Sequentially-coupled space–time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV

We present a sequentially-coupled space–time (ST) computational fluid–structure interaction (FSI) analysis of flapping-wing aerodynamics of a micro aerial vehicle (MAV). The wing motion and deformation data, whether prescribed fully or partially, is from an actual locust, extracted from high-speed, multi-camera video recordings of the locust in a wind tunnel. The core computational FSI technology is based on the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) formulation. This is supplemented with using NURBS basis functions in temporal representation of the wing and mesh motion, and in remeshing. Here we use the version of the DSD/SST formulation derived in conjunction with the variational multiscale (VMS) method, and this version is called “DSD/SST-VMST.” The structural mechanics computations are based on the Kirchhoff–Love shell model. The sequential-coupling technique is applicable to some classes of FSI problems, especially those with temporally-periodic behavior. We show that it performs well in FSI computations of the flapping-wing aerodynamics we consider here. In addition to the straight-flight case, we analyze cases where the MAV body has rolling, pitching, or rolling and pitching motion. We study how all these influence the lift and thrust.

[1]  Tayfun E. Tezduyar,et al.  Flow simulation and high performance computing , 1996 .

[2]  Thomas J. R. Hughes,et al.  NURBS-based isogeometric analysis for the computation of flows about rotating components , 2008 .

[3]  Tayfun E. Tezduyar,et al.  Space–time finite element computation of complex fluid–structure interactions , 2010 .

[4]  Yuri Bazilevs,et al.  Wind turbine aerodynamics using ALE–VMS: validation and the role of weakly enforced boundary conditions , 2012 .

[5]  Tayfun E. Tezduyar,et al.  Fluid–structure interaction modeling of parachute clusters , 2011 .

[6]  T. Hughes.  Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .

[7]  I. Akkerman,et al.  Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method , 2010, J. Comput. Phys..

[8]  I. Akkerman,et al.  Isogeometric analysis of free-surface flow , 2011, J. Comput. Phys..

[9]  S. Mittal,et al.  Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements , 1992 .

[10]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[11]  Wing Kam Liu,et al.  Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆ , 1981 .

[12]  Eugenio Oñate,et al.  A COMPRESSIBLE LAGRANGIAN FRAMEWORK FOR MODELING THE FLUID–STRUCTURE INTERACTION IN THE UNDERWATER IMPLOSION OF AN ALUMINUM CYLINDER , 2013 .

[13]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[14]  Tayfun E. Tezduyar,et al.  Finite elements in fluids: Special methods and enhanced solution techniques , 2007 .

[15]  Yuri Bazilevs,et al.  Computational fluid–structure interaction: methods and application to a total cavopulmonary connection , 2009 .

[16]  Tayfun E. Tezduyar,et al.  Finite Element Methods for Fluid Dynamics with Moving Boundaries and Interfaces , 2004 .

[17]  Roger Ohayon,et al.  Energy approach for static and linearized dynamic studies of elastic structures containing incompressible liquids with capillarity: a theoretical formulation , 2012 .

[18]  Murat Manguoglu,et al.  A parallel sparse algorithm targeting arterial fluid mechanics computations , 2011 .

[19]  Guirong Liu,et al.  A moving-mesh gradient smoothing method for compressible CFD problems , 2013 .

[20]  Yuri Bazilevs,et al.  Fluid–structure interaction simulation of pulsatile ventricular assist devices , 2013, Computational Mechanics.

[21]  Roger Ohayon,et al.  Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems , 2001 .

[22]  Yuri Bazilevs,et al.  Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines , 2012 .

[23]  Tayfun E. Tezduyar,et al.  Finite element methods for flow problems with moving boundaries and interfaces , 2001 .

[24]  Yuri Bazilevs,et al.  Space–Time and ALE-VMS Techniques for Patient-Specific Cardiovascular Fluid–Structure Interaction Modeling , 2012 .

[25]  Arif Masud,et al.  A Multiscale/stabilized Formulation of the Incompressible Navier–Stokes Equations for Moving Boundary Flows and Fluid–structure Interaction , 2006 .

[26]  M. R. Lewis,et al.  A finite-element/boundary-element method for large-displacement fluid-structure interaction , 2012 .

