A Versatile Sharp I nterface I mmersed A Versatile Sharp I nterface I mmersed Boundary Method with Application to Boundary Method with Application to Complex Biological Flows Complex Biological Flows Rajat Mittal Mittal Rajat Mechanical Engineering
Biological Flows Biological Flows � Biomimetics � Biomimetics and and Bioinspired Bioinspired Engineering Engineering – What can we learn from Nature ? What can we learn from Nature ? – – How can we adapt Nature How can we adapt Nature’ ’s s – solutions into engineered solutions into engineered devices/machines ? Flapping flight Drafting devices/machines ? � Biomedical Engineering � Biomedical Engineering Flexible Propulsors Autorotation – Cardiovascular flows Cardiovascular flows – – Respiratory flows Respiratory flows – – Phonatory Phonatory/Speech Mechanisms /Speech Mechanisms – – Biomedical Devices Biomedical Devices –
Inspiration from Dragonflies Inspiration from Dragonflies � Dragonflies Dragonflies � – Existed for 350 million years Existed for 350 million years – – Wingspan from 2 Wingspan from 2 – – 80 cm 80 cm – – Fast and agile Fast and agile – � Wing Design � Wing Design – Thin, lightweight Thin, lightweight – – Vein reinforced – Vein reinforced – Pleated along chord Pleated along chord – – Pterostigma Pterostigma – – Microstructure Microstructure – � Wing Configuration Wing Configuration � – Wing Wing- -wing interaction? wing interaction? – � Wing Flexion? � Wing Flexion?
Computational Modeling Computational Modeling � Need to tackle � Need to tackle – Complex 3D geometries Complex 3D geometries – – Moving boundaries Moving boundaries – – Fluid Structure Interaction Fluid Structure Interaction – – Resolution of vortex dynamics Resolution of vortex dynamics – – Relatively low Reynolds numbers Relatively low Reynolds numbers – � Very challenging for conventional body � Very challenging for conventional body fitted methods. fitted methods. � Immersed Boundary Methods � Immersed Boundary Methods – handle these problems in all their complexity. handle these problems in all their complexity. –
Journal of Computational Physics ViCar3D ViCar3D Volume 227, I ssue 10, 1 May 2008, Pages 4825-4852 Viscous scous Car Cartesian Grid Solver for tesian Grid Solver for 3D 3D Immersed Boundaries Immersed Boundaries Vi � Simulations on non Simulations on non- -conforming Cartesian Grids conforming Cartesian Grids � – Stationary/moving boundaries Stationary/moving boundaries – – Solids/membranes Solids/membranes – � Sharp Interface IBM method Sharp Interface IBM method � – No boundary forcing ( – No boundary forcing (Peskin Peskin et al) et al) – 3D ghost – 3D ghost- -cell methodology cell methodology nd Order Fractional Step Scheme � 2 2 nd � Order Fractional Step Scheme nd Order non � 2 2 nd Order non- -dissipative central dissipative central � difference scheme difference scheme nd order accurate IBM treatment also 2 nd – IBM treatment also 2 order accurate – � Non Non- -uniform meshes uniform meshes � � Geometric Geometric Multigrid Multigrid for Pressure Poisson for Pressure Poisson � � Global � Global Coeff Coeff Dynamic SGS Model Dynamic SGS Model ( (Vreman Vreman) )
ViCar3D ViCar3D � Parallelized � Parallelized � Extensively validated � Extensively validated 2 M pts T=1 T=1 Impulsively Started T=3 T=3 Cylinder Re= 1000 T=5 T=5 Mittal et al Komoutsakos VICAR3D VICAR3D 2008, JCP & Leonard
Closing the Loop for Closing the Loop for CFD in Biology/Biomedical Engineering CFD in Biology/Biomedical Engineering Imaging Imaging Animation Animation (MRI, CT, Laser Scan) (MRI, CT, Laser Scan) Of Geometric Models Of Geometric Models Geometric Models Geometric Models Alias MAYA Alias MAYA Mimics Mimics CFD/FSI Solver CFD/FSI Solver For Complex, Moving For Complex, Moving Organic Shapes Organic Shapes VICAR3D VICAR3D
ViCar3D- -Capabilities Capabilities ViCar3D • "Wake Topology and Hydrodynamic Performance of Low-Aspect-Ratio Flapping airfoil", J. Fluid Mechanics (2006) Vol 566 pp 309-343 . • Low-dimensional models and performance scaling of a highly deformable fish pectoral fin; J. Fluid Mech. (2009), vol. 631, pp. 311–342. • "Computational modelling and analysis of the hydrodynamics of a highly deformable fish pectoral fin." (2010) , Journal of Fluid Mechanics , doi:10.1017/ S0022112009992941.
