Rigid Piston Research Articles

On the sound field of a resilient disk in free space

Radiation characteristics are calculated for a circular planar sound source in free space with a uniform surface pressure distribution, which can be regarded as a freely suspended membrane with zero mass and stiffness. This idealized dipole source is shown to have closed form solutions for its far-field pressure response and radiation admittance. The latter is found to have a simple mathematical relationship with the radiation impedance of a rigid piston in an infinite baffle. Also, a single expansion is derived for the near-field pressure field, which degenerates to a closed form solution on the axis of symmetry. From the normal gradient of the surface pressure, the surface velocity is calculated. The near-field expression is then generalized to an arbitrary surface pressure distribution. It is shown how this can be used as a simplified solution for a rigid disk in free space or a more realistic sound source such as pre-tensioned membrane in free space with non-zero mass and a clamped rim.

Minor losses in high-amplitude acoustic resonators with varying changes in cross section

In a previous paper [J. Acoust. Soc. Am. 112 (2003)], measurements of time-averaged pressure at the closed end of a high-amplitude resonator having a non-uniform cross section were presented. The motivation for this continued work is to better understand minor losses in high-amplitude oscillatory flows through changes in resonator cross section. The resonators consist of two sections of straight brass pipe of different diameters and joined through either step-like or conical couplers. They are driven at the end of the large diameter pipe with a rigid piston. The end of the small tube is rigidly terminated. In the current paper, data obtained from an improved experimental apparatus will be presented. The improvements consist of better temperature control and the ability to measure the power delivered to the resonator by the piston. Subtraction of the linear acoustic boundary-layer losses from the measured input power provides an upper estimate on the power dissipated through other mechanisms. The dependence of the time-averaged pressure and power dissipation on drive amplitude, junction type, and junction location in the standing wave will be discussed. [Research supported by ONR.]

Computational and experimental investigation of minor losses in high amplitude acoustic resonators with varied cross section

Minor losses in high amplitude oscillatory flows through changes in resonator cross section are not well understood. The application of numerical simulation in the study of these losses has shown promise over the past few years. A computational model has been developed based on a time accurate numerical simulation of the full Navier–Stokes equations on parallel computers. A rectangular clustered mesh is used to capture flow field details in the boundary layers and in the vicinity of changes in cross section. Results of simulations are compared to measurements of acoustic and time-averaged pressures at multiple points along the length of resonators and are compared at multiple drive amplitudes. The resonators consist of two sections of straight brass pipe of different diameters and joined through either steplike or conical couplers. They are driven at the end of the large diameter pipe with a rigid piston. The end of the small tube is rigidly terminated. [Research supported by ONR.]

Non‐weak/strong solutions in gas dynamics: a C11p‐version STLSFEF in Lagrangian frame of reference using ρ, u, p primitive variables

AbstractIn this paper, we present computations of the non‐weak solutions of class C11 of transient Navier–Stokes equations for compressible flow in Lagrangian frame of reference using space‐time least squares finite element formulation with primitive variables ρ, u, p. For high speed compressible flows the solutions reported here possess the same orders of continuity as the governing differential equations. The role of diffusion i.e. viscosity (physical or artificial) and thermal conductivity on shock structure is demonstrated. Compression of air in a rigid cylinder by a rigid, massless and frictionless piston is used as a model problem. True time evolutions of class C11 are reported beginning with the first time step until steady shock conditions are achieved. Comparisons with analytical solutions are presented when possible. Copyright © 2001 John Wiley & Sons, Ltd.

NONWEAK/STRONG SOLUTIONS IN GAS DYNAMICS: A C11 p-VERSION STLSFEF IN LAGRANGIAN FRAME OF REFERENCE USING ρ, U, T PRIMITIVE VARIABLES

In this paper we present computations of the nonweak solutions of class C11 of the strong form of transient Navier–Stokes equations for compressible flow in Lagrangian frame of reference using space–time least squares finite element formulation (STLSFEF) with primitive variables ρ, u, T. For high speed compressible flows the solutions reported here possess the same orders of continuity as the governing differential equations (GDEs). It is demonstrated that with this approach accurate numerical solutions of Navier–Stokes equations without any assumptions or approximations are possible. In the approach presented here SUPG, SUPG/DC, or SUPG/DC/LS operators are neither used nor needed. The role of diffusion, i.e., viscosity (physical or artificial) and thermal conductivity on shock structure is demonstrated. Merits of using ρ, u, T as primitive variables over ρ, u, p are discussed. Compression of air in a rigid cylinder by a rigid, massless and frictionless piston is used as a model problem. True time evolutions of class C11 are reported beginning with the first time step until steady shock conditions are achieved. Comparisons with analytical solutions are presented when possible.

