Free Surface Breakup Research Articles

Experimental and numerical study of free water exit and re-entry of a fully submerged buoyant spheroid

The entire process of free water exit and re-entry of a fully-submerged spheroid with a density slightly less than that of water is investigated by using model experiments and numerical simulations. In the experiments, an initially static body with a density slightly less than that of water was released underwater and high-speed photography was used to monitor the motion of the body and the deformation of the free surface. In addition, a numerical method is developed based on the boundary-element method for the velocity potential with fully nonlinear boundary conditions and is used to numerically analyze the free-surface breakup and reformation. Numerical results are quantitatively consistent with experimental data. The results demonstrated that an upward-oriented liquid jet, or “splash,” forms after the body fully re-enters water. It is found that this jet originates from a local high-pressure region just below the free surface that results from the impact of water quickly converging to the vacancy above the body. The local high-pressure region is transient, so the acceleration, pressure, and fluid force exerted on the body are disturbed abruptly. According to the results, initial submergence depth and density of the body are two dominant parameters. Enhancing initial submergence parameter λ or decreasing the body density ρ1 (still larger than a critical density ρ1,c to avoid the body exiting water totally) will induce a more severe impact of converging water after the free surface reforms, and consequently cause larger variations in the amplitude of the fluid force and of the acceleration and in the pressure on the body.

Numerical simulation of water exit of an initially fully submerged buoyant spheroid in an axisymmetric flow

The free water exit of an initially fully submerged buoyant spheroid in an axisymmetric flow, which is driven by the difference between the vertical fluid force and gravity, is investigated. The fluid is assumed to be incompressible and inviscid, and the flow to be irrotational. The velocity potential theory is adopted together with fully nonlinear boundary conditions on the free surface. The surface tension is neglected and the pressure is taken as constant on the free surface. The acceleration of the body at each time step is obtained as part of the solution. Its nonlinear mutual dependence on the fluid force is decoupled through the auxiliary function method. The free-surface breakup by body penetration and water detachment from the body are treated through numerical conditions. The slender body theory based on the zero potential assumption on the undisturbed flat free surface is adopted, through which a condition for full water exit of a spheroid is obtained. Comparison is made between the results from the slender body theory and from the fully nonlinear theory through the boundary-element method, and good agreement is found when the spheroid is slender. Extensive case studies are undertaken to investigate the effects of body density, dimensions and the initial submergence.

Simulation of complete water exit of a fully-submerged body

The whole process of water exit of a fully-submerged rigid body is simulated using the boundary-element method for the velocity potential. A numerical procedure is proposed for the free-surface breakup as well as for body detachment from water. Convergence and sensitivity studies have been conducted for the procedure and consistent results have been achieved. Detailed simulations are undertaken for a spheroid emerging and departing from water. Results are provided for pressure and force on the body, as well as the step-by-step free surface deformation, including the development of the jet and formation of the cavity. The effect of Froude number is investigated, as well as the body shape in terms of the ratio of its horizontal and vertical dimensions.

Numerical simulation of hydro-elastic problems with smoothed particle hydrodynamics method

Violent free surface flows with strong fluid-solid interactions can produce a tremendous pressure load on structures, resulting in elastic and even plastic deformations. Modeling hydro-elastic problems with structure deformations and a free surface breakup is difficult by using routine numerical methods. This paper presents an improved Smoothed Particle Hydrodynamics (SPH) method for modeling hydro-elastic problems. The fluid particles are used to model the free surface flows governed by Navier-Stokes equations, and the solid particles are used to model the dynamic movement and deformation of the elastic solid objects. The improved SPH method employs a Kernel Gradient Correction (KGC) technique to improve the computational accuracy and a Fluid-Solid Interface Treatment (FSIT) algorithm with the interface fluid and solid particles being treated as the virtual particles against their counterparts and a soft repulsive force to prevent the penetration and a corrective density approximation scheme to remove the numerical oscillations. Three typical numerical examples are simulated, including a head-on collision of two rubber rings, the dam break with an elastic gate and the water impact onto a forefront elastic plate. The obtained SPH results agree well with experimental observations and numerical results from other sources.

