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A f A A 

AIAA 2001-2159 

Laminarization of Turbulent Boundary 

Layer on Flexible and Rigid Surfaces 

Lucio Maestrello 

NASA Langley Research Center 

Hampton, VA 

7th AIAA/CEAS Aeroacoustlcs Conference 

28-30 May 2001 
Maastricht, The Netherlands 

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For AlAA-held copyright, write to AIAA Permissions Department, 

1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344. 



Lucio Maestrello 

NASA Langley Research Center 
Hampton, VA 23681-2199 


An investigation of the control of turbulent 
boundary layer flow over flexible and rigid surfaces 
downstream of a concave-convex geometry has been 
made. The concave-convex curvature induces 
centrifugal forces and a pressure gradient on the 
growth of the turbulent boundary layer. The favorable 
gradient is not sufficient to overcome the 
unfavorable; thus, the net effect is a destabilizing of 
the flow into Gortler instabilities. This study shows 
that control of the turbulent boundary layer and 
structural loading can be successfully achieved by 
using localized surface heating because the 
subsequent cooling and geometrical shaping 
downstream over a favorable pressure gradient is 
effective in iaminarization of the turbulence. Wires 
embedded in a thermally insulated substrate provide 
surface heating. The laminarized velocity profile 
adjusts to a lower Reynolds number, and the 
structure responds to a lower loading. In the 
Iaminarization, the turbulent energy is dissipated by 
molecular transport by both viscous and conductivity 
mechanisms. Laminarization reduces spanwise 
vorticity because of the longitudinal cooling gradient 
of the sublayer profile. The results demonstrate that 
the curvature- induced mean pressure gradient 
enhances the receptivity of the flow to localized 
surface heating, a potentially viable mechanism to 
laminarize turbulent boundary layer flow; thus, the 
flow reduces the response of the flexible structure 
and the resultant sound radiation. 

I. Background 

Turbulent boundary layer control is achievable 
experimentally by using localized surface heating in 
a region of pressure gradient. Localized heating 
leads to an increase in stability and critical Reynolds 
number. A new velocity profile adjusts to the 
laminarized Reynolds number, and results in lower 

skin friction and structural loading. This transition 
occurs naturally in high speed flow and causes 
hypersonic flow to be laminar and a hot jet to be 
quieter than a cold jet. The present experiment is 
designed to demonstrate flow stability for subsonic 
boundary layer flow. Laminarization is achieved by 
the natural cooling of the flow downstream of a 
heated wire strip placed on a concave surface. The 
effectiveness of the technique depends on the 
pressure gradient, freestream conductivity, 
diffusivity, temperature, and Reynolds number. The 
coupling between heat flux and streamwise pressure 
gradient influences the stability sufficiendy to 
reverse the state of the flow from turbulent to 

The shear flow over a concave surface is subject 
to centrifugal instability whose inviscld mechanism 
was given first by Rayleigh' (1916) and Reynolds^ 
(1884) and in recent works by Narasimha and 
Sreenivasan;^ Hoffmann, Muck, and Bradshaw;'* 
Hall;5 Floryan;^ Maestrello and El-Hady;'^ and 
Bayliss et al.^ These works have indicated that the 
flow over a concave surface is potentially unstable, 
resulting in two- and three-dimensional disturbances, 
whereas the flow over a convex surface is stabilizing. 
The overall effect of the surface curvature on the 
flow cannot be predicted a priori; it depends on the 
parameters of the flow and initial disturbance. 

