Turbulent Boundary Layer Excitation Research Articles

Turbulent boundary layer noise transmission into an aircraft fuselage—Modeling and analysis

The turbulent boundary layer (TBL) pressure fluctuations on the exterior of an aircraft excite the fuselage structure which in turn radiates noise inside the passenger cabin. In most of the previous analytical and experimental studies of sound transmission loss of structures, only acoustic excitation is considered. It is then assumed that the transmission loss of a structure due to the TBL pressure field will be the same as that for the acoustic field. The main objective of this paper is to examine the effects of the TBL pressure field on the transmission loss of a fuselage structure and compare it with the acoustic transmission loss. The vibration and acoustic response of a circular cylindrical shell due to the TBL excitation is first modeled with a finite-element-based computational approach. The finite-element model of the cylindrical shell panel is validated with the results from classical analytical model. The vibration and acoustic response of an aircraft fuselage due to the TBL pressure field is then calculated using the finite-element model. The incident TBL pressure field is simulated by a cross-spectral formulation of the excitation field. The noise reduction characteristics of the fuselage due to acoustic and TBL pressure fields are compared.

Noise Transmission Through a Vehicle Side Window Due to Turbulent Boundary Layer Excitation

This paper presents results of an investigation on noise transmission through an aluminum panel clamped to a greenhouse vehicle model subject to random acoustics, random vibration, and turbulent boundary layer excitations. Experiments on random acoustics and random vibration excitations were carried out in a reverberation chamber, and those on turbulent boundary layer excitation were conducted in the wind tunnel at the Chrysler Technology Center. The transmitted noise spectra were also calculated using a single computer program VibroAcoustic Payload Environment Prediction System (VAPEPS) based on Statistic Energy Analysis (SEA). The acoustic absorption coefficient (AAC) and the damping loss factor (DLF) for the vehicle were determined based on experimental data. Results showed that the largest differences between the measured and calculated sound pressure levels in any frequency band above 500 Hz were less than 2.5 dB for random acoustics excitation, 5.0 dB for random vibration excitation, and 5 dB for turbulent boundary layer excitation. In spite of the presence of differences in individual frequency bands, the calculated total sound pressure levels compared well with the measured ones. The differences between the calculated and measured total sound pressure levels were 0.7 dB for random acoustics excitation, 0.4 dB for random vibration excitation, and 1.8 dB for turbulent boundary layer excitation.

Robust feedback control of flow-induced structural radiation of sound

A significant amount of the interior noise of aircraft and automobiles is a result of turbulent boundary layer excitation of the vehicular structure. In this investigation, the feasibility of active robust feedback control of the noise due to this type of excitation is studied. The structural sound radiation system investigated is comprised of a simply supported panel excited by turbulent flow. An analytical model of this system is developed to evaluate the robust feedback control system design strategy. The model consists of a modal description of the excitation of the plate by a turbulent boundary layer, a modal representation of the plate vibrations, and an acoustic model of the sound radiated from the plate. Parametric uncertainties of 1% variation in the natural frequencies and 5% variation in the damping ratio are considered. A frequency domain controller design approach is utilized to develop a robust controller. Performance objectives are specified which include output performance of the sound radiated by the plate and control effort constraints on the force applied to the plate by the controller. Plate acceleration feedback is used in an effort to reduce the sound-pressure level. Approximately 16 and 8 dB of sound-pressure level reduction were achieved at the first and third resonances, respectively.

Robust feedback control of flow–induced structural radiation of sound.

A significant component of the interior noise of aircraft and automobiles is a result of the turbulent boundary layer excitation of the vehicular structure. In this investigation the feasibility of active control of wind noise is studied. Initial studies are made by considering the idealized case of sound radiation from a simply supported panel excited by a turbulent flow boundary layer. To study various control system alternatives, a wind noise model is developed. The model consists of a modal model of the excitation of a plate from a turbulent boundary layer, a model of plate vibrations, and a model of the sound radiated from the plate. A frequency‐domain approach, similar to quantitative feedback theory, is utilized in the design of a robust feedback controller. The controller utilizes plate acceleration feedback while maintaining sound‐pressure‐level reduction as the primary design objective. The design method insures that performance and control effort objectives are met for plant and disturbance uncertainty. The controller design method offers flexibility in configuring the size of the controller, and the effect of the performance and control effort objectives on the controller design are easily identified.

