Axisymmetric Cavity Research Articles

High-Speed Jet Formation after Solid Object Impact

A circular disc hitting a water surface creates an impact crater which after collapse leads to a vigorous jet. Upon impact an axisymmetric air cavity forms and eventually pinches off in a single point halfway down the cavity. Two fast sharp-pointed jets are observed shooting up- and downwards from the closure location, which by then has turned into a stagnation point surrounded by a locally hyperbolic flow pattern. This flow, however, is not the mechanism feeding the jets. Using high-speed imaging and numerical simulations we show that jetting is fed by the local flow around the base of the jet, which is forced by the colliding cavity walls. We show how the well-known theory of a collapsing void (using a line of sinks on the symmetry axis) can be continued beyond pinch-off to obtain a new and quantitative model for jet formation which agrees well with numerical and experimental data.

Laser-induced multi-point ignition with single-shot laser using conical cavities and prechamber with jet holes

Laser-induced multi-point ignition techniques with a single-shot unfocused laser have been proposed and experimentally tested by utilizing conical cavities and a prechamber for methane/air mixtures. Flame propagation in a constant-volume engine-like combustion chamber was visualized with high speed shadowgraphy and the pressure history was measured. A conical cavity with an opening near the apex installed in the prechamber and a closed conical cavity in the main chamber could induce two-point laser-induced cavity ignition by the focusing effect along the centerline of the cavity by the reflection of the irradiating laser beam on the axisymmetric cavity surface, leading to a thermal breakdown. An additional ignition could be achieved relatively simultaneously by the rapid ejection of hot burnt gas through the cavity opening to the main chamber. The installation of extra two jet holes provided additional ignitions by the ejections of hot burnt gases into the main chamber, thereby maximum of five ignition sources can be utilized simultaneously in the experiment. The pressure measurements showed that these ignition techniques demonstrated rapid combustion behavior and higher maximum pressure rise, resulting in a significant reduction in the total combustion time comparable to those in practical engines.

An artificial compressibility method for buoyancy‐driven flow in heterogeneous saturated packed beds

PurposeThe purpose of this paper is to focus on modeling buoyancy driven viscous flow and heat transfer through saturated packed pebble‐beds via a set of homogeneous volume‐averaged conservation equations in which local thermal disequilibrium is accounted for.Design/methodology/approachThe local thermal disequilibrium accounted for refers to the solid and liquid phases differing in temperature in a volume‐averaged sense, which is modeled by describing each phase with its own governing equation. The partial differential equations are discretized and solved via a vertex‐centered edge‐based dual‐mesh finite volume algorithm. A compact stencil is used for viscous terms, as this offers improved accuracy compared to the standard finite volume formulation. A locally preconditioned artificial compressibility solution strategy is employed to deal with pressure incompressibility, whilst stabilisation is achieved via a scalar‐valued artificial dissipation scheme.FindingsThe developed technology is demonstrated via the solution of natural convective flow inside a heated porous axisymmetric cavity. Predicted results were in general within 10 per cent of experimental measurements.Originality/valueThis is the first instance in which both artificial compressibility and artificial dissipation is employed to model flow through saturated porous materials.

Porous materials with two populations of voids under internal pressure: I. Instantaneous constitutive relations

