Fully-Coupled Fluid Solid Computation for Simulation of Flutter in Tubes and Tube Arrays

This work is concerned with the modelling of the interaction of a fluid with a rigid or a flexible elastic cylinder in presence of axial or cross-flow. A partitioned procedure is involved to performe the computation of the fully-coupled fluid solid system. The fluid flow is governed by the incompressible Navier-Stokes equations and modeled by using a fractional step scheme combined with a co-located finite volume method for space discretisation. The motion of the fluid domain is accounted for by a moving mesh strategy through an Arbitrary Lagrangian-Eulerian (ALE) formulation. Solid dyncamics is modeled by descrete or beam elements in the linear elasticity framework and systems are solved through a finite element method. The resulting strongly coupled fluid solid set of non linear equations is solved by means of a partitioned solution procedure. A fixed point method combined with under-relaxation is involved to ensure the optimal convergence of the iterative procedure. In the present work two examples are presented to show the methodology robustness and efficiency. The purpose is to attempt to simulate a fluid structure interaction resulting in the development of a dynamic instability induced by a positive damping generation of the system. Both flutter of a flexible cylinder conveying an internal fluid and fluid-elastic instability of a tube array submitted to an external cross flow are investigated numerically. According to first results the partitioned procedure relies on consistant numerical methods ensuring energy conservation at the interface and describing with a sufficient accuracy the mechanical energy transfer between fluid and solid systems through the interface with a limited numerical diffusion. Therefore it seems to be qualitatively convenient for simulation of flutter. For a quantitative evaluation of the methodology further complementary simulations validating these developments from a physical point of view will be required in order to confirm these first trends.