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.     

Self sustained oscillations and collective behaviours in a lattice of jets

Strongly interacting aligned multiple jets are produced behind a perforated plate placed in a uniform flow. The performation patterns investigated experimentally are a square and a triangular lattice of holes with diametersd ranging from 1 mm to 10 mm and of mesh sizeM ranging from 2.54 mm to 25.4 mm. At moderate Reynolds numbers (Re=ud/<3000), each laminar jet develops instabilities causing its effective diameter to increase, thus leading the parallel jets to merge at a distanceL from the plate. The merging distanceL is shown to exhibit a low frequency self sustained oscillation around its mean value with a lateral correlation length much larger than the mesh size. Both the merging distanceL and the oscillation frequency are shown to be functions ofM and of the jet velocity. At larger values ofRe, the merging distance approaches a constant mean value and the amplitude of the oscillations becomes vanishingly small.At the scale of the mesh of the lattice, the oscillating phenomena is shown to result from the local confinement of the jet by its nearby neighbours. This observation is consistent with the fact that when the effect of the nearby jets is simulated by rigid walls, the frequency of the jet's oscillations is found to be of the same order. The influence of the hydrodynamical régime of the individual jets on the oscillations and the role of the lattice pattern on the collective behaviour is discussed on hand of an original model which focuses on the role of the recirculation zone on the delayed non linear saturation of the instabilities of the jet.     

Oscillation of shallow flow past a cavity: Resonant coupling with a gravity wave

Self-excited oscillations of flow past a cavity are generated in a shallow free-surface system. The shear layer past the cavity opening has two basic forms: a separated free-shear flow; and a shear flow along a slotted plate. Instabilities of these classes of shear flows can couple with the fundamental gravity-wave mode of the adjacent cavity. The dimensionless frequencies of both types of oscillations scale on the length of the cavity opening, rather than the gap distance between the slats, i.e., a large-scale instability is always prevalent. A technique of high-image-density particle image velocimetry allows acquisition and interpretation of global, instantaneous images of the flow pattern, including patterns of vorticity and Reynolds stress correlation. Use of a cinema approach provides representations of the timewise evolution of the global, instantaneous flow structure, and thereby definition of the amplitude peaks and phase angles of the coupled fluctuations via auto- and cross-spectral techniques. These methods, along with global, averaged representations of the fluctuating flow field, provide insight into the onset of fully coupled (phase-locked) oscillations of the shear flow past the resonator cavity. The common, as well as the distinctive, features of the resonant-coupled instability of the shear flow past the slotted plate are characterized, relative to the corresponding coupled instability of the free-shear layer. Varying degrees of resonant coupling between the unstable shear layer and the adjacent resonator are attained by variations of the inflow velocity, which yield changes of the predominant oscillation frequency, relative to the resonant frequency of the adjacent cavity. Well-defined, coherent oscillations are indeed attainable for the case of the shear flow along the slotted plate, though their amplitude is significantly mitigated relative to the case of a free-shear layer. The degree of organization of the self-excited, resonant-coupled oscillation and the manner in which it varies with open area ratio and geometry of the plate are interpreted in terms of the flow structure on either side of, and within, the slotted plate; these features are compared with the corresponding structure of the free-shear layer oscillations.     

Influence of flow path modification on oscillation of cavity shear layer

This study investigates the influence on the oscillating characteristics of a cavity shear layer by introducing either a sloped bottom or a flow path modifier at the bottom of the cavity. All the experiments are performed in a recirculating water channel. The laser Doppler velocimetry system and the laser sheet technique are employed to perform the quantitative velocity measurements and the qualitative flow visualization, respectively. The Reynolds number, based on the momentum thickness at the upstream edge of the cavity, is kept at about Re _{θ 0}=194 ± 3.4. It is found that, in addition to the feedback effect, the upstream moving part of the recirculating flow inside the cavity also plays an important role in changing the oscillating characteristics of the unstable shear layer. As the bottom of the cavity is either negatively or positively sloped, the oscillating characteristics of the cavity shear layer are modified to different extents. Significant reduction of the oscillating amplitude within the cavity is found while the bottom slope increases up to d/L=± 2/5. As the bottom slope further increases up to d/L=± 1/2, the self-excited oscillation is completely suppressed. In addition, the ability to suppress the self-excited oscillation by the negative bottom slopes is superior to that in the case of a positive bottom slope. Depending upon the fence locations, the upstream moving part of the recirculating flow will perturb the unstable shear layer at different x/L locations, leading to different oscillating amplitudes. The ability to promote the enlarged oscillating amplitude of the unstable shear layer is better for a fence inclined at a positive angle than for one at a negative angle. Received: 31 May 2000/Accepted: 11 January 2001     

