We experimentally study the airflow in a collapsing cavity created by the impact of a circular disk on a water surface. We measure the air velocity in the collapsing neck in two ways: Directly, by means of employing particle image velocimetry of smoke injected into the cavity and indirectly, by determining the time rate of change of the volume of the cavity at pinch-off and deducing the air flow in the neck under the assumption that the air is incompressible. We compare our experiments to boundary integral simulations and show that close to the moment of pinch-off, compressibility of the air starts to play a crucial role in the behavior of the cavity. Finally, we measure how the air flow rate at pinch-off depends on the Froude number and explain the observed dependence using a theoretical model of the cavity collapse.
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 show that the minimum radius of the cavity scales like $h_0 \propto t'^α$, where $t'$ is the time from collapse. The exponent $α$ very slowly approaches a universal value according to $α=1/2 + 1/(4\sqrt{-\ln(t')})$. Thus, as observed in a number of recent experiments, the scaling can easily be interpreted as evidence of a single non-trivial scaling exponent. O…
New corrections to the equation of motion and total collapsing time of an empty spherical cavity immersed in an infinite incompressible medium are proposed on the assumption of a non-uniform density. The dimensionless number quantifying the corrections with respect to the standard Rayleigh results (coined the $Δ$-factor) is fully independent of other possible contributions like surface tension and viscous terms. The $Δ$-factor effect advocated here can be seen as a direct consequence of a mass-shell non-trivial solution to the continuity equation. The consistency of the corrections with respec…
We present a multiscale approach to simulate the impact of a solid object on a liquid surface: upon impact a thin liquid sheet is thrown upwards all around the rim of the impactor while in its wake a large surface cavity forms. Under the influence of hydrostatic pressure the cavity immediately starts to collapse and eventually closes in a single point from which a thin, needle-like jet is ejected. Existing numerical treatments of liquid impact either consider the surrounding air as an incompressible fluid or neglect air effects altogether. In contrast, our approach couples a boundary-integral …
Soft surfaces impacted by liquid droplets trap more air underneath than their rigid counterpart. The extended lifetime of the air film not only facilitates bouncing behaviours of the impacting droplets but also increases the possibility of an interaction between the air film itself and the air cavity formed inside the droplets by capillary waves. Such interaction may cause rupture of the trapped air film by a so-called dimple inversion phenomenon and suppress bouncing. In this work, we systematically investigate the relation between air cavity collapse and air film rupture for water droplets i…
This work is dedicated to providing a detailed account of the flow dynamics in the closure region of an internal ship air cavity. A geometrically simple multiwave test cavity is considered, and a simulation of the flow is conducted using large-eddy simulation coupled with an algebraic Volume of Fluid interface capturing method. Results reveal that the flow in the closure region is highly unsteady and turbulent. The main cause of this is established to be the pressure gradient occurring due to the stagnation of the flow on the beach wall of the cavity. The pressure gradient leads to a steep inc…
The axisymmetric collapse of a cylindrical air cavity in water follows a universal power law with logarithmic corrections. Nonetheless, it has been suggested that the introduction of a small azimuthal disturbance induces a long term memory effect, reflecting in oscillations which are no longer universal but remember the initial condition. In this work, we create non-axisymmetric air cavities by driving a metal disc through an initially-quiescent water surface and observe their subsequent gravity-induced collapse. The cavities are characterized by azimuthal harmonic disturbances with a single m…
As modern hydrodynamic codes increase in sophistication, the availability of realistic test problems becomes increasingly important. In gas dynamics, one common unrealistic aspect of most test problems is the ideal gas assumption, which is unsuited to many real applications, especially those involving high pressure and speed metal deformation. Our work considers the collapsing cavity and converging shock test problems, showing to what extent the ideal gas assumption can be removed from their specification. It is found that while most materials simply do not admit simple (i.e. scaling) solution…
Air cavities, i.e. air layers developed behind cavitators, are seen as a promising drag reducing method in the maritime industry. Here we utilize the Taylor-Couette (TC) geometry, i.e. the flow between two concentric, independently rotating cylinders, to study the effect of air cavities in this closed setup, which is well-accessible for drag measurements and optical flow visualizations. We show that stable air cavities can be formed, and that the cavity size increases with Reynolds number and void fraction. The streamwise cavity length strongly depends on the axial position due to buoyancy for…
A solid object impacting on liquid creates a liquid jet due to the collapse of the impact cavity. Using visualization experiments with smoke particles and multiscale simulations we show that in addition a high-speed air-jet is pushed out of the cavity. Despite an impact velocity of only 1 m/s, this air-jet attains \emph{supersonic} speeds already when the cavity is slightly larger than 1 mm in diameter. The structure of the air flow resembles closely that of compressible flow through a nozzle -- with the key difference that here the "nozzle" is a \emph{liquid} cavity shrinking rapidly in time.
