Aeolian tones of a plate cascade

A model for the aeroacoustic resonance effects (aeolian tones) excited around a plate cascade in a gas flow is suggested. Methods of calculating the frequencies of natural acoustic oscillations near the cascade are developed. The effect of the cascade geometry and the Mach number of the main flow on the frequencies, abundance, and modes of the natural oscillations is investigated. Anomalous acoustic oscillations near a cyclic plate cascade are shown to exist and are studied. It is shown that there always exist no less than two natural oscillation frequencies in the gas flow near any nontrivial cyclic plate cascade. It has been found that the natural oscillation frequencies can be combined in bundles such that in the case where the number of plates in a period is large the frequencies pertaining to each bundle occupy a certain interval with arbitrary density. The natural oscillations are classified with respect to the form of the eigenfunctions; the classification is based on the theory of representations of groups of locally plane symmetries of the cyclic plate cascade in the solution space. The correctness of the proposed model of the aeroacoustic resonance effects (aeolian tones) excited near a plate cascade in a gas flow is supported by a comparison with the available experimental and theoretical data. On the basis of the investigation performed, some previously unknown physical phenomena are predicted. Thus, the existence of frequency zones or main-flow Mach number ranges on which aeroacoustic resonance phenomena exist near a cyclic cascade with a large number of plates in a period is proved; it is shown that for certain frequencies of the natural oscillations near the cyclic plate cascade the resonance oscillations may be localized in the vicinity of the source; and the existence of narrow-band wave packets slowly propagating along the cascade is demonstrated. Novosibirsk, e-mail: sukhinin@hydro.nsc.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–186, March–April, 2000.     

Eigenoscillations near a plate in a channel

Acoustic eigenoscillations of a gas near a plate in a rectangular channel, i.e., the eigenfrequency of oscillations as a function of the chord length and the position of the plate in the channel, and the form of the eigenfunctions are studied in a two-dimensional formulation. A mathematical model of eigenoscillations near a plate in a channel has been proposed and substantiated, and the dependence of the eigenfrequency of oscillations on the geometric parameters is studied numerically with the use of this model. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 78–90, March–April, 1998.     

Waves ahead of a vertical plate in a channel

The behavior of disturbances propagating with supercritical speed ahead of a plate in a channel is analyzed on the basis of the experimental results obtained by the authors and data taken from the literature. In particular, the transition from smooth to breaking waves has been found to occur at higher propagation speeds than follows from the first approximation of shallow water theory. It has also been found that for waves widely encountered in practice the value of the propagation speed agrees well with the limiting propagation speed of solitary waves obtained on the basis of the complete equations of potential fluid flow. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 82–90, January–February, 1999. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 95-01-01164) and by the Integration Program of the Siberian Branch of the Russian Academy of Sciences under grant No. 97-43.     

Starting flow in a rotating parallel plate channel

The starting flow due to a suddenly applied pressure gradient in a parallel plate channel which is rotating as a system is studied. Exact analytic series solutions to the unsteady Navier-Stokes equations are found by both the Laplace transform method and the separation of parameters method, the latter is shown to be superior. Rotation not only induces a secondary transverse flow but also alters the character of the transient flow rate and velocity profiles. Back flow and inertial oscillations occur, especially at higher rotation rates.     

Unseparated uniform rotational flow past a plate in a channel

The plane problem of a uniform rotational stream of ideal incompressible fluid flowing past a plate in channel with parallel walls is solved analytically. It is found that there is a unique position of the plate in which in experiences the same lift from rotational and potential streams. In an unbounded rotational stream this statement is valid when the ordinates of the plate's mid-point and the point at infinity where the characteristic velocity of the incoming stream is specified are equal.Cheboksary. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 84–91, November–December, 1994.     

Unsteady convective diffusion in a rotating parallel plate channel

The paper presents an exact analysis of the dispersion of a passive contaminant in a viscous fluid flowing in a parallel plate channel driven by a uniform pressure gradient. The channel rotates about an axis perpendicular to its walls with a uniform angular velocity resulting in a secondary flow. Using a generalized dispersion model which is valid for all time, we evaluate the longitudinal dispersion coefficientsK _i (i=1, 2, ...) as functions of time. It is shown thatK ₁=0 andK ₃,K ₄, ... decay rapidly in comparison withK ₂. ButK ₂ decreases with increasing (the dimensionless rotation parameter) for values of upto approximately =2.2. ThereafterK ₂ increases with further increase in and its value gets saturated for large values of (say, 500) and does not change any further with increase in . A physical explanation of this anomalous behaviour ofK ₂ is given.

