Three-Dimensional Computation of Bubbles Near a Free Surface

Journal of Hydrodynamics, Ser. B, 2009

Bubble flow interaction can be important in many practical engineering applications. For instance, cavitation is a problem of interaction between nuclei and local pressure field variations including turbulent oscillations and large scale pressure variations. Various types of behaviours fundamentally depend on the relative sizes of the nuclei and the length scales of the pressure variations as well as the relative importance of bubble natural periods of oscillation and the characteristic time of the field pressure variations. Similarly, bubbles can significantly affect the performance of lifting devices or propulsors. We present here some fundamental numerical studies of bubble dynamics and deformation, then a practical method using a multi-bubble Surface Averaged Pressure (DF-Multi-SAP © ) to simulate cavitation inception and scaling, and connect this with more precise 3-D simulations. This same method is then extended to the study of two-way coupling between a viscous compressible flow and a bubble population in the flow field.

Journal of Computational and Applied Mathematics, 2010

Numerical techniques frequently used for the simulation of one bubble can be classified as interface tracking techniques and interface capturing techniques. Most of these techniques calculate both the flow around the bubble and the shape of the interface between the gas and the liquid with one code. In this paper, a rising axisymmetric bubble is simulated with an interface tracking technique that uses separate codes to determine the position of the gas-liquid interface and to calculate the flow around the bubble. The grid converged results correspond well with the experimental data.

Journal of Computational Physics, 2016

The paper presents a numerical method for the simulation of bubbles with variable shape in the framework of an immersed boundary method. The liquid-gas interface is described analytically by a series expansion in spherical harmonics. Such a representation of the interface is very accurate and robust and the error of the computed surface curvature is substantially smaller compared to a discrete representation of the surface by grid points. The shape of the bubble is computed by minimizing the local displacement energy of pressure and surface tension forces and is coupled to the continuous phase by adapting the Lagrangian surface mesh in each time step. This is done with the constraint of constant bubble volume exactly implemented. As a first step the bubbles are restricted to axisymmetric shapes. The resulting algorithm is thoroughly validated by several numerical tests and finally applied to freely rising bubbles with stationary and oscillatory shape as well. The computed bubble shapes are in very good agreement with experimental and numerical reference data.

Journal of Mechanical Science and Technology, 2012

Bubble rising phenomenon is widely found in many engineering applications including stream generators in power plants. Many experimental and numerical researches have been performed to predict the dynamic behavior of the bubble rising process. Most simulations so far have focused on evolution behavior of the rising bubble itself. Rising bubbles could penetrate through the top free surface which makes the problem much more complicated in addition to the curvature effect on the interface. With top surface, satellite droplets may be generated near breakup region and entrained to rising velocity field. In this paper, the effect of top free surface on rising bubble has been numerically investigated. High-order tetra-marching level contour reconstruction method (LCRM), which is a hybridization of fronttracking and level-set methods has been used to track the gas-liquid interface explicitly. Effects of free surface on the interfacial shape and behavior after breakup are studied with different size and depth of the initial bubble. It has been found that the initial diameter of the bubble is the dominant factor controlling the satellite droplet formation.

2019

Understanding the dynamics of oscillating bubbles beneath a free surface is crucial to many practical applications including airgun-bubble clusters, underwater explosions, etc. In this paper, an experimental and numerical study of the dynamic behaviors of a coalesced bubble near a free surface is conducted, which shows quite different physical features from single bubble dynamics. Firstly, two similar sized underwater discharge bubbles are generated simultaneously beneath a free surface and their complex interactions are experimentally studied with high-speed photography imaging. A strong interaction between two bubbles and the subsequent coalescence are observed when the initial distance between two bubbles is smaller than the maximum equivalent bubble radius. Secondly, both axisymmetric and three-dimensional (3D) boundary integral models are used to simulate the pre-coalescence and post-coalescence of two bubbles. The results obtained by the two models agree well in axisymmetric c...

2016

In this paper, the rising of a single bubble in a viscous liquid and its departure from the free-surface are simulated using a transient 2D/axisymmetric model. To predict the shape of the bubble deformation, the Navier-Stokes equations in addition to an advection equation for liquid volume fraction are solved. A modified Volume-of-Fluid (VOF) technique based on Youngs ’ algorithm is used to track the bubble deformation. To validate the model, the results of simulations for terminal rise velocity and bubble shape are compared with those of the experiments. Next, the effect of different parameters such as initial bubble radius, channel height, and liquid viscosity and surface tension on the shape and rise velocity of the bubble is investigated. Finally, the interaction of the bubble with the free surface during its departure from the liquid is simulated, and the results are compared qualitatively with experimental photographs.

Applied Mathematical Modelling, 2014

A theoretical model has been developed to analyse bubble rise in water and subsequent impact and bounce against a horizontal glass plate. The multiscale nature of the problem, where the bubble size is on the millimetre range and the film drainage process happens on the micrometre to nanometre scale requires the combined use of different modelling techniques. On the macro scale we solve the full Navier-Stokes equations in cylindrical coordinates to model bubble rise whereas modelling film drainage on the micro scale is based on lubrication theory because the film Reynolds number becomes much smaller than unity. Quantitative predictions of this model are compared with experimental data obtained using synchronised high-speed cameras. Video recording of bubble rise and bounce trajectories are combined with interferometry data to deduce the position and time-dependent thickness of the thin water film trapped between the deformed bubble and the glass plate. Bubble rise velocity indicated that the boundary condition at the bubble surface was tangentially immobile. Quantitative comparisons are presented for bubbles of different size to quantify similarities and differences.

The interaction between an explosion bubble and a floating body involves several physical phenomena that an accurate numerical simulation needs to capture. These include proper description of the initial shock wave and its propagation and interaction with the floating body and free surface and the subsequent growth, dynamics, collapse, and interaction of the resulting bubble with the structure. A numerical procedure which links a compressible finite difference flow solver with an incompressible boundary element method was applied to capture both shock and bubble phases efficiently and accurately. Both codes solved the fluid dynamics problem and coupled with a finite element structure code to simulate fluid-structure interaction. This numerical approach was validated by comparing the numerical results with available experimental measurements. The effects of including or neglecting some modeling aspects on the solution were considered.

Physics of Fluids

Using Arbitrary Lagrangian-Eulerian method on an adaptive moving unstructured mesh, we carry out numerical simulations for a rising bubble interacting with a solid wall. Driven by the buoyancy force, the axisymmetric bubble rises in a viscous liquid toward a horizontal wall, with impact on and possible bounce from the wall. First, our simulation is quantitatively validated through a detailed comparison between numerical results and experimental data. We then investigate the bubble dynamics which exhibits four different behaviors depending on the competition among the inertial, viscous, gravitational, and capillary forces. A phase diagram for bubble dynamics has been produced using the Ohnesorge number and Bond number as the two dimensionless control parameters. Finally, we turn to the late stage of the bubble rise characterized by a small flux of liquid escaping from the thin film between the wall and bubble. Since the thin film dynamics can be accurately described by the lubrication approximation, we carry out numerical simulations to compare the simulation results with the predictions of the lubrication approximation. Remarkable agreement is obtained to further demonstrate the accuracy of the simulations.

1996

In many practical applications involving underwater explosions near a solid structure, competition between the forces due to gravity and those due to the presence of a nearby structure leads to highly distorted bubble shapes. In order to accurately simulate such problems, a 3-dimensional model is required. In this paper, we present results of a validation study of DyNeruoWs 3-D Boundary Element Code, 3DvNaFS, that has been successful in predicting and reproducing a host of Narry underwater explosion problerns.