A Study on Annular Leakage-Flow-Induced Vibrations

A flexible rod in annular leakage flow: Influence of turbulence and equilibrium offset, and analysis of instability mechanisms

“…The mentioned studies of Inada (1999), Inada and Hayama (2000), Inada (2004), Li et al (2002), Fujita and Shintani (2001), Fujita et al (2004), Kaneko et al (2000), and Wu and Kaneko (2005) are all based on the (plane, 2-D) leakageflow model of Inada and Hayama (1990). This model uses flow rates rather than flow velocities, an approach that simplifies the underlying Navier-Stokes equations in a very efficient way.…”

“…But in the axisymmetric problems studied by Li et al (2002), Fujita and Shintani (2001), and Fujita et al (2004) the models are restricted to laminar flow only. Most industrial flows of Newtonian fluids (like air and water) are however turbulent, and it is obviously not too reassuring to apply a laminar flow model to highly turbulent flows.…”

“…Paı¨doussis's (2004) monograph contains a comprehensive (200 pages) and wide-ranging review of the entire subject. An example of a recent class (i) study is Li et al (2002) who investigated the stability of a flexibly mounted rigid cylinder in a rigid outer cylinder, allowing for offset (from the axis of the outer cylinder) of the inner cylinders equilibrium. The problem studied in the present work belongs to class (ii).…”

“…These equations are discretized using the Galerkin finite element method (in the form sometimes called the Bubnov-Galerkin method (Cook et al, 1989)). It is worthwhile noting that the Galerkin finite element method is completely equivalent to the 'classical' Galerkin weighted residual method (based on global expansion functions), and the latter method could just as well have been used in the Li et al (2002) use a collocation method to determine both the axial and the circumferential flow rate perturbation. Their approach could also have been applied to the present problem including a flexible rod; we think, however, that the Galerkin finite element-based approach of this paper is simpler.…”

“…The mathematical models developed by Li, Kaneko, andHayama in 2002 andShintani in 2001 are bridged and extended, to account for a flexible rod with equilibrium offset (eccentricity) in laminar or turbulent leakage flow. Stability characteristics are analyzed numerically for a variety of configurations.…”