Threshold condition for spray formation by Faraday instability

2014 ◽  
Vol 759 ◽  
pp. 73-103 ◽  
Author(s):  
Yikai Li ◽  
Akira Umemura
Keyword(s):  
Surface Wave ◽  
Liquid Layer ◽  
Initial Conditions ◽  
Inertial Force ◽  
Wave Mode ◽  
Experimental Investigations ◽  
Threshold Condition ◽  
Liquid Density ◽  
Spray Formation ◽  
Faraday Instability

AbstractA vertically vibrating liquid layer produces liquid ligaments that disintegrate to form a spray with drops of a controllable size. Previous experimental investigations of ultrasonic atomisation have shown that when such a spray forms, there exists a predominant surface-wave mode from which drops are generated with a mean diameter that follows Lang’s equation. In this paper, we determined this predominant surface-wave mode physically and, by utilising the coupled level-set and volume-of-fluid method, we numerically studied the threshold condition for spray formation based on a cell model of the predominant surface wavelength that excludes the effects of the container walls. We defined a condition whereby the broken drop holds a zero area-averaged vertical velocity in the laboratory reference frame as the criterion for the formation of a spray. The results of our calculations indicated that the onset of a spray occurs in the subharmonic unstable region for a threshold dimensionless forcing strength ${\it\beta}_{c}=({\it\rho}_{l}{\it\Delta}_{0}^{3}{\it\Omega}^{2})/{\it\sigma}\sim O(1)$, where ${\it\rho}_{l}$ and ${\it\sigma}$ denote the liquid density and surface tension coefficient, respectively, ${\it\Delta}_{0}$ is the forcing displacement amplitude and ${\it\Omega}$ is the forcing angular frequency. Spray formation due to the Faraday instability can be considered as a process whereby the liquid layer absorbs energy from the inertial force, and releases it by producing drops that leave the surface of the liquid layer. We demonstrated that for a deep liquid layer, the threshold condition for the formation of a spray is determined only by the forcing strength, and is independent of the initial conditions of the liquid surface.

Surface wave mode interactions: effects of symmetry and degeneracy

1989 ◽  
Vol 199 ◽  
pp. 471-494 ◽  
Author(s):  
F. Simonelli ◽  
J. P. Gollub
Keyword(s):  
Surface Wave ◽  
Fixed Points ◽  
Initial Conditions ◽  
Fluid Layer ◽  
Basic Structure ◽  
Wave Mode ◽  
Space Structure ◽  
Mode Competition ◽  
Multiple Attractors ◽  
Rectangular Cell

Parametrically excited surface wave modes on a fluid layer driven by vertical forcing can interact with each other when more than one spatial mode is excited. We have investigated the dynamics of the interaction of two modes that are degenerate in a square layer, but non-degenerate in a rectangular one. Novel experimental techniques were developed for this purpose, including the real-time measurement of all relevant slowly varying mode amplitudes, investigation of the phase-space structure by means of transient studies starting from a variety of initial conditions, and automated determination of stability boundaries as a function of driving amplitude and frequency. These methods allowed both stable and unstable fixed points (sinks, sources, and saddles) to be determined, and the nature of the bifurcation sequences to be clearly established. In most of the dynamical regimes, multiple attractors and repellers (up to 16) were found, including both pure and mixed modes. We found that the symmetry of the fluid cell has dramatic effects on the dynamics. The fully degenerate case (square cell) yields no time-dependent patterns, and is qualitatively understood in terms of third-order amplitude equations whose basic structure follows from symmetry arguments. In a slightly rectangular cell, where the two modes are separated in frequency by a small amount (about 1%), mode competition produces both periodic and chaotic states organized around unstable pure and mixed-state fixed points.

scholarly journals Linking gas and particle ejection dynamics to boundary conditions in scaled shock-tube experiments

2021 ◽  
Vol 83 (8) ◽  
Author(s):  
Valeria Cigala ◽  
Ulrich Kueppers ◽  
Juan José Peña Fernández ◽  
Donald B. Dingwell
Keyword(s):  
Particle Size ◽  
Shock Tube ◽  
Initial Conditions ◽  
Volcanic Eruptions ◽  
Tube Length ◽  
Experimental Investigations ◽  
Clear Correlation ◽  
Angular Deviation ◽  
Dynamic Nature ◽  
Experimental Conditions

AbstractPredicting the onset, style and duration of explosive volcanic eruptions remains a great challenge. While the fundamental underlying processes are thought to be known, a clear correlation between eruptive features observable above Earth’s surface and conditions and properties in the immediate subsurface is far from complete. Furthermore, the highly dynamic nature and inaccessibility of explosive events means that progress in the field investigation of such events remains slow. Scaled experimental investigations represent an opportunity to study individual volcanic processes separately and, despite their highly dynamic nature, to quantify them systematically. Here, impulsively generated vertical gas-particle jets were generated using rapid decompression shock-tube experiments. The angular deviation from the vertical, defined as the “spreading angle”, has been quantified for gas and particles on both sides of the jets at different time steps using high-speed video analysis. The experimental variables investigated are 1) vent geometry, 2) tube length, 3) particle load, 4) particle size, and 5) temperature. Immediately prior to the first above-vent observations, gas expansion accommodates the initial gas overpressure. All experimental jets inevitably start with a particle-free gas phase (gas-only), which is typically clearly visible due to expansion-induced cooling and condensation. We record that the gas spreading angle is directly influenced by 1) vent geometry and 2) the duration of the initial gas-only phase. After some delay, whose length depends on the experimental conditions, the jet incorporates particles becoming a gas-particle jet. Below we quantify how our experimental conditions affect the temporal evolution of these two phases (gas-only and gas-particle) of each jet. As expected, the gas spreading angle is always at least as large as the particle spreading angle. The latter is positively correlated with particle load and negatively correlated with particle size. Such empirical experimentally derived relationships between the observable features of the gas-particle jets and known initial conditions can serve as input for the parameterisation of equivalent observations at active volcanoes, alleviating the circumstances where an a priori knowledge of magma textures and ascent rate, temperature and gas overpressure and/or the geometry of the shallow plumbing system is typically chronically lacking. The generation of experimental parameterisations raises the possibility that detailed field investigations on gas-particle jets at frequently erupting volcanoes might be used for elucidating subsurface parameters and their temporal variability, with all the implications that may have for better defining hazard assessment.

