Axisymmetric Cavity Research Articles

Numerical analysis of polymer injection moulding process using finite element method with marker particles

AbstractA numerical method for analysing an axisymmetric injection moulding process is presented. A consistent approximation to pressure is applied for a penalty function formulation of Galerkin's finite element method. To analyse the moving free surface and visualize the transient flow pattern, marker particles are introduced. An axisymmetric abrupt cavity, which is filled with a generalized Newtonian fluid, is solved to verify the scheme. As a practical example problem, the transient flow through moulds of a memory disc is analysed.

Comparison of a Cavity Solar Receiver Numerical Model and Experimental Data

Results from a numerical model of axisymmetric solar cavity receivers are compared with experimental data for tests of a novel test bed receiver in the Sandia National Laboratories solar furnace. The computed energy transfer rates and temperatures are compared with the experimental data for different receiver geometries, aperture sizes, and operating conditions. In general, the agreement between the numerical model and the experimental data is better for the small-to-midsized apertures than for the large apertures. The analysis indicates that for the larger apertures, the convective heat losses are over predicted. It also suggests that these losses could be better characterized. Sensitivity analyses show that both the total solar energy input rate and the convective heat-loss coefficient significantly affect the receiver thermal performance and that the distribution of the input solar flux significantly affects the temperature distribution in the receiver.

Tone generation by aeroacoustic sources in pipes with flow

Sound production by axisymmetric ring cavities in internal flow has been investigated experimentally. These ring sources generate sound when the acoustic motion in the cavity is in resonance in one of many possible modes. Experimental results agree with predictions of a model eddy-driven oscillator. It is observed that the standing waves produced by reflections from regions upstream and downstream of the source are adjusted by the source such that the source is at a pressure antinode at the condition of maximum sound emission.

Conserved quantities for axisymmetric cavities near boundaries

In axisymmetric irrotational flows of a perfect fluid under gravity there are three basic conserved quantities; axial momentum, energy and a circulation based, radial moment of momentum. This paper adapts these conservation principles to describe cavity collapse adjacent to a rigid boundary in a semi-infinite perfect fluid. They afford a global model accounting for volume change, migration and jet formation; physically the most significant features of bubble collapse close to a rigid boundary.

Flow in the neighborhood of the cusp of an axisymmetric cavity

The steady-state axisymmetric potential flow of an ideal incompressible fluid is considered. The structure of the singularity at the point where the free stream surface leaves the axis of symmetry is investigated.

General formulation for the integrated effective emissivity of any axisymmetric diffuse blackbody cavity

A general method for the precise evaluation of the integrated effective emissivity of a diffuse frustrum-cone cavity is formulated. The mathematical expressions derived can be applied to calculate precisely the integrated emissivity of, or the irradiance of a detector from, any practical axisymmetric cavity with circular symmetry. Some typical values of integrated emissivity are presented for cylinders, cylindro-cones, double cones, and cylindro-inner-cones, and comparisons between such cavities are made.

Slender axisymmetric cavities in a supersonic flow

Slender axisymmetric cavities in a subsonic flow of compressible fluid were investigated in [1–4]. In [5] a finite-difference method was used to calculate the drag coefficient of a circular cone, near which the shape of the cavity was determined for subsonic, transonic, and supersonic water flows; however, in the supersonic case the entire shape of the cavity was not determined. Here, on the basis of slender body theory an integrodifferential equation is obtained for the profile of the cavity in a supersonic flow. The dependence of the cavity elongation on the cavitation number and the Mach number is determined.

Nonlinear wave motions of a liquid in a vibrating axisymmetric cavity

The problem of the nonlinear wave deformation of the free surface of a liquid due to the translational motions of the containing vessel is examined. Bogolyubov's averaging method is used to investigate the characteristics of the wave motions of the liquid in the resonance zones in the case of a cylindrical vessel. Relations are obtained characterizing the variation of the amplitude of the circular wave with the frequencies of the external perturbations in the steady-state wave process; the conditions of occurrence and stability of such processes are analyzed.

