Aeolian tones of a plate in a channel

The conditions of the onset of aeroacoustic resonance phenomena near a plate in a gas flow in a rectangular channel are studied theoretically and experimentally in a two-dimensional formulation. The eigenfrequency as a function of the plate's chord and its position in the channel, the shape of the eigenfunctions, and the effect of the Mach number of the basic gas flow versus the eigenfrequencies and eigenfunctions and the mechanism of self-excited oscillations are determined. A mathematical model by means of which the dependence of the resonance phenomena on the geometrical parameters of the structure were performed is proposed and substantiated. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 69–77, March–April, 1998.     

Oscillations of a plate cascade in a transonic gas flow

The transonic unsteady flow of a gas through a cascade of thin, slightly curved plates is quite complex and has received little study. The main difficulties are associated with the nonlinear dependence of the aerodynamic characteristics on the plate thickness. In [1] it is shown that, for a single thin plate performing high-frequency oscillations in a transonic gas stream, the variation of the unsteady aerodynamic characteristics with plate thickness may be neglected. For a plate cascade, the flow pattern is complicated by the aerodynamic interference between the plates, which may depend significantly on their shape. A solution of the problem of transonic flow past a cascade without account for the plate thickness has been obtained by Hamamoto [2].The objective of the present study is the clarification of the dependence of the aerodynamic characteristics of a plate cascade on plate thickness in transonic unsteady flow regimes. The nonlinear equation for the velocity potential is linearized under the assumption that the motionless plate causes significantly greater disturbances in the stream than those due to the oscillations. A similar linearization was carried out for a single plate in [3]. The aerodynamic interference between the plates is determined by the method presented in [4]. As an example, the aerodynamic forces acting on a plate oscillating in a duct and in a free jet are calculated.     

Linearized theory of a partially cavitating cascade of flat plate hydrofoils

Summary A linearized theory for partially cavitating flow through a cascade of flat plate hydrofoils is developed. Graphs illustrating the variation in lift force, cavity length and downstream conditions with cavitation number are presented.Nomenclature A, B, C constants - a modulus of ₂ - c chord length - l length of cavity in -plane - l _c length of cavity in z-plane - C _L lift coefficient, equation (15) - i –1 - K cavitation number, (1) - p pressure - t auxiliary mapping plane - u velocity component in x-direction - v velocity component in y-direction - V modulus of velocity vector - w u–iv, complex velocity function - x, y coordinates of physical plane - z x + iy - flow angle with respect to chord - stagger angle - transformation plane - solidity c/2 - ( )₁ denotes upstream conditions - ( )₂ denotes downstream conditions - ( )_m mean conditions - ( ) perturbation quantities - (-) complex conjugate quantity     

Unsteady aerodynamic characteristics of a three-dimensional plate cascade in a subsonic gas flow

M. A. Lavrent'ev Institute of Hydrodynamics of the Siberian Division of the Russian Academy of Sciences, 630090 Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 45–55, March–April, 1995.     

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.     

Determining unsteady aerodynamic forces for three-dimensional plate cascade in subsonic gas flow

The general solution for the problem of three-dimensional gas flow through a cascade of plates was obtained in [1], It is shown below that in the considered direct and inverse aerodynamic problems there may exist nontrivial solutions for uniform boundary conditions. The flow regimes for which such solutions exist may be treated as aerodynamic resonance.The examples presented of the calculation for a plate cascade illustrate the behavior of the unsteady aerodynamic forces near the aerodynamic resonance regimes and make it possible to evaluate the limits of applicability of the hypothesis of plane sections. In addition, the calculation results show the possibility of self-induced vibrations of plate cascades with a single degree of freedom in a subsonic gas stream.     

Flow tones in a pipeline-cavity system: effect of pipe asymmetry

Flow tones in a pipeline-cavity system are characterized in terms of unsteady pressure within the cavity and along the pipe. The reference case corresponds to equal lengths of pipe connected to the inlet and outlet ends of the cavity. Varying degrees of asymmetry of this pipe arrangement are investigated. The asymmetry is achieved by an extension of variable length, which is added to the pipe at the cavity outlet. An extension length as small as a few percent of the acoustic wavelength of the resonant mode can yield a substantial reduction in the pressure amplitude of the flow tone. This amplitude decrease occurs in a similar fashion within both the cavity and the pipe resonator, which indicates that it is a global phenomenon. Furthermore, the decrease of pressure amplitude is closely correlated with a decrease of the Q (quality)-factor of the predominant spectral component of pressure. At a sufficiently large value of extension length, however, the overall form of the pressure spectrum recovers to the form that exists at zero length of the extension.Further insight is provided by variation of the inflow velocity at selected values of extension length. Irrespective of its value, both the magnitude and frequency of the peak pressure exhibit a sequence of resonant-like states. Moreover, the maximum attainable magnitude of the peak pressure decreases with increasing extension length.     

Damage cascade in a softening interface

A model describing the damage at an interface which is coupled to an elastic homogeneous block is introduced. Resorting to a real-space renormalization analysis, we show that in the absence of heterogeneity localization proceeds through a cascade of bifurcations which progressively concentrates the damage from the global interface to a narrow region leading to a crack nucleation. The equivalent homogeneous interface behaviour is obtained through this entire cascade, allowing for the analysis of size effects. When random heterogeneities are introduced in the interface, prior to the onset of localization damage proceeds by a sequence of avalanches whose mean size diverges at the first bifurcation point of the homogeneous interface. The large scale features of the bifurcation cascade are preserved, while the details of the late stage are smeared out by the randomness.     

