Turbulent Boundary Layer Wall Pressure Research Articles

On the challenges of estimating the low-wavenumber wall pressure field beneath a turbulent boundary layer using a microphone array

The low-wavenumber components of the turbulent boundary layer (TBL) wall pressure field (WPF) are known to be the primary cause of structural vibration in low-Mach number flows, despite the maximal energy of the TBL being at the convective wavenumber. Existing semi-empirical TBL models show good agreement in predicting the WPF levels in convective region but differ significantly in the low-wavenumber domain. This study aims to highlight the challenges of estimating the low-wavenumber WPF in a TBL using a microphone array. A regularized Fourier-based approach is proposed to numerically study the estimation of the low-wavenumber WPF. Performance of the proposed method is initially evaluated by comparing the estimated WPF against a closed-form input TBL model. Effects of sensor spacing, co-array factor, and sensor distribution on the estimation of the low-wavenumber WPF levels are then investigated. To mimic experimental measurements a virtual acoustic experiment is proposed, involving the synthesis of snapshots of TBL-induced WPF. It is demonstrated that although with relatively small number of snapshots the convective region can be identified, a significant number of snapshots is required to well estimate the TBL low-wavenumber region.

Measurement of turbulent boundary layer unsteady wall pressures beneath elastomer layers of various thicknesses on a plate

The attenuation of turbulence-inducedwall pressure fluctuations through elastomer layers is studied experimentally and analytically. Wall pressure statistics are measured downstream from a backward facing step, with no elastomer present and beneath 2-, 3- and 4-mm-thick elastomers in a water tunnel facility. In the absence of an elastomer layer, the wall pressure spectra, cross-spectra and velocity statistics measured at the various locations downstream from the backward facing step are in excellent agreement with those reported in the archival literature. The streamwise coherence measured beneath the elastomer layers is higher than that measured in the absence of an elastomer layer, an effect which increases with increasing elastomer thickness. It is speculated that this increase in coherence level is due to the ability of the elastomer to support shear stresses, which effectively increases the area over which an eddy influences the normal stresses measured by the pressure sensors. The high-frequency filtering of the elastomers is also observed in the coherence at the smallest streamwise separation. The attenuation of the turbulent boundary layer wall pressure fluctuations through the elastomer layer using an analytical elastomer transfer function is in excellent agreement with the attenuation measured experimentally through all thicknesses of elastomer and at all the free stream velocities at which the experiments are performed.

Stationarity and homogeneity assumptions in wavenumber-frequency representation of turbulent boundary layer wall pressure.

The utility of the wavenumber-frequency spectrum for description and interpretation of wall pressure fluctuations beneath turbulent boundary layers has been amply demonstrated over the past decades. This representation is widely used in modelling the flow-induced noise due to boundary layers developing on vehicle surfaces. A recurring issue concerns the underlying assumptions of stationary and homogeneous wall pressure fields. Even on a flat plate, the turbulent boundary layer thickening violates the homogeneous assumption. A numerical experiment of a spatially evolving turbulent boundary layer on a flat plate provides detailed wall-pressure data to assess the stationarity and homogeneity assumptions in the computation of wavenumber-frequency spectra. High-order statistics, stationarity tests developed for random time series and modern signal processing tools, such as the empirical mode decomposition, are applied. In particular, it is shown that the nonhomogeneity due to the space-varying nature of the turbulent sources does not change the characteristics of the wavenumber-frequency representation of the wall pressure field.

Measurement of turbulent boundary layer unsteady wall pressures beneath elastomer layers of various thicknesses on a plate