Bubble oscillations and motion under vibration

Bubbles under vibration can behave in unusual ways, e.g., moving downward against the force of buoyancy. While the bubble downward motion due to the Bjerknes force is well known at acoustic frequencies close to the bubble resonant frequency, these experiments demonstrate that these effects can be observed at relatively low frequencies as well. Experiments were performed in a thin, quasi-two-dimensional rectangular acrylic box partially filled with 20-cSt PDMS silicone oil with overlying ambient air. The apparatus was subjected to sinusoidal axial vibration that produced breakup of the gas-liquid free surface, producing liquid jets into the air, droplets pinching off from these jets, gas cavities in the liquid from impacts of these droplets, and bubble transport below the interface. Vibration conditions for the attached videos are 280 Hz frequency, 15 g acceleration, and 94 micron peak-to-peak displacement. Behaviors shown in the videos include the following. 1. Free surface breakup into jets and droplets, and formation of bubbles under the free surface. 2. Bubbles thus generated moving downward in the cell. 3. Bubbles attracted to the first bubble deep in the cell and eventually merging to form a large bubble at the base of the cell. 4. Bubble cluster at the base of the cell merging to form a larger bubble, which stabilizes at a levitated location below the free surface and acts to damp out the surface breakup. 5. The levitated bubble interface and its breakup are similar to the free surface breakup into jets and droplets, but the jets in the bubble are facing downward. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Mechanisms of free-surface breakup in vibration-induced liquid atomization

The mechanisms of droplet formation that take place during vibration-induced drop atomization are investigated experimentally. Droplet ejection results from the breakup of transient liquid spikes that form following the localized collapse of free-surface waves. Breakup typically begins with capillary pinch-off of a droplet from the tip of the spike and can be followed by additional pinch-offs of satellite droplets if the corresponding capillary number is sufficiently small (e.g., in low-viscosity liquids). If the capillary number is increased (e.g., in viscous liquids), breakup first occurs near the base of the spike, with or without subsequent breakup of the detached, thread-like spike. The formation of these detached threads is governed by a breakup mechanism that is separated from the tip-dominated capillary pinch-off mechanism by an order of magnitude in terms of dimensionless driving frequency f*. The dependence of breakup time and unbroken spike length on fluid and driving parameters is established over a broad range of dimensionless driving frequencies (10−3<f*<1). It is also shown that the droplet-ejection acceleration threshold âc of low-viscosity liquids depends on the dimensionless drop diameter d̂. Moreover, in the limit d̂⩾20, the droplet-ejection threshold becomes independent of d̂ (âc≈4). This limit state is described by a scaling equivalent to that of Goodridge, Shi, and Lathrop [Phys. Rev. Lett. 76, 1824 (1996)] derived for the onset of droplet ejection from Faraday waves. It is shown in the present study that the acceleration threshold in this limit scales like ac∼f4∕3(σ∕ρ)1∕3.

On droplet formation from capillary waves on a vibrating surface

The formation of sprays from a liquid film on a vibrating surface is used by ultrasonic atomizers for applications ranging from humidification to metal–powder manufacturing. The received opinion in the literature is that droplets are formed periodically from the apexes of an orderly pattern of standing capillary waves, with a wavelength that can be related to vibration frequency by stability analysis. It is described how this assumption may be incorrect in that, after droplet formation commences, the orderliness of the standing–wave pattern is lost due to one or more secondary instability phenomena. These phenomena, which lead to disorderliness, are investigated by using high–speed imaging techniques and a low–frequency vibrating film to model the high–frequency case, because of the difficulty of penetrating clouds of small droplets in the latter case. Different modes of droplet formation are identified and the flow patterns responsible for these modes are discussed. Physical mechanisms are proposed from which it is deduced that only a proportion of standing–wave crests can eject droplets, for a given wall–vibration period, and the identity of these ejecting waves should vary from period to period. The model thus developed demonstrates an apparently random ejection of droplets from one wave cell, even though the model itself is deterministic. The disorder of the capillary waves and the occurrence of several droplet–formation routes are sufficient to explain the range of droplet sizes that is produced by ultrasonic atomization.