FSI Simulation Using a Membrane Model: Inflation of Balloons and Flow Past Sails

Interaction of thin membrane structures with an incompressible Newtonian fluid is numerically studied. A partitioned approach is utilized for solving the coupled fluid-structure equations. Material of the structure is assumed to follow the St. Venant-Kirchhoff’s constitutive law. A simple, robust model for calculating the deformation of the membrane structure, proposed by Taylor et al. (Finite Element Analysis of Membrane Structures. Springer, The Netherlands, pp. 47–68, 2005, [7]), is utilized. Fluid flow is calculated using the SUPG/PSPG stabilized Petrov-Galerkin space-time finite element method. Fluid mesh is updated at each time step, to take into account the deformation of the domain, using pseudo-elastic mesh moving technique. The meshes for the fluid and the membrane have coincident nodes. This allows direct transfer of tractions and velocity between the fluid and the structure. First, inflation/deflation of a spherical balloon is considered for different values of elasticity and density ratio. The shape of an inflated balloon changes from nearly spherical to an elongated one as the value of elasticity is increased. The density ratio is observed to have negligible effect on the inflation rate. Uniform flow past a square piece of initially flat membrane with fixed edges is also studied. Reynolds number based on the edge length is 150. The membrane oscillations achieve a limit cycle in which the deformation of the membrane is similar to the first eigenmode of the structure.