In the last decade, the study of nonlinear and 
chaos control has attracted much attention.^"^^ 
Recently, investigations have shifted to 
spatiotemporal systems to control pattern formation 
including turbulence. Turbulence remains an 
extremely important problem in the science of nature 
and is an example of spatiotemporal chaos. The 
deterministic and chaotic responses need to be 
distinguished from stochastic behavior. Typically, 
random behavior can arise in a number of ways, but 
actually, the behavior is the result of deterministic 

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chaos that appears random because of the lack of 
sufficient information about initial starting 
condition.^*^*^*^"* Vibration control using an actuator 
for stabilizing panel vibration satisfying a nonlinear 
beam equation is studied by Chow and Maestrello^^ 
with a perturbation technique. The vibration control 
principle can also be applied to other problems such 
as nonlinear wave propagation and flow stability and 
control. A potentially less restricted method of 
control is by passive surface heating;'^ Maestrello 
and Ting^^ analyzed this problem by using the 
method of matched asymptotes as a "triple-deck" 
problem. This analysis confirmed that a small 
amount of localized surface heating can excite local 
disturbances which increase the momentum near the 
wall and reduce the displacement thickness and, as a 
result of downstream cooling, laminarize the 
turbulence of the flow. 

In this paper, the effect of the curvature-induced 
pressure gradient on the growth of the turbulent 
boundary layer is studied. In particular, with the use 
of a wire strip on the concave portion of the surface, 
the behavior resulting from an imposed steady 
localized heating is investigated. The boundary layer 
is turbulent, nearly two-dimensional in the mean; 
three-dimensional centrifugal instability is created by 
the largest eddies present in the flow approaching the 
concave portion of the curvature. Centrifugal effects 
can be categorized into three types: (1) change in 
the turbulent structure induced by the wall curvature, 
(2) generation of longitudinal vortices, and (3) effect 
of the longitudinal vortices on turbulent structure- 
Over the concave portion of the surface, vortex cells 
are triggered by the interaction between the 
centriftigal instability and the level of fluctuations 
created by the eddies in the boundary layer. 

Structural vibration and resultant sound radiation 
can also be controlled by suppressing waves on the 
structure rather than by controlling the boundary 
layer itself. One method uses so-called "rubber 
wedges" designed to attenuate waves incident and 
reflecting from the boundaries. Laboratory testing at 
low speed flow and flight testing on a Boeing 727 
airplane at Mach number 0,85 and altitude of 31000 
feet show 15 dB and 8 dB, respectively, of 
broadband acoustic power reduction. The added mass 
for the modified boundaries was approximately 30 
percent of the panel weight. ^^'^^ 

The analysis begins with passive control by 
localized surface heating, and the experiment begins 
with measurements of local fluctuations and mean 

velocities, followed by the distribution of the average 
temperature cooling downstream of the heating wire, 
the sequence of Gortler vortices during 
laminarization stages, and finally the fluctuations 
and mean velocity of the uncontrolled and the 
controlled boundary layer. The analysis of control by 
surface heating is described in Sec. 2. Sec. 3 
describes the configuration geometry and 
instrumentation. Results on the control of Gortler 
instability and laminarization of the boundary layer 
and structural response are described in Sec. 4. 1 and 
Sec. 4.2. 

2. Flow Analysis of Localized Surface Heating and 
Self Downstream Cooling 

Localized surface heating in air alters the growth 
of the flow instabilities by subsequent cooling 
downstream. As a result, the flow stability is 
increased by the modifications of the velocity and 
pressure distributions. The analysis must begin with 
the energy equation, even for incompressible flow. 
The problem deals with a change in thermal 
boundary conditions which, in turn, creates a 
disturbance field in the boundary layer. A heuristic 
argument was presented to explain the equivalence 
between heat flux and effective normal velocity at 
the wall, since the coupling between the thermal and 
mechanical effects is provided by the dependence of 
viscosity on temperature.^^ Qualitative effects on the 
stabilization of the boundary layer due to localized 
heating with subsequent downstream cooling were 
obtained for air because the viscosity ^ increases 
with temperature T\ that is 