This study is devoted to the mechanical behavior of uranium dioxide (UO 2) which is a porous material with two populations of voids of very different size subjected to internal pressure. The smallest voids are intragranular and spherical in shape whereas the largest pores located at the grain boundary are ellipsoidal and randomly oriented. In this first part of the study, attention is focused on the effective properties of these materials with fixed microstructure. In a first step, the poro-elastic properties of these doubly voided materials are studied. Then two rigorous upper bounds are derived for the effective poro-plastic constitutive relations of these materials. The first bound, obtained by generalizing the approach of Gologanu et al. (Gologanu, M., Leblond, J., Devaux, J., 1994. Approximate models for ductile metals containing non-spherical voids-case of axisymmetric oblate ellipsoidal cavities. ASME J. Eng. Mater. Technol. 116, 290–297) to compressible materials, is accurate at high stress-triaxiality. The second one, which derives from the variational method of Ponte Castañeda (Ponte Castañeda, P., 1991. The effective mechanical properties of non-linear isotropic composites. J. Mech. Phys. Solids 39, 45–71), is accurate when the stress triaxiality is low. A N-phase model, inspired by Bilger et al. (Bilger, N., Auslender, F., Bornert, M., Masson, R., 2002. New bounds and estimates for porous media with rigid perfectly plastic matrix. C.R. Mécanique 330, 127–132), is proposed which matches the best of the two bounds at low and high triaxiality. The effect of internal pressures is discussed. In particular it is shown that when the two internal pressures coincide, the effective flow surface of the saturated biporous material is obtained from that of the drained material by a shift along the hydrostatic axis. However, when the two pressures are different, the modifications brought to the effective flow surface in the drained case involve not only a shift along the hydrostatic axis but also a change in shape and size of the surface.

Permanent rotations of a body with a viscous filler suspended on a rod

Problems of the existence, stability, and branching of the permanent rotations of a heavy, dynamically symmetrical rigid body suspended on a rod and which has an axisymmetric ellipsoidal cavity filled with a fluid are discussed. The phenomenological model of the friction of the fluid against the cavity wall proposed by Samsonov is used. All the trivial permanent rotations of the system and the non-trivial rotations that branch off from the trivial ones are found. Their stability and branching are investigated using a modified Routh's theory. The results obtained are presented in the form of an atlas of bifurcation diagrams.

Deformation boundaries of an axisymmetric cavity by gas jets

A method is proposed for calculating small deformations of the boundaries of an axisymmetric cavity with impinging gas jets. No constraints are imposed on the configuration and characteristics of the system of nozzles generating the jets. Numerical results are compared with data obtained by available semi-empirical methods and with experimental data.

Effect of Cavity Width on the Unsteady Pressure in a Low-Mach-Number Cavity

T HE flow over a cavity (Fig. 1) has drawn the attention of many researchers (e.g., see the review articles by Rockwell and Naudascher [1] and Colonius [2]) because of its relevance to a range of engineering applications. These include the flow past windows and sunroofs in automobiles, airplane wheel wells, and dump combustors. The flow in these circumstances is characterized by selfsustained, high-pressure fluctuations, which can produce vibration and fatigue of the underlying structure, a high level of noise, and drastic increase in the drag force on the body containing the cavity. Hence, understanding and controlling the unsteadiness associated with cavity flows are important. Rossiter [3] identified the basic mechanism leading to strong, selfsustained oscillations in cavities. More specifically, he proposed that small disturbances in the shear layer separating at the upstream edge of the cavity are amplified, forming periodic vortex structures that travel downstream and interact with the aft edge of the cavity, generating strong pressurefluctuations. Thesefluctuations propagate (“feedback”) acoustically to the separation edge and reexcite the shear layer, hence, sustaining the cavity oscillations. A notable deviation from the Rossiter mechanism is the case where the vortex structures do not form upstream of the cavity’s aft edge. In this situation, self-sustained oscillations could still exist, but they are driven by convective waves, which cause large lateral motion (or “flapping”) of the shear layer near the downstream lip of the cavity (e.g., Sarohia [4] and Chatellier et al. [5]). Another important aspect of self-sustained oscillations of a cavity is the nature of the feedback. As M ! 0, the disturbance-edge interaction is inefficient in producing acoustic disturbances and the feedback is driven by the conservation of the fluid mass within the cavity (e.g., see Martin et al. [6] and Rockwell [7]). Although there is a large body of literature on cavity flows, very few studies have focused on three-dimensional aspects of the flow. Cell structures along the span of the cavity were found in the experiments of Maull and East [8]. Rockwell and Knisely [9] found that secondary, spanwise-periodic, streamwise vortices formed and distorted the primary spanwise vortex structures. More recently, three-dimensional instability analysis of a two-dimensional cavity flowwas carried out by Bres and Colonius [10]. It was found that the most amplified three-dimensional mode had a typical frequency that was an order of magnitude smaller than the frequency of the selfsustained cavity oscillations. This modewas linked to the centrifugal instability of the primary recirculation flow inside the cavity. The objective of this study is to examine the influence of the cavity width on the behavior of the unsteady pressure acting on the cavity floor and how this behavior depends on Reynolds number. A unique aspect of the present investigation is that an axisymmetric cavity geometry is employed to establish a “reference” condition that is free of any end-wall influences. The behavior of this cavity flow can then be compared against that of finite-width cavities byfilling portions of the axisymmetric cavity (see the next section for further details). It is significant to contrast the present work to the study ofMaull and East [8], who employed a rectangular cavity geometry that had to be terminated with end walls (even for the widest cavity). In addition, Maull and East did not report any quantitative measurements of the cavity unsteadiness. As will be seen, the present findings show that, asM ! 0, the accepted criteria, based on cavity depth and length as well as boundary layer thickness, for the occurrence of self-sustained oscillation are not sufficient to guarantee the establishment of the oscillation. The cavity width must also be accounted for; this offers a possible explanation for the discrepancy between recent (Grace et al. [11] and Ashcroft and Zhang [12]) and earlier studies at a low Mach number.

