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Table Of Integrals Series And Products

Tables of integrals

Location and quantification of noise sources on a wind turbine

https://acoustique.ec-lyon.fr/publi/roger_jsv05.pdf

Back-scattering correction and further extensions of amiet's trailing-edge noise model. Part 1: theory

Acoustic field measurements were carried out on a 94-m-diam three-bladed wind turbine with one standard blade, one blade with trailing-edge serrations, and one blade with an optimized airfoil shape. A large horizontal microphone array, positioned at a distance of about one rotor diameter from the turbine, was used to locate and quantify the noise sources in the rotor plane and on the individual blades. The acoustic source maps show that for an observer at the array position, the dominant source for the baseline blade is trailing-edge noise from the blade outboard region. Because of convective amplification and directivity, practically all of this noise is produced during the downward movement of the blade, which causes the typical swishing noise during the passage of the blades. Both modified blades show a significant trailing-edge noise reduction at low frequencies, which is more prominent for the serrated blade. However, the modified blades also show tip noise at high frequencies, which is mainly radiated during the upward part of the revolution and is most important at low wind speeds due to high tip loading. Nevertheless, average overall noise reductions of 0.5 and 3.2 dB are obtained for the optimized blade and the serrated blade, respectively.

Reduction of Wind Turbine Noise using Optimized Airfoils and Trailing-Edge Serrations

An experimental investigation and analytical modeling were conducted of the broadband self-noise radiated by an industrial cambered airfoil embedded in an homogeneous flow at low Mach number. The instrumented airfoil is placed at the exit of an open jet anechoic wind tunnel. Sound is measured in the far field at the same time as the statistical properties of the wall pressure fluctuations close to the trailing edge. Three different flows with different statistical behaviors are investigated by changing the angle of attack, namely, the turbulent boundary layer initiated by a leading-edge separation, the nearly separated boundary layer with vortex shedding at the trailing edge, and the laminar boundary layer with Tollmien‐Schlichting waves. The far-field spectrum is related to the spectrum and spanwise correlation length of the wall pressure fluctuations. Simple statistical models based on Howe’s theory and on an extension of the original Amiet’s theory show a good agreement with the experimental results. They provide helpful tools to predict the self-noise from subsonic fans in an industrial context.

Broadband Self Noise from Loaded Fan Blades

The present paper is a state-of-the-art of a special class of analytical models to predict the broadband noise generated by thin airfoils in a flow, either clean or disturbed. Three generating mechanisms are addressed, namely the noise from the impingement of upstream turbulence called turbulence-interaction noise, the noise due to the scattering of boundary-layer turbulence as sound at the trailing edge for an attached flow called trailing-edge noise, and the noise generated due to the formation of a coherent vortex shedding in the near wake of a thick trailing edge, called vortex-shedding noise. Different analytical models previously proposed for each mechanism are reviewed, as declinations of the same basic approach inherited from the pioneer work performed by Amiet in the seventies and based on an extensive use of Schwarzschild's technique. This choice is only an alternative to other models available in the literature and is made here for the sake of a unified approach. Issues dealing with the input d...

/pdf/extensions-and-limitations-of-analytical-airfoil-broadband-1c7bfsyd8i.pdf

Extensions and limitations of analytical airfoil broadband noise models

https://acoustique.ec-lyon.fr/publi/moreau_jsv09.pdf

Back-scattering correction and further extensions of Amiet's trailing-edge noise model. Part II: Application

A new set of mean wall pressure data has been collected on a controlled diffusion airfoil at a chord Reynolds number of 1.2 £ £105 in a freejet anechoic wind tunnel. Comparisons of the experimental data with Reynoldsaveraged Navier‐ Stokes (RANS) simulationsin freeairshow signie cant e owe eld and pressure loading differences, indicatingsubstantialjetinterferenceeffects.Toanalyzetheseeffects,asystematicRANS-basedcomputationale uid dynamicsstudyoftheexperimentale owconditionshasbeencarriedout,whichquantie esthestrongine uenceofthe e nite jet (nozzle) width on the aerodynamic loading and e ow characteristics. When the jet width is not sufe ciently large compared to the frontal wetted area of the airfoil, the airfoil pressure distribution is found to be closer to the distribution on a cascade than that of an isolated proe le. The airfoil lift is signie cantly reduced. Accounting for the actual wind-tunnel setup recovers the wall pressure distribution on the airfoil without further empirical angle-of-attack corrections. These jet interference effects could be responsible for the discrepancies among some earlier experimental and computational studies of airfoil self-noise. They should be accounted for in future noise computations to ensure that the experimental e ow conditions are simulated accurately.

/pdf/analysis-of-flow-conditions-in-freejet-experiments-for-41oknv145p.pdf

Michel Roger

Papers

Back-scattering correction and further extensions of amiet's trailing-edge noise model. Part 1: theory

Broadband Self Noise from Loaded Fan Blades

Extensions and limitations of analytical airfoil broadband noise models

Back-scattering correction and further extensions of Amiet's trailing-edge noise model. Part II: Application

Analysis of Flow Conditions in Freejet Experiments for Studying Airfoil Self-Noise