.5 x 106


3333

St ougnesso Off

.024

.020

.016

Cd .012

.008

,004

0,2 -. 8 -,4 O .4 .8 1.2 1.6 2.0C1

(e) R = 14.5 x 10 6 . Concluded.


34

2.0Roughness

1.6 2.2 ii iii

.8

... ... .; jjj ilfi jt,

-1.2

ii , ,I li I lit

- 12 -8 -4 0 4 8 12 16 20

(f) R=17.4x106(M) R : 17.4 x 106.


35

o Off.024 [ On

.020

.0[6

Cd .012

.008

.004

-1.2 -. 8 -. 4 0 .4 .8 1.2 1.6 2.0CI

(f) R = 17.4 x 106. Concluded.


36

it 1 ,2.0 - T - -7 -'2.0 t tii i l il Ro-ughn ess i !!!!!

L 0 Off

i,.! ii ' ' iii i ih !!' " iiiii-i , i " i R u h e siii!i l ii;iii!ii~ i iii!

1 .6 t' o Ofniii' ' ' t !liii!i; - v :iiii-, ii i i

S t it t

t-e : : i ! :i: '. '

it i t ~ S tS ii!,: i : i'!! ! .. . . . . . . . 5 55 ;

c[i~i 4 idi F . i' '

.i q!! ::bl

HH... '" .... ii- i i ..ii iii r !iii ii 01

S it r~S5

Ktk if ij j~{~ {ti '. h i js s i N "js 14 ' . ir *;t t II

~iiii "H iiii! i I ii:!i il :;:: ,,[! ,

, I f iiL i Ipihi l V ' ii 1 714ii:il l iiilil f 1iiih tilh Vl i

•.iliiii I mii::;i::::r: :

a ,deg

(g) R =22.8tx10.


3'7

jiil jj 1 ;it 1 1ii~

111 1 1:ii ii, ill, 4 ~ ilj ijj ii!l~iiii' ": ir;i;~~tr::;

Il [ ill If it H i i lit 1 F lit i uii nii

I i lir: i! , ;tHI~r

O ~ ~ ~ it i ll, 'l: iiiiiii;i;;I; ijHil jjt It (jtRi n~j tii i ; litI~

Irt iti

ILI it ii

litI! i It

I, ,fp 0i ii ', lkiiW.4. i 11P ql'il~~'i

c itm ii

Fiur .- Cotnud

s~ ii H37

.024 iWM M On

.020

.016

Cd

.012

.008

.004

1.2 -. 8 -4 .4 .8 1.2 .6 2.0cl

(g) R = 22.8 x 106. Concluded.


38

-20

-16Cp,critical

Cp min - 12

-8

-40 4 8 12 16 20 24xl06

Figure 6.- Variation of airfoil minimum upper surface pressure coefficient'with Reynolds

numbers. M = 0.22; transition fixed at x/c = 0.05.

- - - - -- - - --

2.0Roughness tLtF : F

, . . .i .. l i.i4L F i::ii :i! : $! : : ! : i i

1.6Iu6 No.60

O No.120t

1.2 A No.180

.8

. T 7 . .. !:... i

i' : i:" i:j i:i ;:i!:i:: i~i'iii7iil

0 - - -

Fit

.... .... .. .....~ili i .....ii : : .. ....... . ii i:ii ii iiiii:

00

.2 " : ;, : '.: F4' E , 0 4 12 F 16.. 2 F

-12 -8=4 0; 4 8 52 16 2(a) Lf adondt

---------- O ff0 No.60

0 No. 120

.020 No.180.020

.0 16

.012

cd

.008

.004

001.2 -. 8 ,4 O .4 .8 1.2 1.6 2.0

Cl

(b) Drag polars.


41

0 Wraparound roughness to 0.04 - - -

ii Strip roughness at 0,04c

1.6

1.2

.8

C1 .4

tur ii 11 i 1 1 : i 4 i i

0

-. 4

-.2

-12 -8 -4 0 4 8 12 16 20

adeg(a) Lift and moment data.

Figure 8.- Effect of the strip and wraparound roughness on section characteristics.

M = 0.15; R = 5.9 ×106; no. 60 grit.

