Acoustic theory of the many-bladed contra-rotating propeller: physics of the wake interaction noise critical sources

Abstract

In the theory of interaction noise from contra-rotating propellers with many blades, the usual far-field radiation formulae can be re-cast as a double integral, over a source surface, which can be evaluated asymptotically solely in terms of the contributions from critical points. The paper shows that these critical points have a particularly interesting physical meaning. They relate to locations on an event line, running between hub and tip, that represent the locus of the wake–blade interactions at a fixed point in time. The event line rotates at the speed of the spinning interaction tone but does not coincide with the radial variation in either the wake location or the rear blade leading edge. At the precise critical locations on the event line, it is shown that the Mach number of the event line is unity in the direction of the observer (the sonic condition) and the tangent to the event line – at a fixed time – is normal to a line drawn between it and the observer (the normal-edge condition). The zero-mode case is also considered, for which we show that, even though the event line rotates at infinite speed, there can still exist locations that satisfy the sonic and normal-edge conditions. The paper also discusses the physical meaning of the lower-order boundary solutions from the hub and tip.