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/O0055 


3 1176 01325 9628 

NASA Technical Memorandum 100053 


NASA-TM- 100053 19880015516 


Characteristics of Merging 
Shear Layers and 
Turbulent Wakes of a 
Multi-Element Airfoil 

Desmond Adair and W. Clifton Horne 


February 1988 


l 


4 


, r-HARCM CENTER 
:-R1 M‘-S A 
;on, Virginia 


(\J/\SA 

National Aeronautics and 
Space Administration 



NASA Technical Memorandum 100053 


Characteristics of Merging 
Shear Layers and 
Turbulent Wakes of a 
Multi-Element Airfoil 

Desmond Adair 
W. Clifton Horne 

Ames Research Center, Moffett Field, California 


February 1988 


ms/\ 

National Aeronautics and 
Space Administration 

Ames Research Center 

Moffett Field, California 94035 






SYMBOLS 


c 

Cf 

C L 

C M 

C P 

FG 

FO 

H 

k 

rU 


n* 


n,s 


P 

R e 

U s 

0 . 

U S 

u x 

U,W,V 


<u 2 > 


<-uv>,<-uw> 


airfoil reference chord 

skin friction coefficient 

lift coefficient airfoil lift/( 1/2)pU 2 c 

oo 

o 

moment coefficient (moment around quarter chord)/( 1/2)pU 

co 

2 

pressure coefficient, (P - P ra )/( 1/2)pU m 

flap gap 

flap overlap 

shape factor, 6*/e 

turbulence kinetic energy 

length scale of free-stream turbulence 

location of 0.5(U m + U g ) 

boundary-layer coordinate system over the flap (normal and tangential 
to local surface) 

static pressure 

reference chord Reynolds number, pU m c/y 
velocity scale 

reference free-stream velocity 
velocity at edge of flap boundary layer 
friction velocity 

mean velocities (in boundary-layer coordinate system and in tunnel 
coordinates downstream) 

U-component of turbulence energy 

Reynolds shear stress 


iii 



<v 2 > 


<w 2 > 


x,z,y 


a 

A 

6 

6 f 

6 * 


6 


y 

v 

P 

e 

Y pu 

<> 


V-component of turbulence energy 
W-component of turbulence energy 

wind tunnel coordinate system (horizontal, vertical, spanwise) 
angle of attack, deg 

length scale of boundary -layer turbulence 
boundary-layer thickness 
flap deflection, deg 

f 6 

boundary-layer displacement thickness, I (1 - U/U )dZ 

J o e 

f 6 

boundary-layer momentum thickness, I U/U e (1 - U/U e )dZ, or flap normal 
angle relative to vertical 

absolute viscosity 

kinematic viscosity 

fluid density 

turbulence dissipation 

probability of downstream velocity 

time or ensemble average 


Subscripts 

e edge of boundary layer 

<» reference free-stream quantity 


Superscripts 

' perturbation from mean value 

m minimum 


iv 



SUMMARY 


Flow characteristics in the vicinity of the trailing edge of a single-slotted 
airfoil flap are presented and analyzed. The experimental arrangement consisted of 
a NACA 4412 airfoil equipped with a NACA 4415 flap whose angle of deflection was 
21.8°. The flow remained attached over the model surfaces except in the vicinity of 
the flap trailing edge where a small region of boundary-layer separation extended 
over the aft 7 % of flap chord. The flow was complicated by the presence of a 
strong, initially inviscid jet emanating from the slot between airfoil and flap, and 
a gradual merging of the main airfoil wake and flap suction-side boundary layer. 
Downstream of the flap, the airfoil and flap wakes fully merged to form an asymmet- 
ric curved wake. 

The airfoil configuration was tested at an angle of attack of 8.2°, at a Mach 
number of 0.09, and chord based Reynolds number of 1.8x10 in the Ames Research 
Center 7- by 10-Foot Wind Tunnel. Surface pressure measurements were made on the 
airfoil and flap and on the wind tunnel roof and floor. It was estimated that the 
wall interference increased the by 1 % and decreased the by 4.5$. Velocity 

characteristics were quantified using hot-wire anemometry in regions of flow with 
preferred direction and low turbulence intensity. A 3-D laser velocimeter was used 
in regions of flow recirculation and relatively high turbulence intensity. 

Detailed measurements of pressure and velocity characteristics are reported in 
the following sections with emphasis on flow over the suction surface of the flap 
and in the downstream wake. The relative importance of the terms in the momentum 
and turbulence kinetic energy equations is quantified for flow in the vicinity of 
the flap trailing edge. 


I . INTRODUCTION 


During takeoff and landing, flow over the aft portion of a multi-element air- 
foil can be subjected to strong adverse pressure gradients and involve merging shear 
layers, strong interaction between the inviscid flow, nonequilibrium turbulent 
boundary layers, streamline curvature, and asymmetric wakes. While prediction of 
such a complicated flow has improved in recent years as higher-order theories such 
as Navier-Stokes solutions (ref. 1) are gradually developed, the current ability to 
calculate these flows is not yet satisfactory (ref. 2). This is due in part to the 
limited availability of measurements necessary for a fuller understanding of flows 
in the neighborhood of the flap trailing edges. Generally, present prediction 
methods still require that the flow remains attached on the downstream element for 
successful theoretical predictions of pressure, mean velocity, and Reynolds 


1 



stress. It is frequently the case, however, that optimum configurations require 
strong flow interaction between wakes and boundary layers (ref. 3), and between 
viscous and inviscid flow regions, and a limited amount of boundary layer 
separation. 

The transport of momentum and energy by turbulence present in flow around 
multi-element airfoils usually plays a dominant role in determining the aerodynamic 
performance of airfoils equipped with mechanical high-lift systems (ref. 4). There- 
fore, development of mathematical models suitable for prediction of flows over and 
downstream of the aft section of a multi-element airfoil depends on sufficient 
knowledge and understanding of these turbulent processes. Of particular interest is 
the relative importance of the terms in the momentum and turbulence kinetic energy 
equations in the merging shear layers, the recirculating region, and the near 
wakes. An improved knowledge of the complex flow interactions associated with the 
confluent boundary layer and merging shear layers to which a computational model 
must be responsive, and for which a turbulence model is adequate, is also desirable 
(ref. 1). 

The present work describes one of a series of experiments designed to improve 
the understanding of turbulent flow over high-lift airfoils as a function of the 
angle of attack. Similar tests have been reported by references 4 and 5 for the 
present two-element airfoil. The first was for a moderate flap deflection angle and 
had no boundary-layer separation, whereas the second had a flap deflection angle 
which led to massive separation over the aft 61/5 of the flap. Work has also been 
completed on the single element NACA 4412 airfoil (ref. 6) operating close to maxi- 
mum lift. Progress as reported, for example, in references 7-9 has been made else- 
where in the provision of mean and turbulence field data for analysis and calcula- 
tion method development of single-element trailing edge flows experiencing separa- 
tion. Similar provision, with the exception of reference 10, is not evident for 
multi-element arrangements. Work related to the present investigation has been 
completed on static pressure measurements, flap optimization and mean velocity 
characteristics described, for example, in references 11 and 12 but turbulence 
quantities are not reported to any extent in these studies. Reference 13 is a 
report on the flow structure of the confluent region of an airfoil wake and turbu- 
lent boundary layer. Basic studies of interest to the present experiment are 
reported in references 14 and 15 where a confluent boundary layer and the initial 
region of boundary-layer separation have been investigated, respectively. 

