Topological fluid dynamics for free and viscous surfaces
Başlık çevirisi mevcut değil.
- Tez No: 402382
- Danışmanlar: PROF. MORTEN BRONS
- Tez Türü: Doktora
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2015
- Dil: İngilizce
- Üniversite: Technical University of Denmark
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Matematik ve Fen Bilimleri Eğitimi Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 204
Özet
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Özet (Çeviri)
In an incompressible fluid flow, streamline patterns and their bifurcations are in-vestigated close to wall for two-dimensional system and close to free and viscous surfaces in three-dimensional system. Expanding the velocity field in a Taylor series, we conduct a local analysis at the given expansion point. Applying the boundary conditions, some relations are obtained among the coefficients of the expansions. Series of coordinate transformations, which preserves the boundary conditions, are used to reduce the number of coefEcients. Finally, using the normal form and unfolding theory, the velocity field is analysed structurally and bifurcation diagrams are obtained. First, two-dimensional viscous flow close to wall for non-simple degenerate crit-ical point is considered depending on three-parameter space. Second, three-dimensional axisymmetric, viscous and steady flow is analysed close to free and viscous surfaces into three situations: Local analysis close to center axis; away from the axis and close to a stationary wall. Next, in the absence of axisymmet-ric condition, three-dimensional viscous flow is consider close to a free surface. As an application of the bifurcation diagrams for three-dimensional axisymmet-ric viscous flow, three different shaped container driven by a rotating top disk is considered. Using a spectral collocation method, a code is constructed to obtain the meridional and swirl velocities. In a result of this code, ali structural changes on the streamline patterns are observed and the occurring bifurcations are determined. These bifurcations are compared with the bifurcations obtained from topologically.
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