Hydrodynamic Coincidence Research Articles

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.

Radiation efficiency of plates subjected to turbulent boundary layer fluctuations.

The modal averaged radiation efficiency of a rectangular plate subjected to turbulent boundary layer fluctuations is discussed in this letter. Numerical results demonstrate that below the hydrodynamic coincidence frequency, the modal averaged radiation efficiency will be larger with the increase of the convection velocity, and an increase of the structural damping will increase the modal averaged radiation efficiency at sub-critical frequencies.

Sound transmission through double cylindrical shells lined with porous material under turbulent boundary layer excitation

This paper investigates sound transmission through double-walled cylindrical shell lined with poroelastic material in the core, excited by pressure fluctuations due to the exterior turbulent boundary layer (TBL). Biot׳s model is used to describe the sound wave propagating in the porous material. Three types of constructions, bonded–bonded, bonded–unbonded and unbonded–unbonded, are considered in this study. The power spectral density (PSD) of the inner shell kinetic energy is predicted for two turbulent boundary layer models, different air gap depths and three types of polyimide foams, respectively. The peaks of the inner shell kinetic energy due to shell resonance, hydrodynamic coincidence and acoustic coincidence are discussed. The results show that if the frequency band over the ring frequency is of interest, an air gap, even if very thin, should exist between the two elastic shells for better sound insulation. And if small density foam has a high flow resistance, a superior sound insulation can still be maintained.

A synthesis approach for reproducing the response of aircraft panels to a turbulent boundary layer excitation

Random wall-pressure fluctuations due to the turbulent boundary layer (TBL) are a feature of the air flow over an aircraft fuselage under cruise conditions, creating undesirable effects such as cabin noise annoyance. In order to test potential solutions to reduce the TBL-induced noise, a cost-efficient alternative to in-flight or wind-tunnel measurements involves the laboratory simulation of the response of aircraft sidewalls to high-speed subsonic TBL excitation. Previously published work has shown that TBL simulation using a near-field array of loudspeakers is only feasible in the low frequency range due to the rapid decay of the spanwise correlation length with frequency. This paper demonstrates through theoretical criteria how the wavenumber filtering capabilities of the radiating panel reduces the number of sources required, thus dramatically enlarging the frequency range over which the response of the TBL-excited panel is accurately reproduced. Experimental synthesis of the panel response to high-speed TBL excitation is found to be feasible over the hydrodynamic coincidence frequency range using a reduced set of near-field loudspeakers driven by optimal signals. Effective methodologies are proposed for an accurate reproduction of the TBL-induced sound power radiated by the panel into a free-field and when coupled to a cavity.

Noise radiation of aircraft panels subjected to boundary layer pressure fluctuations

In this paper, a method which predicts the sound radiation of aircraft panels subjected to turbulent boundary layer excitation is described. The method is the extension of an earlier deterministic approach, where the modal expansion and modal receptance methods were used to predict random noise transmission through curved aircraft panels with stringer and ring frame attachments. Here, with implementation of the Corcos and Efimtsov models to characterize the dynamic surface pressure cross-spectra, closed-form solutions for the panel displacements, radiation and transmission pressures are derived. Numerical examples are presented to illustrate the effects of the stringers, ring frames, hydrodynamic coincidence, curvature, in-plane tension, structural dissipation and composite material on the structural and acoustic response of the panel.

Effects of rib stiffeners on the wave‐number sensitivity of a cylindrical shell to flow excitation

The wave‐number sensitivity (square of the absolute of a normalized spatial Fourier transform of a mode function) of a structural mode determines the degree of the coupling between a structure and the flow‐induced pressure field. It is of engineering interest to evaluate relative contributions to the coupling in the two regions of the wave‐number domain: the high‐wave‐number region, at and near the hydrodynamic coincidence, and the low‐wave‐number region, at and near the modal wave number. Modes in a cylindrical shell can be classified as primarily radial (or flexural), longitudinal (or membrane), or circumferential (or torsional); only the radial modal components are responsible for the coupling with the pressure field. For some unstiffened cylindrical shells (an infinite shell or finite shells with radial constraint at the boundary), these modes are elastically uncoupled. This paper compares the wave‐number sensitivity of an unstiffened shell and that of a rib‐stiffened shell that is calculated from the finite‐element model of the structure. It is found that a circular rib stiffener may cause an elastic coupling between the flexural and membrane modes. This elastic coupling tends to increase the low‐wave‐number sensitivities of the modes that are predominantly flexural and the high‐wave‐number sensitivities of the modes that are predominantly membrane. [Work supported by ONR.]

