Modelagem matemática para a interação fluido-estrutura acoplando escoamentos incompressíveis e viga de Timoshenko

Abstract

Cylindrical bodies subjected to external flow can vibrate due to fluctuations forces induced by eddy structures. These vibrations may induce, by means of a non-linear process, an increase in the drag and lift, thus leading to increased strain on the structures. In addition, the vibrations may cause nucleation and propagation of cracks in the structure leading to failure due to fatigue. This is especially important when these cylinders are tubes through which oil or natural gas are transported and are subject to waves and currents. The main aim of this work is to acquire and broaden the understanding of the influence of proximity to the ground in the fluid-structure interaction process in horizontal pipes anchored by dunes. This study was done by computational solution in parallel atmosphere of the equations that model the phenomenon. These simulations were performed on a pipe length L = 42m and a diameter of 0 = 0,27m in a flow dynamically characterized by Re^ = 1, 73 x 105. Five different distances between the soil and the pipe (gap) were tested, they are: 0,10, 0,20, 0,30, 1 0 e 5 0, where 0 is the structure diameter. In this study, the structural modeling and fluid dynamics modeling are coupled mathematically and numerically, which allows the simulation and analysis with both effects coupled, using a single software tool. The Immersed Boundary Method used in this study, is particularly suitable for problems involving fluid-structure interaction, because the fluid and structure domains are treated independently. The equations that model the flows are solved in an Eulerian field (fixed Cartesian, for example), while the surface of the immersed body is represented by a set of Lagrangian points. Using this methodology, the liquid-solid interface forces are evaluated. These forces are used either in the fluid routine for the imposition of non-slip boundary condition on the boundary between the fluid and the structure, as in the structural routine for calculating the displacements and velocities of the structure. A computer code that enables simulation of three-dimensional incompressible flows with a turbulence model together with Timoshenko beam model was used. The simulations were performed on a high-performance cluster that allowed the use of 80 or 160 processors depending on the case. Even with robust computers and parallel computing, each simulation lasted from 13 to 28 days. The number of computational volumes used to describe the fluid field varied from 5,040,000 to 8,064,000. The results are consistent with what is expected for this type of problem.