Two-point velocity statistics near the trailing edge of a controlled diffusion airfoil are obtained, both experimentally and analytically, by decomposing Poisson's equation for pressure into the mean-shear (MS) and turbulence-turbulence (TT) interaction terms. The study focuses on the modeling of each interaction term, in order to allow for the reconstruction of the wall-pressure spectra from tomographic velocimetry data, without numerically solving for pressure. The two-point correlation of the wall-normal velocity that describes the magnitude of the MS source term is found to be influenced by various competing factors such as blocking, mean-shear, and the adverse mean pressure gradient. The blocking term is found to supersede the other interaction terms close to the wall, making the two-point velocity correlation self-similar. The most dominant TT term that contributes to far-field noise for an observer located perpendicular to the airfoil chord at the mid-span is shown to be the one that quantifies the variation of the wall-normal velocity fluctuations in the longitudinal direction because of the statistical homogeneity of turbulence in planes parallel to the wall. A model to determine the contribution of the TT interaction term is proposed where the fourth-order two-point correlation can be modeled using Lighthill's approximation. However, its contribution toward wall-pressure spectra is found to be substantially lower than the MS term in the present case.

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The characteristics of unsteady surface pressure (USP) created by turbulent flow over a family of asymmetrically beveled trailing edges were studied experimentally. The geometries had a trailing edge angle θ= 25 ^∘ with a flat lower surface and a rounded upper surface with radii of curvature between zero and ten times the airfoil thickness. The Reynolds number was Re= 2.1 × 10 ⁶ based on chord. A detailed description of the USP and flow field around the trailing edge was obtained using remote microphone probes (RMP) and particle image velocimetry (PIV), respectively. The lower surface exhibited USP auto-spectral density magnitudes that were similar to those of a zero-pressure-gradient turbulent boundary layer at higher frequency. The low-frequency pressure fluctuations were influenced by the turbulent wake, leading to large increases in magnitude closer to the trailing edge. An empirical model of these results is proposed. The beveled upper surface was characterized by a region of favorable pressure gradient, followed by a strong adverse pressure gradient. The cases with smaller radius of curvature were found to exhibit separated flow over the trailing edge. The spectral magnitudes were largest in these regions, and significant attention is given to the proper scaling of these results. The PIV measurements provided the length and velocity scales for this purpose.

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Particle image velocimetry for the experimental assessment of trailing edge noise sources has become focus of research in recent years. The present study investigates the feasibility of the noise prediction for high-lift devices based on time-resolved particle image velocimetry (PIV). The model under investigation is a NACA 0015 airfoil with a Gurney flap with a height of 6% of the chord length. The velocity fields around and downstream of the Gurney flap were measured by PIV and used to compute the corresponding pressure fields by solving the Poisson equation for incompressible flows. The reconstructed pressure fluctuations on the airfoil surface constitute the source term for Curle's aeroacoustic analogy, which was employed in both the distributed and compact formulation to estimate the noise emission from PIV. The results of the two formulations are compared with the simultaneous far-field microphone measurements in the temporal and spectral domains. Both formulations of Curle's analogy yield acoustic sound pressure levels in good agreement with the simultaneous microphone measurements for the tonal component. The estimated far-field sound power spectra (SPL) from the PIV measurements reproduce the peak at the vortex shedding frequency, which also agrees well with the acoustic measurements.

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The power spectral density and coherence of temporal pressure fluctuations are obtained from low-repetition-rate tomographic PIV measurements. This is achieved by extension of recent single-snapshot pressure evaluation techniques based upon the Taylor’s hypothesis (TH) of frozen turbulence and vortex-in-cell (VIC) simulation. Finite time marching of the measured instantaneous velocity fields is performed using TH and VIC. Pressure is calculated from the resulting velocity time series. Because of the theoretical limitations, the finite time marching can be performed until the measured flow structures are convected out of the measurement volume. This provides a lower limit of resolvable frequency range. An upper limit is given by the spatial resolution of the measurements. Finite time-marching approaches are applied to low-repetition-rate tomographic PIV data of the flow past a straight trailing edge at 10 m/s. Reference results of the power spectral density and coherence are obtained from surface pressure transducers. In addition, the results are compared to state-of-the-art experimental data obtained from time-resolved tomographic PIV performed at 10 kHz. The time-resolved approach suffers from low spatial resolution and limited maximum acquisition frequency because of hardware limitations. Additionally, these approaches strongly depend upon the time kernel length chosen for pressure evaluation. On the other hand, the finite time-marching approaches make use of low-repetition-rate tomographic PIV measurements that offer higher spatial resolution. Consequently, increased accuracy of the power spectral density and coherence of pressure fluctuations are obtained in the high-frequency range, in comparison to the time-resolved measurements. The approaches based on TH and VIC are found to perform similarly in the high-frequency range. At lower frequencies, TH is found to underestimate coherence and intensity of the pressure fluctuations in comparison to time-resolved PIV and the microphone reference data. The VIC-based approach, on the other hand, returns results on the order of the reference.@en

