U.S. patent application number 10/406940 was filed with the patent office on 2004-10-07 for surface plasma discharge for controlling leading edge contamination and crossflow instabilities for laminar flow.
This patent application is currently assigned to Innovative Technology Licensing, LLC. Invention is credited to Fedorov, Alexander, Malmuth, Norman.
Application Number | 20040195462 10/406940 |
Document ID | / |
Family ID | 33097435 |
Filed Date | 2004-10-07 |
United States Patent
Application |
20040195462 |
Kind Code |
A1 |
Malmuth, Norman ; et
al. |
October 7, 2004 |
SURFACE PLASMA DISCHARGE FOR CONTROLLING LEADING EDGE CONTAMINATION
AND CROSSFLOW INSTABILITIES FOR LAMINAR FLOW
Abstract
The present invention provides a system and method for
controlling leading edge contamination and crossflow instabilities
for laminar flow on aircraft airfoils that is lightweight, low
power, economical and reliable. Plasma surface discharges supply
volumetric heating of the supersonic boundary layers to control the
Poll Reynolds number and the cross flow Reynolds number and delay
transition to turbulent flow associated with the leading edge
contamination and crossflow instabilities. A closed-loop feedback
control system that incorporates these principles includes three
primary components: heat-flow sensors, a PID controller, and plasma
discharge elements. Heat-flow sensors distributed around the
airfoil surface provide root-mean-square (rms) pulsations of the
heat flow to the airfoil skin. These data are fed to the PID
controller to determine the flow state (laminar or turbulent) and
to drive voltage inputs to the plasma discharge elements, which
provide the volumetric heating of the boundary layer on a time
scale necessary to adapt to changing flight conditions and delay
transition to turbulent flow.
Inventors: |
Malmuth, Norman; (Newbury
Park, CA) ; Fedorov, Alexander; (Moscow Region,
RU) |
Correspondence
Address: |
John J. Deinken
ROCKWELL SCIENTIFIC COMPANY LLC
P.O. Box 1085
Mail Code A15
Thousand Oaks
CA
91358-0085
US
|
Assignee: |
Innovative Technology Licensing,
LLC
|
Family ID: |
33097435 |
Appl. No.: |
10/406940 |
Filed: |
April 3, 2003 |
Current U.S.
Class: |
244/205 |
Current CPC
Class: |
B64C 2230/12 20130101;
Y02T 50/10 20130101; Y02T 50/166 20130101; B64C 21/00 20130101;
B64C 23/005 20130101 |
Class at
Publication: |
244/205 |
International
Class: |
B64C 023/00 |
Claims
1. An aircraft, comprising: aAn airfoil having a leading edge,
whereby air flow interacts with the leading edge to create a first
boundary layer, characterized by a Poll Reynolds number, along an
attachment line and a second boundary layer, characterized by a
cross flow Reynolds number, along diverging streamlines, and
pPlasma discharge elements distributed along the attachment
linelocated near the leading edge on the airfoil, said plasma
discharge elements being adapted to generate a plasma to
volumetrically heat the first and seconda boundary layers of
airflow, thereby maintaining the Poll Reynolds number below a first
critical value along the attachment line and maintaining the cross
flow Reynolds number below a second critical value along the
streamlines to delay the onset of turbulent flow as it passes over
the leading edge of the air foil.
2. (Cancelled)
3. The aircraft of claim 12, wherein the plasma discharge elements
comprise multiple pairs of electrodes.
4. (Cancelled)
5. (Cancelled)
6. The aircraft of claim 1, further comprising: hHeat flow sensors
located near the leading edge of the air foil to sense whether the
air flow over the airfoil is laminar or turbulent; and aA
controller that responds to an output of the heat flow sensors to
adjust the plasma discharge elements.
7. The aircraft of claim 6, wherein the heat flow sensors are
located on the airfoil downstream from the plasma discharge
elements.
8. The aircraft of claim 6, wherein the controller responds on a
time-scale sufficient to adapt to changing flight conditions.
9. The aircraft of claim 6, wherein the controller comprises a PID
controller.
