ALBERT

Beschreibung: An analysis is made of sound generation by aerodynamic sources near an acoustically compact body (or compact surface feature on a large boundary) that can deform in an arbitrary manner. It is shown how such problems can be investigated by simple extension of the compact Green's function used in the treatment of compact rigid bodies. It is known that this method can furnish rapid and accurate predictions of sound generated by flows with extensive, non-compact distributions of sources in cases where a numerical treatment requires at best tens or hundreds of hours of CPU time. Illustrative applications are made to study (i) the sound generated by a nominally rigid circular lamina of time-dependent radius held in an irrotational mean stream, and (ii) the production of voiced speech by vorticity interacting with a simple model of the vocal folds. In case (ii), it appears that predictions are represented well by a quasi-static approximation that permits the particular results of this paper and previous investigations to be generalized to arbitrarily configured folds. © 2007 Cambridge University Press.

Beschreibung: The prevailing view of the dynamics of flapping flags is that the onset of motion is caused by temporal instability of the initial planar state. This view is re-examined by considering the linearized two-dimensional motion of a flag immersed in a high-Reynolds-number flow and taking account of forcing by a street of vortices shed periodically from its cylindrical pole. The zone of nominal instability is determined by analysis of the self-induced motion in the absence of shed vorticity, including the balance between flag inertia, bending rigidity, varying tension and fluid loading. Forced motion is then investigated by separating the flag deflection into vortex-induced and self components. The former is related directly to the motion that would be generated by the shed vortices if the flag were absent. This component serves as an inhomogeneous forcing term in the equation satisfied by the self motion. It is found that forced flapping is possible whenever the Reynolds number based on the pole diameter ReD≥ 100, such that a wake of distinct vortex structures is established behind the pole. Such conditions typically prevail at mean flow velocities significantly lower than the critical threshold values predicted by the linear theory. It is therefore argued that analyses of the onset of flag motion that are based on ideal, homogeneous flag theory are incomplete and that consideration of the pole-induced fluid flow is essential at all relevant wind speeds. © 2009 Copyright Cambridge University Press.

Beschreibung: An earlier paper (Howe 1967) considered a non-linear theory of open-channel steady flow of deep water past a slowly modulated wavy wall. The wave pattern on the free surface of the water was obtained as the solution of a stably posed elliptic Cauchy problem, the main feature of the solution being the appearance of a ‘shock’ across which there is an abrupt change of phase. Such phase jumps can occur in a wide range of similar problems, but the advantage of the present case is that it is rather well suited to experimental investigation. This paper is therefore a lead-in to the more general problem of phase jumps, and uses the principle of conservation of energy in conjunction with the earlier solution to predict the possible position of the discontinuity on the free surface of the water. The possible nature of the free surface in the vicinity of the phase jump is also discussed (figure 4). This is a region where the width of the wave troughs becomes dramatically shorter than that of the neighbouring troughs. An approximate method of determining the line along which the phase jump occurs, not depending on a knowledge of the solution of the Cauchy problem, is also presented.

Beschreibung: This paper discusses a general theory of wave propagation through a random medium whose random inhomogeneities are confined to small deviations from the mean. The theory is initially worked out in detail for the propagation of transverse waves along an infinite stretched string whose density is a random function of position. The manner in which the mean wave profile is modified by scattering from the density inhomogeneities is discussed in great detail, with particular emphasis on physical interpretation. The general theory of wave propagation in arbitrary dispersive or non-dispersive media is then discussed, and it is shown how the theory may be extended to wave propagation problems involving scattering from rough boundaries. © 1971, Cambridge University Press. All rights reserved.

Beschreibung: This paper examines the energy conversion mechanisms which govern the emission of low frequency sound from an axisymmetric jet pipe of arbitrary nozzle contraction ratio in the case of low Mach number nozzle flow. The incident acoustic energy which escapes from the nozzle is partitioned between two distinct disturbances in the exterior fluid. The first of these is the free-space radiation, whose directivity is equivalent to that produced by monopole and dipole sources. Second, essentially incompressible vortex waves are excited by the shedding of vorticity from the nozzle lip, and may be associated with the large-scale instabilities of the jet. Two linearized theoretical models are discussed. One of these is an exact linear theory in which the boundary of the jet is treated as an unstable vortex sheet. The second assumes that the finite width of the mean shear layer of the real jet cannot be neglected. The analytical results are shown to compare favourably with recent attenuation measurements. © 1979, Cambridge University Press. All rights reserved.

