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A unique concept of utilizing localized surface compliance is proposed to suppress deep cavity aeroacoustics at a low Mach number. The core idea is to provide local absorption of the energy of aeroacoustic processes supporting cavity flow self-sustained feedback loop responsible for tonal noise generation. The concept is studied with a flow past cavity of length-to-depth ratio of 0.4 at freestream Mach number 0.09 and Reynolds number based on cavity length 4 × 104 using high-fidelity, two-dimensional direct aeroacoustic simulation. Having confirmed the replication of key aeroacoustic processes in the numerical solution through careful validation, localized surface compliance in the form of an elastic panel is strategically introduced to modify every process for cavity noise suppression. The panel natural frequency is set equal to the feedback loop characteristic frequency to facilitate its flow-induced structural resonance for energy absorption. Suppression of cavity noise pressure and power levels by 3.8 and 4.8 dB, respectively, is successfully achieved, together with an unforeseen cavity drag reduction by almost 19%. Comprehensive wavenumber–frequency analyses of the coupled aeroacoustics and flow-induced panel vibration are conducted to uncover the physical mechanism of noise suppression. The results show that the same type of aeroacoustic feedback loop occurs, but its efficacy is significantly reduced due to the exhaustion of aeroacoustic process energy to the flow-induced vibrating panel. The proposed concept is confirmed to be feasible in terms of giving remarkable cavity noise and drag suppression, yet it retains the basic problem geometry intact, which are considered important in many practical applications.

PurposeFor flow around elongated bluff bodies, flow separations would occur over both leading and trailing edges. Interactions between these two separations can be established through acoustic perturbation. In this paper, the flow and the acoustic fields of a D-shaped bluff body (length-to-height ratioL/H= 3.64) are investigated at height-based Reynolds numberRe= 23,000 by experimental and numerical methods. The purpose of this paper is to study the acoustic feedback in the interaction of these two separated flows.Design/methodology/approachThe flow field is measured by particle image velocimetry, hotwire velocimetry and surface oil flow visualization. The acoustic field is modeled in two dimensions by direct aeroacoustic simulation, which solves the compressible Navier–Stokes equations. The simulation is validated against the experimental results.FindingsSeparations occur at both the leading and the trailing edges. The leading-edge separation point and the reattaching flow oscillate in accordance with the trailing-edge vortex shedding. Significant pressure waves are generated at the trailing edge by the vortex shedding rather than the leading-edge vortices. Pressure-based cross-correlation analysis is conducted to clarify the effect of the pressure waves on the leading-edge flow structures.Practical implicationsThe understanding of interactions of separated flows over elongated bluff bodies helps to predict aerodynamic drag, structural vibration and noise in engineering applications, such as the aerodynamics of buildings, bridges and road vehicles.Originality/valueThis paper clarifies the influence of acoustic perturbations in the interaction of separated flows over a D-shaped bluff body. The contribution of the leading- and the trailing-edge vortex in generating acoustic perturbations is investigated as well.

In this paper, a novel passive method for airfoil tonal noise reduction is proposed using a configuration of two segmented elastic panels mounted on the airfoil. Numerical investigation using perturbation evolution method is carried out at a low Reynolds number based on airfoil chord of 5x10 and an angle of attack of 5. The passive method of employing a single panel has shown promising tonal noise reduction capabilities where the resonating panel located just ahead of the sharp growth of boundary layer instability within the airfoil separation bubble provided the strongest reduction of instabilities and noise reduction up to 3 dB has been achieved. The idea is extended in the present study by employing a two-panel configuration based on the localized flow characteristics over the airfoil surface. Five different panel configurations are designed and their effectiveness in terms of tonal noise reduction is evaluated and compared with baseline configuration. The azimuth and spectral analyses indicate the different extent of noise reduction for each configuration and even noise amplification in one of them. A significant noise reduction up to 8 dB is observed for the optimum configuration indicating the effectiveness of this novel method for devices operating at low Reynolds number.

Duct noise control is an important practical problem. This paper explores the vibro-acoustic mechanism of duct noise through the membrane in tandem. Validity and feasibility of the proposed analytical model is demonstrated by comparing existing simplified models and full direct aeroacoustic simulation solved with the CE/SE model. It is shown that the coupling effect between two membranes in tandem is not negligible to predict system response. Moreover, introduction of multimembranes is important or even the only efficient way to apply this passive control method in practice.

A unique concept for suppression of trailing edge noise scattering from a splitter plate in a low Reynolds number flow is proposed. The key idea of the concept is the adoption of a structural compliance system embedded with a finite number of elastic panels. Specific compliance system designs are devised for promotion of panel structural resonance that effectively absorbs broadband flow/acoustic fluctuation energy responsible for noise scattering. The concept is examined using high-fidelity direct aeroacoustic simulation together with spatiotemporal aeroacoustic-structural interaction analysis. The concept is confirmed feasible and outperforms many similar trailing edge noise reduction approaches reported in the literature.

