  Leading- and trailing-edge serrations have been widely used to reduce the
leading- and trailing-edge noise in applications such as contra-rotating fans
and large wind turbines. Recent studies show that these two noise problems can
be modelled analytically using the Wiener-Hopf method. However, the resulting
models involve infinite-interval integrals that cannot be evaluated
analytically, and consequently implementing them poses practical difficulty.
This paper develops easily-implementable noise prediction models for flat
plates with serrated leading and trailing edges, respectively. By exploiting
the fact that high-order modes are cut-off and adjacent modes do not interfere
in the far field except at sufficiently high frequencies, an infinite-interval
integral involving two infinite sums is approximated by a single
straightforward sum. Numerical comparison shows that the resulting models serve
as excellent approximations to the original models. Good agreement is also
achieved when the leading-edge model predictions are compared with experimental
results for sawtooth serrations of various root-to-tip amplitudes. Importantly,
the models developed in this paper can be evaluated robustly in a very
efficient manner. For example, a typical far-field noise spectrum can be
calculated within milliseconds for both the trailing- and leading-edge noise
models on a standard desktop computer. Due to their efficiency and ease of
numerical implementation, these models are expected to be of particular
importance in applications where a numerical optimization is likely to be
needed.
