Turbulent Boundary Layer Excitation Research Articles

A vibration-based method to estimate the low-wavenumber wall pressure field in a turbulent boundary layer

When an elastic structure is excited by a low-speed turbulent flow, it generates flow-induced vibration which is primarily due to the low-wavenumber components of the wall pressure field (WPF) beneath the turbulent boundary layer (TBL). Therefore, to accurately predict the vibration response of the structure, an accurate estimation of the low-wavenumber WPF is needed. While existing TBL models for WPF well predict the convective region, they exhibit significant discrepancies in predicting the low-wavenumber levels. This numerical study aims to explore the feasibility of estimation of the low-wavenumber WPF by analysing vibration data obtained from a structure excited by a TBL. An inverse method is proposed based on the relationship between the TBL forcing function and structural vibrations in the wavenumber domain. The random TBL force is simulated with deterministic loading using the uncorrelated wall plane wave technique. A model of a simply supported plate under a TBL excitation is developed to demonstrate the proposed method. The plate's acceleration data is then used to estimate the WPF in the low-wavenumber range. It is shown how using multiple discrete frequencies in the analysis can reduce the required snapshots for accurate estimation of the WPF.

Experimental validation of vibration similitude laws for stiffened panels excited by a turbulent boundary layer

Stiffened structures excited by a turbulent boundary layer (TBL) occur in many engineering applications, particularly in the aerospace and naval sectors. The structures encountered in these applications are generally large and complex, and carrying out experiments in order to characterize their vibration response can be costly, time-consuming and difficult. To overcome these constraints, the similitude theory can be used to estimate the response of a full scale structure from the response of a reduced scale structure. A simplifying step to determine these similitude laws for stiffened panels consists in modeling the panel as an equivalent orthotropic panel. Then, using the governing equation of the orthotropic panel and considering the TBL excitation, the vibration similitude laws are derived implying similitude conditions to be respected on geometrical and material properties of the structure as well as flow velocity. In this paper, we present the developments of these similitude laws and an experimental validation for panels in air. The similitude conditions are discussed to adequately choose the properties of scaled stiffened panels. Experimental results are presented to show that the structural response of the reference panel can be recovered from the response of the reduced scale panel using the related scaling laws.

Directional excitation of structural vibrations due to correlated sources

Dynamical Energy Analysis (DEA) is an approach used to compute the vibro-acoustic response of complex structures to externally applied high-frequency excitation. DEA tracks the global energy flow in a structure in terms of a local ray tracing approach implemented on meshes. Due to its in-built directional set-up, the approach is ideally suited for modelling the response of structures to directional excitation. Examples thereof are dipole sources or - more generally - correlated and distributed source excitation such as due to a Turbulent Boundary Layer (TBL) excitation across an aircraft wing during flight. We will demonstrate here how such directional sources are implemented in a DEA setting. TBL induced sources or general correlated sources can be described in terms of appropriate force or wave correlation functions (CF). Using Wigner-transformation, these CFs can be associated with a directional energy flow source. Vibrational energy field results are presented for a pair of phase-locked point forces. Results are also presented for 9 point-sources, which demonstrate the ability to channel the energy flow away from the sources by carefully choosing their relative phases. An implementation of this approach within DEA is also presented, with results demonstrating strong agreement with direct calculations.

Low-frequency vibration reduction of an underwater metamaterial plate excited by a turbulent boundary layer

Flow-induced structural noise is an important component of hydrodynamic noise of underwater structures. Local resonance metamaterials are considered to have excellent performance and enormous potential in the field of low-frequency vibration and noise control. To verify its potential, the paper derived the underwater band gap of a lateral local resonance (LLR) plate through the plane wave expansion (PWE). Then, utilizing the modal superposition approach and Rayleigh integral technique, the vibro-acoustic response of a LLR plate under a turbulent boundary layer (TBL) excitation is obtained. Finite element certification is also conducted through an uncorrelated wall plane wave technique. Parametric study is conducted to analyse the factors which influence the control effects. The result shows that the plate exhibits excellent suppression performance for flow-induced vibration at band gap frequencies. The band gaps and suppression ranges generated by the underwater metamaterial plate, are dramatically narrowed due to the thick fluid load. The paper provides theoretical guidance for the control of flow-induced structural vibration and the application of acoustic metamaterials.

Experimental pseudo-equivalent deterministic excitation method extension for low frequency domain applications.

