Vol. 9, No. 2, 2021

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Lie group dynamics of reduced multibody-fluid systems

Zdravko Terze, Viktor Pandža, Marijan Andrić and Dario Zlatar

Vol. 9 (2021), No. 2, 167–177
Abstract

In order to study the dynamics of a multibody system (MBS) moving in ambient fluid, the geometric modeling approach of a fully coupled multibody-fluid system is adopted, incorporating the boundary integral method and time integrator in Lie group setting. The configuration space of the multibody-fluid system is reduced by eliminating fluid variables via symplectic reduction without compromising any accuracy, if the fluid is assumed to be inviscid and incompressible. Consequently, the equations of motion for the submerged MBS are formulated without explicitly incorporating fluid variables, while the effect of the fluid flow on overall MBS dynamics is accounted for by added mass effect on the submerged bodies. By following this approach, the added masses can be computed by the boundary integral functions of the fluid density and the flow velocity potential. Vortex shedding and evolution mechanism is incorporated in the approach, to describe additional viscous effects and include fluid vorticity and circulation in the system dynamics. For vortex modeling, the unsteady potential flow method is utilized, enforcing the Kutta condition on sharp edges of the MBS. In summary, the presented approach exhibits significant computational advantages in comparison to the standard numerical procedures that — most commonly — comprise finite volume discretization of the whole fluid domain and (loosely coupled) separate solvers for fluid and MBS dynamics. The model implementation is demonstrated on the example of the three-body multibody chain.

Keywords
multibody system dynamics, fluid-structure interaction, Lie groups
Mathematical Subject Classification 2010
Primary: 70E55, 74F10, 76M60
Milestones
Received: 9 January 2020
Revised: 8 January 2021
Accepted: 11 March 2021
Published: 31 May 2021

Communicated by Emilio Barchiesi
Authors
Zdravko Terze
Chair of Flight Vehicle Dynamics
Faculty of Mechanical Engineering and Naval Architecture
University of Zagreb
Zagreb
Croatia
Viktor Pandža
Chair of Flight Vehicle Dynamics
Faculty of Mechanical Engineering and Naval Architecture
University of Zagreb
Zagreb
Croatia
Marijan Andrić
Chair of Flight Vehicle Dynamics
Faculty of Mechanical Engineering and Naval Architecture
University of Zagreb
Zagreb
Croatia
Dario Zlatar
Chair of Flight Vehicle Dynamics
Faculty of Mechanical Engineering and Naval Architecture
University of Zagreb
Zagreb
Croatia