1. LARGE-EDDY SIMULATION and LAGRANGIAN TRACKING of a DIFFUSER PRECEDED BY A TURBULENT PIPE Sep 07, 2006 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 b Politecnico di Bari: Dipartimento di Ingegneria Meccanica e Gestionale Centre of Excellence for Computational Mechanics

2. 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.

3. 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

4. LAGRANGIAN PARTICLE TRACKING O(10 5 ) particles having diameter of 10, 20, 50 and 100 m with density of 1000 kg/m 3 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

5. PARTICLE REBOUND Particles rebound on a curved 3D wall. curve equation:

6. 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 .

7. FRAME ROTATION 1.Calculation of angle : 2.Rotation matrix. Position: XYXY = sin  cos  cos  -sin  rzrz = sin  cos  cos  -sin  Ux Uy Ur Uz Velocity:

8. PARTICLE REFLECTION  = reflection coefficient ( = 1 perfect rebound)

9. FINALLY… Particle coordinates and velocities are rotated back by the inverse (transposed) of the rotation matrix. That’s it!