Xiwen Dai

Vortex Shedding and its Nonlinear Acoustic Effect Occurring at a Slit

This paper presents a theoretical study of the nonlinear acoustic properties of a slit in a thin plate subjected to highintensity sound excitation. In the present model, the conventional discrete vortexmethod is employed to simulate the near-field two-dimensional unsteady flow in order to capture the mechanism of the sound–vortex interaction, which is in combination with a spanwise-averaged three-dimensional Green’s function method used to connect the nearfield flow quantities with the far-field sound pressure. This model is compared with an existing particle image velocimetry flow visualization and a direct numerical simulation model, showing good qualitative agreement. It is revealed that the oscillatory slitflow is dominated by a pair of spiral-like counter-rotating vorticesmoving away from the slit and eventually colliding into each other. Because of the vortical flow effect, increases in the sound pressure level result in significant increases in acoustic resistance and modest decreases in acoustic reactance. For the parametric range in this study, increases in the aspect ratio of the slit result in slight increases in acoustic resistance but unnegligible reductions in acoustic reactance. However, the influence of the aspect ratio on acoustic impedance tends to be less important when the sound pressure level exceeds a certain high value.

Discrete vortex model of a Helmholtz resonator subjected to high-intensity sound and grazing flow

In this paper, a theoretical model is developed to study the acoustical response of a Helmholtz resonator as a duct-branched acoustic absorber subjected to both high-intensity sound and grazing flow. The present model is comprised of a discrete vortex model in combination with a one-dimensional duct sound propagation model. The present work is to study the overall effect of incident sound interacting with grazing flow but putting emphasis on the nonlinear or intermediate regime where the sound intensity has a marked or non-negligible influence on the acoustic behavior of the Helmholtz resonator. The numerical results reveal that the flow field around the orifice is dominated by the evolution of the vortex sheet and the flow pattern is influenced by the ratio of the orifice flow velocity to the grazing flow velocity. When the incident sound pressure is high or the resonance occurs, the resonator shows nonlinearity, i.e., the acoustic impedance and absorption coefficient vary not only with duct flow Mach number buy also with incident frequency and incident sound pressure level.

Acoustic of a perforated liner with grazing flow: Floquet-Bloch periodical approach versus impedance continuous approach

The effect of a shear flow on an acoustic liner consisting of a perforated plate backed by cavities is studied. Two different approaches are investigated: First, the duct and the liner are considered as a periodic system while in the second approach the liner is considered as homogeneous and described by an impedance. Those two approaches coincide perfectly without flow for a small hole spacing compared to the acoustic wavelength. This work demonstrates that those two approaches are not wholly consistent when a shear flow is present and reveals some problems in the use of the local impedance with flow. The no-flow impedance cannot be used to describe the liner when a shear flow is present. An equivalent impedance with flow can be defined but it depends on the direction of the incident waves and loses its local characteristic.

An investigation on the characteristics of a non-locally reacting acoustic liner

A finite element acoustic model was proposed for investigating the characteristic of a novel non-locally reacting acoustic liner. This non-locally reacting acoustic liner was based on the so-called multiple cavity resonance mechanism which could broaden the absorption bandwidth. The basic idea of it was that when the back cavity of the liner was partitioned into sub-volumes of different size, multiple resonances relating to different length were produced so that the attenuation peaks came closer and worked jointly to provide high attenuation over a broad frequency band. There were strong coupling effects of the resonances inside the back cavities and in the duct when the sound propagated in the duct installed this non-locally acoustic liner. The proposed finite element acoustic model could simulate the entire sound field both in the duct and inside the back non-uniform cavities of the liner including the strong coupling effects. The comparison between the numerical and the experimental results demonstrated that, the finite element acoustic model was an accurate, stable and rapid method for investigating the acoustic characteristic of this novel non-locally reacting acoustic liner. The numerical study was also targeted for developing an optimal non-locally acoustic liner for engineering applications.

Flow-excited acoustic resonance of a Helmholtz resonator: Discrete vortex model compared to experiments

The acoustic resonance in a Helmholtz resonator excited by a low Mach number grazing flow is studied theoretically. The nonlinear numerical model is established by coupling the vortical motion at the cavity opening with the cavity acoustic mode through an explicit force balancing relation between the two sides of the opening. The vortical motion is modeled in the potential flow framework, in which the oscillating motion of the thin shear layer is described by an array of convected point vortices, and the unsteady vortex shedding is determined by the Kutta condition. The cavity acoustic mode is obtained from the one-dimensional acoustic propagation model, the time-domain equivalent of which is given by means of a broadband time-domain impedance model. The acoustic resistances due to radiation and viscous loss at the opening are also taken into account. The physical processes of the self-excited oscillations, at both resonance and off-resonance states, are simulated directly in the time domain. Results show that the shear layer exhibits a weak flapping motion at the off-resonance state, whereas it rolls up into large-scale vortex cores when resonances occur. Single and dual-vortex patterns are observed corresponding to the first and second hydrodynamic modes. The simulation also reveals different trajectories of the two vortices across the opening when the first and second hydrodynamic modes co-exist. The strong modulation of the shed vorticity by the acoustic feedback at the resonance state is demonstrated. The model overestimates the pressure pulsation amplitude by a factor 2, which is expected to be due to the turbulence of the flow which is not taken into account. The model neglects vortex shedding at the downstream and side edges of the cavity. This will also result in an overestimation of the pulsation amplitude.