10. An aircraft, comprising: aAn airfoil having a leading edge
whereby air flow interacts with the leading edge to creates a first
boundary layers, characterized by a Poll Reynolds number, along an
attachment line that is characterized by a Poll Reynolds number and
a second boundary layer, characterized by a cross flow Reynolds
number, along diverging streamlines that is characterized by a
cross flow Reynolds number, and pPlasma discharge elements
distributed along the attachment line on the leading edge on the
airfoil, said plasma discharge elements being adapted to generate a
plasma to volumetrically heat the first and second boundary layers,
thereby maintaining the to keep said Poll Reynolds number below a
first critical value along the attachment line and maintaining the
cross flow Reynolds numbers below a second respective critical
values along the streamlines to and delay the onset of turbulent
flow.
11. The aircraft of claim 101, further comprising: hHeat flow
sensors located near the leading edge of the air foil downstream
from the plasma discharge elements to sense whether the air flow
over the airfoil is laminar or turbulent; and aA controller that
responds to an output of the heat flow sensors to adjust the plasma
discharge elements.
12. An aircraft, comprising: aAn airfoil having a leading edge,
whereby air flow interacts with the leading edge to create a first
boundary layer, characterized by a Poll Reynolds number, along an
attachment line and a second boundary layer, characterized by a
cross flow Reynolds number, along diverging streamlines, pPlasma
discharge elements distributed along the attachment line located
near the leading edge on the airfoil, said plasma discharge
elements being adapted to generate a plasma to volumetrically heat
the first and second boundary layers, thereby maintaining the Poll
Reynolds number below a first critical value along the attachment
line and maintaining the cross flow Reynolds number below a second
critical value along the streamlines to delay the onset of
turbulent flow hHeat flow sensors located near the leading edge of
the air foil downstream from the plasma discharge elements to sense
whether thea boundary layers are over the airfoil is laminar or
turbulent; and aA controller that responds to an output of the heat
flow sensors to control the plasma discharge elements to generate
thea plasma to volumetrically heat the boundary layer to delay the
onset of turbulent flow.
13. (Cancelled)
14. (Cancelled)
15. A method of delaying the transition to turbulent flow over an
air foil having a leading edge, whereby air flow interacts with the
leading edge to create a first boundary layer, characterized by a
Poll Reynolds number, along an attachment line and a second
boundary layer, characterized by a cross flow Reynolds number,
along diverging streamlines, comprising the steps of:
generatingdischarging a plasma along the attachment line to
volumetrically heat thea boundary layers, of air flowthereby
maintaining the Poll Reynolds number below a first critical value
along the attachment line and maintaining the cross flow Reynolds
number below a second critical value along the streamlines to delay
the onset of turbulent flow as it passes over a leading edge of the
air foil.
16. (Cancelled)
17. (Cancelled)
18. The method of claim 15, further comprising, Sensing the laminar
or turbulent state of the air flow, and Controlling the plasma
discharge.
19. The method of claim 18, wherein the laminar or turbulent state
is sensed downstream from the plasma discharge.
20. A method of delaying the transition to turbulent flow over an
airfoil having a leading edge, wherein air flow interacts with the
leading edge of the airfoil to create a first boundary layer,
characterized by a Poll Reynolds number, along an attachment line
that is characterized by a Poll Reynolds number and a second
boundary layer, characterized by a cross flow Reynolds number,
along diverging streamlines that is characterized by a cross flow
Reynolds number, comprising the steps of: generatingdischarging a
plasma along the attachment line to volumetrically heat the first
and second boundary layers; sensing the laminar or turbulent state
of the air flow downstream for the plasma discharge, and
controlling the plasma discharge, thereby maintaining the Poll
Reynolds number below a first critical value along the attachment
line and maintaining the cross flow Reynolds number below a second
critical value along the streamlines to delay the onset of
turbulent flow so that the Poll Reynolds number and the cross flow
Reynolds number are kept below respective critical levels.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] This invention relates to aircraft laminar flow control
(LFC) systems, and more specifically, to a method and system using
plasma discharge to encourage laminar flow along the surface of a
wing airfoil.
[0003] 2. Description of the Related Art
[0004] Since the 1930s, laminar flow control (LFC) has been touted
as the technology that would enable aircraft to sip fuel and shrug
off drag, slipping through the air with the greatest of ease
without reducing lift. Laminar flow is achieved by reducing the
magnitude of disturbances and instabilities in the very thin and
relatively stagnant layer of air between the skin of an aircraft
and the free-stream air surrounding it call the "boundary layer."
