Papadopoulos, Dimitrios P; (2000) On the unsteady boundary layer and wake of a flat plate, and modeling water flow near a ship-side. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The work in the thesis is concerned with the unsteady laminar two-dimensional flow of an incompressible fluid, at high Reynolds numbers, in the presence of a moving solid surface which is usually taken to be flat. There are two main aspects, one a numerical and analytical study, and the other on modeling. The unsteady flow past a flat plate is examined first, for the case of an impulsively started aligned plate in a free stream. Numerical solutions are obtained by an apparently novel and simple semi-implicit method, both for the plate boundary layer flow solution, which is found to agree with that based on the Blasius and Rayleigh forms, and for the wake solution beyond the trailing edge including the Goldstein near-wake form. Analysis is also performed to check the method in some detail, the numerical accuracy of the method is investigated, and the method is applied to other types of starting motion of the flat plate. The method is subsequently extended to configurations modeling (in an apparently novel way) water flow induced by a flat vertical ship-side which is undergoing upward and/or downward motions partly submerged in a body of water under air. The model of the water flow in the downward case is based on the thin, inner, unsteady boundary layer produced on the ship-side, which is moving in its own plane, and a thick outer region of potential flow that responds to the small efflux or influx due to the ship-side boundary layer. The air-water interface is treated as a free surface, nearly horizontal at the top of the bulk of the water but nearly vertical beside the ship. The latter part of the free surface adjoins the wake of the ship-side boundary layer, this wake being found to be identical with that for which flow solutions are given earlier in the thesis. The junction between the boundary layer and wake, that is the contact point, typically exhibits no relative slip, while at the junction between the two parts of the free surface a tiny passive region forms. Similar modeling applies to upward motions in principle. The Froude number is taken to be large. The numerical work yields the efflux or displacement function for all finite scaled times and analysis is performed for both small and large times. The potential-flow analysis is with the aim of predicting the behaviour with time of the air-water interfaces both at the top and at the side. The effect of reducing the Froude number is also examined. Further applications are considered, including those of a more general case of an inclined ship-side surface undergoing motion and a rotating, partly submerged, circular cylinder.

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