Visualization Tools for Vorticity Transport Analysis in Incompressible Flow November IEEE Vis Filip Sadlo, Ronald CGL - ETH Zurich Mirjam VA TECH HYDRO Switzerland

Vorticity Transport Analysis... 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 (curl of velocity: u) Vortex lines only frozen in ideal fluids ( = 0) Vorticity Transport Analysis –Based on vorticity equation: D /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 ) –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 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

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

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

Vorticity Transport Analysis 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

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

Vorticity Transport Analysis 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

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

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

Vorticity Transport Analysis 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

Vorticity Transport Analysis Applications: Separation Vortex vorticity streamlets

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

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

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

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

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

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

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

Vorticity Transport Analysis Applications: Transient Vortex Rope

Vorticity Transport Analysis 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 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 End Thank you for your attention.