Computational Aeroelasticity of Flying Robots with Flexible Wings

A computational co-simulation framework for flying robots with flexible wings is presented. The authors combine a nonlinear aerodynamic model based on an extended version of the unsteady vortex-lattice method with a nonlinear structural model based on a segregated formulation of Lagrange’s equations obtained with the Floating Frame of Reference formalism. The structural model construction allows for hybrid combinations of different models typically used with multibody systems such as models based on rigid-body dynamics, assumed-modes techniques, and finite-element methods. The aerodynamic model includes a simulation of leading-edge separation for large angles of attack. The governing differentialalgebraic equations are solved simultaneously and interactively to obtain the structural response and the flow in the time domain. The integration is based on the fourth-order predictor-corrector method of Hamming with a procedure to stabilize the iteration. The findings are found to capture known nonlinear behavior of flapping-wing systems. The developed framework should be relevant for conducting aeroelastic studies on a wide variety of air vehicle systems.

[1]  Marco Morandini,et al.  Tightly Coupled CFD/Multibody Analysis of Flapping-Wing Micro-Aerial Vehicles , 2011 .

[2]  Mao Sun,et al.  Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. , 2002, The Journal of experimental biology.

[3]  T. Weis-Fogh.  Quick estimates of flight fitness in hovering animals , 1973 .

[4]  U. Ascher,et al.  Stabilization of Constrained Mechanical Systems with DAEs and Invariant Manifolds , 1995 .

[5]  Bruno A. Roccia,et al.  Computational Dynamics of Flapping Wings in Hover Flight: A Co-Simulation Strategy , 2017 .

[6]  Andrew M. Mountcastle,et al.  Wing flexibility enhances load-lifting capacity in bumblebees , 2013, Proceedings of the Royal Society B: Biological Sciences.

[7]  Adrian L. R. Thomas,et al.  Leading-edge vortices in insect flight , 1996, Nature.

[8]  F. Lehmann,et al.  Elastic deformation and energy loss of flapping fly wings , 2011, Journal of Experimental Biology.

[9]  James D. Baeder,et al.  Computational Investigation of Micro Hovering Rotor Aerodynamics , 2006 .

[10]  Sergio Preidikman,et al.  Modified Unsteady Vortex-Lattice Method to Study Flapping Wings in Hover Flight , 2013 .

[11]  H. Wendland,et al.  Multivariate interpolation for fluid-structure-interaction problems using radial basis functions , 2001 .

[12]  Sayan Gupta,et al.  Dynamical Stability Analysis of a Fluid Structure Interaction System Using a High Fidelity Navier-stokes Solver , 2016 .

[13]  Ali H. Nayfeh,et al.  A numerical method for general, unsteady aerodynamics , 1981 .

[14]  Norbert Kroll,et al.  MEGAFLOW - A Numerical Flow Simulation Tool For Transport Aircraft Design , 2002 .

[15]  Z. J. Wang,et al.  Unsteady forces and flows in low Reynolds number hovering flight: two-dimensional computations vs robotic wing experiments , 2004, Journal of Experimental Biology.

[16]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[17]  Jae-Hung Han,et al.  An aeroelastic analysis of a flexible flapping wing using modified strip theory , 2008, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[18]  Per-Olof Persson,et al.  A Computational Framework for Fluid Structure Interaction in Biologically Inspired Flapping Flight , 2007 .

[19]  Kevin Knowles,et al.  Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 1: Methodology and analysis , 2006 .

[20]  Marco Morandini,et al.  MULTIBODY ANALYSIS OF A MICRO-AERIAL VEHICLE FLAPPING WING , 2011 .

[21]  Toshiyuki Nakata,et al.  A fluid-structure interaction model of insect flight with flexible wings , 2012, J. Comput. Phys..

[22]  J. Katz,et al.  Low-Speed Aerodynamics , 1991 .

[23]  C. Ellington.  The Aerodynamics of Hovering Insect Flight. III. Kinematics , 1984 .

[24]  Danesh K. Tafti,et al.  Effect of Wing Flexibility on Lift and Thrust Production in Flapping Flight , 2010 .

[25]  Yu. A. Kuznetsov,et al.  Applied nonlinear dynamics: Analytical, computational, and experimental methods , 1996 .

[26]  Holger Wendland,et al.  Scattered Data Approximation: Conditionally positive definite functions , 2004 .

