Development and evaluation of lattice Boltzmann models for investigations of liquid break-up

Michael E McCracken, Purdue University

Abstract

In this work, lattice Boltzmann models are developed and evaluated for investigating the break-up of liquid jets. The lattice Boltzmann method (LBM) is a relatively new computational approach. It is based on the resolution of physics at a meso scopic level. At this level, the linkage between properties such as surface tension and intermolecular attraction is more readily represented. Furthermore, the governing equations of the LBM are linear and, when compared to the non-linear Navier-Stokes equations, their discretized formulation is easy to parallelize for use on massively parallel computers. In the first part of this work, an existing lattice Boltzmann method is assessed for accuracy through a series of increasingly complex studies. Single-phase Couette flow, channel flow, and flow in a lid-driven cavity are studied. The computed results from these calculations are all within a few percentage points of their corresponding analytical solutions. The two-phase problems of oscillating liquid cylinders and capillary waves are also studied and results are found to agree within 10% of analytical solutions. A hybrid numerical method is proposed and evaluated, during this initial phase of the work, and it produces, over a large range of physical parameters, more accurate results than conventional numerical methods. Initial work on liquid jet break-up shows that current lattice Boltzmann methods are inherently viscous due to numerical instabilities that occur at lower viscosities. Novel planar and axisymmetric, two-phase, multiple relaxation time (MRT) models are proposed to overcome this limitation. The models have several relaxation parameters, which can be adjusted to enhance numerical stability. These models are evaluated by studying oscillating liquid cylinders, capillary waves, and oscillating ellipsoids, and the results agree within 6% of analytical solutions. Two novel single-phase binary fluid lattice Boltzmann methods are developed and evaluated to simulate two fluids with different molecular weights. Simulations of Rayleigh jet break-up are presented, and the predictions are shown to agree within 10% of analytical and experimental results. Studies of two-phase planar and axisymmetric mixing layers and liquid jets, which show liquid break-up, are discussed.

Degree

Ph.D.

Advisors

Abraham, Purdue University.

Subject Area

Mechanical engineering

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