A new modeled Boltzmann equation (MBE) with four improvements made to conventional MBE is formulated. The first improvement is to include the particle internal rotational degree of freedom in the derivation of a continuous equilibrium velocity distribution function f eq; thus, rendering the MBE applicable to diatomic gas. The second improvement is made in the expansion assumed for fαeq in the lattice Boltzmann equation (LBE). This expansion is expressed in terms of the particle velocity vector (ξ) alone; hence, the LBE is no longer limited by a very low Mach number (M) assumption, and it also allows the LBE to correctly satisfy the zero divergence of the velocity field for incompressible flow. The third improvement is made to eliminate the bounce-back rule used to model no-slip wall boundary condition for fα because the rule leads to leakage at solid walls and mass conservation is compromised. The fourth improvement is carried out to render the modeled LBE truly valid for hydrodynamic flow simulation. Thus improved, the new lattice Boltzmann method (LBM) is no longer subject to the M

This paper presents details of remodelling of an engineering design subject to enhance students’ learning outcome. The subject is offered for second year mechanical engineering undergraduates in the first semester of the academic year. The basic objective of the subject is to introduce the engineering design practice and to build up the essential skills to carry out open-ended engineering design projects systematically. Before remodelling, the subject had been taught and assessed mainly with the use of techniques normally used for knowledge building subjects. Students were given only limited opportunities to actively engage with the content, peers and the facilitator in-class. Considering the reserved nature of Hong Kong students, the subject was remodelled by incorporating carefully selected active learning methods. The scaffolded knowledge integration framework for instructional design is extensively used for this subject remodelling exercise. The remodelled subject was delivered and the learning outcome achievements were assessed using pre and post survey questionnaires, focus group discussion and individual student’s performance records. The assessment results indicate that the new approach of subject delivery and assessment methods are more effective in achieving intended learning outcomes and well accepted by the students.

A novel method for reduction in the airfoil tonal noise using flow-induced vibrations is explored by using a flush-mounted elastic panel over the suction surface of a NACA 0012 airfoil at low Reynolds number of \(5\times 10^4\). The fundamental aim of this approach is to reduce the airfoil tonal noise while maintaining laminar boundary layer over the airfoil with minimum or no penalty on the aerodynamic performance of the airfoil. Direct aeroacoustics simulation using conservation element and solution element method along with linear stability analysis is employed to study the aeroacoustic structural interaction between the flow field and elastic panel. Panel parameters are carefully selected to ensure that the natural frequency of panel in the presence of flow field coincides with the first dominant frequency of naturally evolving boundary layer disturbance on the airfoil suction surface. To gain further insight on the sensitivity of panel parameters on its vibration behavior and magnitude of reduction in tonal noise, a parametric study is also carried out. Contributions of panel density and thickness are found to be dominant in noise reduction. A maximum sound pressure level reduction of 2.74 dB is achieved for the current flow conditions through the proposed strategy.

A novel concept of utilizing distributed surface compliance to achieve airfoil tonal noise reduction at various loading conditions is proposed. The aeroacoustics of airfoil configuration subjected to different loading conditions at angles of attack (AoAs) from 3° to 7° are numerically studied using high-fidelity two-dimensional direct aeroacoustic simulation at Reynolds and Mach numbers of [Formula: see text] and 0.4, respectively. Initially, airfoil configurations mounted with single elastic panel (SEP) at individual AoA are designed with the knowledge of respective rigid airfoil flow characteristics. Stemming from the analysis of noise reduction potential of SEP configurations using a reduced-order modeling approach, a distributed surface compliance (DSC) airfoil configuration utilizing three resonating panels is designed to attain airfoil tonal noise reduction over entire range of AoA. Comprehensive acoustic analyses establish that the DSC airfoil could provide a maximum noise reduction ranging from 3 to 7 dB without any sacrifice in airfoil aerodynamics. The extent of noise reduction with DSC airfoil is found dependent on the flow-induced modal responses of the panels. At lower AoA, the panel(s) resonate in their designed structural modes, which remarkably weaken the flow instabilities convecting over the airfoil suction surface and eventually airfoil noise radiation. At higher AoA, the panel responses deviate from their designed structural mode shapes but could still give less noise reduction. Therefore, the designed DSC airfoil shows a feasible concept for tonal noise reduction over a wide range of operational AoA, which substantiates its applicability for aerodynamic devices at low Reynolds numbers.

This paper reports a detailed numerical study of the aeroacoustics of a NACA 0018 airfoil with a cavity at zero angle of attack, with chord-based Reynolds and freestream Mach numbers at 2×104 and 0...

An in-duct device laid with acoustic liner is a popular noise control option for extensive ductworks carrying unsteady flow in various engineering applications. Besides the conventional absorptive liner, elastic panel liner backed by a cavity emerges as a promising alternative concept that has advantages in providing effective broadband reduction at low frequencies yet with significantly low fluid dynamic pressure loss. The present paper reports a numerical study of aeroacoustic–structural interaction of elastic panel liner exposed to subsonic duct boundary layer flow in time domain and explores its role in liner mitigation of plane wave broadband acoustic excitation. The aeroacoustics of the duct flow and panel dynamics are respectively modeled by the two-dimensional compressible Navier–Stokes equations that solved by the conservation element and solution element (CE/SE) method, and one-dimensional elastic panel equation that is solved with finite difference method. The interaction between aeroacoustics and panel dynamics is resolved with a monolithic coupling scheme that is well validated down to acoustic scales. Special attention is placed on the sensitivity of liner acoustic performance to duct flow Mach number ( M ≤ 0 . 3 ) and the relative directions between duct flow and acoustic excitation. Extensive cross-spectral analyses of acoustic results reveal that the transmission loss of the elastic panel liner is primarily a result of the destructive interference of the incident wave with the scattered wave as well as the dissipation of non-planar waves radiated by the panel vibration. The contribution of interference and dissipation to liner reflection and absorption are particularly pronounced at low and high frequencies respectively. In addition, the effect of flow is not strong for M ≤ 0 . 1 . The presence of flow with the incident wave in the flow direction mainly weakens the reflection. However, the effect of flow with incident waves against the flow largely enhances the absorption. Overall, the elastic panel liner is much more effective when the noise source radiates against the flow.

