Reduced Order Modeling for Sensitivity Analysis of the Fluid-Structure Interactions in a Collapsible Tube

Abstract

Fluid-Structure interaction in a collapsible channel with a flexible wall segment which deforms under the fluid dynamic loads arising from the flow within the channel is considered by using a reduced order model based on the method of principal component analysis developed for unsteady aerodynamic pressures and the structural dynamic state variables by using a series of discrete time results. A computational fluid dynamics approach, based on the finite volume solver is used to solve the discretized Navier-Stokes equations. The structural model of the flexible wall is based on the membrane equation and the membrane tension is varied to study the effects of the structural modeling parameters on the instabilities that arise due to fluid-structu re interaction. It is well known in aeroelasticit y, that fluid-structural coupling based on lagging the fluid dynamics code with the structural dynamics solver can produce spurious numerical phenomena. On the other hand, tightly coupled aeroelastic solvers can be difficult to implement due to numerical ill-conditioning. Using a series of discrete time results, a reduced order model is developed for the unsteady aerodynamic pressure and the structural dynamic state variables based on the method of principal component analysis. This reduced order model now serves as a de-coupler for the fluidstructure interaction. The effects of varying the tension and the inertia of the membrane on the unsteady fluid dynamics are investigated using the reduced order model. The principal component analysis captures the fluid dynamic damping at every time instant in the system dynamics and this knowledge is used to detect the onset of instabilities. A regularization technique is also used to improve the conditioning of the matrices involved in the reduced-order fluid-structure interaction model.