Downstream Perforations for the Reduction of Turbulence-Aerofoil Interaction Noise: Part II - Theoretical Investigation

Abstract

This paper presents a theoretical study of introducing a single gap or slot downstream of the leading edge of a thin rigid plate on aeroacoustic scattering. This is investigated as an elementary model for understanding the effect of downstream perforations on gust-aerofoil interaction noise. Across the slot it is supposed there is zero pressure jump, and a wake is shed from the upstream slot edge such that an unsteady Kutta condition is satisfied. The resulting mixed boundary value problem is reformulated as a Wiener-Hopf problem, and reduced to a singular integral equation suitable for numerical solution. Wave components of the solution may be identified, and plausibly related to diffracted fields by each junction. Theoretical results are compared to experimental results considering sets of perforations. The model is found to be in line with overall qualitative trends in the change in far-field sound power level observed experimentally, but does not account for oscillations from this trend.

Downstream porosity for the reduction of turbulence–aerofoil interaction noise

“…Priddin et al [20] have also explored the noise reduction mechanism of a flat plate upstream of a semi-infinite leading edge subject to a harmonic vortical gust. Predictions of the noise reduction spectra obtained analytically from solutions of the wave equation with appropriate boundary conditions imposed 390 were found to capture the envelope of the experimental noise reduction spectra, but not the distinctive peaks and dips.…”

“…However, the mechanisms proposed in [16,20,21] individually cannot explain the shape of the noise reduction spectra, which comprises a number of distinct peaks at f l d /U c = n, superimposed on a broad 'envelope' that decays with increasing frequency. The peaks are particularly pronounced in the case 400 of the tandem flat plates in Fig.…”

“…Recent, detailed analysis has suggested that all noise reduction mechanisms proposed in [16,20,21] must be simultaneously present to explain the characteristics of the noise reduction spectra described above. In this section, we further develop the simple analytic model proposed in [16] that combines all aforementioned noise reduction mechanisms, namely (i) edge-to-edge interfer-425 ence, (ii) phase inversion due to secondary vorticity, (iii) cut-off effects across the porous section and (iv) reduced effective chord.…”

Investigation of Curle's Dipolar Sources on a Porous Airfoil Interacting with Incoming Turbulence

“…More recently, novel concepts for designing porous airfoils based on nonuniform distributions of porosity have been proposed. Paruchuri et al [19], Palleja-Cabre et al [20], and Priddin et al [21] investigated the leading-edge noise reduction achieved by flat plates with different extents of porous inserts and showed that a single row of holes located downstream of the stagnation point results in significant mitigation at low frequencies without increasing the noise emissions at high frequencies. Ayton et al [22] found that smoothly varying chordwise porosity on a perforated flat plate can be beneficial for reducing trailing-edge noise thanks to the more significant destructive interference of the back-scattered field generated by the impermeable leading edge [23,24].…”

The effect of angle of attack on turbulence interaction noise with a porous leading edge

“…Ocker et al [33] considered a wide range of porous structures for permeable leading edge airfoils to systematically study the effect of the porous structure on turbulence interaction noise and fan noise. Palleja-Cabre et al [36] and Priddin et al [38] experimentally and analytically studied a flat plate in a turbulent stream in a two part study. The flat plate had perforations downstream of the leading edge and demonstrated a noise reduction which is likely attributed to the airfoil acting as though it has a shorter chord.…”