International audience; This paper reports a comprehensive numerical study of noise mitigation performance of elastic panel liner comprising an elastic panel and a cavity beneath exposed to low Mach number grazing flow. A time-domain direct aeroacoustic simulation (DAS) seamlessly coupled with panel dynamics is adopted for its least assumptions taken on duct flow unsteadiness and acoustical behaviors so that both linear and nonlinear aeroacoustic-structural interactions of the problem can be fully explored. The numerical method is well validated with theoretical and experimental works on a liner with thick cavity reported in literature. The noise mitigation of liner with various combinations of cavity depth, panel length and cavity shape, are explored and the present numerical results show that back cavity configuration plays an important role in the liner problem. A decomposition method is applied to DAS acoustic solutions for uncovering the role of aeroacoustically induced panel vibration. The nonlinear effect due to aeroacoustic-structural interaction is found to be of secondary importance. Extensive cross spectral analyses between duct aeroacoustics and panel vibration reveal that the overall liner performance is largely determined by the liner elastic panel whose aeroacoustic and vibration responses are greatly modified by the variations of back cavity acoustics of the back cavity with different shapes. Based on these understandings a new configuration with acoustic absorption materials placed on a cavity wall is proposed. Detailed analysis of its numerical results shows that the introduction of acoustic absorption effectively relieves the cavity acoustics and modifies the panel responses in such a way that an enhanced liner mitigation performance over a broadband can be achieved.

In this paper a novel passive control method is explored for airfoil tonal noise reduction using localized flow-induced vibration of a short elastic panel flush mounted on suction surface of a NACA 0012 airfoil at low Reynolds number. The key idea is to provide local absorption of energy of natural instabilities evolving in the laminar boundary layer by self-sustained flow-induced vibration of a properly designed panel. The panel ultimately acts to weaken the aeroacoustic feedback loop responsible for airfoil tonal noise radiation. Perturbation evolution method with acoustic broadband excitation is utilized to assess the tonal noise reduction potential with various combinations of elastic panel design parameters and optimal resonating and non-resonating elastic panel configurations are determined. Subsequently, direct aeroacoustic simulation of airfoil flow with optimal panel configurations are carried out to uncover the mechanism of tonal noise reduction using localized flow-induced vibration in a quantitative manner. Extensive analysis of numerical results reveals that a resonating panel located just ahead of the sharp growth of boundary layer instability within the airfoil separation bubble provides the strongest reduction of flow instabilities and an overall tonal noise reduction up to 3 dB. Such significant noise reduction is achieved without any sacrifice in the original aerodynamic characteristics of the airfoil. The outcomes of the study evidently suggest that the proposed passive control method with a localized flow-induced panel vibration is effective in suppressing the fundamental mechanism responsible for tonal noise generation of airfoil flow, making it a promising approach for modifying the acoustics of existing aerodynamic or wing profile operating at low Reynolds numbers.

International audience

Vibration of flexible panel induced by flow and acoustic processes in a duct can be used for silencer design, but it may conversely generate noise if structural instability is induced. Therefore, a complete understanding of fluid–structure interaction is important for effective noise reduction. A new time-domain numerical methodology has been developed for the calculation of the nonlinear fluid–structure interaction of an excited panel in internal viscous flow. This paper reports its validation with two experiments. The first aims to validate that the methodology is able to capture flow-induced structural instability and its acoustic radiation. The second one is to show that the methodology captures the aeroacoustic–structural interaction in a low-frequency silencer and its response correctly. The importance of inclusion of viscous effect in both cases is also discussed.

Accurate prediction of the acoustics of fluid-structure interaction is important in devising quieting designs for engineering systems equipped with extensive flow duct networks where the thin duct wall panels are in contact with the flowing fluid. The flow unsteadiness generates acoustic waves that propagate back to the source region to modify the flow process generating them. Meanwhile the unsteady flow pressure excites the thin panels to vibrate, which in turn modifies the flow processes. Evidently a strong coupling between the fluid aeroacoustics and the panel structural dynamics exists. Such coupled physical processes have to be thoroughly understood; otherwise, effective quieting design is never achieved. This paper reports an analysis, using a time-domain numerical methodology the authors have recently developed, of the nonlinear aeroacoustic-structural interaction experienced by a flexible panel in a duct carrying a uniform mean flow. With no mean flow, the numerical results agree well with existing theories and reveal the physics of duct transmission loss. Four regimes of aeroacoustic-structural interaction are identified when the duct flow velocity increases from low subsonic to low supersonic values. Insight in the underlying physics of duct transmission loss at different velocities are highlighted and discussed.

This paper reports an exploratory study of the aeroacoustics of a merging flow at a duct junction with the same width in all branches and different merging angles. The focus is put on the acoustic generation due to the flow unsteadiness. The study is carried out by the direct aeroacoustic simulation (DAS) approach, which solves the unsteady compressible Navier–Stokes equations and the perfect gas equation of state simultaneously using the conservation element and solution element (CE/SE) method. The Mach number based on the maximum inlet velocity of side branch is 0.1 and the Reynolds number of the flow based on duct width and this velocity is 2.3×10 5 . The numerical simulations are performed in two dimensions and the aeroacoustics at different merging angles (30°, 45°, 60° and 90°) are studied. Both the levels of unsteady interactions of merging flow structures and the efficiency of the acoustic generation are observed to increase with the merging angles, where the increase in acoustic efficiency can be up to three orders of magnitude. The major acoustic source is found to be the fluctuating wall pressure induced by the flow unsteadiness in the downstream branch. A scaling law between the wall fluctuating force and the acoustic efficiency is also derived.

