Date of Graduation

1999

Document Type

Thesis

Degree Type

MS

Committee Chair

Ismail Celik

Abstract

Droplet formation is a common phenomenon in turbulent mixing and has many practical applications in emulsion technology, surface agents, and liquid-liquid extraction. The ability to predict the relative sizes and distributions of fluid droplets formed from mixing events is a complex problem which is dependent on many different parameters including geometric considerations, the nature and physical properties of the fluids in question, turbulence parameters, buoyancy and body forces, and flow history. While there have been many researchers who have analyzed this problem for both liquid-liquid and gasliquid systems, the present study will focus only on droplet formation in immiscible liquid-liquid systems. A review of the literature has shown that previous attempts at describing fluid droplet sizes essentially fall into two categories: (1) phenomenological models, and (2) statistical models. The use of phenomenological models usually involves semi-empirical analyses of a particular liquid-liquid or gas-liquid system, and typically employs a force balance to determine the conditions under which droplet formation or breakage occurs. Statistical models, on the other hand, utilize flow history and probability density functions (PDF’s) to determine the size and number distribution of daughter droplets formed from the splitting of larger droplets or the coalescence of smaller ones. In the present study we will adopt many of the methods of the former set of models, resulting in expressions which determine the sizes of the dispersed phase droplets based on local flow parameters including turbulence quantities, appropriate characteristic length scales, and dimensionless parameters such as the gradient Richardson number. While much of the development of the droplet formation/entrainment (DFE) model comes from results from the literature concerning stratified shear flows, the model can be calibrated through the adjustment of certain constants to conform to a wide variety of flow scenarios.

The present study is one element of a larger effort in cooperation with engineers and naval architects at the Naval Surface Warfare Center - Carderock Division (NSWC-CD) in Bethesda, Maryland, as well as faculty and students at Johns Hopkins University in Baltimore, Maryland, to study turbulent mixing events in compensated fuel/ballast tanks used in U.S. naval surface ships. The overall goal of this project at WVU is to develop sub-models for the prediction of the extent and location of mixing of fuel and water, and to estimate the total flow-through time for the fuel, as well as the amount of waterhideout. Water hideout involves the amount of water that remains inside the fuel tanks after refueling is complete (i.e. when the fuel stream reaches the outlet), and presents a concern with regard to efficiency. The fuel/water mixing, on the other hand, represents an environmental concern, as some of the fuel may become entrained in the compensating water that is forced overboard during refueling. The prediction of the size and distribution of the fuel droplets that form during mixing is an integral part of the overall effort, both for accurate predictions of mixing events, as well as in estimating the amount of fuel entrainment that occurs.

Numerical simulations have been performed at West Virginia University using the commercial CFD (Computational Fluid Dynamics) code, CFX-4, developed by AEA Technologies, to assess the performance of the droplet formation/entrainment model for several different flow configurations. These include a stratified shear flow of two immiscible fluids of different densities, and a densely buoyant vertical jet flow of a higher density fluid impinging on a quiescent layer of lighter fluid. The multiphase model used in these simulations was a single fluid, scalar transport (SFST) model, which is a mixture model based on Ishii's drift flux model [22]. The turbulence model used was a modified form of the standard k-e model that includes additional terms to account for the effects of buoyant production/destruction. Both of the flow scenarios in question closely match the conditions for experiments currently being performed at Johns Hopkins University by Dr. Joseph Katz and his associates. In this study, the results of the numerical simulations will be compared with qualitative observations from the experiments, as well as certain quantitative data collected with regard to the mixing length thickness in the case of the shear flow, and the maximum impingement depth in the case of the jet flow study. The results of these simulations indicate logical trends for the size and distribution of the fluid droplets formed, as well as good agreement between the DFE model and the results of the experiments detailed above.

Download

Share

COinS