Suppression of acoustic noise in the measurements of wall pressure fluctuations

It is shown that, in hydrodynamic noise measurements in the presence of acoustic noise acting upon the pressure fluctuation receiver, spatial filtering methods should provide the best results. Active methods are developed for suppressing the acoustic noise that affects a miniature receiver in the course of turbulent pressure fluctuation measurements. The methods are based on complicating the structure of the measuring transducer by introducing an extra compensating sensing element whose characteristics are identical with those of the main sensing element. The spatial filtering of small-scale turbulent pressure fluctuations by a finite-size electroacoustic transducer is used as the basis for the development of noise-compensated measuring systems, as well as methods of measuring the turbulent pressure fluctuations by receivers with noise compensation. A numerical study of the wave-number filtering of acoustic noise in wall pressure measurements by a noise-compensated receiver is performed.     

Measured wavenumber: frequency spectrum associated with acoustic and aerodynamic wall pressure fluctuations

Direct measurements of the wavenumber-frequency spectrum of wall pressure fluctuations beneath a turbulent plane channel flow have been performed in an anechoic wind tunnel. A rotative array has been designed that allows the measurement of a complete map, 63×63 measuring points, of cross-power spectral densities over a large area. An original post-processing has been developed to separate the acoustic and the aerodynamic exciting loadings by transforming space-frequency data into wavenumber-frequency spectra. The acoustic part has also been estimated from a simple Corcos-like model including the contribution of a diffuse sound field. The measured acoustic contribution to the surface pressure fluctuations is 5% of the measured aerodynamic surface pressure fluctuations for a velocity and boundary layer thickness relevant for automotive interior noise applications. This shows that for aerodynamically induced car interior noise, both contributions to the surface pressure fluctuations on car windows have to be taken into account.     

Measurement of wind noise levels in streamlined probes

This paper investigates the wind noise pressure spectra measured by aerodynamically designed devices in turbulent flow. Such measurement probes are often used in acoustic measurements in wind tunnels to reduce the pressure fluctuations generated by the interaction of the devices with the incident flow. When placed in an outdoor turbulent environment however, their performance declines noticeably. It is hypothesized that these devices are measuring the stagnation pressures generated by the cross flow components of the turbulence. Predictions for the cross flow contribution to the stagnation pressure spectra based on measured velocity spectra are developed, and are then compared to the measured pressure spectra in four different probe type devices in windy conditions outdoors. The predictions agree well with the measurements and show that the cross flow contamination coefficient is on the order of 0.5 in outdoor turbulent flows in contrast to the published value of 0.15 for measurements in a turbulent jet indoors.     

Measurement of wall pressure fluctuations in the presence of vibrations induced by a turbulent flow

A systematic study of the methods of measuring wall pressure fluctuations against a background of intense vibrations is carried out. The method of separating the turbulent signal from noise on the basis of monitoring the level of vibration interference is considered. Active methods of vibration control are developed for a miniature receiver of turbulent pressure fluctuations. It is shown that the methods based on the spatial filtering of the noise field offer the greatest promise. The filtering properties of vibration-proof receivers and measuring systems are investigated.     

Spatial filtering of wall pressure fluctuations beneath a turbulent boundary layer

Methods of experimental spatial filtering of wall pressure fluctuations beneath a turbulent boundary layer are developed with the aim of obtaining information on the wave number-frequency spectrum. The spatial filtering of the pressure field components by wave-vector filters is studied. The method of spatial filtering of pressure fluctuations by an acoustic array, i.e., a periodic structure with a finite number of elementary transducers, is analyzed. The relation between the wave number characteristic of the acoustic array and the wave number spectrum of the amplitude distribution of transducer’s local sensitivity is determined. Quantitative estimates are obtained for the sensitivity of the array to the wave number spectrum of turbulent boundary-layer pressures, which is necessary for measuring the wall pressure fluctuations in a turbulent boundary layer by wave-vector filters.     

Measuring surface pressure with far field acoustics

This paper presents measurements of the wavenumber frequency spectrum of wall pressure fluctuations under a turbulent boundary layer made using sound radiated from hydrodynamically smooth ridges in the surface. The measurements also serve as a test of the scattering theory of roughness noise. The radiated sound reveals a cut through the full three-dimensional wavenumber frequency spectrum of the wall pressure at the wavenumber of the surface. Since ridges can be made with very small wavelengths, this technique can be used to probe the structure of the wall pressure spectrum on scales far smaller than those that can be reached using conventional wall-mounted transducers. Furthermore, the method reveals the wavenumber frequency spectrum directly, without the need for multi-point measurements or the spatial Fourier transforming of data. Measured spectra bear a close similarity to Corcos’ and Chase's model forms, and confirm the applicability of the theory of roughness noise and its prediction of roughness noise directivity.     