In transport engineering applications, flow-induced vibrations is an interesting topic to address since it may negatively affect the operation and the response of the system. Wind tunnel facilities are mandatory to test the structure design efficiency or to analyse new material performances under aerodynamic load. However, these experimental tests can be expensive and take a long time to set up and operate; hence, alternative methods for the reproduction of the structural response to a turbulent boundary layer excitation are required to accelerate and improve the experimental setups and provide more data for uncertainty analysis. In this paper, an alternative approach, the eXperimental Pseudo-Equivalent Deterministic Excitation method (X-PEDEM), is here extended for applications in the low frequency domain. An investigation about the applicability of the method in the low frequency domain is conducted, together with an analysis of its main properties. The reliability of the method is then tested numerically by considering different conditions: two different panels, two different boundary conditions, and different asymptotic flow velocities are considered.

Numerical study on the estimation of the low-wavenumber wall pressure field using vibration data

It is known that the low-wavenumber components of the wall pressure field beneath a turbulent boundary layer is the main cause of structural vibration in low Mach number flows. This is because the structure filters the convective ridge of the turbulent boundary layer excitation at frequencies well above the aerodynamic coincidence frequency. This work aims to explore the possibility of estimating the low-wavenumber wall pressure filed by obtaining vibration data from a structure excited by a turbulent boundary layer. To achieve this, an analytical model of a simply-supported plate under turbulent boundary layer is developed and the acceleration data obtained from the plate is used to evaluate the wall pressure field in the low-wavenumber domain. The wall pressure field is modelled using the Goody and Mellen models for auto-spectrum density and cross-spectrum density, respectively. Finally, the estimated pressure field is compared with the input turbulent boundary layer to evaluate the accuracy of the proposed method.

Vibration response of a finite airfoil under turbulent boundary layer excitation

Turbulent boundary layers excite elastic surfaces leading to material fatigue and noise that may be transmitted into the body of a vehicle or reradiated back into the environment. Three different numerical methods, namely the spatial method, the reciprocity method and the uncorrelated wall plane wave method are employed to predict the vibration response of an airfoil excited by a turbulent boundary layer. These methods will be coupled with semi-empirical models which are used to simulate the wall pressure field beneath the turbulent boundary layer. The first method is performed in the spatial domain while the latter two are performed in the wavenumber domain. In this investigation, the efficacy of each of these will be examined when applied to a finite airfoil. The use of the two calculations will be compared to show any advantages in computational time and memory use.

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.

Numerical Investigation of Distributed Speed Feedback Control of Turbulent Boundary Layer Excitation Curved Plates Radiation Noise

The control of decentralized velocity feedback on curved aircraft plates under turbulent boundary layer excitations is numerically investigated in this paper. Sixteen active control units are set on the plate to reduce the vibration and sound radiation of the plate. The computational results from the two methods are compared to verify the accuracy of the numerical model. The plate kinetic energy and the radiated sound power under turbulent boundary layer and control unit excitations are analyzed. The influences of control unit distribution, plate thickness and curvature on radiated sound are discussed. Unlike a flat plate, the control of the lower-order high radiation modes of a curved plate under TBL excitations is critical since these modes predominate the sound radiations. The control of these modes, however, is sensitive to the ratio of the stiffness associated with the membrane tensions to the stiffness associated with the bending forces. This ratio implies that the plate curvature and the thickness play an important role in the control effect. When the plate is thinner and the radius is smaller, the control is less effective.

Vibroacoustic simulations with non-homogeneous TBL excitations: Synthesis of wall pressure fields with the Continuously-varying Uncorrelated Wall Plane Waves approach

A numerical method is presented to predict the vibro-acoustic response of a vibrating structure excited by a spatially inhomogeneous turbulent boundary layer(TBL). It is based on the synthesis of different realizations of the random pressure fluctuations that can be introduced as loadings of a vibro-acoustic model (such as a finite element model). To generate the pressures of the non-homogeneous turbulent boundary layer, the Uncorrelated Wall Plane Wave(UWPW) approach used so far for homogeneous TBL is extended. On a first step, this extension is based on a decomposition of the excited surface into sub-areas and on the averaged TBL parameters for each sub-area. In a second step, it consists in taking into account the interaction between the sub-areas and a refinement of the sub-area decomposition. This leads to the Continuously-varying Uncorrelated Wall Plane Waves (C-UWPW) approach. The accuracy of the proposed approach is investigated on a panel with a varying thickness and excited by a growing TBL triggered at one edge of the plate. The interests of the proposed approach in terms of accuracy and computation time are discussed. Finally, an illustration of the proposed approach to predict the radiated noise from a blade immersed in a water flow is proposed.

Pseudo-equivalent deterministic excitation method application for experimental reproduction of a structural response to a turbulent boundary layer excitation.