By keeping these fluctuations small, the nonlinear interactions
leading to turbulence can be curtailed and/or delayed. Currently,
the most robust methods for controlling the disturbance amplitudes
are based on modifying the boundary layer mean flow via airfoil
geometry (i.e., by tailoring the pressure gradient, C.sub.p) or by
applying surface suction. However, these methods have not delivered
on the promise of LFC.
[0005] Since modifications to the pressure gradient do not actively
consume power, this approach has been termed "natural laminar
flow". The successful application of this approach and attainment
of drag reduction benefits has been demonstrated both theoretically
and in testing for nominally two-dimensional boundary layers. The
main disadvantage of the natural laminar flow approach is that the
modified C.sub.p distribution is generally unacceptable from an
overall airplane performance point of view. For this reason,
natural laminar flow is not frequently used for increasing the
extent of laminar flow.
[0006] The use of suction has also been successfully tested to show
improved laminar flow and reduced drag without the adverse
restrictions on the C.sub.p distribution. However, the suction
approach has its own shortcomings, including increased costs, added
weight, and increased complexity of the overall flow-control system
as compared to the baseline non- suction configuration. These
shortcomings partially offset the performance savings. There are
also potential performance penalties associated with suction
applications, e.g., suction drag and increased roughness
sensitivity due to thinner boundary layers. Additionally, the
porous suction surface can require increased maintenance.
[0007] It is also known to use a combination of suction and
pressure gradient tailoring (termed "hybrid laminar flow control")
to effectively achieve laminar flow with more practical C.sub.p
distributions. While the overall performance of the aircraft is
improved to acceptable levels, the hybrid laminar flow control
approach still suffers the shortcomings of the suction system.
[0008] The application of surface air cooling (to below the
adiabatic surface temperature) has also been theorized to be an
effective flow control technique. The general theory predicts that
cooling of an airflow surface to lower than the adiabatic surface
temperature will cool the passing boundary layer, which in turn
will slow the development and growth of instabilities. Conceived
surface cooling techniques, however, are thought to be impractical
for large surface areas such as those in a large commercial
transport. Because of this, the idea of surface cooling is not
exploited in current aircraft configurations.
[0009] The beneficial effects of surface cooling have also been
theorized to occur by application of local heat to a stable
upstream region of the boundary layer. In theory, the heated
upstream boundary layer then encounters a cooler downstream surface
to result in a net temperature decrease experienced by the boundary
layer that is similar to the net change in temperature achieved by
simply cooling the downstream surface. This approach was
demonstrated experimentally at TsAGI and at I.T.A.M. in Russia
during the mid-to-late 1980's. Specifically, the results showed
that increased laminar flow could be achieved by localized heating
in the leading-edge region of a flat plate. (See for example,
Dovgal, A. V., Levchenko, V. Ya. and Timofeev, V. A. (1990)
"Boundary layer control by a local heating of the wall," from:
IUTAM Laminar-Turbulent Transition, eds. D. Arnal and R. Michel,
Springer-Verlag, pp. 113-121). One of the problems in applying this
alternative technique to airfoils has been the loss of performance
benefit after only a relatively short period of time due to the
transfer of heat from the boundary layer flow to the cooler surface
downstream. As heat is transferred from the boundary layer flow,
the surface temperature rises and the relative temperature
difference between the flow and the surface diminishes. This
reduces the stabilizing effect on the boundary layer and eventually
terminates the laminar-flow benefit.
[0010] U.S. Pat. No. 6,027,078 to Crouch provides a localized
heating system for use with an airfoil having a leading edge
region, a controlled surface extending aft from the leading edge on
one side of the airfoil, and an uncontrolled surface extending aft
from the leading edge region on the opposite side of the airfoil.
The heating system includes an electro-thermal heat source located
at the leading edge region; and a heat sink positioned aft of the
heat source and adapted for heat transfer from the controlled
surface to the uncontrolled surface. The electro-thermal heat
source modifies the pressure distributions around the airfoil to
improve laminar flow. The transfer of heat by the heat sink
improves the boundary layer airflow along the controlled surface.
Crouch's electro-thermal surface heating has a long relaxation time
that makes it ineffective in responding to real-time changes in
flight conditions and is very inefficient in heating flow over the
vehicle surface.