In the following sections, the surface static pressure and detailed velocity 
characteristics are reported for flow over a NACA 4412 airfoil equipped with a 
NACA 4415 flap. An emphasis is put on reporting and analyzing flow over the suction 
surface of the flap and on the downstream wakes. The characteristics were quanti- 
fied using hot-wire anemometry and a 3-D, backscatter, laser velocimeter. The 
relative importance of the terms in the momentum and turbulence kinetic energy 
equations are quantified. 


2 


II. EXPERIMENTAL ARRANGEMENT 


Wind Tunnel and Model 

The test was conducted in the 7- by 10-Foot Wind Tunnel No. 1 at NASA Ames 
Research Center, Moffett Field, California. The closed-circuit wind tunnel has a 
working section 4.57 m in length, a constant height of 2.13 m, and a width which 
varies linearly from an initial value of 3.05 m to a final value of 3.09 m. There 
are no turbulence-reducing screens in the wind-tunnel circuit. The test section RMS 
turbulence levels, u'/U, v'/U, and w'/U, were equal to 0.0025, 0.0085, and 0.0085, 
respectively, for the chosen test conditions. 

A cross section of the airfoil/flap configuration is shown in figure 1 , and the 
model installation is shown in figure 2. It comprises a NACA 4412 main airfoil 
section equipped with a NACA 4415 flap airfoil section. The chord length (c) of the 
main airfoil is 0.90 m and that of the flap 0.36 m. The main airfoil angle of 
attack (a) was 8.2°. The geometric location of the flap relative to the main air- 
foil was specified by the flap gap (FG), the flap overlap (F0), and flap deflection 
(6f) as defined in figure 1. For the pressure and velocity characteristics pre- 
sented in this paper, FG = 0.035 c, F0 = 0.028 c, and 6^ = 21.8°. The model had a 
span of 3.05 m and was mounted horizontally in the test section to reduce optical 
flare when working close to the model surface. The intersections between walls and 
airfoil sections were sealed using felt pads to eliminate leakage between pressure 

and suction flows. Boundary-layer trips, about 0.15-mm thick and 4-mm wide, had a 

saw-tooth leading-edge. They were mounted on the suction and pressure surfaces of 
the main airfoil to ensure uniform flow transition across the span at x/c values 
of 0.025 and 0.010, respectively, from the pressure minimum. A similar trip was 
mounted on the suction side of the flap at an x/c value of 0.008 downstream of the 
flap pressure minimum. 

Surface static pressures were measured at 66 static orifices located on the 

centerline of the main airfoil and at 42 static pressure orifices located on the 

centerline of the flap. Two additional chordwise rows of 56 orifices each on the 
main airfoil and 42 orifices each on the flap were located at 0.35-span and at 
0.65-span. In addition, a spanwise row of 22 upper surface orifices was located at 
the 0.25-chord of the main airfoil and two spanwise rows of 12 upper-surface ori- 
fices each were located at the 0.25-chord and 0.85-chord locations on flap. The 
static pressure at these 350 static-pressure orifices was measured using eight 
48-port scanivalves equipped with ±7 kN/m^ pressure transducers. The transducer 
voltages were digitized and recorded on magnetic tape and the data then reduced to 
coefficient form. Repeatability in surface pressure data proved to be good at all 
test conditions with a maximum change in Cp of 0.6# noted between test runs. 
Integration of the pressure coefficients produced the section force and moment 
coefficients C L and C M . 


3 



Test Conditions 


The data presented in this paper are for a Mach number of 0.09 and a chord 
Reynolds number of 1.8x10^ corresponding to a tunnel velocity (U^) of 30.0 m/sec. 

The velocity was monitored using a Pitot-static probe located 1.4 chord lengths 
upstream of the main airfoil leading-edge and 0.61 m from the wind-tunnel floor. 
Extensive probing of the wind-tunnel wall boundary layers was conducted using tufts 
and surface oil visualization. No evidence of boundary-layer separation could be 
found in those regions. The test conditions resulted in a steady flow field with no 
flow separation over the main airfoil but with a small region of boundary-layer 
separation over the aft 7# of the flap. Streamwise flow fences encircling the main 
airfoil were installed at 0.175-span and 0.825-span locations to shield the central 
airfoil section from tunnel wall boundary layer interference. Tufts and surface oil 
visualization showed the flow to be two-dimensional over the central 65# of the main 
airfoil's span. The two-dimensionality of the flow over the airfoil flap was also 
investigated and tuft patterns are shown on figure 3. Over a stalled flap, it has 
been shown (ref. 16) that the flow can depart significantly from two- 
dimensionality. An effort was made to alleviate this using adjustable flow 
fences. The fences are shown in figure 3 and extended 30# of chord length on the 
upper and lower sides of the flap. It was not possible to use fences which ran the 
full length of the flap as optical access was required by the laser velocimeter. 

The final positions occupied by the flow fences were at 0.36-span and 0.64-span, and 
the two-dimensionality of the flow in the vicinity of the flap trailing-edge was 
estimated to occupy 25# of the flap span. 

In addition to surface oil and tuft visualization, two dimensionality of the 
flow was quantified using pressure and velocity characteristics. Chordwise distri- 
butions of pressure at several spanwise locations as shown on figure 4(a) were taken 
on the model centerline and at 482 mm to each side of the centerline, and are in 
good agreement. Figure 4(b) presents the mean spanwise velocity profiles over the 
flap and in the downstream wake at the centerline of the model. Spanwise velocities 
can be seen to be generally less than 3# of the free-stream velocity. Profiles of 
spanwise Reynolds normal stress are presented in figure 4(c) showing the development 
of main airfoil and flap wakes and their gradual merger. The spanwise Reynolds 
shear stress is also presented in figure 4(c) with values generally tending toward 
zero except in the near wake of the flap where values of around 7# of boundary-layer 
edge velocity can be found. 

For the mean velocity and turbulence measurements, profiles were made normal to 
the main airfoil or flap surfaces upstream of the flap trailing edge as described in 
table 1 and figure 5. In the downstream wake, profiles were made using wind-tunnel 
coordinates. Table 2 presents the orientation of the profiles relative to the 
vertical, the development of the boundary-layer edge velocity, and the physical 
thickness of the boundary layers and free shear layers. 


4 


Instrumentation 


Pressure characteristics were obtained using surface static pressure taps as 
reported in an earlier section. A sting-mounted Pitot-static tube of outside diam- 
eter 6.35 mm was used to obtain pressure measurements in the tunnel and roof 
boundary-layers. Vertical surveys were made at the mid-span location in the plane 
of the reference Pitot-static probe and at 1.5 c downstream of the flap trailing 
edge. 

