Prediction of noise from serrated trailing edges

Abstract

A new analytical model is developed for the prediction of noise from serrated trailing edges. The model generalizes Amiet's trailing-edge noise theory to sawtooth trailing edges, resulting in a complicated partial differential equation. The equation is then solved by means of a Fourier expansion technique combined with an iterative procedure. The solution is validated through comparison with the finite element method for a variety of serrations at different Mach numbers. The results obtained using the new model predict noise reduction of up to 10 dB at 90 • above the trailing edge, which is more realistic than predictions based on Howe's model and also more consistent with experimental observations. A thorough analytical and numerical analysis of the physical mechanism is carried out and suggests that the noise reduction due to serration originates primarily from interference effects near the trailing edge. A closer inspection of the proposed mathematical model has led to the development of two criteria for the effectiveness of the trailing-edge serrations, consistent but more general than those proposed by Howe. While experimental investigations often focus on noise reduction at 90 • above the trailing edge, the new analytical model shows that the destructive interference scattering effects due to the serrations cause significant noise reduction at large polar angles, near the leading edge. It has also been observed that serrations can significantly change the directivity characteristics of the aerofoil at high frequencies and even lead to noise increase at high Mach numbers.

Near-wall pressure fluctuations over noise reduction add-ons

“…13 Results are summarized in Figures 9 and 10. Although the spectra of the pressure fluctuations follow the conventional frequency decay of a turbulent boundary layer (cfr.…”

“…More complicated geometries have been designed by employing slits, 9 brushes, 10 randomly 9 and iron-shaped trailing edges. 11 Although these shapes have proven to reduce noise emissions with respect to the clean trailing-edge configuration, a huge difference subsists between the theoretical predicted noise-reduction intensity 12,13 and the one effectively measured in field. 4 One of the most important analytical models found in literature is the one of Howe 12 where the broadband noise-reduction due to the installation of solid serrated edges on a flat plate is estimated.…”

“…4 One of the most important analytical models found in literature is the one of Howe 12 where the broadband noise-reduction due to the installation of solid serrated edges on a flat plate is estimated. Lyu et al 13 further developed a new semi-analytical model applying the Schwarzschild method of propagation of the pressure fluctuations. Although closer to reality, the final result does not allow yet to explain some of the physical features already at zero angle of attack such as the characteristic cross-over frequency St δ = fδ/V ∞ ≈ 1 (based on the free-stream velocity V ∞ and boundary-layer thickness δ, from XFOIL) 14 after which noise increases again.…”

Aerodynamic noise from rigid trailing edges with finite porous extensions

“…The analytic work of Howe (1998) presents a simplified picture of a line vortex interacting with the trailing edge of a semi-infinite flat plate and predicts the effects of a rigid trailing-edge condition on the acoustic scattering. With this boundary condition being key to the total level of far-field noise generated by turbulence-edge interaction, it is clear why the next steps into the investigation of reducing trailing-edge noise were to consider adapted trailing edge designs, for example a serrated edge (Lyu et al 2016;Oerlemans 2016), a rough surface canopy (Clark et al 2016), or a porous and/or flexible edge (Jaworski & Peake 2013;Schlanderer & Sandberg 2016;Geyer & Sarradj 2014). These adapted designs are inspired by the silent flight of owls, first discussed by (Graham 1934), and now with increasing pressure on the aviation industry to reduce aircraft noise (European Commission 2011) are of great interest worldwide.…”

“…What is common between all those approaches and the one proposed in this paper is the idea of solving parts of the problem and then bringing the parts together in an iterative manner. Recently, the Schwarzschild's series were used in (Lyu et al 2016;Roger & Moreau 2005) but only to obtain the scattered pressure on the surface of the flat plate, and the far-field sound was obtained using the surface pressure integral based on the theories of Kirchhoff and Curle.…”