Modeling and simulations for fluid and rotating structure interactions

In this paper, we study a dynamic fluid-structure interaction (FSI) model for an elastic structure immersed and spinning in the fluid. To describe the motion of a rotating elastic structure, we develop a linear constitutive model, that is suitable for the application of the arbitrary Lagrangian-Eulerian (ALE) method in FSI simulations. Additionally, a new ALE mapping method is designed to generate the moving fluid mesh while the deformable structure spins in a non-axisymmetric fluid channel. The structure velocity is adopted as the principle unknown to form a monolithic saddle-point system together with fluid velocity and pressure. Using the mixed finite element method and Newton's linearization, we discretize the nonlinear saddle-point system, and prove that the discrete saddle-point system is well-posed. The developed methodology is applied to a self-defined elastic structure and a realistic hydro-turbine under a prescribed angular velocity. Numerical validation is also conducted to demonstrate the accuracy of the models and the numerical methods.