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Instationäre konvektive Diffusion in einem rotierenden Parallelplattenkanal

Zusammenfassung In dieser Untersuchung wird eine exakte Analyse der Ausbreitung eines passiven Kontaminierungsstoffes in einer zähen Flüssigkeit gegeben, die, befördert durch einen gleichförmigen Druckgradienten, in einem Parallelplattenkanal strömt. Der Kanal rotiert mit gleichförmiger Winkelgeschwindigkeit um eine zu seinen Wänden senkrechte Achse, wodurch sich eine Sekundärströmung ausbildet. Unter Verwendung eines generalisierten, für alle Zeiten gültigen Dispersionsmodells werden die longitudinalen DispersionskoeffizientenK _i (i=1, 2, ...) als Funktionen der Zeit ermittelt. Es wird gezeigt, daßK ₁=0 gilt und dieK ₃,K ₄, ... gegenüberK ₂ schnell abnehmen.K ₂ nimmt ab, wenn , der dimensionslose Rotationsparameter, bis etwa zum Wert 2,2 ansteigt. Danach wächstK ₂ mit bis auf einem Endwert an, der etwa ab =500 erreicht wird. Dieses anomale Verhalten vonK ₂ findet eine physikalische Erklärung.

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List of symbols C solute concentration - D molecular diffusivity - K _i longitudinal dispersion coefficients - 2L depth of the channel - P ₀ dimensionless pressure gradient along main flow - Pe Péclet number - q velocity vector - Q _x,Q _y mass flux along the main flow and the secondary flow directions - dimensionless average velocity along the main flow direction - (x, y, z) Cartesian co-ordinates Greek symbols dimensionless rotation parameter - the inclination of side walls withx-axis - kinematic viscosity - fluid density - dimensionless time - angular velocity of the channel - dimensionless distance along the main flow direction - dimensionless distance along the vertical direction - dimensionless solute concentration - integral of the dispersion coefficientK ₂() over a time interval     

Fluid–structure interaction of a splitter plate in a convergent channel

The fluid–structure interaction (FSI) of a splitter plate in a convergent channel flow is studied by measuring both the flow field and the plate vibration. Particle Image Velocimetry (PIV) measurements show that the wake generated by the plate is characterized by cellular vortex shedding. Mean and RMS velocities presented in the plane normal to the main flow direction visualize clearly the cellular structure and related secondary flows. To evaluate the energy and spatial organization of the vortex shedding, spectral and correlation estimation methods are adapted to the PIV data. By presenting the spanwise variation of the streamwise spectra along the trailing edge, the nature of the cellular vortex shedding becomes evident. 2D space-correlation function reveals that the shedding in two neighboring cells occurs in a 180-degree phase shift. The vibration of the plate is studied with Digital Imaging (DI) and Laser Vibrometer (LV). The DI is based on images measured by the PIV system. An image-processing algorithm is used to detect the plate tip location and velocity simultaneously with the estimation of the fluid velocity field. The LV is used for the time-resolved measurement of the plate vibration. The results show that the plate vibrates in a very distinct mode characterized by a spanwise standing wave along the plate-trailing edge. This mode, in turn, causes the cellular vortex shedding.     

Cavitation flow around a plate in a channel by a stream of heavy liquid

The nonlinear problem of cavitation flow around a plate by a stream of heavy liquid is investigated in precise formulation; the plate is located on the horizontal floor of a channel when the gravity vector is directed perpendicular to the wall of the channel. Two flow systems are considered-Ryabushinskii's and Kuznetsov's system [1]. This problem was investigated in linear formulation in [2], Similar problems were considered earlier in [3–7] for unrestricted flow. Below, on the basis of a method proposed by Birkhoff [8, 9], all the principal hydrodynamic and geometric characteristics are calculated for the problem being considered.Translated from Ivestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–9, May–June, 1973.     

Convective heat transfer in a parallel plate channel with porous lining

The paper proposes a theoretical model for the study of flow and heat transfer in a parallel plate channel, one of whose walls is lined with non-erodible porous material, both the walls being kept at constant temperatures. The analysis uses Brinkman model in the porous medium and employs the velocity and temperature slips at the interface (the so called nominal surface). The influence of the thickness as well as the permeability of the porous medium on the flow field and Nusselt numbers at the walls is investigated.

