Simulation of RoboTurtle Fluid Dynamics using an Incompressible ALE Method

Abstract

A finite volume implementation of the incompressible Euler and Navier-Stokes equations, expressed in arbitrary Lagrangian-Eulerian (ALE) form, is used to simulate the unsteady hydrodynamics of RoboTurtle, a swimming underwater vehicle employing four identical flapping foils arranged in a sea turtle configuration. The flapping foils are used for both primary propulsion and maneuvering control of the vehicle. Simulation results are first presented for several benchmark problems to validate the ALE algorithm for both viscous and invsicid flows and for flows with moving boundaries. The implementation of the pressure equation and its boundary condition is discussed and a mesh movement algorithm based on linear elastostatics is described and shown to perform well for a benchmark problem. Simulation results for a single RoboTurtle flapping foil are shown to be in reasonably good agreement with experimental force time history data. Simulation results are also shown for the fully configured RoboTurtle at a ‘steady-cruise’ condition using the Euler equations. Simulated force time histories are presented for a forward and aft flapping foil pair and the hydrodynamic interaction between the forward and aft foils is discussed.