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LARGE-EDDY SIMULATION and LAGRANGIAN TRACKING of a DIFFUSER PRECEDED BY A TURBULENT PIPE. Fabio Sbrizzai a , Roberto Verzicco b and Alfredo Soldati a. a Università degli studi di Udine: Centro Interdipartimentale di Fluidodinamica e Idraulica Dipartimento di Energetica e Macchine - PowerPoint PPT Presentation
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LARGE-EDDY SIMULATIONand LAGRANGIAN TRACKING of a
DIFFUSER PRECEDED BY A TURBULENT PIPE
Sep 07, 2006
Fabio Sbrizzaia, Roberto Verziccob and Alfredo Soldatia
a Università degli studi di Udine:Centro Interdipartimentale di Fluidodinamica e Idraulica
Dipartimento di Energetica e Macchineb Politecnico di Bari:
Dipartimento di Ingegneria Meccanica e Gestionale
Centre of Excellence for Computational Mechanics
LARGE-EDDY SIMULATION OF THE FLOW FIELD
• Flow exits from a turbulent pipe and enters the diffuser.
• Kelvin-Helmholtz vortex-rings shed periodically at the nozzle.
• Pairing/merging produces 3D vorticity characterized by different scale structures.
NUMERICAL METHODOLOGY
• Two parallel simulations:
• Turbulent pipe DNS
• LES of a large-angle diffuser
• DNS velocity field interpolated and supplied to LES inlet.
• Complex shape walls modeled through the immersed-boundaries (Fadlun et al., 2000)
L=8 r
l=10 r
r
LAGRANGIAN PARTICLE TRACKING
• O(105) particles having diameter of 10, 20, 50 and 100 m with density of 1000 kg/m3
• Tracked using a Lagrangian reference frame.
• Particles rebound perfectly on the walls.
• How to model immersed boundaries during particle tracking?
BLUE = particles released in the boundary layerRED = particles released in the inner flow
PARTICLE REBOUND
Particles rebound on a curved 3D wall.
curve equation: 112
112 2
sin)(),( Rzz
zzRRzr
LOCAL REFERENCE FRAME
• To properly model particle rebound within Lagrangian tracking, we use a local reference frame X-Y.
• X-axis is tangent to the curve, Y is perpendicular.• Particle bounces back symmetrically with respect to surface normal.• X-Y reference frame is rotated with respect to r-z by angle .
FRAME ROTATION
1. Calculation of angle :
2. Rotation matrix. Position:
12
1
12
12
2cos
2tan
zz
zz
zz
RR
dz
dr
X
Y
=sin cos
cos -sin
r
z
=sin cos
cos -sin
Ux
Uy
Ur
Uz
Velocity:
cRx
cx uRu
PARTICLE REFLECTION
'
''
Q
Q
y
xQ
'
'"
Q
Q
y
xQ
Qy
Qx
Q u
uu
,
,
',
',
'Qy
Qx
Q u
uu
',
',
"Qy
Qx
Q u
uu
Q
Q
y
xQ
= reflection coefficient( = 1 perfect rebound)
'Qy
"Qy
',Qyu
",Qyu
FINALLY…
• Particle coordinates and velocities are rotated back by the inverse (transposed) of the rotation matrix.
• That’s it!
cRz
rT
Q
Q
'
'
cT
Qz
QruR
u
u
',
',