[27]  Yuri Bazilevs,et al.  Free-Surface Flow and Fluid-Object Interaction Modeling With Emphasis on Ship Hydrodynamics , 2012 .

[28]  Yuri Bazilevs,et al.  Fluid–structure interaction modeling of wind turbines: simulating the full machine , 2012, Computational Mechanics.

[29]  Tayfun E. Tezduyar,et al.  SPACE–TIME FLUID–STRUCTURE INTERACTION METHODS , 2012 .

[30]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[31]  Tayfun E. Tezduyar,et al.  Fluid-structure interactions of a parachute crossing the far wake of an aircraft , 2001 .

[32]  Tayfun E. Tezduyar,et al.  Computational Methods for Parachute Fluid–Structure Interactions , 2012 .

[33]  Ming-Chen Hsu,et al.  Computational vascular fluid–structure interaction: methodology and application to cerebral aneurysms , 2010, Biomechanics and modeling in mechanobiology.

[34]  T. Tezduyar.  Computation of moving boundaries and interfaces and stabilization parameters , 2003 .

[35]  Tayfun E. Tezduyar,et al.  Fluid–structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity , 2012 .

[36]  T. Tezduyar,et al.  Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling , 2008 .

[37]  Tayfun E. Tezduyar,et al.  Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces , 1994 .

[38]  Kenji Takizawa,et al.  Computer modeling techniques for flapping-wing aerodynamics of a locust , 2013 .

[39]  T. Hughes,et al.  Isogeometric fluid-structure interaction: theory, algorithms, and computations , 2008 .

[40]  Marek Behr,et al.  Parallel finite-element computation of 3D flows , 1993, Computer.

[41]  A. L. Marsden,et al.  Computation of residence time in the simulation of pulsatile ventricular assist devices , 2014 .

[42]  Yuri Bazilevs,et al.  3D simulation of wind turbine rotors at full scale. Part II: Fluid–structure interaction modeling with composite blades , 2011 .

[43]  Ryo Torii,et al.  Role of 0D peripheral vasculature model in fluid–structure interaction modeling of aneurysms , 2010 .

[44]  Yuri Bazilevs,et al.  A fully-coupled fluid-structure interaction simulation of cerebral aneurysms , 2010 .

[45]  Yuri Bazilevs,et al.  3D simulation of wind turbine rotors at full scale. Part I: Geometry modeling and aerodynamics , 2011 .

[46]  Tayfun E. Tezduyar,et al.  Wall shear stress calculations in space–time finite element computation of arterial fluid–structure interactions , 2010 .

[47]  Tayfun E. Tezduyar,et al.  Sequentially-Coupled Arterial Fluid-Structure Interaction (SCAFSI) technique , 2009 .

[48]  Tayfun E. Tezduyar,et al.  Space–time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters , 2011 .

[49]  Yuri Bazilevs,et al.  Blood vessel tissue prestress modeling for vascular fluid-structure interaction simulation , 2011 .

[50]  Tayfun E. Tezduyar,et al.  Space–time techniques for computational aerodynamics modeling of flapping wings of an actual locust , 2012 .

[51]  René de Borst,et al.  On the Nonnormality of Subiteration for a Fluid-Structure-Interaction Problem , 2005, SIAM J. Sci. Comput..

[52]  Tayfun E. Tezduyar,et al.  Space-time finite element techniques for computation of fluid-structure interactions , 2005 .

[53]  Yuri Bazilevs,et al.  Numerical-performance studies for the stabilized space–time computation of wind-turbine rotor aerodynamics , 2011 .

[54]  Tayfun E. Tezduyar,et al.  Space–time VMS computation of wind-turbine rotor and tower aerodynamics , 2014 .

[55]  S. Mittal,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. II: Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders , 1992 .

[56]  Thomas J. R. Hughes,et al.  Large eddy simulation of turbulent channel flows by the variational multiscale method , 2001 .

[57]  Kenji Takizawa,et al.  Fluid–structure interaction modeling of clusters of spacecraft parachutes with modified geometric porosity , 2013 .

