Self-sustained oscillations of shear flow past a slotted plate coupled with cavity resonance

Shear flow past a slotted plate configuration can give rise to highly coherent, self-sustained oscillations when coupling occurs with a resonant mode of an adjacent cavity. The distinctive feature of these oscillations is that the wavelength of the coherent instability along the plate is of the order of the plate length. This observation is in contrast to previous investigations of flow past perforated or slotted surfaces, where the instability scales on the diameter of the perforation or the gap length of a slot. The present oscillations occur even when the inflow boundary layer is turbulent and an inflectional form of the shear flow cannot develop along the cavity opening, due to the presence of the slotted plate. Instigation of a resonant mode of the cavity, in conjunction with an inherent instability of the shear flow along the plate, gives rise to ordered clusters of instantaneous vorticity and instantaneous velocity correlation. During the oscillation, ejection of flow occurs from the cavity to the region of the shear flow; this ejection is in accord with the convection of the large-scale cluster of vorticity along the slotted plate. This oscillation can be effectively detuned by adjusting the inflow velocity, such that the inherent instability of the shear flow past the slotted plate is no longer coincident with the resonant frequency of the cavity. Certain features of this self-sustained oscillation are directly analogous to recent findings of oscillations due to shear flow past a perforated plate bounded by a cavity, but in the absence of cavity resonance effects.     

Oscillations of flow past perforated and slotted plates: attenuation via a leading-edge ramp

The present investigation aims to attenuate purely hydrodynamic, long-wavelength, self-excited oscillations of flow past a perforated or slotted plate by deflection of the inflow with a small ramp located at the leading-edge of the plate. Digital particle image velocimetry is complemented by unsteady pressure measurements to determine the underlying physics associated with attenuation of the oscillations. Irrespective of whether a perforated or slotted plate is employed, complete attenuation of the pressure fluctuations associated with the oscillation can be achieved for dimensionless deflection ratios of h/L ≥ 0.035, in which h is the height of the ramp and L is the effective plate length. The attenuation of the self-excited oscillation involves: a steady jet at the trailing-edge of the plate directed into the cavity; a lower magnitude upstream-oriented counterflow along the backside of the plate; and jet-like flows through the plate openings to satisfy the entrainment demands of the separating shear layer.     

Quantitative imaging of acoustically coupled flows over symmetrically located side branches

Fully turbulent inflow past symmetrically located side branches mounted in a duct can give rise to pronounced flow oscillations due to coupling between separated shear layers and standing acoustic waves. Experimental investigation of acoustically coupled shear layers was conducted using digital particle image velocimetry in conjunction with unsteady pressure measurements. Global instantaneous and time-averaged flow images, as well as turbulence statistics, were evaluated to provide insight into the flow physics during flow tone generation. The emphasis was on the acoustic response of the resonator during the first and second hydrodynamic modes of the shear layer oscillation. Onset of the locked-on resonant states was characterized in terms of the acoustic pressure amplitude and the quality factor of the corresponding spectral peak. In addition, visco-thermal acoustic damping and patterns of generated acoustic power were calculated using a semi-empirical approach.     

Flow-acoustic coupling in coaxial side branch resonators with rectangular splitter plates

Flow past symmetrically located side branches mounted in a duct can give rise to pronounced flow oscillations due to coupling between separated shear layers and standing acoustic waves. The acoustically-coupled flows were investigated using digital particle image velocimetry (PIV) in conjunction with unsteady pressure measurements. Global instantaneous, phase- and time-averaged flow images were evaluated to provide insight into the flow physics during flow tone generation. Onset of the locked-on resonant states was characterized in terms of the acoustic pressure amplitude and frequency of the resonant pressure peak. Structure of the acoustic noise source was discussed in terms of patterns of generated acoustic power, which was evaluated by applying the vortex sound theory in conjunction with global quantitative flow imaging and numerical simulation of the acoustic field. In addition to the basic side branch configuration, the effect of bluff rectangular splitter plates located along the centerline of the main duct was investigated. The first mode of the shear layer oscillation was inhibited by the presence of the plates, which resulted in substantial reduction of the amplitude of acoustic pulsations and the strength of the acoustic source.     

