Curry, W H

Kuethe, A M

Mckee, P B

English

NASA Technical Reports Server

NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 
TECHNICAL NOTE 1946 
MEASUREMENTS IN THE BOUNDARY LAYER OF A YAWED WING
By A. M. Kuethe, P. B. McKee, and W. H. Curry
University of Michigan 
Washington
September 1949
https://ntrs.nasa.gov/search.jsp?R=19930082619 2020-06-17T22:15:25+00:00Z
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
TECHNICAL NOTE 19146 
MEASUREMENTS IN THE BOUNDARY LAYER OF A YAWED WING

By A. M. Kuethe, P. B. McKee, and W. H. Curry 
SUMMARY 
Measurements of the velocity profiles in the turbulent boundary 
layer on the upper surface of a wing of semielliptical plan form at an 
angle of yaw of 25 0 and angles of attack of 12 0 and 1 0 are reported 
along with pressure distributions. These show considerable spanwise 
flow near the surface. The chordwise (velocity components inclined 250 
to the main wind direction) and spanwise boundary layers were calcu-
lated. The chordwise velocity profiles are in good agreement with 
those obtained at the National Bureau of Standards on an unyawed airfoil 
shape.
INTRODUCTION 
The existence of a spanwise component of velocity near the upper 
surface of a yawed wing is easily demonstrable by means of tufts. 
This component persists over a wide range of angle of attack, 
reaching high values near the stall, and increases in magnitude with 
distance from the root up to a point near the tip. The spanwise flow 
is initiated by a spanwise pressure gradient arising from the displace—j 
nient downstream of the pressure profiles. As a result, slower moving 
air in the boundary layer is transported outward; this causes an 
Increase in boundary—layer thickness near the tip. The wing will there-
fore stall first near the tip unless a strong washout is introduced. 
The study reported here, initiated in 1944, had for its object an 
experimental study of the details of the flow in the boundary layer at 
large angles of attack and sweepback. When the work was begun, a 
sweepback angle of 250 was considered large and most of the measure- - 
ments were made with this condition. 
Recent analyses (references 1, 2, and 3) have shown that for the 
laminar boundary layer on an infinite yawed cylinder the ttchordwisett 
boundary—layer velocity profile, that is, the profile of the velocity 
comDonent normal to the leading edge of the cylinder, is unaffected by 
yaw. Further, if the solution for the chordwise profile is substituted 
in the equation of motion for the spanvise flow, the resulting
2	 NACA TN 1946 
differential equation may be solved, for the spanwise velocity profile. 
While this analysis holds strictly Only for the laminar boundary layer 
on an infinite wing, the results reported here for a turbulent boundary 
layer on a yawed finite wing indicate that in this case as well the 
profile of the chordwise component is relatively unaffected by an angle 
of yaw of 250. 
This investigation was conducted under the sponsorship and with 
the financial assistance of the National Advisory Committee for 
Aeronautics.
APPARATUS AND MFH0D 
The investigation was carried out in the 8—foot open—throat wind 
tunnel at the University of Michigan. The airspeed was 50 miles per 
hour and the corresponding Reynolds number was 700,000 (based on a root 
chord of 18 inches). 
The wing model used for the investigation was of semielliptical 
plan form and Clark Y section.' The seiniaxes of the ellipse were 9 
and 14.8. inches • The wing model was constructed of laminated wood. An 
end plate 40 inches In diameter was secured to the root section. A 
support was attached to the end plate and secured to the tunnel floor 
.so that the wing was in an upright position, as shown in figure 1. 
A hot—wire instrument was adapted for measurements of velocity in 
magnitude and direction. A hot—wire probe in the shape of a V pointed 
into the wind, was used and was calibrated as follows: The potential 
drop across each arm of the V was measured, by means of a potentiometer 
circuit, at a series of angles (in the plane of the V) and airspeeds; 
plotting the sum of the two potential drops against their difference 
permits the drawing of lines of constant speed and direction such as 
are shown in figure 2. The calibrations were carried out in the undis— 
turbed stream, after which the probe was mounted on a micrometer screw 
which projected through the wing, and traverses of speed and direction 
through the boundary layer were taken. At some positions near the 
trailing edge it was necessary to traverse the boundary layer in two 
steps because the total change in wind direction exceeded the range of 
the hot—wire instrument for a given orientation. The instrument was 
1-The Clark Y section was chosen because It is relatively easy to 
construct and because it seems probable that the effects observed would 
be the same, within the experimental error, for any conventional airfoil 
profiles of the same thickness. Low—drag sections, in which a consider-
able area of laminar flow exists, would undoubtedly show different 
effects at low angles of attack.
NACA TN 1946	 tj 
oriented at a large angle to the potential-flow direction for measure-
ments close to the surface, then reoriented at a smaller angle for the 
