Numerical simulation of viscous flow interaction with an elastic membrane

A numerical fluid-structure interaction model is developed for the analysis of viscous flow over elastic membrane structures. The Navier-Stokes equations are discretized on a moving body-fitted unstructured triangular grid using the finite volume method, taking into account grid non-orthogonality, and implementing the SIMPLE algorithm for pressure solution, power law implicit differencing and Rhie-Chow explicit mass flux interpolations. The membrane is discretized as a set of links that coincide with a subset of the fluid mesh edges. A new model is introduced to distribute local and global elastic effects to aid stability of the structure model and damping effects are also included. A pseudo-structural approach using a balance of mesh edge spring tensions and cell internal pressures controls the motion of fluid mesh nodes based on the displacements of the membrane. Following initial validation, the model is applied to the case of a two-dimensional membrane pinned at both ends at an angle of attack of 4° to the oncoming flow, at a Reynolds number based on the chord length of 4 × 103. A series of tests on membranes of different elastic stiffness investigates their unsteady movements over time. The membranes of higher elastic stiffness adopt a stable equilibrium shape, while the membrane of lowest elastic stiffness demonstrates unstable interactions between its inflated shape and the resulting unsteady wake. These unstable effects are shown to be significantly magnified by the flexible nature of the membrane compared with a rigid surface of the same average shape.