Numerical Modeling of Fluid-Structure Interaction in Bio-Inspired Propulsion Thomas Engels To cite this version: Thomas Engels. Numerical Modeling of Fluid-Structure Interaction in Bio-Inspired Propulsion. Fluid mechanics [physics.class-ph]. Aix-Marseille Université; Technische Universität Berlin, 2015. English. tel-01298968 HAL Id: tel-01298968 https://hal.archives-ouvertes.fr/tel-01298968 Submitted on 7 Apr 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial| 4.0 International License Numerical Modeling of Fluid-Structure Interaction in Bio-Inspired Propulsion Thomas Engels Sculpting a lion is actually quite easy. You start with a solid block and simply remove everything that does not look like lion. Dietmar Engels Dedicated to my mum, Margareta Engels, who is doubtlessly the greatest mum ever to walk the planet. UNIVERSITÉ D’AIX-MARSEILLE TECHNISCHE UNIVERSITÄT BERLIN ECOLE DOCTORALE 353 SCIENCES POUR L’INGÉNIEUR: MÉCANIQUE, PHYSIQUE, MICRO ET NANOÉLECTRONIQUE UFR SCIENCES LABORATOIRE DE MÉCANIQUE, MODÉLISATION & PROCÉDÉS PROPRES UMR7340 Thèse présentée pour obtenir le grade universitaire de docteur Discipline : Mécanique et Physique des Fluides Thomas ENGELS Numerical Modeling of Fluid–Structure Interaction in Bio–Inspired Propulsion Soutenue le 10/12/2015 devant le jury : Hao LIU Chiba University, Japan Rapporteur Angelo IOLLO Université de Bordeaux 1 Rapporteur Fritz-Olaf LEHMANN Universität Rostock Examinateur Marie FARGE École Normale Supérieure Paris Examinatrice Dmitry KOLOMENSKIY Chiba University, Japan, Invité Kai SCHNEIDER Aix-Marseille Université Directeur de thèse Jörn SESTERHENN Technische Universität Berlin Directeur de thèse Numerical Modeling of Fluid–Structure Interaction in Bio–Inspired Propulsion Thomas Engels, M.Sc. Der Fakultät Verkehrs- und Maschinensysteme der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften (Dr.-Ing.) genehmigte Dissertation Tag der mündlichen Aussprache: 10.12.2015 Promotionsausschuss: Hao LIU Chiba University, Japan Gutachter Angelo IOLLO Université de Bordeaux 1 Gutachter Fritz-Olaf LEHMANN Universität Rostock Prüfer Marie FARGE École Normale Supérieure Paris Prüfer Dmitry KOLOMENSKIY Chiba University, Japan, Gast Kai SCHNEIDER Aix-Marseille Université Betreuer Jörn SESTERHENN Technische Universität Berlin Betreuer Contents Acknowledgements vii Abstract ix Version abrégée en français xiii I Introduction and basic numerical method 17 1 Introduction 19 2 Basic numerical method 23 2.1 Model equations and penalization method ............ 25 2.2 Model equations in two dimensions ................ 29 2.3 Penalization method for moving and flexible obstacles ..... 29 2.4 Hydrodynamic forces and moments ................ 31 2.5 Wake removal techniques ..................... 33 2.6 Mean flow equations ........................ 34 2.7 Discretization in space ....................... 35 2.8 Discretization in time ........................ 37 2.8.1 Two-dimensional flows ................... 37 2.8.2 Three-dimensional flows ................. 38 2.9 Convergence properties ...................... 39 2.10 Concluding remarks ........................ 40 II Fluid-structure interaction with rigid obstacles 43 3 Virtual insects: modeling and validation 45 3.1 An introduction to insect flight .................. 45 3.2 Virtual insects ............................ 49 3.2.1 Body system ......................... 49 3.2.2 Body shape ......................... 51 3.2.3 Wing system ........................ 52 3.2.4 Wing shape ......................... 53 3.2.5 Power requirement ..................... 55 3.2.6 Governing equations in free flight ............. 56 3.3 Validation case of a falling sphere ................. 58 3.4 Validation case of a rectangular flapping wing .......... 58 3.5 Hovering flight of a fruit fly model ................ 59 iv CONTENTS v 4 Simulation of a model bumblebee in turbulent flow 65 4.1 Introduction ............................. 65 4.2 Bumblebee forward flight in laminar flow ............ 67 4.2.1 Bumblebee model ..................... 67 4.2.2 Wingbeat kinematics and aerodynamic forces and power 68 4.2.3 Wake turbulence generated by the bumblebee ...... 73 4.3 Bumblebee forward flight in turbulent flow ........... 75 4.3.1 Model turbulence: Homogeneous isotropic turbulence . 75 4.3.2 Rescaling to insect dimensions .............. 80 4.3.3 Numerical wind tunnel with turbulent inflow ...... 81 4.3.4 Results ............................ 81 4.3.5 Conclusions and outlook .................. 