A brief outline of the experimental and theoretical investigation of boundary layer instability mechanisms on a swept leading edge at Mach 3.5 is presented. Transition is affected by wind tunnel noise only when roughness is present. Local bar-R sub * Reynolds number and k/eta sub * are useful correlation parameters for a wide range of free stream Mach numbers. Stability theory is in good agreement with the experimental cross flow vortex wavelength. These conclusions are briefly discussed

Beckwith, Ivan E.

Creel, Theodore R., Jr.

Malik, Mujeeb R.

English

NASA Technical Reports Server

 N90- 1255 7
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EXPERIMENTAL AND THEORETICAL INVESTIGATION OF BOUNDARY-LAYER
INSTABILITY MECHANISMS ON A SWEPT
LEADING EDGE AT MACH 3.5
T. R. Creel, Jr.
NASA Langley Research Center
Hampton, Virginia
M. R. Mallk
High Technology Corporation
Hampton, Virginia
I. E. Beckwith
NASA Langley Research Center
Hampton, Virginia
981
https://ntrs.nasa.gov/search.jsp?R=19900003241 2020-03-20T00:51:48+00:00Z
OUTLINE
The figure below gives a brief outline of the experimental and theoretical
investigation of boundary-layer instability mechanisms on a swept leading edge at
Mach 3.5.
0 REVIEW OF TRANSITION BECHANISMS ON SWEPT-LEADING EDGES
0 SWEPT-CIRCULAR CYLINDERS TESTED IN MACH 3.5 PILOT OUIET TUNNEL
- flEASURED RECOVERY TEMPERATURES
- OIL FLOW STUDIES
0 COMPARISON OF THEORY AND EXPERIBENT
0 REVIEW OF STABILITY THEORY
982
TWO MECHANISMS GENERALLY CAUSE TRANSITICN IN THE
LEADING-EDGE REGION OF SWEPT WINGS
Spanwise contamination and cross-flow instability are outlined in the figure
below.
Io
o
SPANWISE CONTAMINATION
SOLVED IN THE EARLY '60's BY:
STRONG LOCAL SUCTION, LEADING-EDGE SUCTION FENCES, X-21
PROTRUDING FAIRED BUMP ATTACHED TO THE W]NG LEADING EDGE
BR[TISH HANDLEY PAGE
CROSS-FLOW INSTABILITY
FIRST OBSERVED BY GRAY AS REGULARLY SPACED STREAKS ]IN SURFACE COATINGS
STREAKS CAUSED BY CO-ROTATING VORTICES RESULTItlG FROM THE INFLECTIONAL
INSTABILITY OF THE CROSSFLOW BOUNDARY-LAYER PROFILES IN THE UPSTREAM
REGIONS OF SWEPT WINGS
983
PHOTOGRAPH OF SWEPT-CYLINDER MODELS 
The models consisted of .030-inch thick stainless steel cylindrical shells 1/2- 
Chromel-alumel thermocouple 
The surfaces of 
and 1-inch outside diameters with both ends sealed and cut-off parallel with the free- 
stream flow direction as illustrated by the photograph. 
wires of .OlO-inch diameter were spot welded to the inside surface of the shells at 
1/4-inch intervals along the entire length of the attachment lines. 
the models were maintained clean and polished with a finish of less than 10 rms micro- 
inches. 
U K ~ G ~ N A L  FAGE 
BLACK AND WHlTE PHOTOGRAPH 
984 
ONE-INCH DIAMETER SWEPT CYLINDERS IN MACH 3.5
PILOT LOW-DISTURBANCE TUNNEL
The models are shown mounted in the nozzle at upstream and downstream positions
with respect to the quiet test core. In the upstream "quiet" test position and with
the bleed valve open, the forward tips of the models were located 5.8-inches
downstream from the nozzle throat (see ref. I). For R = 3 x 105 about 85 percent
and 70 percent of the attachment line spans on the A = 45 ° and 60 ° models,
respectively, were exposed to the extremely low noise levels. As unit Reynolds number
is increased, transition moves upstream on the nozzle walls and thus the corresponding
location of increasing noise measured along the centerllne also moves upstream. This
results in a greater percentage of the attachment line span being exposed to high
noise levels. In the downstream "noisy" test position and with the bleed valve
closed, the entire model was exposed to noise levels ranging from .2 to .5 percent.
Y, in
Nozzle contour__/_,_,_,_/_t3 .
Quiet test p0si_ R oo/in. _, 3.0x 105>,1" 2
(upstream end) ,,_,.<- ,,___. _i_ _ ....
.____-'K_ -J-_- - } --'-_--n.,-II'A_NOZZle eXl[
,_ _(.. "_-._"_'<Z" \ u
FlOW " _-_/....-" _'_ . _L.-- Center li ne
_est Noisy test positioncore
___a (upstream end)
....... X, in.