Upstream of separation and for most of the wake, the flow had a preferred 
direction and comparatively low turbulence intensities. In these regions it was 
possible to quantify the velocity characteristics with stationary hot-wire ane- 
mometry. The sensors were first orientated to measure U, W, u' , w' , and <-uw>, 
followed by an orientation to obtain V, v', and <-uv>, where U, W, and V indicate 
streamwise, cross-stream, and spanwise velocities, respectively. Straight wire 
(DISA 55P10) and cross-wire (DISA 55P64) probes were operated with constant tempera- 
ture anemometers (DISA 55M10) and the instantaneous voltages were recorded digitally 
using an HP 1000 computer prior to analysis. The wires were operated at an overheat 
ratio of 1.8 and large signal amplifiers were used in the processing of the sig- 
nal. The bandwidth of the data acquisition system was 20 kHz and the nonlinear ized 
signals were sampled simultaneously at a rate of 10 samples/sec over a minimum 
period of 100 sec. Calibration of both flow velocity and flow angle was performed 
using a DISA hot-wire calibration rig with the resulting linearizations stored in 
the computer. 

In regions of reversed flow and high turbulence intensity, a 3-D laser veloc- 
imeter (described in refs. 17 and 18) was used. The LV system, shown in figure 6, 
is capable of measuring all three instantaneous velocity components (U,W,V) simulta- 
neously by means of three independent dual beam channels that operate in backscatter 
mode. To improve the sampling rate the method of coupling the three channels as 
reported in reference 15 was modified orthogonal coupling of the colors violet 
(476.5 nm) and green (514.5 nm) of an 8-W argon-ion laser to obtain samples of 
streamwise and cross-stream components of the mean velocity and the stress tensor 
components. This was followed by a second sample using nonorthogonal coupling of 
the blue (488.0 nm) and green colors to obtain the spanwise velocity. Vertical and 
streamwise motions of the focal volume were accomplished by moving the entire laser 
velocimeter on a digitally controlled platform. The repeatable positioning of the 
focal volume was better than 0.5 mm. The support platform was slightly yawed by 2° 
with respect to wind-tunnel coordinates, and was pitched downward by 2.75° to allow 
grazing contact of the focal volume at the semispan of the wing. The small pitch 
and yaw angles of the optical table result in slight coupling of all three velocity 
components and it is estimated that neglect of the spanwise component leads to a 
decrease in U, W, u', and w' of 0.6/S, 0.54$, 1.1%, and 0.92 %, respectively. An 
inherently poor signal-to-noise ratio is common to laser velocimeters using back- 
scatter. To alleviate the problem, it is desirable to minimize the processing 
bandwidth. However, this can lead to biasing of the incoming data. The present 
laser velocimeter incorporates programmable frequency synthesizers that generate 
mixing frequencies for each channel that can be varied under program control to 


5 



maintain the mean signal frequency at the center of the bandwidth. Frequency shift- 
ing by Bragg cells was employed to resolve directional ambiguity in the measured 
velocities. 

The laser was operated at a power setting of between 1.75 and 2 W, and the 
effective probe volume for each channel was found to be 5 mm for the green and 
violet beams and 2.5 mm for the blue. A mineral oil aerosol of nominal particle 
diameter 5 urn was introduced into the diffuser of the closed-circuit wind tunnel to 
provide nearly uniform seeding in the test section. 

Comparison was made between the hot-wire and laser velocimeter measuring tech- 
niques by comparing mean velocity and turbulence characteristics at two streamwise 
locations, the results of which are reported in reference 5. Good agreement was 
found between the two measuring techniques when recirculating flow was not present. 


III. EXPERIMENTAL RESULTS 


Mean Flow-Pressure 

Static pressure distributions measured over the main airfoil and flap surfaces 
at mid-span are presented in figure 7. Boundary-layer separation occurred over the 
aft 7$ of flap chord (2.8$ of chord), and can be recognized by the appearance of a 
short region of constant pressure close to the trailing edge of the flap. A local- 
ized increase in the flap suction pressure was noted at 20$ of flap chord (8$ of 
chord), just downstream of the main airfoil trailing edge. Integration of the 
pressure coefficients produced the section force (C L ) and moment (C M ) coefficients 
for the present setting. The uncorrected values of C L and C M were found to be 
3.19 and 0.99, respectively, and are comparable in magnitude to those reported in 
references 10 and 12. The coefficient of drag, C^, was estimated as 0.066 using a 
velocity profile measured one chord length downstream from the flap trailing edge. 


Wind-Tunnel Wall Interaction 

Static pressure measurements were made along the wind tunnel centerline close 
to the roof and floor of the test section. These measurements are shown in figure 8 
for the present study. The pressure signature on the tunnel walls extended upstream 
to the plane of the reference Pitot-static probe and downstream into the diffuser. 
Velocity profiles in the roof and floor boundary layers at the centerline of the 
tunnel in the plane of the flap trailing edge were obtained to give an indication of 
the displacement effect of the tunnel wall boundary layers. For the roof boundary 
layer, 6, 6*, and 9 were found to be 130 mm, 15 mm, and 12 mm, respectively. For 
the floor the same quantities were 146 mm, 18 mm, and 14 mm, respectively. Also 
presented in figure 8 are static pressure measurements taken along vertical trav- 
erses. These traverses were located at 1.4 chord lengths upstream of the main 
airfoil leading edge and at 1.28 chord lengths downstream of the flap trailing 


6 


edge. Flow angularity, measured using a five-tube Pitot probe in the plane of the 
reference Pitot probe, proved to be within ±0.2° from the tunnel centerline. 

To characterize the effect of tunnel-wall interference, calculations with and 
without wind-tunnel walls were made using the method of reference 19. For a flap 
deflection of 21.8°, the wall interference caused a 7 % increase in and a 4.5 % 

decrease in relative to the unconfined case. The correction for is in 

close agreement with that found when using the method for two-dimensional boundary 
corrections reported by reference 20. Thus it is recommended that the effect of 
wall interference should be taken into account when calculating this flow. 


Mean Flow-Velocity 

The characteristic boundaries and general organization of the flow domains are 
shown in figure 9 where y pu is the fraction of laser velocimeter samples having a 
positive value of streamwise velocity, U. Boundary-layer detachment was noted at 
25 mm upstream of the flap trailing edge and a small region of intermittent separa- 
tion occurred upstream of this. Negative flow was found to persist to about 27 mm 
beyond the trailing edge and a thin region of intermittent negative flow enveloped 
the mean negative flow. The maximum height of the recirculating flow was found to 
be 1 0 mm . 

The mean velocity vectors are plotted in figure 10. The strength of the jet 
emanating from the slot between main airfoil and flap is emphasized and the basic 
structure of the jet is seen to persist downstream of the flap trailing edge. This 
is in strong contrast to the mean velocity characteristics over the flap reported in 
reference 5, where the flap deflection was set at 5° more than the present configu- 
ration. In that case, the jet profile was found to have dissipated 90 mm from the 
main airfoil trailing edge. In common with results reported for single element 
trailing edge separation (ref. 7) the recirculating flow was found to be relatively 
weak in comparison to the mean velocity above. The mean flow streamlines in the 
region of the flap and in the near wake are shown in figure 11. The negative mean 
velocity region was bounded by the zero velocity streamline. In common with the 
flow of reference 9, the present boundary-layer separated under the action of 
adverse pressure gradient with convex curvature present and the curvature of the 
streamlines was less than that of the surface. 