The attenuation of turbulence induced wall pressure fluctuations through elastomer layers was studied experimentally and analytically. Wall pressure statistics were measured downstream from a backward facing step, with no elastomer present and beneath 2, 3, and 4 mm thick elastomers in a water tunnel facility. The step height, h, was 0.635 cm, and the wall pressures were measured at non-dimensional distances of x/h = 10, 24, 36 and 54 downstream from the step. The attenuation of the wall pressure spectra beneath the elastomer layers that was measured experimentally was then compared to analytical model predictions. An analytical elastomer transfer function, which models the transfer of turbulent boundary layer wall pressures on the surface of an elastomer to the normal stresses through the elastomer, was applied to the turbulent boundary layer wall pressure spectra measured in the absence of an elastomer layer and compared to spectra measured beneath the 2, 3, and 4 mm thick elastomers. The attenuation of the turbulent boundary layer wall pressure spectra through the elastomer layer using the analytical elastomer transfer function was in excellent agreement with the attenuation measured experimentally through all thicknesses of elastomer and at all free stream velocities at which the experiments were performed.The attenuation of turbulence induced wall pressure fluctuations through elastomer layers was studied experimentally and analytically. Wall pressure statistics were measured downstream from a backward facing step, with no elastomer present and beneath 2, 3, and 4 mm thick elastomers in a water tunnel facility. The step height, h, was 0.635 cm, and the wall pressures were measured at non-dimensional distances of x/h = 10, 24, 36 and 54 downstream from the step. The attenuation of the wall pressure spectra beneath the elastomer layers that was measured experimentally was then compared to analytical model predictions. An analytical elastomer transfer function, which models the transfer of turbulent boundary layer wall pressures on the surface of an elastomer to the normal stresses through the elastomer, was applied to the turbulent boundary layer wall pressure spectra measured in the absence of an elastomer layer and compared to spectra measured beneath the 2, 3, and 4 mm thick elastomers. The attenuation of...

A Kriging-based elliptic extended anisotropic model for the turbulent boundary layer wall pressure spectrum

The present study addresses the computation of the wall pressure spectrum for a turbulent boundary layer flow without pressure gradient, at high Reynolds numbers, using a new model, the Kriging-based elliptic extended anisotropic model (KEEAM). A space–time solution to the Poisson equation for the wall pressure fluctuations is used. Both the turbulence–turbulence and turbulence–mean shear interactions are taken into account. It involves the mean velocity field and space–time velocity correlations which are modelled using Reynolds stresses and velocity correlation coefficients. We propose a new model, referred to as the extended anisotropic model, to evaluate the latter in all regions of the boundary layer. This model is an extension of the simplified anisotropic model of Gavin (PhD thesis, 2002, The Pennsylvania State University, University Park, PA) which was developed for the outer part of the boundary layer. It relies on a new expression for the spatial velocity correlation function and new parameters calibrated using the direct numerical simulation results of Sillero et al. (Phys. Fluids, vol. 26, 2014, 105109). Spatial correlation coefficients are related to space–time coefficients with the elliptic model of He & Zhang (Phys. Rev. E, vol. 73, 2006, 055303). The turbulent quantities necessary for the pressure computation are obtained by Reynolds-averaged Navier–Stokes solutions with a Reynolds stress turbulence model. Then, the pressure correlations are evaluated with a self-adaptive sampling strategy based on Kriging in order to reduce the computation time. The frequency and wavenumber–frequency wall pressure spectra obtained with the KEEAM agree well with empirical models developed for turbulent boundary layer flows without pressure gradient.

Simulation of turbulent boundary layer wall pressure fluctuations via Poisson equation and synthetic turbulence

Flat plate turbulent boundary layers under zero pressure gradient are simulated using synthetic turbulence generated by the fast random particle–mesh method. The stochastic realisation is based on time-averaged turbulence statistics derived from Reynolds-averaged Navier–Stokes simulation of flat plate turbulent boundary layers at Reynolds numbers $\mathit{Re}_{\unicode[STIX]{x1D70F}}=2513$ and $\mathit{Re}_{\unicode[STIX]{x1D70F}}=4357$. To determine fluctuating pressure, a Poisson equation is solved with an unsteady right-hand side source term derived from the synthetic turbulence realisation. The Poisson equation is solved via fast Fourier transform using Hockney’s method. Due to its efficiency, the applied procedure enables us to study, for high Reynolds number flow, the effect of variations of the modelled turbulence characteristics on the resulting wall pressure spectrum. The contributions to wall pressure fluctuations from the mean-shear turbulence interaction term and the turbulence–turbulence interaction term are studied separately. The results show that both contributions have the same order of magnitude. Simulated one-point spectra and two-point cross-correlations of wall pressure fluctuations are analysed in detail. Convective features of the fluctuating pressure field are well determined. Good agreement for the characteristics of the wall pressure fluctuations is found between the present results and databases from other investigators.