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Konvektive Wärmeübertragung in einem Parallelplattenkanal mit porösem Überzug

Zusammenfassung Die vorliegende Arbeit befaßt sich mit dem Vorschlag eines theoretischen Modells, um die Wärmeübertragung in einem Parallelplattenkanal mit unauswaschbarem porösem Überzug zu studieren. Die Strömung innerhalb des porösen Überzugs ist mit Hilfe der Brinkmannschen Gleichung analysiert. An der Grenze (der sogenannten Nominalfläche) zwischen dem Überzug und der freien Strömung sind die Geschwindigkeitsgleitung und die Temperaturgleitung benutzt. Die Beeinflussung des Geschwindigkeitsfelds und die Nusseltschen Zahlen an den Wänden in Abhängigkeit von der Dicke und der Durchlässigkeit des porösen Überzugs ist untersucht.

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Nomenclature u streamwise velocity in Zone 1 (Fig. 1) - û streamwise velocity in Zone 2 (Fig. 1) - p pressure - coefficient of viscosity of the fluid - k absolute permeability of the material used for lining - density of the fluid - R Reynolds number - the average velocity in Zone 1 (Fig. 1) - T temperature in Zone 1 (Fig. 1) - T temperature in Zone 2 (Fig. 1) - K thermal conductivity in Zones 1 and 2 (Fig. 1) - M ₁ non-dimensional mass flow rate in Zone 1 (Fig. 1) - M ₂ non-dimensional mass flow rate in Zone 2 (Fig. 1) - (Nu)_U Nusselt number at the upper plate (Fig. 1) - (Nu) _L Nusselt number at the lower plate (Fig. 1) - _E experimental value of the temperature in the channel (with porous lining) at a specified point - _E/* experimental value of the temperature in the channel (without porous lining) at a specified point     

Streamwise vibrations of a plate in a viscous fluid flow in a channel,induced by forced transverse vibrations of the plate

Aeroelastic vibrations of a plate aligned at a zero angle of attack in a viscous incompressible fluid flow in a channel with parallel walls are considered within the framework of a plane model. Forced vibrations of the plate in the transverse direction give rise an unsteady component of the flow friction force, induced by the perturbation of the fluid flow velocity by the vibrating plate. Under the assumption of the laminar character of the fluid flow, it is demonstrated that this force can excite streamwise vibrations of the plate if the channel width is small as compared with the plate length; these streamwise vibrations have the same order as the transverse vibrations of the plate excited by external forces.     

Kinematic analysis of disturbed flow past a plate in a channel with porous walls

Analytic expressions for the complex flow potential are obtained in the linear formulation in the neighborhood of a plate at a small angle of incidence and near porous channel walls. The general solution includes the limiting cases of a plate in a channel with impermeable walls and in a jet. Numerical results concerning the effect of porosity on the flow geometry in the neighborhood of the plate and the channel walls are presented. The disturbed-flow velocity distributions along the channel walls and the flow rate of the fluid sinking at infinity are obtained.Cheboksary. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 13–19, July–August, 1995.     

Transient freezing of liquids in forced laminar flow inside a parallel plate channel

A simple analytical approximative solution was given for calculating the time dependent development of the ice-layers at the cooled walls inside a parallel plate channel. By ignoring the effect of acceleration, resulting from converging ice-layers in the axial direction, an analytical solution for the variation of the ice-layer thickness with time and axial position could be obtained. The approximative solution was checked by numerical calculations and good agreement was found.Es wurde ein analytisches Näherungsverfahren entwickelt, das es ermöglicht, die zeitliche Entwicklung der Erstarrungsfronten im gekühlten, ebenen Kanal zu bestimmen. Die Methode liefert unter Vernachlässigung der Beschleunigungsterme durch die konvergenten Eisschichten eine exakte Lösung der Phasengrenzbeziehung. Das Näherungsverfahren wurde mittels numerischer Berechnungen überprüft und stimmt bis zu Wandunterkühlungsverhältnissen vonB=10 sehr gut mit der numerischen Lösung überein.     

Slip flow in the hydrodynamic entrance region of a tube and a parallel plate channel

Summary The problem of slip flow in the entrance region of a tube and parallel plate channel is considered by solving a linearized momentum equation. The condition is imposed that the pressure drop from momentum considerations and from mechanical energy considerations should be equal. Results are obtained for Kn=0, 0.01, 0.03, 0.05, and 0.1 and the pressure drop in the entrance region is given in detail.Nomenclature A cross-sectional area of duct - c mean value of random molecular speed - d diameter of tube - f _p - f _t - h half height of parallel plate channel - Kn Knudsen number - L molecular mean free path - n directional normal of solid boundary - p pressure - p ₀ pressure at inlet - r radial co-ordinate - r _t radius of tube - R non-dimensional radial co-ordinate - Re _p 4hU/ - Re _t 2r _t U/ - s direction along solid boundary - T absolute temperature - u velocity in x direction - u* non-dimensional velocity - U bulk velocity = (1/A) _A u dA - v velocity in y direction - x axial co-ordinate - x* stretched axial co-ordinate - X non-dimensional axial co-ordinate - X* non-dimensional stretched axial co-ordinate - Y non-dimensional channel co-ordinate - eigenvalue in parallel plate channel - stretching factor - eigenvalue in tube - density - kinematic viscosity - i index - p parallel plate - t tube - v velocity vector - gradient operator - ² Laplacian operator     

