Corcos Model Research Articles

Study and modeling of the ultrasonic ambient noise induced by the fluid-structure interaction in a pipe

An elastic guided wave-based structural health monitoring (SHM) system consists in examining the integrity of a structure through the propagation of elastic waves. In this context, passive methods turn initial hindrances into advantages by making use of the ambient ultrasonic noise in a structure in operation, through the cross-correlation. Although they have been empirically applied in several configurations, no model is available to predict the link between the flow regime and the convergence of the ambient noise correlation towards the impulse response of the system. Considering the different parameters involved in the case of a pipe, a physical approach of this issue may be studied through the turbulent boundary layer, which has long been described by the Corcos model. Corcos-like models have essentially been applied so far on the audible range, below 1 kHz, where we are interested in frequencies around 100 kHz, typical for SHM applications. The semi-empirical model allows to determine a wall boundary pressure, which, applied at the pipe's inner boundaries, acts as a source term for ultrasonic elastic waves propagating in the pipe. Our goal is then to study if such a model can be used at these high frequencies to reproduce the experimental observations.

A multivariate and wavelet-based analysis on the wall pressure fluctuations for propellers in ground effect

This study, conducted at the University of Bristol’s aeroacoustic facility, explores the aeroacoustic characteristics of a 10-inch APC propeller in pusher configuration within ground effect conditions. Tested at a rotational speed of 7000 r/min, the propeller’s performance was evaluated at varying distances from the ground. Wall pressure fluctuations near the propeller were measured at eight radial points, complemented by far-field acoustic measurements. Consistent with previous research, distinctive thrust and torque behaviours were observed when operating both in and out of ground effect. Notably, a significant noise increase of approximately 5 dB was observed on the ground’s reflected side, while a reduction of about 14 dB was detected on the shielded side. Higher-order statistical analysis such as skewness and kurtosis revealed substantial effects of tip vortex impingement in ground effect conditions. This study applies two-point statistics and the Corcos model to analyze propeller-induced wall pressure fluctuations. The coherence function effectively captures the intricate dynamics of pressure variations across different spatial locations and frequencies. This approach offers novel insights into the behaviour of boundary layers and flow-induced pressures in the context of propellers operating in the ground effect. Wavelet decomposition was utilized to differentiate the influences of the boundary layer and the acoustic field. This comprehensive analysis highlights the intricate dynamics of propeller operation in ground effect, contributing valuable insights to the field of aeroacoustic research.

Space Launch System Unsteady Forces Developed from Unsteady-Pressure-Sensitive-Paint–Based Corcos Model Parameters

During atmospheric ascent, launch vehicles (LVs) experience large dynamic loads at transonic conditions where aerodynamic buffet is most critical. To estimate buffet loads, coupled loads analyses typically utilize suitable forcing functions, called buffet forcing functions (BFFs). One of the key buffet environment contributors is the turbulent boundary layer (TBL) acting on the LV outer skin. The cross-spectral density function of TBL-induced fluctuating pressures can be estimated using the widely accepted Corcos model. In the context of transonic buffet, the performance of this model is not well established, partly because of lack of data. To fill this gap, NASA recently acquired extremely high-spatial-density data for the Space Launch System vehicle using the unsteady-pressure-sensitive-paint (uPSP) optical measurement technique. A methodology is developed for extraction of the Corcos model parameters using these unique data, with a focus on the LV design application. The model hypotheses are verified, and the model parameters are empirically tuned. For selected panels on the vehicle, force coherence factors are derived based on the Corcos model, and the associated panel BFFs are compared to uPSP data. It is shown that the modeled BFFs are in agreement with direct integration of uPSP data, except for regions where pressure fluctuations are spatially nonuniform. In those regions, the Corcos-based BFFs exhibit inherent limitations of BFF estimation methods that rely on discrete pressure measurements. Lastly, extending the present implementation of the Corcos model to frequencies impacted by vortex-shedding phenomena can result in underconservative BFF estimates at the subharmonic of the vortex shedding.