In the transportation engineering field, the turbulent boundary layer over a structure is one of the most relevant sources of structural vibration and emitted noise. Wind tunnels are still one of the best options for vibroacoustic experimental analyses for this specific problem. However, it is also true that this experimental method is not always affordable, due to several limitations-settings hard to control, time and money consumption, discrepancies among laboratories-that wind tunnel facilities present. It has already developed different methodologies to address this necessity, most of them based on the use of loudspeakers or shakers. In this work, an existing numerical method, called the pseudo-equivalent deterministic excitation method (PEDEM), is further developed for the experimental purpose of reproducing the experimental structural response of a panel subjected to a turbulent boundary layer (TBL) excitation, by using an equivalent rain-on-the-roof excitation instead; different formulations are used for the application of this approximated TBL excitation. The experimental application of PEDEM, here called X-PEDEM, is validated by comparison with experimental results of two different panels analysed in two different wind tunnel facilities.

Vibroacoustic behavior of submerged stiffened composite plates excited by a turbulent boundary layer

This paper presents a modal expansion technique-based method for predicting the vibroacoustic behavior of submerged stiffened composite plates under turbulent boundary layer (TBL) excitation. In the proposed method, the power spectral density of the Goody model is combined with the spatial correlation function in the Corcos form and then used to describe the turbulent fluctuating pressures. In addition, the transverse shear deformation of the stiffened composite plates under simply supported boundary conditions is considered. The contribution of the cross-modal coupling terms and the non-resonant modes to the mean square velocity and radiated sound power are analyzed. The results demonstrate that increasing the structural damping can be an efficient way to reduce the vibroacoustic response; the vibration level can be controlled by increasing the modulus ratio; lastly, the noise level can be reduced by increasing the areal density. The results of the stiffened composite plates show that there is almost no influence on the vibroacoustic response above 100 Hz regardless if the plate is reinforced streamwise or spanwise. However, increasing the length of the sub-panel between two stiffeners can be another effective way to reduce the TBL-induced noise.

Effects of general boundary conditions on vibro-acoustic responses of the panel-cavity system induced by a turbulent boundary layer

This study proposes an analytical method for building a vibro-acoustic model of a panel-cavity system induced by a turbulent boundary layer (TBL) excitation, which is used to study the influences of boundary conditions on the vibro-acoustic responses of the system. In the theoretic model, the elastic restraints at the plate’s edges and the wall impedance of the cavity wall are considered at the same time. Based on the mode expansion, the vibro-acoustic response function of the vibro-acoustic model is built to present the coupling between the TBL and the system constructed by the panel and the cavity. Then, the model is validated by comparing it with the previous study, which shows good agreements. Finally, the effects of the boundary conditions, such as stiffness, damping, and impedance, on the mean quadratic velocity spectra and radiated sound power of the panel-cavity system are studied. It is demonstrated that the decrease of the boundary stiffness makes the radiated sound power of the panel drop above the frequency of the panel third mode. The boundary damping of the panel decreases the vibro-acoustic response of the panel-cavity system by working as an attenuation factor of the boundary. Furthermore, the increase of the radiated sound power with different wall impedances is due to the coupling between the structural mode of the panel and the acoustic mode of the cavity, or the resonance of acoustic mode in the vibration propagation direction.

Development of an innovative noise generation system for turboprop aircraft fuselage testing

This paper presents the development of a cabin noise testing equipment that will be used to evaluate the interior noise of regional aircraft as well as to aid the development of noise reduction techniques. The innovative noise generation system consists of three loudspeaker arrays positioned around the fuselage circumference to synthesize a pressure field that is similar to the pressure field seen by the fuselage during a flight. The acoustic pressure field generated by the loudspeakers is measured by a number of microphones scattered on the fuselage surface. These microphone signals are then fed back to the controller with the purpose of minimising the error between the target pressure field and the measured one by means of an iterative learning approach. The number and location of the microphones used in the control loop are selected through a pre-test optimisation analysis, which aims to reduce the time and cost of the set-up. A small-scale electroacoustic demonstrator has been built to develop the feedback control approach. A frequency domain multi-input multi-output feedback controller is used to replicate the random pressure field generated by the turbulent boundary layer excitation. The multi-harmonics of the propeller induced excitation are then added to the time histories of the broadband noise using a time waveform replication technique. Different arrangements of the driving signal distribution are investigated, and the results are then presented in terms of accuracy of the pressure field reproduction.

Reproduction of the vibroacoustic response of panels under stochastic excitations using the source scanning technique

The reproduction of the vibration and acoustic responses of structures under random excitation such as the diffuse acoustic field or the turbulent boundary layer is of particular interest to researchers and the transportation industry (automobile, aeronautics, etc.). In practice, the characterization of structures under random excitations requires making in-situ measurements or using test facilities such as the wind tunnel, which are complex and costly methods. Based on the previous considerations, the necessity of finding simple, cost-efficient and reproducible alternative methods becomes obvious. The source scanning technique based on a single acoustic source and the synthetic array principle is one of these alternative techniques. The present paper proposes to assess its validity by comparing its results with numerical and experimental ones. An academic case study consisting of a baffled and simply supported aluminum panel under diffuse acoustic field and turbulent boundary layer excitations is considered. The experimental vibration response of the panel as well as the transmission loss using the proposed process are compared to results from random vibration theory on one hand. On the other hand, the same experimental results obtained using the source scanning technique are compared with results obtained with measurements using a reverberant room (diffuse acoustic field) and an anechoic wind tunnel (turbulent boundary layer). These comparisons show good agreement that validate the source scanning technique for the considered panel.

