The study here is concerned with a thin solid body passing through a boundary layer or channel flow and interacting with the flow. Relevant new features from modelling, analysis and computation are presented along with comparisons. Three scenarios of such fluid-body interactive evolution in two-dimensional settings are considered in turn, namely a long body translating upstream or downstream, a long body with little or no translation and a short body with or without translation. The main progress and findings concern predictions of the time taken by the body to traverse the flow and impact upon the underlying wall, the delicate behaviour at the onset of impact, the dependence on parameters such as the initial conditions and the mass and shape of the body, and the influence of streamwise translation of the body in the surrounding fluid flow.
A description is given of recent progress in the understanding of mechanisms in fluid-body interactions where the motion of a body and the motion of the surrounding fluid affect each other substantially. The mathematical modelling of such unsteady interactions is for internal channel and external near-wall flows in two spatial dimensions and time. The emphasis throughout is on analytical developments with accompanying reduced computation. The successive aspects studied here are interactions and impacts in inviscid flows, skimming and sinking, the lift-off, fly-away or bouncing of a body, and viscous effects including especially the interplay between viscous and inviscid contributions. The main findings are concerned with physical and mechanical insights into impact times, lift-off criteria, the borders between impact and fly-away, the principal parameters and their ranges and the influences from body shape and mass.
The study concerns a slender, heavy body moving with streamwise velocity in a boundary layer. Modelling assumptions on body size reduce the governing equations for the body motion to a pair of nonlinear integro-differential equations (IDEs) which displays a wide range of distinguished behaviours, including eventual collision with the wall (‘crash’), escape to infinity (‘fly away’) and repeatedly travelling far from the wall and back again without ever colliding or escaping (‘bouncing’). The paper gives a survey of the variety of behaviour, as well as asymptotic analysis and insight into each category of fluid/body interaction and the conditions under which crash, fly away and bouncing occur.
As an aircraft flies through cloud at temperatures below freezing, it encounters ice particles and supercooled droplets, which results in the accretion of ice onto its surfaces and hence deformation of its aerodynamic shape. This can, in worst cases, cause series accidents. Here, we focus on tackling the common situation where there is a thin layer of water on the aircraft surface and the particles are similarly thin such as to be able to interact with the water layer. Three-way interaction occurs between air, water, and body motion: under suitable assumptions (including that the Reynolds and Froude numbers are large, and that the body is much denser than the air), the model allows the shape of the layer interface and pressure profile beneath the body to be calculated for a given body position. Simultaneously, this in turn allows the forces on the body to be calculated and hence the motion of the particle to be computed in full. The result is a wide range of possible motions of the particle, including both “sink” cases (the particle enters the water and becomes submerged) and “skim” cases (where the particle is launched back off the surface of the water following contact). The latter cases have analogy with traditional “stone skimming/skipping” games. Repeated skims and significant wakes are accommodated rationally.
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