Desenvolvimento de procedimentos de modelagem de interação fluido-estrutura combinando a Teoria de Vigas de Cosserat e a Metologia de Fronteira Imersa

Abstract

The present report describes the research work carried-out with the aim of developing, implementing and evaluating a three-dimensional modeling procedure of fluid-structure phenomena involving slender structures, such as beams, bars and cables. The novel approach adopted consists of the combination of the Cosserat theory applied to slender beams, which accounts for geometrical nonlinearity, and the Immersed Boundary methodology, which is used to represent the interactions between the structural and fluidic domains. The study is included in the scope of Vortex-Induced Vibrations, which is a topic of great interest in the oil industry, especially as related to the modeling of risers used for oil exploitation in deep seas. According to the Cosserat theory, the deformed configuration of the structure is described in terms of the displacement vector of the curved formed by the cross-sections center of area, and the orientation of a vector bases fixed to each cross-section, with respect to an inertial reference frame. The main advantage of this theory is that is geometrically exact. Finite element is employed for discretization of the equations of motion. According to the Immersed Boundary methodology, the solid-fluid interface forces are calculated by enforcing momentum balance to the fluid particles over the interface. The main features of the proposed methodology are evaluated by means of a number of numerical simulations, both in static and dynamic regimes, regarding the structural model, in a first step and the complete fluid-structure model, in a second step. The results obtained enable to evaluate the accuracy and the main advantages and shortcomings of the methodology, especially regarding the numerical aspects. Also, they enabled to put in evidence some relevant phenomenological aspects related to the dynamic behavior of cylindrical structures with various levels of bending flexibility, subjected to transverse flows characterized by different values of the Reynolds number.