A new analytical approach for modelling the added mass and hydrodynamic interaction of two cylinders subjected to large motions in a potential stagnant fluid

摘要

A potential theory is presented for the problem of two moving cylinders, withpossibly different radii, large motions, immersed in an perfect stagnant fluid.We show that the fluid force is the superposition of an added mass term,related to the time variations of the potential, and a quadratic term relatedto its spatial variations. We provide new simple and exact analyticalexpressions for the fluid added mass coefficients, in which the effect of theconfinement is made explicit. The self-added mass (resp. cross-added mass) isshown to decrease (resp. increase) with the separation distance and increase(resp. decreases) with the radius ratio. We then consider the case in which onecylinder translates along the line joining the centers with a constant speed.We show that the two cylinders are repelled from each other, with a force thatdiverges to infinity at impact. We extend our approach to the case in which onecylinder is imposed a sinusoidal vibration. We show that the force on thestationnary cylinder and the vibration displacement have opposite (resp.identical) axial (resp. transverse) directions. For large vibration amplitudes,this force is strongly altered by the nonlinear effects induced by the spatialvariations of the potential. The force on the vibrating cylinder is in phasewith the imposed displacement and is mainly driven by the added mass term. Theresults of this paper are of particular interest for engineers who need to grabthe essential features associated to the vibration of a solid body in a stillfluid.