LINEARIZED THEORY OF THREE-DIMENSIONAL CAVITY FLOW WITH VENTILATION TO THE FREE SURFACE.
CONTROL DATA CORP MELVILLE NY TRG DIV
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A linearized theory is presented of three-dimensional cavity flow past a vertical surface-piercing strut, the cavity being vented to the free surface. The linearization stems from the assumption that both the strut and the cavity to its rear are sufficiently thin for their effect on the flow to be describable in terms of thin-body theory. Accordingly, the linearized disturbance potential is represented by a set of sources - with density function proportional to some thinness parameter -distributed over a domain in the common vertical longitudinal midplane of the strut and cavity. Both the shape of this domain and the source-density function are only partially specified and it is their simultaneous determination that constitutes the central problem of the theory. Mathematically, this problem is equivalent to the solution of a certain two-dimensional integral equation, subject to two side conditions. The linearized formulation indicates that in the case of thin struts whose chord-length and draft are of the same order of magnitude, any flow-speed high enough for the strut to be vented down to its full depth is also high enough for the linearized disturbance potential to satisfy the infinite-speed linearized free-surface condition with good approximation.
- Fluid Mechanics