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The role of coherent structures in low-Reynolds-number turbulent wall flows. Genta Kawahara Graduate School of Engineering Science Osaka University. The role of coherent structures in low-Reynolds-number turbulent square duct flow. Genta Kawahara Graduate School of Engineering Science - PowerPoint PPT Presentation
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The role of coherent structures in The role of coherent structures in low-Reynolds-number turbulent low-Reynolds-number turbulent
wall flowswall flows
Genta KawaharaGenta KawaharaGraduate School of Engineering ScienceGraduate School of Engineering Science
Osaka UniversityOsaka University
The role of coherent structures in The role of coherent structures in low-Reynolds-number turbulent low-Reynolds-number turbulent
square duct flowsquare duct flow
Genta KawaharaGenta KawaharaGraduate School of Engineering ScienceGraduate School of Engineering Science
Osaka UniversityOsaka University
M. Uhlmann, A. Pinelli, A. SekimotoM. Uhlmann, A. Pinelli, A. Sekimoto
Role of coherent structures in plane channel
Periodic solutions in plane Couette flow (K. & Kida 2001)periodic
gentle periodic
Regeneration cycle (Jiménez & Moin1991; Hamilton, Kim & Waleffe 1995)
No regeneration cycle
contours
surfaces
x
contours
surfaces
u
u
Role of coherent structures in plane channel
Periodic solutions in plane Couette flow (K. & Kida 2001)
turbulent(Moser, Kim & Mansour 1999)
laminar
turbulentperiodic
gentle periodic
Coherent structures Prandtl’s wall law⇒(regeneration cycle) (buffer layer)
Secondary flow of Prandtl's second kind
Generation mechanism
・ Statistical budget Kajishima, Miyake, Nishimoto
( 1991 )
・ Transient growth Biau, Soueid & Bottaro (2008)
Other roles of coherent structures
Coherent structures in square-duct turbulenceUhlmann, Pinelli, Sekimoto & K. (2007, 2008)
1/4 cross-section ofsquare-duct
Reb=1100Re=80
Reb=2200Re=150
Near-wall coherent structures ⇒ Secondary flow
Reb=Ubh/> 1100Ub: bulk mean velocity
Coherent structures in square-duct turbulence
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)
h: duct half width
u, v, w xReb=1100
z/h z/h
yh
yh
Velocity and vorticity of mean secondary flow
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)1/4
cross-section (Lx=4h)
u, v, w xReb=1500
z/h z/h
yh
yh
Velocity and vorticity of mean secondary flow
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)1/4
cross-section (Lx=4h)
u, v, w xReb=2200
z/h z/h
yh
yh
Velocity and vorticity of mean secondary flow
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)1/4
cross-section (Lx=4h)
u, v, w xReb=3500
z/h z/h
yh
yh
Velocity and vorticity of mean secondary flow
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)1/4
cross-section (Lx=4h)
Positions of secondary-flow-vortex center
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)
maximum pointof x
z/h
y
h
1/4cross-section
Positions of secondary-flow-vortex center
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)
innerscaling
maximum pointxof
Reb
z+
y+
1/4cross-section
Local wall shear stress
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008) w/
w
(z+h)+
z+h
localmaximum
localminimum
Positions of local maximum and minimum
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)(z+
h)+
Reb
local maximum
local minimum
inner scaling
Identification of center of streamwise vortices
Local maximum point ofLaplacian of pressure
in cross-streamwise plane
Swirl conditionKida & Miura (1998)
streaks
vortices
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)
PDF of position of streamwise-vortex center
Reb=1500
Secondaryflow
yh
yh
z/h
z/h
x<0
x>0PDF
anti-clockwise
clockwise
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)
Reb=2200
Secondaryflow
yh
yh
z/h
z/h
x<0
x>0PDF
anti-clockwise
clockwise
PDF of position of streamwise-vortex center
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)
Identification of position of low-velocity streaks
Reb=2200
y
zx
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)
wx / w
wx / w
Position and number of low-velocity streaks
Reb=1500
wall y/h=1
t+
yh
z/h
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)
maximum minimumwall shear stress
Position of streaks
PDF of vortices
Position and number of low-velocity streaks
Reb=2200
wall y/h=1
t+
yh
z/h
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)
maximum minimumwall shear stress
Position of streaks
PDF of vortices
Reynolds-number dependence of the roles
highReb=2000
Reb
Uhlmann, Pinelli, Sekimoto & K. (2007, 2008)
Concluding remarks
Plane channel 1. Prandtl’s wall law regeneration cycle (periodic solution) ⇒ turbulent velocity profileSquare duct at low Reynolds number 2. Mean secondary flow constrained streamwise vortices ⇒ mean-secondary-flow vortices 3. Wall shear stress constrained low-velocity streaks ⇒ local maximum, minimum of wall shear stress
Roles of near-wall coherent structures
Flow configuration
Dimensionless parameters
Friction velocity
Direct numerical simulation• Time integration
velocity , pressure → fractional-step method semi-implicit 3-stage Runge-Kutta method( Verzicco & Orlandi 1996 )
• Spatial discretization
pseudo-spectral method
streamwise ( ) : Fourier
cross-streamwise ( ) : Chebyshev
Positions of secondary-flow-vortex center
maximum point( elliptic-type )stagnation point of x
z/h z/h
yh
yh
Positions of secondary-flow-vortex center
maximum point( elliptic-type )stagnation point of x
outerscaling
innerscaling
Sign selection of coherent vorticestrajectoriesVortex filament
Viscous (Lamb-Oseen) vortexvorticity (red, anti-clockwise; blue, clockwise)