|Ph.D Thesis||Department of Mechanical Engineering|
|Supervisor:||Prof. Oron Alexander|
|Full Thesis text|
The nonlinear dynamics of an axisymmetric liquid film falling on the outer surface of a vertical, either static or harmonically oscillating in the axial direction, cylinder is investigated. Two corresponding dynamical mathematical models are derived. Using the energy-integral method we derive a set of two coupled partial differential nonlinear evolution equations which constitute a first-order in terms of a small film parameter approximation to the original hydrodynamic equations in the unforced case. Using the Galerkin method a set of two coupled partial differential nonlinear evolution equations is derived to incorporate the boundary condition imparted by the oscillating cylinder.
We carry out the linear stability analysis of the axially uniform axisymmetric flow of a liquid film in the framework of the evolution equations for the two derived models. The results of the linear theory are compared to experiments and to several other relevant linear stability theories available in literature.
Traveling wave solutions of the evolution equations in the case of a static cylinder are investigated numerically using AUTO-software and are favorably compared to experiments and other nonlinear theories describing the dynamics of falling films on a vertical cylinder. A bifurcation structure, both subcritical and supercritical of traveling wave flows is studied for the cases of fluids with both low and relatively large Kapitza number.
Analysis of the time-dependent equations in the case of a static cylinder reveals the existence of both periodic TW and aperiodic non-stationary wave (NSW) flows, and coexistence of flows of the same wavelength consisting of a varying number of drops in the wave shape. Primary and secondary instabilities of bifurcation branches are numerically investigated.
The film evolution, as described by the temporally modulated equations, yields quasiperiodic tori and several kinds of strange attractors: ranging from coherent to fully irregular. It is shown that periodic parametric excitation with the natural forcing frequency affects the spatial topological structure of the interfacial waves and may modify its type. Time-periodic excitation of films falling on a cylinder is found to result in a significant decrease of the wave amplitude in various parameter domains.