Integral parameters for the flow over and downstream of the flap are presented 
in figure 12. The parameters were obtained by integrating the mean velocity pro- 
files from and in a direction normal to the flap surface until the flap trailing 
edge. Downstream 'of the flap trailing edge, the integration was carried out across 
the entire wake in a vertical direction. Shown in figure 12 is the development of 
the displacement and momentum thicknesses for the flap boundary layer, the main air- 
foil wake and the wake downstream of the flap trailing edge. Integration across the 
main airfoil wake showed that both displacement and momentum thickness steadily 
increased as the shear layer met increasingly adverse pressure gradients. In the 
wake, the same quantities gradually decayed and the shape factor (H) defined as 
6*/0 asymptotically approached 1.0. Integration of the mean velocity profiles for 


7 



the inner flap boundary layer up to the edge of the low turbulence jet indicated a 
steady growth in the shape factor. H was found to be 2.89 at 25 mm upstream of the 
flap trailing edge, and just upstream of the flap trailing edge, it was found to be 
3.6. Care should be taken when interpreting the shape factor because of the fact 
that the jet flow has significant turbulence present especially close to the trail- 
ing edge. Reference 21 has shown that this may lead to an overestimation of the 
shape factor. 

Profiles of streamwise mean velocity are shown in figure 13 for the 22 stations 
of table 1 . The velocity profile over the main airfoil is consistent with that 
boundary layer in an adverse pressure gradient. Just downstream of the main airfoil 
trailing edge (station Nos. 4-6), the turbulent boudary layer on the flap was found 
to be initially thin but gradually broadened with downstream distance. The magni- 
tude of the reversed flow in the vicinity of the trailing edge was very small with a 
maximum of 1.2 m/sec noted. The initially inviscid jet dominates the near wall flow 
over the flap. The jet flow structure can be seen in the mean velocity profile 
beyond the flap trailing edge at x/c of 1.322 (station No. 14) separating the main 
airfoil and flap wakes. In the near wake, the strength of the jet gradually decayed 
and at 400 mm (station No. 17) downstream of the main airfoil trailing edge, only a 
remnant of the jet remained. Downstream, the main airfoil and flap wakes fully 
merged. Profiles farther downstream were similar to that at station No. 18 indicat- 
ing the development of an asymmetric wake. 

The cross-stream velocity is presented in figure 14. Generally its value over 
the main airfoil and initial flap surfaces tended to zero. In the vicinity of the 
flap trailing edge, cross-stream velocities in the outer region of the airfoil wake 
reach values of up to 40% of edge velocity and close to the surface negative values 
of just less than 20$ of edge velocity are found. Strong variations in cross-stream 
velocity were found in the wake close to the flap trailing edge. This variation 
tends to diminish with streamwise distance until an almost zero cross-stream veloc- 
ity profile is noted at x/c of 2.558 (station No. 22). 

The laser velocimeter gave information on the probability of downstream flow, 
Ypu ? in fch e vicinity of separation as shown in figure 15. Intermittent reversed 
flow started at 9$ of flap chord length from the flap trailing edge and the y du 
values decreased with downstream distance. Y pu was never found to be zero, indi- 
cating no constant fully reversed flow in any part of the recirculating flow. The 
lowest value of Yp U was found to be 0.2 just after the flap trailing edge. 


Turbulence 

The development of Reynolds stresses over the main airfoil and flap suction 
surfaces and in the downstream wake are shown in figures 16-18. Comparison of the 
data obtained at x/c = 0.989 (station No. 3) with that obtained at x/c = 1.031 
(station No. 5) in figures 16 and 17 shows that there was a slight change (10$) in 
the level of turbulence energy near the centerline of the wake as the boundary layer 
on the upper surface of the wing moved into the near wake. The peak in the stream- 
wise Reynolds normal stresses originating from the main airfoil suction-side 


8 


boundary layer continued to increase with streamwise distance until the flap trail- 
ing edge. This well-accepted trend for flows in strong adverse pressure gradients 
is also noted for the peak in the streamwise Reynolds normal stresses originating 
from the main-airfoil pressure-side boundary layer. Just before the trailing edge, 
these dual peaks have merged to form a broad maximum for the streamwise Reynolds 
normal stress profiles (fig. 16) whereas a distinct minimum still existed in the 
cross-stream Reynolds normal stress profiles (fig. 17) in the region of jet flow. 

The flap boundary layer was found to be initially thin with low turbulence pre- 
sent. Downstream at the flap trailing edge (x/c = 1.308 (station No. 12)) this 
inner layer was still relatively thin but the peak value of streamwise Reynolds 
normal stresses had increased dramatically (by 1 30% ) when compared to its value at 
x/c = 1.031 (station No. 5). This marked increased in the turbulence level for the 
inner flap boundary layer close to the flap trailing edge was also found for the 
cross-stream Reynolds normal stresses. A gradual increase in the turbulence level 
accompanied by a reduction in its width with streamwise distance was noted for the 
low turbulence region of jet flow. 

The Reynolds shear stress profile (fig. 18) just downstream of the main airfoil 
trailing edge (x/c = 1.031 (station No. 5)) shows a 40$ increase in its peak value 
when compared to the profile at x/c = 0.989 (station No. 3). The negative peak in 
the Reynolds shear stress profile emanating from the pressure side main airfoil 
boundary layer was found to grow more negative with streamwise distance over the 
flap. The value of Reynolds shear stress increased in the thin inner flap boundary 
layer with streamwise distance and on approaching boundary layer separation its 
value tended to zero very close to the flap wall. Its value did not go negative as 
would be expected when boundary layer separation is present, possibly because of the 
limitations of the 3-D laser velocimeter in making measurements close to the flap 
surface. 

In the region just downstream of the flap trailing edge, for about 50 mm, both 
the streamwise and cross-stream Reynolds normal stress profiles were double peaked 
and did not exhibit much change near the wake centerline. The suction-side peak in 
the streamwise Reynolds normal stress profiles (fig. 16) increased by some 25 % in 
this region whereas the turbulence energy in the pressure side peak remained fairly 
constant. Downstream rapid changes occurred in the Reynolds normal stress profiles 
(figs. 16 and 17) near the wake centerline, and for both streamwise and cross-stream 
components the pressure side peak gradually decayed and broadened across the 
layer. The streamwise Reynolds normal stresses (fig. 16) developed single peaked 
profiles just after x/c = 2.558. 

In the very near wake, the Reynolds shear stress remained fairly constant in 
the suction-side shear layer even under the combined influence of adverse pressure 
gradient and destabilizing streamline curvature. There was a slight increase in its 
positive peak value from x/c = 1.336 (station No. 15) to x/c = 1.558 (station 
No. 18) after which there was a gradual decay. The negative peak in the Reynolds 
shear stress profile gradually decayed from just downstream of the flap trailing 
edge to x/c = 1.808 (station No. 19) after which it remained fairly constant until 
the final profile measured at x/c = 2.558 (station No. 22). 


