ABSTRACT Title of dissertation: A FLUID-STRUCTURE INTERACTION STRATEGY WITH APPLICATION TO LOW REYNOLDS NUMBER FLAPPING FLIGHT Marcos Vanella Doctor of Philosophy, 2010 Dissertation directed by: Professor Elias Balaras Department of Mechanical Engineering In this work a structured adaptive mesh refinement (S-AMR) strategy for fluid-structure interaction (FSI) problems in laminar and turbulent incompressible flows is developed. The Eulerian computational grid consists of nested grid blocks at different refinement levels. The grid topology and data-structure is managed by usingtheParameshtoolkit. ThefilteredNavier-Stokesequationsareevolvedintime bymeansofanexplicitsecond-orderprojectionscheme, wherespatialderivativesare approximated with second order central differences on a staggered grid. The level of accuracy of the required variable interpolation operators is studied, and a novel divergence-preserving prolongation scheme for velocities is evolved. A novel direct- forcing embedded-boundary method is developed to enforce boundary conditions on a complex moving body not aligned with the grid lines. In this method, the imposition of no-slip conditions on immersed bodies is done on the Lagrangian markers that represent their wet surfaces, and the resulting force is transferred to the surrounding Eulerian grid points by a moving least squares formulation. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 3. DATES COVERED 2010 2. REPORT TYPE 00-00-2010 to 00-00-2010 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER A Fluid Structure Interaction Strategy with Application to Low Reynolds 5b. GRANT NUMBER Number Flapping Flight 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION University of Maryland, College Park,College Park,MD,20742 REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT In this work a structured adaptive mesh renement (S-AMR) strategy for uid-structure interaction (FSI) problems in laminar and turbulent incompressible ows is developed. The Eulerian computational grid consists of nested grid blocks at dierent renement levels. The grid topology and data-structure is managed by using the Paramesh toolkit. The ltered Navier-Stokes equations are evolved in time by means of an explicit second-order projection scheme, where spatial derivatives are approximated with second order central dierences on a staggered grid. The level of accuracy of the required variable interpolation operators is studied, and a novel divergence-preserving prolongation scheme for velocities is evolved. A novel directforcing embedded-boundary method is developed to enforce boundary conditions on a complex moving body not aligned with the grid lines. In this method, the imposition of no-slip conditions on immersed bodies is done on the Lagrangian markers that represent their wet surfaces, and the resulting force is transferred to the surrounding Eulerian grid points by a moving least squares formulation. Extensive testing and validation of the resulting strategy is done on a numerous set of problems. For transitional and turbulent ow regimes the large-eddy simulation (LES) approach is used. The grid discontinuities introduced in AMR methods lead to numerical errors in LES, especially if non-dissipative, centered schemes are used. A simple strategy is developed to vary the lter size for ltered variables around grid discontinuities. A strategy based on explicit ltering of the advective term is chosen to eectively reduce the numerical errors across renement jumps. For all the FSI problems reported, the complete set of equations governing the dynamics of the ow and the structure are simultaneously advanced in time by using a predictor-corrector strategy. Dynamic uid grid adaptation is implemented to reduce the number of grid points and computation costs. Applications to apping ight comprise the study of exibility eects on the aerodynamic performance of a hovering airfoil, and simulation of the ow around an insect model under prescribed kinematics and free longitudinal ight. In the airfoil simulations, it is found that peak performance is located in structural exibility-inertia regions where non-linear resonances are present. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF ABSTRACT OF PAGES RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE Same as 196 unclassified unclassified unclassified Report (SAR) Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 Extensive testing and validation of the resulting strategy is done on a numerous set of problems. For transitional and turbulent flow regimes the large-eddy simulation (LES) approach is used. The grid discontinuities introduced in AMR methods lead to numerical errors in LES, especially if non-dissipative, centered schemes are used. A simple strategy is developed to vary the filter size for filtered variables around grid discontinuities. A strategy based on explicit filtering of the advective term is chosen to effectively reduce the numerical errors across refinement jumps. For all the FSI problems reported, the complete set of equations governing the dynamics of the flow andthestructurearesimultaneouslyadvancedintimebyusingapredictor-corrector strategy. Dynamic fluid grid adaptation is implemented to reduce the number of grid points and computation costs. Applications to flapping flight comprise the study of flexibility effects on the aerodynamic performance of a hovering airfoil, and simulation of the flow around an insect