Computational simulation of buoyancy-driven flows using vortex methods
Egan, Erik Witmer
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https://hdl.handle.net/2142/20972
Description
Title
Computational simulation of buoyancy-driven flows using vortex methods
Author(s)
Egan, Erik Witmer
Issue Date
1989
Doctoral Committee Chair(s)
Higdon, Jonathan J.L.
Department of Study
Chemical and Biomolecular Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Physics, Fluid and Plasma
Language
eng
Abstract
A new vortex method for simulating two-dimensional buoyancy-driven flows is presented. This Lagrangian method utilizes a discrete representation of the known density field along with the vorticity transport equation and Boussinesq approximation to yield the baroclinically-generated vorticity field, also in a discrete form. The corresponding velocity field is then computed using a vorticity-streamfunction scheme similar to the vortex-in-cell approach. Complete simulations for a variety of Rayleigh-Taylor stability problems are presented, as are preliminary results for Rayleigh-Bernard flows.
The discrete vorticity field is made up of vertically-oriented vortex dipole markers. The mutual interactions among these markers are determined by redistributing the dipolar marker vorticity onto a fixed array of true vortices. Standard vortex-in-cell techniques can then be used to generate marker velocities. The vorticity redistribution step is accomplished by matching the far-field velocity of a single dipole marker to that generated by the local grid vortices. The overall simulation method is termed the Dipole-in-Cell approach. Viscous and thermal diffusion effects (for Rayleigh-Benard flows only) are described using a random walk scheme.
"Rayleigh-Taylor simulations for both single- and double-interface geometries show the expected linear and nonlinear flow development, including the recirculation associated with the Kelvin-Helmholtz interfacial instability. The double-interface results show the development of an ""anti-spike"" along the top interface, as seen in other studies. The simulations are also shown to be capable of following the impact of a mass of fluid on solid boundaries and pools of stagnant fluid."
The Rayleigh-Benard results demonstrate the validity of the random walk mechanism for simulating diffusion and the ability to generate rough representations of the classic Benard convection cells. The accuracy of the Benard cell results is limited by the long computation times required to reach steady state for small Rayleigh numbers. For the large Rayleigh number flows of greatest interest, no such problems will occur and the method should be well suited to simulating them. Suggestions are made for method improvements, including extensions to three-dimensional flow problems.
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