This paper describes two accurate Flow-Induced Vibration (FIV) methods used to analyze the induced vibrations caused by the laminar fluid flows in uniform annular geometries. In both methods, the uniform annuli which are composed of two concentric cylinders are considered. The outer cylinder is set on translational oscillation without or with a predetermined mode of vibration and with a known initial velocity. In the first method, the small amplitude motion of the outer cylinder is used to analyze the problem considered by using the direct coupling of the fluid and structure through the accurate simultaneous solution of the Navier-Stokes and structural equations. In the computational domain, the problem has been solved using an accurate time-integration method based on a finite-difference formulation and primitive variables. In this method, the real-time discretization of the Navier-Stokes equations for unsteady incompressible flows is based on a three-time-level implicit scheme. A pseudo-time integration with artificial compressibility is then introduced to advance the solution to a new real-time level. An implicit Euler scheme is used for the pseudo-time discretization, and the finite-difference spatial discretization is based on a stretched staggered grid. In the second method, the Reynolds-averaged Navier-Stokes equations are used to represent the unsteady flow in a nonlinear time-accurate fashion. In this case, the structural model is based on a linear modal model. The fluid mesh is moved at each time-step according to the structural motion, so that the changes in fluid-dynamic damping and flow unsteadiness can be accommodated. Based on the second approach, a code named SURF was generated to handle the solution from the steady state solution till the unsteady one which is in the form of vibratory motion of the outer cylinder. In this way the stability analyses can be performed for the structure by using several modes of vibration of the structure vis-a`-vis to the first method in which only translational motion of the outer cylinder is taken into account. The stability of the outer cylinder assessed by two methods in terms of the damped oscillation of the cylinder represents the decay in the amplitudes of vibration due to the fluid added damping. The results of this research can be used for the FIV and FSI analyses of the annular flows which could be found in many industries.

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