1 / 23

P. LAURE 1 , G. BEAUME 1,2 and T. COUPEZ 2

Direct Numerical Simulation of Solid-Liquid Flow. P. LAURE 1 , G. BEAUME 1,2 and T. COUPEZ 2. ( A. Megally 2 , Th e sis July 2005). 3. 2. 1. Framework. Software. Numerical library : CIMLIB (H. Digonnet, L. Silva, J. Bruchon ) Finite Element Solveur C++ , MPI (parallelized)

randolphs
Download Presentation

P. LAURE 1 , G. BEAUME 1,2 and T. COUPEZ 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Direct Numerical Simulation of Solid-Liquid Flow P. LAURE1,G. BEAUME1,2and T. COUPEZ2 ( A. Megally2 , Thesis July 2005) 3 2 1

  2. Framework Software Numerical library : CIMLIB (H. Digonnet, L. Silva, J. Bruchon) • Finite Element Solveur • C++ , MPI (parallelized) • mesh partitionning • r-adaptation and h-adaptation (C. Gruau) Hardware EII (C. Torrin) • 3 clusters with 64 PC • MecaGrid Poject Monolithic, Multi-Domain, Finite Element methods

  3. Solid-Liquid flows Solid domain  rigid motion

  4. Fluid domain Fiber domain Characteristic Functions (1)  Description of several domains in a single mesh j = fluid or solid (fibers)

  5. Pixels in K Mesh cavity Swith on pixels Fiber domain Characteristic Functions (2) Update with voxelisation method  P0 approximation (VOF) Computation of characteristic function Voxelisation

  6. New Formulation in Solid Domain Rigid motion Boundaryconditions Stress tensor Penalization factor Lagrange multiplier

  7. Simplifications : • only penalization • no inertial effect • no gravity Weak Formulation Rigid motion constraint Mixing relation :

  8. ux uy Computation of Velocity field Penalization ~ 103l Periodic boundary conditions Shear rate

  9. Update solid domain (1) Transport Equation : discontinuous Galerkin method • numerical difusion • need r-adaptation • need more elements

  10. + + D D = = + + D D X O ( ( t t t t ) ) O X V V t t X X = i i O X 2 1 p i X X 2 1 O V Vector orientation Fiber center Update fiber position and orientation Particle method Langrangian updating X2 p VX2 O X1 VX1 Rigid motion VO Advantages • Perfect rigid motion of each fiber • Conservation of the length • No mumerical diffusion 10

  11. Numerical Procedure Voi Velocity field computation finite element method multi-domain approach (1W) Hydrodynamic Interaction Update particle positions Particle method Boundary conditions and collisions 1Wj • Numerical approach similar to Glowinski & Joseph’s modelling [Glowinski 1999] (Fictitious domain method for particulate flows) 11

  12. 2 p 1 T = ( bref + ) bref . g Single Fiber Motion in shear flow Isoline of characteristic function 2D Isoline of characteristic function 3D Shear flow, Periodic Cell Equivalent aspect ratio bref  computed  Find Jeffery's orbit for a shear flow Periodic motion -  Jeffery Evolution of  vs time 12

  13. Hydrodynamical Interactions It is not necessary to have an explicit form (as in [Yamane 1994] , [Fan 1998]) - drag forces - lubrication forces (short range interactions) The central particle moves due to hydrodynamic interactions The period of rotation changes Sphericals particles in Couette Flow 13

  14. Fij as OiOj Spheres – short-range hydr. forces (moderate concentration) Lubrication approximation : repulsion force exerted by j on i // • Modifies uiand moves Oi in the nij direction • Accurate computation needs a small region between two spheres depends on mesh

  15. i dij < 0 j a Examples with Spheres Particule update : Prevent the overlapping a = .005 t = 27 t = 30 15

  16. Examples with fibers No collision strategy 16

  17. 3D Computations Initial time Random orientation Fiber orientation in the shear direction

  18. Perspectives • Lagrange multiplier for rigid motion constraintimprove matrix conditioning • Lagrange multiplier for boundary condition (computations for homogenization studies)impose shear rate instead velocity on boundary • add repulsive forces in the weak formulation • use P1 approximation (« level set ») instead of P0 approximation (VOF) for characteristic functionsbetter description of the solid-liquid interface

  19. Other Examples (1) Interface capturing (O. Basset) : • Navier-Stokes and Levelset + Continuous Galerkin + reinitialization Hamilton-Jacobi • Mesh : 1,499,405 nodes and 8,740,205 elements • 600 time steps • 2 linear systems per increment of 6 millions of unknowns, and of 1.5 millions, respectively : a total of 4 billion and 500 million of unknowns • CPU time : 5 days and 6 hours on a computational grid with 33 processors

  20. Other Examples (2) Falling Sphere in air and liquid : (O. Basset, L. Silva, R. Valette) NS + Level set + Penalization Air rs/rl ~ 8 Liquid

  21. Other Examples (3) Solid objects in an oven ( C. Gruau) NS + Temperature (convection and diffusion) air Solid

  22. Temperature evolution Hot air exit

  23. Other Examples (4) Flow motion induces by moving bodies : (R. Valette, B. Hiroux) Stoke + VOF + Penalization Shear rate between the two screws

More Related