[0011] In summary, the drag reduction benefits of having laminar
airflow have been known for many years, however, there are few
economically viable laminar airflow control systems available. The
general problem has been that the increased costs required to
achieve sustained laminar flow substantially erodes the potential
benefits. Usually, the laminar flow control system does improve
laminar flow over an aerodynamic surface (e.g., wing, nacelle,
vertical tail, etc.) and improve overall aircraft performance, but
the benefits of the system are more than offset by the increased
costs in manufacturing, maintenance, aircraft weight, design
complexity, operational costs, reliability, etc. Thus, a need
exists for a laminar flow control means that is low cost and low
maintenance. The ideal system would further have minimum impact on
the weight and configuration complexity of the aircraft.
SUMMARY OF THE INVENTION
[0012] The present invention provides a system and method for
controlling leading edge contamination and crossflow instabilities
for laminar flow on aircraft airfoils that is light weight, low
power, economical and reliable.
[0013] This is accomplished with plasma surface discharges that
supply volumetric heating of the supersonic boundary layers to
control the Poll Reynolds number and the cross flow Reynolds number
and delay transition to turbulent flow associated with the leading
edge contamination and crossflow instabilities. A closed-loop
feedback control system that incorporates these principles includes
three primary components: heat-flow sensors, a PID controller, and
plasma discharge elements. Heat-flow sensors distributed around the
airfoil surface provide root-mean-square (rms) pulsations of the
heat flow to the airfoil skin. These data are fed to the PID
controller to determine the flow state (laminar or turbulent) and
to drive voltage inputs to the plasma discharge elements, which
provide the volumetric heating of the boundary layer on a time
scale necessary to adapt to changing flight conditions and delay
transition to turbulent flow.
[0014] These and other features and advantages of the invention
will be apparent to those skilled in the art from the following
detailed description of preferred embodiments, taken together with
the accompanying drawings, in which:
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] FIG. 1 is a perspective view of a swept wing aircraft in
flight illustrating the region of the wing subject to laminar flow
control;
[0016] FIG. 2 is an enlarged view of the region of the wing
illustrating airflow at the leading edge;
[0017] FIG. 3 is a cross-sectional view of the wing along section
A-A with the boundary layer transitioning to turbulent flow due to
contamination of the wing leading edge;
[0018] FIG. 4 is a plot of the Poll Reynolds number versus the
roughness height referenced to the boundary layer thickness.
[0019] FIG. 5 is a cross-sectional view of the wing along section
A-A illustrating laminarization of the boundary layer due to plasma
discharge heating in accordance with the invention;
[0020] FIGS. 6a and 6b are an illustration of the amplification of
cross flow vortices in boundary layer and a plot of the cross flow
velocity profile, respectively;
[0021] FIG. 7 is a perspective close-up view of the region of the
wing showing the electrodes and the region of flow heating;
[0022] FIG. 8 is a perspective close-up view of the leading edge of
a wing showing the key components of the present invention
including the electrodes, PID controller and sensors;
[0023] FIGS. 9a and 9b are heat flow signals in laminar and
turbulent flows;
[0024] FIGS. 10a and 10b are side and top views of a plasma
discharge circuit, respectively;
[0025] FIGS. 11a and 11b are a schematic block diagram of the
control system and a flow chart illustrating the closed loop
feedback control scheme, respectively; and
[0026] FIG. 12 is a curve of the Poll Reynolds number as a function
of the wall temperature.
DETAILED DESCRIPTION OF THE INVENTION
[0027] The present invention provides a system and method for
controlling leading edge contamination and crossflow instabilities
of laminar flow on aircraft airfoils that is light weight, low
power, economical and reliable. This is accomplished by plasma
injection into boundary layers to delay leading edge contamination
and crossflow instabilities. Plasma surface discharges are used to
supply volumetric heating of the boundary layer that leads to
stabilization of flow instabilities via reduction of the Poll
Reynolds and cross flow Reynolds numbers and increase of the
boundary layer thickness. A closed-loop feedback control system
that incorporates these principles includes three primary
components: heat-flow sensors, a PID controller, and plasma
discharge elements. The heat-flow sensors distributed over the wing
leading-edge region sense the root-mean-square (rms) heat-flow
pulsations. This data is fed to the PID controller to determine the
flow state (laminar or turbulent) and adjust the drive conditions
for the plasma discharge elements, which provide the volumetric
heating of the boundary layer on a time scale necessary to adapt to
changing flight conditions.