[27]  Hendrik Tennekes,et al.  The simple science of flight : from insects to jumbo jets , 1996 .

[28]  Wei Shyy,et al.  Computational Fluid Dynamics with Moving Boundaries , 1995 .

[29]  Kamesh Subbarao,et al.  Modeling of Flight Dynamics of Morphing Wing Aircraft , 2011 .

[30]  Tamás Kalmár-Nagy,et al.  Can complex systems really be simulated? , 2014, Appl. Math. Comput..

[31]  H. A. Luther,et al.  Applied numerical methods , 1969 .

[32]  Dean T. Mook,et al.  Influence of Spanwise Twisting and Bending on Lift Generation in MAV-Like Flapping Wings , 2017 .

[33]  Kevin Knowles,et al.  Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 2: Implementation and validation , 2006 .

[34]  Inderjit Chopra,et al.  CFD-CSD Coupled Aeroelastic Analysis Of Flexible Flapping Wings For MAV Applications , 2013 .

[35]  M. Dickinson,et al.  Wing rotation and the aerodynamic basis of insect flight. , 1999, Science.

[36]  Sergio Preidikman,et al.  Time-Domain Simulations of Linear and Nonlinear Aeroelastic Behavior , 2000 .

[37]  Matthias Haupt,et al.  Fluid–structure analysis of a flexible flapping airfoil at low Reynolds number flow , 2012 .

[38]  B. Balachandran,et al.  Flexible flapping systems: computational investigations into fluid-structure interactions , 2011, The Aeronautical Journal (1968).

[39]  Adrian L. R. Thomas,et al.  Deformable wing kinematics in free-flying hoverflies , 2010, Journal of The Royal Society Interface.

[40]  C. Ellington,et al.  The mechanics of flight in the hawkmoth Manduca sexta. I. Kinematics of hovering and forward flight. , 1997, The Journal of experimental biology.

[41]  D. Ishihara,et al.  A two-dimensional computational study on the fluid–structure interaction cause of wing pitch changes in dipteran flapping flight , 2009, Journal of Experimental Biology.

[42]  Carlos E. S. Cesnik,et al.  Flapping Wing CFD/CSD Aeroelastic Formulation Based on a Co- rotational Shell Finite Element , 2009 .

[43]  Bauchau Olivier,et al.  Flexible Multibody Dynamics , 2010 .

[44]  Tianshu Liu,et al.  Avian Wing Geometry and Kinematics , 2006 .

[45]  D. Mook,et al.  Extension of a vortex-lattice method to include the effects of leading-edge separation , 1974 .

[46]  Muhammad R. Hajj,et al.  Flight dynamics and control of flapping-wing MAVs: a review , 2012 .

[47]  Hao Liu,et al.  Integrated modeling of insect flight: From morphology, kinematics to aerodynamics , 2009, J. Comput. Phys..

[48]  Bruno A. Roccia,et al.  Development of a Kinematical Model to Study the Aerodynamics of Flapping-Wings , 2011 .

[49]  Joseba Murua,et al.  Applications of the unsteady vortex-lattice method in aircraft aeroelasticity and flight dynamics , 2012 .

[50]  Martin D. Buhmann,et al.  Radial Basis Functions , 2021, Encyclopedia of Mathematical Geosciences.

[51]  B. Balachandran,et al.  Influence of flexibility on the aerodynamic performance of a hovering wing , 2009, Journal of Experimental Biology.

[52]  Chunyong Yin,et al.  Measuring wing kinematics, flight trajectory and body attitude during forward flight and turning maneuvers in dragonflies , 2003, Journal of Experimental Biology.

[53]  S. N. Fry,et al.  The aerodynamics of hovering flight in Drosophila , 2005, Journal of Experimental Biology.

[54]  Bruno A. Roccia,et al.  A Numerical Model to Study the Nonlinear and Unsteady Aerodynamics of Bioinspired Morphing-Wing Concepts , 2015 .

[55]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[56]  Sergio Preidikman,et al.  Numerical Simulations of Interactions Among Aerodynamics, Structural Dynamics, and Control Systems , 1998 .

[57]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[58]  Michael Smith,et al.  The effects of flexibility on the aerodynamics of moth wings - Towards the development of flapping-wing technology , 1995 .