The boundary layer stability, its active control by sound and surface heating and the effect of curvature are studied numerically and experimentally for subsonic flow. In addition, the experimental and flight test data are correlated using the stability theory for supersonic Mach numbers. Active transition fixing and feedback control of boundary layer by sound interactions are experimentally investigated at low speed over an airfoil. Numerical simulation of active control by surface heating and cooling in air shows that by appropriate phase adjustment a reduction in the level of perturbation can be obtained. This simulation is based on the solution of two-dimensional compressible Navier-Stokes equations for a flat plate. Goertler vortices are studied experimentally on an airfoil in the Low Turbulence Pressure Tunnel (LTPT). The flow pattern was visualized using the sublimating chemical technique and data were obtained using a three component laser velocimeter. The effect of curvature on swept leading-edge stability on a cylinder was numerically studied. The results suggest that transition is dominated by traveling disturbance waves and that the waves with the greatest total amplification has an amplitude ratio of e sup 11. Experimental data from the quiet supersonic tunnel and flight tests are analyzed using linear compressible stability theory

Bayliss, A.

Maestrello, L.

Malik, M. R.

Mangalam, S. M.

English

NASA Technical Reports Server

NsS 
BOUNDARY LAYER TRANSITION
L. Maestrello
NASA Langley Research Center
Hampton, Va
/
A. Bayliss
EXXON Corporate Research Science Laboratories
Annandale, NJ
S. M. Mangalam
Analytical Services & Materials, Incorporated
Hampton, Va
M. R. Malik
High Technology Corporation
Hampton, Va
PRECEDING PAGE BLAI_,_ I_OT F|E.,_I'_
'IONALLY BLANK
333
https://ntrs.nasa.gov/search.jsp?R=19880005560 2020-03-20T07:44:16+00:00Z
ABSTRACT
The boundary layer stability, its active control by sound and surface heating
and the effect of curvature are studied numerically and experimentally for subsonic
flow. In addition, the experimental and flight test data are correlated using the
stability theory for supersonic Mach numbers.
Active transition fixing and feedback control of boundary layer by sound
interactions are experimentally investigated at low speed over an airfoil. It is
shown that a nonintrusive narrow heating strip causes abrupt changes in velocity
profile and triggers instant transition at favorable pressure gradients. Sound
interaction at normal incident angles produces significant reduction in velocity
perturbations in the region of transition.
Numerical simulation of active control by surface heating and cooling in air
shows that by appropriate phase adjustment a reduction in the level of perturbation
can be obtained. This simulation is based on the solution of two-dimensional
compressible Navier-Stokes equations for a flat plate.
G_rtler vortices are studied experimentally on an airfoil in the Low
Turbulence Pressure Tunnel (LTPT). The flow pattern is visualized using the
sublimating chemical technique and data are obtained using a three component laser
velocimeter. It is observed that the vortex wavelength is preserved in the
streamwise direction but varies with the G_rtler number as predicted by linear
stability theory.
The effect of curvature on swept leading-edge stability on a cylinder is
numerically studied. The results suggest that transition is dominated by traveling
disturbance waves and that the wave with the greatest total amplification has an
amplitude ratio of e II. Without the curvature this ratio is increased to e 17.
Experimental data from the "quiet" supersonic tunnel and flight tests are
analyzed using linear compressible stability theory. The data are obtained on a
5-degree half angle cone with unit Reynolds numbers between 9 to 27 million. The
analysis shows that transition could be correlated by the e N method with N in the
range of 9 to II.
334
ACTIVE CONTROL OVER AN AIRFOIL
This presentation describes an experiment on active control over an airfoil
surface in air. This experiment was conducted at CALTECH where Liepmann et al.
(ref. I) in an earlier experiment demonstrated flow control by active surface
heating in water.
Two concepts of control were investigated. The first was active transition
fixing by surface heating in the region of favorable pressure gradient to prevent
laminar separation at high angles of attack. In this region the flow is highly