Many metropolitan cities suffer from a shortage of land supply, which results in new development in areas with high building density. Construction activities, particularly piling processes, may generate excessive ground-borne vibrations. The nearby sensitive people, facilities and buildings (e.g. hospitals and healthcare institutions) are often vulnerable to such excessive vibrations. However, the impact of construction-induced vibrations on sensitive medical equipment is rarely discussed. The vibration limits commonly adopted by the construction industry are mainly with regard to structural safety, which are considerably greater than the tolerable limits for sensitive medical equipment. This case study evaluates the potential effect of ground vibrations induced by piling activities on sensitive medical equipment. The ground-borne vibrations induced by two piling methods are quantified by field measurements. The indoor floor vibrations are simulated using building models. The vibration limits for a large number of sensitive items of medical equipment are established through questionnaires to the manufacturers. The potential risk to the functionality of the concerned equipment is illustrated by comparing the tolerable vibration limits with the predicted vibration levels.

The space-time conservation element and solution element (CE/SE) scheme has caught many attention in aeroacoustic research community as an alternative numerical strategy for direct aeroacoustic simulation (DAS). As a result of its strict conversation of flow flux in both space and time, the low-order CE/SE scheme possesses excellent non-dissipative characteristics, expedient in calculating low Mach number DAS which requires uniform numerical accuracy to resolve the widely disparate flow and acoustic scales of the problem. In this paper, an attempt of validating a simplified Courant Number Insensitive CE/SE scheme using carefully selected aeroacoustic benchmark problems is reported. Excellent agreement with the benchmark results obtained firmly establishes that CE/SE scheme is a viable scheme for resolving the nonlinear physics of low Mach number aeroacoustic problems.

Tyre/road noise is becoming a more and more significant source of road traffic noise as engines become quieter. To reduce the traffic noise nuisance, low noise road surfaces and tyres have been adopted in noise sensitive areas. The durability and persistency of these low noise road surfaces and tyres are of great concerns. This study aims to quantify the effects of road and tyre deterioration on tyre/road noise. The results show that the tyre/road noise measured on five types of low noise surface material increased by 1.2–1.5 dB(A) per year. The tyre rubber hardness increased by 0.6 shore-A value per month. The tyre/road noise level increased by 0.08–0.48 dB(A) for every unit of shore-A value increase, depending on the road surface material. It is evident that the minimum effect of the test tyre aging on tyre/road noise measurement is 0.6 dB(A) per year.

The acoustic spectra of noise radiation from a turbulent non-premixed inverse diffusion flame were measured and the effect of the point of observation, air jet Reynolds number and overall equivalence ratio on the spectra were examined. The tests were conducted in a wide range of air and fuel flow rates and both the non-reacting and reacting cases were considered and discussed. For the non-reacting case, the noise emitted from the cold flow is mainly generated by the central air jet, with only a small role played by the fuel jets. The dominance of the noise produced by the air jet is confirmed by the observation that the cold flow noise is a strong function of the air jet flow rate or air jet Reynolds number. The spectral features of the noise from the combusting flames differ significantly from those of the cold flow noise due to the chemical reactions. Upon combustion, the noise radiated from the flames significantly overwhelms the corresponding cold flow noise in the range of frequency under consideration (80–3000 Hz). The distance of the point of observation only affects the magnitude of the sound pressure level while both the shape and magnitude of the sound pressure level are influenced by the azimuth of the point observation. The total sound pressure level increases with Re, while the effect of Ф on the total sound radiation level indicates that the highest level of noise occurs as complete combustion is approached.

In-duct devices are commonly installed in flow ducts for various flow management purposes. The structural construction of these devices indispensably creates disruption to smooth flow through duct passages so they exist as structural discontinuities in duct flow. The presence of these discontinuities provides additional possibility of noise generation. In real practice, in-duct devices do not exist alone in any duct system. Even though each in-duct device would generate its own noise, it might be possible that these devices could be properly arranged so as to strengthen the interference between individual noise; thus giving rise to an overall reduction of noise radiation in the in-duct far field. This concept of passive noise control is investigated by considering different configurations of two structural discontinuities of simple form (i.e., a cavity) in tandem in an unconfined flow and in opposing setting within a flow duct. It is known that noise generated by a cavity in unconfined domain (unconfined cavity) is strongly dependent on flow-resonant behavior within the cavity so the interference it produces is merely aeroacoustic. The objective of the present study is to verify the concept of passive noise reduction through enhancement of aeroacoustic interference due to two cavities by considering laminar flow only. A two-dimensional approach is adopted for the direct aeroacoustic calculations using a direct numerical simulation (DNS) technique. The position and geometries of the cavities and the Mach number are varied; the resultant aeroacoustic behavior and acoustic power are calculated. The numerical results are compared with a single cavity case to highlight the effect of introducing additional cavities to the aeroacoustic problem. Resonant flow oscillations occur when two unconfined cavities are very close and the associated acoustic field is very intense with no noise reduction possible. However, for duct aeroacoustics, it is found that a 7.9 db reduction of acoustic power in the downstream side of the duct or a total reduction of ∼6 db is possible with opposing cavities having an offset of half a cavity length. In addition, the reduction is shown to be free from lock-on with trapped modes of the ducts with cavities.

a splitting method to solve the modeled lattice Boltzmann equation. The splitting technique permits the boundary conditions for the lattice Boltzmann equation to be set as conveniently as those required for the finite difference solution of the Navier–Stokes equations. It is shown that the compressible Navier–Stokes equation can be recovered fully from this approach; however, the formulation requires the solution of a Poisson equation governing a secondorder tensor. Thus constructed, the method has no arbitrary constants. The proposed method is used to simulate thermalCouette flow,aeroacoustics,andshockstructureswithanextendedthermodynamicsmodel.Thesimulations are carried out using a high-order finite difference scheme with a two-dimensional, nine-velocity lattice. All simulations are performed using a single relaxation time and a set of constants deduced from the derivation. It is found that the finite difference lattice Boltzmann method is able to correctly replicate viscous effects in thermal Couette flows,aeroacoustics,andshockstructures.Thesolutionsobtainedareidenticaleithertoanalyticalresults,or obtained by solving the compressible Navier–Stokes equations using a direct numerical simulation technique.

