Fundamentals and Applications of Modern Flow Control (Progress in Astronautics and Aeronautics)

563 Pages·2009·8.41 MB·English

by  R. Joslin

Fundamentals and Applications
of Modern Flow Control
Edited by
Ronald D. Joslin
Offi ce of Naval Research
Arlington, Virginia
Daniel N. Miller
Lockheed Martin Aeronautics Company
Fort Worth, Texas
Volume 231
PROGRESS IN
ASTRONAUTICS AND AERONAUTICS
Frank K. Lu, Editor-in-Chief
University of Texas at Arlington
Arlington, Texas
Published by the
American Institute of Aeronautics and Astronautics, Inc.
1801 Alexander Bell Drive, Reston, Virginia 20191-4344
The cover images are declared a work of the U.S. Government. The shadowgraph image showing jet
vectoring is courtesy of Jeffrey D. Flamm, NASA Langley Research Center, and presented in AIAA
Paper 2005-3503. The XV-15 tilt rotor image that was used in a modern fl ow control fl ight experiment
is courtesy of NASA Dryden Flight Research Center (EC80-13848).
American Institute of Aeronautics and Astronautics, Inc., Reston, Virginia
1 2 3 4 5
Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. Printed in the United
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Print ISBN 978-1-56347-983-0
e-book ISBN 978-1-56347-988-5
Progress in Astronautics and Aeronautics
Editor-in-Chief
Frank K. Lu
University of Texas at Arlington
Editorial Board
David A. Bearden Eswar Josyula
The Aerospace Corporation U.S. Air Force Research Laboratory
John D. Binder Gail Klein
viaSolutions Jet Propulsion Laboratory
Steven A. Brandt Konstantinos Kontis
U.S. Air Force Academy University of Manchester
Jose Camberos Richard C. Lind
U.S. Air Force Research Laboratory University of Florida
Richard Curran Ning Qin
Delft University of Technology University of Sheffi eld
Sanjay Garg Oleg Yakimenko
NASA Glenn Research Center U.S. Naval Postgraduate School
Christopher H. Jenkins
Montana State University
Foreword
It is a delight to thumb through this volume that provides a thorough coverage
of modern fl ow control concepts and aerospace applications. The integration of
sensors, actuators, and controls of different scales is a hallmark of many of these
modern concepts. The chapters are written by well-known experts in a readable
style. The material allows the reader to quickly grasp concepts and develop a
sense of the state-of-the-art. It also serves as a platform from which to develop
new concepts. The material will be of great value to workers in this fi eld for years
to come.
Frank K. Lu
Editor in Chief
Progress in
Astronautics and Aeronautics
vii
Nomenclature
A = reference area
ref
A = slot area
slot
A = tip displacement
tip
AR = wing aspect ratio
a,A = Fourier mode amplitude; area, m2
B = blowing ratio (v /v )
jet in
B = unsteady blowing coeffi cient, ruA /r U A =m˙ /r U A
c j j jet • • ref j • • ref
B = electrohydrodynamic body force
E
b = wing span, or slot width
C = nozzle discharge coeffi cient
d,prim
C = constant for DES
DES
C = nozzle thrust effi ciency
fg,sys
C = orientation tensor for polymer chains
i,j
C = wing lift coeffi cient
L
C = wing maximum lift coeffi cient
L,max
C = sectional lift coeffi cient
l
C = wing moment coeffi cient
M
C = sectional moment coeffi cient
m
C ,c = pressure coeffi cient; specifi c heat constant
p p
C = suction surface arc-length
s
C = axial chord
x
C = mixing-layer length-scale constant
0
C = effective correction, C (1 -V / V )
m net m 0 jet
cs = constant for Smagorinsky model
c = wing chord length (m)
c = specifi c heat at constant volume
v
c,c = non-dimensional aerodynamic forces
x y
c = ambient sound speed
0
c = momentum coeffi cient (sometimes defi ned as ru2 h /q L); steady
m t j,rms s •
momentum coeffi cient, J/q L
•
·c Ò = unsteady momentum coeffi cient
m
D = blade spacing in y; cylinder diameter; jet diameter; drag
DC = duty cycle
DL/T = airframe download (vertical drag)/rotor thrust
d = separation distance of electrode
e
d = hole diameter; distance; disturbance; blade span
E = total energy per unit volume
E = electric fi eld vector
E = electric fi eld
fi eld