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.     

Forced oscillations of a rotating shaft with nonlinear spring characteristics and internal damping (1/2 order subharmonic oscillations and entrainment)

Nonlinear forced oscillations of a rotating shaft with nonlinear spring characteristics and internal damping are studied. In particular, entrainment phenomena at the critical speeds of 1/2 order subharmonic oscillations of forward and backward whirling modes are investigated. A self-excited oscillation appears in the wide range above the major critical speed. The amplitude of this oscillation reaches a limit value and then a self-sustained oscillation occurs. In the vicinity of a 1/2 order subharmonic oscillation of a forward whirling mode, a self-excited oscillation is entrained by a subharmonic oscillation. In the vicinity of a 1/2 order subharmonic oscillation of a backward whirling mode, either a self-excited oscillation or a subharmonic oscillation occurs.Experiments were made by an elastic rotating shaft with a disc. Nonlinearity in its restoring force was due to an angular clearance of a bearing and internal damping was due to friction between the shaft and an inner ring of the bearing. A self-excited oscillation was observed in the range above the major critical speed and this self-excited oscillation was entrained by a 1/2 order subharmonic oscillation of a forward whirling mode.Nomenclature O–xyz rectangular coordinate system - , _x, _y inclination angle of a shaft and its projections on the xz- and yz-planes - _x, _y inclination angles in rotating coordinates - , polar coordinates - I _p polar moment of inertia of a rotor - I diametral moment of inertia of a rotor - i _p ratio of I _p to I - dynamic unbalance of a rotor - rotating speed (angular velocity) - F magnitude of a dynamic unbalance force, F = (1 – i _p )² - c external damping coefficient - h internal damping coefficient - t time - D _x , D _y internal damping terms in stationary coordinates - D _x , D _y internal damping terms in rotating coordinates - N _x , N _y nonlinear terms in restoring forces     

Effect of weak compressibility of a fluid on bubble-bubble interaction in strong acoustic fields

The effect of weak compressibility of a fluid on the interaction between spherical bubbles in a strong acoustic field is considered. A small parameter ɛ which represents the ratio of the characteristic velocity of radial oscillations of the bubbles to the speed of sound in the fluid is used as a parameter characterizing the fluid compressibility. The equations governing the interaction between two bubbles are derived with an accuracy O(ɛ) in the case in which the ratio of the characteristic velocities of their translational and radial motions is of the order of ɛ. It is shown that neglecting the fluid compressibility effect due to the bubble interaction can lead to either enhancement or attenuation of their radial oscillations following the main compression stage, variation in the oscillation frequency, the bubble approach velocity, and the velocity of the spatial motion of the coupled pair, and the bubble approach and collision rather than their moving away from one another with the formation of a coupled pair.     

Numerical analysis of characteristic features of shallow and deep cavity in supersonic flow

Flow past open cavities are numerically simulated at a Mach number of 1.5, and Reynolds number, based on initial momentum thickness at the front lip of cavity, of 3333 for variable depths (D) with constant length (L). The dominant frequency of oscillation shows a sudden jump when there is a transition from shallow (L/D > 1) to deep cavity (L/D < 1). The vorticity thickness displays two different growth rates along the length of cavity: (1) initial lower spreading rate, followed by (2) higher spreading rate. The lower spreading rate of shear layer is dictated by the type of cavity (either shallow or deep), while the higher spreading rate is directly related to the amplitude of oscillations. Proper orthogonal decomposition (POD) is implemented to visualise the coherent structures based on their energy content. The first two POD spatial structures in the shallow cavity represent vortex shedding, while in the deep cavity, they comprise vortex pairing interactions as in mixing layer. The higher POD modes contain coherent structures at mixed frequencies. The behaviour of coherent structures associated with a temporal frequency is further investigated using dynamic mode decomposition (DMD). The higher DMD modes confirm the dominance of mixing layer behaviour in the deep cavity.     

