Added Mass and Damping for Cylinder Vibrations Within a Confined Fluid Using Deforming Finite Elements

Abstract

Added mass and fluid damping coefficients for vibrations of an inner cylinder that is enclosed by a concentric outer cylinder are determined by finite element analysis of the unsteady, laminar, incompressible flow in the annulus. Continuously deforming space-time finite elements are used to track the moving cylinder and the changing shape of the space domain. For small cylinder vibration amplitudes, the present results agree well with the work of earlier investigators who solved the linearized Navier-Stokes equations on a fixed mesh. Fluid damping coefficients are shown to increase with vibration amplitude. Added mass coefficients may either increase or decrease with increasing vibration amplitude.