Measurement of sound emitted by flying projectiles with aeroacoustic sources

Training projectiles with axisymmetric ring cavities that produce intense tones in an airstream were shot in a straight-line trajectory. A ground-based microphone was used to obtain the angular distribution of sound intensity produced from the flying projectile. Data reduction required calculation of Doppler and attenuation factors. Also, the directional sensitivity of the ground-mounted microphone was measured and used in the data reduction. A rapid angular variation of sound intensity produced from the projectile was found that can be used to plot an intensity contour map on the ground. A full-scale field test confirmed the validity of the aeroacoustic concept of producing a relatively intense whistle from the projectile, and the usefulness of short-range flight tests that yield acoustic data free of uncertainties associated with diffraction, reflection, and refraction at jet boundaries in free-jet tests.

Rain simulation studies for high-intensity acoustic nose cavities

Unarmed plastic projectiles can be equipped with small axisymmetric cavities for the generation of intense tones that are useful in training maneuvers. Attention is presently given to the simulation of rainfall in an airstream and the effect of rain droplet impingement on the nose of projectiles, and especially to any penetration or accumulation of water at the base of the cavity that might increase the fundamental cavity frequency and/or reduce the intensity of sound production during rain conditions.

Yaw and spin effects on high‐intensity sound generation and on drag of whistling projectiles

Projectiles containing axisymmetric ring cavities constitute aeroacoustic sources. These produce high‐intensity tones that are used for coding in the simulation of area weapons effects (SAWE) system. Experimental data obtained in a free‐jet facility are presented describing the effects of yaw, spin, and geometric projectile parameters on sound pressure and drag. In general, the sound pressure decreases with increasing yaw angle whereas the drag increases. Spin tends to increase sound‐pressure levels because of a reduction in asymmetry of flow. Drag increases at zero yaw approximately as the 2.5 power of sound wavelength. Drag increase appears to be due to energy loss by sound radiation at low wavelengths and due to wake modification at large wavelengths.

Boundary element analysis of axisymmetric resonant cavities

Two numerical techniques are applied to boundary element analysis of axisymmetric modes of a cylindrical resonant cavity. One of the techniques is based on a novel expression for the fundamental solution of the axisymmetric Helmholtz equation with double exponential formulas. The other is an integral equation method in which the fundamental solution of the Laplace equation is used by considering the axisymmetric Helmholtz equation as the axisymmetric Laplace equation with an inhomogeneous term. Axisymmetric modes of a cyclindrical resonant cavity are analyzed by these techniques, and the resonant wave numbers are obtained with high accuracy. These results show that the axisymmetric resonant cavities can be analyzed by the boundary element method. >

Thin axisymmetric cavities in a subsonic compressible flow

The investigation of subsonic compressible flow past thin axisymmetric cavities carried out in [1–3] is continued by the method of asymptotic expansions. The dependence of the elongation of the cavity on the cavitation number and the Mach number is obtained.

High-intensity tone generation by aeroacoustic sources

An experimental investigation has been carried out on the production of high-intensity tones by axisymmetric ring cavities. Maximum sound production occurs during an acoustic resonance at Strouhal numbers, which depend only on the local flow velocity independent of cavity location. Values of sound pressure of about 115 dB at 1-m distance can be generated by axisymmetric ring cavities on projectiles moving at a relatively low flight speed equal to 70 m/s. Frequencies in the audible range up to several kilohertz can be generated aeroacoustically. A simple analytical model has been developed to explain the experimental observations.

Eigenfrequencies of axisymmetric cavities: Numerical calculations

The eigenfrequencies of axisymmetric, hard‐walled acoustic cavity resonators have been calculated by using an integral‐equation representation of the Helmholtz equation with Neumann boundary conditions. For axisymmetric shapes, the integral equation is one‐dimensional. Numerical results have been obtained for a perfect sphere, and for slightly deformed spheres, and for cylinders with an internal sphere on axis. The results for slightly deformed spheres are in close agreement with the predictions of boundary‐shape perturbation theory, from which they typically differ by less than 6 parts in 106. The results for cylinders with internal spheres are in excellent agreement with measurements [M. Barmatz et al., J. Acoust. Soc. Am. 73, 725–732 (1983)].