42

0 iiiii li iiii~ii :1~::-I: :

;iiiillr ii;; iijj/ i;;iii~i~ii ll~t I: iiii~ilii j:iirii '7 1ll :l:;::: il

Tliti :: ::i;i: !~LLL1

-12 -8 4 0 4 8 12 16 2aideg

(a) Lift and moment data. "':'i'' "

Figure B.i,: .i !:i- E thestrp an wrparond oughesson sctin chracerisicsM = .15;R = .9 106; no 60 rit

42~iiiiitiiii''' 1:i11 ~ ~ ::I: i

.028o Wraparound roughness to 0.04c- Strip roughness at 0.04C

.024

.020

.016

cd

.012

.oos-

.008

.004

-1.2 -. 8 -,4 0 .4 .8 1.2 1.6 2.0Cl

(b) Drag polars.


43

i.8 7o Model smooth 1:1Up "I'll

[] NASA standard roughness "i ....I 6 .. ... ,. -.-iE, ,,~li u ,~~~jYW-;~~~t~

7 1T 1 1 1

II .I

1.4I H-i I i

-i i I ii .. . . ....max . , I 1 4

-•i 8 -" " ' . . .

1 .2 il j__ : '1 !- f 4

24 T 4 5 I 20 3IT

"R

Fr P iati o it

Jill 1 LI

1 t 2 3 4 5 0, 10 1 ,0 30 0

RFigure 9.- Variation of maximum lift coefficient with Reynolds number. M = 0.22.

.014-- -- os Model smooth

- ,,, 0 NASA standard roughness

+ F 7 , TjTi.012 -i

o~: _L _ i , ii"j' --

" i ! In ....I l

006 ' " '" '"001 2l ff 0 03X

minicd 1-T

-- 4 IT --

-T TT 1 : I 7 Ii T1'

.008 r 10. Vaiaio 4- minmu rAgL- IT- fcin lith Renod'nmbr I =4

-T j; Jill

LIuL

.006 ii,

-1 7T,.04 112 51 2 0xO

,, i ii'RFigue 1.- ariaionof inium dag oeficint wth eynldsnumbr. = .22

. 3 1 ' 4f0 . ..... .. ... ..

H it. ... : !2i .2i M

44 ';i i ii.36iil ii i i!'ii. ... ::-

• ,:: i0 0ii' : '

.4

.15-

it i:i iL 1i I f!

1.2 .28 )

Ii~ ............

.8 ~ ~ 4

,: '{-! :':i!Iiiiii , liii Ii~ii jjii j ,F:3 :

N I 4. , .... .. ... .- I.24444 i , .......... it *t))*.+4o8 ~ .4.4 i~t,,i,1ii iir ii'li"l .: 114 4 E *4** 4

iiii 1 .... lit Itiil~ijli !ii ililiii jIII ti! t;!! 1 Ifiili~iiii ""'"

~44~ , 4. 44 11, 41144+1414 {( )I 4t4).))

U -i H I f!'

- i; iiti- iljjf tt ri

H~ ~ ~~i , !, ::,: ::: iiiiHi :: (:: i (H ,!

-.1 + -, ,j ........ I'tiVtii4t 1414f ji'[j 1t ~ir

" !i!! ii!((t' ...... , ,, (J ((!( i' ... .... ,iii,

Oh :fi ... . ), . .. . .. f) )

-2 -8 4 0 4 8 12 16 20

cz,deg(a) Lift and moment data.

Figure 11.- Effect of Mach number on section characteristics

and chordwise pressure distributions. R = 5.9 X 106;transition fixed at x/c 0.05.

46

lit!

1V il . ii 1iilfil l 11 i 1-,I ll M8 r;:;, 71 t I li

ii ti itii

- 1.2 I'il: q'i il'JiT 11 If f ff I'll i i iili ii i N it

ki i i l t Iti id 1 111 "' 1 1 l 1 ]1 il li i l i i

Oiltim it ijjjjiti fl i iI ; i

H , Hit!; 0I 11:ii ; i ! ; il 1 ::i::I

If I~

1 i 4 ! TI 1 11 il T I 11 i -i!1 iil;

M i lit

[ fiii '"~i l 11 it 11114 N

.2 lit 1[4

-8 -4 4 8 12 16 20ji iiii '!ii il:ii~i '.I i I i~ t I iiiir~i 'I;I, ii !;1a : de g

(a) Lift and moment data.I~i::!ii ;i1i ii/i~ji

Figre 1.-Effct f Mch umbr o setio chraceriticandchodwie pessre istibuion. R= 59 X10

transtionfixe at / =0.05461

o 0.10.024. .15

<> .22

.020 A .28

- .36

.0 16

Cd

.012

.008

.004

0- 1.2 -. 8 -. 4 0 .4 .8 1.2 1.6 2.0

cl

(b) Drag polars.