Characteristics of Oscillations in Supersonic Open Cavity Flows

Characteristics of oscillations in supersonic open cavity flows are investigated numerically using hybrid RANS/LES (Reynolds-Averaged Navier-Stokes/Large Eddy Simulation) method. The oscillation regimes and feedback mechanisms for the supersonic cavity flows are identified and analyzed. The calculation captures a mixed shear-layer/wake oscillation mode in the flow of Ma = 1.75, where these two modes occur alternately. The shear-layer mode and wake mode are driven by vortex convection-acoustic feedback and absolute instability, respectively. In particular, the results indicate that the feedback-acoustic-wave in the shear-layer mode is probably generated by the reflection of the downstream-traveling pressure wave, associated with the shed vortex in the shear layer, on the aft wall. The cavity flow of Ma = 2.52 is then simulated to see the influence of Mach number. It is found that the increase of Mach number may decrease the amplitude of the fluctuations in the shear layer, inhibiting the transition to wake mode. Furthermore, the influence of upstream injection is also studied, where the results show that the injection only weakens the oscillations and faintly shifts the resonant frequencies.     

Generation of tones due to flow past a deep cavity: Effect of streamwise length

Shear flow past a deep cavity can generate self-sustained oscillations, including locked-on flow tones, due to coupling between the inherent instability of the separated shear layer and an acoustic mode of the cavity resonator. This investigation focuses on the dimensionless pressure amplitude response within a deep cavity, as a function of the streamwise length of the cavity opening; for each length, the pressure response is characterized over a wide range of dimensionless inflow velocity. Criteria for locked-on flow tones are assessed. They include a measure of the strength of lock-on, SoL and the quality factor Q. All self-excited oscillations are assessed using both of these criteria, in order to interpret dimensionless forms of the fluctuation pressure amplitude. The dimensionless pressure amplitude response of the cavity involves several successive regimes, due to variations of streamwise length L of the cavity opening. These regimes are defined in relation to L/θ, where θ is the momentum thickness of the inflow boundary layer. Below a minimum value of L/θ, flow tones cannot be generated. Furthermore, these regimes are defined in terms of the possible hydrodynamic modes (stages) of the unsteady shear layer and the acoustic modes of the deep cavity.     

Attenuation of cavity internal pressure oscillations by shear layer forcing with pulsed micro-jets

Experimental results concerning the pressure oscillations induced by a grazing flow over a deep cavity like a Helmholtz resonator are presented. The study deals with the forcing of the neck shear layer instability in an opened-loop control scheme by means of pulsed micro-jets. The effects of the frequency and amplitude are investigated. It is found that efficient attenuation of the pressure oscillations can be reached when the forcing frequency is larger than the cavity resonance frequency. Then the shear layer is locked with the forcing and resonance with the cavity is lost, inducing a significant decrease of the acoustic pressure level in the cavity. Effects of the jet amplitude are weak, a very small amplitude being capable of forcing the shear layer. By contrast, when the forcing frequency is lower than the cavity resonance frequency (the forcing wave length is greater than twice the neck length) the forcing is ineffective.     

Imaging of the self-excited oscillation of flow past a cavity during generation of a flow tone

Flow through a pipeline-cavity system can give rise to pronounced flow tones, even when the inflow boundary layer is fully turbulent. Such tones arise from the coupling between the inherent instability of the shear flow past the cavity and a resonant acoustic mode of the system. A technique of high-image-density particle image velocimetry is employed in conjunction with a special test section, which allows effective laser illumination and digital acquisition of patterns of particle images. This approach leads to patterns of velocity, vorticity, streamline topology and hydrodynamic contributions to the acoustic power integral. Comparison of global, instantaneous images with time- and phase-averaged representations provides insight into the small-scale and large-scale concentrations of vorticity, and their consequences on the topological features of streamline patterns, as well as the streamwise and transverse projections of the hydrodynamic contribution to the acoustic power integral. Furthermore, these global approaches allow the definition of effective wavelengths and phase speeds of the vortical structures, which can lead to guidance for physical models of the dimensionless frequency of oscillation.     

