Fluid-wall interactions in a deformable system

Abstract

The purpose of this work is the modeling and the analysis of fluid-wall interactions in a deformable cylindrical cavity which has one single orifice for inflow and outflow. The model is used to study the dynamical behavior of a non linear oscillatory coupled system. Indeed, the deformation of the cavity can be large, therefore the fluid contained inside the cavity changes greatly. Our analysis describes the behavior of the system according to its characteristic parameters. A dimensional analysis of the set of coupled equations describing the dynamical behavior of both the incompressible fluid and the cavity wall is performed. We show that such a behavior can be characterized by five dimensionless parameters. The equations are then solved by using the so-called time-staggered scheme which allows to integrate separately the equations describing the structure and the fluid dynamics during each time step. The fluid part is discretized by the finite difference method associated with an Arbitrary Lagrangian Eulerian formulation of the governing fluid dynamics equations and the structure part including the motion of the piston by a Runge-Kutta method. For an harmonic excitation, we show that after a transient phase, the response of the system is both anharmonic and periodic, with a fundamental period equal to that of the excitation. Moreover, we study the respective influence of the wall rigidity, the fluid viscosity and the inertia effects, for different magnitudes of the excitation. Using an approximation of the damping force associated with the viscous effects of the dynamical flow, we complete this study by showing how the system of equations can be decoupled.