Trailing edge noise theory for rotating blades in uniform flow

TL;DR

This paper introduces a new analytical formulation for trailing edge noise from rotating blades, clarifies the correct version of Schlinker and Amiet's theory, and defines its range of validity based on frequency and flow conditions.

Contribution

It derives a simplified form of Schlinker and Amiet's theory and compares it with a new formulation to establish the correct version and its applicability range.

Findings

The correct form of Schlinker and Amiet's theory is identified.

The theory is valid at high frequencies with Helmholtz number > 1.

The new formulation accounts for mean flow and spanwise effects.

Abstract

This paper presents a new formulation for trailing edge noise radiation from rotating blades based on an analytical solution of the convective wave equation. It accounts for distributed loading and the effect of mean flow and spanwise wavenumber. A commonly used theory due to Schlinker and Amiet (1981) predicts trailing edge noise radiation from rotating blades. However, different versions of the theory exist; it is not known which version is the correct one and what the range of validity of the theory is. This paper addresses both questions by deriving Schlinker and Amiet's theory in a simple way and by comparing it to the new formulation, using model blade elements representative of a wind turbine, a cooling fan and an aircraft propeller. The correct form of Schlinker and Amiet's theory (1981) is identified. It is valid at high enough frequency, i.e. for a Helmholtz number relative to chord greater than one and a rotational frequency much smaller than the angular frequency of the noise sources.