带喷流激波针流动特性实验研究

采用动态测力、动态测压和纹影等风洞实验技术,对加装了带喷流激波针的钝头体的绕流特性、稳定和非稳模态的形成条件和机理进行了研究.结果表明:带喷流激波针流场存在稳态和非稳态两种模态,超声速喷流的压比大于临界压比时流动处于稳定模态,反之则为非稳模态;增大激波针长度可减小钝头体阻力,但达到一定长度后,进一步减阻的效果不再显著;增大喷流压比能够有效减弱再附激波强度,有利于缓解单独激波针的肩部热斑问题;非稳模态下波系自激振荡对再附激波在钝头体表面所围的区域影响剧烈,振荡是周期性的,且存在确定的主导频率,主导频率随喷流压力比增大而减小;自激振荡的产生是由于喷流出口周围的反压在喷流压比小于临界压比时无法获得持续的平衡而导致.      

Shear layers of a circular cylinder with rotary oscillation

The behavior of the separated shear layers and the near wake of a circular cylinder with small-amplitude rotary oscillations (Ω₁ = 0.05−0.15 for f _f/f _o ≤ 1.25) were investigated experimentally at Re = 3,700. Measurements of an unforced cylinder were also made for 2,000 ≤ Re ≤ 10,000 to better understand the effects of rotary oscillations. The results show that the shear-layer vortices formed closer to the cylinder and the distance separating them was found to decrease with cylinder oscillations. The shear-layer frequency, however, increased with increasing forcing frequency f _f. The formation-region length l _f decreased significantly with increasing f _f while decreased to a lesser extent with increasing normalized oscillation amplitude Ω₁. The shear layer also diffused to a length L _d larger than that of an unforced cylinder, while the l _f-L _d-Strouhal frequency offsetting mechanism was generally maintained. The near wake was of lower momentum compared to an unforced cylinder, and the transverse velocity fluctuations associated with the unforced vortex-shedding frequency f _o always presented a local peak at f _f/f _o = 0.5, regardless of Ω₁ tested.     

Large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure

Basic equations for large deflection theory of thin orthotropic circular plate with variable thickness are derived in this paper. The modified iteration method is adopted to solve the large deflection problem of thin orthotropic circular plate with variable thickness under uniform pressure. If ε=0, then the solution derived from the result in this paper coincides completely with the result given by J. Nowinski (using perturbation method) for solving large deflection problem of thin orthotropic circular plate with constant thickness under uniform pressure.     

Quasi-periodic oscillation envelopes and frequency locking in rapidly vibrated nonlinear systems with time delay

The effect of time-delayed feedback and fast harmonic excitation (FHE) on stationary periodic vibration and quasi-periodic responses in a parametric and self-excited weakly nonlinear oscillator is analyzed in this paper. The method of direct partition of motion and two stages of multiple scales analysis are conducted to obtain analytical approximation for quasi-periodic oscillation envelopes and frequency-locking area near primary resonance. A parameter study shows that, in the absence or the presence of high-frequency excitation, time-delayed feedback may reduce significantly the amplitude and the envelopes of quasi-periodic oscillations leading to a quasi synchronization of the response over the whole frequency range around the resonance. The results presented for the parameters tested agree well with results obtained by numerical simulation.     