Spatial filtering of wall pressure fluctuations. Methods of direct measurements of wave number-frequency spectra

The problems of spatial filtering of turbulent aerohydrodynamic noise sources are considered in connection with the problem of the direct measurements of wave number-frequency spectra of turbulent pressure fluctuations. The methods of wave-vector filtering of turbulent pressure fluctuations with the use of an acoustic array, i.e., a periodic structure with a finite number of elementary rectangular pressure transducers, are analyzed. Original versions of the wave number-frequency spectrum analyzer that allows the reconstruction of the wave number spectrum from the results of measurements are developed. The filtering characteristics of such analyzers are studied, and the relation between the wave number characteristic of an acoustic array and the wave number spectrum of the amplitude distribution of transducer’s local sensitivity over the aperture is determined.     

Wall pressure fluctuation spectra due to boundary-layer transition

Boundary-layer transition has been expected to be an important contributor to sensor flow-induced self-noise. The pressure fluctuations caused by this spatially bounded, and intermittent, phenomenon encompass a very wide range of wavenumbers and temporal frequencies. Here, we analyze the wavevector–frequency spectrum of the wall pressure fluctuations due to subsonic boundary-layer transition as it occurs on a flat plate under zero-pressure gradient conditions. Based on previous measurements of the statistics of the boundary-layer intermittency, it is found that transition induces higher low-streamwise wavenumber wall pressure levels than does a fully developed turbulent boundary layer that might superficially exist at the same location and at the same Reynolds number. The transition zone spanwise wavenumber pressure components are virtually unchanged from the fully developed turbulent boundary-layer case. The results suggest that transition may be more effective than the fully developed turbulent boundary layer in forcing structural excitation at low Mach numbers, and it may have a more intense radiated noise contribution. This may help explain increases in measured sensor self-noise when the sensors are placed near the transition zone. We believe, based on the presented analytical calculation and numerical simulation, that the rapid growth and subsequent decay of turbulent spots in the intermittent transition zone causes the higher low-(streamwise) wavenumber spectra.     

Wave number-frequency spectrum of turbulent pressure fluctuations: Methods of measurement and results

The methods proposed earlier for measuring the wave number-frequency spectrum of wall pressure fluctuations beneath a turbulent boundary layer are considered: the spatial filtering of the pressure field components by special-purpose transducers (wave filters) and the digital processing of signals obtained from an array of transducers. It is shown that, for the wave filters, transducers with a rectangular shape of sensitive surface rather than those with a circular one are necessary. Results of measuring the wave number-frequency spectrum of turbulent pressure fluctuations in a low-noise wind tunnel are presented. The measurements are performed with the use of four wave filters consisting of rectangular transducers with a constant sensitivity distribution over their surfaces. The mathematical model of the wave number-frequency spectrum proposed earlier by the authors is compared with the measurement data reported by Abraham and Keith. The model is used for processing the results of measurements in the wind tunnel. The measured spectra are compared with the data obtained by Martin and Leehey.     

The scaling of the wall pressure fluctuations in polymer-modified turbulent boundary layer flow

Wall pressure fluctuations and integrated skin friction were measured beneath a turbulent boundary layer that was modified by adding drag-reducing polymer to the pure water flow. The measurements were performed on an axisymmetric model, equipped with an isolated cylindrical drag balance section, and placed in the test section of the 0.3048-m-diam water tunnel at ARL Penn State. Data were acquired at a free-stream velocity of 10.7 m/s with pure water and with polymer added to the water at concentrations of 1, 5, 10, and 20 weight parts per million. Nondimensionalization of the wall pressure fluctuation frequency spectra with traditional outer, inner, and mixed flow variables failed to adequately collapse the data. The mean square wall pressure fluctuations were found to scale linearly with the wall shear stress. Polymer addition had little effect on the characteristic time scale of the flow. These properties were used to develop a novel form of the nondimensional wall pressure fluctuation spectrum that provided the best collapse of the measured data.     