9 


IV. DISCUSSION 


The flow in the vicinity of the main airfoil trailing edge was subjected to 
adverse pressure gradients with no boundary layer separation present. A universal 
velocity profile has been proposed preference 23 for such flows providing that for 
a given velocity profile (<-uw>) max /u <i > 1.5 (as was found in the present flow) 
where u t is the friction velocity. The proposed similarity parameters used in the 
universal velocity profile were a velocity scale U s and a length scale A, where 



L is the distance from the wall to the maximum shear location. Velocity profiles 
measured in the suction-side boundary layer of the main airfoil are compared with 
the Perry-Schof ield proposal in figure 19. Good agreement is noted except for the 
profile taken at the trailing edge. In the original Perry-Schof ield analysis of 
attached boundary layers, the quadratic turbulence terms were neglected as making 
negligible contributions to the shear stress. The proposal of reference 24 to 
redefine [<-uw>^^]__ v . and L using a "pseudo shear stress" to alleviate this dis- 
agreement has been used in references 25 and 26. The "pseudo shear stress" was 
defined as 



dn 

I max 


Agreement between the profile taken at x/c = 0.989 and the Perry-Schof ield 
proposal was improved when the "pseudo shear stress" was used. In common with the 
findings of reference 25, increase scatter with increasing adverse pressure gradi- 
ents was noted in the velocity profiles. 

Flow structure was obtained for the near wall region in the attached boundary 

layer and reversed flow regions over the flap. The velocity at the edge of the flap 

boundary layer (U fi ) was used to plot the Clauser charts in figure 20. It can be 

seen from the plots of U/U g versus log(nU g /v) that a law-of-the-wall profile is 

evident. This is in agreement with the findings of reference 13. The skin friction 
(C|») values deduced from these Clauser charts and listed in figure 20 may be in 
error. Normally the flow above a boundary layer has no — or at most very low — 
turbulence present. In the present study, the flap boundary layer lies beneath a 
jet whose turbulence intensity increases with streamwise distance, and it has been 
recently realized that a change in the combination of free-stream turbulence 


10 



intensity and length scale will cause the skin friction to change (ref. 21). The 
empirical parameter 



has been suggested to correct for the imposition of free-stream turbulence on the 
skin friction coefficient (ref. 21). is the length scale of the free stream 
turbulence defined as 


d(<u 2 >) ( 

dx 


-«u*»3« 

,u 


(3) 


While noting that in the present flow the free-stream length scale and turbu- 
lence was increasing with streamwise direction, whereas it was decreasing in the 
flow of reference 21, use of the correction technique suggests that for x/c = 1.127 
the Cf value found from figure 20 may be estimated low by as much as 18$. 

Reference 13 has proposed a single algebraic formulation to describe the mean 
velocity profiles for the main airfoil wake such as 

1“ - - U J -- [' - - "«]/["* - "J]J W 

In this equation, U g refers to the shear-layer edge velocity, nn to the location 
of minimum mean velocity, and n* to the ordinate of the point wnen the velocity 
is 0.5 (U m + U g ). Because of the asymmetric nature of the wake, it is evident that 
the wake should be subdivided with U e representing the upper and lower shear-layer 
edge velocities as appropriate. Profiles of the present data taken in the main 
airfoil wake over and downstream of the flap are shown in figure 21. The proposed 
velocity profile represents the present data with reasonably good accuracy although 
more scatter was noted in the present measurements than found by Bario in refer- 
ence 13. This is a similar result to that reported in reference 10. It would 
appear that the use of velocity and length scales in the form of equation (4) will 
successfully collapse the mean velocity profiles of the airfoil wake. Turbulence 
quantities are also important in this region but it is doubtful that scaling similar 
to that for the mean velocity profiles can be applied because of their complexity. 

Reynolds shear correlation coefficient <uw>/[<u > • <w > ] is shown in 

figure 22 for flow over the suction side of the flap and including the main airfoil 
wake. In general, the profiles are similar in nature to those found in reference 13 
with an maximum absolute value of 0.52. This higher-than-normal value (usually the 
Reynolds shear correlation coefficient's value never exceeds 0.48 (ref. 27)) was 
explained in reference 13 as being in accordance with the presence of large eddies 
in the turbulent flow for low Reynolds number flows. This may be the explanation, 
but it is also the case that the maximum correlation value found in the present flow 
is within experimental error of that found by reference 27. 


11 



The terms in the streamwise and cross-stream momentum equations were examined 
using the measurements described in the previous sections. The momentum equations 
in two dimensions are 

it 1M u — - - — 3 <- uw > 3 <u 2 > 

U 3X + W 3Z = ~ p 3X + 3Z " 3X 

( 5 ) 

? 

II 3W 3M 1 3P 3<-uw> 3<W > 

U 3X + W 3Z ” ~ p 3Z + 3X ” 3Z 

The terms are plotted in figures 23 and 24 where the locations shown were at 
35# and 3.5# of flap chord upstream of the flap trailing edge, and at 14# of flap 
chord downstream of the flap trailing edge. At the first location, the main airfoil 
wake and flap boundary layer had not merged; and at the second location, there was a 
small region of boundary layer separation close to the surface and significant 
turbulence in the jet. At the location in the wake some intermittent backflow was 
still present. For both momentum equations the viscous terms were neglected as they 
proved to be much smaller than the remaining terms. For the streamwise momentum 
equation at the upstream location, the pressure gradient is opposed mainly by the 
Reynolds normal and shear gradients close to the flap wall whereas convection is 
dominant farther out in the profile because of the presence of the low turbulence 
jet. Downstream at x/c = 1.296 the Reynolds normal and shear stress component are 
important close to the wall. Convection is seen to be important for 
0.2 < n/6 < 0.4 again because of the presence of the jet. Downstream in the wake 
the Reynolds shear stress gradient becomes the dominant quantity in the vicinity of 
the flap trailing edge. 


An increase by an order of magnitude in the maximum cross-stream pressure 
gradient was found when its value at the upstream location was compared with those 
in the vicinity of the trailing edge. At the station x/c = 1.187, the cross-stream 
pressure gradient is principally opposed by the Reynolds normal stress gradient with 
convection playing a minor role. Downstream at x/c = 1.296 the Reynolds normal 
stress gradient is important in the cross-stream momentum equation especially close 
to the wall in the vicinity of boundary-layer separation. This was also reported in 
references 8 and 12. In the wake, the cross-stream pressure gradient generally 
decreases across the shear layers except for a small region downstream of the flap 
trailing edge where large values are noted balancing convection and the Reynolds 
normal stress gradient terms. 


The 'turbulence kinetic energy equation is 


U 3k W 3k 
2 3x + 2 3Z 



. . 3U ,2. . 2. . 3U 

<UW> 3Z~( <U> ~ <W> ^3x +e 


( 6 ) 


where the terms on the left-hand side are advection and on the right-hand side are 
turbulent diffusion, turbulent-shear-stress production, normal stress production and 
dissipation, respectively. The terms of the equation are plotted in figure 25. The 
turbulence energy equation components were examined for the same locations as for 
the momentum transport equations. Dissipation was not measured and appears in the 
imbalance of figure 25. At x/c = 1.187 advection was found to be important in the 


12 


jet flow whereas shear-stress production was dominant close to the flap wall and in 
the lower half of the airfoil wake. Close to the flap trailing edge of the wake all 
three terms' advection, shear stress production and normal stress production become 
important at various regions of the two stations examined. Shear stress production 
is very prominant in the near wake close to the flap trailing edge and in the main 
airfoil wake. 