Surface heating with subsequent downstream cooling 
changes the velocity profile due to the dependence 
of viscosity on temperature. An extra term (djjJdT) 
(dT/dy) (du/dy) appears on the right-hand side of the 
momentum equation for an incompressible boundary 
layer where y is the coordinate normal to the surface. 
Here ji, T, u, and y are nondimensional quantities, 
and u is the velocity. In the experiment described in 
this paper, a concave-convex surface is used to 
laminarize the turbulent boundary layer. A thin 
nickel-chromium wire strip embedded in the concave 
part of the curved surface is heated by a steady 
electric current. Local heating and subsequent 
downstream cooling changes the velocity profile and 
pressure distribution where the surface geometry 
changes from a concave to a convex surface and 
then to a flat region. The favorable effect can be 

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assessed where the temperature reaches an ambient 
value over the flat region. It is well-known that such 
a sudden local change of the boundary condition 
creates a disturbed flow field in the boundary near 
the heating strip. The present problem differs from 
that in work done by Stewartson^^ and Smith^' 
because of a sudden change in the thermal boundary 
condition as described by Liepmann, Brown, and 

The analysis begins with the energy equation for 
an incompressible flow. The governing equations 
in dimensionless quantities for uP-hx^yJ), \^^\x,y,t), 
T^^^ix^yJ), and jP^{xj), corresponding to velocities u 
and V, temperature T, and pressure p for the lower 
deck are shown as follows with the superscripts 
indicating the order of the perturbation in the 
expansion schemes and identifying the corresponding 
power of e: 

4'^+v^/> = 


«P> + ^yu^P + P v^^) = -/^\x, t) + ^^^ + Aprj^) (2) 

r/^> + Pyri^) = (Pr)-'rf 


1 AJit)d^ 



where A is equal to d \n{v) f d \n{T\ Pr is the 
Prandtl number at Tq, and P is the slope of the 
velocity profile at the wall. The variation of viscosity 
with temperature in the momentum equation, 
because it is associated with pressure gradient, 
becomes the mechanism that effectively alters the 
turbulent boundary layer. For the Blasius profile, P 

equals 0.33206. Notice the AP T^^^ dependency of u 

and T due to the forcing term for u^'^\ yM\ and p^^h 
The term A^{xj) is given by Hilbert transforms,^^ 


A{xj) = ^~^u^^hx,y^ooj) 

On the heating wire, it is assumed that 

This analysis provides the solution of the velocity 
and pressure distributions. If the frequency is finite, 
0(1), the full unsteady analysis has to be carried 
out. In the usual linearized incompressible equations, 
the unsteady term and the last term in equation (2) 
are absent; the energy equation for temperature is 
not needed for the solution of the velocity 
disturbances. An example of the pressure distribution 
pO) ^ -(A/?/pf/o e-^) is plotted in Fig. 1 with 

A;c = 0.75 and AT = lOOX (AT is the temperature 
of the heating strip above the plate temperature). For 
X < 0, the pressure distribution decreases slightly; 
for x> 0, increases drastically over the heating strip 
to reach a maximum at the end of the strip and 
decreases drastically downstream. Heating of the air 
destabilizes over the heating strip because dju/dT is 

greater than zero, but it stabilizes downstream of the 
heating strip. The overall values for temperature 
change AT, Prandtl number Pr, and A are given in 
Table 1. The contribution of the steady-quasisteady 
terms depends on the size of AT and d^ldT, 

whereas the unsteady terms depend on frequencies 
and phases. 

Table 1. Values for Temperature Change AT, 
Prandtl Number Pr, and A 

A7, °C 






COS cot 

3. Configuration Geometry and Instrumentation 

The experiment is conducted in an open-circuit 
wind tunnel with a 38.1- by 38.1-cm test section at a 
speed of 36.6 m/s on a plate 4.8 m long. (See Fig. 2.) 
A portion of the plate is concave and a portion is 
convex with flat regions upstream and downstream 
(Fig. 2). Upstream, the plate features an elliptic 
leading edge with a thickness of 2.54 cm, and 
downstream it features a trailing edge with 
controllable angle flap. The concave-convex portion 
is described by a seventh-degree polynomial with the 
first three derivatives continuous at botji ends. This 
degree of smoothness is designed to prevent 
singularities from being generated at the points 
where the surface becomes flat. This geometry was 
selected to illustrate the effect of curvature-induced 
pressure gradient flow and flexible structure stability. 
The concave portion has an adverse pressure gradient 
and the mean flow decelerates, whereas downstream 
the curvature becomes convex and produces a 
favorable pressure gradient and the flow accelerates. 