A wavenumber analysis of the coupling of a structural mode and flow turbulence

Previous studies of the coupling of a structural mode and the pressure field induced by a highly subsonic turbulent boundary layer have been concentrated on the determination of the relative contributions by two regions of the wavenumber domain: the high-wavenumber region, at and near the hydrodynamic coincidence, and the low-wavenumber region, at and near the modal wavenumber. The corresponding contribution to the coupling by the intermediate-wavenumber region that lies between the high- and low-wavenumber regions has not received proper attention. In this paper, formulae to estimate the contributions to the coupling by the three wavenumber regions are derived for some homogeneous structural panels with various boundary conditions, and numerical results are evaluated and compared. The relative contributions to the coupling among the three wavenumber regions vary with boundary condition, mode order number, and the ratio of the structural free wavenumber and the convective wavenumber at the modal resonance frequency. It is found that situations exist in which the contribution by the intermediate-wavenumber region may be significant.

A wavenumber domain analysis of the coupling of a structural mode and flow turbulence

Previous studies on the coupling of a structural mode and the pressure field induced by a turbulent boundary layer have concentrated on the determination of the relative contributions of two regions of the wavenumber domain; the high-wavenumber region at and near hydrodynamic coincidence and the low-wavenumber region at and near the structural free wavenumber. The corresponding contribution to the coupling by the intermediate-wavenumber region that lies between the high- and low-wavenumber regions has not received proper attention. In this paper, formulas to estimate the contributions to the coupling by the three wavenumber regions are derived, and numerical results are evaluated and compared. It is found that situations exist in which the contribution by the intermediate-wavenumber region may be significant. [Work supported by ONR.]

Structural Excitation by a Turbulent Boundary Layer: An Overview

Thirty years of theoretical and experimental research have yet to resolve a number of questions regarding the vibratory response of, and acoustic radiation from, a structure excited by a turbulent boundary layer (TBL). The most important questions are: (a) Can the TBL be characterized as a Thevenin source—particularly when vibratory power flow into the structure is maximized at hydrodynamic coincidence? Alternatively, at what level does structural vibration fundamentally change the character of the TBL? (b) Is the low wave number portion of the wall pressure spectrum of dominant importance in structural excitation away from hydrodynamic coincidence? Or do structural discontinuities cause the convective ridge of wall pressure to be of greater practical interest? (c) Can one quantify the radiation from a turbulent boundary layer about a rigid finite body? Is it dipole or quadrupole? What is the role of fluctuating wall shear stress? Current research on dense fluid loading and on modeling the behavior of the TBL is yielding new, and sometimes surprising, answers to some of these questions. Free resonant structural vibration in the dense fluid limit and the use of a bounded, non-causal, Green function representing the TBL are two of the surprises discussed.

Mono-coupled periodic systems with a single disorder: Response to convected loadings

This paper presents a general theory of the forced response under convected loading of mono-coupled periodic systems with a single disorder. The general expressions derived have been used to study the response of an infinite periodic beam on simple supports with one of the support spacings different from all the others. Convected harmonic pressure fields and frozen random pressure fields have been considered. Computer studies are presented showing the moment response at supports and the space-time-averaged responses in the disorder and in the nearby periodic beam elements. High response levels can occur due to (i) resonances of the beam length disorder against the stiffness of the attached periodic systems and (ii) hydrodynamic coincidence vibration occurring in the periodic beam. The frequency zones in which these high responses may occur are identified. The high response due to the resonance (ii) is restricted to the vicinity of the disorder, whereas that due to coincidence occurs throughout the system. Computed results show that the highest response levels do not necessarily occur in the beam length disorder, but may occur in one of the nearby periodic beam elements. The dependence of the maximum response levels on the magnitude of the disorder has been investigated. The conditions under which small disorders may be neglected have been pointed out.