We simulated aerodynamic sound in a two-dimensional mixing layer using the finite difference lattice Boltzmann method (FDLBM). We introduced a finite difference scheme, called the dispersion relation preserving (DRP) scheme, into the FDLBM to carry out an accurate simulation of aerodynamic problems. The scheme is designed such that the dispersion relation of the finite difference scheme is the same as that of the original partial differential equations and is useful for acoustic simulations. A turbulent flow field was simulated by large-eddy simulation (LES), using the Smagorinsky model, and the results were compared with those from a direct simulation based on the Navier–Stokes equations to confirm the usefulness of this method. The combination of the FDLBM and the DRP scheme was shown to be very effective for direct simulations of aerodynamic sound.

This paper reports on an attempt to simulate acoustic waves scattering using a finite-difference lattice Boltzmann method based on an alternative lattice equilibrium particle distribution function constructed for compressible thermal fluids. The studies focus on acoustics scattering by a zero-circulation vortex and by an isolated thermal source with no heat gain/loss. Two limiting cases of each type of scattering are examined; one is the case of an incoming acoustic wave with a short wavelength, and the other has a relatively long wavelength compared with the characteristic dimension of the obstacle. These scattering problems have been treated previously using a conventional lattice Boltzmann method and a gas-kinetic scheme. The results showed that these methods were only able to simulate the short wavelength limit case with fair accuracy for the two types of acoustics scattering considered. Because the present approach is able to recover the compressible Navier―Stokes equations with correct fluid properties, the finite-difference solution of the proposed alternative modeled lattice Boltzmann equation allows the limiting cases of the acoustics scattering problems to be calculated without numerical instability. The results thus obtained are in agreement either with analysis or with results obtained from direct aeroacoustics simulations employing the compressible Navier―Stokes equations.

A modified equilibrium distribution function for the Bhatnagar-Gross-Krook-type modeled Boltzmann equation has recently been proposed. The function was deduced using acoustics scaling to normalize the equation and allowed a correct recovery of similarly normalized Euler equations. It is a combination of a Maxwellian distribution plus three other terms that are moments of particle velocity. The lattice counterpart of the modified equilibrium distribution function also led to an exact recovery of the Euler equations; therefore, there is no Mach number limitation in the entire approach. This lattice counterpart was able to replicate aeroacoustics problems involving vorticity-acoustic and entropy-acoustic interactions correctly, and the simulations were carried out using a finite difference lattice Boltzmann method employing only a two-dimensional, nine-velocity lattice. Thus formulated, the numerical scheme has no arbitrary constants and all calculations were carried out using one single relaxation time and a set of constants derived from the analysis. This paper investigates the validity and extent of the formulation to capture shocks and resolve contact discontinuity and expansion waves in one- and two-dimensional Riemann problems. The simulations are carried out using the same two-dimensional, nine-velocity lattice, and identical set of constants and relaxation time; they are compared with theoretical results and those obtained by solving the Euler equations directly using Harten's first-order numerical scheme. Good agreement is obtained for all test cases. However, the modified equilibrium distribution function is not suitable for shock structure simulation; for that, an exact recovery of the Navier-Stokes equations is required.

The Bhatnagar, Gross, and Krook modeled Boltzmann equation has been applied to simulate different fluid dynamics problems with varying degrees of success. However, its application to direct aeroacoustic computation is less successful. One possible reason could be its inability to recover the state equation correctly for a diatomic gas and hence an inaccurate determination of the speed of sound. The present study reports on the development of an improved modeled Boltzmann equation for aeroacoustics simulation. The approach is to modify the Maxwellian distribution normally assumed for the equilibrium particle distribution function. Constraints imposed are the exact recovery of the state equation for a diatomic gas and the Euler equations without invoking the small Mach number assumption. Thus formulated, a distribution function consisting of the Maxwellian distribution plus three other terms that attempt to account for particle-particle collisions is obtained. A velocity lattice method is used to solve the improved modeled Boltzmann equation using an equivalent lattice equilibrium distribution function. The simulations are validated against benchmark aeroacoustic problems whose solutions are deduced from a direct numerical simulation of the Euler equations. The results of the improved modeled Boltzmann equation obtained using a smaller computational domain are in excellent agreement with those deduced from direct numerical simulation using a larger computational domain, thus verifying the viability and correctness of the modified equilibrium distribution function.

A direct force measurement technique employing piezoelectric load cells is used to experimentally investigate a two-dimensional airfoil (NACA 0012) undergoing dynamic stall. The load cells are installed at each end of the airfoil and give the force response in two directions in the plane normal to the airfoil axis during oscillations. Experiments are carried out at a Reynolds number based on the airfoil chord equal to 7.7×104, and at four reduced frequencies, k=0.005, 0.01, 0.02, and 0.04. Phase-averaged lift of the airfoil undergoing dynamic stall is presented. It is observed that hysteresis loops of the lift occur both when the airfoil is pitched to exceed its static stall limit and when it is still within its static stall limit, and they grow in size with increasing k at the same pitching mean angle of attack and pitching amplitude. Both the lift and the drag induced by the pitching motion are further analyzed using the methods of higher order correlation analysis and continuous wavelet transforms to undercover their nonlinear and nonstationary features, in addition to classical FFT-based spectral analysis. The results are quantitatively illustrated by an energy partition analysis. It is found that the unsteady lift and drag show opposite trends when the airfoil undergoes transition from the pre-stall regime to the full-stall regime. The degree of nonlinearity of the lift increases, and the lift show a nonstationary feature in the light-stall regime, while the nonlinearity of the drag decreases, and the drag shows nonstationary feature in both the light-stall and the full-stall regimes. Furthermore, the lift and the drag have significant nonlinear interactions as shown by the correlation analysis in the light-stall regime.