Comparison of Corcos-Based and Experimentally Derived Coherence Factors for Buffet Forcing Functions

In this paper, high-spatial-resolution unsteady pressure-sensitive paint (UPSP) data are utilized to compare two methods for panel buffet forcing function (BFF) estimation for the Space Launch System (SLS). Such methods are based on discrete pressure measurements within a panel but employ coherence factors to account for partially correlated fluctuating pressures across the whole panel. In one method, coherence factors are derived based on the Corcos model, whereas the second method utilizes experimentally derived coherence factors. To simulate discrete measurements using UPSP data, suitable subsets of the data are extracted. When full UPSP resolution is retained, UPSP data provide a benchmark to assess discrete-measurement-based methods. The analysis focuses on the peak SLS buffet environment located downstream of the forward attachment hardware (FAH) between the core stage and solid rocket boosters. Trends of the Corcos-based and experimentally derived coherence factors are in reasonable agreement with the benchmark. However, at certain frequencies, experimentally derived coherence factors are sensitive to the separation distance between pressure measurements utilized to compute coherence lengths. Such sensitivity originates from deviation of the experimentally based coherence function from an exponential decay assumption. On the other hand, the present implementation of the Corcos model fails to capture certain nonturbulent boundary-layer-related environments, such as a subharmonic of FAH vortex shedding. For all methods presented in this paper, at near-transonic conditions, increased pressure coherence and spatial nonuniformity lead to BFF overestimation and sensitivity to the pressure measurement location within the panel.

Investigation of sound transmission through a finite length cylindrical shell in the presence of an exterior turbulent boundary layer

This paper studies sound transmission through a thin cylindrical shell of finite length. The structure is subjected to an exterior turbulent boundary layer (TBL) excitation and the boundary conditions of its two ends are considered as simply-supported. The classical shell theory (CST) is employed to derive wave propagation in the cylindrical shell, and the Corcos model is applied to describe pressure fluctuation due to TBL. According to the existence of two axial and radial modes, a complete convergence study is presented. To examine sound transmission through the structure, a comprehensive parameters study is provided on the resulting power spectral density (PSD) of the kinetic energy. To validate the results of the present method, the statistical energy analysis (SEA) method is used. For this purpose, modeling is performed by SEA in VA One software, which shows the high accuracy of the results of the present method. The analytical predictions suggest that the sound insulation performance of such a finite length structure is enhanced considerably by increasing the thickness of the shell in a broad-band frequency range. Similar effects on sound transmission are observed for Young’s modulus and density of the shell particularly in the low and high-frequency ranges, respectively. Whereas, enhancing the turbulent pressure and freestream velocity adversely affects sound radiation into the structure.

Wind-induced noise estimation of wind speed and direction within urban microspaces: Characterizing flow condition of urban environments

In this work, the flow conditions within urban microspaces are predicted from wind-induced noise. Wind speed and direction are estimated by fitting the spatial coherence of the wind noise distribution among closely spaced microphones measurements to the Corcos model in the least squares sense. The estimated wind speed and direction are compared to measure results. The estimated flow conditions of the measured urban areas are discussed.

Acoustic optimization design of porous materials on sandwich panel under flow-induced vibration

In this study, porous sound-absorbing materials used as a lining in double-panel structure applications (such as high-speed train body structures) to limit flow-induced vibration interior noise were studied, and acoustic optimization design was performed. First, in the wavenumber domain, the cross-spectrum Corcos model was used to characterize the dynamic hydrodynamic pressure of turbulence. Biot’s theory is used to model the porous materials. The transmission loss (TL) of the sandwich panel were also determined based on the model superposition method. Three types of sandwich panel structures were considered: air–air (A–A), bonded-bonded (B–B), and bonded-air (B–A). The TL of the three structure types under hydrodynamic pressure was used to evaluate the suppression of flow-induced vibration interior noise in porous materials. The effects of flow velocity, thickness and density of the porous material, and three types of polyimide foam on the TL characteristics of the sandwich panel were investigated. The results show that the flow velocity has a significant influence on the TL of the sandwich panel. The TL of the sandwich panel decreases by 3–4 dB when the flow velocity increases by 100 km/h The B–A configuration has satisfactory sound insulation performance at most frequencies. With an increase in material thickness, the TL of the sandwich panel structure first increases and then decreases, and the material density mainly affects the TL of the structure at intermediate and high frequencies. Based on the objectives of maximizing the average transmission loss (TLavg) and minimizing the structural weight, the acoustic optimization design of the B–A structure was performed, and the balance between the two objective functions was achieved by a nondominated sorting genetic algorithm (NSGA-Ⅱ). The TLavg s of the sandwich panel structure increased by 5.2 dB when the total mass of the structure was decreased by 0.2 kg.

