École Nationale Supérieure de
Techniques Avancées

Résumé

A new theoretical approach is presented for the case of small oscillation of two cylinders immersed in a viscous stagnant fluid to obtain the fluid forces imposed to the cylinders and the f luid added coefficients. The problem is represented in a bipolar system coordinates and an approach based on the Helmholtz decomposition is utilized. To solve the Helmholtz equation, it is proposed a solution based on a perturbation series and an asymptotic development. This study focus on the results obtained for the order 0 development. The forces imposed to the bodies is shown to be a linear combination of the cylinders accelerations and velocities, through the fluid added coefficients. To validate the results obtained, it is considered a study case of two equal size cylinders, with one of them stationary while the other performs harmonic movements. It is shown that the as the Stokes number and separation distance increases, the f luid force decreases and the fluid self aded coefficients decreases, tending to the case of an isolated cylinder immersed in a perfect fluid. The cross added coefficients increases with Stokes number and separation distance. The fluid added coefficients vary with Sk−1/2. The theoretical approach utilized in this work offers a simple method to consider the influence of the viscous and confinement effects in moving cylinders immersed in a fluid. The results of the theoretical approach utilized in this paper is presented and corroborated with numerical simulation.