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The surface contains a thermally insulated substrate 
(Space Shuttle tile). The flow behaviors caused by 
imposed steady heating from two wires in the 
concave portion were investigated. The wires are 
nickel-chromium strips with resistance about 4 Q/m, 
The wires are held in position under tension during 
the heating and cooling cycles. The power supply 
operates in a direct-current mode in a manner similar 
to that of a previous experiment using leading edge 
heating on a flat plate. '^ The heater current and 
voltage are continuously monitored, and they are 
used to determine the total power input during the 
control cycle. The surface temperature downstream 
of the heating wires is measured by a line of 
thermocouples placed along the sidewall comer of 
the tunnel test section. Downstream of the concave- 
convex curvature, the surface is flat, and a flexible 
aluminum plate is located 40 cm from the curvature. 
The plate, 45 by 20.3 by 0.08 cm, with clamped 
edges is mounted flush with the surface and is used 
to study the structural loading. The rest of the surface 
is rigid. A hot-wire probe, accelerometer, wall 
pressure transducer, temperature sensors, and infrared 
thermography^^ were used to evaluate the flow and 
structure response. The infrared thermography 
technique is a nonintrusive method to investigate the 
changes of the Gortler vortices with temperature 
gradient. The wind tunnel geometry, flow quality, 
and background noise permits a study of the 
laminarization control problem of a turbulent 
boundary layer at low speed. 

4. Experimental Results 

The mean velocity profiles, perturbation 
velocity, and the infrared thermogram of the 
developing vortices over the concave-convex surface 
are evaluated. The uncontrolled boundary layer is 
turbulent upstream and downstream of the curvatures. 
The concave curvature has a destabilizing effect 
because it increases the levels of Reynolds shear 
stress and turbulent energy and enhances the 
turbulent mixing, whereas the convex curvature has a 
stabilizing effect on Reynolds shear stresses and 
turbulent energy level; turbulent mixing has a 
decreasing level compared with an equivalent 
straight shear layer flow. 

4.1. Gortler Instability. Perturbation Velocity, Mean 
Velocity, and Laminarization of Turbulence 

The perturbation velocity u{x,t) versus r, the 
mean velocity profile yix)/ 6 (x) versus u{x)IUo, and 
the frictional velocity u{x)lu^{x) versus yu^ (x)fv at 

location jcj are shown in Fig. 3, where u{x,t) is the 
local fluctuation velocity, y is the coordinate, is 
boundary layer displacement thickness, u is mean 
velocity, U^ is freestream velocity, u^ is frictional 
velocity, and v is kinematic viscosity. The location 
of xj is 40 cm upstream of the curvature. A wind 
tunnel condition is chosen from the calibration runs 
based on flow, vibration, and noise quality. From the 
mean velocity profiles and perturbation velocity, one 
can deduce that the uncontrolled boundary layer is 
turbulent at freestream velocity, Uq = 36.6 m/sec, 
and Reynolds number, Rq (xi) = 2010. The frictional 
velocity profiles are comparable with standard wall 
law, flat plate, turbulent boundary layer. 

