A Nonlinear ODE System for the Unsteady Hydrodynamic Force -- A New Approach

TL;DR

This paper introduces a nonlinear ODE system as a reduced-order model to accurately predict the unsteady hydrodynamic force on a cylinder, capturing the complete force history without extensive simulations.

Contribution

The paper presents a novel two-ODE model that considers the total hydrodynamic force and relates model parameters to Reynolds number for efficient force prediction.

Findings

Model accurately predicts force histories

Parameters relate to Reynolds number

Effective within Reynolds range 100-500

Abstract

We propose a reduced-order model for the instantaneous hydrodynamic force on a cylinder. The model consists of a system of two ordinary differential equations (ODEs), which can be integrated in time to yield very accurate histories of the resultant force and its direction. In contrast to several existing models, the proposed model considers the actual (total) hydrodynamic force rather than its perpendicular or parallel projection (the lift and drag), and captures the complete force rather than the oscillatory part only. We study and provide descriptions of the relationship between the model parameters, evaluated utilizing results from numerical simulations, and the Reynolds number so that the model can be used at any arbitrary value within the considered range of 100 to 500 to provide accurate representation of the force without the need to perform time-consuming simulations and solving the partial differential equations (PDEs) governing the flow field.