Coupled Multibody-Fluid Dynamics Simulation of Flapping Wings

Abstract

This paper deals with the coupled structural and fluid-dynamics analysis of flexible flapping wings using multibody dynamics. A general-purpose multidisciplinary multibody solver is coupled with a computational fluid dynamics code by means of a general-purpose, meshless boundary interfacing approach based on Moving Least Squares with Radial Basis Functions. The general-purpose, free software multibody solver MBDyn is used. A nonlinear 4-node shell element has been used for the structural model. The fluid dynamics code is based on a stabilized finite element approximation of the unsteady Navier-Stokes equations. The method (often referred to in the literature as G2 method) has been implemented within the programming environment provided by the free software project FEniCS, a collection of libraries specifically designed for the automated and efficient solution of differential equations. FEniCS provides extensive scripting capabilities, with a domain-specific language for the specification of variational formulations of Partial Differential Equations that is embedded within the programming language Python. This approach makes it possible to easily and quickly build complex simulation codes that are, at the same time, extremely efficient and easily adapted to run in parallel. The coupling of the multibody and Navier-Stokes codes is strictly enforced at each time step. The fluid dynamics discretization is automatically refined to keep the error on the overall lift and drag coefficients below a user-defined tolerance. The method is first tested by computing the drag force of a non-oscillating NACA 0012 airfoil traveling in air. Subsequently, the drag and lift forces on a rigid and flexible oscillating NACA 0012 wing are compared with experimental data. Encouraging results obtained from the modeling and analysis of the dynamics and aeroelasticity of flexible oscillating wing models confirm the ability of the structural and fluid dynamics models to capture the physics of the problem.