Low-frequency sound generation by an individual open-ocean breaking wave

Bubble cloud resonances have been proposed as an explanation of the low-frequency acoustic radiation produced by breaking waves. A previous model [H. N. Ogũz, J. Acoust. Soc. Am. 95, 1895–1912 (1994)] considered excitation of the bubble cloud by a rigid piston at the base of a hemispherical bubble cloud. The present model considers excitation of the cloud by individual point sources within the cloud. A Green’s function is obtained for a point source displaced from the origin of a hemispherical bubble cloud beneath a pressure release surface. The method of images and superposition allow one to obtain the field generated by a distribution of point sources within the bubble cloud. The frequency-dependent radiation pattern for two distributions of point sources within the cloud is obtained. Distributing the point sources within the forward sector of the bubble cloud generates spectral characteristics consistent with measured open-ocean breaking wave spectra.

A Flat Dilatometer to Operate in Glacial Tills

Abstract The Marchetti flat dilatometer is a simple to operate in-situ testing device that was designed for use in clays, silts, and sands. A new dilatometer has been developed for use in a greater variety of soil types, in particular glacial tills. This probe is more robust than the Marchetti dilatometer because it uses a rigid piston instead of a flexible membrane to load the soil. The new dilatometer is also a research dilatometer incorporating a displacement transducer and pressure transducer. This allows an applied pressure displacement curve to be produced. Tests have been carried out at several sites to compare results from the two dilatometers, check the robustness of the new dilatometer, and produce data to establish new correlations.

Continental collision, gravity spreading, and kinematics of Aegea and Anatolia

We have carried out experiments using a layered medium of sand and silicone to investigate the lateral extrusion of a material which spreads over its own weight while being compressed by the advance of a rigid indenter. Boundary conditions in the box mimic those prevailing in the Anatolian‐Aegean system. Both shortening in front of the rigid piston, which models the northward motion of Arabia, and extension resulting from the gravity spreading of the sand‐silicone layer are necessary to initiate the lateral extrusion. Strike‐slip faults accommodate the lateral escape and link the normal faults accompanying gravity spreading with the thrust faults in front of the rigid indenter. Strike‐slip faults begin to accommodate extrusion at a late stage in the experiments after the normal and thrust faults have developed. Experiments also show that the initial geometry of the boundary of the spreading layer may result in the formation of two arcs behind which material extends, in a manner analogous to the Hellenic and Cypriot arcs, without invoking a rheological change at the junction of the two arcs. The experiments also suggest that southward motion of the eastern, part of the spreading region is compensated by the northward advance of the piston, which is a possible explanation for the slower movement of the Cypriot arc compared to the Aegean arc.

Rigid piston approximation for computing the transfer function and angular response of a fiber-optic hydrophone.

The transfer function of a fiber-optic hydrophone (FOH) is computed for various fiber core radii. The hydrophone is modeled as a rigid disk, with plane waves impinging at normal or oblique incidence. The total sound field is written as the sum of the incident field and the field diffracted from the hydrophone. The diffracted field is approximated by the field generated by a vibrating planar piston in an infinite rigid baffle. For normal incidence and a pointlike fiber core, an analytical solution is presented. For finite fiber core radii, and for oblique incidence, the transfer functions are computed numerically. The calculated transfer functions exhibit an oscillatory frequency dependency that is most pronounced for small fiber cores. The solution for a core radius of 2.5 microm can be very well approximated by the analytical solution for a pointlike core at frequencies of up to 30 MHz. The results for normal incidence can be directly employed to deconvolute ultrasonic pressure signals measured with an FOH. From the transfer functions for oblique incidence, the angular response of the hydrophone is calculated. The angular response obtained here differs significantly from the model commonly used for piezoelectric hydrophones. The effective hydrophone radius derived from the angular response shows a strong frequency dependency. For low frequencies, it is found to be larger than the outer fiber radius, whereas it generally lies between the outer radius and the fiber core radius for frequencies above 10 MHz.