47,

-7.2 L

-6.8 - M C. critical -100 0.10 - 66.9

O .22 - 13.4

-6.4 1- .28 - 8.1 -9

A .36(stalll - 4.7

-6.0 - Upper surface -- Lower surface

-5.6 - - - - --7

Cp

-5.2 - - - - - - -6

-4 .8 - i --- - - -5

-4.4 -4

-4.0 - - - - - - - - -\

-3. 0 .04 .08 .12

x/c

-3.2

Cp

-2.8

- - - - - - - - -

-2.4

-2.0 -

-1.6

-1.2

1 02 .2 . 4 .5 .6 .7 .8 .9 1.0

x/c

(c) Chordwise pressure distributions; a = 120


48

Cp Cp, mn

-20

C, maxl.4 - 12

1.2 -8

1.0 -4

o .I .2 .3 .4 O .1 .2 .3M M

Figure 12.- Variation of maximum lift coefficient and airfoil minimum upper surface pressure

coefficient with Mach number. R = 5.9 x 106; transition fixed at x/c = 0.05.

1.6 -

Airfoil a R

1.2- 0 NACA 6 5 1- 2 13 0.50 3.OxlO

1.2 / - NACA 651-212 .60 3.0 (ref. I)S- - - NACA 65,-213 .50 2.3 (ref.7)

.8

.4

-. 4 .024

0-- ----- --O ----t-- -3- -

-8 - -- .02 --

--------

-12 _ - .016-

---------- --- C d - \cd

(m 0 a-- .0082-- -a-.0

-. 1 -- - - - - -- \ - .004-

.2 O-12 -8 -4 0 4 8 12 16 20 -1.2 -. 8 -. 4 0 .4 .8 1.2 1.6

a,deg

(a) R= 2.3 x 10 6 and 3.0 x 106

Figure 13.- Comparison of section characteristics for NACA 6 5 1- 2 1 2 (a 0.60) and 651-213 (a = 0.50)

airfoils. Models smooth; M < 0.22.

Airfoil a0 NACA 651-213 0.50

1.6 NACA 651-212 .60(ref.1)

1.2

c .4

-1.2 - .016

.8-/d -

0 - --- .012

-,.0

04

-. 2 -00-12 -8 -4 0 4 8 12 16 20 -1.2 -. 8 -,4 0 .4 .8 1.2 1.6 2.0

a,deg CI

(b) R 6.0 x 106


o Upper surfaceo Lower surface

-2.4 Theory

-2.0 -

-I.6

Cp -.8

-. 4

0

.4

.8

1.20 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

x/c

(a) a =-4.10.

Figure 14.- Comparison of experimental and theoretical chordwise pressure

distributions. M = 0.22; R = 5.9 x 106; model smooth.

52

-2.4o Upper surfacee Lower surface

-2.0 - - Theory

-1.6

-1,2

-. 8

cp

-. 4 I -z

.4

.8

1.20 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

x/c

(b) a = 0.00.


53

-2.4o Upper surfacee Lower surface

-20 - -- Theory

-1.6

-1.2

-. 8

Cp ,- -

S -. --

.4

.8

1. 20 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/C

(c) a = 0.600.


54

-2.4-

0 Upper surface-2.0 -

e Lower surface- - - Theory

-1.6

-1.2

Cp -. 8

.4--

.8 -

1.20 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/C

(d) a = 2.10.


55

-2.4O Upper surfacee Lower surface

-2.0-- - - -Theory

-1.6

-1,2

-. 8 _ ) .- --

Cp

.4 (

1.20 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/C

(e) a = 4.10


56

-4. -

0 Upper surfacee Lower surface

--4.4 - - Theory

-4.0

-3.6-0

-3.2

0

-2.4 .

-2.0

0Cp -1.6

-,2-

0-.8 - I-.4 --

.4

1.20 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/c

(f) =8.3.


