Axisymmetric Cavity Research Articles

Про стійкість обертання вільної системи двох пружно зв’язаних гіроскопів Лагранжа, один з яких має ідеальну рідину

On the basis of the known equations of motion of the system of coupled gyrostats by P. V. Kharlamov and the state function by S. L. Sobolev, the equations of rotation of a free system of two elastically coupled Lagrange gyroscopes were derived, one of which has an arbitrary axisymmetric cavity completely filled with an ideal incompressible fluid. The rigid bodies are connected by an elastic restoring spherical hinge. A transcendental characteristic equation of the perturbed uniform rotation of the mechanical system under consideration is derived. Taking into account the fundamental tone of the fluid oscillation, a characteristic equation of the fifth order is obtained. On the basis of the Liénard – Chipart criterion written in the inor form, the necessary conditions for the stability of the uniform rotation of the Lagrange gyroscopes and the fluid are written out as a system of four inequalities. With respect to the elasticity coefficient, these inequalities have degrees 1, 3, 6 and 8, respectively. Analytical studies of the leading coefficients of these stability conditions are carried out. It is shown that when the center of mass of the first solid body with liquid or the second does not coincide with the common point of these bodies, then at sufficiently large values of the elasticity coefficient the necessary stability conditions will always be satisfied. In the absence of elasticity in the hinge, the characteristic equation has a double zero root and in this case the stability conditions require additional studies. The obtained stability conditions are exact for an ellipsoidal cavity and approximate for other axisymmetric cavities. To clarify the obtained glass conditions for these voids, it is necessary to take into account additional tones of oscillation of an ideal liquid.

The resonant behavior of airborne standing-wave acoustic levitators based on arrays of ultrasonic transducers

Recently airborne standing-wave acoustic levitation has seen great advances, and its applicability has been broadened due to the development of cavities constructed with arrays of compact ultrasonic sources. Yet, the numerical methods employed to study and predict the pressure distributions inside these cavities do not consider the effect of multiple reflections on the boundaries, hiding their resonant effects. This work presents an analytical, numerical, and experimental study of the effect of multiple reflections inside ultrasonic cavities based on arrays of transducers exhibiting their influence on the pressure amplitudes of focused standing waves. Our numerical results come from a modified version of the Matrix Method to numerically compute the multiple wave reflections of cavities constructed by two opposite arrays of multiple compact sources as boundaries. The correlation between numerical and experimental results reveals that intra-cavity reflections are relevant in focused axisymmetric cavities based on two arrays of multiple ultrasonic sources having a considerable impact on the amplitude of the standing waves and consequently, on the acoustic levitation performance. Thus, intra-cavity reflections must be considered for optimal cavity designs.

Collapse of an axisymmetric cavity during slow movements of a cylinder in a liquid after a separation impact

Collapse of an axisymmetric cavity during slow movements of a cylinder in a liquid after a separation impact

Investigation of ignition and flame propagation in an axisymmetric supersonic combustor with laser-induced plasma

The ignition and flame propagation in an axisymmetric supersonic combustor were investigated. The laser-induced plasma was employed to ignite the supersonic inflow with a speed of Mach 2.5 and a total temperature of 1486 K. A direct-connect axisymmetric model scramjet with a fully transparent glass combustor was built, which enabled the circumferential and axial flame propagation in the cavity-based axisymmetric supersonic combustor to be visualized by the high-speed photography from the endoscopic and external views, respectively. An initial flame kernel is produced by the laser-induced plasma and propagates to the cavity leading edge along the axial direction. The establishment of the cavity shear-layer flame facilitates circumferential flame propagation. The circumferential flame propagation is coupled with the axial propagation, eventually generating a loop-shaped flame with a central-hole. Acceleration of the flame propagation can be observed, especially when the global equivalence ratio is increased. A plausible explanation for the flame propagation in the axisymmetric supersonic combustor was found using URANS numerical simulation. The axisymmetric cavity generates a low-speed loop-shaped recirculation region and thickened cavity shear-layer with an appropriate local equivalence ratio, resulting in the simultaneous axial and circumferential flame propagation. The increased temperature in the cavity and the thickened cavity shear-layer during the flame propagation produce a more intense heat release and mass transfer, leading to faster flame propagation.

