Samuel Sinayoko

Flow decomposition and aerodynamic sound generation

An approximate decomposition of fluid-flow variables satisfying unbounded compressible Navier–Stokes equations into acoustically radiating and non-radiating components leads to well-defined source terms that can be identified as the physical sources of aerodynamic noise. We show that, by filtering the flow field by means of a linear convolution filter, it is possible to decompose the flow into non-radiating and radiating components. This is demonstrated on two different flows: one satisfying the linearised Euler equations and the other the Navier–Stokes equations. In the latter case, the corresponding sound sources are computed. They are found to be more physical than those computed through classical acoustic analogies in which the flow field is decomposed into a steady mean and fluctuating component.

A Trailing-Edge Noise Model for Serrated Edges

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. This paper is concerned with the development of a theoretical model for the prediction of the sound radiated by serrated trailing-edges. The proposed model is based on Fourier expansion and Amiets formulation. By using an iterative PDE-solving procedure, the scattered pressure field on the surface of an airfoil with sawtooth trailing-edge serrations is obtained. The far-field sound is then evaluated using the surface pressure integral based on the theories of Kirchhoff and Curle. The power spectral density (PSD) of the far- field sound is then related to the wavenumber spectral density of the hypothetical surface pressure under the turbulent boundary layer that would exist when the trailing-edge is absent. Numerical evaluation of the new model has shown better agreement than that obtained using Howes model. Based on the new model, the sound reduction achieved by a trailing-edge with sharp sawtooth serrations is around 5-10 dB for a wide frequency range. This result agrees better with experiments, in which the average sound reduction is reported to be 5-7 dB. The results obtained using the new analytical model also agree well with FEM computations, suggesting that the model developed in this paper can capture the essential physics and give correct predictions for the sound generated by serrated trailing- edges. In the end, the physical mechanism of noise reduction is found to be the destructive interference effect of the scattered pressure field.

Trailing edge noise theory for rotating blades in uniform flow

This paper presents a new formulation for trailing edge noise radiation from rotating blades based on an analytical solution of the convective wave equation. It accounts for distributed loading and the effect of mean flow and spanwise wavenumber. A commonly used theory due to Schlinker and Amiet predicts trailing edge noise radiation from rotating blades. However, different versions of the theory exist; it is not known which version is the correct one, and what the range of validity of the theory is. This paper addresses both questions by deriving Schlinker and Amiets theory in a simple way and by comparing it with the new formulation, using model blade elements representative of a wind turbine, a cooling fan and an aircraft propeller. The correct form of Schlinker and Amiets theory is identified. It is valid at high enough frequency, i.e. for a Helmholtz number relative to chord greater than one and a rotational frequency much smaller than the angular frequency of the noise sources.

Noise prediction for serrated leading-edges

© 2016, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. Amiet’s theory offers an efficient and accurate means of predicting trailing edge and leading edge noise, but it assumes that the edge is straight and cannot be applied to serrated edges. Serrations are known to be effective at reducing trailing edge and leading edge noise, but little theoretical work has been carried out on predicting the amount of noise reduction. A recently developed model that generalises Amiet’s theory for trailing edge noise with sawtooth trailing edges predicts noise reduction levels of 5-10 dB that are close to experimental measurements. Such generalised Amiet’s theory has yet to be developed for serrated leading edges. There is currently no analytical model that is applicable to serrated leading edges, and such model could play a key role in the design of quieter turbofan engines. This paper derives a generalised Amiet model for predicting leading edge noise with a sawtooth leading edge and validates the noise prediction against experimental results. This work will shed light into the noise reduction mechanism due to serrated leading edges and will help design more effective serrations.

Nonlinear and linear noise source mechanisms in subsonic jets

Noise source mechanisms are studied for a numerical dataset of a low Reynolds number laminar jet with a Mach 0.9 jet exit velocity (Suponitsky et al., J. Fluid Mech., Vol. 658, 2010) and two experimentally obtained datasets of high Reynolds number, Mach 0.4 and 0.6 turbulent jets (Cavalieri et al., AIAA Vol. 2011-2743, 2012). The objective of the study is to discern the source mechanism, linear or non-linear, by which acoustic radiation is obtained from wave-packets in the context of laminar and turbulent jets. For the laminar jet, it is shown numerically using a Linearized Euler Equation (LEE) solver that the sources of sound stem from a non-linear coupling of hydrodynamic waves. The nonlinear nature of the source mechanism explains why Linear Parabolized Stability Equation (LPSE) formulations are unable to reproduce the relevant near field dynamics at low Reynolds numbers. For the turbulent jets however, experimental evidence indicates that linear wavepackets are likely to be the source mechanism for acoustic radiation. To verify this, a fluctuating boundary condition is incorporated into the LEE solver such that a single frequency hydrodynamic wave is set up. This is used to investigate how the results from linear wavepackets compare with those found from LPSE and experiments. It is found that the power spectral density of the axial velocity fluctuations obtained by LEE shows a close match with those obtained from the LPSE and experiments, and it is also observed that downstream of the potential core, LEE results match more closely with experiments in this regard than do LPSE results. However, although the linear wavepackets formed using a fluctuating boundary condition do radiate sound, a comparison of the far-field directivity results show that the amplitude of the sound produced is significantly lower than those observed in experiments. Based on these results, LEE with a fluctuating boundary condition proves to be more useful in reproducing the near flow field of a turbulent jet but does not appear to be accurate in directly predicting the radiated far-field sound.

