Simulation of RoboTuna Fluid Dynamics Using a New Incompressible ALE Method

Abstract

†A new finite volume method for the incompressible Navier-Stokes equations, expressed in arbitrary Lagrangian-Eulerian (ALE) form, is used to simulate the inviscid forced-motion hydrodynamics of the robotic fish RoboTuna. Results are first presented for Taylor decaying vortex flow and oscillating cylinder flow to validate the ALE algorithm for moving boundary problems. A mesh movement algorithm based on a modified form of the Laplace equation is then described and shown to perform well for a benchmark mesh movement problem as well as for the RoboTuna simulation. Finally, results for RoboTuna are presented and compared with previously reported results using a nonlinear potential flow method and with experimental data. ver the last decade or so, one class of problems in computational fluid dynamics that has undergone substantial development is the class where the fluid domain boundary is either explicitly time-dependent or is unknown a priori and determined, in a coupled fashion, as part of an unsteady flow solution. Free surface, fluid-structure interaction, and forced-motion flows are typical of problems in this class. A natural way to formulate moving boundary problems is the so-called arbitrary Lagrangian-Eulerian (ALE) form of the fundamental conservation laws where the domain boundary and interior control surfaces are allowed to move arbitrarily in time and which recovers the Eulerian and Lagrangian forms as special limiting cases of the general ALE form. Here, a new finite volume method for the incompressible Euler and Navier-Stokes equations, expressed in ALE form, is used to simulate the inviscid forced-motion fluid dynamics of the robotic fish RoboTuna 1,2 . The flow solver used in the present investigation is an extension of a method recently proposed by us 3,4 to three-dimensional flows involving large boundary deformation. Results are first presented for two rudimentary flow problems with exact solutions to establish the accuracy of the method. A mesh movement algorithm based on a modified form of the Laplace equation is also described and shown to perform well for a benchmark grid movement problem as well as for the RoboTuna simulation. The computed force and power time histories for the unappended RoboTuna morphology with ‘case 2’ swimming kinematics are then presented and compared with previously reported results using a nonlinear potential flow method 2 and with available experimental data 2