Time-marching analysis of fluid-coupled systems with large added mass

Time-marching stability analysis of fluid-structure interaction problems is considered in this paper. The Navier- Stokes equations and the equation of motion of the structure are integrated simultaneously in time in a coupled manner to assess structural dynamics and thereby the possibility for flutter and/or divergence. A method developed by the authors for the incompressible Navier-Stokes equations consists of combining a Runge-Kutta time integration for the structure with a three-point backward time discretization for the fluid. Problems have been encountered with that method, however, when the fluid-added mass is larger than the structural mass, leading to numerical instability in the integration scheme. A cure to remedy these difficulties is proposed in this paper. It consists of introducing estimates for the added mass, obtained, for example, from potential flow calculations, into the structural equation so as to cancel the fluid inertial forces. To illustrate the possibilities of the method, analysis of the free vibrations of two coaxial cylinders coupled by annular fluid is performed.