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

',

',