Control of panel response to turbulent boundary-layer and acoustic excitations

Nonlinear response of a panel structure results when forced by a subsonic turbulent boundary layer and puretone sound in a wind tunnel. It is a coupled problem, where flow, structure, and sound interact. The structure exhibits a broadband response typical of turbulent boundary-layer loading with superimposed pure tone and harmonics over the band, a process which is statistically stationary, but non-Gaussian. The mechanism is an energy transfer process : the amount of energy supplied to the harmonics is removed from the low-frequency band and the fundamental tone. The objective is to control the nonlinear wave using a time-harmonic actuator tone. Full control is almost achieved using a single controller. Two steps are taken : first, control the harmonics by feeding the energy back into the fundamental and low-frequency band, and second, control the fundamental tone to shift the energy further back into the low-frequency band. Consequently, the response of the panel is reduced to the broadband level of the turbulent boundary-layer excitation, a reduction in peak amplitude power level by 20 dB or more. The experiments are motivated by considerations for aircraft interior noise and structural response.

Feedback control of sound radiation from a plate excited by a turbulent boundary layer

In this paper it is shown that the problem of applying active control to a simply supported plate excited by a turbulent boundary layer can be presented in a form which allows the application of optimal control theory. Linear regulator theory and stochastic linear regulator theory are briefly summarized. The approach taken follows that of Baumann et al. who show that the optimal control theory can be applied to structural acoustic problems if the sound power radiated by the structure is estimated from the vibration signal by means of a ‘‘radiation filter.’’ A modal model for the vibration of an elastic structure is presented and the state space realization of the model is given. It is shown that a simple Corcos model of the turbulent boundary layer excitation can be modeled by using a number of ‘‘excitation filters.’’ The state space realization of these filters can be combined with the state space model of a vibrating plate to give a model to which optimal control theory can be applied. In similar fashion the sound power radiated by the plate can be estimated by means of a radiation filter matrix. A detailed account of the calculation of such a radiation filter matrix is given. The state space forms of the excitation filters and radiation filter matrix can be combined with the state space model of the plate to give a system state space realization which can be used in the solution of a linear quadratic regulator problem. Optimal control analysis is then applied to the state equations and optimal reductions in the far-field radiated power are obtained for various arrangements of control forces. These results give insight into the possibilities for obtaining useful reductions in turbulent boundary layer induced noise in aircraft by the application of feedback control.

Responses of finite baffled plate to turbulent flow excitations

Formulations for estimating dynamic and acoustic responses of a finite baffled plate subject to turbulent boundary-layer excitations are presented. In deriving the formulations, the effects of structural nonlinearities induced by in-plane forces and shearing forces due to stretching of plate bending motion are considered. The excitation force due to turbulent flow is expressed in terms of a sum of two components. One component corresponds to a fluctuating pressure field due to acoustic radiation, which is determined analytically for both supersonic and subsonic flows. The other component corresponds to a fluctuating pressure field due to a turbulent boundary layer, which is determined experimentally. The cross-power spectra of the plate flexural displacement and the radiated acoustic pressure are shown to be directly related to that of the turbulent boundary layer. In addition to the plate dynamic and acoustic responses, a stability analysis is given using the basic existence-uniqueness theorem. In particular, stable conditions for a linearized system are obtained via the Routh algorithm. It is shown that temporal instability can be induced by the added stiffness due to acoustic radiation in the presence of mean flow. The effect of the added stiffness increases quadratically with the mean flow speed.

Waves on panel structures from turbulent boundary layer excitations

Response and acoustic radiation measurements from aircraft-type panels forced to vibrate by turbulent boundary layer flow are made in a quiet air duct facility and in a wind tunnel. Two types of aluminum structure are used: a newly developed panel with irregular, protruding, varying-thickness wedges at the upstream and downstream boundaries (fractal-type geometry) and a standard aircraft fuselage sidewall panel. Both panels have the same mass and exposed surface area to the flow. The new panel boundary has an extended perimeter with a gradual change in mass stiffness toward the center. The objective is to control the radiated acoustic pressure field. This is achieved by controlling the convective waves reflecting at the upstream and downstream boundaries of the panel. The geometry of the boundary is designed to induce a mismatch and randomness in wave motion along the direction of flow, resulting in significant attenuation of the amplitude of the incident and reflected waves.

