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Vorticity as a signature of interfaces and wakes

Vorticity as a signature of interfaces and wakes. G.-H. Cottet Laboratoire Jean Kuntzmann, Grenoble. Outline: Vorticity and interfaces variable density flows fluid-structure interaction Vorticity and wakes 3D aspects control A glance at vortex particle methods.

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Vorticity as a signature of interfaces and wakes

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  1. Vorticity as a signature of interfaces and wakes G.-H. Cottet Laboratoire Jean Kuntzmann, Grenoble

  2. Outline: • Vorticity and interfaces • variable density flows • fluid-structure interaction • Vorticity and wakes • 3D aspects • control • A glance at vortex particle methods

  3. Formulation vorticity / density gradients (cf C. Anderson, JCP’82): Variable density fluids Primitive variables: 2 incompressible fluids with surface tension: level-set type formulation (Hou-Osher): Surface tension term:

  4. Rising bubbles Interface and vorticity for N=256 and N=512

  5. cloud of dust on slope Kelvin-Helmholtz instability Interaction with boundary layer and ejection

  6. Other interface problem: fluid interacting with rigid body (with Coquerelle & Cani, 2006) Two approaches: solve separately fluid and solid and impose continuity Consider system as single flow with variable density and Constitutive laws Second approach more numerically efficient

  7. Curl of the equation gives: Two vortex generators on the interface Idea: formulate problem as a penalization model : where is the rigid displacement obtained by averaging velocities over S and l>>1.

  8. 64 X 64 X 64

  9. Tumbling of spheres Validation against ALE methods Flow physics for visualization

  10. Vorticity and wakes In 3d, vorticity is a lagrangian vector (satisfies same equation as transport of lines) Orientation matters a lot: illustration in cylinder wake control

  11. Control of wake by enhancing 3d instabilities Goal : minimize drag Starting point: optimal belt actuator (tangential body velocities) obtained for 2D cylinders by genetic algorithms (Milano & Koumoutsakos, 2002): Tangential velocity profile

  12. Optimization on a small number of harmonics of the span, by “brute force” area bombing (12h/run) (with Hildebrand, Poncet, Kiumoutsakos, 2006)

  13. Result: compared to 2D optimal control, with same energy, improvement in drag reduction by a factor 4 (same factor for Re=1000 !)

  14. Drag reduction mechanism: streamwise vorticity attached to the body delays shedding Top view of vorticity Close up braids of streamwise vorticity

  15. A glance at vortex particle methods Incompressible 3D Navier-Stokes equations Random walk or vorticity exchange + « blob » regularization : d -> z and Biot-Savart law: u=u(w)

  16. As such, the method is useless: • Too expansive • Particle deformation prevents accuracy • -> need to rely on a grid to • -compute fields • -remesh particles -> frustrating (or not ..) -> but understanding why remeshing is necessary is useful ..

  17. In velocity form, energy transfer between scales at particle p given by Claim: remeshing necessary because particle methods create small and large scale (-> backscatter) Amount of backscatter and transfer to small scales can be evaluated through numerical analysis of enstrophy budget

  18. Dissipation to small scales given by : Sub grid scale dissipation in turbulent channel flow: particle model vs dynamic model 2D turbulent flow: subgrid dissipation correlates with saddle points

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