Date of Award

2016

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences (PhD)

Administrative Home Department

Department of Mathematical Sciences

Advisor 1

Franz X. Tanner

Advisor 2

Kathleen A. Feigl

Committee Member 1

Zhengfu Xu

Committee Member 2

Song-Lin Yang

Abstract

Computational methods for the investigation of drop deformation, drop breakup and drop solidification are developed and implemented in the open source computing environment OpenFOAM® [63]. The goal of this research is to simulate these drop phenomena by resolving all the relevant time and length scales in order to obtain correlations and statistical information which then can be used in the modeling of dispersed multiphase flows such as sprays. The use of such models is central for the simulation of dispersed multiphase flows because present-day computational technology does not have the capacity to resolve millions of droplets, as is typically encountered in sprays.

There are three aspects to this thesis. Three types of simulations are performed. First, the two-phase flow solver, interFoam, is modified to allow for simulating a moving droplet in an external airflow within a fixed computational domain. The modified solver is then used for the modeling and simulation of deformation and breakup of drops in axisymmetric and three dimensional symmetric flows, and the results are utilized to validate drop deformation and breakup theories, and to derive statistical information for the product drop size distributions in the various flow regimes. The Taylor Analogy Breakup (TAB) model has been modified and this modified TAB model is also presented and validated.

Second, the feasibility and accuracy of calculating convective heat transfer coefficients using CFD is studied for two test cases: the flow between parallel flat plates and the flow past a cylinder. The feasibility and accuracy is demonstrated and achieved by comparing the results with the literature.

Third, for the investigation of the solidification of drops, an enhanced enthalpy- porosity model [6] is presented and implemented into OpenFOAM® to form a new solver, modPolyMeltFoam. Two test cases are used to validate the model and its implementation: the pure natural convection of water in a cavity and the solidification of water in a cavity. These tests show that the code performs very well comparing with results from the literature. The code is then coupled with the conjugate heat transfer solver, chtMultiRegionFoam, to create the solver modFluidFluidChtMultiRegionFoam which is able to simulate a stationary water droplet solidifying in a cold airflow. The results of the solidification studies are used to obtain correlations for the convective heat transfer coefficients, which in turn can be utilized in the modeling of freezing sprays where the solidification of millions of droplets needs to be described.

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