V. CONCLUDING REMARKS 


Measurements of the mean values of pressure and velocity have been presented 
for the flow over and in the downstream wake of a single-slotted airfoil/flap con- 
figuration. The results indicate a rapid growth of turbulence in the inner boundary 
layer in the vicinity of the flap trailing edge. The initially inviscid jet had a 
dominant influence on the near wall flow over the flap and in the near wake. There 
is a log-linear region in the flap boundary layer but care may be needed in deducing 
the skin friction caused by the presence of substantial turbulence in the jet flow 
above. The Reynolds normal stress gradient in the cross-stream momentum equation 
proved to be important for the flow over the flap and in the near wake. 

The model was relatively large when compared to the wind-tunnel cross- 
section. Thus it is recommended that the effects of wind-tunnel wall interference 
should be considered when calculating the flow field. 


ACKNOWLEDGMENTS 


The authors gratefully acknowledge the support and helpful suggestions of 
Mr. V. Corsigilia and Dr. L. Olson during the experimental phase of the work. 


13 


REFERENCES 


1. Schuster, D. M. ; and Birkelbaw, L. D.: Numerical Computations of Viscous 

Flowfields about Multiple Component Airfoils. AIAA Paper 85-0167, Jan. 

1985. 

2. Cebeci, T.; Stewartson, K.; and Whitelaw, J. H. : The Calculation of Two- 

Dimensional Flow Past Airfoils. Numerical and Physical Aspects of 
Aerodynamic Flows II. Springer-Verlag, 1 983 . 

3. Loudet, C.: Contribution Theorique et Experimentale a L'Etude des Grilles 

D'Aubes en Tandem a Forte Deflexion et a Forte Change. Thesis, Institut von 
Karman, Belgique, 1971. 

4. Olson, L. E. ; and Orloff, K. L.: On the Structure of Turbulent Wakes and 

Merging Shear Layers of Multielement Airfoils. AIAA Paper 81-1238, June 

1981. 

5. Adair, D.; and Horne, W. C.: Characteristics of a Separating Confluent 

Boundary-Layer and the Downstream Wake. NASA TM- 100046, 1987. 

6. Wadcock, A. J.: Investigation of Low-Speed Turbulent Separated Flow Around 

Airfoils. NASA CR-177450, 1987. 

7. Nakayama, A. : Measurements of Attached and Separated Turbulent Flows in the 

Trailing-Edge Regions of Airfoils. Numerical and Physical Aspects of 
Aerodynmic Flows II. Springer-Verlag, 1984. 

8. Viswanath, P. R.; and Brown, J. L.: Separated Trailing-Edge Flow at a 

Transonic Mach Number. AIAA J., vol. 21, no. 6, 1983, pp. 801-807. 

9. Adair, D. : Characteristics of a Trailing Flap Flow with Small Separation. 

Expts. in Fluids, vol. 5, 1987, pp. 114-128. 

10. Braden, J. A.; Whipley, R. R.; Jones, G. S.; and Lilley, D. E.: Experimental 

Study of the Separating Confluent Boundary-Layer. NASA CR-3655, 1983. 

11. van den Berg, B.: Boundary Layer Measurements on a Two-Dimensional Wing with 

Flap. NLR Report TR 79009U, National Aerospace Lab., Amsterdam, 1979. 

12. Ljungstrom, B.: Wind Tunnel High Lift Optimization of a Multiple Element 

Airfoil. FFA TN AU-778, The Aeronautical Research Institute of Sweden, 

1976. 

13. Bario, F.; Charnay, G.; and Papailiou, K. D.: An Experiment Concerning the 

Confluence of a Wake and a Boundary Layer. J. Fluids Eng., vol. 104, 1982, 
pp. 18-24. 


14 


14. Pot, P. J.: A Wake Boundary Layer Mixing Experiment. Turbulent Shear Flows II 

(Ed. Bradbury), Springer-Verlag, 1979. 

15. Simpson, R. L.; Chew, Y. T.; and Shivaprasad, B. G.: The Structure of a 

Separating Boundary Layer. Parts 1-3, J. Fluid Mech., vol. 113, 1981, 
pp. 23-90. 

16. Winkelmann, A. E.: Flow Fields Surveys of Separated Flow on a Rectangular 

Planform Wing. AIAA Paper 81-0255, Jan. 1981. 

17. Orloff, K. L.; Snyder, P. K. ; and Reinath, M. S. : Laser Velocimetry in the 

Low-Speed Wind Tunnels at Ames Research Center. NASA TM-85885, 1984. 

18. Snyder, P. K.; Orloff, K. L.; and Reinath, M. S.: Reduction of Flow- . 

Measurements Uncertainties in Laser Velocimeters with Nonorthogonal 
Channels. AIAA J., vol. 22, no. 8, 1984, pp. 1115-1123. 

19. Maskew, B. : Program VSAERO, a Computer Program for Calculating the Non-Linear 

Aerodynamic Characteristics of Arbitrary Configurations. NASA CR— 166476 , 

1982 . 

20. Rae, W. H.; and Pope, A.: Low-Speed Wind Tunnel Testing. Wiley, New York, 

1984. 

21. Hancock, P. E.; and Bradshaw, P.: The Effect of Free-Stream Turbulence on 

Turbulent Boundary Layers. J. Fluids Eng., vol. 105, 1983, pp. 284-289. 

22. Chevray, R. ; and Kovasznay, L. S. G.: Turbulence Measurements in the Wake of a 

Thin Flat Plate. AIAA J., vol. 7, no. 8, 1969, pp. 1641-1643. 

23. Perry, A. E.; and Schofield, W. H. : Mean Velocity and Shear Stress 

Distributions in Turbulent Boundary Layers. Phys. Fluids, vol. 16, no. 12, 
1973, pp. 2068-2074. 

24. Simpson, R. L.; Strickland, J. H.; and Barr, P. W. : Features of a Separating 

Turbulent Boundary Layer in the Vicinity of Separation. J. Fluid Mech., 
vol. 79, no. 3, 1977, pp. 553-594. 

25. Schofield, W. H.: Two-Dimensional Separating Boundary Layers. AIAA J., 

vol. 24, no. 10, 1986, pp. 1611-1620. 

26. Nakayama, A.: Characteristics of the Flow Around Conventional and 

Supercritical Airfoils. J. Fluid Mech., vol. 160, 1985, pp. 155-179. 

27. Murlis, J.; Tsai, H. M. ; and Bradshaw, P.: The Structure of Boundary Layers at 

Low Reynolds Numbers. J. Fluid Mech., vol. 122, 1982, pp. 13-56. 