57

-4.8o o Upper surface

e Lower surface

-4.4 - Theory

-4.0 -0

.-3.6

-3.2 - 9

-2.8 + -8

-2.4 Cp -7

\

k -6-2.0-- -6

C- -.6 -5--0 .04 .08 .12X/C

'O(b

-1,2 1 2 ' I0

-. 4

.4 -


-58

.2 ----- - - - - - - - - - - -

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0x/c


58

-4.8 0 Io Upper surfacee Lower surface

-4.4 - -12

-4.0 i -II

-3.6 -10

-3.2 Cp _ 9

-2.8 -80

-2.4 7

-2.0 - 6C

Cp -1.6 - -50 .04 .08 .12

X/C

-1.2

D 0 /

.4

.4

.8 - --

1.20 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/C

(h) a = i5.1 0


59

-4.8 -1

O Upper surfacee Lower surface

-4.4 -13

-3,6 0

-3.2 i ----- 10

0C

-2.8 --- 9

0

-2.0 -7

Cp -1.6 -6

-1.2 0 5 0 4 x/c .0 8 .12

O o

-. 8 - 0

-. 4_-- .- ,-

0 -

.4

.8 -

1. 2 -0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

X/c

(i) a =16.20.


60

2.4o Experiment

- Theory2.0

1.2

.8

cl

.4

-1.2

-. I

-. 12 -8 -4 0 4 8 12 16 20 2

a,deg

(a) R = 3.0 x 10 6 ; model smooth.

Figure 15.- Comparison of experimental and theoretical section

characteristics. M = 0.22.

61

.024o Experiment

Theory

.020

.016

cd 012

.008

.004

0

-1.2 -. 8 -. 4 0 .4 .8 .2 1.6 2.0

Cl

(a) R = 3.0 x 10 6 . Concluded.


62

2.4 -o Experiment

- - - Theory

2.0

1.6

1,2

8

,4

0

-. 4

-. 8

1.2

0

Cm

-22 -8 -4 0 4 8 12 16 20

a ,deg

(b) R = 5.9 x 106; model smooth.


63

.028o Experiment

Theory

.024

.020

.016

cd

.012

.008

.004

2 -. 8 -,4 0 .4 .8 1.2 .6 2.0Cl

(b) R = 5.9 x 106 . Concluded.


64

Swep TM MUM MUM 8 MtMOM o Experiment

MMOMW 1 -4 SM Theory

1.11MMU MUN a8HM i 4I i i El iff 1

1.2 111 ii:iii iiiiiliil i

Haii~ l 000 HM~

1, itit i ill tll U l

it HI I 1 81 i!&i:;j j iiliil!itlj: iiii i fllii:Ii: l iiliiij lit!lll :

il000 11 ij;ER E!E EU

t:til H i Ii ii: ; ... Im m U !R 0

lit Ill i.: it ;' l i .E a li W i u m

I t ....:: !iiliilif lit Ili Ii i i Uilil ?ll li!!lii !:: ' ;I:: ::

-. 0 m Wli t 11:1 1;1: H1 O I il til i i l l ill 1 ; i ;1- ~~iT~F ... liilit ... i 1; 1 llj/lij iiliiii~ ~i ::ilit, 1: i i:: l:: ii t l i t it ,

lili~l::lit iiii mi liq i l I: 0 il::1

'TElTHi ill i::! iU:I' i ;l ml.it tillEEM .i it IE lit il 00 imE

it 1H"E iH i ill l : 11 ll! jl m

.4

:11 . :: i I;; inj iiiiit 11" lil i !; ti):lll ii il ::: l:: :::

m~li Il Hitm 1MRHE 1 M'M

p' i i1 till I: it ill, Ii '-til I 'I I ; 1! l T ;1 it

-12 Ht:0 2 S 2.a.deg

i !!:I i'i~f~i :':'"' !' ': lit, WIii:! T WI h

till R; =t 118 xl 10o moe smooth.i 15.- Cinued.,

t lI l~ !! .ll i 1ii , 1 I d i i ii iiH I il !H H 11111 W ;!i:: l ii till 1 ii ii i li i t iii il :;! w il

0 i li l i l l! ii:: litiiiiiit l ll 1 1 1 : li i11 Ii: q llilit IMil: ii l !I i I iii Il !t/

c I I"~'i; illM !ill : I! iil ' i H it ti i !! J

H I ii~ i ... iii ill iii! Iiii iii ili il iiii ti l;iiiii I ill Hill Ii11 !I'll I i t iiii

till T "" tt" JH jlji ll Jj i lt M l!)1 m i

acde

(c) R 11.8 x 10 6 ; model smooth.iii~i iFigre 5. Cotined

::1 'iiiiii6 5

.0280 Experiment- Theory

.024

.020

.0 1 6

Cd

.012

.008

.004

-1.2 -. 8 -. 4 0 .4 .8 1.2 1.6 2.0cl

(c) R = 11.8 x 106 . Concluded.


