Decomposition of the forces on a body moving in an incompressible fluid
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Abstract
The identification of separate physical features contributing to the force
resultants on a moving body is useful for insight into the associated flow, and for conceptual modelling. A natural approach is to seek a component due to viscosity and an inviscid' remainder. It is also attractive to invoke the well-known decomposition of the velocity field into irrotational and rotational parts, and apportion the force resultants accordingly. Unfortunately, this leads to coupled contributions; the resultants nominally associated with the rotational velocities depend also on the irrotational velocity field. Here, an alternative is presented, in which the inviscid resultants are split into independent
convective' and 'accelerative' components. The former are associated with the pressure field that would arise in an inviscid flow with (instantaneously) the same velocities as the real one, and with the body's velocity parameters --- angular and translational --- unchanging. The latter correspond to the pressure generated when the body accelerates from rest in quiescent fluid with its given rates of change of angular and translational
velocity. They are reminiscent of the classical, `added-mass', force resultants associated with irrotational flow, but differ crucially in applying without restriction. They are also simpler than the developed expressions for the added-mass force and moment. Finally, the force resultants due to viscosity also include a contribution from pressure. Its presence is necessary because the convective and accelerative components alone are insufficient to satisfy the equations governing the pressure field, but its existence does not seem to have been widely recognised.
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1469-7645