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The conceptual designing of rotating machines such as fans, wind turbines, contra-rotating open rotors and helicopter blades require low-cost, easy-to-run tools which allow quick noise assessments and optimization analyses underlying this phenomenon. The state-of-the-art numerical and experimental methods are far more expensive to conduct an optimisation study, whereas inexpensive methods like the analytical ones can have significant errors in realistic geometries at high-frequency ranges, higher angles of attack. The response to large coherent disturbances and the statistical modeling of turbulence is required because turbulence, by far its nature, is stochastic. Determining the accurate unsteady response of airfoil is crucial for noise prediction.
The primary goal of the project is to develop a new low-cost and easy-to-use numerical technique for aero-acoustic designs, focused primarily on airfoil-turbulence interaction. The development of the statistical method is divided into three sections; namely - 1) calculating the background flow, 2) modeling of statistically optimized inflow disturbance, 3) constructing a vortex database to predict the noise in multiple flow fields characterized by different values of turbulent intensities and length scales.
In the framework of this work a new approach to model inflow turbulence, a significant noise-generating element, is suggested, which does not depend on heavy computations requiring supercomputers. Through this approach, the influence of turbulence parameters on the noise generated in turbomachinery can be quantified. The approach also considers the geometrical parameters of the airfoil in the noise prediction.
The background flow is numerically simulated via solving the vorticity transport equations in the Lagrangian form (vortex methods).
The acoustic influence of a finite number of vortices, characterized by all the possible combinations of size, circulation and injection position/time defined using the ranges of probability distribution functions, released from injection points upstream of the airfoil are precomputed and stored in a matrix. The method is computationally inexpensive compared to classical vortex methods since the effect due to particles are precomputed, stored in a/an matrix/array. The matrix can be called as a library while predicting the noise from a specific airfoil.
The use of open-porous, flow-permeable materials is one possible method to reduce the generation of flow induced noise, for example at the trailing edge of wings or airfoils. Subject of the present dissertation is an experimental study of the noise generation at the trailing edge of porous airfoils compared to that of a non-porous reference airfoil of equal chord length. This includes the investigation of the mechanisms responsible for the noise reduction. Additionally, it is of special interest how the different parameters of the porous materials affect the noise generation. Detailed experiments were conducted on a non-porous reference airfoil and a set of 16 porous airfoils at various flow speeds in an open jet wind tunnel. All measurements were performed in subsonic flow, the corresponding maximum chord based Reynolds number is approximately 780,000. The porous materials are mainly characterized by their air flow resistivity. The acoustic measurements were performed using microphone array technology and the resulting data were processed by the application of an advanced three-dimensional beamforming algorithm. To include the aerodynamic efficiency of the porous airfoils in the analysis of the potential trailing edge noise reduction, the corresponding lift forces and drag forces have been measured. Additional hot-wire measurements in the turbulent boundary layer of a subset of the airfoils were performed to enable conclusions on the physical mechanisms that are responsible for the trailing edge noise reduction. In the examined range of frequencies, it was found that a noticeable trailing edge noise reduction can be achieved through the use of porous airfoils despite losses in aerodynamic efficiency. The highest noise reduction per unit lift force was measured for porous airfoils with medium to high air flow resistivities. While a trailing edge noise reduction was observed mainly at medium frequencies, the trailing edge noise spectra of porous airfoils with low and medium air flow resistivities were found to exceed the trailing edge noise of the reference airfoil at high frequencies. This is assumed to be a contribution of surface roughness noise, since the porous materials are characterized by an increased surface roughness compared to the rather smooth surface of the reference airfoil. The boundary layer thickness as well as the boundary layer displacement thickness of the porous airfoils are noticeably larger than that measured at the reference airfoil. The examination of spectra of the turbulent velocity fluctuations showed that the peak measured above the trailing edge of the porous airfoils is at a noticeably lower frequency than that measured at the reference airfoil. Additionally, turbulence spectra measured at different chord positions along the surface of the airfoils revealed that the cause of the measured trailing edge noise reduction at medium and high frequencies may be a shift of the spectra toward lower frequencies with increasing chord position. And while this shift could be observed for both the reference airfoil and the porous airfoils, it is notably stronger for the porous airfoils. The results of the hot-wire measurements also lead to the assumption that the high frequency range of the velocity fluctuations is damped when the turbulence convects over the surface of the porous airfoils, an effect called hydrodynamic damping. Based on turbulence spectra measured above the trailing edge of five airfoils, a simple trailing edge noise prediction model was developed following the fundamental theory by Ffowcs Williams and Hall on the generation of noise in the vicinity of the edge of a semi-infinite flat plate. It is thereby assumed that the spectral shape of the trailing edge noise is related to the spectral shape of the turbulent velocity fluctuations in close proximity to the trailing edge, while the overall amplitude is determined by a convection velocity that is proportional to the mean flow velocity of the fluctuations. One possible application of the resulting model is the prediction of the trailing edge noise based on the input of the measured turbulence spectrum and the corresponding mean flow velocity close to the trailing edge of an airfoil. A more convenient application of the model is the trailing edge noise prediction based on an estimated turbulence spectrum and the corresponding mean flow velocity based on approximations developed in the present dissertation, without the necessity of detailed constant temperature anemometry measurements. The agreement between predicted and measured trailing edge noise spectra was found to be satisfying for both cases, especially when considering the rather basic approach of the model.