First models for structural energy transmission decoupling in the high frequency regime under aerodynamic excitations

In the wind tunnel facility, a test structure is often used for measuring its vibrational response to the aerodynamic excitation. A support is needed to sustaining the structure and it is mandatory that this support does not influence the vibrational energy to be measured. To this aim, the maximum amount of energy decoupling between the structure and the support is desired. This work is focused around a quick method to estimate this decoupling by using simplified models for the Turbulent Boundary Layer (TBL) excitation and for the structural response. Specifically, the Equivalent Rain-on-the-roof excitation is invoked with a Statistical Energy Analysis model for the structure. Some simple design rules are proposed and based on little information leading to foresee the difference of vibrational velocity levels between the two structural systems. A simplified test-case is used for the first investigations and a complex structure is finally conceived thinking to vibroacoustic measurements in a large wind tunnel facility. Although some results are largely expected, the global approach is promising.

Analytical and numerical prediction of acoustic radiation from a panel under turbulent boundary layer excitation

The vibroacoustic response of a simply supported panel excited by turbulent flow is analytically and numerically investigated. In the analytical model, the radiated sound power is described in terms of the cross spectrum density of the wall pressure field and sensitivity functions for the acoustic pressure and fluid particle velocity. For the numerical model, a hybrid approach based on the finite element method is described in which the cross spectrum of the wall pressure field is represented by a set of uncorrelated wall plane waves. Realisations of the wall pressure field are used as deterministic input loads to the panel. The structural and acoustic responses of the panel subject to turbulent boundary layer excitation are then obtained from an ensemble average of the different realisations. Analytical and numerical results are compared with experimental data measured in an anechoic wind tunnel, showing good agreement. The effect of adding stiffeners on the vibroacoustic response of the panel is also examined using the proposed numerical approach.

Aeroelastic Effects on Wave Propagation and Sound Transmission of Plates and Shells

Modal approaches are often preferred to the wave-based ones for the evaluation of instability conditions in classical nonlifting aeroelasticity of plates and shells. Here, within a wave-based finite element framework, sub- and supersonic aerodynamic models are introduced to analyze the effect of self-excited aerodynamic loading terms on the dispersive characteristics of structural waves. The method is validated by using a specific literature test case and is applicable on both isotropic and multilayered flat and curved structures. The sound transmission is also computed under sub- and supersonic turbulent boundary-layer excitations: the effect of including or neglecting the aeroelastic coupling is discussed.

A hybrid numerical approach to predict the vibrational responses of panels excited by a turbulent boundary layer

In this work, a hybrid numerical approach to predict the vibrational responses of planar structures excited by a turbulent boundary layer is presented. The approach combines an uncorrelated wall plane wave technique with the finite element method. The wall pressure field induced by a turbulent boundary layer is obtained as a set of uncorrelated wall pressure plane waves. The amplitude of these plane waves are determined from the cross spectrum density function of the wall pressure field given either by empirical models from literature or from experimental data. The response of the planar structure subject to a turbulent boundary layer excitation is then obtained from an ensemble average of the different realizations. The numerical technique is computationally efficient as it rapidly converges using a small number of realizations. To demonstrate the method, the vibrational responses of two panels with simply supported or clamped boundary conditions and excited by a turbulent flow are considered. In the case study comprising a plate with simply supported boundary conditions, an analytical solution is employed for verification of the method. For both cases studies, numerical results from the hybrid approach are compared with experimental data measured in two different anechoic wind tunnels.

Vibroacoustic responses of a heavy fluid loaded cylindrical shell excited by a turbulent boundary layer

A fully coupled structural–acoustic model of a cylindrical shell under external turbulent boundary layer excitation is herein developed. The numerical process requires computation of the wall pressure cross spectral density function as well as sensitivity functions for the fluid-loaded cylindrical shell. A semi-empirical model from literature is used to describe the wall pressure field induced by the turbulent boundary layer in the wavenumber–frequency domain. An analytical expression of the wall pressure field for a flat surface is adapted to describe the wall pressure field for a cylindrical surface. Circumferential sensitivity functions are derived using a wavenumber-point reciprocity principle. Results for the near-field and far-field acoustic pressure spectra are presented. Contributions of individual circumferential modes to the acoustic pressure spectra are examined, showing distinct trends below and above the ring frequency. The proposed method is computationally efficient and provides an effective approach to investigate vibroacoustic responses for maritime platforms.