A Comparison of Euler and Navier-Stokes Simulations with Experiment for a Flapping Hydrofoil

Abstract

A new finite volume implementation of the incompressible Navier-Stokes equations, expressed in arbitrary Lagrangian-Eulerian (ALE) form, is used to simulate both the viscous and inviscid forced-motion hydrodynamics of a single isolated flapping hydrofoil. The flapping foil is used for both primary propulsion and maneuvering control on the MIT Flapping Foil Vehicle (FFV) employing four identical flapping foils in a sea turtle configuration. 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 the force time histories generated by the flapping foil using both the Euler and Navier-Stokes equations are shown to be in reasonably good agreement with experimental data for the single set of kinematic parameters investigated. A significant Reynolds number dependency is observed in the unsteady thrust component of force generated by the foil that is absent in the other force components.