A continuum method for modeling surface tension

The numerical simulation of flows with interfaces and free-surface flows is a vast topic, with applications to domains as varied as environment, geophysics, engineering, and fundamental physics. In engineering, as well as in other disciplines, the study of liquid-gas interfaces is important in combustion problems with liquid and gas reagents. The formation of droplet clouds or sprays that subsequently burn in combustion chambers originates in interfacial instabilities, such as the Kelvin-Helmholtz instability. What can numerical simulations do to improve our understanding of these phenomena? The limitations of numerical techniques make it impossible to consider more than a few droplets or bubbles. They also force us to stay at low Reynolds or Weber numbers, which prevent us from finding a direct solution to the breakup problem. However, these methods are potentially important. First, the continuous improvement of computational power (or, what amounts to the same, the drop in megaflop price) continuously extends the range of affordable problems. Second, and more importantly, the phenomena we consider often happen on scales of space and time where experimental visualization is difficult or impossible. In such cases, numerical simulation may be a useful prod to the intuition of the physicist, the engineer, or the mathematician. A typical example of interfacial flow is the collision between two liquid droplets. Finding the flow involves the study not only of hydrodynamic fields in the air and water phases but also of the air-water interface. This latter part

Direct numerical simulation of free-surface and interfacial flow

Impact of water droplets on a flat, solid surface was studied using both experiments and numerical simulation. Liquid–solid contact angle was varied in experiments by adding traces of a surfactant to water. Impacting droplets were photographed and liquid–solid contact diameters and contact angles were measured from photographs. A numerical solution of the Navier–Stokes equation using a modified SOLA‐VOF method was used to modeldroplet deformation. Measured values of dynamic contact angles were used as a boundary condition for the numerical model. Impacting droplets spread on the surface until liquid surface tension and viscosity overcame inertial forces, after which they recoiled off the surface. Adding a surfactant did not affect droplet shape during the initial stages of impact, but did increase maximum spread diameter and reduce recoil height. Comparison of computer generated images of impacting droplets with photographs showed that the numerical model modeled droplet shape evolution correctly. Accurate predictions were obtained for droplet contact diameter during spreading and at equilibrium. The model overpredicted droplet contact diameters during recoil. Assuming that dynamic surface tension of surfactant solutions is constant, equaling that of pure water, gave predicted droplet shapes that best agreed with experimental observations. When the contact angle was assumed constant in the model, equal to the measured equilibrium value, predictions were less accurate. A simple analytical model was developed to predict maximum droplet diameter after impact. Model predictions agreed well with experimental measurements reported in the literature. Capillary effects were shown to be negligible during droplet impact when We≫Re1/2.

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Capillary effects during droplet impact on a solid surface

Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

https://escholarship.org/content/qt4nc7s7bp/qt4nc7s7bp.pdf?t=p21n9r

Second-order accurate volume-of-fluid algorithms for tracking material interfaces

In this report a simple, but powerful, computer program is presented for the solution of two-dimensional transient fluid flow with free boundaries The SOLA-VOF program, which is based on the concept of a fractional volume of fluid (VOF), is more flexible and efficient than other methods for treating arbitrary free boundaries SOLA-VOF has a variety of user options that provide capabilities for a wide range of applications Its basic mode of operation is for single fluid calculations having multiple free surfaces However, SOLA-VOF can also be used for calculations involving two fluids separated by a sharp interface In either case, the fluids may be treated as incompressible or as having limited compressibility Surface tension forces with wall adhesion are permitted in both cases Internal obstacles may be defined by blocking out any desired combination of cells in the mesh, which is composed of rectangular cells of variable size SOLA-VOF is an easy-to-use program Its logical parts are isolated in separate subroutines, and numerous special features have been included to simplify its operation, such as an automatic time-step control, a flexible mesh generator, extensive output capabilities, a variety of optional boundary conditions, and instructive internal documentation

SOLA-VOF: a solution algorithm for transient fluid flow with multiple free boundaries

The volume of fluid (VOF) technique is presented as a simple and efficient means for numerically treating free boundaries embedded in a calculational mesh of Eulerian or Arbitrary-Lagrangian-Eulerian cells. It is particularly useful because it uses a minimum of stored information, treats intersecting free boundaries automatically, and can be readily extended to three-dimensional calculations.

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R.S. Hotchkiss

Papers

SOLA-VOF: a solution algorithm for transient fluid flow with multiple free boundaries

A fractional volume of fluid method for free boundary dynamics