Flow Visualization. Flow Visualization. Part 1 (out of 3) Introduction, Overview. Overview: Flow Visualization, Part 1. Introduction, overview
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1 Overview:, Part 1 Part 1 (out of 3) Introduction, overview Flow data Simulation vs. measurement vs. modelling 2D vs. surfaces vs. 3D Steady vs time-dependent d t flow Direct vs. indirect flow visualization Experimental flow visualization Basic possibilities PIV + Example Eduard Gröller, Helwig Hauser 2 Introduction, Overview Introduction: FlowVis = visualization of flows Visualization of change information Typically: more than 3 data dimensions General overview: even more difficult Flow data: nd nd data, 1D 2 /2D 2 /nd 2 (models), 2D 2 /3D 2 (simulations, measurements) Vector data (nd) in nd data space User goals: Overview vs. details (with context) Eduard Gröller, Helwig Hauser 4 Flow Data Where do the data come from: Flow simulation: Airplane- / ship- / car-design Weather simulation (air-, sea-flows) Medicine (blood flows, etc.) Flow measurements: Wind tunnel, fluid tunnel Schlieren-, shadow-technique Flow models: Differential equation systems (ODE) (dynamical systems) Eduard Gröller, Helwig Hauser 5 Flow Data Specification Simulation: Flow: set of samples (n dimensions of data), e.g. given on curvilinear grid Most important primitive: tetrahedron (cell) Measurement: Flow-vectors: reconstruction out of correlations, often calculated on regular grids Modelling: Flow: analytic formula, can be evaluated everywhere Eduard Gröller, Helwig Hauser 6
2 Data Source Examples 1/2 Data Source Examples 2/2 Eduard Gröller, Helwig Hauser 7 Eduard Gröller, Helwig Hauser 8 Simulation vs. Measurement vs. Modelling Simulation: Flow space modelled with grid FEM (finite elements method), CfD (computational fluid dynamics) Measurements: Optical methods + pattern recognition, e.g.: PIV (particle image velocimetry) Models: Differential equation systems dx/dt Comparison with Reality Simulation Experiment Eduard Gröller, Helwig Hauser 9 Eduard Gröller, Helwig Hauser 10 2D vs. Surfaces vs. 3D 2D/Surfaces/3D Examples 2D-Flow visualization 2D 2D-Flows Models, slice flows (2D out of 3D) Visualization of surface flows 3D-flows around obstacles Boundary flows on surfaces (2D) 3D-Flow visualization 3D 3D-flows Simulations, 3D-models Eduard Gröller, Helwig Hauser 11 Surface Eduard Gröller, Helwig Hauser 2D 12 3D
3 Steady vs. Time-Dependent Flows Time-Dependent vs. Steady Flow Steady (time-independent) flows: Flow static over time v(x): R n R n, e.g., laminar flows Simpler interrelationship Time-dependent d (unsteady) flows: Flow itself changes over time v(x,t): R n R 1 R n, e.g., turbulent flows More complex interrelationship Eduard Gröller, Helwig Hauser 13 Eduard Gröller, Helwig Hauser 14 Time-Independent (Steady) Flow Data Time-Independent (Steady) Data Data size in the course of time: Eduard Gröller, Helwig Hauser 15 Eduard Gröller, Helwig Hauser 16 Time-Dependent (Unsteady) Data Time-dependent (unsteady) Data Historical development: Eduard Gröller, Helwig Hauser 17 Eduard Gröller, Helwig Hauser 18
4 Direct vs. Indirect Direct flow visualization: Overview on current flow state Visualization of vectors Arrow plots, smearing techniques Indirect flow visualization: Usage of intermediate representation: vector-field integration over time Visualization of temporal evolution Streamlines, streamsurfaces Direct vs. Indirect Flow Vis. Example Eduard Gröller, Helwig Hauser 19 Eduard Gröller, Helwig Hauser 20 With Smoke rsp. Color Injection Experimental Optical Methods, etc. Injection of color, smoke, particles Optical methods: Schlieren, shadows Eduard Gröller, Helwig Hauser 22 Example: Car-Design Ferrari-model, so-called fivehole probe (no back flows) PIV: Particle Image Velocimetry Laser + correlation analysis: Real flow, e.g., in wind tunnel Injection of particles (as uniform as possible) At interesting locations: 2-times fast illumination with laser-sliceslice Image capture (high-speed camera), then correlation analysis of particles Vector calculation / reconstruction, typically only 2D-vectors Eduard Gröller, Helwig Hauser 23 Eduard Gröller, Helwig Hauser 24
5 PIV - Measurements Setup and typical result: Example: Wing-Tip Vortex 1/7 Problem: Air behind airplanes is turbulent Eduard Gröller, Helwig Hauser 25 Eduard Gröller, Helwig Hauser 26 Example: Wing-Tip Vortex 2/7 Vortex: dangerous! Example: Wing-Tip Vortex 3/7 Therefore: keep distance! Eduard Gröller, Helwig Hauser 27 Eduard Gröller, Helwig Hauser 28 Example: Wing-Tip Vortex 4/7 Tests in wind tunnel: Example: Wing-Tip Vortex 5/7 Then: Visualization! Eduard Gröller, Helwig Hauser 29 Eduard Gröller, Helwig Hauser 30
6 Example: Wing-Tip Vortex 6/7 Example: Wing-Tip Vortex 7/7 Eduard Gröller, Helwig Hauser 31 Eduard Gröller, Helwig Hauser 32 Visualization of Models Dynamical Systems Dynamical Systems Visualization Differences: Flow analytically def.: dx/dt = v(x) Navier-Stokes equations E.G.: Lorenz-system: dx/dt = (y-x) ) dy/dt = rx-y-xz dz/dt = xy-bz Larger variety in data: 2D, 3D, nd Sometimes no natural constraints like noncompressibility or similar Eduard Gröller, Helwig Hauser 34 Visualization of Models Sketchy, hand drawn Visualization of 3D Models Eduard Gröller, Helwig Hauser 35 Eduard Gröller, Helwig Hauser 36
7 with Arrows with Arrows Hedgehog plots, etc. Aspects: Direct Normalized arrows vs. scaling with velocity 2D: quite usable, 3D: often problematic Sometimes limited expressivity (temporal component missing) Often used! Eduard Gröller, Helwig Hauser 38 Arrows in 2D Scaled arrows vs. color-coded arrows Arrows in 3D Following problems: Ambiguity Perspective Shortening 1D-objects in 3D: difficult spatial perception Visual clutter Improvement: 3D-arrows (help to a certain extent) Eduard Gröller, Helwig Hauser 39 Eduard Gröller, Helwig Hauser 40 Arrows in 3D Compromise: Arrows only in slices Arrows in 3D Well integrable within real 3D: Eduard Gröller, Helwig Hauser 41 Eduard Gröller, Helwig Hauser 42
8 Acknowledgments For material for this lecture unit Hans-Georg Pagendarm Roger Crawfis Lloyd Treinish David Kenwright Terry Hewitt etc. Eduard Gröller, Helwig Hauser 43
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