Dynamics of coaxial cylinders in laminar annular flow by simultaneous integration of the Navier-Stokes and structural equations

A computational method has been developed to study fluid-structure interaction problems. It has been applied to a few cylindrical annular configurations containing incompressible laminar flow; one side of the annulus, either the centre-body or the outer containing duct, is supposed to be flexibly supported, and thus to be susceptible to flow-induced instabilities at sufficiently high flow velocities. The dynamical analysis is performed in the time rather than the frequency domain. The structure is perturbed from its equilibrium postion by imposing an initial displacement shape; it is then released, and the evolution of the motion is tracked in time while simultaneously solving the structural and Navier-Stokes equations, employing a second-order Runge-Kutta scheme for the structure and a three-point backward implicit time integration for the fluid. Numerical simulations of the free vibrations of a cylinder delimiting uniform or stepped annular flow regions have put in evidence the existence, in some cases, of a divergence-type instability. Coefficients of added stiffness have also been computed.