On the use of the method of matched asymptotic expansions in propeller aerodynamics and acoustics

Abstract

The applicability of the method of matched asymptotic expansions to both propeller aerodynamics and acoustics is investigated. The method is applied to a propeller with blades of high aspect ratio, in a uniform axial flow. The first two terms of the inner expansion and the first three terms of the outer expansion are considered. The matching yields an expression for the spanwise distribution of the downwash velocity. A numerical application shows that the first two terms of the inner solution do not yield an acceptable approximation for the downwash velocity. However, recasting the analytical expressions into an integral equation, similar to Prandtl's lifting line equation for wings, yields results for both aerodynamic and acoustic quantities, which agree well with experimental results. The method thus constitutes a practical analysis method for conventional propellers.