1. 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

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

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

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

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

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

7. 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

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

9. Vorticity Transport Analysis... 9 Related Work Vortex core lines –Levy et al. 1990: based on helicity (u ) –Banks et al. 1995: -predictor, p-corrector –Strawn et al. 1998: height ridges of || || –Sahner et al. 2005: valley lines of 2 Vortex regions –Jeong et al. 1995: 2 : based on eigenvalues of S 2 + 2 of u –Silver et al. 1996: tracking of isosurfaces of || || Vortex lines –Sadlo et al. 2004: vortex lines with || ||-proportional density Stream surface based –Laramee et al. 2006: -texture advection on stream surfaces

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

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

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

13. Vorticity Transport Analysis... 13 Vorticity Equation Again, restrict analysis to || || Quantities for Visualization for Non-Uniform Viscosity stretching/tiltingdiffusion ( 0 because of numerics)

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

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

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

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

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

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

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

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

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

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

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

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

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

27. 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

28. 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

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