A Semipotential Flow Theory for the Dynamics of Cylinder Arrays in Cross Flow

Abstract

This paper presents a semianalytical model, involving the superposition of the empirically determined cross flow about a cylinder in an array and the analytically determined vibration-induced flow field in still fluid, for the purpose of analyzing the stability of cylinder arrays in cross flow and predicting the threshold of fluidelastic instability. The flow field is divided into two regions: a viscous bubble of separated flow, and an inviscid, sinuous duct-flow region elsewhere. The only empirical input required by the model in its simplest form is the pressure distribution about a cylinder in the array. The results obtained are in reasonably good accord with experimental data, only for low values of the mass-damping parameter (e.g., for liquid flows), where fluidelastic instability is predominantly caused by negative fluid-dynamic damping terms. For high mass-damping parameters (e.g., for gaseous flows), where fluidelastic instability is evidently controlled by fluid-dynamic stiffness terms, the model greatly overestimates the threshold of fluidelastic instability. However, once measured fluid-dynamic stiffness terms are included in the model, agreement with experimental data is much improved, yielding the threshold flow velocities for fluidelastic instability to within a factor of 2 or better.