The choice of the geometry in Fig. 2 permits 
laminarization of the boundary layer downstream of a 
concave-convex curvature by localized heating on 
the concave portion of the surface, whereas the flow 
remains intermittently turbulent upstream. The 
average surface temperature distribution T/Tj^f 
downstream of the heating wires decays 
exponentially with distance to cause the flow to 
laminarize (T^^f is the ambient temperature of the 
wind tunnel surface). (See Fig. 4.) Figures 5(a) to 
5(f) show the infrared thermogram vorticity patterns 
over the concave-convex curvature. The Gortler 
vortices originate from the concave portion of the 
surface, and they become stabilized over the convex 
portion of the surface as the temperature -decays with 
distance. Stability of the vortices is indicated by the 
increase in wavelength and a sudden increase in size 
as the number of vortices reduces. The temporal 
stages toward laminarization are related to the 
thermoconductivity gradient of the surface and flow 
characteristics. Distinct features in the time 
sequences of the vorticity pattern are shown in each 
step. (See Fig, 5.) During control stages, the heat 
flux through the wire is gradually increased until the 
reversion from a turbulent to a laminar state is 
established. Then the amount of heat flux is reduced 
by 25 percent equivalent to 200 W after establishing 
laminarization of the turbulent boundary layer. The 
analysis in Sec. 2 can provide the guidelines. 
The Gortler patterns stretch downstream over the 
convex portion with increased stability as the 
temperature decreases with distance (Fig. 5(a)). The 
perturbations of the flow over the heating wires 
amplify a region of unfavorable pressure gradient, 
and then the perturbation decays due to cooling in 
the region of favorable gradient. This reversion in the 
amplification is due to both geometrical shaping of 
the curvature profile and surface cooling with 
downstream distance. The figure also indicates that 

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the changing pattern is not two-dimensional. In 
Figs. 5(b), 5(c), and 5(d), the temperature of the 
wire increases (red indicates the higher and blue the 
lower temperature). The decrease in wall 
temperature with downstream distance causes drastic 
changes in vorticity; the boundary layer laminarizes 
in the process. In the laminarized state only two 
large vortices remain, the spatial change is an 
indication of stabilization (Figs. 5(e) and 5(0). The 
vorticity is concentrated in the core surrounded by a 
large-scale motion with small-scale vortices 
embedded within; it is possible to recognize 
successive changes as the wire temperature 

The temporal sequences of the velocity 
perturbations, prior, during, and after laminarization, 
are shown in Fig. 6, at X2 located 40 cm downstream 
of the flexible panel. Six successive time step 
intervals At are shown, from the turbulent state, time 
step 1, to laminar state, time step 6. The features 
seen during transition are like the features seen in a 
turbulent spot, that is, time step 5. The perturbations 
in time steps 2, 3, and 4 have a higher amplitude 
than in the turbulence in step 1 and should be 
interpreted as the envelop of all the possible types of 
disturbance amplification. The process of 
laminarization also indicates a change in Reynolds 
numbers from Rq ix2) - 2728 in turbulent state to 
^e (^2) = 983 in laminarized state. These changes in 
perturbation velocity and mean velocity profiles are 
shown in Fig, 7. The mean profile (Fig. 7(c)) 
changes from turbulent in the initial stage, to 
laminarized in the final stage resembling the Blasius 
profile. The perturbation velocity changes also 
indicate laminarization of the turbulence. During the 
control stages, as heat on the wire strips increases, 
the boundary layer at X] becomes intermittently 
turbulent with an oscillation in Rq (xi) between 5 to 
15 percent from its original value. 

The pressure gradient in the control region of the 
heating wires and downstream is essential in order to 
maintain the coupling between the thermal gradient 
and sublayer because coupling heat input with the 
flow at zero pressure gradient is virtually impossible. 
This important feature "pressure gradient" is 
indicated on the right-hand side of the momentum 
equation (eq. (2)) with viscosity as a function of 
temperature. The rate of cooling with distance is the 
stabilizing mechanism; as a result, the critical 
Reynolds number increases. There is no bounded 
limit on how far laminarization can be extended 
because the stability increases with the increasing 

ratio between local heat flux and thermal 
conductivity and temperature. The whole 

laminarization process looks like transition to 
turbulence in reverse as it can be observed from a 
fixed point. 