66

2.4 4i ,io Experiment

:ll1-lT1flI. . ..' Theory

2.0t II lilt IU H", illIiiii

1.6lit- it I 'I lit 1UP , liii~i iii ifll 1 Il tIili iklit iii W ij li llfi il

ilithii tii V! 1 111ql 1 1 ll !itfiiti 1 13 11 Ili illllt i~llttt iitil~ll

- : lii 111 !1 1 , it:,. i li~i lt Illiff iliiiii ill N IA lilt lliiiiIIIIiII

1 lit lilt iq li i iiilitl ill liij li t 4l

1.2 ii'";

iiili'iMl HIWINNIIIH Ill'' liti~ it

.8 i i.8 il tll i itil i! i it T Al!il l il i

N i iiflliflili 1; 1 WINN ONONlii lfit 1111 i~TjfTiiiiiI 11

.411t,

;

1:::: it i 111 11 l I I 111 ild it Ii j it Ill il 61 it I i l tl iiII 11

4til 1i i I w w l-l 1 0 T

-.4

-. 8

-I.2

.I li

Cm

-12 -8 I I0 4 8 12 16 20a,deg

(d) 1R = 22.8 × 10; model smooth.


67

.028o Experiment

Theory

.024

.020

.OI 6

Cd

.012

.004

01-1.2 -. 8 -. 4 0 .4 .8 1.2 1.6 2.0

C1

(d) R = 22.8 x 106. Concluded.


68

2.4

o ExperimentTheory

2.0

1.6

1.21

c I

.4

0

-. 4

-. 8

-1.2

.1

0

-. 2

-.412 - -4 0 4 8 12 16 20

adeg(e) RF = 5.9 x 106; transition fxed at x/c = 0.05.


69

U110 Jil M mll l

.028 iio Experiment

0 - -- TheoryI

.020

.01 6'

.0 2t " iiiiiiii:

-.2 -. 8 - 4 0 . 8 I 16 i20

(e) = 5.9 x 16 IConcluded


.0 1 . ....8 -. ... 6


70

L-72-3634

Figure 16.- Calibration probe mounted in wind tunnel.

ORIGINAL PA 71

iOoR QOBcuMT9~ts

Center of rotation

Pref I-sidewall circular plates

Pt,p Typical pp

Airflow Tunnel \ Probe

Pt,ref

-140 -120 -100 -80 -60 -40 -20 0 20 40 60x,in.

I I i I I i I I I I I-350 -300 -250 -200 -150 -100 -50 0 50 100 150

x ,cm

Figure 17.- General calibration arrangement.

.24

.22M INp

Pt,ref,obsolute Mov.20 9 lb/in; kN/ma

4f W 0 14.7 101.3 0.222t [ 60,0 413.7 .2 7

0 120.0 827.4 .22

.24

.22

Mp Center of rotation.20 of circular plates

NiW

.20

.18-72 -64 -56 -48 -40 -2 -24 -16 -8 8 16 24 32 40x in.

I I I I I I I I I I I I I I I-180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100

x ,cm

Figure 18.- Typical probe Mach number distribution along longitudinal center line of tunnel.

-4C,

Pt,ref ,absoluteIb/ine kN/m

0 14.7 101.30 30.0 206.8

1.02 0 45.0 310.360.0 413.7

rms values 6 91.0 627.41.01 11 120.0 827.4

C.F.

1.00 M

.04 .08 .12 .16 .20 .24 .28 .32 .36 .40 .44Mayo

(a) Calibration factor (C.F.) as a function of May.

40800

riiT33(10) Speed control

tank pressure, q, kN/m2

q,lb/ft2 400 150 Ib/i 0

I200 1 M I I

obs olute14.7 Ib/in

101.3 kN/m'

(b) Variation of q with M for constant values of Reynolds number.

Figure 19.- Calibration factor and operational characteristics of Langleylow-turbulence pressure tunnel.

NASA-Langley, 1975 L-9773

nasa technical nasa tm x-3160

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