The broadband noise generated by the scattering of turbulent flow at the trailing edge of a NACA 0018 airfoil with trailing edge serrations is investigated, varying both the airfoil angle of attack and serration flap angle. Acoustic emissions from the trailing edge are measured using a microphone array. The noise level is observed to be higher than that of the airfoil without serrations at frequencies beyond a crossover value. The latter is found to scale with a characteristic Strouhal number based upon the boundary layer thickness and the freestream velocity. A satisfactory collapse of the results under varying angles of attack and freestream velocities is observed. The modifications of the hydrodynamic behavior and the noise increase are linked by high-speed observations conducted with particle image velocimetry. An increase in the energy of turbulent fluctuations is also observed at the expected crossover frequency. The dominant cause of the increased noise is thereby identified at the pressure side edge of the serrations at a given flap angle.

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The trailing edge of a NACA 0018 airfoil is modified through the attachment of serrations with different degrees of permeability. Acoustic beamforming is used to inspect the turbulent boundary layer-trailing edge noise emissions from the unmodified and serrated trailing edges. Different freestream velocities and angles of attack are investigated. The serration permeability is prescribed by having slits cut into the solid surface of the serrations in two different configurations. The results indicate that a certain benefit in noise reduction is obtained from a mixed solid/slitted configuration, while a fully slitted configuration loses most of the noise reduction performance.@en

Trailing edge serrations have been proven to work as a passive noise reduction device. Nevertheless, they have also previously been found to increase noise in a particular frequency range, argued in earlier research to be due to the misalignment of the serrations with the direction of the flow in the wake. It emerges as a high-frequency noise increase in a broadband region of the spectrum. This study investigates the effect of serration-flow misalignment on the noise emissions using acoustic beamforming, and finds a correlation with observations made on the flow using particle image velocimetry (PIV). The hydrodynamic source of the noise increase is hereby identified, and a Strouhal number relation for the high-frequency noise increase is proposed@en

The present study investigates the feasibility of high-lift devices noise prediction based on measurements of time-resolved particle image velocimetry (TR-PIV). The model under investigation is a NACA 0015 airfoil with Gurney flap with height of 6% chord length. The velocity fields around and downstream the Gurney flap are measured by PIV and are used for the PIV-based noise predictions. The predictions are assessed via microphone measurements. Since the Gurney flap height is much smaller than the emitted acoustic wavelength, the source of noise can be considered compact and the integral implementation of Curle's analogy based on the unsteady aerodynamic loads can be followed. The results are compared with the simultaneous microphone measurements in terms of time histories and power spectra. The integral formulation of Curle's analogy yields acoustic sound pressure levels in good agreement with the simultaneous microphone measurements for the tonal component. All the calculated far-field noise power spectra reproduce the peak at vortex shedding frequency, which also agrees well with the microphone measurements.@en

Trailing edge and wake flows are of interest for a wide range of applications. Small changes in the design of asymmetrically beveled or semi-rounded trailing edges can result in significant difference in flow features which are relevant for the aerodynamic performance, flow-induced structural vibration and aerodynamically generated sound. The present study describes in detail the flow field characteristics around a family of asymmetrically beveled trailing edges with an enclosed trailing-edge angle of 25 ∘ and variable radius of curvature R. The flow fields over the beveled trailing edges are described using data obtained by particle image velocimetry (PIV) experiments. The flow topology for different trailing edges was found to be strongly dependent on the radius of curvature R, with flow separation occurring further downstream as R increases. This variation in the location of flow separation influences the aerodynamic force coefficients, which were evaluated from the PIV data using a control volume approach. Two-point correlations of the in-plane velocity components are considered to assess the structure in the flow field. The analysis shows large-scale coherent motions in the far wake, which are associated with vortex shedding. The wake thickness parameter yf is confirmed as an appropriate length scale to characterize this large-scale roll-up motion in the wake. The development in the very near wake was found to be critically dependent on R. In addition, high-speed PIV measurements provide insight into the spectral characteristics of the turbulent fluctuations. Based on the time-resolved flow field data, the frequency range associated with the shedding of coherent vortex pairs in the wake is identified. By means of time-correlation of the velocity components, turbulent structures are found to convect from the attached or separated shear layers without distinct separation point into the wake.@en

