Modelling unsteady self-excited wind force on slender prisms in a turbulent flow

A mathematical model to quantify the unsteady self-excited forces (USEFs) acting on a slender prism was developed, to address the shortcomings of the classical quasi-steady theory employed to predict the galloping instability of slender prisms. The unsteady aerodynamic force and galloping response of a prism were measured from a hybrid aeroelastic-pressure balance (HAPB) that can synchronously observe unsteady pressure and aeroelastic response. It was found that the galloping response predicted by the unsteady aerodynamic force is in close agreement with the experimental result whereas the quasi-steady theory cannot predict the galloping instability. According to an energy equivalent method, the unsteady aerodynamic force was quantitatively decomposed into three components: an aerodynamic damping force component, an aerodynamic stiffness force component and a residual force (buffeting force) component. Subsequently, a nonlinear mathematical model for the USEF which is a 1st-order polynomial function representing the aerodynamic damping and stiffness force components, was established. The results indicated that the 1st-order model was effective in predicting the galloping response of the prism. It was also demonstrated that the model can be used to predict the galloping instability of prisms with different mass-damping ratios.