e = electron charge
c
e = internal energy per unit volume
xiii
xiv
F,G,H = inviscid fl ux vectors
F+ = reduced forcing frequency (sometimes defi ned as f X /U )
e te •
F = force vector
i
F = represents nonlinear terms
i,j
F = force from Hooke’s law
k
F,G,H = viscous fl ux vectors
v v v
F(t) = unsteady force applied to fl uid
f = control input or frequency; Peterlin function; fl ux
f = body force per unit volume
B
f = Helmholtz frequency
H
f ,f¢ = forcing function for immersed boundary method
b b
f = diaphragm natural frequency
d
f = nondimensional frequency; forcing function
e
f = forcing function in discrete forcing approach
i
f = frequency
j
f = forcing function due to fi ber stress
m
f = maximum frequency
max
f = minimum frequency
min
f = pulsation frequency
pulsing
f = resonant frequency
res
f = natural shedding frequency
s
f,g,h = viscous term groupings
v v v
f = fi rst resonant frequency of ZNMF actuator
1
f = second resonant frequency of ZNMF actuator
2
f = mixing-layer reduced excitation frequency, f X /U
~+ e te •
f = fi ltered or Favre-averaged quantity
f¯ = fi ltered or Reynolds-averaged quantity
f¢ = fl uctuating quantity
G = transfer function of the system; LES convolution kernel
G(s) = transfer function
G(jw) = frequency response
GR = gear/pulley ratio
g(q) = top-hat function
j
g = gap distance
H = heat fl ux and work done by stresses
k
H = transfer-function norm (rms over frequency)
2
H = transfer-function norm (maximum over frequency)
•
h,h = slot height; rectangular jet height
slot
h = wall roughness height
k
·JÒ = periodic component of momentum
J = steady component of momentum; coordinate transformation Jacobian
jw = frequency-domain axis
K = transfer function of the controller
k = effective stiffness; turbulent kinetic energy; wave number; spring
constant; reduced airfoil oscillation frequency, pfc/U
•
k = wave-number vector
i
L = differential operator
xv
L = loop transfer function, GK; characteristic body length scale, m; lift;
turbulent length scale
L¢ = modifi ed discrete operator
L/D = lift-to-drag ratio
Lo =C (U -U )/2pf
0 2 1 e
L = fl ap length from slot to trailing edge
f
L = reference length
ref
Ma,M = Mach number
M,M = peak Mach number of the oscillatory jet
j jet
M = component of Mach number in direction r
r
M = rotor advance ratio (forward fl ight speed/blade rotation tip speed)
u
m = effective mass
m˙ = mass fl ow rate
m˙ = mass fl ow rate of jet
jet
N = number of grid points
N = number of slots/holes
h
N = number of micro-jets
m
n = unit normal to surface pointing into the fl uid
i
Pr = Prandtl number
Pr = turbulent Prandtl number
t
P,p = pressure
p = compressive stress tensor
i,j
p = maximum rms pressure
max
p = minimum rms pressure
min
Q = vector of conserved variables
Q = subgrid scale of Reynolds heat fl ux
k
Q = output volume fl ow rate
out
Q(t) = volume velocity
q = freestream dynamic pressure, _1 ; r U2
q•(t) = state variables 2 • •
R = strength of spanwise vortices, (U -U )/(U +U ); gas constant
1 2 1 2
Re,Re = Reynolds number based on chord length (sometimes defi ned
c
asU c/n)
•
Re = Reynolds number based on boundary layer thickness d
d
Re = Reynolds number based on momentum thickness q
q
r = vector of known terms in discrete forcing approach
r = distance from location in fl ow to observer
r = separation vector between two beads
r = vortex radius corresponding to V
1 q,max
r = vortex radius corresponding to edge of the vortical region
2
S = sensitivity transfer function, or blade spacing in y
St = Strouhal number, f L/U
e •
|S| =÷2S S
i,j i,j
S = rigid surface present in the acoustic fi eld
0
S (w) = power spectrum of the unsteady loading
FF
S (w) = power spectrum of the unsteady surface pressure
PP
S = strain rate tensor
i,j
xvi
S (w) = power spectrum of the acoustic pressure
pp
s = slot width/span; arclength; (complex) Laplace variable, s+jw
s = fl ap span, _ 1
Tf = period or t3ime, s; temperature; complementary sensitivity transfer
function
T = term in quasi-1D model
T = total stress tensor; Lighthill stress tensor
i,k