Experimental research on axisymmetric folded-combined cavity CO 2 laser

Rationality and feasibility of axisymmetric folded-combined cavity CO 2 laser which is reported in this paper have been proved by principle experiments. The laser lays a foundation to manufacture higher power CO 2 lasers whose output power can easily reach 1 kW. Faculas at different positions in free space and facula of nine beams which pass through the beam focusing optics have been obtained. Analyses of the experimental results are made. These analyses lay a foundation for beam transformation, transmission and shaping.

Radiative Properties of Blackbody Calibration Sources:Recent Advances in Computer Modeling

The radiative characteristics (spectral effective emissivity, spectral radiance, and radiance temperature) of blackbody calibration sources widely used in radiation thermometry are an important subject for advanced computer modeling by the Monte Carlo method. An algorithm and code for stochastic modeling of the radiant heat transfer inside cavities has been developed on the basis of the reciprocity principle and backward ray tracing. The importance sampling technique has been applied to generate the reflected rays according to the surface reflection model that can be a linear combination of the following primary models: Lambertian, Specular, and TETRA (a microfacet model of random tetrahedral pits that mimics reflections from a rough surface). A wide range of axisymmetrical cavities, cylindrical cavities with an inclined flat bottom, and a rectilinear grooved radiator of polygonal profile have been implemented. Various conditions of observation can be modeled to compute appropriate radiation characteristics. A number of different temperature distributions can be assigned to the same node set on the cavity surface, so several related tasks can be modeled in a single run. The results obtained for the radiative properties of isothermal and non-isothermal non-diffuse blackbodies used for the calibration of infrared radiation thermometers are presented and discussed.

An Experimental Study of Water-Assisted Injection Molding of Plastic Tubes with Dimensional Transitions

This report was made to experimentally study water assisted injection molding of plastic tubes with dimensional transitions. Experiments were carried out on an 80-ton injection-molding machine equipped with a lab scale water injection system, which included a water pump, a pressure accumulator, a water injection pin, a water tank equipped with a temperature regulator, and a control circuit. The materials used for the experiments included an amorphous polystyrene and a semi-crystalline polypropylene. Two types of water injection pins, the orifice and the porous type, combined with two ``float-shape'' axisymmetric cavities were used to mold the plastic parts. After molding, the hollowed core ratios of molded parts were measured. Various processing variables were studied in terms of their influence on the residual wall thickness and hollowed core ratio of water assisted injection molded parts: melt temperature, mold temperature, water temperature, water pressure, water injection delay time and water hold time, and melt short shot size. The core-out geometries in water-assisted injection molded parts were also compared to those in gas-assisted injection molded products. It was found that the porous type water pin molded plastic tubes had a more uniform thickness distribution than the orifice type water pin and the ring type gas pin. Additionally, the experimental result suggests that the water injection delay time and short shot size were the principal parameters affecting the core out behavior of molded d-2d-d tubes, while the core-out geometries of the d-4d-d tubes were mainly influenced by the melt and mold temperatures, water pressure and water injection delay time, and melt short shot size.