traverse, of the remainder of the boundary layer. Calibrations were 
made before and after each traverse and the run was discarded if the 
calibrations deviated from each other by more than 30 in direction or 
more than 5 feet per second in airspeed. These values indicate the 
approximate limits of the accuracy of the results. 
The measurements reported here were made at the positions shown 
in figure 3 for a sweepback angle of 270 at angles of attack of 120 
and 140 . Observations were made at other angles of attack and for 
angles of sweepback of 00 to 300 but these were not extensive enough 
to permit conclusions to be drawn and are therefore not included in 
this report. 
Preliminary observations included tuft observations and an inves- 
tigation of boundary-layer transition at 250 sweepback by the method of 
reference i. A mixture of camphor and ether was sprayed on the upper 
wing surface and after it had dried the wind' was turned on. Because of 
the greater rate of evaporation of the camphor in a turbulent boundary 
layer, the line of demarcation between camphor layer and clean surface 
is taken to be the line at which transition takes place. Observations 
were visual since the contrast was not great enough for photographic 
methods. 
After the hot-wire measurements were completed, copper tubes were 
embedded in the wing flush with the upper surface and extending in the 
spanwise direction. Holes were drilled in the tubes at 11 spanwise 
stations so that the pressure profile could be measured at any station 
by closing the other 10 holes with airplane-model glue. The pressures 
were measured on a multiple manometer. Pressure distributions at 
angles of attack of 12 0 , lIi°, and 150 at an angle of yaw of 25 0
 were 
measured and pressure gradients were calculated. 
RESULTS AND DISCUSSION 
The camphor-evaporation tests described in the preceding section 
indicated that, for the results given here (250 sweepback, 120
 and 140 
angles of attack), transition on the upper surface occurred well within 
the first 10 percent of the local chord from the leading edge. Hence 
the main scale effect on these results is, in all likelihood, that 
associated with the turbulent boundary layers. 
The tuft photographs of figure 1 show the over-all character of 
the flow at 250 sweepback at angles of attack from 120 to 16. 0 . Even 
at an angle of attack of 120 there is considerable spanwise flow near
11.	 NACA TN 1946 
the trailing edge. This spanwise component becomes more and more 
pronounced as the angle of attack increases and some unsteadiness of 
the flow, as evidenced in the photographs by appreciable angular devi-
ation between adjacent tufts, is noticeable at an angle of attack 
Of 130. This tendency continues and., at a 140 angle of attack, at 
least the tip portion appears to be stalled.. The stalled area 
increases with angle of attack until at 16.50 it extends over the rear 
half of at least the outer third of the wing. 
Figures 4 and 5 show spanwise and chord.wise velocity profiles 
along the lines designated 1 and 2, respectively, In figure 3 for an 
angle of attack of 1149. As the trailing edge is approached, the chord-
wise profiles show qualitatively the change characteristic of a turbu-
lent boundary layer in an adverse pressure gradient. The spanwise 
profiles indicate that the spanwise boundary layer is considerably 
thinner, than the chordwise. On the other hand, the calculations of 
Sears and Wild (references 1 and 3, respectively) show that, for 
laminar flow over an infinite yawed cylinder, the two boundary layers 
are of approximately the same thickness. For a finite wing such as is 
used in the measurements reported here, there is a spanwise component 
near the wing due to the trailing vortex system. On the upper surface 
this component will be toward the root and will therefore oppose the 
outward spanwise flow due to sweepback. It will furthermore be vari-
able with distance from the surface. Hence any comparison between 
spanwise velocity profiles for finite and infinite wings must take into 
account the trailing vortex system. 
The change in flow direction through the boundary layer is quite 
large. The maximum change ch measured, for position 2-d of figure 5, was 
about 1000. 
The chordwise profile of figure 5, position 2-d, shows a region of 
reverse flow near the surface. In a two-dimensional.flow the point 
where the reverse flow begins, in general, marks the beginning of a 
turbulent wake in which the fluctuations are so high as to preclude 
measurements of mean-velocity profiles. In this case, however, while 
fluctuations were greater than nearer the leading edge, they were not 
especially troublesome. On the other hand, at the two outermost 
positions of figure 3 the fluctuations were too high to permit observa-
tions. These positions were therefore presumed to be in the turbulent 
wake; the pressure gradients of figure 6 bear out this presumption. 
Accordingly, the criterion for the point where the turbulent wake 
begins on a yawed wing does not appear to be clearly defined. The most 
reasonable criterion seems to be (Vvv	 0 where V I is the )y=o 
absolute velocity and y is the coordinate normal to the surface.
NACA TN 19 146
	