Effects of solid and slotted baffles on the convection characteristics of backward-facing step flow in a channel

This study investigates the enhancement of the laminar forced convection characteristics of backward-facing step flow in a two-dimensional channel through the installation of solid and slotted baffles onto the channel wall. The effects of the height of baffle H _b, inclination of baffle installation ϕ_b, height of slot in baffle H _t, inclination of slot in baffle ϕ_t, and distance between the backward-facing step and baffle D on the flow structure, temperature distribution and Nusselt number variation for the system at various Re are numerically explored. Results show that a slotted baffle can enhance the average Nusselt number for the heating section of channel plate by the maximum 190% when Pr=0.7, H _s=0.5, L=5, H _b ≤ 0.3, W _b ≤ 0.2, 0.1 ≤ D ≤ 0.5, 0° ≤ ϕ_b ≤ 45°, H _t ≤ 0.1, 0° ≤ ϕ_t ≤ 45° and 50 ≤ Re ≤ 400. As for the solid baffle, the enhancement may be up by 230%. The solid baffle might cause the re-separation of main stream, and consequently result in poor local heat transfer coefficient in the end region of heating section. This disadvantage can be obviously improved as the baffle is slotted. Besides the penalty of increase in pressure drop due to the baffle installation is much higher for the situation with solid baffle.     

Large-scale structures of turbulent flows over an open cavity

Low Mach number turbulent flows over an open cavity were studied to investigate the quantitative characteristics of large-scale vortical structures responsible for self-sustained oscillations. Wind tunnel experiments with particle image velocimetry (PIV) were conducted in the range of the ratio of cavity length (L) to depth (D), 1<L/D<4, when the incoming boundary layer is turbulent at Re_θ=830 and 1810. Self-sustained oscillation modes were classified by varying the conditions of L/D and Re_θ. The oscillation modes were consistent with the number of vortical structures existing between the leading and trailing edges of the cavity. Proper orthogonal decomposition (POD) was employed to the spatial distributions of vertical velocity correlations on the lip line of cavity geometry. By examining the conditionally averaged distributions of the correlation coefficients of POD, the spatial characteristics of large-scale vortical structures for self-sustained oscillations were examined.     

Nonlinear oscillations of a floating elastic plate

The multi-scales method is used to derive third-order equations of gravitational bending oscillations of a thin elastic plate floating on the surface of a homogeneous perfect incompressible fluid of finite depth. The equations incorporate the compressive force and nonlinear acceleration of vertical displacements of the plate. Based on these equations, the deflection of the plate and the velocity potential of the fluid induced by a traveling periodic wave of finite amplitude are expanded into asymptotic series to terms of the third order of smallness. The dependence of the oscillation characteristics on the elastic modulus and thickness of the plate, compressive force, the initial length and steepness of the wave is analyzed     

Effect of nozzle thickness on the self-excited impinging planar jet

The self-excited oscillation of a large aspect ratio planar jet impinging on a flat plate is investigated experimentally at a single transonic jet velocity to clarify the effect of varying the jet thickness on pattern of jet oscillation and frequency of resulting acoustic tone. The study has been performed for a series of jet thicknesses, 1 mm to 4 mm, each of which is tested for the complete range of plate position, i.e. impingement distance, over which acoustic tones are generated. The results reveal that the jet oscillation is controlled by a fluid-dynamic mechanism for small impingement distances, where the hydrodynamic flow instability controls the jet oscillation without any coupling with local acoustic resonances. At larger impingement distances, a fluid-resonant mechanism becomes dominant, in which one of the various hydrodynamic modes of the jet couples with one of the resonant acoustic modes occurring between the jet nozzle and the impingement plate. Within the fluid-resonant regime, the acoustic tones are found to be controlled by the impingement distance, which is the length scale of the acoustic mode, with the jet thickness having only minor effects on the tone frequency. Flow visualization images of the jet oscillation pattern at a constant impingement distance show that the oscillation occurs at the same hydrodynamic mode of the jet despite a four-fold increase in its thickness. Finally, a feedback model has been developed to predict the frequency of acoustic tones, and has been found to yield reasonable predictions over the tested range of impingement distance and nozzle thickness.     

