Generation of locked-on flow tones: Effect of damping

The overall objective of this investigation is to determine the effect of variable damping on the pressure response of a deep cavity. The pressure fluctuations arise from coupling between the unsteady shear layer along the cavity opening and a resonant mode of the cavity. The damping of the cavity is tuned to desired values without changes of geometry or other parameters.The amplitude of the cavity pressure fluctuation as a function of flow velocity is characterized for the first, second and third acoustic modes of the cavity. For each mode, variation of the value of damping over a relatively wide range yields corresponding attenuation of the pressure amplitude. For higher acoustic modes and sufficiently large damping, abrupt decreases of the pressure amplitude occur at threshold values of flow velocity.The variable damping of the deep cavity does not significantly alter the eigenfrequencies of the system. The peak response amplitude of the pressure fluctuation, however, occurs at a value of Strouhal number that increases with increasing values of damping. Moreover, this peak response amplitude, when normalized by the free stream dynamic head, generally shows a linear variation with the value of damping, for three acoustic modes of the cavity.The strength of lock-on of the pressure oscillation, as a function of the degree of damping, is evaluated in terms of the coherent and broadband pressure amplitudes. Both amplitudes are attenuated for increased damping; the difference between them, however, remains relatively large (40 dB minimum), thereby indicating well-defined lock-on, even when the amplitude of the spectral peak of the coherent component is substantially attenuated.     

Capillary cavity flow past a circular cylinder

Cavity flow past a circular cylinder is considered accounting for the surface tension on the cavity boundary. The fluid is assumed to be inviscid and incompressible, and the flow is assumed to be irrotational. The solution is based on two derived governing expressions, which are the complex velocity and the derivative of the complex potential defined in an auxiliary parameter region. An integral equation in the velocity magnitude along the free surface is derived from the dynamic boundary condition. The Brillouin–Villat criterion is employed to determine the location of the point of flow separation. The cases of zero surface tension and zero cavitation number are obtained as limiting cases of the solution. Numerical results concerning the effects of surface tension and cavitation development on the cavity detachment, the drag force and the geometry of the free boundaries are presented over a wide range of the Weber and the cavitation numbers.     

Nonlinear aspects of supersonic flow past a cavity

Study of supersonic flow over wall-mounted cavities for two different length/depth (L/D) ratios is carried out experimentally. Unsteady pressure measurements were made on the front and aft walls of the cavity. Data analysis was performed on the experimental results so obtained. Spectra of the unsteady pressure data exhibit multiple tones. Higher-order spectral technique is implemented on the unsteady pressure data to ascertain whether these multiple tones are due to possible nonlinear interactions between the primary cavity modes (Rossiter modes) or not. Significant nonlinear interactions in the form of both sum and difference frequencies between the cavity modes are observed in both the cavities. The spectra of the cavity with L/D ratio 2 show distinct peaks due to nonlinear interactions while the cavity with L/D ratio 3 does not exhibit observable peaks in the spectra. The spectra of both the cavities show presence of low-frequency peaks of significant amplitudes. These low-frequency modes interact with the primary cavity modes to produce significant bicoherence values. The reasons for their existence could not be predicted. It is identified that the dominant mode in the spectra of the cavities is critical for most of the interactions observed.     

Hypersonic flow past a plate of finite length

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 66–73, September–October, 1991.     

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.     

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.     

Numerical simulation of laminar viscous supersonic flow past a two-dimensional cavity

A systematic study of laminar viscous supersonic flows past rectangular cavities in a flat plate was carried out on the basis of the numerical integration of the Navier-Stokes equations. The greater part of calculations was performed at a Mach number of the outer flow equal to 3 and at a surface temperature amounting to 20% of the stagnation temperature. The pressure, surface friction and heat flux profiles on the plate and on the cavity walls and bottom, together with the streamline pattern, were obtained for various Reynolds numbers.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 27–33, November–December, 1994.     

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.     

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.     