THE OSCILLATION MODE OF INCOMPRESSIBLE CAVITY FLOW

采用二维大涡模拟方法进行了空腔水流场的数值计算, 考察空腔前缘动量损失厚度及来流速度等因素如何影响空腔流的振荡, 同时考察了空腔长深比与空腔流振荡模式的关系. 用空腔水流场的粒子图像测速测量结果验证了数值计算的可信性.结果表明, 空腔水流是否发生振荡取决于壁面摩擦速度.瞬时涡结构和空腔阻力系数2个方面的特征显示空腔水流场有2种典型的振荡模式, 剪切层模式与尾流模式, 确定振荡模式的关键因素是空腔长深比.     

Shallow cavity flow tone experiments: onset of locked-on states

Fully turbulent inflow past a shallow cavity is investigated for the configuration of an axisymmetric cavity mounted in a pipe. Emphasis is on conditions giving rise to coherent oscillations, which can lead to locked-on states of flow tones in the pipe–cavity system. Unsteady surface pressure measurements are interpreted using three-dimensional representations of amplitude–frequency, and velocity; these representations are constructed for a range of cavity depth. Assessment of these data involves a variety of approaches. Evaluation of pressure gradients on plan views of the three-dimensional representations allows extraction of the frequencies of the instability (Strouhal) modes of the cavity oscillation. These frequency components are correlated with traditional models originally formulated for cavities in a free-stream. In addition, they are normalized using two length scales: inflow boundary-layer thickness and pipe diameter. These scales are consistent with those employed for the hydrodynamic instability of the separated shear layer, and are linked to the large-scale mode of the shear layer oscillation, which occurs at relatively long cavity length. In fact, a simple scaling based on pipe diameter can correlate the frequencies of the dominant peaks over a range of cavity depth.The foregoing considerations provide evidence that pronounced flow tones can be generated from a fully turbulent inflow at very low Mach number, including the limiting case of fully developed turbulent flow in a pipe. These tones can arise even for the extreme case of a cavity having a length over an order of magnitude longer than its depth. Suppression of tones is generally achieved if the cavity is sufficiently shallow.     

Effect of finite cavity width on flow oscillation in a low-Mach-number cavity flow

The current study is focused on examining the effect of the cavity width and side walls on the self-sustained oscillation in a low Mach number cavity flow with a turbulent boundary layer at separation. An axisymmetric cavity geometry is employed in order to provide a reference condition that is free from any side-wall influence, which is not possible to obtain with a rectangular cavity. The cavity could then be partially filled to form finite-width geometry. The unsteady surface pressure is measured using microphone arrays that are deployed on the cavity floor along the streamwise direction and on the downstream wall along the azimuthal direction. In addition, velocity measurements using two-component Laser Doppler Anemometer are performed simultaneously with the array measurements in different azimuthal planes. The compiled data sets are used to investigate the evolution of the coherent structures generating the pressure oscillation in the cavity using linear stochastic estimation of the velocity field based on the wall-pressure signature on the cavity end wall. The results lead to the discovery of pronounced harmonic pressure oscillations near the cavity’s side walls. These oscillations, which are absent in the axisymmetric cavity, are linked to the establishment of a secondary mean streamwise circulating flow pattern near the side walls and the interaction of this secondary flow with the shear layer above the cavity.     