Acoustic optimization design of window of high-speed train under flow-induced vibration

In this study, the sound optimization design of a high-speed train window structure under a turbulent boundary layer (TBL) pressure fluctuation is investigated. First, the Corcos model is used to characterize the cross-spectrum of the dynamic surface pressure, and analytical solutions of the window speed response, radiated sound power, and transmission loss (TL) are obtained. The effects of the cavity thickness, cavity damping, panel thicknesses, and panel damping on the TL were investigated by numerical examples. In the structural sound optimization process, the quality reduction and the sound response are essentially in conflict with each other; therefore, non-dominated sorting genetic algorithm (NSGA)-II is adopted for a dual-objective design. The numerical results show that the train speed has a significant influence on the TL of the window structure, which decreases by 4 dB when the train speed increases by 100 km/h. With the increase in the train speed, the effect of improving the TL of the window structure by increasing the thickness and damping of the window cavity gradually decreases. The TL of the window structure is more sensitive to the thickness of the window panels than that of other panels parameters; however, the thickness sensitivity decreases with the increase in the speed, whereas the improvement effect of panel damping on the TL increases with the increasing train speed. The Pareto optimal design of the window structure at 350 km/h was obtained using the NSGA-II optimization design method. The optimal design reduced the mass by 41.6 % and increased the average transmission loss (TLavg) increased by 6.2 dB compared to those of the original window structure.

Wind speed and direction estimation based on the spatial coherence of closely spaced microphones.

Wind-induced noise recorded with a compact microphone array can be exploited to infer the mean velocity of the free-field airflow. In this work, a model-based method to estimate the wind flow speed and direction is proposed that uses spectro-spatial correlations of closely spaced microphone signals. As shown in a recent work by the present authors, the normalized cross-power spectral density of flow-induced noise measured with closely spaced microphones, also referred to as the spatial coherence, can be approximated by a semi-empirical model, named the Corcos model. Due to the dependency of the Corcos model on the airflow velocity, the measured spatial coherence provides information on the sought quantity. Speed and direction can be resolved by fitting the measured spatial coherence to the analytical Corcos model in the least squares sense. The accuracy of the proposed method is investigated across a range of wind speed between 0.5 and 12 ms-1 and all directions, using observation lengths from 5 s to 1 h. The audio samples under test were recorded indoors and outdoors and labeled by an ultrasonic anemometer. The evaluation results show that the accuracy can be increased by reducing the time resolution.

Coherence of wall pressure fluctuations in zero and adverse pressure gradients

The wall pressure fluctuations induced by turbulent boundary layers on a flat plate model were measured with an L-shaped array of Kulite miniature pressure sensors. By installing a NACA airfoil above the plate with an adjustable angle of attack, different adverse pressure gradients were produced on the plate. The streamwise and spanwise coherence and coherence lengths of the wall pressure fluctuations are calculated for zero and adverse pressure gradient flows. The effect of the pressure gradient on the coherence and coherence lengths in both streamwise and spanwise directions is quantified. Based on the results of the present test cases and selected published datasets in zero pressure gradients, covering the range of Reynolds numbers based on the momentum thickness between 3300 and 42000, the Reynolds number dependence of the streamwise wall pressure coherence is discussed and mathematically expressed. A coherence length model for zero pressure gradient boundary layers, taking into account the Reynolds number effect, is proposed based on scaled spectra of the coherence lengths. In comparison with the other published models, the present model achieves a considerable improvement of the prediction accuracy for boundary layer flows, covering a large range of Reynolds numbers. Furthermore, an evaluation of the Corcos model and the Smol’yakov and Tkachenko model for prediction of the off-axis coherence of the fluctuating wall pressure field is made.

A formulation for turbulent-flow-induced vibration of elastic plates with general boundary conditions

A formulation for studying the vibration characteristics of the rectangular plate with general boundary conditions excited by the turbulent boundary layer is developed in this paper. The Rayleigh-Ritz method, modified Fourier spectral approach, and the classical theory of elastic plates are employed to establish the vibration model of the rectangular plate. Besides, the sound pressures are calculated by the Rayleigh integral and the turbulent boundary layer pressure field is described by the cross-spectral density expression of the Corcos model. The power spectral density of vibration characteristics can be obtained according to the stochastic theory. The results indicated that the power spectral density of responses calculated in this paper are consistent with those in the references, which validate the accuracy of the developed formulation. The innovation of this formulation lies in the application of modified Fourier spectral approach to the turbulent-flow-induced vibration for the first time. The velocity power spectral density of the plate with classical and elastic boundary conditions are studied, and the influences of the boundary conditions are discussed. The boundary conditions affect the vibration response by controlling the system stiffness of the plate. Moreover, the influences of turbulent flow speed and direction under different boundary conditions are studied. It is found that the increasing turbulent flow speed leads to the increase of the vibration level, and the growth rate is similar under different boundary conditions. The velocity power spectral densities are slightly different when a turbulent flow along the short side and long side of the plate.