Decentralized active control of turbulent boundary induced noise and vibration: a numerical investigation

Noise and vibration induced by turbulent boundary layer (TBL) wall pressure is a widespread issue for aircrafts and vehicles. One way to alleviate this problem is to enhance the structure’s sound isolation performance using active structural acoustic control. It is often difficult and costly to generate TBL excitation in laboratories for academic research, especially when the convection velocity is high. Thus, a numerical investigation in the early stages of research is appropriate. This paper proposes a prototyping method. The updated TBL semi-empirical model is chosen through a detailed survey of relevant literature. A tensioned panel used as a control target is intended to simulate realistic aircraft flight conditions. Decentralized control law is considered for active control. A finite element model is built which takes into account the property of TBL excitation. A model reduction technique is also adopted to decrease the order of the analysis model. Numerical simulation results show that the pre-stress effect and the hydrodynamic coincidence have a significant influence on plate vibro-acoustic performance and control channel number selection. Decentralized control of the tensioned plate structure under the pressure of TBL excitation is revealed in this work. A virtual prototyping loop justifies the control law’s effectiveness for analyzing TBL excitation. Finally, the procedure proposed may be extended to use in other models or real-life applications.

Acoustic responses of the composite sandwich plates with lattice truss core to the subsonic turbulent boundary layer

Acoustic responses of composite sandwich plates with lattice truss core to the subsonic turbulent boundary layer are investigated. The lattice truss core is composed of four sets of orthogonal stiffeners, two sets of oblique rods and one set of vertical columns, which establishes a significant transfer path of the reactive loadings. Bending and axial motion of the vertical columns makes a great impact on the power spectral density (PSD) of the transverse displacements for the sandwich plates with lattice truss core. The convective region of the high subsonic turbulent boundary layer pressure fluctuation spectra is the predominant vibrational source in the wide frequency bands, which makes the skin plate effectively radiate sound power into the mean air flow and the trim plate transmit sound waves into the static air by wavenumber conversion. Radiated acoustic power of skin plate is much larger than transmitted sound power of the trim plate and the sandwich plates can attenuate wave propagation of the airflow turbulent wall-pressure. The principal energy of the turbulent boundary layer wall-pressure for the water flow with a low speed can be transformed into the vibrational and acoustic energy of the sandwich plates in the low frequency band, to great extent.

Impact of the chosen turbulent flow empirical model on the prediction of sound radiation and vibration by aircraft panels

A precise definition of the turbulent boundary layer excitation is required to accurately predict the sound radiation and surface vibration levels, produced by an aircraft panel excited turbulent flow during flight. Hence, any existing inaccuracy on turbulent boundary layer excitation models leads to an inaccurate prediction of the panel response. A number of empirical models have been developed over the years to provide the turbulent boundary layer wall pressure spectral density. However, different empirical models provide dissimilar predictions for the wall pressure spectral density. The objective of the present study is to investigate and quantify the impact of the chosen empirical model on the predicted radiated sound power, and on the predicted panel surface acceleration levels. This study provides a novel approach and a detailed analysis on the use of different turbulent boundary layer wall pressure empirical models, and impact on mathematical predictions. Closed-form mathematical relationships are developed, and recommendations are provided for the level of deviation and uncertainty associated to different models, in relation to a baseline model, both for panel surface acceleration and radiated sound power.

A Generalized Corcos model for modelling turbulent boundary layer wall pressure fluctuations

A turbulent boundary layer (TBL) can be an important source of noise and vibration and its simulation is still an open research challenge. The stochastic pressure distribution associated with turbulence can significantly excite a structure that radiates acoustic power. In such a situation, a good description of the wall pressure field is necessary for an accurate prediction of the vibration and noise propagation. In order to tackle this issue, many TBL models have been developed since the 50s. Among others, the Corcos model has been widely used, especially because of its advantageous mathematical features. However, a major drawback is the small rate of decay for wavenumbers below the coincidence frequency.This paper presents a novel Generalized Corcos model that allows controlling the decay in the wavenumber domain below the convective peak, yet preserving similar mathematical advantages. Such a model is built on a two-dimensional Butterworth filter, whose orders allow to modify the shape of the TBL and possibly to adapt it to different flow configurations. The main aim of this work is to compare and position the Generalized Corcos model with respect to the existing models and to highlight its possible applications.

On the sensitivity of sound power radiated by aircraft panels to turbulent boundary layer parameters

The objective of the present study is to investigate and quantify how sensitive the response of an aircraft panel is to the change of the turbulent flow parameters. Several empirical models currently exist that provide the turbulent boundary layer wall pressure cross spectrum. These wall pressure cross spectrum models are usually dependent on four parameters: the reference power spectrum, the flow convective velocity, and the coherence lengths in streamwise and spanwise directions. All the proposed models provide different predictions for the wall pressure cross spectrum. Also, real flow conditions over aircraft do not conform to the ideal behavior of the turbulent boundary layer pressure predicted by the models. In this context, the questions that this work aims to explore are “What is the impact of different wall pressure estimates in the radiated sound power?” and “What is the effect of the range of possible flow conditions on the radiated sound power?”. For that objective, data from flight tests and estimates provided by the empirical models are used to predict radiated sound power, and the results are compared. A sensitivity analysis is performed and the relative contribution of each boundary layer parameter to the radiated sound power is obtained.

