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.

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The use of streamwise finlets as a passive flow and aerodynamic noise-control technique is considered in this paper. A comprehensive experimental investigation is undertaken using a long flat plate, and results are presented for the boundary layer and surface pressure measurements for a variety of surface treatments. The pressure–velocity coherence results are also presented to gain a better understanding of the effects of the finlets on the boundary layer structures. The results show that the flow behaviour downstream of the finlets is strongly dependent on the finlet spacing. The use of finlets with coarse spacing leads to a reduction in pressure spectrum at mid- to high frequencies and an increase in spanwise length scale in the trailing-edge region due to flow channelling effects. For the finely distributed finlets, the flow is observed to behave similarly to that of a permeable backward-facing step, with significant suppression of the high-frequency pressure fluctuations but an elevation at low frequencies. Furthermore, the convection velocity is observed to reduce downstream of all finlet treatments. The trailing-edge surface pressure spectrum results have shown that, in order to obtain maximum unsteady pressure reduction, the finlet spacing should be of the order of the thickness of the inner layer of the boundary layer. A thorough study is provided for understanding of the underlying physics of both categories of finlets and their implications for controlling the flow and noise generation mechanism near the trailing edge.

Passive control of trailing edge noise using complex periodic trailing edge serrations is investigated. The airfoil is modelled as a semi-infinite flat plate with a periodic trailing edge, set at zero angle of attack to a low Mach number flow. Analytical expressions have been derived for the far-field acoustic frequency spectrum for different serrations, namely, sawtooth, sinusoidal, slitted, slitted-sawtooth and sawtooth-sinusoidal. Numerical results have been presented for these serrations over a wide range of frequencies. It has been shown that the noise reduction from serrated trailing edges is a sensitive function of the complexity of the serration geometry and that the noise generation efficiency can be significantly reduced by applying complex periodic serrations to the trailing edge of the airfoil. Our numerical investigations have also shown that the slitted-sawtooth serration is the most effective design for reducing the trailing edge noise, particularly at low and mid frequencies. The theoretical results presented in this paper complement the experimental study presented by M. Gruber et al. [1]. Nomenclature = Cartesian coordinate system , = incident and scattered pressure fields = blocked pressure ⁄ = acoustic wavenumber = angular frequency = source term at position = Green's function = boundary layer turbulent wavenumber vector = streamwise and spanwise wavenumbers = surface pressure wavenumber-frequency spectrum = acoustic pressure frequency spectrum = serration profile = amplitude and spatial periodicity of the sawtooth serration, Fig. 2 = amplitude and spatial periodicity of the sinusoidal serration, Fig. 3 = amplitude and width of the slitted serration, Fig. 4 = mean flow speed = convection velocity ( ) ⁄= nondimensional frequency = density and speed of sound of the medium = boundary layer thickness = polar and azimuthal angles of the observer from the trailing edge j = imaginary number

An analytical model is developed for the prediction of noise radiated by an aerofoil with leading edge serration in a subsonic turbulent stream. The model makes use of the Fourier Expansion and Schwarzschild techniques in order to solve a set of coupled differential equations iteratively and express the far-field sound power spectral density in terms of the statistics of incoming turbulent upwash velocity. The model has shown that the primary noise reduction mechanism is due to the destructive interference of the scattered pressure induced by the leading edge serrations. It has also shown that in order to achieve significant sound reduction, the serration must satisfy two geometrical criteria related to the serration sharpness and hydrodynamic properties of the turbulence. A parametric study has been carried out and it is shown that serrations can reduce the overall sound pressure level at most radiation angles, particularly at small aft angles. The sound directivity results have also shown that the use of leading edge serration does not particularity change the dipolar pattern of the far-field noise at low frequencies, but it changes the cardioid directivity pattern associated with radiation from straight-edge scattering at high frequencies to a tilted dipolar pattern.

Aerodynamic and aeroacoustic performance of airfoils fitted with morphing trailing edges are investigated using a coupled structure/fluid/noise model. The control of the flow over the surface of an airfoil using shape optimization techniques can significantly improve the load distribution along the chord and span lengths whilst minimising noise generation. In this study, a NACA 63-418 airfoil is fitted with a morphing flap and various morphing profiles are considered with two features that distinguish them from conventional flaps: they are conformal and do not rely on conventional internal mechanisms. A novel design of a morphing flap using a zero Poisson's ratio honeycomb core with tailored bending stiffness is developed and investigated using the finite element model. While tailoring the bending stiffness along the chord of the flap yields large flap deflections, it also enables profile tailoring of the deformed structure which is shown to significantly affect airfoil noise generation. The aeroacoustic behaviour of the airfoil is studied using a semi-empirical airfoil noise prediction model. Results show that the morphing flap can effectively reduce the airfoil trailing edge noise over a wide range of flow speeds and angles of attack. It is also shown that appropriate morphing profile tailoring improves the effect of morphing trailing edge on the aerodynamic and aeroacoustic performance of the airfoil.

This paper is concerned with the application of porous treatments as a means of flow and aerodynamic noise reduction. An extensive experimental investigation is undertaken to study the effects of flow interaction with porous media, in particular in the context of the manipulation of flow over blunt trailing edges and attenuation of vortex shedding. Comprehensive boundary layer and wake measurements have been carried out for a long flat plate with solid and porous blunt trailing edges. Unsteady velocity and surface pressure measurements have also been performed to gain an in-depth understanding of the changes to the energy–frequency content and coherence of the boundary layer and wake structures as a result of the flow interaction with a porous treatment. Results have shown that permeable treatments can effectively delay the vortex shedding and stabilize the flow over the blunt edge via mechanisms involving flow penetration into the porous medium and discharge into the near-wake region. It has also been shown that the porous treatment can effectively destroy the spanwise coherence of the boundary layer structures and suppress the velocity and pressure coherence, particularly at the vortex shedding frequency. The flow–porous scrubbing and its effects on the near-wall and large coherent structures have also been studied. The emergence of a quasi-periodic recirculating flow field inside highly permeable surface treatments has also been investigated. Finally, the paper has identified several important mechanisms concerning the application of porous treatments for aerodynamic and aeroacoustic purposes, which can help more effective and tailored designs for specific applications.

a b s t r a c tThis study is concerned with the application of porous coatings as a passive flow control method for reducing the aerodynamic sound from tandem cylinders. The aim here is to perform a parametric proof-of-concept study to investigate the effectiveness of porous treatment on bare tandem cylinders to control and regularize the vortex shedding and flow within the gap region between the two bluff bodies, and thereby control the aerodynamic sound generation mechanism. The aerodynamic simulations are performed using 2D transient RANS approach with k À ω turbulence model, and the acoustic computations are carried out using the standard Ffowcs Williams-Hawkings (FW-H) acoustic analogy. Numerical flow and acoustic results are presented for bare tandem cylinders and porous-covered cylinders, with different porosities and thicknesses. Experimental flow and acoustic data are also provided for comparison. Results show that the proper use of porous coatings can lead to stabilization of the vortex shedding within the gap region, reduction of the vortex shedding interaction with the downstream body, and therefore the generation of tonal and broadband noise. It has also been observed that the magnitude and the frequency of the primary tone reduce significantly as a result of the flow regularization. The proposed passive flow-induced noise and vibration control method can potentially be used for other problems involving flow interaction with bluff bodies.