Self-sustained azimuthal aeroacoustic modes. Part 1. Symmetry breaking of the mean flow by spinning waves

In this paper, we study the aeroacoustic instability which occurs in a deep axisymmetric cavity in a turbulent pipe flow. This phenomenon is the axisymmetric counterpart of the classical whistling of a rectangular deep cavity subject to a grazing flow. The whistling of such axisymmetric cavity originates from the interaction of the coherent fluctuations of the vorticity at the cavity's opening with one of its trapped azimuthal or radial acoustic modes. We focus here on the situation involving the first pure azimuthal mode, which is trapped in the cavity. As a consequence of the rotational symmetry of the configuration, azimuthal modes are actually pairs of degenerate eigenmodes, or almost degenerate in the presence of small asymmetries. Therefore, the aeroacoustic instabilities exhibit more complex mechanisms than in the case of a rectangular deep cavity. In particular, we show that self-sustained spinning modes induce a symmetry breaking of the mean flow and we will elucidate the details of this phenomenon. To that end, simultaneous acoustic and time-resolved stereoscopic particle image velocimetry (PIV) measurements are performed. They reveal that when large-amplitude aeroacoustic waves spin around the cavity, a quasi-steady mean flow starts whirling slowly in the opposite direction to the wave propagation. A linear perturbation analysis around an axisymmetric mean flow confirms the experimental observations: although the incoming pipe flow is not swirling, the hydrodynamic component of the aeroacoustic wave induces such whirling motion of the mean flow because of the forcing from the steady part of the coherent Reynolds stress tensor.

Self-sustained azimuthal aeroacoustic modes. Part 2. Effect of a swirling mean flow on the modal dynamics

The whistling induced by a low-Mach turbulent flow through a deep axisymmetric cavity in a duct is investigated theoretically and experimentally. The experiments include acoustic measurements and stereoscopic particle image velocimetry (PIV). The paper focuses on the effect of a mean swirl on the dynamics of the azimuthal aeroacoustic modes. The mean swirl in the cavity has two origins: one component is imposed by a controlled tangential air injection upstream of the cavity, and the other component spontaneously arises under the action of the self-sustained azimuthal aeroacoustic mode, as explained in the companion paper, Part 1 (Faure-Beaulieu, Xiong, Pedergnana & Noiray, J. Fluid Mech., vol. 971, 2023, A21). Experiments show that the dynamics of the aeroacoustic wave is influenced by the imposed swirl. In particular, the spinning wave propagating against the swirl is promoted. To explain this, a linear perturbation analysis is performed around an incompressible mean swirling flow obtained from RANS simulations. It reveals that the dominant shear layer modes of azimuthal order 1 and −1 involved in the whistling phenomenon are helical modes winding respectively with and against the swirl, and spinning respectively in counterswirl and co-swirl directions. The counterswirl hydrodynamic mode is the least damped of the two, which is in agreement with the experimental observations. Finally, a low-order model based on the wave equation is derived. With only a few parameters, it fully reproduces the experimental observations for a wide range of imposed swirl intensity in the duct flow, and it allows us to disentangle the mechanisms responsible for this complex aeroacoustic instability.

Axisymmetric slender magnetic cavities

The pressure at the boundary of a slender body of revolution immersed in a subsonic or supersonic flow may be found by classical asymptotic analysis. The inverse problem, to find the shape of the cavity knowing the pressure, is a physically relevant question as applied to the study of magnetic cavities. The equation determining this shape turns out to be a nonlinear one involving a convolution term. While this equation is extremely difficult to solve, estimates may be found that constrain the functional form of the inner magnetic field in order for the cavity to exist. Also the study of the Fourier transform of the convolution term yields some light on the behavior of the solution; for the supersonic case an approximation may be found by solving a sequence of ordinary differential equations.

Plasmonic Cavity Formation by Circular and Spiral Corrugations

Metal surfaces with sub-wavelength structures form a plasmon polariton-like surface mode, i.e., spoof-plasmon. The spoof-plasmon on a corrugated disk propagates radially and is reflected at the edge, resulting in formation of plasmonic cavity. With a concentric circular corrugation, the excited spoof-plasmons form an axisymmetric plasmonic cavity. With a spiral corrugation, the spoof-plasmons have non-zero orbital angular momenta and form a non-axisymmetric plasmonic cavity. Spoof-plasmons consisting of the plasmonic cavity transfer their angular momenta to radiation waves via the corrugated hollow waveguide by conserving their topological charges.