On the hydrodynamic and acoustic wall pressure fluctuations in turbulent pipe flow due to a 90° mitred bend

When the fully-developed turbulent flow in a pipe of circular cross-section is forced to negotiate a 90° mitred bend, flow separation occurs at the inner and outer corners of the bend, with random switching of the separation regions from one side of the plane of symmetry of the bend to the other (as was previously observed by Tunstall and Harvey). The resulting disturbance to the fluctuating pressure field consists of intense non-propagating fluctuations over the region of the inner-wall separation, which near re-attachment have a maximum rms value of about 33% of the undisturbed centre-line dynamic pressure, but are rapidly attenuated with downstream distance from the bend. Beyond about 12 diameters downstream the only remaining disturbance is an acoustic field comprising propagating higher order modes and plane waves, the latter making the larger contribution to the overall mean square pressure. Extensive spectral measurements of the wall pressure field for flow Mach numbers in the range 0·2-0·5 are presented, and regions where higher order modes are detectable are identified. Downstream of the bend, wall pressure spectra generally have two local maxima at frequencies below those at which higher order acoustic modes can propagate. They occur at Strouhal numbers of about 0·4 and 1·6, and turbulent fluctuations at these frequencies in the vicinity of the bend appear to be mainly responsible for the generation of plane acoustic waves. The former Strouhal number does not vary significantly with streamwise position but decreases slightly with increasing flow speed; the latter is somewhat more sensitive to both flow speed and streamwise position. Upstream of the bend wall pressure spectra exhibit only the maximum at a Strouhal number of about 0·4.     

Experimental estimate of wave spectra of wall pressure fluctuations of the turbulent boundary layer in the subconvective region

A technique is developed for measuring the intensity of the frequency-wave spectrum components of wall pressure fluctuations of the turbulent boundary layer in a quiet aeroacoustic installation with the use of wave filters in the form of rectangular plates. Aluminium-alloy and organic-glass plates of various thickness under a fine-meshed screen are used, set up rigidly flush with the polished wall of the working part of the installation. The experimental data testify to the fundamental possibility of determining the field components of wall pressure fluctuations of the turbulent boundary layer using similar wave filters in the subconvective region, where a substantially lower pressure fluctuation intensity is observed in comparison to the intensity in the region of the convective maximum of the frequency-wave spectrum at a small flow velocity.     

High-Reynolds-number turbulent-boundary-layer wall pressure fluctuations with skin-friction reduction by air injection

The hydrodynamic pressure fluctuations that occur on the solid surface beneath a turbulent boundary layer are a common source of flow noise. This paper reports multipoint surface pressure fluctuation measurements in water beneath a high-Reynolds-number turbulent boundary layer with wall injection of air to reduce skin-friction drag. The experiments were conducted in the U.S. Navy's Large Cavitation Channel on a 12.9-m-long, 3.05-m-wide hydrodynamically smooth flat plate at freestream speeds up to 20 ms and downstream-distance-based Reynolds numbers exceeding 200 x 10(6). Air was injected from one of two spanwise slots through flush-mounted porous stainless steel frits (approximately 40 microm mean pore diameter) at volume flow rates from 17.8 to 142.5 l/s per meter span. The two injectors were located 1.32 and 9.78 m from the model's leading edge and spanned the center 87% of the test model. Surface pressure measurements were made with 16 flush-mounted transducers in an "L-shaped" array located 10.7 m from the plate's leading edge. When compared to no-injection conditions, the observed wall-pressure variance was reduced by as much as 87% with air injection. In addition, air injection altered the inferred convection speed of pressure fluctuation sources and the streamwise coherence of pressure fluctuations.     

Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method

The objective of this paper is to assess the accuracy and efficiency of the immersed boundary (IB) method to predict the wall pressure fluctuations in turbulent flows, where the flow dynamics in the near-wall region is fundamental to correctly predict the overall flow. The present approach achieves sufficient accuracy at the immersed boundary and overcomes deficiencies in previous IB methods by introducing additional constraints – a compatibility for the interpolated velocity boundary condition related to mass conservation and the formal decoupling of the pressure on this surfaces. The immersed boundary-approximated domain method (IB-ADM) developed in the present study satisfies these conditions with an inexpensive computational overhead. The IB-ADM correctly predicts the near-wall velocity, pressure and scalar fields in several example problems, including flows around a very thin solid object for which incorrect results were obtained with previous IB methods. In order to have sufficient near-wall mesh resolution for LES and DNS computations, the present approach uses local mesh refinement. The present method has been also successfully applied to computation of the wall-pressure space–time correlation in DNS of turbulent channel flow on grids not aligned with the boundaries. When applied to a turbulent flow around an airfoil, the computed flow statistics – the mean/RMS flow field and power spectra of the wall pressure – are in good agreement with experiment.     