Transmission of a turbulent boundary layer wall pressure field through an elastomeric coating

The wall pressure fluctuations beneath a turbulent boundary layer introduce flow-induced noise and vibration which limits the performance of acoustic arrays. One method for mechanically filtering this energy is to separate the acoustic sensors from the fluid–solid interface with an elastomeric coating. Long wavelength acoustic energy is transmitted across the coating, and shorter wavelength energy from convected turbulence is attenuated. Experiments were conducted in an acoustically quiet water tunnel to measure the wall pressure fluctuations under 0.635mm and 1.27mm thick elastomeric coatings. Autospectra, magnitude and phase of the coherence, and convection velocities are presented for the range of Reynolds numbers 7540<Reθ<16,100. The autospectra display an exponential decay which increases with increasing frequency and coating thickness. A modified model of that given by Blake (1984) is shown to accurately predict the attenuations in the autospectra. The cross-spectral model given by Corcos (1963) is shown to be valid for measurements of the wall pressure coherence beneath the coatings.

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.

Comparison of theoretical and experimental wall pressure wavenumber–frequency spectra for axisymmetric and flat-plate turbulent boundary layers

The measurement and analysis of turbulent boundary layer wall pressure fluctuations using a wavenumber filter of sensors provide quantitative knowledge of turbulence physics. In addition, the sources of flow-induced noise and vibration for towed SONAR arrays can be determined. An axisymmetric turbulent boundary layer can have significantly different features than those of a comparable flat-plate boundary layer. Here, a detailed comparison of the distribution of wall pressure energy in both wavenumber and frequency between flat-plate and thick axisymmetric boundary layers is presented. The background theory of wavenumber–frequency spectra and state-of-the-art models for flat-plate boundary layers are discussed. The widely used model of Chase (1987), valid for flat-plate boundary layers over a wide range of Reynolds numbers, is used and combined with a sensor response function to allow the effects of spatial averaging to be considered. It is demonstrated that when measured boundary layer parameters for the axisymmetric case are used in the Chase flat-plate model, the results accurately predict the axisymmetric boundary layer wall pressure measurements.

Removing unwanted signals from wall pressure and vibration measurements on a structure subjected to turbulent boundary layer excitation.

Fluid‐structure interaction experiments typically involve measurements of the excitation force (or pressure) and the corresponding vibration response to the excitation. In addition to desired flow information, measured turbulent boundary layer wall pressure data often include unwanted signals such as acoustic pressures and vibration induced pressures. Measured vibration data on a structure can also include unwanted electrical noise and vibration energy from adjacent structures. A noise removal technique is presented, which allows one to remove an unlimited number of unwanted correlated signals from a set of measured data. In its simplest form, this technique is related to the coherent output power. However, the more general technique provides an ability to remove multiple signals and to retain complex values (magnitude and phase). These advantages can yield significantly greater information of the flow field and structure under investigation. This technique is demonstrated using measurements from an aluminum cylinder internally filled with water flowing at 20 ft/s.

Comparison of semi-empirical models for turbulent boundary layer wall pressure spectra

This paper reviews the development of semi-empirical models which calculate the turbulent boundary layer wall pressure frequency spectra. Various models published from the late 1960s to 2004 are reviewed, and the pressure spectra calculated using these models are compared to measured data obtained at various flow conditions at a substantially wide range of Reynolds number and boundary layer thickness. The experimental data consists of flows on flat surfaces in air and cylindrical surfaces in water. A summary of the results on the applicability and limitation of each of the models compared is discussed. A model is identified that provides a good overall prediction of the frequency spectra for all cases evaluated. The readers may use the information presented to choose a model appropriate for their specific applications.

