# Current and Recent Research Projects

## Bubbly Channel Flows

Bubbly flows in vertical pipes and channels are encountered in a wide variety of industrial systems. Simulations of nearly spherical bubbly flows in vertical channels show that the bubbles move towards the wall for upflow and away from the wall 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 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 is strongly influenced by the precence of the bubbles. Results from several simulations, fully resolving the flow around each bubble, are used to study the effect of void fraction and bubble size for turbulent downflow. Deformable bubbles, in turbulent upflow, in contrast to the nearly spherical bubbles, remain in the middle of the channel. Research supported by DOE. More Information.

## Simulations of Nucleate Boiling Flows

Research supported by Sandia National Laboratory.

## Algorithms for Topology Changes in Front-Tracking Simulations

Accomplishing topology changes is frequently viewed as a major problem with the use of marker points to track fluid interfaces. We have recently developed an algorithm that so far seems to be completely general. The process consists of two relatively separate steps: finding close interfaces and changing the topology to the new configuration. For the first step we have develop two methods, one based on sorting the front objects into local groups and then conducting a search within each group, and another method where we used the fixed grid to identify values of the marker function that indicate that another front segment is nearby. Both approaches appear to work well. For the second step we proceed through several operations where parts of the change are performed on the whole front simultaneously, before the next step of the topology change is done. Doing the changes globally, rather then locally, results in a relatively simple algorithm. The present algorithm is only concerned with achieving the topology change. Capturing exactly when a thin films rupture requires the inclusion of models for the physical processes responsible for the rupture, and has not been done yet. Research supported by NSF.

## Simulations of Film Boiling Flows

The growth of boiling bubbles is studied by direct numerical simulations where the flow field is fully resolved and the effects of inertia, viscosity, surface deformation, heat conduction and convection, as well as the phase change, are accounted for. Boiling involves both fluid flow and heat transfer and thus requires the solution of the Navier-Stokes and the energy equations. The numerical method is based on writing one set of governing transport equations which is valid in both the liquid and vapor phases. We investigate boiling of a vapor film beneath a liquid layer in two and three dimensions by direct numerical simulation. A front tracking/ finite difference technique is used to solve for the velocity and temperature field in both phases and to account for inertia, viscosity and surface deformation. In two dimensions, three layers of fluid are used to simulate the cyclic nature of film boiling. The Jacob number is small so that the time scale for the vapor formation is much smaller than the time scale for the bouyancy driven motion that pulls the bubble away from the wall. The result is the formation of a mushroom shaped bubble. When Jacob number is decreased further, the frequency of bubble generation is decreased but amplitude of transient heat flux is increased. Three-dimensional simulations are carried out for two fluid layers of fluid at two different Grashof number and for only a cycle. These results show similar behavior as those of the two-dimensional ones. Research supported by NASA.

## Bubble Induced Drag Reduction

Experimentally it has been found that it is possible to reduce the friction drag of submerged bodies by the injection of a modest amount of air into the turbulent boundary layer. The mechanism by which bubbles reduce drag has, however, been essentially unknown. In this project, the effect of the bubbles on the wall-drag in a turbulent channel flow was examined by direct numerical simulations (DNS). A front-tracking/finite volume method was used to fully resolve all flow scales, including the bubbles and the flow around them, for bubbles injected near the walls in the so-called "minimum turbulent channel." The result showed that slightly deformable bubbles located near the walls can lead to a significant reduction of the wall drag. The mechanism for the drag reduction appears to be the suppression of streamwise vorticity as the bubbles passed over them, forcing mutual cancellation with wall bounded vortices of the opposite sign. Spherical bubbles, on the other hand, lead to a large increase in drag when they collide with the wall. The size of the bubbles was about fifty wall units, comparable to what is found in experiments where the bubbles are injected through the wall. The effect of the bubbles on the various averaged quantities describing the turbulent flow were also examined. Research supported by DARPA.

## Homogeneous Bubbly Flows

Direct numerical simulations have recently emerged as a viable tool to understand finite Reynolds number multiphase flows. The approach parallels direct numerical simulations of turbulent flows, but the unsteady motion of a deforming phase boundary add considerable complexity. Here, studies of flows containing many bubbles and drops are presented. The Navier-Stokes equations are solved by a finite difference/front tracking technique that allows the inclusion of fully deformable interfaces and surface tension, in addition to inertial and viscous effects. A parallel version of the method makes it possible to use large grids and resolve flows containing a few hundred bubbles. Simulations of the motion of two- and three-dimensional finite Reynolds number buoyant bubbles in a periodic domain have shown, for example, that finite Reynolds number effects are important even at O(1) Reynolds numbers, how the small scale structure changes as the Reynolds number is increased, and how the large scale evolution can by affected by a relatively small increase in the deformability of the bubbles. Research supported by ONR and NSF. More Information.

## Electrohydrodynamic Multiphase Flow

An electric field can induce both normal and tangential forces on a fluid interface and it is well known that depending on the ratio of the conductivities and the dielectric properties of the continuous and dispersed phase, drops will deform into a prolate or oblate shape. The deformation of a single drop has been examined both analytically and computationally and the interaction of two drops has been examined for two drops in zero Reynolds number flow. When electric fields are applied to a suspension of drops in a channel, the drops deform and the induced fluid motion can lead to strong interaction of the drops. Numerical simulations of finite Reynolds number droplet suspensions, using a front tracking method, are presented here. The results show that the droplet interactions enhance coalescence and can dramatically change the phase distribution. The dependency of the behavior on the governing parameters is discussed. Research supported by NASA.

## Atomization and Droplet Dynamics

Combustion of liquid fuels is the primary means of power generation for airplanes, as well as most land-based vehicles. To burn the liquid it is essential to break it up into as fine drops as possible to increase the surface area. Atomization is therefore a key element of successful combustion of liquid fuels. While major progress has been made in the modeling of sprays, the initial atomization, usually characterized as the primary breakup of jets and the secondary breakup of drops, remains poorly understood. Numerical simulations are now providing a new way to look at atomization, promising to unravel details that have been completely unavailable. By representing the governing physical laws on fine discrete grids, it is possible to reproduce many aspects of the atomization on computers. The complete computer generated record allows visualization and analysis of the processes that has not been possible before. Research supported by AFOSR and NSF.

## Computations of Solidification

Nearly all man-made metal products are in a liquid form at some point and then solidify in the manufacturing process. The formation of microstructure during solidification has a great influence on the final product properties. Dendritic microstructure results from undercooling of the melt and particularly common for binary alloys, where variable solute concentration can lead to localized constitutional undercooling. However, undercooling of a pure material can also lead to dendritic microstructure. The effect of melt metal flow on the microstructure has been studied extensively due to its importance. Experimental results shows that fluid flow can have significant impact on the growth of the microstructure. Research supported by NASA.

## Vortex-Based Large Eddy Simulations

A three dimensional vortex in cell method is presented to follow the unsteady motion of inviscid vortex sheets. The vortex sheet is described by a moving unstructured triangular grid, consisting of points connected by elements. Each triangular element carries three circulations on its edges. As the vortex sheet deforms, points and elements are added and deleted to maintain the resolution of the sheet. The method is validated by comparing the evolution of a starting jet with computations using an axisymmetric vortex blob method. The rapid increase in the area of the vortex sheet as the jet becomes fully three-dimensional requires excessive amount of elements and to allow long time computations, an algorithm that merges parallel elements is developed. In this way it is possible to control the number of surface elements required. Research supported by GRI.

Maintained by webmaster@wpi.eduLast modified: Jan 29, 2008, 05:29 EST