# Current Research of Dr. Gretar Tryggvason

Dr. Tryggvason conducts his research in the Hessert Laboratory for Aerospace Research.

## Multiphase Flows

Multiphase flows are ubiquitous is Nature and industrial processes. Rain, breaking waves, sprays, bubbly flows, and boiling, are only a few examples. Accurately predicting the behavior of such flows is critical for the air-ocean exchange of heat and mass in climate modeling, for atomization and clean combustion of liquid fuels, for heat transfer in conventional and nuclear power plants, for selectivity in chemical reactions in bubble columns, and many other systems of immerse economic importance. In many cases the flow is well described by continuum theories (the Navier-Stokes equations) but the range of scales for the systems that we are interested in makes it impractical to compute the behavior of the full system using those equations. Numerical models of industrial scale systems generally rely on a multiscale approach where conservation equations are solved for the average or large scale dynamics of the system and closure models are used to account for unresolved processes. Developing closure models for the unresolved processes is central to multiphase flow research.

Direct Numerical Simulations, where fully resolved numerical simulations of systems that are small enough so that all continuum length and time-scales can be fully resolved, but large enough for non-trivial scale interactions to take place, are used to examine the dynamics of well-defined multiphase systems offer the best way to develop closure models for industrial models. My group has pioneered such studies over the last decade and a half and we have been able to contribute major new insights for a large number of specific multiphase flow problems. A significant fraction of our studies has been devoted to bubbly flows, where we have contributed to an understanding of how bubble interactions affect the dynamics of homogeneous bubbly flows, explained the structure of bubbly flows in laminar and turbulent flows in vertical channels, and explained how bubbles injected into a turbulent boundary layer can cause drag reduction, for example. We have also examined many aspects of instabilities and breakup of fluid-fluid interfaces, including the formation of drops, provided quantitative data for the collision of drops, explained the role of inertia in "shear-breakup" of drops, and for thermocapillary migration of many drops and droplet suspensions subject to electric fields we have found mechanisms leading to patterns formation. For other studies see my publication list.

## Numerical Methods for Complex Flows

In the early nineties my students and I developed one of the first computational method capable of accurately capturing the unsteady motion of multiphase flows where surface tension, inertia, and viscosity all must be accounted for. The method is based on explicitly following the fluid interface by identifying it by a connected set of marker points that are advected by the fluid velocity. The interface tracking algorithm is coupled with a relatively conventional Navier-Stokes solver on a regular, fixed, staggered grid. The method has been evolved and improved many times since its introduction, such as by improving the restructuring of the moving front as it is evolved with the flow and by new ways to find surface tension. It has also been extended in various ways to account for more complex physics, such as the addition of temperature and electric fields and phase change to simulate solidification and boiling.

The method has been implemented in several codes for 2D and 3D flows and newer versions of the codes include advanced advection methods and pressure solvers. A code for parallel computers was also developed several years ago. The codes, which have been distributed widely as FTC2D, FTCAXI, FTC3D, and FTC3D-PARALLEL, have been written to be simple, transparent, and easily modified, thus providing a foundation which can be extended by adding new physics and capabilities.

## Energy Studies

Multiphase flow is, of course, directly related to energy. I have, however, engaged in a few energy studies that have not involved multiphase flows. Those include GRI funded work done in collaboration with Prof. W.J.A. Dahm at the University of Michigan to develop methods for predicting flow and combustion in natural gas utility furnaces. The method consisted of a flow solver using a vortex sheet formulation and a flame sheet model for the combustion. The goal was to develop modeling capabilities that could help evaluate pollution mitigation strategies, with a particular focus on NO_x. This work eventually lead to the foundation of a small software/consulting company (NGB Technologies, Inc.) that for a few years had an office with a couple of employees.

I am currently involved in two NSF funded studies of wind energy, both in collaboration with Prof. D. Olinger at WPI. Both projects are geared at developing wind energy where the wind is blowing strongest. In the first project we are examining the dynamics of floating wind turbines. In addition to the wind generally blowing stronger far off shore, such installations generally have less visual impact than on-land or near shore wind turbines. Floating turbines have recently received considerable attention and Statoil in Norway deployed a prototype in the summer of 2010. Our focus is on developing fully validated computational methods to predict the dynamics of floating turbines in rough seas and allow testing of designs aimed at minimizing the motion and load on the structure.

In the second project we are examining the dynamics of tethered kites, used for the electricity generation. The motivation for considering kites is twofold. First of all, they allow us to harvest wind energy at high altitudes, where it is stronger. Secondly, it may be possible to keep the construction very simple and the cost low. Electricity generation by conventional methods is highly optimized, producing vast quantities of energy at incredibly low cost. Thus, cost is the single most important consideration for renewable energy. The systems that we are considering here---a tethered kite, driving a ground based generator---offers a very simple construction but posed significant control challenges. Here we plan to couple advanced control strategies with detailed numerical simulations of the unsteady flow around a moving kite.