CS53000 - Spring 2020 Introduction to Scientific Visualization Topics in Flow Visualization Lecture 15 April 14, 2020
Outline Vortices Flow separation and attachment Lagrangian Coherent Structures CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 2
Vortices Intuitive notion http://www.cse.ohio-state.edu/~jiang/Vortex/ieeeVis02.ppt CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 3
Vortices Intuitive notion http://www.cse.ohio-state.edu/~jiang/Vortex/ieeeVis02.ppt CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 4
Introduction A vortex is the rotating motion of a multitude of material particles around a common center H. J. Lugt, The dilemma of defining a vortex , Recent Developments in Theoretical and Experimental Fluid Mechanics, Springer, 1979 A vortex exists when its streamlines, mapped onto a plane normal to its core, exhibit a circular or spiral pattern, under an appropriate reference frame ( → self referential!) S. K. Robinson, Coherent motions in the turbulent boundary layer , Ann. Rev. Fluid Mech., vol. 23, 1991 A vortex is comprised of a central core region surrounded by swirling streamlines L. M. Portela, Identification and characterization of vortices in the turbulent boundary layer . Ph.D. thesis, Stanford University, 1997 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 5
Vortices Vortex core Line-type center of swirling motion (skeleton) Region surrounded by swirling streamlines Vortex region Includes surrounding streamlines Vortex boundary CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 6
Region-based Definitions Simple criteria ⇤ � = ⇥ � ⇤ High vorticity magnitude (quantifies flow rotation) v Low pressure (swirling motion around region of low pressure) � · ⌅ h n = ⌅ v h = ⌅ � · ⌅ v High helicity: , norm. hel.: (vorticity in flow | ⌅ � || ⌅ v | direction) Thresholds on these quantities yield regions Bounded by isosurfaces Visualized by volume rendering CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 7
<latexit sha1_base64="c4d4R13GKNk/a9ygIJMIfF/dwF0=">AB/nicbVDLSgNBEOyNrxhfq+LJy2AQvBh2o6AXIehFckogL0jWMDuZTYbMPpiZFcKy4K948aCIV7/Dm3/jJNmDJhY0FXdHe5EWdSWda3kVtZXVvfyG8WtrZ3dvfM/YOWDGNBaJOEPBQdF0vKWUCbilO5Gg2Hc5bvju6nfqRCsjBoqElEHR8PA+YxgpW+uZRHd2gnicwSaroHFUfGmlSTvtm0SpZM6BlYmekCBlqfOrNwhJ7NAEY6l7NpWpJwEC8UIp2mhF0saYTLGQ9rVNMA+lU4yOz9Fp1oZIC8UugKFZurviQT7Uk58V3f6WI3kojcV/O6sfKunYQFUaxoQOaLvJgjFaJpFmjABCWKTzTBRDB9KyIjrLNQOrGCDsFefHmZtMol+6JUrl8WK7dZHk4hM4AxuoAL3UIMmEjgGV7hzXgyXox342PemjOymUP4A+PzB87MlBw=</latexit> Region-based Definitions Lambda 2 criterion λ 2 ≤ 0 Derived from Navier-Stokes equation Idea: split Jacobian into symmetric ( S) and J = � ⇤ v S = J + J T antisymmetric (Q ) parts: Q = J − J T 2 2 S 2 + Q 2 Constraint on medium eigenvalue of : Correspond to local minima of pressure Widely used in practice (standard) J. Jeong, F. Hussain, On the Identification of a Vortex , J. Fluid Mechanics, 1995 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 8
Region-based Definitions Lambda 2 criterion Isosurface of Lambda 2 (-0.1) Picture by M. Rütten, DLR Göttingen CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 9
Vortex Core Line Extraction Topology Line-type separatrix of spiral saddle is a vortex core M. Tobak, D. J. Peake, Topology of 3D separated flow , Ann. Rev. Fluid Mech., vol. 14, 1982 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 10
Vortex Core Line Extraction Predictor/Corrector algorithm Correlation between vorticity direction and pressure minimum along vortex core Vorticity direction (predictor) Pressure minimum in normal plane (corrector) D. Banks, B. Singer, Vortex tubes in turbulent flows: Identification, representation, Reconstruction , IEEE Visualization 1994 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 11
Vortex Core Line Extraction Predictor/Corrector algorithm Combined with thresholding in normal plane to yield tubes D. Banks, B. Singer, Vortex tubes in turbulent flows: Identification, representation, Reconstruction , IEEE Visualization 1994 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 12
Vortex Core Line Extraction First-order method Piece-wise linear interpolation Line-type center of swirling motion extracted as intersection of spiral saddle’s separatrix with cell interior Sketch by M. Roth D. Sujudi, R. Haimes, Identification of swirling flow in 3D vector fields , AIAA Paper 95-1715, 1995 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 13
Vortex Core Line Extraction First-order method Vortex cores have zero curvature Disconnected segments Correct in linear flows Sketch by M. Roth D. Sujudi, R. Haimes, Identification of swirling flow in 3D vector fields , AIAA Paper 95-1715, 1995 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 14
Vortex Core Line Extraction D. Kenwright, R. Haimes, Vortex identification - applications in aerodynamics: A case study , IEEE Visualization 1997 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 15
Vortex Core Line Extraction Parallel Operator: previous methods rely on the parallelism of two vector fields Sujudi/Haimes (first-order) v/ / ⌅ a ⌅ Velocity parallel to acceleration Parallel Operator applied point-wise yields continuous lines R. Peikert, M. Roth, The Parallel Vectors Operator - A Vector Field Visualization Primitive , IEEE Visualization 1999 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 16
Galilean Invariance Fundamental principle in physics (Newton) Vortex core lines should be independent of particular inertial reference frame Streamline-based methods depend on particular frame of reference λ 2 Region-based definitions ( e.g. , ) are galilean invariant CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 17
Galilean Invariance Idea: derive line-type information from region-type scalar criterion by extract ridge / valley lines CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 18
J. Sahner, T. Weinkauf, H.-C. Hege, Galilean Invariant Extraction and Iconic Representation of Vortex Core Lines , Eurographics 2005. CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 19
Time-Dependent Vortices • Lagrangian Averaged Vorticity Deviation: • Add up vorticity deviation from regional average along path lines • Convex regions surround large local maxima are (resilient) Lagrangian vortices G. Haller, A. Hadjighasem, M. Farazmand, F. Huhn, Defining Coherent Vortices Objectively from the Vorticity , J. Fluid Mech. 795, 2016. 20 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization
CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 21
CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 21
Definition(s) of Flow Separation Flow abruptly leaves or returns to solid body (2D/3D phenomenon) Occurs along separation / attachment lines Critical in low speed flight configurations (takeoff, landing) Reduced lift Control issues Beneficial for delta wings and fighter aircrafts CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 22
Definition (s) of Flow Separation Visualization of separation / attachment lines On embedded surface Visualization vs. extraction of lines Based on analysis of wall streamlines in shear stress vector field (no slip boundary conditions) No formal characterization “Streamlines tend to accumulate” Heuristics needed CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 23
Definition(s) of Flow Separation D. Kenwright, C. Henze, C. Levit, Feature Extraction of Separation and Attachment Lines , IEEE TVCG 5(2), 1999 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 24
Topological Approach In 2D: separation and attachment points are critical points of tangential velocity J. Helman, L. Hesselink, Visualizing Vector Field Topology in Fluid Flow Data Sets , IEEE Computer Graphics and Applications 11(3), 1991 CS530 / Spring 2020 : Introduction to Scientific Visualization. April 13, 2020 Advanced Flow Visualization 25
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