receptive to surface heating and one can trigger small or large amplitude
disturbances as well as trigger instant transition with a single control element
shown schematically in the upper part of the figure.
The second control concept investigated was the interaction of sound at near
normal incidence with transitional flow over the airfoil to reduce amplitude of the
fluctuations.
METHODS OF CONTROL
Controlbyactivesurfaceheating-topreventseparationathighangleofattack
Control element
Control by sound - to reduce amplitude perturbation at transition
Sound
IIII
335
RESULTS
The photograph (next page) on the top left shows a view of the airfoil with
two sets of surface heaters mounted flush with the surface - one each in the
favorable (near leading edge) and unfavorable pressure gradient (downstream)
regions. The experiment was conducted at freestream velocities up to 12 m/s with
corresponding Reynolds number of 3.6x10 6 per meter.
Active transition fixing was accomplished by exciting the flow with a wave
packet input to the heaters (HO) located near the leading edge. The output
response was recorded by a hot-wire (HW) located downstream. The velocity
perturbation as a function of time is shown in the bottom left picture where abrupt
changes indicate instant transition. Similar input to the heaters located in the
unfavorable pressure gradient region showed only marginal effects. This shows that
the flow is receptive to outside disturbances only in the region of favorable
pressure gradient.
The figures on the right show the effectiveness of boundary layer control by
sound interactions in the region of transition. The sound was produced by a
speaker mounted in the wall of the tunnel above the airfoil. The _peaker was
driven by a feedback loop between the heater input and hot-wire output. The top
picture shows the uncontrolled response, while the bottom one shows the feedback
controlled response. It is evident that dramatic amplitude reduction is achieved.
Similar reduction was noticed with pure tone and random signal. It is observed
that at the control output the amplitude of the lower frequencies is reduced
drastically at the expense of an increase in the background disturbance which is
dominated by higher frequencies. Thus, it is clear that the flow will not return
to its uncontrolled state.
In conclusion, these methods are powerful and practical techniques of flow
control. Nonintrusive transition fixing could be utilized to prevent separation in
ducts as well as augment maximum lift on airfoils. Interaction of sound with the
flow is an effective way to control amplitude growth even for transitional flow.
336
ORIGINAL PAGE IS 
OF POOR QUALrrV 
337 
AMPLITUDE CONTROL BY HEATING AND COOLING
This figure concerns a numerical study of the concept of active control by
growing disturbances in an unstable, compressible boundary layer by using time
periodic, localized surface heating and cooling. The study is based on solving
2-D, compressible, time dependent Navier-Stokes equations on a flat plate.
The computational domain is shown on the left of the figure. Starting with
a steady state solution, perturbations in the form of the Orr-Sommerfeld solution
are superimposed at inflow. At the top and downstream boundaries characteristics
radiation conditions are used. At the plate no slip and specified temperature
boundary conditions are used. For control, the temperature boundary condition is
modified locally over the width of the strip using a steady and unsteady component
with phase input. The method of solution is an explicit predictor-corrector
technique which is fourth order accurate in space and second order in time.
The figure on the right shows the effect of active control on the growth of
disturbance amplitude for a Mach number of 0.4 and a freestream Reynolds
number/foot of 3xlO 5. The disturbance growth is plotted in terms of the RMS of
mass flux versus Reynolds number based on the local displacement thickness. The
control strip of width equal to three times the displacement thickness is located
at the Reynolds number of 1263. The amplitude growths are compared between the
uncontrolled and controlled cases with heating and cooling.
Since steady state heating is destabilizing in air while cooling stabilizes, it
is necessary to use a 180 ° phase difference between heating and cooling for
unsteady control. The figure shows a reduction in the amplitude growth for both
heating and cooling compared to the uncontrolled case. A reduction of about 6% is