Vorticity field in a cascade model of turbulence

We propose a model which interprets the behavior of the spontaneous singularity and the intermittent structure in fully developed turbulence simultaneously. The model is justified in the framework of a cascade model of turbulence.     

On the unsteady motion of a biplane cascade

Many studies have been devoted to the questions of unsteady flow about a moving cascade of profiles which are located at the same distance t from one another. However, the unsteady motion in a fluid of a single-row multiplane cascade consisting of a finite or infinite number of profile systems (groups) has received little study. It is assumed that in such a cascade each i-th system (group) of profiles has its own pitch t_i (i=1, 2,, s) and constant phase shift _i of the oscillations between neighboring profiles. The distance h_i between the multiplane cascade profile groups is different; h_it_i. Such cascades arise, for example, in the solution of the problem of the motion of one or two profiles under the free surface of a weightless liquid at a distance h from a solid wall. In the present paper we consider as an example the unsteady motion of a biplane cascade in an incompressible inviscid fluid. We obtain an expression for the complex flow velocity outside the cascade profiles and outside its vortex trails. The corresponding integral equation is obtained for the unknown function u ()-the discontinuity of the tangential component of the velocity along the vortex trail. The solution of this equation is written out for harmonic oscillations of the profiles.     

Cavitating flows through a cascade of flat plates

The purpose of this research is to consider the flow through a cascade of bluff bodies, behind which there exist cavities, by using the free streamline theory. When the wake extends to infinity, both the free surface and the velocity on the free surface are unknown and the cavitation number cannot be specified arbitrarily. Given the geometry of the cascade, a numerical method is described in which we obtain the shape of the free surface and the cavitation number. We obtain the relationship between the contraction coefficient, cavitation number and drag coefficient.     

Differential tones in a damped mechanical system with quadratic and cubic non-linearities

The combination tones of differential type are studied in a non-linear damped mechanical system of two degrees of freedom with quadratic and cubic non-linearities and excited by two external harmonic forces with different frequencies. Approximate steady state solutions and the corresponding Galerkin approximations of high order are obtained and error bounds are given. For a certain frequency the existence of three exact periodic solutions is proved by Urabe's method.     

Flutter of a rectangular plate

We address theoretically the linear stability of a variable aspect ratio, rectangular plate in a uniform and incompressible axial flow. The flutter modes are assumed to be two-dimensional but the potential flow is calculated in three dimensions. For different values of aspect ratio, two boundary conditions are studied: a clamped-free plate and a pinned-free plate. We assume that the fluid viscosity and the plate viscoelastic damping are negligible. In this limit, the flutter instability arises from a competition between the destabilising fluid pressure and the stabilising flexural rigidity of the plate. Using a Galerkin method and Fourier transforms, we are able to predict the flutter modes, their frequencies and growth rates. The critical flow velocity is calculated as a function of the mass ratio and the aspect ratio of the plate. A new result is demonstrated: a plate of finite span is more stable than a plate of infinite span.     

Turbulent wake behind a T-shaped plate: Comparison with a cross-shaped plate

The wake behind T-shaped intersecting flat plates has been studied by direct numerical simulations and compared with the wake behind intersecting plates forming a cross. The Reynolds number based on the uniform inflow velocity and the plate width d was 1000. Similar to the cross-plate the vortex shedding was suppressed in a 4d wide intersection region with a substantial base suction pressure reduction. Shear-layer (K-H) instabilities have been observed and its characteristic frequency obtained. In contrast to the cross-plate, a main feature of the mean wake structure behind the T-plate is the formation of two symmetrically positioned swirling vortices close to the internal corners of the T. This was examined by considering pressure contours and the turbulent production terms of mean streamwise vorticity. In spite of some similarities, major features of the wake behind the T-plate turned out to be distinctly different from the wake behind a cross-plate configuration.     

Comparison of the vortex shedding behavior of a single plate and a plate array

This study compares the shedding behavior around and downstream of a single plate positioned in a flow field alone with the shedding behavior around and downstream of the same plate positioned in an array of identical plates. The shedding frequencies and corresponding Strouhal numbers based on chord [S _r (c)] and based on thickness [S _r (t)] are obtained using a hot-wire anemometer. In comparison with the plate positioned as a single plate, the same plate placed in a plate array shows increases in S _r (c) of up to 55.5% and produces a dominant peak in the power spectra that is wider by a factor of 3.5. In contrast to the single-plate results, which exhibit step changes in S _r (c) of about 0.6 at c/t ≈ 6, 8 and 11, the plate positioned in an array shows only one abrupt transition at c/t ≈ 4. Received: 26 January 1999/Accepted: 7 February 2000     

Magnetoelastic vibration of a plate

Summary The propagation of plane harmonic waves in a thin flat homogeneous isotropic plate of finite width and infinite length permeated by a constant magnetic field is examined. The frequency equations corresponding to the symmetric and antisymmetric modes of vibration of the plate are obtained, and some limiting cases of the frequency equations are then discussed.     

Stokes flow due to the sliding of a smooth plate over a slotted plate

The Stokes flow due to the sliding of a smooth plate over a slotted plate and a bottom fixed plate is solved by eigenfunction expansions and matching. The streamlines show recirculating bubbles near the slots. The drag depends on the void ratio and the relative positions of the three plates. It is found that the Navier condition is in general not satisfied for a slotted plate.