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Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
, 1981
"... Several methods have been previously used to approximate free boundaries in finite difference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efficient than other metho ..."
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Cited by 603 (3 self)
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Several methods have been previously used to approximate free boundaries in finite difference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efficient than other methods for treating complicated free boundary configurations. To illustrate the method, a description is given for an incompressible hydrodynamics code, SOLAVOF, that uses the VOF technique to track free fluid surfaces.
A HighOrder Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows
, 1997
"... We present a numerical method for computing solutions of the incompressible Euler or NavierStokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties. The method is based on a secondorder projection method for variable d ..."
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Cited by 54 (8 self)
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We present a numerical method for computing solutions of the incompressible Euler or NavierStokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties. The method is based on a secondorder projection method for variable density flows using an "approximate projection" formulation. The boundary between the fluids is tracked with a secondorder, volumeoffluid interface tracking algorithm. We present results for viscous RayleighTaylor problems at early time with equal and unequal viscosities to demonstrate the convergence of the algorithm. We also present computational results for the RayleighTaylor instability in airhelium and for bubbles and drops in an airwater system without interfacial tension to demonstrate the behavior of the algorithm on problems with larger density and viscosity contrasts. 1. Introduction Fluid flows with free surfaces or material interfaces occur in a large number of natural and ...
Capillary effects during droplet impact on a solid surface
, 1996
"... 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 we ..."
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Cited by 38 (3 self)
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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 SOLAVOF method was used to model droplet 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
Reviewnumerical models for dilute gasparticle flows.
 Journal of Fluids Engineering.
, 1982
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On the flow past a magnetic obstacle
, 2006
"... This paper analyses numerically the quasitwodimensional flow of an incompressible electrically conducting viscous fluid past a localized zone of applied magnetic field, denominated a magnetic obstacle. The applied field is produced by the superposition of two parallel magnetized square surfaces, u ..."
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Cited by 8 (2 self)
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This paper analyses numerically the quasitwodimensional flow of an incompressible electrically conducting viscous fluid past a localized zone of applied magnetic field, denominated a magnetic obstacle. The applied field is produced by the superposition of two parallel magnetized square surfaces, uniformly polarized in the normal direction, embedded in the insulating walls that contain the flow. The area of these surfaces is only a small fraction of the total flow domain. By considering inertial effects in the analysis under the low magnetic Reynolds number approximation, it is shown that the flow past a magnetic obstacle may develop vortical structures and eventually instabilities similar to those observed in flows interacting with bluff bodies. In the small zone where the oncoming uniform flow encounters the nonnegligible magnetic field, the induced electric currents interact with the field, producing a nonuniform Lorentz force that brakes the fluid and creates vorticity. The effect of boundary layers is introduced through a friction term. Due to the localization of the applied magnetic field, this term models either the Hartmann braking within the zone of high magnetic field strength or a Rayleigh friction in zones where the magnetic field is negligible. Finite difference numerical computations have been conducted for Reynolds numbers Re=100 and 200, and Hartmann numbers in the range 1 Ha 100 (Re and Ha are based on the side length of the magnetized square surfaces). Under these conditions, a wake is formed behind the obstacle. It may display two elongated streamwise vortices that remain steady as long as the Hartmann number does not exceed a critical value. Once this value is reached, the wake becomes unstable and a vortex shedding process similar to the one observed in the flow past bluff bodies is established. Similarities and differences with the flow around solid obstacles are discussed.
A Computational Method for Free Surface Hydrodynamics, American Society of Mechanical Engineers 80C2/PVP144
, 1980
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A Numerical Study on The Solidification of Liquid Metal Droplets Impacting onto a Substrate
"... The problem of normal incidence impact with solidification of a spherical liquid metal droplet onto a rigid planar substrate is studied. The NavierStokes equations are solved using a finitevolume formulation with a fixed grid. The free surface of the droplet is tracked by the volumeoffluid (VOF) ..."
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Cited by 2 (1 self)
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The problem of normal incidence impact with solidification of a spherical liquid metal droplet onto a rigid planar substrate is studied. The NavierStokes equations are solved using a finitevolume formulation with a fixed grid. The free surface of the droplet is tracked by the volumeoffluid (VOF) method. The surface tension on the droplet surface is evaluated by a continuum surface force (CSF) model. The energy equation is modeled by using an enthalpybased formulation. The method developed provides a comprehensive model of the dynamic and thermal aspects of the impact process. The effects of several parameters on the spread of the droplet on the substrate are determined. A correlation for the maximum spread factor is obtained and is in agreement with the experimental data available in the literature. 3 NOMENCLATURE C p : specific heat d max : maximum diameter of droplet after impact d : diameter of droplet h : sensible enthalpy h c : heattransfer coefficient k : thermal conduct...
ThermalFluid Flow Transport Phenomenon over SlotPerforated Flat Plates Placed in Narrow Channel
"... A numerical study is performed to investigate unsteady, twodimensional, incompressible laminar flow over both sides of a slotperforated flat surface, which is placed in a narrow channel. Emphasis is placed on the effect of the blockage factor, that is, the ratio of plate thickness to channel widt ..."
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Cited by 1 (0 self)
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A numerical study is performed to investigate unsteady, twodimensional, incompressible laminar flow over both sides of a slotperforated flat surface, which is placed in a narrow channel. Emphasis is placed on the effect of the blockage factor, that is, the ratio of plate thickness to channel widthW on the heattransfer performance and the velocity and thermal fields. It is found from the study that 1) when the slot width is increased, the alternating change in the fluid flow disturbs the thermal boundary layer formed along the plate and induces mixing of the upper and lower streams of the plate downstream from the slot, resulting in an amplification of heattransfer performance; 2) heattransfer performance at the rear plate is induced with an increase in slot width and Re; and 3) by contrast, heattransfer performance is attenuated with an increase in the blockage factor, whose effect becomes larger in the lower region of the Reynolds number. Nomenclature B = channel length, m d = slot width, m h = local heattransfer coefficient on the plate,W=m2=k,
A Numerical Correlation for The Solidification of Liquid Metal Droplets Impacting onto a Substrate
"... The problem of normal incidence impact with solidification of a spherical liquid metal droplet onto a rigid planar substrate is studied. The NavierStokes equations are solved using a finitevolume formulation with a fixed grid. The free surface of the droplet is tracked by the Volume of Fluid (VOF) ..."
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Cited by 1 (0 self)
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The problem of normal incidence impact with solidification of a spherical liquid metal droplet onto a rigid planar substrate is studied. The NavierStokes equations are solved using a finitevolume formulation with a fixed grid. The free surface of the droplet is tracked by the Volume of Fluid (VOF) method. The surface tension on the droplet surface is evaluated by a Continuum Surface Force (CSF) model. The energy equation which includes both convectiondiffusion heat transfer and a mushyregion for the phase change (solidification) is modeled by using an enthalpybased formulation. The method developed provides a comprehensive model of the dynamic and thermal aspects of the impact process. A parametric study has been performed. The effects of several parameters on the spread of the droplet on the substrate are determined. The information is used to develop, via dimensional analysis, a relationship between nondimensional numbers and the spread factor. A correlation that predicts the s...