4.2. Panel Structure Response and Control 

The response of the panel is induced by the 
convecting boundary layer loading, both turbulent 
and laminar. The static pressure difference across the 
panel is 2.5 kg/m^, the static deflection is less than 
the panel thickness. The pressure difference has an 
effect on the structural response. The response is 
measured by an accelerometer at the panel center. 

The normalized power spectral density G(f) of 
the acceleration for the turbulent and the laminarized 
boundary layer loading is shown in Fig. 8. No attempt 
is made to measure the spatiotemporal response. The 
spectrum is dominated by the lower frequencies, an 
expected result for low speed boundary layer loading. 
The controlled spectrum has a lower amplitude than 
the uncontrolled one; their differences increase with 
frequency (Fig. 8). At the low frequencies, the 
reduction in power is approximately 7 dB; at high 
frequencies, more than 10 dB. Laminar boundary 
layer loading reduces the structural response with 
respect to the turbulent boundary layer. The acoustic 
background noise of the facility did not permit 
measurement of the acoustic power (radiated) by the 
panel. From the response, one expects that the 
acoustic spectrum will be dominated by the low 
frequencies with a lower level for the laminarized 
boundary layer loading than for the turbulent one. 
Larger differences in structural response are expected 
for higher speed flow, since the convected waves of 
the panel dominate the response over a wider 

5. Conclusions 

An investigation of the control of the turbulent 
boundary layer over rigid and flexible surfaces 
downstream of a concave-convex geometry was 
made. Heating was applied at the concave surface. 
Pressure gradient forces crucially influence the 
control of turbulence. The Gortler spatial pattern that 
extends over the curvature is marked by changes of 
vorticity over time. The physical significance is that 
the cooling pattern over a favorable gradient is a 
gain in stability of the flow. Laminarization reduces 
the Reynolds number, spanwise vorticity, wall 
pressure fluctuations, and structural loading. The 

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effectiveness of the technique depends on pressure 
gradient, freestream conductivity, diffusivity, 
temperature, and Reynolds number. The coupling 
between heat flux and streamwise pressure gradient 
influences the stability sufficiently to reverse the 
state of the flow. The drawback of using such a 
control system is that the power required can be 
higher than the power reduction in the system 
response. Potential applications include aircraft and 
ground vehicles where concave-convex surfaces are 
typically found on the windshield region as well as 
on a flat surface where a local pressure gradient is 


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American Institute of Aeronautics and Astronautics 

3 r 

2 - 


-2 -1 

■ Heating strip 
J I I I 



Figure 1. Pressure distributions induced by steady 
surface heating. 

- Elliptical 
leading edge 

- Space Shuttle tile 
with embedded 
heating wires 


Rigid plale cover 

Figure 2. Experimental model. 

40 I- 


t, sec 
a) Velocity fluctuation. 

20 r 



b) Mean velocity profile. 







c) Frictional velocity profile. 
Figure 3. Turbulent boundary layer at location x, 

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10 r 


Distance, cm 


Figure 4. Average surface temperature downstream of heating. 

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c) Turbulent vortices. 


d) Transitional vonices. 


e) Laminarized vortices. f) Laminarized vortices. 

Figure 5. Time sequence of Gortler vortices over concave-convex curvature during laminarization stages. 

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Time step 

= 2 


wfc,0 ^ 


^.^V — ^^ 

40 I- 


I I I I 1 

.1 .2, .3 .4 .5 

Af, sec 

Figure 6. Fluctuation velocity for successive time steps A? from turbulent to laminarized state at location Xj. 

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40 1- 


t, sec 
a) Uncontrolled velocity fluctuation. 




t, sec 

b) Controlled velocity fluctuation. 




o Uncontrolled 
• Controlled 

c) Mean velocity profile. 


o Uncontrolled 
• Controlled 

^^m •• 

1 10 10^ 10^ 10^ 


d) Frictional velocity profile. 

Figure 7. Turbulent and laminarized boundary layer at location Xi. 





Figure 8. Response of the panel structure forced by turbulent and laminarized boundary layers. 

American Institute of Aeronautics and Astronautics