Mode transition and oscillation suppression in supersonic cavity flow

Supersonic flows past two-dimensional cavities with/without control are investigated by the direct numerical simulation(DNS). For an uncontrolled cavity, as the thickness of the boundary layer declines, transition of the dominant mode from the steady mode to the Rossiter Ⅱ mode and then to the Rossiter Ⅲ mode is observed due to the change of vortex-corner interactions. Meanwhile, a low frequency mode appears. However, the wake mode observed in a subsonic cavity flow is absent in the current simulation.The oscillation frequencies obtained from a global dynamic mode decomposition(DMD)approach are consistent with the local power spectral density(PSD) analysis. The dominant mode transition is clearly shown by the dynamic modes obtained from the DMD. A passive control technique of substituting the cavity trailing edge with a quarter-circle is studied. As the effective cavity length increases, the dominant mode transition from the Rossiter Ⅱ mode to the Rossiter Ⅲ mode occurs. With the control, the pressure oscillations are reduced significantly. The interaction of the shear layer and the recirculation zone is greatly weakened, combined with weaker shear layer instability, responsible for the suppression of pressure oscillations. Moreover, active control using steady subsonic mass injection upstream of a cavity leading edge can stabilize the flow.     

Instabilities in viscoelastic flow past a square cavity

Elastic flow transitions in viscoelastic flow past a square cavity adjacent to a channel are reported. The critical conditions for the onset of flow transitions and the qualitative and quantitative characterization of the secondary flows generated by the instability have been examined using streakline photography and instantaneous pressure measurements. Cellular type of instabilities inside the cavity is observed for flow rates beyond a critical value. Small and large scale eddies are observed at high flow rates. The flow inside the cavity and in the channel upstream and downstream of the cavity becomes weakly time-dependent for high flow rates.     

Flow around a NACA0018 airfoil with a cavity and its dynamical response to acoustic forcing

Trapping of vortices in a cavity has been explored in recent years as a drag reduction measure for thick airfoils. If, however, trapping fails, then oscillation of the cavity flow may couple with elastic vibration modes of the airfoil. To examine this scenario, the effect of small amplitude vertical motion on the oscillation of the shear layer above the cavity is studied by acoustic forcing simulating a vertical translation of a modified NACA0018 profile. At low Reynolds numbers based on the chord (O(10⁴)), natural instability modes of this shear layer are observed for Strouhal numbers based on the cavity width of order unity. Acoustic forcing sufficiently close to the natural instability frequency induces a strong non-linear response due to lock-in of the shear layer. At higher Reynolds numbers (above 10⁵) for Strouhal number 0.6 or lower, no natural instabilities of the shear layer and only a linear response to forcing were observed. The dynamical pressure difference across the airfoil is then dominated by added mass effects, as was confirmed by numerical simulations.     

Wave generation on an interface by vortex disturbances in a shear flow

A linear problem of oscillations of an interface in a two-layer system, in which the upper layer is at rest and the lower layer has a constant velocity shear, is considered. The dynamic perturbations in the lower layer are represented as the sum of vortex and wave disturbances (disturbances with zero vorticity). It is shown that in the shear flow the evolution of the vortex disturbances with a nonsmooth or a singular initial vorticity distribution can result in the resonant excitation of waves on the interface. The occurrence of the resonance corresponds to the coincidence of the oscillation frequencies of the perturbations of both classes. In the absence of hydrodynamic instability of the shear flow, the resonant excitation can be one of the main mechanisms of wave generation in two-layer systems.     

Investigation of a combustion driven oscillation in a refinery flare: Part B: Visualisation of a periodic flow instability in a bifurcating duct following a contraction

