Asghar Esmaeeli

A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number

Buoyancy-driven motion of bubbles is examined by direct numerical simulations. Two cases, with 48 monodispersed bubbles at two different gas∕liquid combinations, of deformable and nearly spherical bubbles, are simulated. For the nearly spherical bubbles Eo=0.5, and for the deformable ones Eo=4, and for both cases N=8000 and α=5.8%. This results in Re¯=91.5 and We¯=0.53 for the nearly spherical system and Re¯=77.6 and We¯=3 for the deformable one. The simulations show path oscillations of the bubbles in both cases and shape oscillations of the deformable bubbles. At quasi-steady-state, the distribution of the deformable bubbles is relatively uniform but the spherical bubbles are distributed nonuniformly as a result of the formation of horizontal “rafts.” For both cases, however, the probability density functions of the fluctuation velocities of the bubbles are found to be approximately Gaussian. The temporal autocorrelation functions of the fluctuation velocities show that the horizontal components become ...

Computations of Explosive Boiling in Microgravity

Dynamics of the explosive growth of a vapor bubble in microgravity is investigated by direct numerical simulation. A front tracking/finite difference technique is used to solve for the velocity and the temperature field in both phases and to account for inertia, viscosity, and surface deformation. The method is validated by comparison of the numerical results with the available analytical formulations such as the evaporation of a one-dimensional liquid/vapor interface, frequency of oscillations of capillary waves, and other numerical results. Evolution of a three-dimensional vapor nucleus during explosive boiling is followed and a fine scale structure similar to experimental results is observed. Two-dimensional simulations yield a similar qualitative instability growth.

Computations of Multiphase Flows

Abstract Computational studies of multiphase flows go back to the very beginning of Computational Fluid Dynamics. It is, however, only during the last decade that direct numerical simulations of multiphase flow have emerged as a major research tool. It is now possible, for example, to simulate the motion of several hundred bubbles and particles in simple flows and to obtain meaningful averaged-quantities that can be compared with experimental results. Much of this progress has been made possible by methods based on the ‘one-fluid’ formulation of the governing equations, in addition to rapidly increasing computational power. Here, we review computations of multiphase flows with particular emphasis on finite Reynolds number flows and methods using the ‘one-fluid’ approach. After an overview of the mathematical formulation and the various ‘one-fluid’ methods, the state-of-the-art is reviewed for three problems: Dispersed bubbly flows, microstructure formation during solidification, and boiling. For the first example numerical methods have reached the maturity where they can be used in scientific studies. For the second and third examples, major numerical development is still taking place. However, progress is rapidly being made and it is realistic to expect large-scale simulations of these problems to become routine within a few years.

Dielectrophoretic- and electrohydrodynamic-driven translational motion of a liquid column in transverse electric fields

Computer simulations are performed to study translational motion and deformation of a liquid column or jet, in a plane perpendicular to its axis, due to a transverse electric field. A front tracking/finite difference scheme is used in conjunction with the Taylor-Melcher leaky dielectric theory to solve the governing equations. The column is confined within a rectangular channel, wall-bounded in the vertical direction and periodic in the horizontal direction. It is shown that perfect dielectric columns move toward electrode wall of shorter initial distance, but the leaky dielectric columns may move toward or away from it, depending on the relative importance of the ratios (drop fluid to suspending fluid) of their electric permittivity and conductivity. Furthermore, the degree of interface deformation might increase or decrease with the initial separation distance from the shorter electrode wall due to the same factor. Scaling arguments are used to discern the correlation between the translational velocity ...

Flow patterns and deformation modes of coaxial liquid columns in transverse electric fields

Steady-state flow patterns and deformation modes of coaxial liquid columns in transverse electric fields are studied analytically. The governing creeping flow equations are solved for Newtonian and (mutually) immiscible fluids in the framework of leaky dielectric theory. A detailed analysis of the electric and flow fields is presented and it is shown that there will be four possible flow patterns in and around the columns, in terms of the direction of the external flow (top-to-sides/bottom-to-sides vs. sides-to-top/sides-to-bottom) and the number of vortices (single vortex vs. double vortices) in the shell, and that the senses of the net electric shear stresses at the inner and the outer interfaces and their relative importance are the key parameters in setting these patterns. Equilibrium shapes of the interfaces are also found and it is shown that there are four distinct modes of deformation, depending on the governing nondimensional parameters of the problem. The instability of the jet is also examined qualitatively using the observations pertaining the instability of single-phase drops and jets and the scaling arguments based on the present solution.Graphical abstract

Studies of Bubbly Channel Flows by Direct Numerical Simulations

Recent DNS studies of buoyant bubbly flows in vertical channels are discussed. Simulations of nearly spherical bubbly flows in vertical channels show that the bubbles move towards the walls for upflow and away from the walls for downflow in such a way that the core is in hydrostatic equilibrium. For downflow the wall-layer is free of bubbles but for upflow there is an excess of bubbles in the wall-layer. The liquid velocity in the core is nearly uniform. For laminar downflow the velocity in the wall-layer can be computed analytically and for turbulent flow the velocity is given (almost) by the law of the wall. For upflow the velocity in the wall-layer is strongly influenced by the presence of the bubbles. We conclude by discussing briefly bubble coalescence and topology induced flow regime changes.