Blast wave effects on decoupling with axisymmetric cavities

Summary. An expiosion is considered in an initially air-filled, underground spherical cavity to which is connected a long, cylindrical tunnel. The cavity and tunnel size are, taken together, equivalent in volume to a fully decoupled spherical cavity (in accordance with the Latter criterion). Calculations indicate that, when the air is at standard conditions, the shock speed in the tunnel, D, is of the same order as the sound speed in the surrounding rock medium, cL. Moreover, the blast wave is approximately quasi-steady, and can be represented by a simple analytical function. This in turn permits a closed form solution for the far-field seismic amplitude spectrum. It is found that the low-pass filtering effectiveness of the tunnel is largely diminished unless D/cL s 1. With air-filled cavities, and depending on the source-receiver orientation, the spectral amplitude can actually exceed significantly the equivalent volume-sphere result. For practical purposes, this means that unless the cavity and tunnel are initially evacuated, say with a steam ejector system, the high-frequency decoupling capability will be no better, and possibly worse, than a conventional spherical cavity of the same total volume.

Modelling intergranular cavity growth with special reference to the mechanism of coupled diffusion and power-law creep

Intergranular cavity growth in creep is studied numerically on the basis of an unconstrained cavity growth model embracing all the important features of contemporary models except the possible assistance of grain boundary sliding. The model describes cavity growth over a very broad region of conditions, specifically those under which power-law creep becomes an important component of cavity growth and, at the same time, surface diffusion is much slower than grain boundary diffusion. A numerical method based on the finite difference technique is developed and applied. The results of modelling are presented, and emphasize axisymmetric cavity shape development during growth from a spherical-cap shape to a non-equilibrium or crack-like shape, i.e. axial cavity sections are shown, revealing cavity profiles in various stages of growth. Also, the corresponding profiles of the local normal stress field representing the field of chemical potential across the grain boundary facet are presented. Since the radial cavity growth rate ȧ as well as the jacking velocity ż changes markedly during growth, the time to fracture t f was accepted as an appropriate cavity growth characteristic. The time to fracture was computed using the simplest fracture criterion, i.e. that fracture occurs at the instant at which the cavity radius a becomes equal to the half-cavity spacing b. The relationship between time to fracture t f and the average normal stress σ av acting on the grain boundary facet are compared with those predicted by current cavity growth models. In general, the agreement is satisfactory; some differences between the present results and the predictions can probably be accounted for by the radial cavity growth rate changing markedly during cavity growth, associated with marked changes in cavity shape.

Two‐ and three‐dimensional steady quasi‐linear infiltration from buried and surface cavities using boundary element techniques

A general numerical method is presented for solving the problem of quasi‐linearized steady infiltration from general two‐dimensional and axisymmetric surface cavities and from a general cavity buried at an arbitrary depth in either a two‐ or three‐dimensional semi‐infinite porous medium. Numerical results are compared with known analytical results for the cases of a shallow circular pond and a circular cylindrical cavity and a spherical cavity buried in an infinite medium. Further results are presented graphically illustrating the effect of an upper surface on the flux from a circular cavity and also the effect on the size of the effective wetted region. Two‐dimensional surface cavities are also investigated, and the dependence of the flux on geometry, gravity, and capillarity is examined.

Propagation of high-frequency harmonic elastic waves arising in the surface perturbation of an axisymmetric cavity

Propagation of high-frequency harmonic elastic waves arising in the surface perturbation of an axisymmetric cavity

The effect of flow oscillations on cavity drag

An experimental investigation of flow over an axisymmetric cavity shows that self-sustained, periodic oscillations of the cavity shear layer are associated with low cavity drag. In this low-drag mode the flow regulates itself to fix the mean-shear-layer stagnation point at the downstream corner. Above a critical value of the cavity width-to-depth ratio there is an abrupt and large increase of drag due to the onset of the ‘wake mode’ of instability. It is also shown by measurement of the momentum balance how the drag of the cavity is related to the state of the shear layer, as defined by the mean momentum transport $\rho\overline{u}\overline{v}$ and the Reynolds stress $\rho\overline{u^{\prime}v^{\prime}}$, and how these are related to the amplifying oscillations in the shear layer. The cavity shear layer is found to be different, in several respects, from a free shear layer.