Fluid–structure interaction with a Finite Element–Immersed Boundary approach for compressible flows

Abstract

This paper presents the mathematical modeling and numerical simulations of fluid–structure interaction (FSI) problems. The fluid domain is discretized using a Cartesian block-structured mesh and solved using the Finite Volume Method (FVM), using the LES methodology with Smagorinsky turbulent closure model. The fluid flow in the system is considered compressible, with properties that vary. The Immersed Boundary Method (IBM) is used to model the solid–fluid interface, and the structure deformation was solved using the Finite Element Method (FEM). The Multi-direct Forcing Scheme is used to calculate the fluid-dynamics forces through the IBM. After calculating the fluid forces exerted on the solid, the forces are interpolated and transferred to the FEM model, providing the deformation of the structure at each time step. The structural domain was discretized with Hexahedral eight-noded element with extra shape functions. The simulations were carried out using MFSIm (in-house code), a multiphysics simulation framework developed by the Fluid Mechanics Laboratory of the Federal University of Uberlândia with financial support from Petrobras. This paper demonstrates the practical application of FSI analysis in an industrial context, specifically focusing on a pipeline system within a Fluid Catalytic Cracking Unit (FCCU) used in the oil and gas industry. The analysis involves the use of butterfly valves positioned at different angles of opening. The results are treated statistically, and a surface response is generated. Machine learning is employed to predict the surface response, showing the valve configurations that yield the maximum and minimum displacement magnitudes of the evaluated structural probes.