4 6 8 10 12 14
r---.. A = 45° 60°
"--. /--7 i---_
Quiet test -- _c j ..-" /core _ / /_._ .. /
! //,,./ ....-"--1 / / _--Centerline
Flow _1 / ,7- 7- "T_U .....
- 7;fI / # ..J II /--'2 / ""
I -*t._ "*-''- t 2
u._-.- 3 Z, in.
_-- Flat walls 4
985
TRANSITION ON THE ATTACHMENT LINE
Recovery factors obtained at both low and high noise conditions for A = 60 ° are
summarized here where r is plotted against R D for selected values of s from several
runs (Ref. i). The trip height is k=.004 inch'and the trip was located at s=6 inches
for these data. The results for no trip (circle symbols and s = 5 in.) and also
up§tream of the trip (square symbols and s = 5 in.) show transition at R ,D = 7.5 x
105 for both low and high noise (flagged symbols). This transition Reynolds number is
in agreement with Poll's criteria (Ref. 2). However, downstream of the trip (s =
10 in.) transition occurs at lower values of R_,D = 3 or 4 x 105 dependin_ on the
tunnel noise. Clearly, the tunnel noise appears to enhance the effect of the trips
but has no effect when there is no trip.
/__--__ Plain symbols: Low noise
Moo =----3..5 "_s'_,, ,_,_ Flagged symbols: High noise
- ".88 .
.86
Recovery
factor, r 84 _1 s,_in.
• Laminar-/ l I I" ° ->'5 no trip
' I [] 5 upstream of trip
.82 l I [ 0 10 k=.O04 in.
(k/6lT -'='57 .67 i_.,_,i.z_-Poll's R%criteria
• 80 , , , _ A_ i
105 2 4 6 8 106 2
R
_,D
986
TRANSITIONONTHEATTACHmeNTLINE
Typical effects of tunnel noise and a trip on attachment llne transition for the
h = 45° model are shown in the figure. Data without a trip and with a trip height (h)
= .O02-inches are presented for a Reynolds numbers range of 2 x 105 < R D < 1.7 x
106. The trip was located at s = 5.5 inches for these data. The high tunnel noise
enhances the effect of the trip for 5 x 105 < R_,D < 6.5 x 105. Upstream of the trip
(s = 5 in.) or with no trip, transition occurred at R_,D = 7 x 105 independent of
tunnel noise. This value of (R D)T is somewhatsmaller than Poll's R, criteria
(Ref. 2) for no end disturbances _n low-speed flow and is also somewhatsmaller than
the Bushnell/Huffman supersonic criteria of (R ,D)T > 8 x 105 (Ref. 3).
MOO
Recovery
factor, r
=3.5
" _----_ _ Plain symbols: Low noise
I" "x_ r_ Flagged symbols: High noise
.88 F s "_,,,_ __
.86 I-CP- 5-- no trip / <_"
I-_ _ 5 upstream of trip [ / _
7
.82 ,aminar _ I I I I-- Poll's R_ criteria
(k/5) T=.47.51 .1 /.
•80 ' ' ' ' _ '_ _
105 2 4 6 8 106 2
R
OO,D
987
EFFECTS OF TRIP HEIGHT AND NOISE ON ATTACHMENT-LINE TRANSITION
To facilitate comparisons with Poll's data for trip wires in low-speed flow (Ref.
2), the local reference temperature parameters R, and k/q, are plotted for all the
present transition-onset data for the A = 45 ° and 60 ° models and D = l-lnch. The
trend of (R*)T with (k/q,) T are similar to those of Poll with respect to the effects
of "critical" roughness heights. These critical roughness heights correspond to the
values of k/q, where the transition Reynolds numbers are first reduced significantly
as k/q, is increased. Thus, for A = 45 °, the critical value;_ are k/n, = 1.4 and
1.6 for high and low noise, respectively. For A = 60 °, the c:_itical values are
k/q, = 0.85 and 0.95 for high and low noise, respectively. These latter values may
be compared with Poll's critical values for A = 60 ° of d/q = 0.6 to 0.8. Poll's
subcritical values of _ were approximately 600 to 750, depending on the distance
from the trip. It is apparent_ that the present subcritical va]Lues of (R*)T for both
sweep angles and the critical k/q, values for A = 60 ° agree reasonably well with
Poll's values for A = 60 °.
Trip
location
A s, s,
Noise deg in. in.
8OO_r__ I_ Low
0 High
13 Low
600 0 High
400 _ I_ _"
e'-_%%.
200
45 7 5.5
45 7 5.5
60 I0 6
60, I0 6
I I I
0 1 2 3
I kln:) T
988
OIL FLOW PATTERNS WITH TRIP (K = .004-IN.) AT 
S = 6-IN. A = 60°, D = 1-IN., R = 4.6 X 10 5 
OD ,D 
Typical photographs of oil flow patterns on the A = 600 model are shown in this 