[58]  T. Daniel,et al.  The Journal of Experimental Biology 206, 2979-2987 © 2003 The Company of Biologists Ltd , 2022 .

[59]  Thomas J. R. Hughes,et al.  Patient-specific isogeometric fluid–structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device , 2009 .

[60]  Yuri Bazilevs,et al.  Computational Fluid-Structure Interaction: Methods and Applications , 2013 .

[61]  Yuri Bazilevs,et al.  ALE-VMS AND ST-VMS METHODS FOR COMPUTER MODELING OF WIND-TURBINE ROTOR AERODYNAMICS AND FLUID–STRUCTURE INTERACTION , 2012 .

[62]  A. Korobenko,et al.  STRUCTURAL MECHANICS MODELING AND FSI SIMULATION OF WIND TURBINES , 2013 .

[63]  Tayfun E. Tezduyar,et al.  Fluid–structure interaction modeling and performance analysis of the Orion spacecraft parachutes , 2011 .

[64]  T. Tezduyar,et al.  A parallel 3D computational method for fluid-structure interactions in parachute systems , 2000 .

[65]  G. Liu,et al.  Immersed smoothed finite element method for fluid–structure interaction simulation of aortic valves , 2012 .

[66]  Wulf G. Dettmer,et al.  On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction , 2008 .

[67]  Tayfun E. Tezduyar,et al.  METHODS FOR FSI MODELING OF SPACECRAFT PARACHUTE DYNAMICS AND COVER SEPARATION , 2013 .

[68]  Yuri Bazilevs,et al.  CHALLENGES AND DIRECTIONS IN COMPUTATIONAL FLUID–STRUCTURE INTERACTION , 2013 .

[69]  Yuri Bazilevs,et al.  Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment , 2014 .

[70]  Tayfun E. Tezduyar,et al.  PARALLEL FINITE ELEMENT SIMULATION OF 3D INCOMPRESSIBLE FLOWS: FLUID-STRUCTURE INTERACTIONS , 1995 .

[71]  Tayfun E. Tezduyar,et al.  Modeling of fluid–structure interactions with the space–time finite elements: contact problems , 2008 .

[72]  Yuri Bazilevs,et al.  Toward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS , 2012 .

[73]  Tayfun E. Tezduyar,et al.  Space-Time Computational Techniques for the Aerodynamics of Flapping Wings , 2012 .

[74]  Roland Wüchner,et al.  Isogeometric shell analysis with Kirchhoff–Love elements , 2009 .

[75]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .

[76]  T. Tezduyar,et al.  Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique , 2008 .

[77]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[78]  Tayfun E. Tezduyar,et al.  Multiscale sequentially-coupled arterial FSI technique , 2010 .

[79]  Genki Yagawa,et al.  Accurate fluid-structure interaction computations using elements without mid-side nodes , 2011 .

[80]  T. Tezduyar,et al.  A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. I: The concept and the preliminary numerical tests , 1992 .

[81]  E. Oñate,et al.  A coupled PFEM–Eulerian approach for the solution of porous FSI problems , 2012, Computational Mechanics.

[82]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[83]  T. Hughes,et al.  Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow , 2006 .

[84]  Murat Manguoglu,et al.  Solution of linear systems in arterial fluid mechanics computations with boundary layer mesh refinement , 2010 .

[85]  S. Yoshimura,et al.  Parallel BDD-based monolithic approach for acoustic fluid-structure interaction , 2012 .

[86]  Tayfun E. Tezduyar,et al.  Fluid–structure interaction modeling of ringsail parachutes , 2008 .

[87]  Tayfun E. Tezduyar,et al.  Space–time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle , 2012 .

[88]  Tayfun E. Tezduyar,et al.  Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods , 2008 .

[89]  T. Tezduyar,et al.  Stabilized space–time computation of wind-turbine rotor aerodynamics , 2011 .

[90]  Tayfun E. Tezduyar,et al.  Modelling of fluid–structure interactions with the space–time finite elements: Solution techniques , 2007 .

[91]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[92]  Yuri Bazilevs,et al.  The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches , 2010 .

[93]  Tayfun E. Tezduyar,et al.  Multiscale space–time fluid–structure interaction techniques , 2011 .