Vibration response of spacecraft shrouds toin-flight fluctuating pressures

Results are presented for the vibration response of a spacecraft shroud to a range of inflight fluctuation pressures. An Atlas-Agena 15 degree cone-cylinder shroud was analyzed during the present study, and three critical flight Mach numbers were considered. At transonic Mach numbers considered during this investigation ( M ∞ =0·7 and M ∞ =0·8), the aerodynamic flow over the shroud is complex, involving zones of regular attached flow, separated flow, shock wave oscillation and modified attached flows induced by local thickening of the boundary layer. The overall shroud vibration levels for a particular Mach number were determined by initially calculating the mean square acceleration levels induced by the fluctuating pressures distributed over an individual zone, and then summing mean square acceleration levels in one-third octave bands over all zones. Over most of the frequency range of interest, the vibration levels induced during transonic flight are considerably higher than the vibration levels induced during maximum dynamic pressure ( q max ) at M ∞ =2·0. At frequencies well above the ring frequency of the shroud, however, this situation is reversed, and vibration levels during q max are higher than those during transonic flight. This is shown to be due to hydrodynamic coincidence effects where matching between the flexural and pressure wavelengths results in a number of near-coincident modes contributing significantly to the vibration levels. A discussion is given of the relative effects of the various fluctuating pressure environments distributed over discrete zones on the shroud surface. For the shroud analyzed, the separated flow at transonic Mach numbers contributes little to the overall vibration response in the lower third octave bands, most of the vibration being induced by the thickened boundary layer aft of the re-attachment point. At frequencies well above the ring frequency of the shroud, however, the overall vibration response is induced almost exclusively by the separated flow. Shock wave oscillation was found to contribute very little to the vibration levels of the shroud analyzed during this study, primarily because of the mis-match between the low-frequency spectral content of this environment and the lower bound frequencies of the shroud modes. For certain spacecraft shrouds or space vehicle structures where the structural modes have much lower resonant frequencies than the present shroud, the shock wave oscillation may possibly be more severe in terms of induced vibration response.

Transduction of Boundary-Layer Noise by a Rectangular Panel

The response and consequent sound radiation of a thin rectangular panel excited by convected boundary-layer turbulence has been examined. By taking averages over a frequency band, and including many modes in this average, the detailed characteristics of the system are bypassed and only gross features such as panel modal density, ratio of radiation to total resistance, and the boundary-layer characteristics are of interest. A large portion of the sound power is transmitted in the region of the hydrodynamic coincidence condition. The hydrodynamic coincidence frequency is the most important feature in determining the shape of the transmitted power spectrum, and the power law for the total power radiated. Good agreement between theory, and experiment serve to verify the basic assumptions of the theory.

Flow-Noise Research Related to the Sonar Self-Noise Problem

A sonar dome is excited into bending vibration by random pressure fluctuations of turbulent-boundary-layer flow over the dome. A reverberant acoustic field is set up within the dome. The field appears as an important source of self-noise in the sonar transducer at moderate to high ship speeds. Much of the research on the corresponding aerodynamic-noise problem is directly applicable to the study of this underwater-noise problem; in particular, work characterizing the random pressure field for subsonic boundary-layer flows may be carried over directly. Dome response and the consequent internal acoustic radiation, however, are severely influenced by internal and external water loading. In addition, hydrodynamic coincidence effects play a markedly different rôle in the underwater problem than in the aerodynamic problem. Those aspects of flow-noise research pertinent to the sonar self-noise problem are reviewed in this paper, and directions for further research upon the influence of water loading in the prediction of self-noise levels are pointed out.