# Fluid-structure-interaction

**Case Study – Simulation of Fluid Structure Interaction**

**Objective**

Simulation of Fluid Structure Interaction (FSI) problems are concerned with the interaction between moving fluids and the structural deformations of elastic structures. Airfoils, combustion engines, compressors, containers and the human blood flow and lung systems are examples of engineering applications and natural phenomena where the effects of fluid structure interaction are critical to take into consideration. Due to the large number of relevant engineering applications, it is important to develop methodologies which can model these effects. With inspiration from the famous scientific Turek and Hron problem in [1], we demonstrate how fluid structure interaction simulations can be used to time-dependently simulate the strong coupling between a moving fluid and an elastic structure.

**Simulation setup**

The Turek and Hron benchmark is inspired by the well-studied flow around a cylinder and takes basis in a cylinder with an elastic tail placed in a horizontal channel and subjected to a vertical flow. The flow is assumed laminar, incompressible and time-dependent and the solid is assumed compressible, linear elastic and time-dependent. As the magnitude of the structural deformations are significant for the studied problem, the coupling between the structural deformations and the fluid flow is modeled via an interface model and a deformable mesh formulation. The fluid structure interaction simulation uses a second order Newmark time-stepping scheme to model the time-dependent behavior of the finite element formulation of the elastic structure and the finite volume formulation of the fluid flow. For illustrative purposes, the problem is constrained to two-dimensional modelling and laminar flows, however the methodology generalizes to more complex modelling.

**Results**

From the fluid structure interaction simulation the follow results were found. As the fluid enters the transition regime from steady to unsteady, the pressure field and the traction forces of the fluid on the structure becomes asymmetric. Due to the time varying and asymmetric forces and the coupling between the fluid and the structure, the structure begins to oscillate. The deformable mesh formulation stabilizes the shape of the cells and ensures that no remeshing is required during each time-steps. To demonstrate the mesh deformation formulation, we have added a picture of the mesh in the undeformed and a deformed state:

With reference to the time-series of the structural deformations, the pressure field and the velocity field in the figures below, we notice that the structural deformations are large in magnitude compared to the length scales of the fluid flow.

The reaction forces from the fluid on the structure can be used to illustrate the coupling between the fluid and the structure. The reaction forces and the von Mises stresses in the solid has been plotted in the time series below:

The case study serves as an example of a problem, in which it is critical to model the effects between the fluid and the structural deformations. If your company faces problems, where the fluid-structure-interaction effects are important, Aerotak can provide specialist and knowhow to solve the problems.

[1] Turek, Stefan, and Jaroslav Hron. "Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow." Fluid-structure interaction. Springer, Berlin, Heidelberg, 2006. 371-385.