Study on Radiated Noise of a Panel under Fluctuating Surface Pressure Due to an Idealized Side Mirror

As traditional automobiles develop towards new energy vehicles, the noise, vibration and harshness (NVH) performance of automobiles is facing new challenges. Without the cover of the traditional engine noise and inlet and exhaust noise, the high-speed wind noise becomes more prominent. Thus, research on the calculation method of vehicle interior noise in high-speed driving condition is needed. However, vehicle body structure is complex, and the external excitation components are complicated. In order to analyze the method of predicting the vehicle interior noise at high speed, an idealized side mirror model is taken as the research object in this paper and the radiated noise of a panel under the fluctuating surface pressure (FSP) due to the idealized side mirror is studied. The FSP of the panel is first studied by the numerical simulations of incompressible and compressible flow field. For the incompressible flow field, the Corcos turbulent boundary layer (TBL) model is established to simulate the convective component and the boundary element method (BEM) is used to extract the acoustic component. Subsequently, the Corcos model coupling BEM method, the random modal force coupling BEM method and the deterministic modal force coupling BEM method are used separately to calculate the noise of the panel under the FSP. For the compressible flow field, the convective and acoustic component in the fluctuating pressure are separated by the wavenumber-frequency spectrum (WFS) method. The radiated noise of the panel under the FSP is calculated again by using the WFS, the method of random modal force and the method of deterministic modal force, respectively. Then, the computational time of the six methods of incompressible and compressible calculation is compared. Finally, a fast and accurate method of calculating the panel radiated noise under FSP is obtained by comparing the computational accuracy with the experimental results and combining the computational time: the method of incompressible random modal force. This method can be used to quickly and accurately analyze the vehicle interior noise at high speed, and to optimize the exterior protrusions and the vehicle sound package for improving the vehicle NVH performance at high speed.

A New Turbulent Wall-Pressure Fluctuation Model for Fluid–Structure Interaction

Abstract Most fluid flows of practical applications are turbulent. In flows involving interactions with flexible structures, such as an aircraft skin, the knowledge of turbulent wall-pressure fluctuations is critical. Both measurements and direct numerical simulations of the wall-pressure fluctuations are difficult and costly. Therefore, the use of the semi-empirical turbulent wall-pressure fluctuation models is wide spread. One of the most widely used models is that due to Corcos (Resolution of Pressure in Turbulence,” J. Acoust. Soc. Am., 35(2), pp. 192–199). The biggest advantages of this model are simplicity and ease of use. However, the model has several weaknesses as well and therefore many models have been proposed to address them. In this paper, we briefly review existing models and then propose a model that remedies their weaknesses. The proposed model keeps the simplicity of the Corcos model and it is given in both space-frequency and wavenumber-frequency spaces. The new model accurately captures the convective peak and shows better agreement with experimental data at lower wavenumbers.

A Unified Methodology to Evaluate the Radiated Noise Due to Turbulent Boundary Layer Flows

For vibro-acoustic applications, a turbulent wall pressure (TWP) fluctuations model was derived. The model is based on the resolution of Poisson's equation. The pressure is characterized in time and space through its spectrum in the frequency wave-number domain. The developed model follows trends commonly observed using Corcos model in a large frequency range but also shows new behaviors for low and high frequencies. The radiated noise due to TWP fluctuations is then computed in accordance with the form of the TWP spectrum. A specific computational methodology is proposed to perform the calculation without introducing limiting hypothesis on the radiated impedance.

난류 경계층 가진에 의한 소나돔 음향창 구조물의 음향 방사 파워

This paper presents analysis results on the acoustic radiated power from the rubber-inserted flat acoustic window of sonar dome, which is excited by pressure fluctuation of turbulent flow. Analysis is based on the well-known RKU theory, Corcos model and modal approach. It is found that increasing the loss factor has less effect on decreasing the radiated sound power despite of significant decrease of vibration level. In addition, increasing the thickness of the rubber layer, under same total thickness, can increase the vibration level in the high frequency range. However, the acoustic radiated power is similar or less than that of the thinner rubber layer.

Flow-induced vibration analysis of a vehicle's front side window glass

This study analyses the flow-induced vibration of a car's front side window glass. The following working steps were carried out: experimental modal analysis to yield the dynamic characteristics of the system; wind tunnel experiments and corresponding numerical simulations with a computational fluid dynamics (CFD) code to acquire the pressure field including the fluctuations on the side glass; and a MATLAB implementation of the vibration velocity response calculated with the Corcos model and Mellen elliptical model. The MATLAB model calculates the averaged vibration velocity response by means of the pressure loading from the wind tunnel test or from the CFD simulations as well as by means of the result of the experimental modal analysis. The hereby calculated vibration response of the side glass has been validated by the results of laser Doppler vibrometer measurements in the wind tunnel. Through parameter study with the MATLAB algorithm, it was found that flow convective velocity with U c = 0.6*U, flow decay rates with α x = 0.1 and α z = 0.77 could be considered as the suitable values for the structure vibration velocity response calculation in this type of flow with a low Mach number.