A flow visualisation study was performed to investigate a periodic flow instability in a bifurcating duct within the tip of the flares at the Shell refinery in Clyde, NSW, to verify the trigger of a combustion-driven oscillation proposed in Part A of this study, and to identify its features. The model study assessed only the flow instability, uncoupled from the acoustic resonance and the combustion that are also present in the actual flare. Three strong, coupled flow oscillations were found to be present in three regions of the fuel line in the flare tip model. A periodic flow separation was found to occur within the contraction at the inlet to the tip, a coupled, periodic flow oscillation was found in the two transverse “cross-over ducts” from the central pipe to the outer annulus and an oscillating flow recirculation was present in the “end-cap” region of the central pipe. The dimensionless frequency of these oscillations in the model was found to match that measured in the full-scale plant for high fuel flow rates. This, and the strength of these flow oscillations, gives confidence that they are integral to the full-scale combustion-driven oscillation and most likely the primary trigger. The evidence indicates that the periodic flow instability is initiated by the separation and roll-up of the annular boundary layer at the start of the contraction in the fuel section of the flare tip. The separation generates an annular vortex which interacts with the blind-ended pipe downstream, leading to a pressure wave which propagates back upstream, initiating the next separation event and repeating the cycle. The study also investigated flow control devices with a view to finding a practical approach to mitigate the oscillations. The shape of these devices was constrained to allow installation without removing the tip of the flare. This aspect of the study highlighted the strength and nature of the coupled oscillation, since it proved to be very difficult to mitigate the oscillation in this way. An effective configuration is presented, comprising of three individual components, all three of which were found to be necessary to eliminate the oscillation completely.     

Aeolian Tones of a Honeycomb Lattice Cell

Aeroacoustic resonant oscillations (aeolian tones) are studied for flow past two plates forming a cross in a square cross section channel. Possible oscillation modes are classified on the basis of admissible symmetry groups and the existence of the modes is proved. The infinite linear system of equations for these modes obtained by the sewing method was simplified and studied numerically. Curves of eigenfrequency versus plate length are constructed. The form of the eigenfunctions is studied.     

The study of self-sustained oscillating plane jet flow impinging upon a small cylinder

 Experimental studies of a plane jet impinging upon a small circular cylinder are conducted by hot-wire measurements. The cylinder is located on the jet centerline within the potential-core region. The jet–cylinder interactions on the instability shear layer frequency, the cylinder wake shedding frequency, and the induced self-sustained oscillation phenomenon are carefully investigated. Test data indicate that the self-sustained flow oscillation is mainly generated by the resonant effect of the flow between the jet exit and the cylinder. Its resonant frequency is found to vary linearly and exhibits jump-stage pattern as a function of the distance between the jet exit and the cylinder. The feedback mechanism and the hydrodynamic instability theorem are proposed to predict correctly the frequency jump position, wave number and the convection speed of the self-sustained oscillating flow for different jet exit velocities. Received: 15 July 1998/Accepted: 9 December 1998     

Study on forced shear flow by a oscillating spoiler

In the present paper, numerical solution of the two-dimensional unsteady Navier-Stokes equations is used to study the forced shear flow induced by a spoiler's periodical up and down oscillation on a flat plate. The paper studies the evolution of growing, shedding, merging and decaying of vortices due to the spoiler's oscillation, particularly the dependence of the forced shear flow on the reduced frequency. Results show that the reduced frequency is a key factor in controlling the growing and the shedding of vortices in the shear layer. The instantaneous streamlines and the equi-vorticity contours, as well as the surface pressure distributions, have also been investigated. Numerical results agree well with corresponding experimental ones. The study is helpful for understanding the physical mechanism of shear flow control.     

Experimental investigation of coaxial side branch resonators

Digital particle image velocimetry is employed to investigate acoustically-coupled flow past a coaxial deep cavity (side branch) resonator mounted in a duct. The emphasis is on the effect of the separation between the coaxial side branches on the interaction between separated shear layers that form across the side branch openings. Various resonator geometries are characterized in terms of patterns of instantaneous and time-averaged flow velocity, vorticity, and streamline topology at several phases of the acoustic cycle. In addition, phase-averaged images of the flow in conjunction with unsteady pressure measurements are evaluated in order to provide insight into the mechanisms of acoustic power generation. Generally speaking, the acoustic source undergoes a significant transformation as the distance between the coaxial side branches changes. As the distance between the side branches decreases, interaction between the associated oscillating shear layers results in substantial changes in the spatial structure of the acoustic source region.