5 
According to the work of Von Doenhoff and Tetervin (reference 5) 
on the characteristics and separation of the two-dimensional turbulent 
boundary layer, the velocity profiles plotted against y/e constitute 
a one-parameter family, depending only on H- o */e, where * and 9 
are, respectively, the displacement and momentum thickness of the 
boundary layer. For laminar flow over a yawed airfoil, Wild (refer-
ence 3) calculated	 9, and	 where x and z are, 
respectively,the coordinates in the chordwise and spanwise directions. 
They are defined as follows: 
= fo, ( 	
Ui ) 
= f(l_)dY 
fi
--'---dy (.1
	
 
-I-I	 L 
e zz = I	 !_dy 
'do 
where u1 and w1 are, respectively, the chordvise and spanwise 
velocities at the outer edge of the boundary layer, and 5 is the 
boundary-layer thickness. 
Two sets of curves are shown in figure 7. The long-dashed curves 
were reported by Dryden (reference 6) on the basis of measurements on 
the two-dimensional flow over an airfoil shape at a high Reynolds 
number. The short-dashed curves were taken from the compilation by 
Von Doenhoff and Tetervin of a large nunthér of measurements on airfoils 
(reference 5)
.
 It appears that experimental points for the yawed wing 
reported here agree better with Dryden's curves, though there is a 
slight systematic deviation from the curve at y19 = i/u. His curves 
extend only to if = 2.8; the results in figure 7 indicate that the 
extrapolation to if = 3.2 is well justified. The results indicate 
that for angles of yaw up to 250 the turbulent chordwise profiles are 
In good agreement with two-dimensional results. It is quite possible 
that appreciable systematic differences will occur at higher angles of 
yaw.
6
	
