WALL FREE SHEAR FLOW
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WALL FREE SHEAR FLOW Turbulent flows free of solid boundaries JET Two-dimensional image of an axisymmetric water jet, obtained by the laser-induced fluorescence technique. (From R. R. Prasad and K. R. Sreenivasan, Measurement and interpretation of fractal dimension of the scalar interface in turbulent flows, Phys. Fluids A, 2:792–807, 1990) x y Irrotational Turbulent
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WALL FREE SHEAR FLOW. Turbulent flows free of solid boundaries. Irrotational. JET. y. x. Turbulent. - PowerPoint PPT Presentation
Transcript of WALL FREE SHEAR FLOW
WALL FREE SHEAR FLOWTurbulent flows free of solid boundaries
JET
Two-dimensional image of an axisymmetric water jet, obtained by the laser-induced fluorescence technique. (From R. R. Prasad and K. R. Sreenivasan, Measurement and interpretation of fractal dimension of the scalar interface in turbulent flows, Phys. Fluids A, 2:792–807, 1990)
x
y
Irrotational
Turbulent
WAKE
http://www.ifh.uni-karlsruhe.de/science/envflu/
SHEAR LAYER
Laser-Induced Fluorescence (LIF) VISUALIZATION OF AN AXISYMMETRIC TURBULENT JET, C. Fukushima and J. Westerweel, Technical University of Delft, The Netherlands
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x
Laser-Induced Fluorescence (LIF) VISUALIZATION OF AN AXISYMMETRIC TURBULENT JET, C. Fukushima and J. Westerweel, Technical University of Delft, The Netherlands
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Turbulent Kinetic Energy (q2) Balance in a Jet
2
2222 wvu
q
x
y
q2
<v2 > <u2 >
<w2 >
-<uv >
y
m2 /s
2
2
2222 wvu
q
Laser-Induced Fluorescence (LIF) VISUALIZATION OF AN AXISYMMETRIC TURBULENT JET, C. Fukushima and J. Westerweel, Technical University of Delft, The Netherlands
x
Turbulent Kinetic Energy (q2) Balance in a Jet
02
22
0 vpvqyy
uuvyqv
xqu
No local accelerationsNo viscous transportPart of the shear production = 0No buoyancy production
wgxuuueuuqup
xdtdq
oj
ijiijijj
oj21 2
2
x
y
02
22
0 vpvqyy
uuvyqv
xqu
ym2 /s
3
Gai
nLo
ss
xqu
2
yqv
2
yuuv
02 vpvq
y
http://www.symscape.com/node/447
U0
WALL-BOUNDED SHEAR FLOW
Nominal limit of boundary layer
0.99U0
Viscous sublayer
For fully developed, bounded turbulent flow (not changing in x):
zxp
0 uwzu
viscous Reynolds
zxp
0Function of x only Function of z only
CONSTANTS!
uwzu
z
centerline or surface
zu
Stress distribution is then LINEAR
zzuw
xuu
0
1in boundary layer over flat plate (no press grad):
uwzu
z
zedge of boundary layer
stress is now a function of x and z
Near the wall – Different Layers
zuu ,,, 0
http://furtech.typepad.com/
z
ū (x)
u(x,z)
0,Only involve mass dimension
Should appear together in nondimensional groups
0
* u Friction Velocity
zuuu ,,*
zuuu ,,*
This relates 4 variables involving the dimensions of length and timeAccording to the PI THEOREM, this relationship has 4 variables and 2 dimensions
Then, only two (4 – 2) non-dimensional groups can result:
zfzuf
uu
*
*
Law of the Wall
Inner part of the wall layer, right next to the wall, is called the viscous sublayer – dominated by viscous effects
Z+ is a distance nondimensionalized by the viscous scale z*u
*uu
*uu
z z
z (m
) = z
+ν/u
*
viscous sublayer
zu
0
zu 0gintegratin
zuu
*:onalnondimensi
buffer layer
logarithmic layer
5~z
*uu
z
viscous sublayer
buffer layer
logarithmic layer
zfzuf
uu
*
*
outer layer
FzF
uUu
*
Velocity defect law
Law of the wall
dzdfu
zu
2*
ddFu
zu *
zfz
ddF
1
Karman constant = 0.41
Equating and multiplying times z/u*
zfz
ddF
1
Karman constant = 0.41
Integrating: Azzf ln1
BF
ln1
From experiments: 5ln1 *
*
zu
uu 1ln1
*
z
uUu
*uu
z
Velocity distributions for theOverlap layer,Inertial sublayer,Logarithmic layer
Logarithmic velocity distribution near a boundary can also be derived from dimensional analysis
zu
can only depend on z, and the only relevant velocity scale is u*
zu
zu *1
Czuu ln*
*zu
*uu
*
5u
*
30u
*
300u
0@0 zzu 0
* lnzzuu
0
* lnzzuu
m005.0sm04.0
0
*
zu
0
* u
Pa20
Data from Ponce de Leon Inlet
FloridaIntracoastal Waterway
Florida