t = time, Tw ; or thickness
U,V,W = mean velocity components in x,y,z directions
U = solution vector
U,U = convection velocity
c
U = peak mean slot velocity
j
U = jet core velocity
–O
U = mean velocity of two streams, _ 1 (U +U )
U = freestream velocity 2 1 2
•
u,v,w = coherent velocity fl uctuations
c c c
u = boundary-layer edge velocity
e
u;u,v,w = velocity components in x,y,z directions
i
u = peak jet velocity
j
u = peak rms jet velocity
uj¢e,trvm¢s,w¢ = velocity fl uctuations
u = friction velocity, ÷t /r
t w
u* = friction velocity
V = total velocity magnitude; volume
V = breakdown voltage
B
V ,V = ac voltage
ac a
V = velocity of surface
i
V = boundary layer control jet velocity
jet
V = normal jet velocity/blade tip velocity
n
V = volume of the region containing turbulence; external fl ow speed
o
V,V,V = mean velocity components in x,r,q directions
x r q
v = velocity vector
i
v* = boundary-layer displacement velocity
We = Weissenberg number
w = rectangular jet width
X = coordinate vector of kth Lagrangian point
k
X = distance from control location to trailing edge
te
x;x,y,z = coordinates measured from the leading edge of model
i
y = sensor measurement
y = position vector
i
y ,y = information for control theory
1 2
y = center of a plane mixing layer
0
y = distance from the wall at which U= _1U
y2 = distance from the wall at which U=U 2 max
m max
(y¯,z¯) = vortex centroid
Z = generalized impedance, effort/fl ow
z = output variables in control theory
xvii
Greek
a = angle of attack; collision effi ciency factor
a = static stall angle
s
b = slot control angle; ratio of solvent to mixture viscosity
b = constant in k-w turbulence models
1
G = vortex strength; wing bound circulation
G¢ = vortex strength
G = boundary of domain W
b b
g = loss coeffi cient; wing vortex sheet strength, dG¢/dy; specifi c heat
ratio,c /c
p v
DH = viscous head-drop
D¯ = isotropic grid scale
Dx = cell size in x direction
d = fl ap defl ection angle; boundary-layer thickness
d* = boundary layer displacement thickness
d = parameter in body force expression
b
d = Kronecker delta
i,j
d = thermal boundary layer thickness
T
d f,d F = fl ap defl ection angle
e = turbulent dissipation rate
e = dielectric permittivity
0
ε = dielectric coeffi cient
ε = permutation tensor
i,j,k
h = Kolmogorov length scale, (n3/e)1/4
h = nozzle vectoring effi ciency
q = skew angle; momentum thickness; observer angle to direction
of force
q = frequency of applied voltage
f
k = coeffi cient of thermal conductivity
L = Sweep-back angle
l = acoustic wavelength
l = Debye length
d
m = dynamic viscosity
n = kinematic viscosity, m/r
n = kinematic eddy viscosity
t
x,h,z = curvilinear coordinate components
r = density, kg/m3
r = charge density
c
r = jet density, kg/m3
jet
r = ambient density
0
r¢ = density perturbation
r = freestream density, kg/m3
•
s = viscous stress tensor
ik
t = Kolmogorov time scale, (n / r)1/2; duty cycle
t = subgrid scale; Reynolds stress tensor
ik
tp = polymer stress tensor
ik
t = wall shear stress
w
xviii
t* = retarded time
F = potential function
f = phase difference; represents fl ow fi eld variables; observer angle to
direction of fl ow
j = pitch angle
j = phase difference
phase
Y = observer angle to trailing edge
W = domain
W,W = subdomains
f b
w = frequency, rad/s; dissipation per unit k; angular frequency
w = component of vorticity; coeffi cients of interpolation scheme
i
w = reduced frequency (normalized on semichord and fl ow velocity)
r
w,w = streamwise and spanwise vorticity
x z
wˆ = modifi ed dissipation per unit k
Subscripts and Superscripts
e = boundary-layer edge
G = ghost cell
i = inboard
in = inlet conditions
j, jet = forcing amplitude; jet
le = leading edge
max = maximum
min = minimum
o = outboard
out = outlet conditions
ref = reference
rms = root mean squared
sep = separated region
t = tip
te = trailing edge
tot = total
w = wall
x,y,z,t = derivative with respect to x,y,z,t
0 = stagnation-point conditions
• = freestream quantity
+ = distance in wall units
Special Symbol
· Ò phase-averaged quantity