One-channel Ka-band pulse compressor

A compact rf pulse compressor, fed by a phase-modulated pulse, is described for producing high-power flattop pulses at Ka-band. The compressor consists of a single axisymmetrical cavity operating in a combination of ${\mathrm{TE}}_{0n}$ modes ($n=1$, 2, 3), that have zero electric fields at the walls. This feature enhances the breakdown strength of the system and makes it possible to increase the output power, as compared with a traditional SLED-II pulse compressor. Advantages include use of one channel instead of two, and no requirement for a 3-dB hybrid coupler. This 34 GHz one-channel pulse compressor (OC SLED-II) is designed to multiply peak power produced by the Yale/Omega-P Ka-band magnicon amplifier (30--40 MW, $0.5--1\text{ }\text{ }\ensuremath{\mu}\mathrm{s}$) by $(3--4)\ensuremath{\mathbin:}1$ and to compress in time by $(5--6)\ensuremath{\mathbin:}1$. The efficiency of the proposed compressor is similar to that of SLED-II. Results of low-power tests carried out on a 30 GHz prototype of the compressor are discussed.

Theory of the Collapsing Axisymmetric Cavity

We investigate the collapse of an axisymmetric cavity or bubble inside a fluid of small viscosity, like water. Any effects of the gas inside the cavity as well as of the fluid viscosity are neglected. Using a slender-body description, we compute the local scaling exponent alpha=dlnh_{0}/dlnt' of the minimum radius h_{0} of the cavity, where t' is the time from collapse. The exponent alpha very slowly approaches a universal value according to alpha=1/2+1/[4 square root [-ln(t')]]. Thus, as observed in a number of recent experiments, the scaling can easily be interpreted as evidence of a single nontrivial scaling exponent. Our predictions are confirmed by numerical simulations.

On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices

We investigate the Jacobi-Davidson algorithm for solving the time-harmonic Maxwell equation in axisymmetric vertical cavity surface emitting lasers (VCSELs). We compare various strategies in the extraction and extension phase of the algorithm and discuss their properties with complex-symmetric eigenvalue problems obtained from PML encoated resonator cavities.

The effect of cavity geometry on the nucleation of bubbles from cavities

The heterogeneous nucleation of gas bubbles from cavities in a surface in contact with a liquid is a widely recognized phenomenon. This process has previously been theoretically analyzed extensively for a conical crevice, although in practice a wide range of cavity geometries might be expected. The method of analysis originally presented by Atchley and Prosperetti [J. Acoust. Soc. Am. 86, 1065-1084 (1989)] for the unstable growth of a gas-liquid interface in a conical crevice is here extended to any axisymmetric cavity geometry and four such different geometries are analyzed. Although the method presented neglects gas transfer, and therefore is most directly suitable for acoustic cavitations, this method is still valuable in comparing the nucleation behavior of different cavity types. It is found that once the interface has emerged outside the cavity, its behavior is determined by the size of the cavity's opening. Given that the behavior of the interface once it is outside the cavity will also be determined by the local flow conditions, the threshold for unstable growth of the interface inside the cavity leading to its emergence is the important value and will determine differences between cavity geometries in practice, as shown in the examples presented.