indicated for heating with an overheat of IO00°F, and a 12% reduction is indicated
with cooling for a temperature difference of 300°F.
The numerical simulation demonstrates that either heating or cooling can be
used effectively to reduce the level of growing disturbances in a boundary layer.
A larger reduction can be obtained by use of multiple control strips placed
successively downstream with appropriate phase adjustment.
338
AMPLITUDE CONTROL BY HEATING AND COOLING
Y
I
inflow [Computationa] domoinI] 0utf]ow
---b II
I
Solve 2-D unsteady, compressible
Navier - Stokes equations
• Control by localized, periodic
surface heating and cooling
• Moo =0.4, Re/ft =3 x 105
8-
o o
6- o
-----.-... Uncontrolled
0 Cooled //0 0
5- 0 Heated /_n 0
/"4
- /o O3
2-j- £ Locationo1strip
1 "" I I -- I l I
1.0 I.I 1.2 L3 1.4 I.5
× i0"3
Re6"
339
GORTLER VORTEX EXPERIMENT
Gortler vortices arise in boundary layers along concave surfaces due to
centrifugal effects and are one of three known types of flow instabilities that
lead to boundary layer transition. Advanced laminar-flow control (LFC)
supercritical airfoils have concave curvature near the leading edge of the lower
surface, as shown in the schematic diagram for the airfoil model. Pairs of
counter-rotating, streamwise vortices, well known as Gortler vortices, develop in
the concave region as shown in the accompanying sketch for the vortex flow
pattern. Here, U is the external flow velocity, a is the boundary layer
thickness parameter, r is the radius of curvature, and _ is the G_rtler-vortex
wavelength.
The 1.83-meter chord airfoil model shown in the schematic diagram was tested
in the NASA Langley Low Turbulence Pressure Tunnel (LTPT). Gortler vortices were
observed using a sublimation technique and velocity measurements were made with
Laser Velocimetry. The airfoil model has a concave test region extending from
17.5% chord to 27.5% chord. The attached laminar boundary layer was insured by
means of suction through a 0.Ii x O.76-meter perforated titanium panel located in
the compression part of the concave region. The 10% chord flap at the trailing edge
was used to adjust the leading-edge stagnation point. The chord Reynolds number was
varied from 1.0 million to 5.9 million, yielding a Gortler number range of 29 to 46.
MODEL SCHEMATIC DIAGRAM
B Concove
test region Suction
Test _:__"-_1 _- ---_ 10% c flop
Insert A_
GORTLER VORTEX FLOW PATTERN
340
A t h i n  l a y e r  o f  s o l i d  wh i te  bephenyl ma te r ia l  was sprayed on the  b lack  
model sur face t o  v i s u a l i z e  t h e  f l o w  p a t t e r n  developed due t o  t h e  presence of 
G E r t l e r  v o r t i c e s  i n  the  boundary l a y e r  along the  concave t e s t  reg ion .  
p a t t e r n  i s  made v i s i b l e  due t o  the  d i f f e r e n t i a l  sur face shear s t ress  d i s t r i b u t i o n  
under the  l a y e r  o f  coun te r - ro ta t i ng  p a i r s  o f  streamwise v o r t i c e s .  
b lack  and wh i te  bands c o n s t i t u t e s  a p a i r  o f  v o r t i c e s  and represents  the  wave- 
l eng th  o f  these v o r t i c e s .  
G o r t l e r  number o f  36 i s  shown i n  the  accompanying photograph ( f low i s  from 
bottom t o  top  i n  the  photograph). 
The f low 
A s e t  of 
A rep resen ta t i ve  f l o w  p a t t e r n  corresponding t o  a 
Laser ve loc imeter  measurements o f  streamwise v e l o c i t i e s  a t  d i f f e r e n t  chord 
l o c a t i o n s  as w e l l  as a t  var ious  he igh ts  above the  sur face were used t o  determine 
the  vor tex  wavelength. A f i xed ,  e s s e n t i a l l y  uni form, vo r tex  spacing was observed 
i n  the  concave zone by both f l o w  v i s u a l i z a t i o n  and l a s e r  v e l o c i t y  measurements 
a t  each ex te rna l  f l o w  cond i t i on .  As i n  a l l  prev ious experiments, t he  dimensional 
wavelength was preserved i n  t h e  f l o w  d i r e c t i o n ,  b u t  u n l i k e  the  e a r l i e r  experiments, 
t he  wavelength was observed t o  vary  apprec iab ly  w i t h  G o r t l e r  number. 
v a r i a t i o n  i n  the  wavelength w i t h  G i j r t l e r  number i s  shown i n  the  lower f i g u r e  
where i t  i s  compared w i t h  r e s u l t s  based on l i n e a r t h e o r y  obtained by computing 
wavelength corresponding t o  maximum amp1 i f i c a t i o n  cond i t i ons .  
The 
341 
CALIBRATION OF STABILITY THEORY FOR TRANSITION PREDTCTION