Beschreibung: This paper examines the theory of the interaction of sound with a slit-perforated screen in the presence of a uniform, subsonic tangential mean flow on both sides of the screen. The sound induces vortex shedding from sharp edges of the screen. The coupling of this vorticity with the mean flow leads to a significant modification in the predicted acoustic properties as compared with those predicted by the classical treatments of Rayleigh (1897) and Lamb (1932). In particular a considerable portion of the incident acoustic energy can be lost during the interaction, and is convected away in the mean flow in the form of localized vortical disturbances. The analytical results provide theoretical support for the use of perforated plates to inhibit the onset of cavity resonances in, for example, cross-flow heat exchangers. © 1980, Cambridge University Press. All rights reserved.

Beschreibung: The stability of weakly compressible boundary-layer flow over a spring-mounted piston is examined theoretically by modelling the mean boundary layer at low Strouhal numbers by means of a step-function velocity profile. This constitutes a prototype problem for the treatment of the interaction of unsteady boundary-layer flow with a compliant surface, and the present discussion complements a recent analysis due to Ffowcs Williams and Purshouse by incorporating the influence of flow separation at the edges of the piston. This is effected analytically by application of the unsteady Kutta condition at both the leading and trailing edges of the piston. At high Reynolds numbers and in the case of light fluid loading itis predicted that the separated flow can cause piston flutter. Stability criteria are derived for a rectangular piston of large aspect ratio. © 1982, Cambridge University Press. All rights reserved.

Beschreibung: The compression wave generated by a high-speed train entering a tunnel is studied theoretically and experimentally. It is shown that the pressure rise across the wavefront is given approximately by where ρo, U, M, Ao and A respectively denote the mean air density, train speed, train Mach number, and the cross-sectional areas of the train and the uniform section of the tunnel. A monopole source representing the displacement of air by the train is responsible for the main pressure rise across the wave, but second-order dipole sources must also be invoked to render theoretical predictions compatible with experiment. The principal dipole is produced by the compression wave drag acting on the nose of the train. A second dipole of comparable strength, but probably less significant in practice, is attributed to 'vortex sound' sources in the shear layers of the back-flow out of the tunnel of the air displaced by the train. Experiments are performed that confirm the efficacy of an 'optimally flared' portal whose cross-sectional area S(x) varies according to the formula where x is distance increasing negatively into the tunnel, ℓ is the prescribed length of the flared section, and AE is the tunnel entrance cross-sectional area, given by This portal is predicted theoretically to cause the pressure to increase linearly with distance across a compression wavefront of thickness ∼ ℓ/M, which is very much larger than in the absence of flaring. The increased wave thickness and linear pressure variation counteract the effect of nonlinear steepening of the wave in a long tunnel, and tend to suppress the environmentally harmful 'micro-pressure wave' radiated from the far end of the tunnel when the compression wave arrives. Our experiments are conducted at model scale using axisymmetric 'trains' projected at U ∼ 300 k.p.h. (M ≈ 0.25) along the axis of a cylindrical tunnel fitted with a flared portal. The blockage Ao/A = 0.2, which is comparable to the larger values encountered in high-speed rail operations.

Beschreibung: The Kraichnan-Phillips theorem asserts that, for incompressible, homogeneous, turbulent flow over a plane, rigid wall, the wall-pressure wavenumber-frequency spectrum P as the planar wavenumber k 0 provided the frequency o =(= 0. A proof of this theorem is given by use of a general formula that expresses the normal force on an arbitrary rigid body in terms of volume and surface integrals involving the vorticity. Implications for the theory of flow-induced surface vibrations are briefly discussed. © 1992, Cambridge University Press. All rights reserved.

Beschreibung: A reappraisal is made of the Brown & Michael (1954, 1955) equation that is widely used to model high-Reynolds-number vortex shedding in two dimensions by rectilinear vortices of time-dependent circulations. It is concluded that the equation introduces an unbalanced and unacceptable surface force that can significantly influence predicted flow characteristics. A corrected equation is derived which removes this force, and is applied to determine the sound generated at low Mach numbers when a line vortex translates around the edge of a rigid half-plane. The solution of this problem in the absence of vortex shedding (Crighton 1972) is extended by permitting shedding to occur at the edge in accordance with the unsteady Kutta condition. The shed vorticity is assumed to roll-up into a concentrated core whose motion is calculated by both the emended and original Brown & Michael equations. The two models exhibit large qualitative differences in the predicted wake flow near the edge; both predict significant reductions in the radiated sound, but the reduction is smaller by about 4 dB for the emended Brown & Michael equation.