MS4.1 - Computational Fluid-structure Interaction

The study of the interaction between waves and porous structures is of great importance in offshore engineering. These are often used to dissipate the energy of incoming waves and protect structures or land. For this reason, with time a few porous models have been implemented in CFD solvers, mostly focused on the simulation of large fixed porous structures. These models represent an alternative to a microscopic representation of the porous region. In fact, often only the macroscopic effects, e.g. the total hydrodynamic force on the structure, are of interest. In these cases, a porous model can be used to model the flow-structure interaction, reducing the computational burden. Currently, in OpenFOAM®, it is only possible to define a static porous region. This derives from the main use of these models. However, it would be useful to allow the definition of dynamic regions. This would, for example, enable the use of porous regions for the study of perforated floating structures and moving porous objects. Generally speaking, in OpenFOAM®, a volumetric porous region is introduced with a similar approach to what is done for many embedded methods. In fact, a set of cells are marked to track the location of a fictitious solid within the fluid mesh. Then, a forcing term is introduced in the momentum equation to simulate the presence of the body. This is the same procedure used in the Immersed Boundary Method (IBM) in its continuous forcing formulation. In this work, a new solver, called porousIbFoam, is developed to solve the Volume-Averaged Reynolds-Average Navier-Stokes (VARANS) equations inside a volumetric porous region using a continuous forcing IBM. Compared to the porous media implemented in OpenFOAM®, this does not require a conformal mesh and, in principle, it allows the definition of dynamic porous regions. The use of a simple Cartesian mesh represents an important advantage also when dealing with complex geometries as it eliminates any meshing problem. The solver is tested by simulating a static porous cylinder in a 2-dimensional constant flow at both Re=40 and Re=100. Both quantitative and qualitative results are promising. More tests, including the interaction with waves, are currently being performed. Because of the embedded formulation, the standard OpenFOAM® postprocessing functions cannot always be used. Therefore, an alternative way to compute the forces on the porous surface is currently under development. So far, the solver presents a speedup value of 1.88 compared to traditional conformal mesh solvers.

Fluid-structure interaction of thin, flexible structures is extremely common in nature and engineering, from leaf fluttering to parachute inflation. Numerical simulation of those systems is of interest in many fields of engineering but is challenging for a number of reasons; the low bending rigidity of the structure and the usually small thickness result in very large deformations. Additionally, the added mass effect can be significant and lead to inherent difficulties for partitioned fluid-structure interaction simulations. This paper presents a general and robust method for fluid-structure interaction of thin structures undergoing large displacement and large added mass effects by coupling an immersed boundary method with a finite element shell model. Special care is taken in the immersed boundary method to ensure the pressure boundary condition is enforced for deforming bodies via a variable coefficient Poisson's equation. The method can accurately simulate the fluid velocity and pressure induced by dynamic bodies undergoing large displacements using a computationally efficient pressure projection finite volume solver. The structural solver can be applied to bending and membrane-related problems, making our partitioned solver very general. To simulate problems under large added mass effects with our partitioned approach, we use a strongly coupled algorithm with an iterative Quasi-Newton method to determine the fluid-structure balance at the interface. We avoid the expensive computation of the inverse Jacobian within this root-finding iteration by constructing it from input-output pairs. These pairs are formed using the interface displacement and traction vector from the previous time steps. The solution to this under-determined system is achieved through a least square approach. The resulting Interface Quasi Newton from an Inverse Least Square problem (IQN ILS) scheme is efficient and can be applied to complex problems where the large computational cost of computing the inverse Jacobian is avoided. To demonstrate the efficiency of this coupled solver, we first simulated the quasi-steady flow around a membrane airfoil, showing near second-order convergence in space of our algorithm and very good agreement with the reference data. We then demonstrate the stability and accuracy of our solver for a flapping flag with vanishing bending stiffness. Flapping frequency and amplitude agree well with the literature. With an inverted flag, we then show that the solver is efficient and accurate under large added mass effects, with excellent agreement with the different flapping modes observed in the literature and their transition regions. Finally, we apply our coupled solver to the flapping of a flexible swimmer in a quiescent flow. We replicate experiments where a tapered flexible foil undergoes pure heave, applied to its leading edge with the trailing edge free to oscillate. The system's flexibility results in propulsion for a range of frequencies, and we compare it to the experimental findings. We perform both 2 and 3-dimensional simulations of the system. We show the correlation between the trailing edge flapping amplitude and propulsive efficiency. Finally, we use modal decomposition to distinguish between various structural responses at various frequencies.