Visualization Tools for Vorticity Transport Analysis in Incompressible Flow

1
Visualization Tools forVorticity Transport
Analysisin Incompressible Flow

• November 2006 - IEEE Vis
• Filip Sadlo, Ronald Peikert _at_ CGL - ETH Zurich
• Mirjam Sick _at_ VA TECH HYDRO Switzerland

2
Motivation

• Analyze vortex creation/dynamics

Vortex core lines (black)
3
Motivation

• Analyze vortex creation/dynamics

Vortex core lines (black)
4
Motivation

• Analyze vortex creation/dynamics

Vortex core lines (black)
5
Motivation

• Analyze vortex creation/dynamics

Vortex core lines (black)
Upstream path lines
6
Motivation

• Vortices and shear flow closely related
• Analysis of vorticity w (curl of velocity Ñu)
• Vortex lines only frozen in ideal fluids (n 0)
• Vorticity Transport Analysis
• Based on vorticity equation
• Dw/Dt (see later)

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
Overview

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

9
Related Work

• Vortex core lines
• Levy et al. 1990 based on helicity (uw)
• 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

10
Vorticity Equation

• Navier-Stokes
• Vorticity Equation

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

11
Quantities for Visualization

• Vorticity Equation
• Restrict analysis to w

stretching
stretching/tilting
diffusion
tilting
(¹ 0 because of numerics)
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
13
Quantities for Visualizationfor Non-Uniform
Viscosity

• Vorticity Equation
• Again, restrict analysis to w

stretching/tilting
diffusion
(¹ 0 because of numerics)
14
Visualization MethodsPathline Plots
s gt 0 s lt 0 d gt 0 d lt 0 D w

• pathline (fits D/Dt)
• plot w along pathline
• s, d bands around w
• pos. above, neg. below
• s, d decompose Dw/Dt

15
Visualization MethodsStriped Pathlines

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

16
Visualization MethodsStriped Pathlines

• tube around pathline
• tube radius w
• color code for each segment
• data stripes error stripes

17
Visualization MethodsStriped 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

18
ApplicationsSeparation Vortex
vorticity streamlets
19
ApplicationsSeparation Vortex
vortex (high helicity)
shear flow (low helicity)
20
ApplicationsSeparation Vortex
gain by stretching and loss by diffusion
almost pure advection
diffusion from boundary
21
ApplicationsSeparation Vortex
Linked view
wall distance indicators
boundary shear flow (low wall distance)
22
ApplicationsRecirculation and Vortex
vortex
recirculation zone
boundary shear flow
23
ApplicationsRecirculation and Vortex
gain by stretching loss by diffusion
loss by stretching and diffusion
24
ApplicationsBifurcation
reception of vorticity from boundary shear
gain by stretching loss by diffusion
almost pure advection
25
ApplicationsBifurcation
Courant number indicating high simulation error
26
ApplicationsTransient Vortex Rope
27
ApplicationsTransient Vortex Rope
diffusion front of boundary shear flow
frequencies of wall distance and stretching sign
differ -gt alternating sign due to moving vortex
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
End

• Thank you for your attention.