Visualization Tools for Vorticity Transport Analysis in Incompressible Flow November 2006 - IEEE Vis...

Visualization Tools forVorticity Transport

Analysisin Incompressible Flow

November 2006 - IEEE Vis

Filip Sadlo, Ronald Peikert @ CGL - ETH Zurich

Mirjam Sick @ VA TECH HYDRO Switzerland

Vorticity Transport Analysis ...

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Motivation

• Analyze vortex creation/dynamics

Vortex core lines (black)


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Motivation




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Motivation




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Motivation


Vortex core lines (black) Upstream path lines


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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)


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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


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Overview

• Related Work• Vorticity Equation• Quantities for Visualization• Visualization Methods• Applications• Conclusion


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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 S2 + 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


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Vorticity Equation

• Navier-Stokes

Vorticity Equation

2p

t

uu u u

2

t

ω

u ω ω u ω

• velocity u, pressure p• uniform density • uniform viscosity


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Quantities for Visualization

• Vorticity Equation

• Restrict analysis to ||||

2

t

ω

u ω ω u ω

stretching/tilting diffusion

ωω u

2

t ω ω

ω

ωu ω ω u ω

LHS ( 0 because of numerics)

ωω u

ω ωstretching

ω ωtilting


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Vorticity Equation and Turbulence Models

• Two-equation turbulence models (k-, k-, SST) Introduce modified pressure, modified

viscosity

• Navier-Stokes

Vorticity Equation

2 2e e

p

t

uu u u S

2 2 2e e et

ω

u ω ω u ω u S

• velocity u, pressure p’• uniform density • non-uniform viscosity e • / 2T S u u

additional diffusion terms


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• Vorticity Equation

• Again, restrict analysis to ||||

2 2 2e e et

ω

u ω ω u ω u S

Quantities for Visualization

for Non-Uniform Viscosity

stretching/tilting diffusion

ωω u

2 2 2e e et ω ω

ω

ωu ω ω u ω u S

LHS ( 0 because of numerics)

ωω u


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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


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Visualization Methods:Striped Pathlines

• tube around pathline• tube radius: ||||• color code for each segment data stripes


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• tube around pathline• tube radius: ||||• color code for each segment data stripes + error stripes


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(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


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Applications:Separation Vortex

vorticity streamlets


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shear flow (low helicity)

vortex (high helicity)


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diffusion from boundary

gain by stretching and loss by diffusion

almost pure advection


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Linked view

boundary shear flow (low wall distance)

wall distance indicators


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Applications:Recirculation and Vortex

boundary shear flow

recirculation zone

vortex


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Applications:Recirculation and Vortex

loss by stretching and diffusion

gain by stretching loss by diffusion


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Applications:Bifurcation

gain by stretching loss by diffusion

almost pure advection

reception of vorticity from boundary shear


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Applications:Bifurcation

Courant number indicating high simulation error


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Applications:Transient Vortex Rope


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Applications:Transient Vortex Rope

diffusion front of boundary shear flow

frequencies of wall distance and stretching sign differ -> alternating sign due to moving vortex


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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


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End

Thank you for your attention.

Visualization Tools for Vorticity Transport Analysis in Incompressible Flow November 2006 - IEEE Vis...

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