عنوان

Kavitasyon çökmesiyle oluşan, yerçekimi etkisindeki serbest yüzeyli akışların asimtotik davranışı

Number

TL58124

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Kavitasyon çökmesiyle oluşan, yerçekimi etkisindeki serbest yüzeyli akışların asimtotik davranışı

General Material Designation

[Thesis]

First Statement of Responsibility

Fetahu, Elona

Subsequent Statement of Responsibility

Yılmaz, Oğuz

Name of Publisher, Distributor, etc.

Izmir Institute of Technology (Turkey)

Date of Publication, Distribution, etc.

2020

Text of Note

90 p.

Dissertation or thesis details and type of degree

Ph.D.

Body granting the degree

Izmir Institute of Technology (Turkey)

Text preceding or following the note

2020

Text of Note

In this thesis, the gravity driven potential flows that result from cavity collapse are studied. Initially, the collapse of a vertical cylindrical cavity of circular cross sections surrounded by a liquid region is examined for two different situations. In the first one the cavity has same depth as the fluid and in the second one the cavity starts from the free surface and has less depth than the fluid. The problem is formulated by using a small parameter that represents the short duration of the stage. The first problem, as the radius and the centre of the cavity approach infinity, reduces to the classical two-dimensional dam break problem solved by Korobkin and Yilmaz (2009). The singularity of the radial velocity at the bottom circle is shown to be of logarithmic type. In the second problem, where the cavity is less deep than the fluid, the flow region is separated into two regions: the interior one, which is underneath the cylindrical cavity and above the rigid bottom, and the exterior one, which is the rest of the flow. The corresponding new problems are solved separately and then the coefficients are found by applying the matching conditions at the interface, where the fluid radial velocities and pressures coincide. On the limiting case, the problem reduces to the two-dimensional dam break flow of two immiscible fluids by Yilmaz et al. (2013a). Singularity at the bottom circle of the cavity is observed, which is of the same type as in the latter paper. Next, a third problem studies the gravity driven flow caused by the collapse of a rectangular section of a vertical plate. During the early stage, the flow is described by the velocity potential. Attention is paid to determining the velocity potential and free surface shapes. The solution follows the Fourier series method in Renzi and Dias (2013) and the boundary element method in Yilmaz et al. (2013a). Singularity is observed at the side edges and lower edge of the rectangular section. The horizontal velocity of the initially vertical free surface along the vertical line of symmetry of the rectangle is the same to the one in the two-dimensional problem Korobkin and Yilmaz (2009). The singularities observed in these problems lead to the jet formation for the initial stage. The methods applied in these computations are expected to be helpful in the analysis of gravity-driven flow free surface shapes. This thesis is a contribution towards the 3-D generalizations of dam break problems.

Subject Term

Mathematics

Fetahu, Elona

Yılmaz, Oğuz

Izmir Institute of Technology (Turkey)

Electronic name

p

[Thesis]

276903

a

Y