The starting mechanism of wave-induced flow through a sharp-edged orifice

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Abstract
Following weak plane shock diffraction at a knife-edge situated in a duct, a two-dimensional vortex sheet springs from the salient edge. The method of ‘vortex discretization’ is used, in conjunction with a Schwarz-Christoffel transformation, to develop a two-dimensional potential model for this constrained form of vortex generation. The analysis is independent of empirical parameters and describes, qualitatively, the pattern of streamlines through the orifice. Flow-visualization photographs are presented which illustrate the spiral shape of the starting vortex. Although of a limited nature, quantitative experimental vortex growth rates have been obtained and are compared with initial growth rates predicted theoretically. The results are discussed together with other aspects of the problem, including the limitations of the theory. An extension of vortex discretization is developed whereby the pressure distribution remote from the vortex sheet can be calculated. The combination of flow separation and the associated static wall pressure distribution gives theoretical insight into the mechanism of flow through an orifice.

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