Indentation of volcanic edifices by the ascending magma

Abstract The process by which magma ascends into and deforms a volcanic edifice is studied by analogue modelling. A control experiment is conducted with a wooden piston moving vertically into a sand cone. This reveals a well-defined fault pattern that makes it possible to draw the main compressive stress trajectory within the cone during the ascent of the piston. This makes it possible to show that the deformational process is that of indentation of the cone by the rigid piston. Experiments with an indenter that is viscous, as in nature, show that the motion of the viscous body is controlled by the first fault created in the cone. This fault serves as a structural guide, making the viscous body deviate from the vertical and resulting in deformation of the flank of the cone, which bulges out. Other major shear faults that were observed in the control experiment are then inhibited and do not form. This result emphasizes that the structural evolution of an indentation process within a brittle cone and at low rate depends on the rheology of the indenter.

Three apparently paradoxical results of sound radiation theory

Three important generally accepted theoretical results challenge physical interpretation either by being apparently paradoxical or by embodying a surprising coincidence. The first two results bear on the radiation loading of effectively infinite force- or line-excited elastic plates; the third result bears on the radiation loading of an unbaffled rigid piston.

BEM Computations Of A Finite-length AcousticHorn And Comparison With Experiment

Classical horn theory calculates the throat impedance to predict the performance of a finite length horn by using the exit boundary condition that the impedance there is that of a rigid piston in an infinite baffle. Historically such calculations have not seemed to produce good correlation between the radiated pressure response in the far-field and the calculated throat impedance. In this re-examination of horn theory, the throat impedance is calculated for a finite three-dimensional exponentially-flared horn by the Boundary Element Method representing the hom boundaries by planar elements. The calculated impedance, for the without and with finite-baffle cases, is compared with the classical theory and computed far-field response. The computed results are also compared with a novel measurement technique for measuring the throat acoustic impedance using a fiber-optic probe for determining the loudspeaker driver motion. It is shown that there is excellent correlation between the frequency peaks in the far-field pressure and the throat impedance both for the BEM calculations and for the experimental measurements.

Radiation from point sources within a bubble cloud

Bubble cloud resonances have been proposed as an explanation of the low-frequency acoustic radiation produced by breaking waves. A previous model [H. N. Og̃uz, J. Acoust. Soc. Am. 95, 1895–1912 (1994)] considered excitation of the bubble cloud by a rigid piston at the base of a hemispherical bubble cloud. The present model considers excitation of the cloud by individual points sources within the cloud. A Green’s function is obtained for a point source displaced from the origin of a hemispherical bubble cloud beneath a pressure release surface. The radiation pattern for multiple point sources distributed within a slice of the hemispherical cloud is obtained by superposition and the method of images. The effects of bubble cloud characteristics on the radiation field will be shown for various frequencies and ranges of point source depths. The method presented here is applicable to modeling sound generation of breaking waves having bubble clouds that are not amenable to being modeled by a hemispherical geometry. For instance, bubble clouds produced by breaking surf might be modeled more accurately using a cylindrical bubble cloud geometry. [Work supported by ONR.]

STUDY OF THE FORCED RESPONSE OF A CLAMPED CIRCULAR PLATE COUPLED TO A UNI-DIMENSIONAL ACOUSTIC CAVITY

The subject of this paper is an experimental and analytical study of a structural-acoustical coupling problem. To simplify the issue, the analytical model considered here consists of a uni-dimensional acoustic cavity coupled to a one-degree-of-freedom system (mass, spring and damper). An harmonic excitation force is applied to the mass of the oscillator. In the theoretical analysis, the uni-dimensional cavity is subjected, in correspondence of its end sections, to boundary conditions, which are either the usual ones (closed or open ended) or those deriving from the coupling with the oscillator. This simple model proved to be very useful to investigate the influence of the variation of both the geometrical parameters (i.e., the length of the cavity) and the physical parameters (i.e., mass, damping coefficient and stiffness of the oscillator). The analytical results are compared to those obtained experimentally on a real coupled system, consisting of a cavity enclosed by an acoustically rigid steel cylinder, closed at one end by a movable, acoustically rigid piston and at the other end by a flexible plate, clamped around its edge by the cylinder. Thus the length of the cavity can be varied by simply moving the rigid piston.

