Amiet theory extension to predict leading-edge generated noise in compact airfoils

This paper extends the Amiet theory to frequencies where the airfoil can be considered a compact noise source. The original Amiet theory proposes to apply the Schwarzschild theorem in an iterative procedure, which generally leads to noise over-prediction at low-frequencies. To overcome this problem, this paper proposes two extra iterations to the theory aiming to improve convergence. Since the second iteration of the classical Amiet theory presents approximate analytical solutions, this paper proposes correction formulas for maintaining the solution accuracy of further iterations written in terms of analytical expressions. Results show that adding two extra iterations contribute to improved convergence, and consequently improved noise prediction, in the frequency range of interest for applications such as contra-rotating-open-rotors, wind-turbines and turbomachines. Comparison with experiments shows significant improvement at frequencies where the airfoil is considered a compact noise source.