[0028] As shown in FIGS. 1 and 2, aircraft 10 designed for
high-speed flight generally have wings 12 with swept leading edges
14. The free stream 16 interacts with the leading edge 14 of wing
12 and forms three-dimensional flow containing boundary layers 18
and 20 along attachment line 22 and diverging streamlines 24,
respectively.
[0029] The flow in the boundary layer 18 is characterized by the
Poll Reynolds number R* where 1 R * = W e * v e * ( 1 ) * = v e * /
( U e X ) y = 0 ( 2 )
[0030] where .DELTA.* is the boundary layer thickness, W.sub.e is
the flow velocity along attachment line 10;
.differential.U.sub.e/.differential.X is the chordwise velocity
gradient at the attachment line; subscript "e" denotes flow
characteristics at the upper edge of boundary layer 18; v.sub.e* is
kinematic viscosity evaluated at the reference temperature
T.sub.v=0.1(T.sub.w-T.sub.e)+0.6(T.sub.r-T.sub.e) (3)
[0031] where T.sub.w is wall temperature and T.sub.r is recovery
temperature. Directions of U and W are given by velocity triangle
25; coordinates X, Y, Z are shown in FIG. 2.
[0032] As shown in the cross-section view of wing leading edge 14
in FIG. 3, the boundary layer flow 18 along attachment line 22 may
be contaminated by roughness elements 26 on wing 12, which induce
flow disturbances 28. If the Poll Reynolds number R* is larger than
a critical level 30, shown in FIG. 4, as a function of the ratio of
the roughness height d to the boundary layer thickness .DELTA.*,
then roughness elements 26 cause a transition of boundary layer 18
to turbulent flow 32. Turbulent flow 32 propagates along
streamlines 24 and covers the major portion of the wing surface. As
shown in FIG. 4, for R* below R.sub.*C.apprxeq.250 32, the flow
stays laminar irrespective of the roughness height. Plasma heating
increases gas temperature T.sub.e and wall temperature T.sub.w that
leads to increasing of kinematic viscosity v.sub.e* and decreasing
of R*. in accordance with (1)-(3). This allows for maintaining of
the Poll Reynolds number below critical level 30. In this case,
flow disturbances 28 induced by roughness elements 26 dissipate
downstream and laminar boundary layer 18 does not transition to
turbulent flow as shown in FIG. 5. Moreover, the boundary layer
thickness .DELTA.* increases due to the plasma heat, which in turn
leads to a reduction of the relative roughness height
d/.DELTA..sub.*.
[0033] Another mechanism of laminar-turbulent transition is
associated with the amplification of cross flow vortices 34 in the
boundary layer 20 along streamlines 24 as schematically shown in
FIG. 6a. When the amplitude of cross flow instability is larger
than a critical level, vortices 34 breakdown into turbulent spots
36 and eventually the flow becomes turbulent. The growth rates of
vortices 34 depend on the cross flow Reynolds number R.sub.CF,
which is 2 R CF = w m 10 v e ( 4 )
[0034] where w.sub.m is the maximum of cross flow velocity in
boundary layer 20 and .delta..sub.10 is the vertical distance from
the wall at which cross flow velocity 38 is w=0.1w.sub.m as shown
in FIG. 6b.
[0035] Experiments on swept wings at low speeds indicate that the
first appearance of cross flow vortices 34 corresponds to
R.sub.CF,0.apprxeq.145, and the transition front is close to the
wing leading edge at R.sub.CF,1.apprxeq.200. To account for
compressibility effects at high speeds, the cross flow Reynolds
number is scaled as 3 R _ CF = R CF 1 + - 1 2 Pr M e 2 , ( 5 )
[0036] where .gamma. is specific heat ratio, Pr is Prandtl number
and M.sub.e is local Mach number at the upper edge of boundary
layer 20. For {overscore (R)}.sub.CF<{overscore (R)}.sub.CF,0,
cross flow vortices are stable and laminar-turbulent transition due
to cross flow instability does not occur. As in the case of leading
edge contamination, plasma heating increases gas and wall
temperatures, which leads to an increase of kinematic viscosity
v.sub.e and a reduction of {overscore (R)}.sub.CF. Thus plasma
heating can maintain the cross flow Reynolds number below the
critical level {overscore (R)}.sub.CF,0 and avoid transition of the
flow to a turbulent state.
[0037] Plasma surface discharges are used in this invention to
supply volumetric heating of the boundary layer to reduce the Poll
Reynolds and cross flow Reynolds numbers to maintain laminar flow.