On the two dimension applications of high-order vector finite elements to the study of electromagnetic resonance

A set of hybrid vector–scalar finite elements for curved-triangle meshes is developed. These elements are applied to the study of electromagnetic resonance problems in which the variation in the field components along one coordinate is known in advance. The field component along this coordinate is modelled with polynomials of degree q. The other two field components are modelled with two dimension vector edge elements containing all irrotational functions up to polynomial degree m. Spurious modes are avoided only when q=m+1. The performance of these elements to order 4 is explored by applying them to some waveguides and axisymmetric cavities containing sharp edges, curved boundaries and/or uniaxially anisotropic materials.

軸対称キャビティを有するノーズコーンの空力特性

In this paper, a concept of a new variable-geometry aerodynamics device, which is designated “Multiple-Row-Disk (MRD) device,” is introduced. The MRD device divides large separation region around the shaft of an aerospike into several small cavity flows with multiple disks arranged on the shaft. Experimental studies on aerodynamic characteristics of conical nose with axisymmetric cavities were conducted in order to evaluate a feasibility and a fundamental characteristics of the MRD device. It was found that the MRD device could improve not only drag characteristics compared to the conventional aerospikes, but also static longitudinal stability characteristics compared to the conical nose.

1511 軸対称キャビティで発生する共鳴音と速度変動との相関(J11-2 流れと音の相関計測,J11 流体関連の騒音と振動)

1511 軸対称キャビティで発生する共鳴音と速度変動との相関(J11-2 流れと音の相関計測,J11 流体関連の騒音と振動)

Direct numerical simulation of strong compression of the axisymmetric gas cavity in a liquid

A technique for computing strong compression of an axisymmetric gas bubble in a liquid by direct numerical simulation based on the equations of fluid dynamics is presented. This technique uses a scheme of the second-order accuracy in space and time for smooth solutions. Some results of numerical investigation of efficiency of this technique are given. It is established that this technique is much more effective than the classical first order accurate Godunov scheme widely known in the literature.

Stability of a rotating spacecraft partially filled with liquid: The case of several cavities

This paper is the second part of work [1] and contains generalizations of the results of studying the stability of a rotating spacecraft with a cavity partially filled with liquid for the case of spacecraft with several cavities. These cavities can be embodied, first of all, by tanks containing liquid fuel components filling the tanks to a small depth. A particular example of spacecraft with two fuel tanks is considered. It is shown that the results obtained in [1], which relate to a rotating object with a single axisymmetric cavity of arbitrary configuration partially filled (to a small depth) by low-viscosity liquid, admit generalization at rather natural limitations on an object with several cavities [3]. When referring to formulas from [1], the latter are marked by superscript.

Modeling of ductile fracture: Application of the mechanism-based concepts

This paper summarizes our recent studies on modeling ductile fracture in structural materials using the mechanism-based concepts. We describe two numerical approaches to model the material failure process by void growth and coalescence. In the first approach, voids are considered explicitly and modeled using refined finite elements. In order to predict crack initiation and propagation, a void coalescence criterion is established by conducting a series of systematic finite element analyses of the void-containing, representative material volume (RMV) subjected to different macroscopic stress states and expressed as a function of the stress triaxiality ratio and the Lode angle. The discrete void approach provides a straightforward way for studying the effects of microstructure on fracture toughness. In the second approach, the void-containing material is considered as a homogenized continuum governed by porous plasticity models. This makes it possible to simulate large amount of crack extension because only one element is needed for a representative material volume. As an example, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a modified Gologanu–Leblond–Devaux model [Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Tech. 116, 290–297; Gologanu, M., Leblond, J.B., Perrin, G., Devaux, J., 1995. Recent extensions of Gurson’s model for porous ductile metals. In: Suquet, P. (Ed.) Continuum Micromechanics. Springer-Verlag, pp. 61–130] is used to describe the evolution of void shape and void volume fraction and the associated material softening, and the material failure criterion is calibrated using experimental data. The calibrated computational model successfully predicts crack extension in various fracture specimens, including the compact tension specimen, middle crack tension specimens, multi-site damage specimens and the pressurized cylindrical shell specimen.