Simulations of propelling and energy harvesting articulated bodies via vortex particle-mesh methods

Abstract The emergence and understanding of new design paradigms that exploit flow induced mechanical instabilities for propulsion or energy harvesting demands robust and accurate flow structure interaction numerical models. In this context, we develop a novel two dimensional algorithm that combines a Vortex Particle-Mesh (VPM) method and a Multi-Body System (MBS) solver for the simulation of passive and actuated structures in fluids. The hydrodynamic forces and torques are recovered through an innovative approach which crucially complements and extends the projection and penalization approach of Coquerelle et al. [1] and Gazzola et al. [2] . The resulting method avoids time consuming computation of the stresses at the wall to recover the force distribution on the surface of complex deforming shapes. This feature distinguishes the proposed approach from other VPM formulations. The methodology was verified against a number of benchmark results ranging from the sedimentation of a 2D cylinder to a passive three segmented structure in the wake of a cylinder. We then showcase the capabilities of this method through the study of an energy harvesting structure where the stocking process is modeled by the use of damping elements.

[1]  Auke J. Ijspeert,et al.  Biorobotics: Using robots to emulate and investigate agile locomotion , 2014, Science.

[2]  G. Cottet,et al.  EULERIAN FORMULATION AND LEVEL SET MODELS FOR INCOMPRESSIBLE FLUID-STRUCTURE INTERACTION , 2008 .

[3]  Chengjie Wang,et al.  Strongly coupled dynamics of fluids and rigid-body systems with the immersed boundary projection method , 2015, J. Comput. Phys..

[4]  Philippe Angot,et al.  A penalization method to take into account obstacles in incompressible viscous flows , 1999, Numerische Mathematik.

[5]  F. Noca,et al.  A COMPARISON OF METHODS FOR EVALUATING TIME-DEPENDENT FLUID DYNAMIC FORCES ON BODIES, USING ONLY VELOCITY FIELDS AND THEIR DERIVATIVES , 1999 .

[6]  I. Akhtar,et al.  Hydrodynamics of a tandem fish school with asynchronous undulation of individuals , 2016 .

[7]  M. Lighthill Note on the swimming of slender fish , 1960, Journal of Fluid Mechanics.

[8]  P. Koumoutsakos,et al.  Simulations of optimized anguilliform swimming , 2006, Journal of Experimental Biology.

[9]  Jeong-Woo Choi,et al.  Phototactic guidance of a tissue-engineered soft-robotic ray , 2016, Science.

[10]  J. Dabiri Biomechanics: How fish feel the flow , 2017, Nature.

[11]  Liang Wang,et al.  Where is the rudder of a fish?: the mechanism of swimming and control of self-propelled fish school , 2010 .

[12]  Frédéric Boyer,et al.  Improved Lighthill fish swimming model for bio-inspired robots: Modeling, computational aspects and experimental comparisons , 2014, Int. J. Robotics Res..

[13]  P. Koumoutsakos,et al.  Optimization of trailing vortex destruction by evolution strategies , 2000 .

[14]  A. Ijspeert,et al.  From Swimming to Walking with a Salamander Robot Driven by a Spinal Cord Model , 2007, Science.

[15]  Keiji Kawachi,et al.  Regular Article: A Numerical Study of Undulatory Swimming , 1999 .

[16]  K. Namkoong,et al.  Numerical analysis of two-dimensional motion of a freely falling circular cylinder in an infinite fluid , 2008, Journal of Fluid Mechanics.

[17]  Dmitry Kolomenskiy,et al.  Numerical simulation of fluid-structure interaction with the volume penalization method , 2015, J. Comput. Phys..

[18]  Emmanuel Maitre,et al.  Convergence Analysis of a Penalization Method for the Three-Dimensional Motion of a Rigid Body in an Incompressible Viscous Fluid , 2010, SIAM J. Numer. Anal..

[19]  Williams,et al.  Self-propelled anguilliform swimming: simultaneous solution of the two-dimensional navier-stokes equations and Newton's laws of motion , 1998, The Journal of experimental biology.

[20]  Jeff D Eldredge,et al.  Numerical simulations of undulatory swimming at moderate Reynolds number , 2006, Bioinspiration & biomimetics.

[21]  Jerrold E. Marsden,et al.  Locomotion of Articulated Bodies in a Perfect Fluid , 2005, J. Nonlinear Sci..

[22]  R. Glowinski,et al.  A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow , 2001 .

[23]  Jeff D. Eldredge,et al.  Passive locomotion of a simple articulated fish-like system in the wake of an obstacle , 2008, Journal of Fluid Mechanics.

[24]  P. Koumoutsakos MULTISCALE FLOW SIMULATIONS USING PARTICLES , 2005 .

[25]  Neelesh A. Patankar,et al.  A fast projection scheme for the direct numerical simulation of rigid particulate flows , 2005 .

[26]  Petros Koumoutsakos,et al.  Simulations of single and multiple swimmers with non-divergence free deforming geometries , 2011, J. Comput. Phys..

[27]  Joe J. Monaghan,et al.  SPH simulations of swimming linked bodies , 2008, J. Comput. Phys..

[28]  Neelesh A. Patankar,et al.  A new mathematical formulation and fast algorithm for fully resolved simulation of self-propulsion , 2009, J. Comput. Phys..

[29]  Petros Koumoutsakos,et al.  Iterative Brinkman penalization for remeshed vortex methods , 2015, J. Comput. Phys..

[30]  Mathieu Coquerelle,et al.  ARTICLE IN PRESS Available online at www.sciencedirect.com Journal of Computational Physics xxx (2008) xxx–xxx , 2022 .

[31]  Frédéric Boyer,et al.  Poincaré–Cosserat Equations for the Lighthill Three-dimensional Large Amplitude Elongated Body Theory: Application to Robotics , 2010, J. Nonlinear Sci..

[32]  Gilles Carbou,et al.  Boundary layer for a penalization method for viscous incompressible flow , 2003, Advances in Differential Equations.

[33]  Jeff D. Eldredge,et al.  Dynamically coupled fluid-body interactions in vorticity-based numerical simulations , 2008, J. Comput. Phys..

[34]  Thomas Gillis,et al.  An efficient iterative penalization method using recycled Krylov subspaces and its application to impulsively started flows , 2017, J. Comput. Phys..

[35]  Chang Shu,et al.  Simulation of fish swimming and manoeuvring by an SVD-GFD method on a hybrid meshfree-Cartesian grid , 2010 .

[36]  M. Lighthill Large-amplitude elongated-body theory of fish locomotion , 1971, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[37]  Randall J. LeVeque,et al.  An Immersed Interface Method for Incompressible Navier-Stokes Equations , 2003, SIAM J. Sci. Comput..

[38]  Kai Schneider,et al.  Simulation of forced deformable bodies interacting with two-dimensional incompressible flows: Application to fish-like swimming , 2015 .

[39]  Anthony Leonard,et al.  Flow-induced vibration of a circular cylinder at limiting structural parameters , 2001 .

[40]  P. Koumoutsakos,et al.  Computing the force distribution on the surface of complex, deforming geometries using vortex methods and Brinkman penalization , 2016, 1610.04398.

[41]  Petros Koumoutsakos,et al.  An immersed boundary method for smoothed particle hydrodynamics of self-propelled swimmers , 2008, J. Comput. Phys..

[42]  Xinghua Chang,et al.  A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations , 2009 .

[43]  Alessandro Curioni,et al.  Billion vortex particle direct numerical simulations of aircraft wakes , 2008 .

[44]  M. Spong,et al.  Robot Modeling and Control , 2005 .