An analysis of a turbine blade fatigue life that includes the physics of fluid–structure interaction on the high cycle fatigue (HCF) life estimate of turbine blades is carried out. The rotor wake excitation is modeled by rows of Karman vortices superimposed on an inviscid uniform flow. The vortex-induced vibration problem is modeled by a linear cascade composed of five turbine blades and the coupled Euler and structural dynamics equations are numerically solved using a time-marching boundary element technique. The analysis can be applied to any blade geometries; it is not limited to the blade geometry considered here. Two major design parameters have been identified; the ratio of blade spacing to blade chord length s/c of the stator, and the normalized frequency parameter c/d which is related to the wake passing frequency of the rotor. For a rigid cascade, it is found that aerodynamic resonance prevails at the resonant c/d values corresponding to an isolated blade while s/c is responsible for the level of the aerodynamic response. If the central blades were elastic, the parameter s/c plays a different role in the fluid–structure interaction problem. With a c/d that could lead to structural resonance for an isolated blade, changing s/c would stabilize the aerodynamic and structural response of the elastic blade in a cascade. On the contrary, an improper choice of s/c might turn the elastic blade response into structural resonance even though the oncoming c/d is non-resonant. The results of the nonlinear effects of c/d and s/c could be used together with the Campbell diagram to obtain an improved HCF design of rotor–stator pair.

A lattice Boltzmann method that can recover the first coefficient of viscosity and the specific heat ratio correctly has been adopted for one-step aeroacoustic simulations because it can recover the speed of sound correctly. Instead of solving the Navier-Stokes equations as in the case of direct numerical simulation, the lattice Boltzmann method only needs to solve one transport equation for the collision function. Other flow properties are obtained by integrating this collision function over the particle velocity space. The lattice Boltzmann method is effective only if appropriate nonreflecting boundary conditions for open computational boundaries are available, just like the direct numerical simulation. Four different nonreflecting boundary conditions are commonly used with direct numerical simulation for one-step aeroacoustic simulations. Among these are the characteristics-based method, the perfectly matched layer method, the C 1 continuous method, and the absorbing layer method. Not all nonreflecting boundary conditions are applicable when used with the lattice Boltzmann method; some might not be appropriate, whereas others could be rather effective. This paper examines some existing nonreflecting boundary conditions plus other new proposals, their appropriateness, and their suitability for the lattice Boltzmann method. The assessment is made against two classic aeroacoustic problems: propagation of a plane pressure pulse and propagation of acoustic, entropy, and vortex pulses in a uniform stream. A reference solution is obtained using direct numerical simulation assuming a relatively large computational domain without any specified nonreflecting boundary conditions. The results, obtained with a computational domain half the size of that used for the direct numerical simulation calculations, show that the absorbing layer method and the extrapolation method with assumed filter perform the best.

This paper reports a study of the ability of an improved LBM in replicating acoustic interaction. With a BGK model with two relaxation times approximating the collison term, the improved LBM is shown not only able to recover the equation of state, but also replicates the specific heat ratio, the fluid viscosity and thermal conductivity correctly. With these improvements, the recovery of full set of unsteady compressible Navier-Stokes equations is possible. Two complex aeroacoustic interaction problems, namely the interaction of three fundamental aeroacoustic pulses and scattering of short wave by a zero circulation vortex, are calculated. The LBM solutions are compared with DNS results. In the first case it has been shown that the improved LBM is as effective as the DNS in simulating aeroacoustic interaction of three pulses. Both methods obtain essentially same results using same truncated domains. In the scattering problem, LBM is able to replicate the directivity of scattered acoustic wave from the vortex but it does not accurately reproduce the symmetry as calculated using DNS.

Aerodynamic surfaces for subsonic flight vehicles are usually designed primarily with the cruise condition in mind. With this objective in mind, the design of these aerodynamic surfaces, which usually exist as airfoils on the vehicles, are in general suboptimal for actual situation because they must be used for takeoff, landing, and maneuver in addition to cruise condition [1]. Therefore, it would be always desirable to design an airfoil with the ability to adapt to its current flow condition and alter its shape to remain the efficiency at any speed. The present paper reports a design of an airfoil with NACA 0012 profile which aims to deform the airfoil shape under the actuation the shape memory alloy (SMA) actuators embedded in it. The SMA actuators design to alter the aerodynamic lift and drag in a subsonic flow. The feasibility of the design is examined and discussed in the light of the change in lift to drag ratio and the power budget of the actuation.

A numerical investigation of sound absorption by an in-duct orifice with and without flow was carried out using a sixth-order finite difference direct numerical simulation (DNS) scheme with explicit fourth-order time marching to solve the governing Navier–Stokes equation. The DNS scheme has previously been validated against benchmark aeroacoustic problems and good agreement was obtained. Thus, it was applied to simulate the acoustic impedance of a circular orifice with different openings and a laminar flow through the same orifice. Both discrete frequency and broadband excitations were studied. When the in-duct orifice is exposed to discrete frequency sound wave in the absence of flow, alternate vortex shedding on both sides of the orifice is observed. The strength of shed vortices is stronger at low frequencies and thus the reduction of sound energy is higher. These vortices dissipate while moving away from the orifice. Therefore, the process provides a mechanism for adsorption of incident sound. The numerical results of broadband excitation indicate that small orifice opening is a more efficient sound absorber whereas a large opening is more or less transparent to the incident wave. The absorption, reflection and transmission coefficients of the in-duct orifice are calculated by a transfer function method. It is found that the sound coefficients are strongly dependent on the orifice opening size and frequency. In the presence of a flow, only alternate vortex shedding on one side of the orifice is observed. In spite of this, the results show that sound absorption behavior is very similar to the no flow case, i.e., sound absorption is more effective with small orifice.

