A new fluid-structure coupling model: Case of a pipe under internal pressure

Abstract

This work presents the eigenfrequencies of a study on the fluid-structure interaction for a pipe with a circular section, under pressure constraints in laminar, incompressible and irrotational flow, followed by a comparison between stiffness coupling and bar coupling with different geometric ratio Radius/Length; Radius/Thickness, as a frequency geometric identity of the pipe in the industry. The realization of this study is to have better coupling, where we use the relations of mechanical behaviour of the solid on displacement-stress and for the fluid, we use the Navier-Stokes equations in cylindrical coordinates under the speed-stress form transformed into displacement by the Galerkin-Temp theory. Either the force of the fluid will be distributed on the internal surface of the cylinder by the coupling (interface) between fluid and solid. To obtain the results of the eigenfrequencies we used the hierarchical finite element method (HFEM) for both mechanical and fluid entities. For the natural frequencies, we apply the hierarchical finite elements of the Legendre polynomial which is defined in a well-known interval, thanks to this mathematical calculation we arrive at the general equations of motion matrix form of the solid, the interface and the fluid. The calculation was carried out by a MATLAB programme which determines the eigenfrequencies of the evolved system by different geometric and physical parameters mentioned. We validated this work by a table of comparison between the experimental values and the values of the programme.