Multi scale Color Coding Of Fluid Flow Mixing Indicators Along Integration Lines

1. Multi scale Color Coding Of Fluid Flow Mixing Indicators Along Integration Lines SandeepKhurana, Marcel Ritter (speaker), Nathan Brener, BijayaKarki, Werner Benger, Somanth Roy, SumantaAcharya, S. SitharamaIyengar WSCG 2012, Plzen

2. Outline • Motivation • CFD Simulation Dataset • Computation • Multi Scale Color Coding Approach • Rendering • Results

3. Outline • Motivation • CFD Simulation Dataset • Computation • Multi Scale Color Coding Approach • Rendering • Results

4. Motivation • Simulation generates scalar data which is essential to understand the phenomenon in the system • Visualize data with large variations, give local and global knowledge at the same time • Small variations - clearly distinguishable • Better understanding of the data [Kindlmann1998]

5. Outline • Motivation • CFD Simulation Dataset • Computation • Multi Scale Color Coding Approach • Rendering • Results

6. CFD Simulation Dataset

7. CFD Simulation Dataset • Stirred tank reactors are used in many industries to mix chemicals • Understanding the fluid dynamics is critical for product yield • The simulation under study has two reagents being mixed using an impeller with blades pitched at 45-degree angle

8. CFD Simulation Dataset Specifications: • Multi block (2088 blocks) curvilinear grid • Has about 3.1 million cells, 5700 timesteps • File size: originally 500 GB, optimized 280 GB (removed duplication of position field at every timestep) • Fields available • Position • Velocity • Pressure

9. Outline • Motivation • CFD Simulation Dataset • Computation • Multi Scale Color Coding Approach • Rendering • Results

10. Computation Pathlines: Also known as characteristic lines, a technique that is used to visualize advection of massless particles along the flow of the vector field. Particle traces or pathlinesare computed in order to determine the locations of a particle previously represented as a bubble Example showing a pathlineand particle velocity

11. Computation • Seeding points - 516 • Two spheres inside the stirred tank • Represent fluid particles

12. Computation • Non trivial task – Find which cell contain particle (for interpolation) • Why? Curvilinear multiblock grid • Used a KDTree and an uniform grid look up structure to find candidate curvilinear grid cells • Velocity interpolated using a direct trilinear interpolation using world coordinates • It decides if a point is located inside a cell by evaluating the plane equations for each face of the cell

13. Computation • Also involves derived quantities computation • Quantities we computed were • Curvature • Torsion • Specific measure of length generation • To compute these quantities we computed • Acceleration (first derivative of velocity) • Jerk (second derivative of velocity) • Higher order differentiation formulas were used that employ 5 points rather than 3 points in the central, forward and backward difference formulas

14. Computation Definition of curve: In differential geometry, a curve q is a function that maps a real-valued parameter s to a point q(s) within a differential manifold M. Variation of the curve parameter s defines the tangential vector along the curve.

15. Computation • Derived quantities of a curve: • Curvature with derivatives: • Torsion • Specific measure of length generation [Ottino]where λ = δ/L , δ being the increase in path length (which is proportional to the magnitude of the velocity) and L being the total path length (before the d increment) at a particular time t.

16. Outline • Motivation • CFD Simulation Dataset • Computation • Multi Scale Color Coding Approach • Rendering • Results

17. Multi Scale Color Coding • To visualize the entire range of scalar field values including small, medium and large values • Uniform color coding often gives a single predominant color • Multi scale color coding helps to give smallas well as large variations at the same time

18. Multi Scale Color Coding • Our approach: Histogram based scalar value extraction • Creating a number of bins, each representing a range of scalar values • Parameters for multi scale • Number of divisions • Scalar values for each scale • Colors to map them

19. Outline • Motivation • CFD Simulation Dataset • Computation • Multi Scale Color Coding Approach • Rendering • Results

20. Rendering • ‘Illuminated Streamlines’ method [Zockler] • Rendering is fast and interactive • A realistic visualization by incorporating depth perception • Phong lighting model is used • Intensity is defined as where L denotes the light direction, V the viewing direction and R the unit reflection vector (the vector in the L-N-plane)

21. Rendering • But for lines the unique normals and reflection vectors are undefined. So, intensity can be made dependent on the tangential vector T instead as

22. Outline • Motivation • CFD Simulation Dataset • Computation • Multi Scale Color Coding Approach • Rendering • Results

23. Results Comparison of uniform(left) and multi scale(right) color coding for the length generation mixing indicator

24. Results Comparison of uniform(left) and multi scale(right) color coding for the curvature values

25. Results Comparison of uniform(left) and multi scale(right) color coding for the torsion values

26. Results Also FrenetRibbons [FrenetRibbon2010] were used to geometrically see the particle trace, they: • geometrically encode curvature and torsion • provide one more degree of freedom to the geometry i.e. surface • Added multi scale color coding on torsion values

27. Results • Areas with a lot of twist correlate to high torsion whereas the areas which seems consistently straight might have different colors due to change in their torsion values.

28. References

29. Thank You • Sandeep Khurana [1] • Nathan Brener [1] • BijayaKarki [1] • Werner Benger [2,3] • Somanth Roy [4] • SumantaAcharya [5] • Marcel Ritter [6] • S. SitharamaIyengar [7] [1] Department of Computer Science, Louisiana State University, USA [2] Center for Computation & Technology, Louisiana State University, USA [3] Institute for Astroand Particle Physics, University of Innsbruck, Austria [4] Dept. of Mechanical Engineering, Indian Institute of Technology, India [5] Dept. of Mechanical Engineering, Louisiana State University, USA [6] Inst. of Basic Sciences in Civil Engineering, University of Innsbruck, Austria [7] School of Computing & Info. Sciences, Florida International University, USA