Generalized lift force model under vortex shedding

Abstract

This paper proposes a generalized model for vortex shedding around a static cylinder. This model is a first step to bridge the gap between two existing families of Vortex Induced Vibration (VIV) models , namely (1) stochastic spectral models and (2) wake-oscillator models with coupled fluid and structural equations. The first family is experimentally-based while the models of the second family typically rely on theoretical and phenomenological concepts. These models use a Van der Pol, Rayleigh or a combination of both oscillators for the lift equation. The proposed model generalizes these models by combining all third degree terms in the case of a static model, i.e. by considering the equation of the fluid oscillator only. It is possible to enrich existing models with a more complex parametric model because its parameters are identified from experimental data. A second specificity of the proposed model stems from the observation that, for a static cylinder in low turbulence flow, the envelope of the measured lift force is not perfectly mono-harmonic, nor deterministic. Turbulence in the wake is expected to create fluctuations in the lift envelope. In the proposed model, stochasticity is consequently introduced to reproduce these fluctuations. It is based as an additive exogenous noise as an input to the generalized shedding model, using a Von Karman spectrum. Its coefficients are adjusted so that the model reproduces the probability density function of the measured lift envelope (and its power spectral density). The methodology is applied to Wind Tunnel data of a static circular cylinder in subcritical and postcritical regimes. This set of data is used to identify the coefficients of non-linear terms and Von Karman spectrum. The lift fluctuation coefficient generated with the model matches results available in the literature for the considered regimes. This work focuses on a methodology to obtain a generalized vortex shedding model from experimental data measured on a static body. It can be applied to other cylinder cross-sections or even extended to cylinders arranged in tandem.