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Short Time Behaviour of Dam Break Flow Involving Two Liquids
(Izmir Institute of Technology, 2018) Isıdıcı Demirel, Damla; Yılmaz, Oğuz
The two dimensional dam break problem for wet bed case is investigated. The leading order and the second order problem are stated in nondimensional form. Solution to the leading order problem by using three different methods is given and explained in detail. Both Fourier series method and Galerkin method have difficulties on its own because of the singularity at the triple point. Although the singularity is ignored in Galerkin method, the method does not work except for the interface. Thus conformal mapping techniques is preferred because of the convenience and the strength of the complex analysis. The velocity profiles at whole boundary are obtained by using this conformal mapping. The second order solution of velocities are also obtained by using the same conformal mapping. On the other hand, the domain decomposition method (DDM) is applied for the second order dam break problem of dry bed case. The leading order solution helped to determine the suitable parameters for DDM. The leading order and second order solution of the free surfaces give a more realistic shape using the Lagrangian solution at the upper corner point. We assume this work contains useful and applicable methods in it for gravity driven flows and it will wake up different perspectives in readers mind.
Vortex Dynamics in Domains Whith Boundaries
(Izmir Institute of Technology, 2011) Tülü, Serdar; Yılmaz, Oğuz
In this thesis we consider the following problems: 1) The problem of fluid advection excited by point vortices in the presence of stationary cylinders (we also add a uniform flow to the systems). 2) The problem of motion of one vortex (or vortices) around cylinder(s). We also investigate integrable and chaotic cases of motion of two vortices around an oscillating cylinder in the presence of a uniform flow. In the fluid advection problems Milne-Thomson's Circle theorem and an analyticalnumerical solution in the form of an infinite power series are used to determine flow fields and the forces on the cylinder(s) are calculated by the Blasius theorem. In the "two vortices-one cylinder" case we generalize the problem by adding independent circulation k0 around the cylinder itself. We then write the conditions for force to be zero on the cylinder. The Hamiltonian for motion of two vortices in the case with no uniform flow and stationary cylinder is constructed and reduced. Also constant Hamiltonian (energy) curves are plotted when the system is shown to be integrable according to Liouville's definition. By adding uniform flow to the system and by allowing the cylinder to vibrate, we model the natural vibration of the cylinder in the flow field, which has applications in ocean engineering involving tethers or pipelines in a flow field. We conclude that in the chaotic case, forces on the cylinder may be considerably larger than those on the integrable case depending on the initial positions of the vortices, and that complex phenomena such as chaotic capture and escape occur when the initial positions lie in a certain region.

Phd Degree / Doktora

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