ThevalidityofthelatticeBoltzmannmethodfordirectaeroacousticssimulationsdependsonitsabilitytocorrectly recovertheequationofstateofthegasanditsdynamicviscosity.ThispaperpresentsalatticeBoltzmannmethodwith tworelaxationtimestocarryoutthedirectaeroacousticssimulationsofatwo-dimensionalGaussiansoundpulseina uniform flowoverarangeofMachnumbers(M)varyingfrom0.01to0.9.Itisassumedthatthereisnoshockpresent intherangeofMachnumberstested.Asixth-order finite-differenceschemeisusedtoevaluatetheconvectivetermin the modeled Boltzmann equation, and a second-order Runge–Kutta scheme is used to forward march in time. Thus solved, the calculations show that the wave propagation speed (c) over the range 0:01 � M � 0:9, determined from the deduced equation of state and from the propagation of the pulse, are in good agreement with theoretical analysis and direct numerical simulation results obtained by solving the unsteady compressible Navier–Stokes equations using a low-dispersive and low-dissipative finite-difference scheme. The specific heat ratio (� ) for a diatomic gas is recovered correctly and so is the dependence of the internal energy on � . Thus, the proposed lattice Boltzmann method is valid for direct aeroacoustics simulations at very low to near transonic M.

Introduction O NE-STEP numerical simulations of aeroacoustics problems have been studied for quite some time. The proposed methods usually solve the fully unsteady compressible Navier–Stokes equations, thus allowing the far-field sound and the near-field aerodynamics to be determined without modeling the source terms in the wave equation. Because of the very small energy of the acoustics field, a low dispersive and low dissipative scheme is always required if wave propagation were to be resolved accurately in an aeroacoustics computation. Besides, precise boundary conditions also play a key role in aeroacoustics computations. At the inflow and outflow boundaries, the assumed computational boundaries should allow the aerodynamic field to pass freely with minimal reflection, while at the same time they should be nonreflecting for the incident acoustic waves. Otherwise the spurious erroneous waves reflecting from the boundaries would contaminate the numerical simulation, decrease the computational accuracy, and might even drive the solution toward a wrong time-stationary state. Therefore, it is necessary to formulate truly nonreflecting conditions at these computational boundaries. The most widely used Navier–Stokes characteristics-based boundary conditions (NSCBC) (see Refs. 1–4) for unsteady flows has been proven accurate only if the wave incidence is normal to the computational boundary. Numerical instabilities at other incident angles are intolerable; the instabilities are further amplified in the presence of strong mean shear. Consequently, damping techniques or filtering with a buffer region between the physical domain and outflow boundaries is commonly invoked in the use of NSCBC.5 In addition to suppressing instabilities, the damping or filtering is so constructed that it renders the flow at the end of the buffer region more one dimensional; thus, the residual wave will be relatively more normal to the computational boundary prescribed for NSCBC. Two kinds of buffer regions are commonly adopted for one-step aeroacoustics simulation: the absorbing boundary condition (ABC)

The lattice Boltzmann method (LBM) is a numerical simplification of the Boltzmann equation of the kinetic theory of gases that describes fluid motions by tracking the evolution of the particle velocity distribution function based on linear streaming with nonlinear collision. If the Bhatnagar‐Gross‐Krook (BGK) collision model is invoked, the velocity distribution function in this mesoscopic description of nonlinear fluid motions is essentially linear. This intrinsic feature of LBM can be exploited for convenient parallel programming, which makes itself particularly attractive for one-step aeroacoustics simulations. It is shown that the compressible Navier‐Stokes equations and the ideal gas equation of state can be correctly recovered by considering the translational and rotational degrees of freedom of diatomic gases in the internal energy and using a multiscale Chapman‐Enskog expansion. Assuming two relaxation times in the BGK model allows the temperature dependence of the first coefficient of viscosity of diatomic gases to be replicated. The modified LBM model is solved using a two-dimensional 9-discretized and a twodimensional 13-discretized velocity lattices. Three cases are selected to validate the one-step LBM aeroacoustics simulation. They are the one-dimensional acoustic pulse propagation, the circular acoustic pulse propagation, and the propagation of acoustic, vorticity, and entropy pulses in a uniform stream. The accuracy of the LBM is established by comparing with direct numerical simulation (DNS) results obtained by solving the governing equations using a finite difference scheme. The tests show that the proposed LBM and the DNS give identical results, thus suggesting that the LBM can be used to simulate aeroacoustics problems correctly.

Sound radiation due to unsteady interaction between an inviscid vortex (which models a turbulent eddy) and a finite length flexible boundary in a two-dimensional space is studied using potential theory and the matched asymptotic expansion technique. The Mach number of the vortex propagation is kept below 0.15. Results suggest that the monopole field created by the volumetric flow induced by the vibrating flexible boundary dominates the overall acoustic power radiation. The longitudinal dipole directly due to the transverse vortex acceleration is only important when the vortex is moving over the flexible boundary. The longitudinal dipole resulting from the boundary vibration gains slightly in importance in the strong vortex case, but the corresponding transverse dipole remains negligible for the cases considered in the present study. The two longitudinal dipoles give rise to biased radiation directivities on both sides of the flexible boundary.

