Sound from a propeller at angle of attack: a new theoretical viewpoint

Accurate prediction of propeller noise is required to satisfy airplane noise certification regulations and environmental concerns. Propellers typically operate with their shafts at some angle to the flight direction but this factor has been ignored in noise calculations until recently. In this paper, far field noise formulas are devel­oped by applying the free-space Green’s function for the convected wave equation to loading sources on a propeller whose shaft may be at an angle to the flight direction. The resulting inflow angularity influences noise in two distinct ways. First, loading is modulated causing generation of more efficient radiation modes. Second, the radiation modes themselves are modified, causing a further efficiency increase. The first effect is well known; the second effect has only recently been recognized and is the focus of this paper. The noise formulas exhibit the same spinning mode behaviour seen in previous analyses but with higher levels radiated into the crossflow. Since the modes are no longer purely spinning, the term ‘wobbling mode’ has been coined to describe their behaviour. This paper summarizes the earlier literature on this subject, explores the radiation formulas in detail, and presents some calculations that illustrate the magnitude of the angular inflow effect. It is shown that the inflow angle influences modal efficiency only through changing the Mach number of the source relative to the observer.