LOW REYNOLDS NUMBER AERODYNAMICS OF FLAPPING AIRFOILS IN HOVER AND FORWARD FLIGHT A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY ERKAN GÜNAYDINOĞLU IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN AEROSPACE ENGINEERING SEPTEMBER 2010 Approval of the thesis: LOW REYNOLDS NUMBER AERODYNAMICS OF FLAPPING AIRFOILS IN HOVER AND FORWARD FLIGHT submitted by ERKAN GÜNAYDINOĞLU in partial fulfillment of the requirements for the degree of Master of Science in Aerospace Engineering Department, Middle East Technical University by, Prof. Dr. Canan Özgen ____________ Dean, Graduate School of Natural and Applied Sciences Prof. Dr. Ozan Tekinalp ____________ Head of Department, Aerospace Engineering Assoc. Prof. Dr. D. Funda Kurtuluş ____________ Supervisor, Aerospace Engineering Dept., METU Examining Committee Members: Prof. Dr. İsmail H. Tuncer ____________ Aerospace Engineering Dept., METU Assoc. Prof. Dr. D. Funda Kurtuluş ____________ Aerospace Engineering Dept., METU Prof. Dr. Yusuf Özyörük ____________ Aerospace Engineering Dept., METU Asst. Prof. Dr. Oğuz Uzol ____________ Aerospace Engineering Dept., METU Dr. Mustafa Kaya ____________ The Scientific & Technological Council of Turkey (TUBİTAK-SAGE) Date: 13 / 9 / 2010 I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Last Name : Erkan Günaydınoğlu Signature : iii ABSTRACT LOW REYNOLDS NUMBER AERODYNAMICS OF FLAPPING AIRFOILS IN HOVER AND FORWARD FLIGHT Günaydınoğlu, Erkan M.Sc., Department of Aerospace Engineering Supervisor : Assoc. Prof. Dr. D. Funda Kurtuluş September 2010 , 73 pages The scope of the thesis is to numerically investigate the aerodynamics of flapping airfoils in hover and forward flight. The flowfields around flapping airfoils are computed by solving the governing equations on moving and/or deforming grids. The effects of Reynolds number, reduced frequency and airfoil geometry on unsteady aerodynamics of flapping airfoils undergoing pure plunge and combined pitch-plunge motions in forward flight are investigated. It is observed that dynamic stall of the airfoil is the main mechanism of lift augmentation for both motions at all Reynolds numbers ranging from 10000 to 60000. However, the strength and duration of the leading edge vortex vary with airfoil geometry and reduced frequency. It is also observed that more favorable force characteristics are achieved at higher reduced frequencies and low plunging amplitudes while keeping the Strouhal number constant. The computed flowfields are compared with the wide range of experimental studies and high fidelity simulations thus it is concluded that the present approach is applicable for investigating the flapping wing aerodynamics in iv forward flight. The effects of vertical translation amplitude and Reynolds number on flapping airfoils in hover are also studied. As the vertical translation amplitude increases, the vortices become stronger and the formation of leading edge vortex is pushed towards the midstroke of the motion. The instantaneous aerodynamic forces for a given figure-of-eight motion do not alter significantly for Reynolds numbers ranging from 500 to 5500. Keywords: Unsteady Aerodynamics, Micro Aerial Vehicles, Flapping Airfoils v ÖZ HAVADA ASILI KONUMDA VE İLERİ UÇUŞTA ÇIRPAN KANAT KESİTLERİNİN DÜŞÜK REYNOLDS SAYILI AERODİNAMİĞİ Günaydınoğlu, Erkan Yüksek Lisans, Havacılık ve Uzay Mühendisliği Bölümü Tez Yöneticisi : Doç. Dr. D. Funda Kurtuluş Eylül 2010, 73 Sayfa Bu tezin amacı havada asılı konumda ve ileri uçuşta çırpan kanat kesitlerinin aerodinamiğini sayısal olarak incelemektir. Kanat kesitleri etrafındaki akış alanları korunum denklemlerinin hareketli ve/veya bozulan çözüm ağları üzerinde çözümü kullanılarak hesaplanmıştır. Reynolds sayısının, indirgenmiş frekansın ve kanat kesiti geometrisinin ileri uçuşta daimi olmayan çırpan kanat aerodinamiğine etkisi sade- dalma ve dalma-yunuslama hareketi için incelenmiştir. 