model under prescribed kinematics and free longitudinal flight. In the airfoil simulations, it is found that peak performance is located in structural flexibility-inertia regions where non-linear resonances are present. A FLUID STRUCTURE INTERACTION STRATEGY WITH APPLICATION TO LOW REYNOLDS NUMBER FLAPPING FLIGHT by Marcos Vanella Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2010 Advisory Committee: Elias Balaras, Associate Professor (Chair) Balakumar Balachandran, Professor Peter Bernard, Professor Kenneth Kiger, Associate Professor Sung Lee, Professor (Dean’s Representative) (cid:13)c Copyright by Marcos Vanella 2010 Dedication To my dear parents, Leonardo and Susana. ii Acknowledgments I would like first to express my heartfelt gratitude to my advisor, Prof. Elias Balaras for his relentless guidance during the course of my graduate studies at the University of Maryland. His approach towards research, where the direction is defined, but the means are provided by creativity and dedication, has been most stimulating to me. He has been equally supportive in both, good periods and hard times of my graduate life. I would also like to thank the members of the committee, Prof. Balakumar Balachandran, Prof. Peter Bernard, Prof. Kenneth Kiger and Prof. Sung Lee for carefully reading this dissertation and providing many constructive suggestions and comments. I want to thank Prof. Balachandran for teaching me several courses in the areas of dynamics and vibration, and for his help and discussions on the studies on flexibility of airfoils and rigid body modeling of flapping flight systems. I would also like to thank Prof. Ugo Piomelli for teaching me courses in computational fluid dynamicsandturbulencesimulations, andforhisguidanceandhelpduringourwork on large eddy simulation for adaptive grids. I thank Prof. Amr Baz for teaching me courses in control theory and vibration control, and for his generous help in class and research activities. My most sincere gratitude goes also to Prof. Sergio Preidikman, for his in- valuable help at the beginning of my career, for his work on the two-link dynamical model of an airfoil, and his help and company on other academic and life endeavors. I am most indebted to my dear wife Patricia, for her love, unconditional sup- port and goodwill over all these years. She is the base on which this milestone is iii founded. I kindly thank my lab mates Jianming Yang, Senthil Radhakrishnan and Niko- laos Beratlis for their help and support during the beginning of my graduate studies. With the latter individual I have shared countless research discussions and fun sit- uations along the way, which bring great memories. I thank my colleague Patrick Rabenold, the math-guy, who provided the seminal work on adaptive mesh refine- ment for incompressible flow using the Paramesh(cid:13)c package. I also thank my fellow labmatesGrigoriosPanagakos, KhaledAbdelaziz, DonDaniel, ClarenceBaney; and the nonlinear duo: Tim Fitzgerald and Marcelo Valdez, with whom I have developed singular but generalized forms of friendship. Finally, the support provided by the Air Force Research Laboratory through- out the course of this work is greatly appreciated. iv Table of Contents List of Tables vii List of Figures viii List of Abbreviations xv 1 Introduction 1 1.1 Motivation and objectives . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Prior work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Immersed boundary reconstruction 14 2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Eulerian and Lagrangian forcing on immersed boundary methods . . 16 2.3 Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.1 MLS reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3.2 Calculus of surface forces . . . . . . . . . . . . . . . . . . . . . 26 2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.1 Accuracy study . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.2 Oscillating cylinder in a cross-flow . . . . . . . . . . . . . . . . 30 3 Adaptive mesh refinement for fluid-structure interaction problems 34 3.1 Adaptive mesh refinement . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1.1 Grid topology . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1.2 Prolongation and restriction operators . . . . . . . . . . . . . 37 3.1.3 Treatment of the block boundaries . . . . . . . . . . . . . . . 42 3.1.4 Temporal integration scheme . . . . . . . . . . . . . . . . . . . 43 3.1.5 Fluid-structure interaction algorithm . . . . . . . . . . . . . . 46 3.2 Numerical studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.1 Taylor-Green vortex . . . . . . . . . . . . . . . . . . . . . . . 49 3.2.2 Vortex ring impinging on a wall . . . . . . . . . . . . . . . . . 55 3.2.3 Fluid-Structure interaction of two falling plates . . . . . . . . 61 3.2.4 Three dimensional example: Sphere-wall collision . . . . . . . 64 4 Large eddy simulation for discontinuous grids 72 4.1 Mathematical formulation . . . . . . . . . . . . . . . . . . . . . . . . 72 4.1.1 Explicit filtering of the non-linear term . . . . . . . . . . . . . 74 4.2 Spatially decaying isotropic turbulence past a refinement interface . . 75 4.2.1 Computational setup . . . . . . . . . . . . . . . . . . . . . . . 76 4.2.2 Single-grid calculations . . . . . . . . . . . . . . . . . . . . . . 80 4.2.3 Two-level computations with the LDEV model . . . . . . . . . 81 4.2.4 Two-level simulations with the Smagorinsky model . . . . . . 88 v