Flexural instability and sound amplification of a membrane-cavity configuration in shear flow

The scattering of sound by a membrane-covered cavity in a duct with shear flow is calculated with a linear model based on the multimodal method. The model is verified by comparison against the previous experiments focused on sound suppression of a stable system with high-tension membranes and a low-speed flow. It is shown in this paper that such a situation is drastically changed when the flow velocity is larger than the in vacuo flexural wave speed of the membrane. One of the neutral hydrodynamic modes can be destabilized under certain conditions, and this flexural instability can lead to sound amplification. For a given flow profile, the axial growth rate of the instability increases with the mean flow velocity but saturates at high velocities. For a given mean flow velocity, there is an optimum boundary layer thickness for the instability. Increasing the structural damping tends to stabilize the instability and thus inhibit the sound amplification.

Plate Thickness Effect on Orifice Impedance with Nonlinear Acoustic/Grazing Flow Interaction

This paper presents a theoretical study of the acoustic properties of a small rectangular orifice in a plate of finite thickness, in the presence of both grazing flow and high-intensity sound wave. The present investigation has three basic objectives. The first is to study the plate thickness effect on acoustic properties of the orifice. The second is to study the interaction of high-intensity sound with grazing flow. The third objective is to present flow details around the orifice. On the assumption of large aspect ratio, a 2D discrete vortex method is employed to provide the near field unsteady flow simulation results that are then substituted into a spanwise-averaged 3D Green function integral formula to develop a quasi3D model. Depending on this strategy, the nonlinear acoustic impedance of the orifice is calculated from the average flow velocity through the orifice. The reactance of the orifice increases markedly with the increase of the plate thickness, and the reactance results of the finite-thickness plate are apparently larger than the one of the zero-thickness plate. The calculated resistance reveals that the acoustic property of the orifice undergoes a transition from linear to nonlinear, as the sound pressure amplitude increases; the grazing flow velocity has influence on the transition SPL, resulting from the interaction. More detailed analyses of the effects of the grazing flow and the incident sound wave on the acoustic properties of the orifice are carried out. The vortex shedding process at the orifice edge and the evolution of the shed vortex sheet are simulated, the simulation results exhibit the major features of the vortex sheet, such as the rolling up nature and the “flapping” motion of the shear layer over the orifice.

Linear sound amplification and absorption in a corrugated pipe

Linear sound propagation in an axisymmetric corrugated pipe with shear flow is studied numerically and experimentally. The acoustic and hydrodynamic perturbations are described by the linearized Euler equations (LEEs) in a parallel shear flow. Wave propagation and scattering are computed by means of a multimodal method where the disturbances are expressed as a linear combination of acoustic modes and hydrodynamic modes. The Floquet-Bloch approach is used to calculate the wavenumber in the periodic system. Both sound amplification and absorption, depending on the Strouhal number, are well predicted compared to experiments, which means that the flow-acoustic coupling in the system is effectively described by the present model. It is also shown that the corrugated pipe can amplify the sound even if the shear layer over the cavities is stable everywhere.

Simulation of Sound Generated by Large-Scale Vortices in a Shear Layer by Hybrid DVM/APE Approach

In this paper, sound generated by large-scale votices in a two-dimensional low-Mach number turbulent shear layer is investigated. A hybrid DVM/APE (Discrete-Vortex Model and Acoustic Perturbation Equations) approach is proposed to study this vortex sound phenomenon. A discrete-vortex model is used to simulate unsteady fluid motions of the trailing edge shear layer. A conformal mapping is applied to solve the 2D inviscid flow near the half plane, which is originally used for the problem of a slit geometry. At the trailing edge of the plane, the effect of fluid’s viscosity is imposed by a vortex shedding model and Kutta condition. The unsteady flow field is obtained after DVM simulation. The background mean flow field is acquired by a time-average algorithm. Then, acoustic perturbation equations are solved to obtain the acoustic field by CAA approaches with both acoustic sources and the background mean flow field determined from the results of DVM. Results demonstrate that this hybrid DVM/APE method is a feasible approach to simulate sound generated by the motions of vortices.