15 



TABLE 1.- VELOCITY SURVEY STATIONS (refer to figure 5) 


Station 

number 

x/c 

Type of shear 
layer 

Orientation of 
survey line 

1 

0.495 

Boundary layer 

Normal 

to airfoil surface 

2 

0.756 

Boundary layer 

Normal 

to airfoil surface 

3 

0.989 

Boundary layer 

Normal 

to airfoil surface 

4 

1.000 

Wake 

Normal 

to flap surface 

5 

1.031 

Wake and boundary layer 

Normal 

to flap surface 

6 

1.091 

Confluent boundary layer 

Normal 

to flap surface 

7 

1.127 

Confluent boundary layer 

Normal 

to flap surface 

8 

1.187 

Confluent boundary layer 

Normal 

to flap surface 

9 

1.236 

Confluent boundary layer 

Normal 

to flap surface 

10 

1.284 

Separated boundary layer 

Normal 

to flap surface 

11 

1.296 

Separated boundary layer 

Normal 

to flap surface 

12 

1.308 

Separated boundary layer 

Normal 

to flap surface 

13 

1.315 

Wake with recirculating flow 

Tunnel 

coordinates 

14 

1.322 

Wake with recirculating flow 

Tunnel 

coordinates 

15 

1.336 

Wake with recirculating flow 

Tunnel 

coordinates 

16 

1.364 

Wake 

Tunnel 

coordinates 

17 

1.447 

Wake 

Tunnel 

coordinates 

18 

1.558 

Wake 

Tunnel 

coordinates 

19 

1.808 

Wake 

Tunnel 

coordinates 

20 

2.058 

Wake 

Tunnel 

coordinates 

21 

2.308 

Wake 

Tunnel 

coordinates 

22 

2.558 

Wake 

Tunnel 

coordinates 


16 




TABLE 2.- SUCTION-SIDE SURFACE 


Station 

number 

x/c 

u e' 

m/s 

fi 0.995' 

mm 

0, 

Deg 

1 

0.495 

49.82 

18 

13 

2 

0.756 

48.92 

23 

17 

3 

0.989 

46.79 

36 

23 

4 

1.000 

45.00 

82 

8 

5 

1.031 

44.71 

88 

14 

6 

1.091 

43.52 

95 

28 

7 

1.127 

42.65 

114 

33 

8 

1.187 

41.6 

127 

37 

9 

1.236 

40.07 

152 

43 

10 

1.284 

33.20 

175 

43.5 

11 

1.296 

30.30 

180 

43.8 

12 

1.308 

29.35 

190 

44 


WAKE 


Station 

number 

x/c 

U (Upper), 
m/s 

U (Lower), 
m/s 

*0.995' 

mm 

13 

1.315 

35.57 

29.95 

190 

14 

1.322 

33.09 

29.44 

195 

15 

1.336 

31.63 

29.07 

197 

16 

1.364 

30.77 

28.95 

205 

17 

1.447 

30.38 

28.30 

200 

18 

t.558 

29.94 

28.49 

203 

19 

1.808 

28.96 

28.23 

206 

20 

2.058 

28.60 

28.98 

210 

21 

2.308 

28.57 

28.73 

215 

22 

2.558 

28.33 

28.31 

220 


17 








TUNNEL ROOF 



AIRFOIL 

COORDINATES 


WAKE 

COORDINATES 


TUNNEL FLOOR 


Figure 1.- Installation of airfoil in the Ames 7- by 10-Foot Wind Tunnel 


Figure 2.- Photograph of model installation in the Ames 7- by 10-Foot Wind Tunnel 





Figure 3.- Flow visualization of the flap trailing-edge region using tufts. 


19 


12 


10 
8 
6 

°P 

4 
2 
0 
-2 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

Xfc 


♦ Sparwise Location y/c 

_3 

ll 

0.0 □ 

3 055 ♦ 





I ' " I 1 1 I 



Figure 4(a).- Spanwise mean pressure measurements. 


20 




















<-uv>/U e 2 x10 2 <-uv>/U e 2 x10 2 


Figure 4(c) . (cont'd)- Spanwise 



<-uv>/U e 2 x10 2 <-uv>/Ug 2 x10 2 


s shear stresses in the downstream wake. 










I\J 

<r> 



1.2 


i.oH 


0.8 H 


rVS 


0.6 


0.4 H 


0.2 H 



<-uv>/U e 2 x10 2 


Figure 4(c) . (concluded)- Spanwise 


Xfc- 1.127 


• 2-1 


x/C- 1.236 


D 

1.0- 

a 

□ 


a 

□ 


a 

a 

0.8- 

a 

a 


a 

a 


a 

a 


a 


0.6- 

a 

□ 

rVS 

a 



a 



a 

a 



a 

0.4- 

a 

a 



a 


a 


a 

a 


a 

a 

a 

0.2- 

a 

a 

a 

a 


a 

a 


a 

a 

a 


a 

i 

Q.u n 

■ 


0.0 0.1 - 0.1 0.0 0.1 


<-uv>/U e 2 x102 


<-uv>/U e 2 x10 2 


shear stresses upstream of separation. 









2 


4 

S 

6 

11.12 

IB 19 20 21 22 

t I I i I 

13.14.1S.16 

EXPERIMENTAL PROFILES 
• HOTWIRE 
■ LDV 

Figure 5.- Orientation and location of velocity profiles. 


Z-DRIVE MOTOR 




Figure 6.- 3-D Laser velocimeter in relation to the wind-tunnel and model. 


27 





*• r 


5 ' 1 

0.2 -0 


a 

a 

■ 

.1 0.0 0.1 



Floor 


0.5 




-2 -1 


0 1 

x/c 


■u.h r 


a 


- 0.8 ^ 
- 0.1 


I 


■ 

0.0 



Figure 8.- Tunnel wall pressure measurements. 



Figure 9.- Flow domains in the vicinity of the airfoil flap trailing edge 





I 



Figure 10.- Vectors representing mean velocity in the vicinity of recirculation. 



Figure 11.- Streamlines in the vicinity of recirculation. 


30 





Figure 12.- Integral parameters of mean-flow development. 


31 




Figure 13.- Distribution of streamwise mean velocity (Station numbers refer to 

Table 1 and Fig. 5). 




Figure 13.(cont'd)- Distribution of strearawise mean velocity (Station numbers 

refer to Table 1 and Fig. 5). 




Figure 13.(cont'd)- Distribution of streamwise mean velocity (Station numbers 

refer to Table 1 and Fig. 5). 


DDQ 



Figure 13.(cont'd)- Distribution of streamwise mean velocity (Station numbers 

refer to Table 1 and Fig. 5). 




0.20.00.20.40.60.81.01.2 

-0.20.00.20.40.60.81.01.2 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 

u/u e 

u/u e 

u/u e 

U/U e 


Figure 13.(cont'd)- Distribution of streamwise mean velocity (Station numbers 

refer to Table 1 and Fig. 5). 










Figure 13. (concluded)- Distribution of streamwise mean velocity (Station numbers 

refer to Table 1 and Fig. 5). 



refer to 







6 



0.0 0.2 0.4 
w/u e 


Lon numbers 






in of cross-flow mean velocity (Station numbers 
o Table 1 and Fig. 5). 







an 









in of cross-flow mean velocity (Station numbers 
Table 1 and Fig. 5). 



.2 


10 


1.2 


-fcr 

cr\ 




LOH 


0.8 H 


o.a H 
rV5 | 


O.A A 


0.2 


0.0 


0.0 


Y PU 


Y PU 


Figure 15.- Probability 


of positive velocity 
Table 1 and Fig. 5 ] 





□a □ □ a a a □ □ □ 












Figure l6.(cont'd)- Distribution of Reynolds normal stresses (Station numbers refer 

to Table 1 and Fig. 5). 