Flow-induced vibration of an elastic airfoil due to the wake propagating from an upstream cylinder at a Reynolds number of 10 000 based on cylinder diameter D was investigated. A laser vibrometer was employed to measure the bending and torsional vibration displacements at the mid-span of the airfoil and the cylinder. The dimensionless gap size S/D between the two structures was selected as the governing parameter of the flow-induced vibration problem. It is found that the vibration amplitudes of the elastic airfoil and the vortex shedding frequency of the coupled cylinder–airfoil system are strongly dependent on S/D, due to the different fluid–structure interaction experienced by the airfoil at various S/D. Strong vortex-induced vibration of the airfoil appears to be excited by the organized Karman-vortex-street (KVS) vortices in the cylinder wake for S/D>3 and becomes stabilized for S/D⩽3. However, as a result of the shear-layer-induced vibration at an appropriate frequency, structural resonance is also found to occur even though the airfoil is located in the stabilizing range. The occurrence of structural resonance is further supported by a complementary experiment where the slender structure is an elastic flat plate. This phenomenon indicates that assuming the structures in any fluid–structure interaction problem to be rigid is not appropriate, even though they might appear to be highly stiff. The experimental results were used to validate a numerical model previously developed to estimate the structural responses in complicated fluid–structure interaction problems.

Aerodynamic and structural resonance of an elastic airfoil in a uniform stream with oncoming vortices was investigated experimentally and numerically. An experiment was designed to create two parallel rows of vortices that serve as external excitation for the symmetric airfoil (NACA 0012). The vortices were produced by two identical side-by-side circular cylinders of diameter D in a uniform stream located at a fixed distance ahead of the airfoil. The whole arrangement was placed symmetrically about the midplane in the test section of a wind tunnel. Reynolds numbers ranging from ∼8 × 10 4 to ∼2 x 10 5 were selected because the Strouhal number was essentially constant in this range. A range of D was selected to provide a corresponding range of shedding frequencies f s that could lead to both aerodynamic and structural resonance of the airfoil. A hot-wire anemometer and a dual-beam laser vibrometer were used to measure the wake pattern and the vortex convection velocity, and the airfoil response, respectively. The airfoil displacement amplitude at structural resonance increases by many fold compared to its value far away from resonance and the airfoil goes into a limit-cycle oscillation behavior

Fluid-structure interaction problem is relevant to the quieting design of flow ducts found in many aeronautic and automotive engineering systems where the thin duct wall panels are directly in contact with a flowing fluid. A change in the flow unsteadiness, and/or in the duct geometry, generates an acoustic wave which may propagate back to the source region and modifies the flow process generating it (i.e. an aeroacoustic process). The unsteady pressure arising from the aeroacoustic processes may excite the flexible panel to vibrate which may in turn modify the source aeroacoustic processes. Evidently there is a strong coupling between the aeroacoustics of the fluid and the structural dynamics of the panel in this scenario. It is necessary to get a thorough understanding of the nonlinear aeroacoustic-structural coupling in the design of effective flow duct noise control. Otherwise, an effective control developed with only one media (fluid or panel) in the consideration may be completely counteracted by the dynamics occurring in another media through the nonlinear coupling. The present paper reports an attempt in developing a time-domain numerical methodology which is able to calculate the nonlinear fluid-structure interaction experienced by a flexible panel in a flow duct and its aeroacoustic-structural response correctly. The developed methodology is firstly verified able to capture the acoustic-structural interaction in the absence of flow where the numerical results agree with theory very well. A uniform mean flow is then allowed to pass through the duct so as to impose an aeroacoustic-structural interaction on the flexible panel. As a result, the nonlinear coupling between the flow aeroacoustics and panel structural dynamics are found completely different from the case without mean flow. A discussion of the new physical behaviors found is given.

A numerical study of the aerodynamic noise generated when an airfoil/blade in a uniform flow is excited by an oncoming vortical flow is reported. The vortical flow is modelled by a series of flow convected discrete vortices representative of a Karman vortex street. Such noise generation problems due to fluid–blade interaction occur in helicopter rotor and turbomachinery blades. Interactions with both rigid and elastic airfoil/blade are considered. Under a vortical excitation, aerodynamic resonance of the airfoil/blade at certain excitation frequencies is found to occur and loading noise is generated due to the fluctuations of the aerodynamic loading on the airfoil/blade. For an elastic blade, due the occurrence of structural resonance incited by the flow-induced vibration of the airfoil/blade, a stronger loading noise is generated. The associated thickness effect due to the airfoil/blade vibration is extremely weak. The magnitude of the noise was found to depend on the frequency of the oncoming vortical flow and the geometry and rigidity of the blade.

An analysis of the evolution and sound radiation of a slender vortex ring with initial weak perturbation in free space has been done. Depending on the integer wavenumber of perturbation, the circulation and the core size of the vortex ring, the perturbation evolves in either stable or unstable modes. Both stable and unstable evolutions radiate sound in the far field, and the vortex acceleration of the vortex has been found to be a major sound radation mechanism. A stably perturbed vortex ring radiates stronger sound than an unstable one. The finding of the present study explains some experimental observations of sound from an isolated vortex ring.

This paper reports a numerical study of the interactions of two coaxial thin vortex ring pairs and their far-e eld sound generation. Out of the different varieties of widely differing near-e eld vortex patterns, four basic types of interactions with their associated different degrees of amplie cation and attenuation of the far-e eld sound are identie ed. These four types are found to depend on the circulation ratio, radius ratio, separation ratio, and phase. The suppression of the interaction, caused by the introduction of the control vortex ring pair, results in the slight and moderate attenuation of sound. The initial and continuous rapid and intense interactions with either vortex rings of thecontrolpairare responsibleforthemoderateamplie cation and intenseamplie cation, respectively. This study, thus, establishes the importance of the understanding of the interaction dynamics and their patterns on the far-e eld sound generated. Except for the results of intense amplie cation, the results generally agree with coaxial jets of normal and inverted mean velocity proe les.