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 ...

Motivation

• Analyze vortex creation/dynamics

Vortex core lines (black)

Motivation

Vortex core lines (black) Upstream path lines

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)

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

Overview

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

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

Vorticity Equation

• Navier-Stokes

Vorticity Equation

uu u u

u ω ω u ω

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

Quantities for Visualization

• Vorticity Equation

• Restrict analysis to ||||

u ω ω u ω

stretching/tilting diffusion

ωω u

t ω ω

ωu ω ω u ω

LHS ( 0 because of numerics)

ωω u

ω ωstretching

ω ωtilting

Vorticity Equation and Turbulence Models

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

viscosity

• Navier-Stokes

Vorticity Equation

2 2e e

uu u u S

2 2 2e e et

u ω ω u ω u S

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

additional diffusion terms

• Vorticity Equation

• Again, restrict analysis to ||||

2 2 2e e et

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

ωu ω ω u ω u S

LHS ( 0 because of numerics)

ωω u

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

Visualization Methods:Striped Pathlines

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

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

(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

Applications:Separation Vortex

vorticity streamlets

shear flow (low helicity)

vortex (high helicity)

diffusion from boundary

gain by stretching and loss by diffusion

almost pure advection

Linked view

boundary shear flow (low wall distance)

wall distance indicators

Applications:Recirculation and Vortex

boundary shear flow

recirculation zone

vortex

Applications:Recirculation and Vortex

loss by stretching and diffusion

gain by stretching loss by diffusion

Applications:Bifurcation

gain by stretching loss by diffusion

almost pure advection

reception of vorticity from boundary shear

Applications:Bifurcation

Courant number indicating high simulation error

Applications:Transient Vortex Rope

diffusion front of boundary shear flow

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

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

Thank you for your attention.

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

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