Linear compressible stability theory was used to analyze supersonic
transition data for I0 ° sharp tip cones at zero angle of attack. Recent flight
data at M = 1.2 to 1.9 for a cone mounted on the nose of an F-15 aircraft were
used. Data obtained in the Langley Mach 3.5 Pilot Low-Disturbance Tunnel were
also used. Integration of theoretical disturbance amplification rates for
Tollmien-Schlichting (T-S) waves along the cone from the neutral stability
point to the measured location of transition onset yields the amplification
N factor.
The Gortler instability is usually dominant on concave walls and is
observed as small counter-rotating vortices aligned with the flow. Transition
was measured for laminar boundary layer flow on the concave walls of quiet
wind tunnel nozzles where the local Mach numbers varied from 1.6 to 4.9. The
N factors for both types of instabilities varied from about 9 to ii as
illustrated in the next figure.
Mach number > 1
M=1.2 t: M
Cone
(T-S instability)
N- 9-11
Concave wall
(C-.-.-_rtlerinstability)
N= 9-11
N = In A/A o =/amplif_atkm rate
(REF. 2)
342
TRANSITION N FACTORS
The plot on the left shows the envelope curves N as a function of the
dimensionless frequency parameter (F = 2_f ve/Ue 2 x 10 5) for T-S waves on
cones. The maximum amplification occurs at the peak of the curves where N varies
from about 9 to II at the measured location of transition for both the flight data
and the quiet wind tunnel data. This agreement indicates that the low-disturbance
environment of flight is correctly simulated in this tunnel.
The plot on the right shows the variation of N with the ratio of vortex
wavelength (or vortex width) to boundary layer thickness for the GSrtler
instability on the concave wall of the Mach 3.5 Pilot Low-Disturbance Wind Tunnel
over a range of unit Reynolds numbers. Again, the peak values of N vary from
about 9 to II at the measured locations of transition. Note that transition always
occurred when the vortex wavelength was about the same as the local boundary layer
thickness.
TS waves on
12
10
8
N 6
4
2
0
Normalized frequency
- ,-Maximum values-,
I-
I-- " Quiet wind tunnel
/ Flight 2
/ I I I I I
1 2 3 4 5 0
.4 .6.81
N: In AIA o
cones G6rtler vortices on concave wall
12- Unit Reynolds
m
I II I I I II I
2 4 6 810 20
Vortex wavelength
Boundary-layer thickness
343
CURVATURE EFFECTS ON SWEPT LEADING-EDGE FLOW STABILITY
The stability of the three-dimensional laminar boundary layer on the windward
face of a long cylinder was solved by a computational scheme that includes the body
curvature RI and the streamline curvature R2. The maximum growth rates are
integrated to the measured locations of transition on a cylinder in a low-speed
wind tunnel at velocities from 25 to 180 ft/sec. When the curvature terms are
omitted, as in previous investigations, the amplitude ratio was approximately
e 17. When all curvature terms are properly accounted for, the amplitude ratio is
about eII in good agreement with the supersonic results of the two preceding
figures as well as with various other types of subsonic flows.
streamlin(r_.,/2_ External e
N
(REF. 3)
0 -
16-
12-
8-
4-
0
Two curvature effects:
• Body,R1
• Streamline,R2
No curvature
/
/
//
/
/ / curvature
/_1 1 I J
.1 .2 .3 .4
x/C
344
•.
.
REFERENCES
Liepmann, H. W. and Nosenchuck, D. M.: Active Control of Laminar Turbulent
Transition. J. of Fluid Mechanics, vol. 118, 1982, pp. 201-204.
Beckwith, I. E.; Malik, M. R.: and Chen, F. J.: Nozzle Optimization Study for
Quiet Supersonic Wind Tunnels• AIAA Paper No. 84-1628, June 1984.
Malik, M. R.: Instability and Transition in Supersonic Boundary Layers. ASME
Symposium on Turbulent and Laminar Boundary Layers--Their Control and Flow
Over Compliant and Other Surfaces, New Orleans, LA, February 12-16, 1984.
•
.
.
.
BIBLIOGRAPHY
Maestrello, L.: Active Transition Fixing and Control of the Boundary Layer in
Air. AIAA Paper 85-0564, March 1985.
Bayliss, A.; Maestrello, L.; Parikh, P.: and Turkel, E.: Numerical Simulation
of Boundary Layer Excitation by Surface Heating/Cooling. AIAA Paper 85-0565,
March 1985.
Man_alam, S. M.; Dagenhart, J R.: Hepner, T. E.: and Meyers, J. F.: The
Gortler Instability on an Airfoil. AIAA Paper 85-0491, January 1985.
Malik, M. R. and Poll, D. I. A.: Effect of Curvature on Cross-Flow
Instability. Second IUTAM Symposium on Laminar-Turbulent Transition,
Novosibirsk, USSR, July 9-13, 1984.
345


Boundary layer transition

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