Experimental investigation of the hypersonic low-density flow past a half-closed cylindrical cavity

Hypersonic (M=21) flow past a half-closed cylindrical cavity with a beveled upstream-facing open end was experimentally investigated in a self-oscillatory regime. The Reynolds numbers, based on the largest dimension of the inlet orifice, were Re=8.5·10³ and 2.5·10⁴. The dependence of the pressure fluctuation intensity within the cavity on the fluctuation frequency and the angle between the oncoming stream and the plane of the inlet orifice was determined. The measured data were analyzed on the basis of existing models of fluctuation generation. An electron-beam technique was used to measure the distributions of the average and fluctuation densities in the outer stream. The amplitude and phase characteristics of the outer fluctuations were determined and their relation with the pressure fluctuations within the cavity was established.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 155–160, November–December, 1996.     

Laminar boundary layer in a flow past an aerofoil with a circular cavity

The paper describes a numerical study of a method of preventing the separation of a laminar boundary layer from the forward section of a symmetric aerofoil, the flow past which does not separate at zero angle of incidence. In order to increase the maximum angle of incidence at which the flow has still not separated, a circular cavity (vortex cell) located almost completely inside the aerofoil is introduced on the segment vulnerable to separation. The asymptotics of the corresponding flow at high Reynolds number are described using the Prandtl-Batchelor model. Krasnodar. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 52–57, March–April, 1998. The work was financially supported by the International Science Foundation (grants M4K000 and M4K300) and by the Russian Foundation for Fundamental Research (project No. 96-01-01290).     

Effect of streamwise structures on heat transfer in a hypersonic flow in a compression corner

Coefficients of heat transfer to the surface in a laminar hypersonic flow (M _∞ = 21) over plane and axisymmetric models with a compression corner are presented. These coefficients are measured by an infrared camera. The parameters varied in the experiments are the angle of the compression corner and the distance to the corner point. Characteristics of the flow with and without separation in the corner configuration are obtained. The measured results are compared with direct numerical simulations performed by solving the full unsteady Navier-Stokes equations. Experiments with controlled streamwise structures inserted into the flow are described. A substantial increase in the maximum values of the heat-transfer coefficient in the region of flow reattachment after developed laminar separation is demonstrated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 112–120, July–August, 2009.     

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.     

Generation of coherent structures in supersonic flow past a finite-span flat plate

The formation of coherent structures on a flat plate in a supersonic flow is numerically investigated both in the case of strong shock incidence on the plate and in the problem of oncoming harmonic waves having an intensity of 1–5% of the freestream pressure P ₀. The same mechanism of the coherent structure formation is noticed in both nonstationary problems; it is due to the manifestation of the secondary instability generated in the gas flow owing to the influence of the vortices formed at the lateral edges of the plate. An analysis of the incident wave enhancement at the rear of the plate is made for different wave intensities and wavelength to plate width ratios. The flow patterns in the plate wake indicate the generation of an intense expansion wave in this region, which accelerates the gas flow to the freestream velocity.     

Effect of streamwise and spanwise electric fields on transient growth in a two-fluid channel flow

A linear model of a two-fluid channel flow under streamwise/spanwise electric field is built. Both the fluids are assumed to be incompressible, viscous and perfectly dielectric. The effect of the streamwise and spanwise electric fields on transient behavior of small three-dimensional disturbances is studied. The numerical result shows that the streamwise electric field suppresses transient growth of the disturbance with spanwise uniform wave number. The spanwise electric field diminishes transient growth of the disturbance with streamwise uniform wave number. Two peaks of optimal growth are detected in the wave number plane. The peak at relatively large spanwise wave number is dominated by the lift-up mechanism and little influenced by electric field. Differently, the peak at relatively small wave number is associated with the characteristic of the interface and possibly influenced by electric field. The effect of the Weber number, the Reynolds number and the relative electrical permittivity on optimal growth is studied as well. A scaling law is obtained for relatively small Weber numbers and relatively large Reynolds numbers.     