Experiments on the aeroacoustic whistling of a cylindrical cavity

An air flow going through an axisymmetric cavity can interact with the acoustic modes of this cavity and produce loud self-sustained acoustic oscillations. Acoustic measurements reveal that the nature of the acoustic mode undergoes complex dynamics, alternating between phases where we observe a spinning wave with periodic inversions of its rotation direction, and phases where a high-amplitude mode is constantly spinning in the same direction. Stereoscopic particle image velocimetry gives the 3 velocity components in a 2D plane, allowing to identify the main hydrodynamic structures involved in the instability and the interactions of these structures with the mean flow and the acoustic oscillations.

Акустика и гидродинамика импакта капли: два режима излучения звуковых пакетов

The paper studies acoustic signals in two modes of merging with water in a freely falling water droplet by the matched optical and acoustic methods. Only the primary sound packet was observed in the intrusive mode at the low drop speed, when the cavity was formed with a delay in the colored wake of the inflowing liquid. Experiments demonstrated the drop speed influence on the primary signal parameters. At the high droplet speed, the cavity started to form from the moment of the initial contact. The flow pattern became more complicated, the droplet substance was distributed over the emerged cavity surface and the grown crown in the form of separate fibers forming the line and mesh structures. The falling section of the primary acoustic signal was formed by a group of pulses with the complex spectral composition. Further, one or more low-frequency sound packets were registered after the pause. Spectral portrait of the secondary packets was related to the shape of the detached gas cavity. Smooth axisymmetric cavity was radiating the monochromatic packet. The complex-shaped cavity was transforming into a gas bubble and emitting the multi-frequency signal. Duration and amplitude of the secondary sound signals were depending on the transformation rate of the separated gas cavity into a smooth spheroidal bubble. The acoustic signal parameters were changing nonmonotonically with increasing velocity of the merging drop

Analytical Description of an Axisymmetric Supercavitation Bubble in a Viscous Flow

One of the basic elements which characterizes flow regimes, is viscosity. This element has typically been neglected in research on supercavitational flows, describing and predicting supercavitation bubbles geometry and formation using non-viscous potential flows. Arguing that the viscosity effect is much smaller than the inertial effect at high flow speeds, the viscosity has been ignored and the only parameter for modeling the flow has been the cavitation number. However, for some situations and conditions, the viscosity was found to be significant and crucial for the bubble geometry and formation, especially at the supercavitation bubble detachment point, hence some investigations based on numerical calculations have taken viscosity into account. This paper presents an analytical model of an axisymmetric supercavitation bubble in a viscous flow according to Serebryakov annular model for calculation of axisymmetric cavity flows. Viscosity effect on the bubble geometry is suggested, and an analysis for validation and examination is presented as well. The results show the change of the bubble formation from past models due to the viscosity, and offer a more accurate description of the bubble geometry close to the detachment point. Moreover, the slenderness parameter is calculated and presented for supercavitation bubbles in a viscous flow together with its dependency on Reynolds number and the cavitation number. The analysis reveals that the slenderness parameter increases with increasing both the cavitation number and Reynolds number, where the latter has a substantial effect.

Supersonic flow investigation of a drag reducing conical spike on a hemispherically blunted nose body

Experiments and computations were made at a Mach number of 2.0 on a hemispherical blunt nose body with a conical spike of L/D ratio = 1.0. Attempts were made to alter the axisymmetric cavity formation between the spike tip head and the blunt base body. Qualitative measurements and quantitative details indicate the changes which support the drag reduction beyond the conventional sharp spike. Additional drops in drag values were observed by the techniques used in the present investigation. A linear trend of drag reduction is obtained with conical spikes which lead to the drag of a pure conical body.

Comparison of 2.5D finite element formulations with perfectly matched layers for solving open axisymmetric electromagnetic cavity problems

AbstractAxial symmetry in time‐harmonic electromagnetic wave problems can be exploited by considering a Fourier expansion along the angular direction, reducing fully three‐dimensional computations to two‐dimensional ones on an azimuthal cross section. While this transition leads to a significant decrease in computational effort, it introduces additional difficulties, which necessitate appropriate finite element (FE) formulations. By combining the latter with perfectly matched layers (PML), open problems can be considered. In this work, we compare and discuss the performance of different combinations of axisymmetric FE formulations and PMLs, using a dielectric sphere in open space as a test case. As an application example, a superconducting Fabry–Pérot photon trap is considered.