60000 ile 10000 arasındaki Reynolds sayılarında her iki hareket boyunca kaldırma kuvveti artışına neden olan esas mekanizmanın dinamik taşıma kaybı olduğu görülmüştür. Bunun ile birlikte hücum kenarı girdabının gücü ve kanat üzerinde kalma süresi kanat kesiti geometrisi ve indirgenmiş frekans ile değişmektedir. Ayrıca yüksek indirgenmiş frekans ve düşük dalma genliklerinde, Strouhal sayısı sabit tutulurken, daha uygun kuvvet özellikleri elde edildiği görülmüştür. Hesaplanan akış alanları geniş çaplı deneysel çalışmalarla ve yüksek kesinlikli benzetimlerle karşılaştırılmış ve mevcut yöntemin ileri uçuşta çırpan kanat aerodinamiğini araştırmak için uygulanabilir olduğu vi gösterilmiştir. Havada asılı konumdaki kanat kesiti aerodinamiğine Reynolds sayısının ve düşey öteleme genliğinin etkileri de incelenmiştir. Düşey öteleme genliği artarken, girdapların daha güçlü olduğu ve hücum kenarı girdabının oluşumunun hareketin ortalarına doğru ilerlediği görülmüştür. Sekiz şeklinde hareket eden kanat kesitlerinin anlık kuvvetlerinin 500 ile 5500 Reynolds sayıları arasında önemli bir ölçüde değişmediği gözlemlenmiştir. Anahtar Kelimeler: Zamana Bağlı Aerodinamik, Mikro Hava Araçları, Çırpan Kanat Kesitleri vii To my parents viii ACKNOWLEDGMENTS I would like to express my deep and sincere gratitude to my supervisor Assoc. Dr. D. Funda Kurtuluş, whose kindness, patience, academic experience and knowledge is invaluable for me at all steps of this thesis study. Without her enthusiasm, energy and support, I could not be able to complete this study I would like to thank my jury members Prof. Dr. İsmail H. Tuncer, Prof. Dr. Yusuf Özyörük, Asst. Prof. Dr. Oğuz Uzol and Dr. Mustafa Kaya for reviewing my thesis. I would like to thank Mert, Engin, Sezgi, Efe, Bayram, Yashar, Hasan, Seyfullah, Eser and Sedat for being with me on the boot camps of Aerospace Engineering Department where we spent half of our lives. Lastly, but most importantly, I would like to express my eternal gratitude to my parents for their love, support and encouragement throughout my life. This study was supported by 105M230 TUBITAK project. ix TABLE OF CONTENTS ABSTRACT ....................................................................................................... iv ÖZ….. ................................................................................................................ vi ACKNOWLEDGMENTS ................................................................................. ix TABLE OF CONTENTS .................................................................................... x LIST OF TABLES ............................................................................................ xii LIST OF FIGURES ......................................................................................... xiii CHAPTERS 1. INTRODUCTION........................................................................... 1 2. LITERATURE SURVEY ............................................................... 3 2.1 Forward Flapping Flight Studies ......................................... 4 2.2 Hovering Studies ................................................................. 6 3. NUMERICAL METHOD ............................................................. 11 3.1 Governing Equations ........................................................ 11 3.2 Computational Grid and Boundary Conditions ............... 13 3.3 Grid and Time-step Refinement Study ............................ 16 3.4 Forward Flight Kinematics .............................................. 17 3.5 Hovering Kinematics ....................................................... 18 3.6 Significant Non-dimensional Parameters ......................... 19 4. FORWARD FLIGHT RESULTS ................................................. 21 x