A Model of Piston Secondary Motion and Elastohydrodynamic Skirt Lubrication

A model of elastohydrodynamic lubrication of piston skirts in reciprocating engines was developed in the context of a simulation of piston secondary motions. The piston secondary dynamics, skirt lubrication and skirt elastic deformation problems are simultaneously solved in the calculation. The model can represent both conventional and two-piece articulated pistons and also includes a treatment of wristpin lubrication. Skirt deformations are calculated using a skirt compliance matrix derived from a finite element model of the piston. The model was exercised by calculating piston secondary motions and skirt deformations for a heavy-duty truck diesel piston at various operating conditions. Results show that peak skirt radial deformations can exceed the skirt-liner radial clearance and strongly depend on load. Articulated piston skirt deformations were shown to be significantly larger than those in conventional piston skirts. Consideration of skirt elastic deformations significantly affected (rigid piston) motion and skirt friction predictions, highlighting the importance of an elastohydrodynamic model.

Diffraction impulse response of rectangular transducers

A closed-form expression for the impulse velocity potential of rectangular pistonlike transducers, without any far field or paraxial approximation, is presented. The classical time-domain impulse response approach is used considering free-field, rigid baffle, and pressure release boundary conditions. Previous approaches to the rigid baffled rectangular piston require the use of superposition methods in order to find a general solution numerically. These must add or subtract, according to the field point location, the analytical expressions that were derived only for specific field points or geometrical regions. In this paper the complexity introduced by the geometrical discontinuities of rectangular apertures is analyzed. A new compacting methodology is proposed and applied to obtain a general solution for the impulse response. This new solution provides the value of the impulse response directly in the time domain, without requiring superposition methods. In addition, a closed-form solution for the pressure impulse response is also presented. This can be useful for physical insight and a qualitative analysis of transient and continuous wave pressure fields. Also included is a description of the temporal behavior of the impulse velocity potential and the pressure impulse response for field points in different regions. The proposed solution allows an efficient and accurate computation of pressure fields under realistic excitations. Several examples illustrate the use of this new solution in the computation of transient pressure waveforms, when wideband and relatively narrow-band excitation pulses are used. Three-dimensional plots of the peak amplitude of the transient pressure near field are presented, and certain characteristics are analyzed using the pressure impulse response.

Self and mutual radiation resistance measurement of two closely located loudspeakers.

In an active noise control or in sound reproduction, it is important to know self and mutual radiation impedances of sound sources. Since the total radiated power from sound sources is determined by self and mutual radiation resistances and velocities of the radiating surfaces, it is possible to determine the radiation resistances from the measurement of radiated power and velocities. Radiation resistances of two loudspeakersmeasured in a large meeting room are on the same order of a rigid piston in an infinite baffle, but show large irregularities due to complex radiation conditions. The mutual radiation resistance decreases significantly by increasing the distance between the loudspeakers.

A criterion for an energy vortex in a sound field

Measurements with intensity meters have shown that energy vortices exist in certain sound fields. In these vortices, sound energy flows around closed paths, in the steady state. Vortices occur in some sound fields (e.g., that of a point source near a reflecting edge), but not in others (e.g., that of a plane rigid piston in a plane rigid baffle). It is shown that in a two-dimensional or axisymmetric sound field, a necessary and sufficient condition for a vortex to exist is the presence of an isolated maximum or minimum in the stream function. Two examples are given for a vortex in (a) a duct of square cross section, and (b) the field of two monopole sources, one of which just extinguishes the other. Some relations for the interaction between two monopole sources are also given.

Equal-energy streamlines

Energy streamlines show the direction of energy flow in a sound field: The intensity vector at any point is tangential to the streamline passing through that point. In earlier work, a procedure for computing energy streamlines was described [J. Acoust. Soc. Am. 78, 758–762 (1985)], but it did not give equally spaced streamlines. The latter have certain advantages, and a method for computing them is presented here. It is shown that in sound fields which vary in only two space dimensions, a scalar stream function exists, the contours of which are the energy streamlines. The stream function is obtained from the intensity function (or values) by an integration procedure. Examples of equally spaced streamlines are given for the point-driven, fluid-loaded plate, and for the baffled rigid piston.

Diffraction correction for a radiation force measurement on an infinite plane target

A discussion is given of a rigorous diffraction correction for acoustic dosimetry by a radiation force measurement on an infinite plane target. As an example, analytical results are presented for circular radiators of different velocity distributions and diameter-to-wavelength ratios, including baffled rigid piston, simply supported piston, clamped piston, and Gaussian radiators.