# Investigation of Fluid-Structure Interaction Induced Bending for Elastic Flaps in a Cross Flow
## 1 Introduction
Considering a flexible plate as one of the test examples, the free-end deflection and drag coefficients measurements for Reynolds numbers ranging from \(100\)-\(1600\) with and without the effect of gravity and buoyancy forces are presented. Initially, the results of the baseline case with experimental data [29] are compared and then new simulations are offered for future benchmark cases. Moreover, the plate test case is used as a model to investigate the dynamic interaction of aquatic plants. The method overall leads to a numerical stability for all test cases. The dynamic changes in the structure could possibly affect many aspects of fluid forces and present interesting fluid performance. Therefore, it is an important aspect for multiphase flow industrial applications. To compute such problems, tip-displacement of a rubber beam in a two-phase flow of air and oil was examined using a two-way coupled FSI [30]. A benchmark case [31] was simulated and previously published data of simulations and experiments were compared in terms of beam tip-deflection. The difference between 2D and 3D simulations has been clearly explained as well. A scheme that has treated the deflection line of single and tandem beam configurations is presented byxtmann et al. [32]. It is attained by interacting both experiments and direct numerical simulations (DNS) for Reynolds numbers ranging from \(1\)-\(60\) in a viscous fluid. Bending is calculated via beam bending theory. Bending lines of simulations and experiments demonstrate a good agreement for both single and tandem arrangements. A prediction model for cross flow velocity is offered. Moreover, local drag coefficient along pillar is computed and an empirical model based on drag coefficient is tested and proposed. Furthermore, a two-way coupled FSI study for different rows of flexible flaps is conducted to investigate the wavering behavior at the tip of flaps and development of vortices in the gap among the flaps. Experiments have been performed for water and glycerin against the silicon rubber flaps, reaching the maximum Reynolds number of \(120\), and the resulting tip-deflection of flaps is compared experimentally and numerically [5]. Investigating transient directional deformations of flexible obstacles by means of different numerical algorithms has been a subject of various studies involving the relevance of the extended arbitrary Langrangian Eulerian (ALE) method [33] and monolithic solvers [34; 35]. The test problemspresented [33] can be used as a benchmark for the formulation of numerical problems involving 2D FSI with immersed structures that have large displacements. While 2D benchmark cases, free-surface flows and test cases of an elastic obstacle and plate have been presented for monolithic approaches and validated with other numerical methods [34; 35]. Similarly, for the analysis of hemodynamic problems, a new and more sophisticated computational formulation named immersed structural potential method (ISPM), based on the original IBM, is presented. The novel method accounts for the computation of FSI force field at the fluid mesh and description of cardiovascular tissue scheme by viscoelastic fiber-reinforced constitutive models. A new time-integration method is also introduced for the computation of a deformation gradient tensor. Three advancement cases of deformable cylinders and flapping membranes are presented. The study is applicable for highly complex FSI problems incorporating large deformations under pulsating flows and sinking and floating rigid bodies [36]. To describe the deflection of flaps and moving boundaries, the fluid- solid interface-tracking/interface-capturing technique (FSITICT) is applied to the FSI problem with ALE interface tracking and Eulerian interface tracking. The method is demonstrated by test FSI cases. First, test computations are performed for two flapping membranes and the second test case is composed of one flapping membrane and a movable, elastic arterial-structure.