# Investigation of Fluid-Structure Interaction Induced Bending for Elastic Flaps in a Cross Flow
## 2 Material and Method
### Fluid equations
#### 2.2.2 Computational Model  
The fluid domain is modeled by ANSYS-FLUENT for flaps immersed in a glycerin environment as depicted in Figure 2c. Because of the low Reynolds number range, a laminar fluid model is chosen. For an effective simulation in comparison to the experiments, a fixed coordinate system is used. The constant flow velocity as'velocity inlet' is given for the input conditions, plate and flap are assigned as walls with a 'no slip' boundary condition while the top walls, remaining bottom parts and sides are assigned as'slip walls' and 'pressure outlet' is defined for 0 Pa at the outlet conditions. A non-dimensional Reynolds number Re is defined as Re = _vw/v_ based on the flow velocity \(v\), flap width \(w\) and fluid kinematic viscosity \(v\). The inlet flow velocities, \(v\), ranging from 0.125-0.5 m/sec are given as input values based on the identified Reynolds number. The engineering parameters used for the computations are listed in Table 1. Due to subsonic incompressible flow field, pressure based solver with coupled scheme is used and second order implicit transient formulation is employed for modeling the unsteady flow. Figure 2: (**a**) Flap configuration; (**b**) Bending definitions; (**c**) Computational domain. **Five mm thick flap:**  
Initially, simulations were performed for a flap of 5 mm thickness. To consider mesh independence, three different meshes were tested to explore the effect of mesh resolution on a flap bending. This mesh resolution was needed to compensate for the effect of computational time such as the computational time increasing after coupling the computational fluid dynamics (CFD) and FEA models [41]. Bending line convergence for different meshes was attained with coarser to finer: mesh 1: 52,486 elements, mesh 2: 101,641 elements and mesh 3: 137,693 elements. So, mesh 3 was chosen for the final solution, although this number of elements may vary since flap deforms and dynamic meshing takes place. Bending convergence is shown in Figure 3 whereas different meshes before and after flap deformations are depicted in Figure 4. Moreover, the difference between results obtained with mesh 2 and 3 is small, showing that grid convergence is attained. The difference between mesh 2 and 3 in terms of bending x and height y is 0.53% and 1.1% respectively. As the large fluid domain is present, it is only desirable to have high mesh resolution around the flap and the dynamic mesh region in order to have influence of pressure and deformation gradient. For a 3D dynamic mesh domain in Fluent, a structured mesh cannot be applied [41]. For that reason, a tetrahedron unstructured mesh was chosen around the flap, though the rest of the fluid domain was designed as a structured mesh. To simulate the flap movement, both smoothing and remeshing methods were used in the dynamic mesh region such that the displacement of the flap was large compared to the grid size. Dynamic meshing is needed for both surface and volume mesh in 3D cases and it is necessary to retain element quality for both surface and volume meshes otherwise simulations may result in errors and computational differences [41]. Considering remeshing parameters, mesh scale information was followed and a minimum cell size of \(6\times 10^{-4}\) m and a maximum cell size of 0.04 m were used as input values. In addition, the interface is allocated as'system coupling' in dynamic mesh zones under dynamic mesh settings with a cell thickness of 0.6 mm along the wall. To provide a balance \begin{table}
\begin{tabular}{c c c} \hline \hline
**Fluid-Glycerin** & Density, \(\rho^{\text{f}}\) & 1220 kg/m\({}^{3}\) \\  & Dynamic viscosity, \(\mu\) & 1 kg/m s \\ \hline \multirow{6}{*}{**Structure-Flap**} & Length, L & 100 mm \\  & Width, w & 20 mm \\  & Thickness, b & 5 mm, 10 mm \\ \cline{1-1}  & Density, \(\rho^{\text{s}}\) & 1030 kg/m\({}^{3}\) \\ \cline{1-1}  & Young’s modulus, E & 1.23 MPa \\ \cline{1-1}  & Poisons ratio, \(\
u\) & 0.3 \\ \cline{1-1}  & Shear modulus, G & 0.473 MPa \\ \hline \hline \end{tabular}
\end{table}