Extraction of the acoustic component of a turbulent flow exciting a plate by inverting the vibration problem

An improvement of the Force Analysis Technique (FAT), an inverse method of vibration, is proposed to identify the low wavenumbers including the acoustic component of a turbulent flow that excites a plate. This method is a significant progress since the usual techniques of measurements with flush-mounted sensors are not able to separate the acoustic and the aerodynamic energies of the excitation because the aerodynamic component is too high. Moreover, the main cause of vibration or acoustic radiation of the structure might be due to the acoustic part by a phenomenon of spatial coincidence between the acoustic wavelengths and those of the plate. This underlines the need to extract the acoustic part. In this work, numerical experiments are performed to solve both the direct and inverse problems of vibration. The excitation is a turbulent boundary layer and combines the pressure field of the Corcos model and a diffuse acoustic field. These pressures are obtained by a synthesis method based on the Cholesky decomposition of the cross-spectra matrices and are used to excite a plate. Thus, the application of the inverse problem FAT that requires only the vibration data shows that the method is able to identify and to isolate the acoustic part of the excitation. Indeed, the discretization of the inverse operator (motion equation of the plate) acts as a low-pass wavenumber filter. In addition, this method is simple to implement because it can be applied locally (no need to know the boundary conditions), and measurements can be carried out on the opposite side of the plate without affecting the flow. Finally, an improvement of FAT is proposed. It regularizes optimally and automatically the inverse problem by analyzing the mean quadratic pressure of the reconstructed force distribution. This optimized FAT, in the case of the turbulent flow, has the advantage of measuring the acoustic component up to higher frequencies even in the presence of noise.     

A wave field synthesis approach to reproduction of spatially correlated sound fields

This article discusses an open-loop wave field synthesis (WFS) approach for the reproduction of spatially correlated sound fields. The main application concerns laboratory reproduction of turbulent boundary layer wall pressure on aircraft fuselages and measurement of their sound transmission loss. The problem configuration involves reconstruction of random sound pressure distributions on a planar reproduction surface using a planar array of reproduction monopoles parallel to the reproduction plane. In this paper, the WFS formulation is extended to sound fields with imposed time and spatial correlation properties (or equivalently imposed cross-spectral density in the frequency and wave number domains). Numerical examples are presented for the reproduction of a propagating plane wave, diffuse acoustic field and wall pressure in subsonic or supersonic turbulent boundary layers. The reproduction accuracy is examined in terms of the size of the source plane and reproduction plane, their separation, and the number of reproduction sources required per acoustic wavelength. While the reproduction approach cannot reconstruct sub-wavelength correlation scales of subsonic turbulent boundary layers, it effectively reconstructs correlation scales larger than the acoustic wavelength, making it appropriate for diffuse acoustic field and supersonic turbulent layers.     

Acoustic Transducer of Turbulent Pressure Fluctuations in a Temperature-Stratified Medium

The operation of an acoustic transducer in a temperature-stratified medium is investigated. The formation of a response of piezoceramic transducers of pressure fluctuations under the action of temperature fluctuations in a working medium on the sensor element is considered. The attenuation of the temperature signal of a pressure transducer in a turbulent boundary layer is calculated numerically. The effect of distortions of the spectral levels of pressure fluctuations detected by a sound transducer in the field of temperature inhomogeneities is investigated for the example of measurements of turbulent pressure fluctuations in a boundary layer during vertical ascent of the device to the surface from a specified depth in a deep sea.     

The rôle of surface shear stress fluctuations in the generation of boundary layer noise

The influence of unsteady wall shear stress on boundary layer noise and wall pressure fluctuations is discussed. It is argued that in the acoustic analogy theory of boundary layer noise the surface shear stress “dipole” characterizes acoustic propagation and not generation. Analytical results are presented in support of this view which, in addition, indicate that the effect of the surface dipole is to dininish rather than enhance boundary layer radiation at low Mach numbers.     

Measurements of roughness noise

Experiments have been performed on the roughness noise produced by a two-dimensional turbulent wall jet boundary layer flowing over short fetches of sandpaper roughness. A range of rough surface sizes were studied from hydrodynamically smooth through fully rough. Velocity measurements were made to document the form of the wall jet boundary layer and the influence of the roughness upon it. Acoustic measurements showed background noise levels to be very low so that the sound produced by the rough surfaces could be clearly detected with signal to noise ratios as large as 20 dB. Even hydrodynamically smooth roughness was found to produce noise, conclusively indicating the presence of scattering as a source mechanism. Variations of the roughness noise spectra with flow speed and roughness size are found to be inconsistent with any simple parameter scaling. Boundary layer wall pressure fluctuation measurements made within the roughness fetches reveal a spectral form quite different than the roughness noise, and fluctuation levels some 50-70 dB higher. Despite these differences the wall pressure and roughness noise are found to be very simply related, at least at lower frequencies (<6 kHz). The roughness noise spectrum varies closely as the product of the wall pressure spectrum, the frequency squared, and the mean-square roughness height. This is the scaling predicted by scattering theory and implies a major simplification to the problem of roughness noise prediction for stochastic surfaces.