Effect of freestream nonequilibrium on flow past a wedge

We examine the effect of flow freezing in the nozzle of a hypersonic wind tunnel on the parameters of nonequilibrium flow past a wedge.Zhigulev's solution [1] for vibrational relaxation is extended to the nonequilibrium freestream case.It is shown that in this case the perturbations of the frozen-flow parameters behind the oblique shock wave can change sign if the flow in the working section deviates significantly from equilibrium.A method is proposed for converting experimental results obtained in tunnels with frozen flow to the case of equilibrium freestream flow past the body.The author wishes to thank O. Yu. Polyanskyi and V. P. Agavonov for their interest in this study.     

Symmetric vortex shedding in the near wake of a circular cylinder due to streamwise perturbations

Symmetric perturbations imposed on cylinder wakes may result in a modification of the vortex shedding mode from its natural antisymmetric, or alternating, to a symmetric one where twin vortices are simultaneously shed from both sides of the cylinder. In this paper, the symmetric mode in the wake of a circular cylinder is induced by periodic perturbations imposed on the in-flow velocity. The wake field is examined by PIV and LDV for Reynolds numbers about 1200 and for a range of perturbation frequencies between three and four times the natural shedding frequency of the unperturbed wake. In this range, a strong competition between symmetric and antisymmetric vortex shedding occurs for the perturbation amplitudes employed. The results show that symmetric formation of twin vortices occurs close to the cylinder synchronized with the oscillatory component of the flow. The symmetric mode rapidly breaks down and gives rise to an antisymmetric arrangement of vortex structures further downstream. The downstream wake may or may not be phase-locked to the imposed oscillation. The number of cycles for which the symmetric vortices persist in the near wake is a probabilistic function of the perturbation frequency and amplitude. Finally, it is shown that symmetric shedding is associated with positive energy transfer from the fluid to the cylinder due to the fluctuating drag.     

Direct numerical simulation of three-dimensional flow past a yawed circular cylinder of infinite length

Direct numerical simulation of flow past a stationary circular cylinder at yaw angles (α) in the range of 0–60° was conducted at Reynolds number of 1000. The three-dimensional (3-D) Navier–Stokes equations were solved using the Petrov–Galerkin finite element method. The transition of the flow from 2-D to 3-D was studied. The phenomena that were observed in flow visualization, such as the streamwise vortices, the vortex dislocation and the instability of the shear layer, were reproduced numerically. The effects of the yaw angle on wake structures, vortex shedding frequency and hydrodynamic forces of the cylinder were investigated. It was found that the Strouhal number at different yaw angles (α) follows the independence principle. The mean drag coefficient agrees well with the independence principle. It slightly increases with the increase of α and reaches a maximum value at α=60°, which is about 10% larger than that when α=0°. The root-mean-square (r.m.s.) values of the lift coefficient are noticeably dependent on α.     

Flow in a spherical cavity due to a stokeslet

The earth is considered as a rigid spherical cavity of radius a filled with a highly viscous incompressible fluid of viscosity η. The non-axisymmetric problem of flow due to a stokeslet of strength F/8πη located at (0, 0, c), c < a with its axis along OX, O being the centre of the sphere, is discussed for small Reynolds numbers. The expressions for velocity and pressure are obtained in terms of A(r, θ, φ) and B(r, θ, φ), biharmonic and harmonic functions respectively, using a sphere theorem for non-axisymmetric flow inside a sphere. The drag on the sphere exerted by the fluid is found to be independent of the location of the stokeslet.     

Unsteady convection in a cavity due to pyrolysis

Unsteady convection in a square enclosure produced by pyrolysis of combustible wall is numerically studied. Gas phase processes including mass, momentum and heat transfers are coupled with solid phase processes, heat conduction and thermal degradation (pyrolysis) through conditions at the solid interface. For the gas phase, the unsteady two dimensional Navier-Stokes equations are written in stream-function vorticity formulation under the Boussinesq approximation. Solid phase processes are described by a conduction equation. This study examines the results obtained in the case of a right combustible wall, and compares them with the case of a floor combustible wall.