NCA TN 1946 
The two-dimensional results reported by Dryden and by Von Doenhoff 
and Tetervin Indicated that separation occurred. when H reached a 
value of 2.6 to 2.8. Figure 7 shows, however, that, for the yawed wing, 
separation has not yet occurred for H = 3.18. For the separated 
chordwise profile of figure 5, H = 6.7. 
The values of	 and Hz were .calculated for a number of 
spanwise profiles but no systematic behavior could be detected. For 
Instance, in figures Ii. and 5 the values of these quantities are given 
along with 5*, 9, and H1. While H1 shows a steady increase as 
the trailing edge is approached, no such consistent trend is shown 
by H. As was pointed out earlier, one would expect the trailing 
vortex sheet to have an influence on the spanwise velocities, so that 
if the experiment were carried out for an airfoil which spanned a 
tunnel it is possible that the results would show a systematic depend-
ence on H. 
Von Doenhoff and Tetervin (reference 5) developed a method., based 
on the Von K&ma'n integral relation and on empirical results for calcu-
lating the growth of the turbulent boundary layer on a two-dimensional 
wing. They 'calculated H and 0 for several cases and found good 
agreement with experiment. 
Although the method was worked out for the two-dimensional case, 
an attempt was. made to apply it to the chordwise flow for the yawed 
finite wing. The faired measured values of H1 and exx for the 
first station along each of fourchordwise lines were taken as a 
starting point and the method was used to predict the values of. H. 
and 9xxas functions of x. Near the root the agreement with experi-
ment was fair but for other positions the deviation was marked.. In all 
cases the predicted. H1 increased much more rapidly with x than did 
the- measured values, especially near the trailing edge. 
For these calculations the pressure gradients shown In figure 6 
were used. These vectors represent the pressure gradient in magnitude 
and direction for three angles of attack. The change in the gradients 
near the tip for angles, of attack of l4.0 and 15 shows the change caused 
by tip stalling.
CONCLUSIONS 
On the basis of the results of measurements of the velocity 
profiles in the turbulent boundary layer of a yawed wing and analyses 
of the results, the following conclusions are drawn:
NACA TN 19146	 7 
1. The chord.wise flow in the turbulent boundary layer of a finite 
wing at an angle of yaw of 25 0
 may be expressed: 
f ((Hx 
U1 
The functional relationship is very nearly the same as that reported 
in NACA Technical Note 1168 for the unyawed wing. The extrapolation of 
the curves given in NACA Technical Note 1168 from Hx = 2.8 to H = 3.2 
in the present paper seems well justified. 
2. The maxinrin measured value of Hx
 for an unseparated chordwise 
profile was 3.18. For the unyawed wing the measurements of NACA 
Report 772 and NACA Technical Note 1168 showed that separation occurred 
for values of H of 2.6 to 2.8. 
3. The separation point for the chordwise profile does not neces-
sarily mark the beginning of the-turbulent wake for a yawed cylinder. 
The criterion for the beginning of the turbulent wake is 
probably (tVI)	 = 0, where IVI is the absolute velocity. 
Ii. The boundary layer for the chordwise flow is considerably 
thicker than that for the spanwise flow. The spanwise flow due to the 
trailing vortex system of a finite wing probably causes the distribution 
of this component to be highly dependent on the lift of the wing. 
University of Michigan 
Ann Arbor, Mich., April 22, 1949
8	 NACA TN 1946 
RW!S 
1. Sears, W. R: The Boundary Layer of Yawed. Cylinder. Jour. Aero. 
Sc., vol. 15, no. 1, Jan. 1948. 
2. Jones, Robert T.: Effects of Sweepback on Boundary Layer and 
Separation. NACA TN 1402, 1947. 
3. Wild, J. M.: The Boundary Layer of Yawed Infinite Wings. Jour. 
Aero. Sc., vol. 16, no. 1, Jan. 1949, pp. 11.1-45. 
4. Preston, J. H., and Sweeting, N. E.: Experiments on the Measurement 
of Transition Position by Chemical Methods. R. & M. No. 2014, 
British A.R.C., 1945. 
5. Von Doenhoff, Albert E., and Tetervin, Neal: Determination of 
General Relations for the Behavior of Turbulent Boundary Layers. 
NACA Rep. 772, 1943- 
6. Dryden, Hugh L.: Some Recent. Contributions to the Study of Tran-
sition and Turbulent Boundary Layers. NACA TN 1168, 1947.
a = 120. 
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NACA TN 1946 
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Figure 1.- Photographs of wing model mounted in tunnel for tuft studies. 
Sweepback angle, 250; various angles of attack a.•
Page intentionally left blank 
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NACA TN 1946	 11 
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Figure 2.- Calibration curved of hot-wire unit. The abscissa is the sum of the 
voltage drops across the two arms of the V unit, the ordinate is the 
difference. Calibrations were made at various angles of yaw * at air-
speeds of 15, 30, and 60 miles per hour. The curves for intermediate 
velocities are interpolated. Triangles represent the separate points of a 
traverse of the boundary layer. Positive values of * indicate Outward 
flow; * measured from free-stream direction.
12	 -	 NACA TN 1946 
Figure 3.-- Diagram of wing showing positions at which measurements were 
made. The system for the chordwise and spanwise directions is shown. 
The points at which measurements of velocity profiles were made are 
indicated by crosses. Sweepback angle, 25; angle of attack, 12 0 and 14°.
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Measurements in the boundary layer of a yawed wing

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