General solution for unsteady annular flows between concentric cylinders and annular flow-induced instabilities

The aim of this Thesis is to obtain time-accurate solutions of the Navier-Stokes equations for laminar incompressible unsteady flows generated by oscillating boundaries in an annular region made from two concentric cylinders. For this, a time-dependent coordinate transformation is first used to obtain a fixed computational domain. The resulting governing equations in the fixed domain are discretized in real time based on a three-time-level implicit scheme. A pseudo-time integration with artificial compressibility is then used to reduce the resulting coupled discretized equations in delta form to set a decoupled scalar tridiagonal systems.;The method of solution has been applied to various 3-D unsteady flows in annular geometries, as well as to 2-D annular flows. The numerical results obtained are compared with those based on a mean position analysis, without transformation, for small-amplitude oscillation. This comparison shows that the time-dependent coordinate transformation is necessary to obtain accurate solutions for larger-amplitude oscillations.;The mean-position approach has also been applied to the analysis of axially variable annular configurations. The results obtained show more pressure recovery after a diffuser section with 6;A comprehensive experimental study was conducted to validate the theoretical results in the range of laminar flow. The results obtained were in good agreement with the numerical results, specially with those obtained by the time-dependent coordinate transformation. Experiments were also conducted for turbulent flow.;Based on the theoretical models developed, a computational method has been used to study fluid-structure interaction phenomena. It was applied to several cylindrical annular configurations in which one side of the annulus, the outer cylinder, is assumed to be flexibly supported, and thus to be susceptible to flow-induced instabilities. The structural and N-S equations were solved simultaneously by employing the numerical method developed for the unsteady flow and a fourth-order Runge-Kutta scheme for the structural motion. The numerical results thus obtained have predicted the stability of the structure for different annular geometries. The structure having a uniform annular geometry was shown to be more damped, while the annular geometry with a backward facing step is less damped. The study of the structure for a uniform annular geometry in the case of the rocking motion of the outer cylinder predicts an instability in the form of flutter of the outer cylinder.