SURFACE-WAVE PROPAGATION OVER PLANE-LAYERED DIELECTRICS

1963 ◽  
Vol 41 (2) ◽  
pp. 405-413
Author(s):  
D. Morris
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Experimental Investigations ◽  
Total Field ◽  
Power Variation ◽  
Surface Wave Propagation ◽  
Dielectric System ◽  
Layered Dielectrics ◽  
Layered Dielectric ◽  
The Waves

A two-layer dielectric system, consisting of a thin polystyrene sheet on top of water, is examined as a possible guiding structure for surface waves. Experimental investigations, at a frequency of 9.35 Gc/sec, of the phase velocity of the waves close to the surface of the upper layer, and the power variation with height above it, are described. A slow wave was found to propagate near the surface and its phase velocity was found to agree with that predicted theoretically for a TM surface wave. Qualitative agreement between the experimental and theoretical power variation with height confirmed the existence of a surface-wave contribution to the total field above such a layered dielectric system.

scholarly journals Effect of Spheroidization Annealing on Pearlite Banding

2019 ◽  
Vol 949 ◽  
pp. 40-47 ◽  
Author(s):  
Sergey Guk ◽  
Eva Augenstein ◽  
Maksim Zapara ◽  
Rudolf Kawalla ◽  
Ulrich Prahl
Keyword(s):  
Empirical Model ◽  
Initial Conditions ◽  
The Other ◽  
Experimental Investigations ◽  
Initial State ◽  
Ferritic Matrix ◽  
Other Hand ◽  
Initial States ◽  
Hot Rolled

The present paper deals with the influence of the duration of isothermal spheroidization annealing on the evolution of pearlite bands in various initial states. In this study, two initial conditions of the steel 16MnCrS5 are considered: a) industrially hot-rolled pearlite structures in their ferritic matrix and b) a specifically adjusted microstructure in the lab condition. Based on the experimental investigations and quantitative microstructural analyses, an empirical model for the prediction of pearlite banding within a broad range of annealing durations could be derived. Both, experiment and model, agree that pronounced pearlite bands in the initial state almost disappear after 25 h of spheroidization annealing. On the other hand, a marginal degree of pearlite banding in the initial state increases slightly during annealing. This fact could be explained by inhomogeneous cementite formation inside and outside the primary segregation regions of manganese.

Bubble and conical forms of vortex breakdown in swirling jets

2019 ◽  
Vol 873 ◽  
pp. 322-357 ◽  
Author(s):  
Pradeep Moise ◽  
Joseph Mathew
Keyword(s):  
Vortex Breakdown ◽  
Initial Conditions ◽  
Azimuthal Velocity ◽  
Linear Instability ◽  
Subcritical State ◽  
Experimental Investigations ◽  
Global Mode ◽  
Swirling Jets ◽  
Conjugate State ◽  
Centreline Velocity

Experimental investigations of laminar swirling jets had revealed a new form of vortex breakdown, named conical vortex breakdown, in addition to the commonly observed bubble form. The present study explores these breakdown states that develop for the Maxworthy profile (a model of swirling jets) at inflow, from streamwise-invariant initial conditions, with direct numerical simulations. For a constant Reynolds number based on jet radius and a centreline velocity of 200, various flow states were observed as the inflow profile’s swirl parameter $S$ (scaled centreline radial derivative of azimuthal velocity) was varied up to 2. At low swirl ($S=1$) a helical mode of azimuthal wavenumber $m=-2$ (co-winding, counter-rotating mode) was observed. A ‘swelling’ appeared at $S=1.38$, and a steady bubble breakdown at $S=1.4$. On further increase to $S=1.5$, a helical, self-excited global mode ($m=+1$, counter-winding and co-rotating) was observed, originating in the bubble’s wake but with little effect on the bubble itself – a bubble vortex breakdown with a spiral tail. Local and global stability analyses revealed this to arise from a linear instability mechanism, distinct from that for the spiral breakdown which has been studied using Grabowski profile (a model of wing-tip vortices). At still higher swirl ($S=1.55$), a pulsating type of bubble breakdown occurred, followed by conical breakdown at 1.6. The latter consists of a large toroidal vortex confined by a radially expanding conical sheet, and a weaker vortex core downstream. For the highest swirls, the sheet was no longer conical, but curved away from the axis as a wide-open breakdown. The applicability of two classical inviscid theories for vortex breakdown – transition to a conjugate state, and the dominance of negative azimuthal vorticity – was assessed for the conical form. As required by the former, the flow transitioned from a supercritical to subcritical state in the vicinity of the stagnation point. The deviations from the predictions of the latter model were considerable.

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