Air Flow and Particle Trajectories around Aircraft Fuselages. I: Theory

Abstract
A potential-flow sink-source technique is used to model the flows around fuselage shapes. It is shown that the flow in any plane can be approximated reasonably well using an axisymmetric model of similar shape and that at a few fuselage radii from the nose the flow is determined principally by the size of the fuselage radius. Departures from the free-stream velocity are typically less than 10% and vary as the inverse square of the scaled distance from the nose. Analyses of water drop trajectories around three different aircraft shapes show that two of the more important features of the trajectories, the width of the shadow zone and the concentration enhancement factors, can be described quite generally in terms of a scaled fuselage radius and a parameter similar to the Stokes number. Thus the maximum width of the shadow zone is shown to be about one-fifth of the fuselage radius and occurs for a combination of particle size and aircraft speed for which the modified Stokes parameter has a value of about 6.

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