A general acoustic energy-spectral method for axisymmetric cavity with arbitrary curvature edges

An efficient acoustic energy-spectral method for axisymmetric cavity with arbitrary curvature edges is proposed in this study. The multi-segment strategy and multi-point mapping technique are used to formulate the acoustic model, which can overcome the geometric difficulties of using orthogonal polynomials to construct sound pressure functions in irregular physics fields. In order to ensure the conditions of acoustic compatibility between sub-cavities and improve the accuracy of the solution, an acoustic penalty parameter is firstly introduced. The mixed series, consisting of orthogonal polynomials and Fourier series for circumferential variables, is applied to expand the sound pressure variables. The effects of some key parameters, including mapping node, penalty parameter, truncated terms as well as number of segments, on the convergence of the developed formulation are elucidated in detail. After that, two segmented acoustic cavities with variable curvature edges is investigated, in which the consistent FEM reference solutions are also involved. All these investigations exhibit the excellent accuracy and potential of the present formulation in analyzing the acoustic mode and response of axisymmetric cavity with arbitrary curvature edges. And the presented numerical results from the developed method can also serve as a reference for further acoustic study of axisymmetric cavity with complex geometry.

Characteristics of Oscillation in Cavity of Helmholtz Nozzle Generating Self-excited Pulsed Waterjet

Cavity flow oscillations in the axisymmetric cavity are critical to the operating efficiency of self-excited pulsed waterjets, which are widely employed in many practical applications. In this study, the behaviors of a turbulent flow in axisymmetric cavities causing cavity flow oscillations are investigated based on wall pressure characteristics. Experiments are performed using four Helmholtz nozzles with varying length-to-radius ratios at flow velocities of 20–80 m/s. Three orders of hydrodynamic modes in axisymmetric cavity are obtained through the spectral analysis of wall pressure. Based on the experimental results, the empirical coefficient of Rossiter’s formula is modified, and the values of the parameter phase lag and the ratio of convection velocity to free stream velocity are obtained as 0.061 and 0.511, respectively. In addition, the spectral peak with a relatively constant frequency shows that the flow-acoustic resonance is excited significantly. A modified model is introduced based on the fluidic networks to predict the lock-on frequency. The results obtained can provide a basis for the structural optimization of the nozzle to improve the performance of self-excited pulsed waterjets.

Effect of laser radiation on liquid evaporation from a bounded cavity

A physical and mathematical model is developed for the liquid evaporation from an axisymmetric cavity in a metal plate under the parametric action of laser radiation (LR). A hypothesis is proposed for the formation of a steam – liquid mixture (SLM) in a cavity with liquid during LR. As a result of the numerical solution of the developed physical and mathematical model, the dependences of the change in the mass and temperature of the SLM in the cavity during LR were established, as well as the energy costs for heating, evaporation of the liquid and the costs of heating the cavity wall with constant and pulsed LR were determined. A comparative analysis of the results of physical and mathematical modeling with the known results of experimental investigations showed a discrepancy in the mass of the evaporated liquid up to 3.33% and in the temperature up to 1.28%.

Axisymmetric free-surface flow simulation using the moving surface mesh particle method and application to drop formation

It is difficult to accurately simulate axisymmetric free-surface flows with surface tension and topological changes, such as drop formation through a nozzle. A promising numerical method that can achieve this goal is the moving surface mesh particle method. It incorporates a moving surface mesh to explicitly represent a free-surface boundary, which enables accurate free-surface tracking and surface tension calculation. In the present study, this method is extended to an axisymmetric coordinate system. In the axisymmetric simulation, particles moving in a Lagrangian fashion result in significantly non-uniform particle distributions, leading to numerical instabilities. To circumvent this issue, a new algorithm is developed for determining the particle movement in an ALE fashion by considering a two-dimensional continuity equation. Moreover, in order to deal with the topological change arising from breakup of liquid domain, a simple algorithm employing surface mesh splitting is developed. The proposed method is verified using fundamental test cases such as axisymmetric cavity flow, axisymmetric patch test, spherical droplet oscillation, and hanging droplet. Therein, precise agreements to reference solutions are confirmed. Furthermore, the proposed method is applied to the numerical simulation of dripping faucet. As a result, complex drop formation phenomena are successfully simulated with reasonable computational cost. The numerical results are also shown to agree well with the experimental measurement in the literature, from which the validity of the proposed method is demonstrated.