Laminar mixed convection on a horizontal plate of finite length in a channel of finite width

The steady two-dimensional laminar mixed-convection flow past a horizontal plate of finite length is analysed for large Péclet numbers, small Prandtl numbers and weak buoyancy effects. The plate is placed in a channel of finite width, with the plane walls of the channel being parallel to the plate. The temperature of the plate is assumed to be constant. The hydrostatic pressure difference across the wake behind the plate is compensated by a perturbation of the inviscid channel flow. This outer flow perturbation affects the temperature distribution in the thermal boundary layer at the plate and the heat transfer rate, respectively. Solutions in closed form are given. The forces acting on the plate due to the potential flow perturbation are also determined.     

Thermophoretic augmentation of particle deposition in natural convection flow through a parallel plate channel

Present paper deals with temperature driven mass deposition rate of particles known as thermophoretic wall flux when a hot flue gas in natural convection flow through a cooled isothermal vertical parallel plate channel. Present study finds application in particle filters used to trap soot particles from post combustion gases issuing out of small furnaces with low technical implications. Governing equations are solved using finite difference marching technique with channel inlet values as initial values. Channel heights required to regain hydrostatic pressure at the exit are estimated for various entry velocities. Effect of temperature ratio between wall and gas on thermophoretic wall flux is analysed and wall flux found to increase with decrease in temperature ratio. Results are compared with published works wherever possible and can be used to predict particle deposition rate as well as the conditions favourable for maximum particle deposition rate.     

Flutter of an elastic plate in a channel flow: Confinement and finite-size effects

When a cantilevered plate lies in an axial flow, it is known to exhibit self-sustained oscillations once a critical flow velocity is reached. This flutter instability has been investigated theoretically, numerically and experimentally by different authors, showing that the critical velocity is always underestimated by two-dimensional models. However, it is generally admitted that, if the plate is confined in the spanwise direction by walls, three-dimensionality of the flow is reduced and the two-dimensional models can apply. The aim of this article is to quantify this phenomenon by analysing the effect of the clearance between the plate and the side walls on the flutter instability. To do so, the pressure distribution around an infinite-length plate is first solved in the Fourier space, which allows to develop an analytical model for the pressure jump. This model is then used in real space to compute instability thresholds as a function of the channel clearance, the plate aspect ratio and mass ratio. Our main result shows that, as the value of the clearance is reduced, the convergence towards the two-dimensional limit is so slow that this limit is unattainable experimentally.     

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.     

Time-dependent interaction between two inviscid fluid flows separated by a semi-infinite non-rigid plate in a flat-walled channel

The problem of the time-dependent interaction between two inviscid weightless fluids separated by a semi-infinite non-rigid plate in a channel with fixed rigid walls is solved in the linear approximation. The general case of deformation and harmonic oscillations of the plate (flapping mover) are considered. The time-dependent hydrodynamic reaction forces, the position of the interface, and the dynamic characteristics of the mover are determined. Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 67–76, January–February, 1997.     

Transient conjugated mixed-convective heat transfer in a vertical plate channel with one wall heated discretely

 This study presents a numerical solution of the unsteady conjugated mixed-convection heat transfer in a vertical plate channel with one wall suddenly subjected to either isoflux or isothermal discrete heat sources. The effects of the dimensionless heat source length H ₁, the dimensionless spacing between heat sources H ₂, the dimensionless channel length L, the dimensionless heated-plate thickness B _l, the wall-to-fluid conductivity ratio K and the ratio of Grashof number to Reynolds number Gr/Re on the interface heat flux, Nusselt number and bulk fluid temperature are discussed in detail. Results show that the discrete heating can cause the heat transfer direction conversely from the fluid to the heated plate during the transient period, which is more significant for the cases with larger L and H ₂. For the system with isoflux discrete heat sources, the time required to reach the steady-state is shorter for larger H ₂. While the trend is reverse for system with isothermal discrete heat sources. Additionally, a higher ratio of the input energy is axially conducted through the plate wall from heated sections to unheated regions for a larger H ₂ and B _l or smaller L. Received on 9 November 1998