figure. Also shown is a small trip (identified in the picture, of height h = .004- 
inch, which results in k/6 = .7) fixed to the attachment line at 6-inches from the 
upstream tip of the model. For this run, the wavelength of the vortices measured from 
the more closely spaced oil-flow streaks, increased from X = .03 to .04-inch as the 
angular distance from the attachment line is increased from 9 = 70" to 90".  
Normalized by the attachment boundary-layer thickness, these values give A/6 = 5 to 7 
for this Reynolds number of R = 4.6 x 10 . S 5 
",D 
989 
O I L  FLOW PATTERNS DOWNSTREMI OF TRIP 
This figure shows more of the downstream part of this model for the same run. 
The wide streaks have been completely obliterated downstream of the trip by turbulent 
boundary-layer flow. 
ORIGINAL PAGE 
mCK AND WHITE PHOTOGRAPH 
990 
COMPARISON OF THEORY AND EXPERIMENTS
The stability of three-dimensional boundary-layer flow on the 60 ° swept cylinder
was examined for R ,D = 4.6 x 105 . Compressible linear stability equations were
solved by the metho_ used in reference 4. Computed wavelength of the most amplified
stationary cross-flow disturbances is plotted in the figure as a function of the
azimuthal angle 8 from the attachment llne. The figure also contains wavelength
values measured on the oil flow photographs. Both the magnitude of the wavelength and
its variation with 8 are well predicted by the theory.
WAVE-LENGTH OF STATIONARY CROSS-FLOW DISTURBANCES. R. D --- q.6 x 10 5
.05
),,IN
.Otl
.03
.02
.0]
I I I I I
0 20 qo 60 80 100
G, DEG-
991
INSTABILITY OF BOUNDARY LAYER ON SUPERSONIC SWEPT ATTACHMENT LINE
The instability of a boundary layer at the attachment line of a swept cylinder
was theoretically investigated. The results of this investigation are documented
below.
0
0
0
0
CALCULATIONS USING COMPRESSIBLE LINEAR STABILITY THEORY PERFORMEDFOR
A = GO° AND _. = 3.5
BOUNDARYLAYER SUBJECT TO TOLLM1EN-SCHLICHTIN6 TYPE INSTABILITY
OBLIgUE WAVES WITH WAVE ANGLES AROUNDGO° ARE MOST AMPLIFIED
COMPUTEDCRITICAL REYNOLDS NUMBER IS Re = 240.
WALL COOLING IS STABILIZING. EXAMPLE: THE CRITICAL REYNOLDS NUMBERDOUBLES IF
Tw/TAo = .8
ATTACHMENT LINE BOUNDARYLAYER SUBJECT TO FINITE AMPLITUDE SUBCRITICAL
INSTABILITY- DISTURBANCES SUCH AS WALL ROUGHNESSMAY CAIISE PREMATURE
TRANSITION
992
INSTABILITYOF BOUNDARYLAYERIN SWEPTLEADING-EDGEREGION
The figure below outlines the results regarding the instability of a boundary
layer on the attachment line of a swept cylinder at Math = 3.5.
0 COMPRESSIBLELINEAR STABILITY ANALYSISOF THE THREE-DIMENSIONAL
BOUNDARYLAYERHASBEENPERFORMEDBOTHFORTHE STATIONARYAND
NON-STATIONARYWAVES
0 CROSS-FLOWVELOCITYPROFILEDOWNSTREAMIN ATTACHMENTLINE HAS
INFLECTIONPOINT ANDTHUSIS SUBJECTEDTO INVISCID (RAYLEIGH)
INSTABILITY
0 COMPUTATIONSSHOWTHATNON-STATIONARYWAVESAMPLIFYMORETHAN
THE STATIONARYONES
993
CONCLUSIONS
I. Transition is affected by wind-tunnel noise only when roughness is present.
2. Local R, Reynolds number and k/n, are useful correlation parameters for a wide
range of free stream Mach numbers.
3. Stability theory is in good agreement with the experimental cross-flow vortex
wavelength.
994
REFERENCES
Io
.
o
.
Creel, T. R.; Beckwith, I. E., and Chen, F.-J.: Transition on Swept Leading Edges
at Math 3.5. Accepted for publication in the Journal of Aircraft. October 1987.
Poll, D. I. A.: Transition Description and Predictiion in Three-Dimenslonal
Flows. Agard-R-709, June, 1984.
Bushnell, D. M., and Huffman, J. K.: Investigation of Heat Transfer to a Leading
Edge of a 76 ° Swept Fin With and Without Chordwise Slots and Correlations of
Swept-Leadlng-Edge Transition Data For Mach 2 to 8. NASA TMX-1475, 1967.
Malik, M. R.: COSAL - A Black-Box Compresslble Stability Analysis Code for
Transition Prediction in Three-Dimensional Boundary Layers. NASA CR-165915, 1982.
995


Experimental and theoretical investigation of boundary-layer instability mechanisms on a swept leading edge at Mach 3.5

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