An acoustic space-time and the Lorentz transformation in aeroacoustics

In this paper we introduce concepts from relativity and geometric algebra to aeroacoustics. We do this using an acoustic space-time transformation within the framework of sound propagation in uniform flows. By using Geometric Algebra we are able to provide a simple geometric interpretation of the space-time transformation, and are able to give neat and lucid derivations of the free-field Greens function for the convected wave equation and the Doppler shift for a stationary observer and a source in uniform rectilinear motion in a uniform flow.

An integral formulation for wave propagation on weakly non-uniform potential flows

Abstract An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels for wave propagation on non-uniform flow. The integral solution is formulated using a Green׳s function obtained by combining the Taylor and Lorentz transformations. Although most conventional approaches based on either transform solve the Helmholtz problem in a transformed domain, the current Green׳s function and associated integral equation are derived in the physical space. A dimensional error analysis is developed to identify the limitations of the current formulation. Numerical applications are performed to assess the accuracy of the integral solution. It is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field, and as a means of solving scattering problems by rigid surfaces in non-uniform flows. The results show that the error associated with the physical model deteriorates with increasing frequency and mean flow Mach number. However, the error is generated only in the domain where mean flow non-uniformities are significant and is constant in regions where the flow is uniform.

On separating propagating and non-propagating dynamics in fluid-flow equations

ltering the ow eld. Two linear ltering strategies are investigated: one is based on a dierential operator, the other employs convolution operations. Convolution lters are found to be superior at separating radiating and non-radiating components. Their ability to decompose the ow into non-radiating and radiating components is demonstrated on two dierent ows: one satisfying the linearized Euler and the other the Navier-Stokes equations. In the latter case, the corresponding sound sources are computed. These sources provide good insight into the sound generation process. For source localization, they are found to be superior to the commonly used sound sources computed using the steady part of the ow.

Trailing edge noise prediction for rotating serrated blades

Serrations have been widely studied in the case of stationary blades, as an efficient method for reducing trailing edge noise. However, most of the problems involving trailing edge noise are related to rotating blades and it is not known how rotation affects the efficiency of serrations. This paper tackles this problem using an efficient analytical model for predicting trailing edge noise radiation for rotating serrated blades. The model combines Howes low Mach number isolated airfoil theory with Amiets rotating airfoil technique. The paper also outlines a theory that generalizes Amiets stationary airfoil the- ory to serrated trailing edges. Three different types of serrations - sinusoidal, sawtooth and slitted-sawtooth - are investigated for a model wind turbine blade element. The inuence of the serrations width, depth, and slits, on noise radiation is compared to known results valid for stationary blades. The best serrations are narrow (relative to the boundary layer thickness) and deep. Rotation has been found to have little impact on the performance of serrations at low Mach numbers.

GEOMETRIC ALGEBRA AND AN ACOUSTIC SPACE TIME FOR PROPAGATION IN NON-UNIFORM FLOW

This study aims to make use of two concepts in the field of aeroacoustics; an analogy with relativity, and Geometric Algebra. The analogy with relativity has been investigated in physics and cosmology, but less has been done to use this work in the field of aeroacoustics. Despite being successfully applied to a variety of fields, Geometric Algebra has yet to be applied to acoustics. Our aim is to apply these concepts first to a simple problem in aeroacoustics, sound propagation in uniform flow, and the more general problem of acoustic propagation in non-uniform flows. By using Geometric Algebra we are able to provide a simple geometric interpretation to a transformation commonly used to solve for sound fields in uniform flow. We are then able to extend this concept to an acoustic spacetime applicable to irrotational, barotropic background flows. This geometrical framework is used to naturally derive the requirements that must be satisfied by the background flow in order for us to be able to solve for sound propagation in the non-uniform flow using the simple wave equation. We show that this is not possible in the most general situation, and provide an explicit expression that must be satisfied for the transformation to exist. We show that this requirement is automatically satisfied if the background flow is incompressible or uniform, and for both these cases derive an explicit transformation. In addition to a new physical interpretation for the transformation, we show that unlike previous investigations, our work is applicable to any frequency.