The present study employs simultaneous planar TR-PIV and microphone measurements to obtain the flow dynamics and aeroacoustic causality correlation associated with a Gurney flap of various sizes in case of low Mach and high Reynolds number flows. The objectives are to investigate the secondary shedding mode for the case of a turbulent boundary layer and to understand the mechanism of noise generation by identifying structures that are highly correlated with far field pressure fluctuations. The instantaneous velocity and vorticity fields show the flapping motion of the wake and the coherent vortex shedding process. The tonal peaks are clearly audible and correspond to the vortex shedding frequency. The PSD of the flow fluctuations and acoustic spectra did not indicate a secondary mode of shedding in case of turbulent boundary layer. The Strouhal numbers of the vortex shedding are found to be close to that of a bluff body in a flow. Causality correlation between pressure fluctuations in the far-field and the near field fluctuations indicates that the vertical velocity in the wake of the model is highly correlated with the far-field pressure fluctuations. This study provides an example of the potential of the causality correlation technique in identifying flow structures/regions highly correlated with noise in case of complex high-lift devices, making it possible to design flaps with lower acoustic emissions.@en

Coherent vortex shedding from blunt and beveled trailing edges generates tonal noise, which is usually undesired. To obtain a better understanding of the noise generation under such conditions, the flow field around a beveled trailing edge was characterized for Reynolds numbers based on the bluntness ranging from 2.5 × 104 to 5.1 × 104. Flow field statistics were obtained by means of planar high-speed two-component and stereoscopic particle image velocimetry measurements. The development of the shear layers and vortex roll-up is described in the present study. Related length scales, the vortex formation length, and wake thickness parameter were derived from the measurements. Noise emission due to vortex shedding was predicted from an analytic solution, derived from diffraction theory and the reversed Sears’ problem, and compared to acoustic phased array measurements. This approach has previously been shown to provide accurate results for sharply truncated edges, but questions with regard to the applicability with different trailing edge geometries remained open. The prediction required the auto-spectral density, correlation length, and convective velocity of the upwash velocity component in the vortex formation region. Direct application with data obtained from particle image velocimetry measurements showed an overestimation of about 20 dB when compared to the acoustic measurements. The results thus showed that the prediction of vortex shedding noise based on the simplified wake model and diffraction theory is not generally applicable.@en

The three-dimensional flow field over the suction side of a NACA 0018 airfoil with trailing-edge serrations was studied by means of time-resolved tomographic particle image velocimetry. Mean flow results show that the boundary layer thickness decreases along the streamwise direction with a corresponding reduction of the size of the turbulent structures developing over the suction side of the serrations. At a positive angle of attack, streamwise-oriented and counter-rotating vortices aligned with the edge of the serrations are found to be the main features of the mean flow field. Their formation is attributed to the pressure imbalance between the two sides of the airfoil and the mixing layer at the edge. They locally modify the effective angle seen by the turbulent flow approaching the serrated edge. This effect may contribute to the serration underperformance in terms of noise reduction reported in literature. The spatial distribution of the spectra of the source term of the Poisson equation, which relates the velocity field to pressure fluctuations, suggests that the contribution of the serrations to far-field broadband noise is a function of the streamwise location. This observation is congruent with the spectra of the wall-normal and spanwise velocity fluctuations, which typically show low intensity close to the tips of the individual serrations. It follows that analytical models must take into account the local contribution to the far-field noise induced by the streamwise variation of the hydrodynamic pressure on the serration surface.@en

A novel approach for trailing-edge noise diagnostics with low-repetition rate Particle Im- age Velocimetry systems is presented. The approach is based on the application of di_rac- tion theory and implements a recently developed single-snapshot pressure reconstruction in boundary layers using the Vortex-in-cell method in combination with a frozen turbulence assumption to estimate the relevant statistical descriptors of the surface pressure _eld. The present communication describes the required planar and tomographic Particle Im- age Velocimetry experiments with a high spatial-dynamic-range system and demonstrates the applicability of the approach by comparison of hydrodynamic and acoustic pressure statistics with available data. The frequency spectra of the hydrodynamic pressure near the surface are found to be sensitive to the model employed for the convective velocity in the application of the frozen turbulence assumption for reduced frequencies f_?=u1 > 0:5 (2:3kHz). For lower reduced frequencies, excellent agreement with the reference data is observed. @en

The flow past a NACA 0018 airfoil with sawtooth trailing edge serrations has been investigated using stereoscopic particle image velocimetry (PIV). The serration flap angle and airfoil incidence are varied in order to study the effect of secondary flow establishing between the suction and pressure sides of the serrations. The flow topology around the serrations is inferred from the analysis of time-averaged streamlines close to the airfoil surface and from the wall-normal flow velocity in between serrations. Additional PIV measurements with a plane in cross-flow highlight the formation of streamwise vortex pairs. The flow behavior is further characterized in terms of its turbulence statistics. Noise emissions are measured with an acoustic phased array in combination with beamforming. The serrations are found to be effective in reducing noise, and their application is studied for different degrees of airfoil incidence and serration flap angle.@en