As shown in FIG. 7, pairs of electrodes 40 are distributed along
attachment line 22 on the leading edge 14. In region 42 around
attachment line 22, the flow temperature increases due to Joule
heating produced by plasma discharges between the pairs of
electrodes 40. The increase in flow temperature reduces the Poll
Reynolds and cross flow Reynolds numbers to below their critical
levels to maintain laminar flow
[0038] FIG. 8 shows a closed-loop laminar flow control system that
incorporates these principles. The system includes three primary
components: heat-flow sensors 44, a PID controller 46, and plasma
discharge electrodes 40 installed along attachment line 22 on wing
12. Heat-flow sensors 44 are distributed along the wing-span
downstream from plasma discharge electrodes 40. Sensors 44 provide
heat flow pulsations 48 (in laminar flow) and 50 (in turbulent
flow) on the wing surface as shown in FIGS. 9a and 9b. The
pulsation amplitude q strongly depends on the flow state: in
laminar flow q is an order of magnitude smaller than that in
turbulent flow (compare 48 and 50). The difference between rms
fluctuations in turbulent and laminar flows allows for
determination of the flow state (laminar or turbulent). This data
is fed to a PID controller 46 to identify the flow state and adjust
the voltage required for plasma discharge electrodes 40 that
provide the volumetric heating of boundary layer 18 along
attachment line 22 on a time scale necessary to adapt to changing
flight conditions. Electrodes 40 are suitably located near
attachment line 22 at cruise flight conditions. For laminar flow
control, PID controller 46 controls the flow heating at the level
required for maintaining the laminar flow.
[0039] As shown in FIG. 10a, plasma discharge electrodes 40 are
suitably flush mounted in a dielectric substrate 52. As shown in
FIG. 10b, discharge 54 occurs across a gap between electrodes 40.
Voltage generator 56 provides enough potential to break down the
air gap. Typical component parameters are a 10 kV direct voltage
supply with 50 Hz frequency connected to a 50-150 mA working
current and 600-800 V discharge gap voltage with the arc supporting
40- 100 W of electrical power. Above the breakdown potential, PID
controller 46 controls the potential to adjust the amount and
location of volumetric heating. Other embodiments may use corona,
spark, slipping or sliding discharges.
[0040] As shown in FIGS. 11a and 11b, PID controller 46 receives
the heat flow readings from heat-flow sensors 44 (step 100), and,
based on these readings, compares the measured flow state to the
desired laminar state (step 102). If flow is laminar, the
controller continues to monitor the heat flow readings (step 104).
If not, the PID controller increases voltages for voltage generator
56 to drive plasma discharge elements 40 (step 106) to provide
plasma discharge Joule heating to reduce the Poll Reynolds number
with the control law based on a curve 60 in FIG. 12 and the cross
flow Reynolds number (step 108). Steps 100, 102, 106 and 108 are
repeated to converge to the desired laminar flow and continuously
adapt to changing flight conditions.
[0041] The general calibration and empirical testing for
characterizing laminar and turbulent flow states are known in the
art. The contribution of the present invention is to realize that
plasma discharges can be used to provide volumetric heating on a
short time scale of microseconds to adjust the Poll Reynolds number
to achieve laminar flow and to estimate the amount of Joule
heating, e.g. plasma discharge, required to achieve the goal. To
provide the basis for the control law for the scheme in FIGS. 11a
and 11b, particularly step 106, a first-cut theoretical model was
developed to evaluate the Poll Reynolds number as a function of the
wall temperature. This dependence 60 is shown in FIG. 12 for a
leading edge of 1-inch diameter and 68 degrees sweep for flight at
altitude 15 km and a Mach number of 2. As the wall temperature
increases, the Reynolds number R* decreases and quickly falls below
the critical level R*.sub.C=250. This trend verifies the premise
that a plasma discharge can effectively control leading edge
contamination. A similar dependence can be obtained for the cross
flow Reynolds number {overscore (R)}.sub.CF and used for evaluation
of plasma heating level required for stabilization of cross flow
vortices 34.
[0042] While several illustrative embodiments of the invention have
been shown and described, numerous variations and alternate
embodiments will occur to those skilled in the art. Such variations
and alternate embodiments are contemplated, and can be made without
departing from the spirit and scope of the invention as defined in
the appended claims.
* * * * *