Effects of materials, damping, and static load constraints on the radiation from flow-excited plates

Turbulent boundary-layer (TBL) wall-pressure fluctuations due to fluid flow over the surface of a finite plate excite a flexural vibration response. At frequencies below the coincidence frequency the acoustically slow flexural waves radiate into the fluid as a result of interactions with boundary discontinuities. Relatively simple formulas can be derived that relate the radiated power due to TBL excitation to the dimensions and material properties of the plate. Static load requirements determine the relationship between plate thickness and support spacing for a given plate material. Alternative plate materials include various metals (steel, aluminum, titanium) and composites (e.g., glass or graphite-reinforced epoxy). Applied damping treatments can also be considered as a means of reducing plate response and radiation. This paper examines the issue of plate design for reduced radiation by considering material and damping alternatives in finite plates subject to static load constraints.

Plate acceleration and sound transmission due to random acoustic andboundary-layer excitation

The 'APEPS statistical energy analysis model is used in the frequency range of 315-5000 Hz to predict the acceleration response and sound transmission of plates that are exposed to random acoustic or turbulent boundary-layer excitation. Good agreement was found with measured noise reduction data for aluminum, acrylic, and graphite-epoxy plates with length and width larger than the acoustic wavelength. The VAPEPS predicted acceleration response of a 12 X 8 X 0.040-in. plate, installed in a 1-in. thick rigid plate inside a wind tunnel, agreed well with measured data for a stationary (random acoustic) as well as for a convected (turbulent boundary layer) pressure field. It was found that lowest order plate modal frequencies increase most with free flow velocity U. The overall acceleration level as well as the transmitted sound pressure level due to turbulent boundary-layer excitation were close to a Us.' dependence. Excitation by a laminar boundary layer resulted in a U3.6 dependence. Measured noise reduction data for random acoustic excitation of the plate in the wind tunnel fell between the VAPEPS predicted curves for resonant and nonresonant sound transmission showing the limitations of statistical energy analysis to accurately predict sound transmission at low modal densities. The noise reduction of the plate, when backed by a shallow cavity and excited by a turbulent boundary layer, was predicted using a simplified theory based on the assumption of adiabatic compression of the fluid in the cavity. VAPEPS predicted plate acceleration response was used as input in the noise reduction prediction, and reasonable agreement was found with the measured noise reduction in the frequency range of 315-1000 Hz.

Frequency-flow speed dependence of structural response to turbulent boundary layer pressure excitation

A rectangular simply supported plate is used to illustrate the differing dependencies on center frequency and flow speed of the spatially averaged one-third-octave band mean squared acceleration levels of a structure due to different mechanisms of response to turbulent boundary layer (TBL) excitation. The two mechanisms described are direct excitation of resonant modes by the TBL components in the neighborhood of the wave numbers of the resonant modes, and the coupling into the resonant modes of those TBL components in the neighborhood of the TBL convective peak. Estimates of the mean-squared response are made for different representations of the TBL wave-number-frequency spectrum. When determination of the dominant response mechanism is important, it appears that it can be made by performing a regression analysis on measured results and comparing the derived parameters to the alternative theoretical estimates.

Diffraction radiation produced by turbulent boundary layer excitation of a panel

An analysis is made of the mechanisms by which sound is produced during low Mach number turbulent boundary layer excitation of a finite panel in a thin plate. The principal source of radiated noise is diffraction at the joints, where the panel is attached to the supporting side-plates, of flexural vibrations excited either directly by the low wavenumber, sub-convective components of the wall pressure fluctuations, or indirectly by diffraction at joints of the very much more energetic, high wavenumber boundary layer pressures. Fluid loading modifies the mechanical properties of the joints. Whereas in vacuo a joint may be sufficiently massive, say, to produce total reflexion of flexural modes and effect the establishment of a strong reverberant field when the panel is subject to external forcing, fluid loading provides a channel by means of which flexural waves can be efficiently transmitted across a joint and thereby reduce reverberant intensities. Numerical results are given for a steel plate in water, with either clamped or pinned joints, and also for the case of a “floating” panel, whose edges are free to vibrate without restraint.

