LARGE-EDDY SIMULATION
and LAGRANGIAN TRACKING of a
DIFFUSER PRECEDED BY A TURBULENT
PIPE
Fabio Sbrizzaia, Roberto Verziccob and Alfredo Soldatia
a
Università degli studi di Udine:
Centro Interdipartimentale di Fluidodinamica e Idraulica
Dipartimento di Energetica e Macchine
b
Politecnico di Bari:
Dipartimento di Ingegneria Meccanica e Gestionale
Centre of Excellence for Computational Mechanics
Sep 07, 2006
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 largeangle diffuser
• DNS velocity field
interpolated and
supplied to LES
inlet.
• Complex shape
walls modeled
through the
immersedboundaries
(Fadlun et al.,
2000)
l=10 r
r
L=8 r
LAGRANGIAN PARTICLE TRACKING
• O(105) particles having
diameter of 10, 20, 50
and 100 mm 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 layer
RED = particles released in the inner flow
PARTICLE REBOUND
Particles rebound on a curved 3D wall.
curve equation:
  z  z1 
r ( z, )  ( R2  R1 ) sin 
  R1
 2 z2  z1 
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 q.
FRAME ROTATION
  z  z1 
dr  R2  R1  

tan  

 cos
dz  z2  z1  2
 2 z2  z1 
1.
Calculation of angle q:
2.
Rotation matrix. Position:
X
sinq
cosq
r
=


x  Rc
Y
cosq
-sinq
z
Velocity:
Ux
sinq
cosq
Ur
cosq
-sinq
Uz


u x  R  uc
Uy
=
PARTICLE REFLECTION
 = reflection coefficient
( = 1
perfect rebound)
 xQ '
Q'  
 yQ '
u x ,Q '
uQ '  
u y ,Q '
y Q ' u y ,Q '
 xQ
Q
 yQ
u x ,Q
uQ  
u y ,Q
yQ " u y ,Q"
 xQ '
Q"  
   yQ '
uQ "
u x ,Q '

   u y ,Q '
FINALLY…
• Particle coordinates
and velocities are
rotated back by the
inverse (transposed)
of the rotation
matrix.
• That’s it!
rQ ' 
T 
  R c
zQ ' 
u r ,Q ' 
T 
  R  uc
u z ,Q ' 