ViCar3D- -Capabilities Capabilities ViCar3D • "Propulsive Efficiency of the Underwater Dolphin Kick in Humans", Journal of Biomechanical Engineering, Vol. 131, May 2009 • "A computational method for analysis of underwater dolphin kick hydrodynamics in human swimming", Sports CFD of the dolphin kick Biomechanics, 8(1), pp. 60-77, March 2009. • "A comparison of the kinematics of the dolphin kick in humans and cetaceans", Human Movement Science, Vol.28, pp.99-112, 2009
High Re?? High Re?? • Re c = 10 5 • 512x256x32 • 128 CPUs • Nonlinear dynamics and synthetic-jet-based control of a canonical separated flow. J. Fluid Mech., doi:10.1017/ S002211201000042X
Flight Maneuvers in Insects Flight Maneuvers in Insects Gravity Side View Top View � Maneuver: change in heading and/or speed � Maneuver: change in heading and/or speed � Insects display a large array of maneuvers � Insects display a large array of maneuvers
Flapping Frequency and Maneuvering Flapping Frequency and Maneuvering � High frequency flappers (f > 150 Hz) � High frequency flappers (f > 150 Hz) �� � = θ + θ – Bees, Flies, wasps etc Bees, Flies, wasps etc – T I C θθ – τ τ turn τ flap > 10 τ – turn > 10 flap τ ~ I / C θθ – Minute changes in kinematics Minute changes in kinematics – turn required to execute turn. (Dickinson et al) (Dickinson et al) required to execute turn. – Stroke plane/amplitude/pitch angle Stroke plane/amplitude/pitch angle – � Low frequency flappers (f < 50 Hz) � Low frequency flappers (f < 50 Hz) – Moths, butterflies, locusts etc. Moths, butterflies, locusts etc. – – τ τ turn τ flap ~ τ – turn ~ flap – Turns can be executed in O(1) flap if wings can produce Turns can be executed in O(1) flap if wings can produce – sufficient turning moments. sufficient turning moments. – Does this happen?? Does this happen?? –
+ + + • Turning in a Monarch Butterfly + • Sequence shows 1.5 flaps • >90 o change in heading ! • Turning distance < body size + • Turn on a dime! + +
How does the Butterfly do this ? How does the Butterfly do this ? Deformable Wings Deformable Wings � Wings deform significantly � Wings deform significantly � Greater repertoire of wing Greater repertoire of wing � kinematics. kinematics. – Large left Large left- -right wing right wing – asymmetries asymmetries � What causes deformation � What causes deformation – Flow and inertia induced – Flow and inertia induced deformation. (Daniels et al Daniels et al) ) deformation. ( – Also active deformation through Also active deformation through – action of direct muscles on action of direct muscles on axillary sclerites axillary sclerites (wing joint). (wing joint). � Perhaps even active control of Perhaps even active control of � deformability ?? deformability ??
Wing Flexion: Wing Flexion: Enabler of other Flight Modes Enabler of other Flight Modes Clap & peel enabled by wing flexion COBRE Insect Videogrammetry Lab Moth in Climbing Flight
Integrated Approach Integrated Approach � High Speed � High Speed Videogrammetry Videogrammetry – JHU Laboratory for JHU Laboratory for Bioinspired Bioinspired Engineering Engineering – – Tyson Hedrick Lab (UNC) Tyson Hedrick Lab (UNC) – � Structural parameterization � Structural parameterization ( (Vallance Vallance Lab, GWU) Lab, GWU) – Wing Wing – – Body Body – � High Fidelity Computational Modeling of � High Fidelity Computational Modeling of Aerodynamics and Aero- -Structural Interaction Structural Interaction Aerodynamics and Aero – Sharp Interface Immersed Boundary Method Sharp Interface Immersed Boundary Method – – Direct and Large Direct and Large- -Eddy Simulation Eddy Simulation – – Wing deformation modeling using FEM Wing deformation modeling using FEM –
Hawkmoth in Hover in Hover Hawkmoth Hedrick Lab (UNC) Hedrick Lab (UNC)
Animated Model Rendered for CFD Animated Model Rendered for CFD � Moth body based Moth body based � on high- -res laser res laser on high scan. scan. � Animation created � Animation created in MAYA by in MAYA by matching high matching high speed video. speed video.
Vortex Dynamics Vortex Dynamics � � Strong spiral LEV on Strong spiral LEV on downstroke. . downstroke � � Vortex ring shed at the Vortex ring shed at the end of downstroke downstroke from from end of each wing. each wing. � � Weak LEV on upstroke Weak LEV on upstroke
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