Experimental study of internal noise on a shell submitted to boundary layer excitation

A study has been done of the acoustic performance of elastic material shells, surrounded by a heavy fluid, submitted to a turbulent boundary layer excitation. Measurements of internal noise levels under localized excitation, in frequency bands, show good agreement with the result given by a statistical energy model. These results show significant effects of the structural properties and material for a given shell shape. The results agree well with noise and vibration measurements in a reciprocity situation (action of an internal noise source on the structure). Flexural waves in the shell material, although subsonic, play a major role.

The vibrations and radiated noise associated with a constrained spherical shell in response to a turbulent boundary layer excitation

An analysis is presented of a constrained, fluid‐loaded, thin spherical shell subjected to a random pressure field associated with a turbulent boundary layer (TBL) excitation. The constraint is modeled as an axisymmetric, radially oriented impedance ring and the TBL is defined in terms of a cross‐spectral density. Numerical results are generated for the spectrum density of the shell response as well as for the associated radiated pressure field. It is shown that under the assumption of an effectively delta function‐like correlation length for the TBL pressure field, the constraint can have a far greater effect on the radiated pressure than on the overall response of the shell itself.

Random Vibration of a Compliant Wall

A random vibration analysis for the response of a compliant wall, consisting of an elastic base plate, a low modulus viscoelastic substrate and stretched skin, subjected to turbulent boundary layer excitation is presented. Compliant walls have the potential to reduce aerodynamic drag in flight vehicles. The cross-power spectral density of surface displacement is calculated as a function of design variables . Three examples are presented and their response statistics are examined in relation to wave drag and roughness drag. Both subsonic and supersonic turbulence is considered. The work should be useful as a guideline for the experimental investigation of the drag reduction concept by the use of a compliant wall.

Measurement of Low-Wavenumber Components of Turbulent Boundary Layer Wall Pressure Fluctuations

A taut 2 in. by 20 in. rectangular membrane was mounted flush in one wall of a subsonic wind tunnel with its long dimension in the direction of mean flow. Measurements were taken of the displacement response at the membrane midpoint to turbulent boundary layer excitation. The determination of response spectral density at resonances up to that of the (19, 1) mode for several tunnel speeds, together with measurement of membrane loss factors at these resonances, permitted calculation of low-wave-number components of wall pressure wavenumber-frequency spectral density well separated from the convective ridge. Results are compared with convective ridge levels measured previously in the same facility. Acoustic contamination was determined from the cross spectrum of settling chamber pressure and test section wall pressure. The membrane response to acoustic excitation alone was found to be appreciably below the total response. [Work supported by the Naval Ship Systems Command.]

Vibration measurements of an airplane fuselage structure I. Turbulent boundary layer excitation

The measured response of an airplane fuselage structure to turbulent boundary layer excitation is presented for two locations on the fuselage and three flight Mach numbers. At certain flight conditions and structural locations the vibration field shows broadband convection in the downstream direction, but at other locations and flight conditions the progressive wave system is replaced by standing waves. The presence of broadband convection can be related to the occurrence of aerodynamic coincidence, which is associated with high correlation in broad and narrow frequency bands. In the circumferential direction the vibration correlation is much lower than that in the flow direction, the correlation between adjacent panels being essentially zero.

Interior noise radiated by an airplane fuselage subjected to turbulent boundary layer excitation and evaluation of noise reduction treatments

The acoustic power radiated by an airplane fuselage structure exposed to a turbulent boundary layer pressure field has been measured at two flight Mach numbers. For a single fuselage panel the radiated power is approximately 90 and 70 dB relative to 10 −13 W at Mach 0·85 and 0·55 respectively. Damping tape and rubber wedge treatments, applied to the structure, reduce the acoustic radiation but they are more effective at Mach 0·85 than at Mach 0·55 The flight test data are in poor agreement with available wind tunnel measurements, indicating the need for improvements in scaling laws.

Turbulent Boundary Layer of Space-Flight Vehicle

The turbulent boundary layer (TBL) is an important aerodynamic environment for major portions of a space-vehicle structure. For most launch vehicles, the period of large dynamic pressure, and hence strong TBL excitation, coincides with supersonic flight. This implies high-speed convection of the pressure-field speeds generally in excess of the bending-wave speed on the structure. New procedures for calculating the response of cylindrical structures to a high-speed TBL have recently been developed at BBN. These procedures require information concerning the TBL pressure spectrum that can, in part, be related to flight data obtained from flush-mounted microphones. The use of these flight data for response estimation is the topic of this paper.