Title page for ETD etd-11102010-201447

Type of Document

Dissertation

Author

Wang, Yaohong

Author's Email Address

yw03c@fsu.edu

URN

etd-11102010-201447

Title

Numerical Methods For Two-Phase Jet Flow

Degree

Doctor of Philosophy

Department

Mathematics, Department of

Advisory Committee

Advisor Name	Title
Mark Sussman	Committee Chair
Brian Ewald	Committee Member
Jack Quine	Committee Member
Xiaoming Wang	Committee Member
Farrukh S. Alvi	University Representative

Keywords

linear stability analysis
level set
volume constraint
jet flow

Date of Defense

2010-10-27

Availability

unrestricted

Abstract

Two numerical methods are developed and analyzed for studying two-phase jet flows. The first numerical method solves the eigenvalue problem for the matrix system that is constructed from the pseudo-spectral discretization of the 3D linearized, incompressible, perturbed Navier-Stokes (N-S) equations for two-phase flows. This first numerical method will be denoted as LSA for “linear stability analysis.” The second numerical method solves the 3D (nonlinear) N-S equations for incompressible, two-phase flows. The second numerical method will be denoted as DNS for “direct numerical simulation.” In this thesis, predictions of jet-stability using the LSA method are compared with the predictions using DNS. Researchers have not previously compared LSA with DNS for the co-flowing two-phase jet problem. Researchers have only recently validated LSA with DNS for the simpler Rayleigh-Capillary stability problem [77] [20] [103] [26]. In this thesis, a DNS method has been developed for cylindrical coordinate systems. Researchers have not previously simulated 3D, two-phase, jet flow, in cylindrical coordinate systems. The numerical predictions for jet flow are compared: (1) LSA with DNS (2) DNS-CLSVOF with DNS-LS, and (3) 3D rectangular with 3D cylindrical. “DNS-CLSVOF” denotes the coupled level set and volume-of-fluid method for computing solutions to incompressible two-phase flows [99]. “DNS-LS” denotes a novel hybrid level set and volume constraint method for simulating incompressible two-phase flows [89]. The following discoveries have been made in this thesis: (1) the DNS-CLSVOF method and the DNS-LS method both converge under grid refinement to the same results for predicting the break-up of a liquid jet before and after break-up; (2) computing jet break-up in 3D cylindrical coordinate systems is more efficient than computing jet breakup in 3D rectangular coordinate systems; and (3) the LSA method agrees with the DNS method for the initial growth of instabilities (comparison method made for classical Rayleigh-Capillary problem and co-flowing jet problem). It is found that for the classical Rayleigh-Capillary stability problem, the LSA prediction differs from the DNS prediction at later times.

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