Temporal and spatial evolution of cavitating bubbles and coherent structures in a confined submerged jet shear layer

PurposeThe study aims to display the bubbles' evolution in the shear layer and their relationship with the pressure fluctuations. Furthermore, the coherent structures of the first six modes are extracted, in order to provide insight into their temporal and spatial evolution and determine the relationship between cavitating bubbles and coherent structures.Design/methodology/approachIn the present study, numerical simulations of submerged jet cavitating flow were carried out at a cavitation inception condition inside an axisymmetric cavity using the large eddy simulation (LES) turbulence model and the Schnerr–Sauer (S–S) cavitation model. Based on snapshots produced by the numerical simulation, dynamic mode decomposition (DMD) was performed to extract the three-dimensional coherent structures of the first six modes in the shear layer.FindingsThe cavitating bubbles in the shear layer are deformed to elongated ellipsoid shapes by shear forces. The significant pressure fluctuations are induced by the collapse of the biggest bubble in the group. The first mode illustrates the mean characteristics of the flow field. The flow in the peripheral region of the shear layer is mainly dominated by large-scale coherent structures revealed by the second and third modes, while different small-scale coherent structures are contained in the central region. The cavitating bubbles are associated with small size coherent structures as the sixth or higher modes.Practical implicationsThis work demonstrates the feasibility of LES for high Reynolds number shear layer flow. The dynamic mode decomposition method is a novel method to extract coherent structures and obtain their dynamic information that will help us to optimize and control the flow.Originality/value(1) This paper first displays the three-dimensional coherent structures and their characteristics in the shear layer of confined jet flow. (2) The relationship of bubbles shape and pressure fluctuations is illustrated. (3) The visualization of coherent structures benefits the understanding of the mixing process and cavitation inception in jet shear layers.

Нелинейные колебания поверхности раздела двух жидкостей при угловых колебаниях бака

The development of rocket and space technology in recent years has led to the widespread use of various cryogenic liquids. To increase the shelf life of cryo-products on board spacecraft or in tankers of future space filling stations, it is proposed to create a certain stock of cryo-product, which is simultaneously in a two-phase or three-phase state and forms layers of liquid. The paper considers the problem in a nonlinear formulation about the oscillations of the interface of a two-layer liquid in an arbitrary axisymmetric cavity of a solid body performing angular oscillations around a horizontal axis. For the considered class of cavities with an arbitrary bottom and a lid, the nonlinear problem is reduced to the sequential solution of linear boundary value problems. Nonlinear differential equations describing the oscillations of the interface between two liquids in the vicinity of the main resonance are obtained. In the case of a circular cylindrical cavity with flat bottoms, solutions of boundary value problems in the form of cylindrical functions were used to calculate linear and nonlinear hydrodynamic coefficients depending on the depth and density of the upper liquid.

Sound-Absorption Mechanism of Structures with Periodic Cavities

A simplified finite element method (FEM) simulation method has been established and validated for analyzing the sound absorption mechanism of structures with periodic axisymmetric cavities. Combined with genetic algorithm, the simplified FEM method is used to optimize the sound absorption coefficient of the structure containing periodic cylindrical cavities and variable cross section cavities. The result of variable section cavities is much better than the case of cylindrical cavities. The effect of cavity shape on sound absorption mechanism is discussed through energy dissipation, structure deformation and modal analysis of the absorption structures. It is found that the cavity structure resonances include bending vibration of the surface layer and radial motion of particles near the cavities. The radial motion also changes along the axial direction. Adding geometric design parameters of the cavity cross section are conducive to moving the radial mode to low frequency. The radial vibration has a great influence on absorption performance, which is more conducive to promoting the conversion of longitudinal waves into transverse waves with more energy dissipation. Finally, a better sound absorption performance is obtained by introducing the material parameter of Young's modulus into the optimization model, indicating that comprehensive consideration of geometry and material parameters for optimization is expected to obtain the desired sound absorption structure in engineering practice.