Effect of pressure-dependent slip on flow curve multiplicity

Various microstructural pictures for slip at polymer/solid interfaces lead to relations which have a region where multiple values of slip velocity are predicted for the same shear stress. This leads to the expectation of multivalued flow curves, which has been verified in specific cases by numerous researchers. We study the effect of pressure dependence on flow curve multiplicity using a simple multivalued slip relation to model the phenomena of hysteresis and spurt flow in polymer extrusion. A continuation technique is used to trace out the boundaries of the region of flow curve multiplicity as pressure drop and die length to diameter (L/D) ratio are changed. Results for Newtonian, shear thinning and viscoelastic constitutive equations show that, despite the multivalued nature of the slip model, multiplicity (and thus hysteresis) is absent at high L/D.  For the sake of completeness, we also carry out time-dependent simulations at constant piston speed taking fluid compressibility into account. These simulations show that oscillations in the pressure drop and exit volumetric flow rate result only if the system is operated in the multiplicity region of the steady state flow curve, in agreement with the results of similar simulations by researchers using various multivalued slip models without pressure dependence. The results demonstrate that a multivalued slip model does not guarantee multiplicity in the flow curve for the constant pressure drop operation, nor oscillations for constant piston speed operation. Received: 18 August 1997 Accepted: 30 March 1998     

Self-sustained oscillations of turbulent flows over an open cavity

The mechanism of self-sustained oscillations in laminar cavity flows has been well characterized; however, the occurrence of self-sustained oscillations in turbulent cavity flows has only previously been characterized by direct observation of flows. Here, the quantitative characteristics of vortical structures in turbulent flows over an open cavity were determined, and then statistical properties were examined for evidence of self-sustained oscillations. Specifically, instantaneous velocity fields were measured using PIV and wall pressure fluctuations were determined from microphone data. Cavity geometries of L/D = 1 and 2, where L and D are the length and depth of the cavity, respectively, were used under conditions where the incoming boundary layer was turbulent at Re _θ  = 830. Statistical analyses were applied based on the instantaneous velocity fields of PIV data. The spatial distributions of vertical velocity correlations (v–v) showed alternating patterns that reflect the organized nature of the large-scale vortical structures corresponding to the modes of N = 2 for L/D = 1 and N = 3 for L/D = 2. These values were consistent with the numbers of vortical structures obtained from a modified version of Rossiter’s equation. Furthermore the numbers of vortical structures determined in the statistical analyses were consistently observed in instantaneous distributions of the swirling strength (λ _ci). The incoming turbulent boundary layer can give rise to the formation of large-scale vortical structures responsible for self-sustained oscillations.     

Adaptive wall functions for the v2‐f turbulence model

Adaptive wall functions for the v²‐f turbulence model have been derived for the flow over a flat plate at zero pressure gradient. These wall functions were implemented via tables for the turbulence quantities and the friction velocity u_τ. A special treatment for the ε and f boundary conditions is proposed. On fine grids (y⁺<1) this approach yields results consistent with the wall integration solution. Detailed numerical results are presented for a zero pressure gradient boundary layer and separated flow over a ramp. Copyright © 2006 John Wiley & Sons, Ltd.     

CHARACTERISTIC OF DROPLET OSCILLATION ON THE SURFACE OF RECTANGULAR HYDROPHOBIC GROOVES

液滴振荡行为是液滴运动中的重要伴随现象,具有重要科研价值.由于液滴撞击疏水沟槽板时运动行为与光滑表面明显不同,可以推测疏水沟槽表面液滴振荡特性也将会呈现与众不同的行为特点.采用高速摄像技术,研究了矩形疏水沟槽表面上水滴高度和接触线振荡行为随沟槽尺寸和撞击速度的变化规律.结果发现,矩形疏水沟槽造成的各向润湿异性使得振荡过程中水滴在平行沟槽方向上的接触线长度大于垂直方向,但并不影响水滴高度方向上衰减振荡的周期,即水滴振荡周期与沟槽间距无关;同时由于疏水沟槽表面上存在能垒束缚效应,致使水滴振荡过程中接触线的铺展和回缩运动不服从典型阻尼振荡规律,而呈现振荡数次后直接趋稳的特点.如水滴以0.61 m/s撞击时,接触线经历2次振荡后即维持稳定,但此时水滴仍在持续振荡中.另外,还初步分析了水滴振荡周期与沟槽间距无关的原因.