Computations of Boiling Flows

Numerical simulations of boiling flows are discussed. The change of phase from liquid to vapor and vice-versa usually takes place in a highly unsteady manner where the phase boundary is very convoluted. Direct numerical simulations therefore require the accurate solution of the Navier-Stokes equations and the energy equation in each phase and the correct incorporation of the unsteady phase boundary. Such simulations, where the motion of an unsteady phase boundary is followed for a sufficiently long time to allow computation of average heat transfer are very recent. Here, we will describe one method that has been used successfully to simulate boiling flows and show a few examples of studies using the method.Copyright

Direct Numerical Simulations of Flows With Phase Change

During the last decade, direct numerical simulations of multiphase flow have emerged as a major research tool. It is now possible, for example, to simulate the motion of several hundred bubbles and particles in simple flows and to obtain meaningful average quantities that can be compared with experimental results. These systems are, however, still very simple compared to those systems routinely encountered in engineering applications. It is, in particular, frequently necessary to account for phase change, both between solid and liquid as well as liquid and vapor. Most materials used for manmade artifacts are processed as liquids at some stage, for example, and the way solidification takes place generally has major impact on the properties of the final product. The formation of microstructures, where some parts of the melt solidify faster than others, or solidify with different composition as in the case of binary alloys, is particularly important since the size and composition of the microstructure impact the hardness and ductility, for example, of the final product. Boiling is one of the most efficient ways of removing heat from a solid surface. It is therefore commonly used in energy generation and refrigeration. The large volume change and the high temperatures involved can make the consequences of design or operational errors catastrophic and accurate predictions are highly desirable. The change of phase from liquid to vapor and vice-versa usually takes place in a highly unsteady manner with a very convoluted phase boundary. Numerical simulations are therefore essential for theoretical investigations and while a few simulations of both problems have been published, the field is still very immature. In the talk the author gives a brief overview of the state of the art and discusses recent simulations of boiling and solidification in some detail. The progress made during the last few years in simulating the motion of multiphase flows without phase change has relied heavily on the so-called “one-fluid” formulation of the governing equations. In this approach one set of equations is written for all the phases involved. The formulation allows for different material properties in each phase and singular terms must be added at the phase boundaries to correctly incorporate the appropriate boundary conditions. The key challenge is to correctly advect the phase boundary and a number of methods have been proposed to do so. Those include the Volume-Of-Fluid (VOF), the level-set, the phase field methods, as well as front-tracking methods where the boundary is explicitly tracked by connected marker points [1]. The last approach, front tracking, has been particularly successful and is used for the examples shown here. In both boiling and solidification it is necessary to solve the energy equation, in addition to conservation equations for mass and momentum, and account for the release/absorption of latent heat at the phase boundary. The latent heat source also determines the motion of the phase boundary relative to the fluid. In boiling there is significant volume expansion as liquid is transformed into vapor and this expansion must be accounted for in the mass conservation equation. For solidification the volume expansion can often be neglected, but the transformation of the liquid into a stationary solid poses new computational challenges. An example of a bubble undergoing vapor explosion is shown in figure 1. The bubble is initially started as a small nearly spherical sphere in superheated liquid confined in a domain that is periodic in two directions, with a solid wall at the bottom and open on the top to allow outflow as the bubble expands. In this case the domain is resolved by a 643 grid. As the bubble grows, the interface becomes unstable, developing a corrugated shape (usually referred to experimentally as a “black bubble” since the corrugated surface is opaque). The increase in surface area greatly affects the growth rate of the bubble. Figure 2 shows one example of a simulation of the growth of a dendrite of pure material in uniform flow. The domain is a square resolved by a 2563 grid. A uniform inflow is specified on the left boundary, the top and bottom boundaries are periodic, and all gradients are set to zero at the outlet boundary. The temperature of the incoming flow is equal to the undercooled temperature and as latent heat is released at the phase boundary, the flow sweeps it from the front to the back. This results in a thinner thermal boundary layer at the tip of the upstream growing arm and a relatively uniform temperature in the wake. The growth rate of the upstream arm is therefore enhanced and the growth of the downstream arm is reduced.Copyright

Computational Studies on the Behavior of an Interface Separating Two Fluids Under Uniform Electric Field

Direct Numerical Simulations (DNS) are carried out to study the dynamics of a horizontal interface separating two fluids, having different electrical properties, under the influence of a uniform electric field. A front tracking/finite difference scheme is used, in conjunction with Taylor’s leaky dielectric model, to solve the governing electrohydrodynamics equations in both fluids at finite Reynolds numbers. The methodology and the code is validated by comparing the results with those of the analytical studies developed at the linear stability limit and it is shown that a very good agreement exists between the two. The results of this study show interesting interface behavior depending on the parameters of the problem. In all the cases considered, the interface becomes unstable beyond a critical voltage and starts to oscillate as it moves toward its steady-state shape which is a vertical column pointing from the liquid of higher electric conductivity to the one with a lower conductivity. The shape of the column, however, will vary depending on the individual governing parameters.Copyright

Computational Studies of EHD-Enhanced Condensation Heat Transfer on a Downward-Facing Horizontal Plate

This study aims to investigate the effect of uniform electric fields on the enhancement of condensation heat transfer from a downward facing horizontal plate by direct numerical simulations. The governing equations of fluid flow and electric field are solved using a front tracking/finite difference technique in the framework of Taylor’s leaky dielectric model. The electric force comprises of the dielectrophoretic and the Coulomb forces. Both forces act on the phase boundary and their relative magnitude and directions affect the condensation rate. For the results shown here, the condensate drops are more elongated compared to the those in zero-electric field. It is shown that the electric field enhances the condensation rate in two ways: by increasing the number of the drops that are generated per unit surface due to destablizing the interface and by increasing the frequency of drop generation and pinch off. The mechanism of elongation of the condensate drops are explained by detailed examination of the distribution of the electric field at the phase boundary.© 2009 ASME