Low-wave-number turbulent boundary layer wall pressure measurements from vibration data on a cylinder in pipe flow

Low-order vibration modes of a cylinder subjected to a fully developed turbulent boundary layer (TBL) in a pipe are measured and used to determine the low-wave-number content of energy in the boundary layer. The experiment is conducted using a 6-in.-diameter, thin-walled, aluminum test section filled with water flowing at 20 ft/s. Coupling of certain cylinder modes in the axial and radial directions allows use of the inverse method to determine the wave-number levels of TBL wall normal pressure and wall shear stress in the flow direction. These measurements are used to evaluate commonly used empirical models of the TBL wave-number pressure spectrum attributed to Corcos (1963) and Chase (1987) at lower wave numbers than have previously been reported. Preliminary results from several higher order cylinder modes confirm prior experimental findings that the Corcos model overestimates the low-wave-number pressures for these conditions by nearly 20 dB. The Chase model provides estimates within 3 dB of the measured low-wave-number pressure spectrum. [Work supported by Navsea 073R.]

Effect of a downstream ventilated gas cavity on turbulent boundary layer wall pressure fluctuation spectra

An analytical and experimental investigation is made of the effect of a 2-D ventilated gas cavity on the spectrum of turbulent boundary layer wall pressure fluctuations upstream of a gas cavity on a plane rigid surface. The analytical model predicts the ratio of the wall pressure spectrum in the presence of the cavity to the blocked wall pressure spectrum that would exist if the cavity were absent. The ratio is found to oscillate in amplitude with upstream distance (−x) from the edge of the cavity. It approaches unity as −ωx∕Uc→∞, where ω is the radian frequency and Uc is the upstream turbulence convection velocity. To validate these predictions an experiment was performed in a water tunnel over a range of mean flow velocities. Dynamic wall pressure sensors were flush mounted to a flat plate at various distances upstream from a backward facing step. The cavity was formed downstream of the step by injecting carbon dioxide gas. The water tunnel measurements confirm the predicted oscillatory behavior of the spectral ratio, as well as its relaxation to unity as −ωx∕Uc→∞. For −ωx∕Uc&amp;gt;7 the cavity has a negligible influence on the upstream wall pressure fluctuations.

An experimental-based model for prediction of flow noise with drag reducing polymers

The drag reduction characteristics of certain high molecular weight polymers have been studied by various investigators. Because of the polymer’s ability to reduce turbulent shear stress and dependence of the boundary layer wall pressure spectral amplitude on the shear stress, polymer has the potential to suppress noise and vibration caused by the boundary layer unsteady pressures. Compared to its effect on drag reduction, polymer additive effects on turbulent boundary layer (TBL) wall pressure fluctuations have received little attention. Kadykov and Lyamshev [Sov. Phys. Acoust. 16 (1970) 59], Greshilor et al. [Sov. Phys. Acoust. 21 (1975) 247] showed that drag reducing polymer additives do indeed reduce wall pressure fluctuations, but they have not established any scaling relationship which effectively collapse data. Some effort has been made by Timothy et al. [JASA 108 (1) (2000) 71] at Penn State University to develop a scaling relationship for TBL wall pressure fluctuations that are modified by adding drag reducing polymer to pure water flow. This paper presents a theoretical model based on the work of the Timothy et al. team at ARL, Penn State University. Through this model one can estimate, reduction in TBL flow induced noise and vibration for rigid smooth surfaces due to release of drag reducing polymers in boundary layer region. Using this theoretical model, flow noise as experienced by a typical flush mounted hydrophone has been estimated for a smooth wall plate as a function of polymer additive concentration. Effect of non-dimensionalisation of the wall pressure fluctuations frequency spectra with traditional outer, inner and mixed flow variables will also be addressed in the paper. The paper also covers a model based on molecular relaxation time in polymer additives which not only reduce drag but also flow induced noise up to certain polymer concentration.

Vibrations of infinite plates and the mean value vibrations of finite plates excited by turbulent boundary layer flows

The vibration response of a turbulent boundary layer (TBL) excited flat plate is analyzed using a finite-element model and infinite plate theory. For the finite-element models, discretization sufficient to resolve the convective fluctuations in the flow excitation field is used for the study. Clamped boundary conditions are assumed for the finite-element models and analyses are conducted at a variety of flow speeds and structural loss factors. Two equivalent TBL wall pressure excitation models are applied to the plates: (1) a modified Corcos cross-spectrum model for the finite-element models, and (2) a wave-vector-frequency spectrum model (the Fourier transform of the modified Corcos cross spectra) for the infinite plate theory. The TBL wall pressure autospectrum is approximated using the model derived by Smolyakov and Tkachenko. The infinite plate predicts the mean value response of the finite plate very well for all speeds and loss factors considered, showing consistency with Skudrzyks mean value theory and its usefulness for generating sound and vibration estimates.