Vibrational response of a rectangular duct of finite length excited by a turbulent internal flow

Gas transport ductwork in industrial plants or air conditioning networks can be subject to vibrations induced by the internal flow. Most studies in this matter have been carried out on circular ducts. This paper focuses specifically on the vibratory response of a rectangular duct of finite length excited by an internal turbulent flow. A semi-analytical model taking into account the modal response of the structure due to both aerodynamic and acoustic contributions is derived. The aerodynamic component of the excitation is applied on the basis of Corcos model where the power spectral density of the wall pressure is determined experimentally. The acoustic component is based on the propagating modes in the duct where the acoustic modal contribution are extracted via cross-spectral densities. The vibrational response is given for a 0.2 × 0.1 × 0.5 m3 duct made of 3 mm steel plates excited by 20 m/s or 30 m/s flows. Comparisons between experimental results and numerical predictions show a good agreement. The competition between acoustic and aerodynamic components is highlighted.

Sound Radiation Analysis of a Front Side Window Glass of DrivAer Model under Wind Excitation

To study the car radiated noise caused by turbulent pressure fluctuation on the side glass under wind excitation, a clay model of DrivAer was constructed except that the front left side window was built with real glass. Firstly, the constraint boundary condition of the side glass was set equivalent to a series of springs for the modelling with Finite Element Method (FEM). Then, a platform based on Matlab‐Abaqus cosimulation was originally developed, and the genetic algorithm was applied to find out the best fitted spring stiffness, which was used to build the equivalent model. Then working as excitation, the Corcos model was applied to calculate the power spectrum density of the turbulence pressure fluctuations acting on the side glass. Subsequently, the finite element modal superposition method was used to solve the vibroacoustic coupling equation to get the noise level of the driver’s ear position in the vehicle interior. Finally, the surface vibration velocity distribution of side glass under wind excitation was measured with Laser Vibrometer and then with Boundary Element Method (BEM), the radiated noise into interior was calculated as well (semisimulation). Through comparison of these two results, it shows good agreement up to 1000 Hz. It demonstrates that the above method is applicable to calculate the sound radiation caused by the side glass’ vibration at the low and middle frequency range. Therefore, an approach of calculating sound radiation of a vibrating glass caused by the air convective pressure fluctuation was explored.

Modification of turbulent boundary layer model based on wall fluctuations measurement

A modified turbulent boundary layer (TBL) model based the measurement performed in wind tunnel is proposed to investigate the turbulent boundary layer excitation which usually causes serious vibration of the aircraft structure. The Corcos model is the widely used and classical TBL model to simulate the fluctuating pressure excitation over the aircraft structure. However, the assumption of the non-pressure gradient in boundary layer limits its application in a high-speed flow. To extend the classical model to satisfy the high-speed flow, a modified model based on the measurement in wind tunnel is used to modify the Corcos model. To show the superiority of the modified model developed in this study, different TBL models are used to describe theoretical results and experimental results, respectively. The research results demonstrated that the modified model of TBL excitation could make a better agreement with the test results in wind tunnel than that of the classical Corcos model. Meanwhile, such simpler expression of the modified model shows its great convenience to resolve the engineering problems.

Active control of turbulent boundary layer sound transmission into a vehicle interior

In high speed automotive, aerospace, and railway transportation, the turbulent boundary layer (TBL) is one of the most important sources of interior noise. The stochastic pressure distribution associated with the turbulence is able to excite significantly structural vibration of vehicle exterior panels. They radiate sound into the vehicle through the interior panels. Therefore, the air flow noise becomes very influential when it comes to the noise vibration and harshness assessment of a vehicle, in particular at low frequencies. Normally, passive solutions, such as sound absorbing materials, are used for reducing the TBL-induced noise transmission into a vehicle interior, which generally improve the structure sound isolation performance. These can achieve excellent isolation performance at higher frequencies, but are unable to deal with the low-frequency interior noise components. In this paper, active control of TBL noise transmission through an acoustically coupled double panel system into a rectangular cavity is examined theoretically. The Corcos model of the TBL pressure distribution is used to model the disturbance. The disturbance is rejected by an active vibration isolation unit reacting between the exterior and the interior panels. Significant reductions of the low-frequency vibrations of the interior panel and the sound pressure in the cavity are observed.