87 III Fluid-structure interaction with flexible obstacles 89 5 Extension of the numerical method for flexible obstacles 91 5.1 Solid model: non-linear beam equation .............. 92 5.1.1 Numerical solution ..................... 96 5.1.2 Quantitative validation of the solid model ........ 97 5.2 Coupling fluid and solid ...................... 97 5.2.1 Construction of the mask function for flexible objects .. 97 5.2.2 Force interpolation ..................... 99 5.2.3 Time stepping of the coupled system ........... 101 5.2.3.1 Semi-implicit staggered scheme ......... 102 5.2.3.2 Iterative scheme ................. 103 5.3 Validation tests of the fluid-structure interaction module .... 105 5.3.1 Energy budget ....................... 105 5.3.2 Two-dimensional validation: Comparison with Turek et al. .............................. 106 5.3.3 Three-dimensional validation: Thrust generated by a heaving plate ........................ 111 6 Two-dimensional fluid-structure interaction 115 6.1 Fluttering instability of flexible foils ................ 115 6.1.1 Variation of the Reynolds number ............. 117 6.1.2 Influence of the stiffness and the transition to chaos .. 122 6.2 Thrust generation by flexible heaving foils ............ 127 6.2.1 Introduction ........................ 127 6.2.2 Single wing section ..................... 127 6.2.3 Two wing sections ..................... 130 vi CONTENTS 7 Three-dimensional fluid-structure interaction: Application to swim- ming 133 7.1 Materials .............................. 134 7.2 Rectangular swimmers: influence of the aspect ratio ...... 135 7.3 Non-rectangular swimmers: influence of the fin shape ..... 138 7.4 Conclusion ............................. 141 IV Conclusion and perspectives 143 V Appendices 149 A Parallel implementation 151 A.1 Data distribution .......................... 151 A.2 Parallel scaling ........................... 152 B Details on the solid model and its numerical solution 153 B.1 Beam equation with non-constant coefficients .......... 153 B.2 Discretization in space and time .................. 154 C Curriculum Vitae 169 D List of publications 173 Bibliography 173 Acknowledgements First of all, I want to express my upmost gratitude to my two supervisors, Kai Schneider in Marseille and Jörn Sesterhenn in Berlin, for their constant support over the four years of this PhD program. I am very grateful for the freedom of spirit they allow and the degree of independence that comes with it, and for trusting me to succeed this way. I want to express the same grati- tude to Dmitry Kolomenskiy, who was my informal supervisor during the past five years, starting during my masters. He is also the main reason I became interested in the field of biomechanics and insect flight, so I would like to thank him for the great inspiration. Malcolm Roberts was very helpful teaching me good practices of open-source programming and general code development, and I benefited a lot from his presence in Marseille. My work would have been much harder without the excellent computer ex- perts in both laboratories, Michel Pognant and Dominique Fougère in Mar- seille and Martin Franke and Lars Oergel in Berlin, and I would like to thank them for their kin support. Moving twice a year between different countries was a difficult task, but it would have been twice as difficult without the help of the director of M2P2, Patrick Bontoux, who helped me each year finding an apartment, rapidly sign- ing papers and even lending me his car. I want to thank Fritz-Olaf Lehmann and Masateru Maeda for the fruitful dis- cussions on insect flight, and especially Fritz-Olaf Lehmann for the help and advice preparing our joint research proposals. I am grateful for countless meetings with Romain Nguyen van Yen on the penalization method, which unfortunately didn’t result in a new active penal- ization method, but was fruitful nonetheless, and Marie Farge for her support, especially regarding wavelets, adaptivity and the research proposals. It was very nice to have discussions with Julius Reiss, Jens Brouwer, Juan- Jose Pena-Fernandez, Matthias Lemke, Lewin Stein, Stefano Alois, Sergio Bengoechea Lozano, Robert Wilke and Sonja Hoßbach in the laboratory in vii Berlin, and Amin Ghaffary, Stéphane Viazzo, Matthieu Leroy, Gustavo Lopez, Braulio Bernales and Marianna Pepona in Marseille. I would also thank Margareta Engels for the effort of no longer beginning a phone call with “why didn’t you call?”, and my good friends Juliana Börner,