American Institute of Aeronautics and Astronautics 1 Shape Optimization and Fluid Dynamic Analysis of a Translating Flexible Body Scott L. Thomson 1 Brigham Young University, Provo, UT, 84663 The translation (swimming) of an oscillating, slender, flexible body through an initially stationary fluid was explored using computational models and optimization routines. The computational model included fully-coupled two-dimensional fluid and solid finite element domains. The body leading edge was subjected to a prescribed vertical sinusoidal displacement, whereas the entire body was free to move horizontally. Large body deformation resulted in thrust production and horizontal body translation. Gradient-based optimization methods were used to find the body shape that yielded the maximum horizontal displacement over one period of vertical oscillation. It is shown that a tapered body with a “rounded” leading edge achieved significantly greater horizontal velocity than a body of uniform thickness. The computational domains, numerical models, optimization routines, and model verification studies are described. The predicted responses of uniform and optimal bodies are compared, and the sensitivity of horizontal displacement to body shape is quantified. I. Introduction he purpose of this paper is to explore the response of an optimized slender body translating (“swimming”) through an initially stationary fluid. The research is motivated by previous experimental studies of propulsion generated by flapping motion. A review of the literature on this topic is not attempted here. Among the most relevant include studies on a sinusoidally pitching and plunging airfoil 1 , a sinusoidally-plunging airfoil with a flexible trailing edge 2 , and an oscillating fin 3 . Heathcote and Gursul 2 performed experiments on a rigid airfoil with a very thin plate attached to the trailing edge. Various plate thicknesses were studied and the presence of an optimal thickness for thrust coefficient generation was noted, although identification of a truly “optimal” configuration was not the goal of the study. In the present paper, a computational model of a body translating through a fluid is presented. The model included separate, but coupled, fluid and solid domains. Combinations of sliding and deforming meshes allowed for large fluid and solid domain displacements. Verification studies were performed to explore sensitivity to grid size and time step size. The model was coupled with optimization routines to search for the optimal shape for maximizing horizontal displacement. The purpose of the optimization algorithm was not for design; but rather, it was intended to be used as an efficient tool for exploring the parameter space, from which further models may be investigated in more detail. II. Numerical Methods A. Coupled Fluid-Solid Model Fully-coupled fluid and solid domains were modeled in two dimensions using the finite element method with the commerical code ADINA (ADINA R&D, Inc., Watertown, MA). The fluid domain was governed by the unsteady, incompressible, viscous Navier-Stokes equations. The modeled fluid was water (ρ fluid = 1000 kg/m 3 , μ = 0.001 Pa·s). A laminar flow model was used. The solid domain was based on the large deformation of a linearly-elastic steel material model (ρ solid = 7861 kg/m 3 , E = 210 GPa, ν = 0.3). The solid domain was 0.09 cm long and was of variable thickness, as discussed below. The fluid domain dimensions and boundary conditions are noted in Fig. 1. No external fluid forces were applied; thus the only fluid motion was that which resulted from motion of the solid body. 1 Assistant Professor, Mechanical Engineering, 435 CTB, AIAA Member. T 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition 4 - 7 January 2010, Orlando, Florida AIAA 2010-1432 Copyright © 2010 by Scott Thomson. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.