Water entry of small hydrophobic spheres on an axisymmetric wavefield
Brown University（布朗大学）；Georgia Institute of Technology（佐治亚理工学院）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Naval Undersea Warfare Center（海军水下战中心）
Topological singularities occur in a broad range of physical systems, including collapsing stars and pinching fluid interfaces. They are important for being able to concentrate energy into a small region. Underwater air bubbles in particular appear in many practical applications, including new technologies to reduce skin drag on cargo ships. Previous theories show that just before an air bubble pinches off, the neck looks like a cylinder at its very smallest point. Unusually, however, the neck approaches this shape so gradually that the theoretical cylinder solution is not reached in practice;…
Middle turbinate resection significantly alters the anatomy and redistributes the inhaled air. The superior half of the main nasal cavity is opened up, increasing accessibility to the region. This is expected to increase inhalation dosimetry to the region during exposure to airborne particles. This study investigated the influence of middle turbinate resection on the deposition of inhaled pollutants that cover spherical and non-spherical particles (e.g. pollen). A computational model of the nasal cavity from CT scans, and its corresponding post-operative model with virtual surgery performed wa…
Our study provides the first experimental investigation of the internal flows of ventilated partial cavitation (VPC) formed by air injection behind a backward-facing step. The experiments are conducted using flow visualization and planar particle image velocimetry (PIV) with fog particles for two different cavity regimes of VPC, i.e., open cavity (OC) and two-branch cavity (TBC), under various range of free stream velocity (U) and ventilation rates (Q). Our experiments reveal similar flow patterns for both OC and TBC, including forward flow region near the air-water interface, reverse flow reg…
A circular disc impacting on a water surface creates a remarkably vigorous jet. Upon impact an axisymmetric air cavity forms and eventually pinches off in a single point halfway down the cavity. Immediately after closure 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 {\it not} the mechanism feeding the two jets. Using high-speed imaging and numerical simulations we show that jetting is fed by the local flow around the base of t…
Airflow through the nasal cavity exhibits a wide variety of fluid dynamicsbehaviour due to the intricacy of the nasal geometry. The flow is naturallyunsteady and perhaps turbulent, despite CFD in the literature that assumesa steady laminar flow. Time-dependent simulations can be used to generatedetailed data with the potential to uncover new flow behaviour, although theyare more computationally intensive compared with steady-state simulations. Furthermore, verification of CFD results has relied on reported pressure drop(e.g. nasal resistance) across the nasal airway although the geometries use…
Recent experiments on coating flows and liquid drop impact both demonstrate that wetting failures caused by air entrainment can be suppressed by reducing the ambient gas pressure. Here, it is shown that non-equilibrium effects in the gas can account for this behaviour, with ambient pressure reductions increasing the gas' mean free path and hence the Knudsen number $Kn$. These effects first manifest themselves through Maxwell slip at the gas' boundaries so that for sufficiently small $Kn$ they can be incorporated into a continuum model for dynamic wetting flows. The resulting mathematical model…
We consider the problem of oscillation damping in air of a thermally actuated microlever as it is gradually approached towards an infinite wall in parallel geometry. As the gap is decreased from 20 nm down to 400 nm, we observe the increasing damping of the lever Brownian motion in the fluid laminar regime. This manifests itself as a linear decrease with distance of the lever quality factor accompanied by a dramatic softening of its resonance, and eventually leads to the freezing of the CL oscillation. We are able to quantitatively explain this behavior by analytically solving the Navier-Stoke…
In modern transport systems, passengers' comfort is greatly influenced by flow-induced noise. In this study we investigate a generic deep cavity with an overhanging lip, mimicking a door gap in a vehicle, that is overflowed by air at two different free stream velocities, 26.8m/s and 50m/s. The turbulent boundary layer and the acoustic waves interact with the cavity's geometry and form a strong feedback mechanism. In the present work, we focus on the details of the compressible turbulent flow structures and their variations concerning the velocity, the boundary layer as well as the domain dimen…
The study of cavity flow is one of the most important research topics of unsteady aerodynamics. Supersonic turbulent flows over a cavity are mostly encountered in missiles, turbomachinery, and high-speed aircraft. The turbulence inside the cavity gives rise to excess drag, acoustic waves, pressure fluctuations, and vibrations which may lead to numerous problems like excess fuel consumption, failure of missile trajectory or mechanical parts, and aerodynamic heating. We conduct numerical simulations to investigate the flow and compare our results to existing experimental data to show quantitativ…
In 1904, while experimenting with high-speed photography, Lucien Bull recorded a pellet passing through a soap bubble. We investigate the dynamics that allow for a rigid body to pass through a hemispherical soap film without rupturing it. In this fluid dynamics video spheres were dropped from rest above a hemispherical soap film. At impact, the soap film stretches into a cavity around the sphere. As the sphere continues to descend, the film cavity pinches off and the film returns to its initial hemispherical shape. Upon closer observation of the film-sphere-air interface, the stability of the …
The stability of high-end piezo-acoustic drop-on-demand (DOD) inkjet printing is sometimes compromised by the entrainment of an air bubble inside the ink channel. Here, bubble pinch-off from an acoustically driven meniscus is studied in an optically transparent DOD printhead as a function of the driving waveform. We show that bubble pinch-off follows from low-amplitude higher-order meniscus oscillations on top of the global high-amplitude meniscus motion that drives droplet formation. In a certain window of control parameters, phase inversion between the low and high frequency components leads…
