Measurement, scaling and optimal dimensions of airfoil leading-edge serrations in isotropic turbulence

Noise reduction results are presented for a set of leading edge serrations on a flat plate airfoil in isotropic turbulence, obtained from integrated beamforming results. Triangular, sinusoidal, and tangent serration profiles have been investigated, as well as a modified sinusoid which consists of a sinusoid at the tip and a tangent curve at the root. The serrations have a non-dimensional amplitude and wavelength of $h/c=0.065$ and $\lambda /{\Lambda }_t$ between 0.7 and 15 respectively, where $h$ is the serration amplitude, $c$ is the chord length, $\lambda$ is the serration wavelength and ${\Lambda }_t$ is the spanwise integral length scale of the incoming flow. All serrations show a reduction in noise level compared to the straight leading edge reference case. Between 2 and $3\mathrm{dB}$ noise reduction was observed for all cases at a Strouhal number based on $h$, $S{t}_h$, with value 0.1. Above $S{t}_h=0.3$, leading edge noise reduction increases with frequency and peaks at a serration wavelength of $\lambda /{\Lambda }_t=1$, a trend that holds for all shape profiles investigated. In this higher frequency range, subtle variations in shape profile significantly vary the noise reduction qualities. The modified sinusoidal profile outperforms all others up to $S{t}_h=1$, as long as the serration wavelength is shorter than $\lambda /{\Lambda }_t=4$. At higher frequencies, the modified sinusoidal serrations have a similar noise reduction to the triangular and tangent curve serrations, which reaches a maximum of $9\mathrm{dB}$ for serrations with $\lambda /{\Lambda }_t=4$. Overall sound pressure level results show the noise reduction in this high-frequency regime is independent of the Reynolds number. Fluctuating pressure measurements at the roots of the sinusoidal serration are used to extend previously published models of the optimal serration wavelength. For the current data set, the optimal serration wavelength approaches $\lambda /{\Lambda }_t=2.7$ at high Reynolds numbers. Furthermore, a reinterpretation of historical data, combined with the present data set, shows the optimal serration wavelength depends upon the ratio of serration amplitude to streamwise turbulent length scale $h/{\Lambda }_x$.