Figure l6.(cont'd)- Distribution of Reynolds normal stresses (Station numbers refer 

to Table 1 and Fig. 5). 






<u 2 >/U e 2 x10 2 <u 2 >/U 0 2 x1O 2 <u 2 >/U e 2 x10 2 


Figure l6.(cont'd)- Distribution of Reynolds normal stresses (Station numbers refer 

to Table 1 and Fig. 5). 



22 


U 2 >/U e 2 x102 


<u 2 >/U e 2 x10 2 



<u 2 >/U e 2 x10 2 


Figure 1 6. (concluded)- Distribution of Reynolds normal stresses (Station numbers 

refer to Table 1 and Fig. 5). 









• 2-1 


• 2*1 


6 





<w 2 >U e 2 x102 <w2>/U e 2 x102 <w 2 >/U e 2 x10 2 


Figure 17.(cont'd) - Distribution of Reynolds normal stresses (Station numbers 

refer to Table 1 and Fig. 5). 



1 . 2 - 
1.0 H I 


7 




o.o H 1 1 

0.0 1.0 2.0 



rV5 


1.2 


i.o H 


0.8 H 


0.6-1 


0.4 i 


0.2 H 


0.0 


□ 

D 


n 

B 


□ 

a 

a 


B 

□ 

□ 

□ 


a 

□ 


2 


<w 2 >/U e 2 x10 2 


<w 2 >U e 2 x10 2 


<w 2 >/U e 2 x10 2 


Figure 17.(cont'd) - Distribution of Reynolds normal stresses (Station numbers 

refer to Table 1 and Fig. 5). 


a b 










19 



□ 

a 

□ 

Q 

□ 

□ 

B 

a 

a 

a 

a 

□ 

□ 

, 


n 

2 


w 2 >/U 0 2 x1O 2 


<w 2 >/U e 2 x10 2 


<w 2 >U e 2 x102 


Figure 17.(cont'd) - Distribution of Reynolds normal stresses (Station numbers 

refer to Table 1 and Fig. 5). 



22 


□ 

a 


a 

□ 


a 

a 

□ 

0 

a 

a 

Q 

B 


1 

2 


\w 2 >/U e 2 x10 2 


<w 2 >/U e 2 x10 2 


<W 2 >/U e 2 x10 2 


Figure 17. (concluded) - Distribution of Reynolds normal stresses (Station numbers 

refer to Table 1 and Fig. 5). 





-uw>/U e 2 x 10 2 


<-uw>/U 0 2 x1O 2 


<-uw>/U e 2 x10 2 


Figure 18.- Distribution of Reynolds shear stresses (Station numbers refer to 

Table 1 and Fig. 5). 






b □ n 






Figure l8.(cont'd)~ Distribution of Reynolds shear stresses (Station numbers 

refer to Table 1 and Fig. 5). 


bob 










Figure 18. (cont'd)- Distribution of Reynolds shear stresses (Station numbers 

refer to Table 1 and Fig. 5). 







21 


□ 

a 



T 1 I 


10 12 



Hiw>/U e 2 x10 2 


<-uw>/U e 2x10 2 


<-uw>/U e 2 x102 


Figure 18. (concluded)- Distribution of Reynolds shear stresses (Station numbers 

refer to Table 1 and Fig. 5). 




Figure 19.- Mean velocity profiles normalized by Perry-Schof ield (1973) profile. 
Solid lines are the limits of scatter in data used by Perry and Schofield. 



Figure 20.- Near-wall mean velocities upstream of and in the vicinity of the 

backflow. 


69 





[U-UJ/IU 



l n “ n Um 1 ^ t n -"uml 


Figure 21.- The velocity distribution in the main airfoil wake. Solid lines 

derived from Equation 4. 


70 




0.0 0.2 0.4 0.6 0.8 1.0 1.2 

n/8 


Figure 22.- Shear correlation coefficient. 


71 




Figure 23.- Terms in the streamwise momentum transport equation. 





erms 






Terms x 10 



Figure 25.- Terms in the turbulence kinetic energy transport equation. 








NASA 

Natonai ^ronautcs and 
Space Administration 


1. Report No. 


Report Documentation Page 


2. Government Accession No. 


3. Recipient's Catalog No. 


NASA TM-100053 

4. Title and Subtitle 


5. Report Date 


February 1988 

Characteristics of Merging Shear Layers and Turbulent Wakes of a Multi-Element - Performjng organization Code 
Airfoil 


7. Author(s) 


Desmond Adair and W. Clifton Horne 


8. Performing Organization Report No. 

A-88048 


10. Work Unit No. 


9. Performing Organization Name and Address 

Ames Research Center 
Moffett Field, CA 94035 


12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 
Washington, DC 20546-0001 


505-60-21 


11. Contract or Grant No. 


13. Type of Report and Period Covered 
Technical Memorandum 


14. Sponsoring Agency Code 


15. Supplementary Notes 

Point of Contact: W. Clifton Horne, Ames Research Center, MS 247-2 Moffett Field, CA 94035 
(415) 694-6680 or FTS 464-6680 


16. Abstract 

Flow characteristics in the vicinity of the trailing edge of a single-slotted airfoil flap are presented and analyzed. The 
experimental arrangement consisted of a NACA 4412 airfoil equipped with a NACA 4415 flap whose angle of deflection 
was 21.8°. The flow remained attached over the model surfaces except in the vicinity of the flap trailing edge where a 
small region of boundary -layer separation extended over the aft 7% of flap chord. The flow was complicated by the pre- 
sence of a strong, initially inviscid jet emanating from the slot between airfoil and flap, and a gradual merging of the main 
airfoil wake and flap suction-side boundary layer. Downstream of the flap, the airfoil and flap wakes fully merged to form 
an asymmetric curved wake. 

The airfoil configuration was tested at an angle of attack of 8.2°, at a Mach number of 0.09, and chord based Reynolds 
number of 1.8 X 10 6 in the Ames Research Center 7- by 10-Foot Wind Tunnel. Surface pressure measurements were made 
on the airfoil and flap and on the wind tunnel roof and floor. It was estimated that the wall interference increased the Cl 
by 7% and decreased the C M by 4.5%. Velocity characteristics were quantified using hot-wire anemometry in regions of 
flow with preferred direction and low turbulence intensity. A 3-D laser velocimeter was used in regions of flow recirculation 
and relatively high turbulence intensity. 

Detailed measurements of pressure and velocity characteristics are reported in the following sections with emphasis 
on flow over the suction surface of the flap and in the downstream wake. The relative importance of the terms in the 
momentum and turbulence kinetic energy equations is quantified for flow in the vicinity of the flap trailing edge. 


17. Key Words (Suggested by Author(s)) 
Turbulent separated flow 
Multi-element airfoil 
3-D laser velocimeter 


18. Distribution Statement 

Unclassified-Unlimited 


Subject Category - 34 


19. Security Classif. (of this report) 
Unclassified 


20. Security Classif. (of this page) 
Unclassified 


21. No. of pages 

78 


NASA FORM 1626 OCT 86 


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