Abstract
To calculate the energy costs of swimming or flying, it is crucial to evaluate the drag force originating from skin friction. This topic seems not to have received a definite answer, given the difficulty in measuring accurately the friction drag along objects in movement. The incoming flow along a flat plate in a flapping normal motion has been considered, as limit case of a yawed cylinder in uniform flow, and applying the laminar boundary layer assumption it is demonstrated that the longitudinal drag scales as the square root of the normal velocity component. This lends credit to the assumption that a swimming-like motion may induce a drag increase because of the compression of the boundary layer, which is known as the 'Bone-Lighthill boundary-layer thinning hypothesis'. The boundary-layer model however cannot predict the genuine three-dimensional flow dynamics and in particular the friction at the leeward side of the plate. A multi-domain, parallel, compact finite-differences Navier-Stokes solution procedure is considered, capable of solving the full problem. The time-dependent flow dynamics is analysed and the general trends predicted by the simplified model are confirmed, with however differences in the magnitude of the friction coefficient. A tentative skin friction formula is proposed for flow states along a plate moving at steady as well as periodic normal velocities.
Highlights
There has been a considerable amount of studies on the energetics of swimming over the past decades and in particular on drag reduction mechanisms
The incoming flow along a flat plate in a flapping normal motion has been considered, as limit case of a yawed cylinder in uniform flow, and applying the laminar boundary layer assumption it is demonstrated that the longitudinal drag scales as the square root of the normal velocity component
X ≤ 36, that is discarding the portions of the plate near the leading and trailing edges, provides drag values of 0.34 and 0.58 for the motionless plate and moving plate, respectively, that is a drag increase the skin of 70% friction for the plate with the periodic normal one would get with formula (5.1)
Summary
Particular on drag reduction mechanisms (for a fairly recent review, see [1]). While many investigations focused on the drag reduction mechanisms employed by aquatic animals, Lighthill. The plate with finite span is a limit case of this model problem and the scaling of the boundary-layer thinning hypothesis is retrieved This skin friction enhancement can be understood as resulting from the acceleration of the fluid particles, and in [15] a two-dimensional model problem which takes into account this effect has been proposed, by confining the flow between the lower moving plate and a free upper boundary at height s/2. The numerical solution procedure must be capable of handling the plate’s edges, which are singularities for the flow field, and the numerical method has to be sufficiently accurate as to provide reliable skin friction values This is achieved by using a multi-domain approach together with a high-order compact finitedifferences discretization, and full three-dimensional simulations have been undertaken in this work for different uniform plate velocities.
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