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Visualization Tools for Vorticity Transport Analysis in Incompressible Flow

Visualization Tools for Vorticity Transport Analysis in Incompressible Flow. November 2006 - IEEE Vis Filip Sadlo, Ronald Peikert @ CGL - ETH Zurich Mirjam Sick @ VA TECH HYDRO Switzerland. Motivation. Analyze vortex creation/dynamics. Vortex core lines (black). Motivation.

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Visualization Tools for Vorticity Transport Analysis in Incompressible Flow

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  1. Visualization Tools forVorticity Transport Analysisin Incompressible Flow November 2006 - IEEE Vis Filip Sadlo, Ronald Peikert @ CGL - ETH Zurich Mirjam Sick @ VA TECH HYDRO Switzerland

  2. Motivation • Analyze vortex creation/dynamics Vortex core lines (black) Vorticity Transport Analysis ...

  3. Motivation • Analyze vortex creation/dynamics Vortex core lines (black) Vorticity Transport Analysis ...

  4. Motivation • Analyze vortex creation/dynamics Vortex core lines (black) Vorticity Transport Analysis ...

  5. Motivation • Analyze vortex creation/dynamics Vortex core lines (black) Upstream path lines Vorticity Transport Analysis ...

  6. Motivation • Vortices and shear flow closely related • Analysis of vorticity w (curl of velocity: Ñ´u) • Vortex lines only frozen in ideal fluids (n = 0) • Vorticity Transport Analysis • Based on vorticity equation: Dw/Dt = … (see later) Vorticity Transport Analysis ...

  7. Motivation • Avoid integration of quantities along paths • Accumulation of error • Too high simulation error in practical CFD • Additional parameters • Expensive • Quantities locally in space-time • Advection aspect by pathlines + derivatives • Static visualization Vorticity Transport Analysis ...

  8. Overview • Related Work • Vorticity Equation • Quantities for Visualization • Visualization Methods • Applications • Conclusion Vorticity Transport Analysis ...

  9. Related Work • Vortex core lines • Levy et al. 1990: based on helicity (u·w) • Banks et al. 1995: w-predictor, p-corrector • Strawn et al. 1998: height ridges of ||w|| • Sahner et al. 2005: valley lines of l2 • Vortex regions • Jeong et al. 1995: l2: based on eigenvalues of S2 + W2 of Ñu • Silver et al. 1996: tracking of isosurfaces of ||w|| • Vortex lines • Sadlo et al. 2004: vortex lines with ||w||-proportional density • Stream surface based • Laramee et al. 2006: w-texture advection on stream surfaces Vorticity Transport Analysis ...

  10. Vorticity Equation • Navier-Stokes • Vorticity Equation • velocity u, pressure p • uniform density r • uniform viscosity n Vorticity Transport Analysis ...

  11. Quantities for Visualization • Vorticity Equation • Restrict analysis to ||w|| stretching stretching/tilting diffusion tilting (¹ 0 because of numerics) Vorticity Transport Analysis ...

  12. Vorticity Equation and Turbulence Models • Two-equation turbulence models (k-e, k-w, SST) • Introduce modified pressure, modified viscosity • Navier-Stokes • Vorticity Equation • velocity u, pressure p’ • uniform density r • non-uniform viscosity ne additional diffusion terms Vorticity Transport Analysis ...

  13. Quantities for Visualizationfor Non-Uniform Viscosity • Vorticity Equation • Again, restrict analysis to ||w|| stretching/tilting diffusion (¹ 0 because of numerics) Vorticity Transport Analysis ...

  14. Visualization Methods:Pathline Plots s > 0 s < 0 d > 0 d < 0 D || w || • pathline (fits D/Dt) • plot ||w|| along pathline • s, d: bands around ||w|| • pos. above, neg. below • s, d decompose D||w||/Dt Vorticity Transport Analysis ...

  15. Visualization Methods:Striped Pathlines • tube around pathline • tube radius: ||w|| • color code for each segment • data stripes Vorticity Transport Analysis ...

  16. Visualization Methods:Striped Pathlines • tube around pathline • tube radius: ||w|| • color code for each segment • data stripes + error stripes Vorticity Transport Analysis ...

  17. Visualization Methods:Striped Pathlines • Evenly-timed segments (show velocity) • Evenly-spaced segment lengths • With error stripes • Normalized data stripes • Scaling instead of normalization • As (a) with striped slices • With error stripes Vorticity Transport Analysis ...

  18. Applications:Separation Vortex vorticity streamlets Vorticity Transport Analysis ...

  19. Applications:Separation Vortex vortex (high helicity) shear flow (low helicity) Vorticity Transport Analysis ...

  20. Applications:Separation Vortex gain by stretching and loss by diffusion almost pure advection diffusion from boundary Vorticity Transport Analysis ...

  21. Applications:Separation Vortex Linked view wall distance indicators boundary shear flow (low wall distance) Vorticity Transport Analysis ...

  22. Applications:Recirculation and Vortex vortex recirculation zone boundary shear flow Vorticity Transport Analysis ...

  23. Applications:Recirculation and Vortex gain by stretching loss by diffusion loss by stretching and diffusion Vorticity Transport Analysis ...

  24. Applications:Bifurcation reception of vorticity from boundary shear gain by stretching loss by diffusion almost pure advection Vorticity Transport Analysis ...

  25. Applications:Bifurcation Courant number indicating high simulation error Vorticity Transport Analysis ...

  26. Applications:Transient Vortex Rope Vorticity Transport Analysis ...

  27. Applications:Transient Vortex Rope diffusion front of boundary shear flow frequencies of wall distance and stretching sign differ -> alternating sign due to moving vortex Vorticity Transport Analysis ...

  28. Conclusion • Tools for analysis of vortex dynamics • Allow analysis of vortex creation • Results well consistent with theory • Vorticity advected from boundary shear flow • Vorticity cannot be created inside fluid with constant density (baroclinic vorticity generation) • Dominant mechanism in vortex regions: gain by vortex stretching together with loss by diffusion Vorticity Transport Analysis ...

  29. End Thank you for your attention. Vorticity Transport Analysis ...

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