Eğrisel bir bölgede Stokes akış probleminin analitik çözümü
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Date
2019
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Publisher
Aksaray Üniversitesi Fen Bilimleri Enstitüsü
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info:eu-repo/semantics/openAccess
Abstract
Bu tez çalışmasında endüstrinin birçok alanında kullanılan bazı kavite akış problemlerinden bazıları ele alındı. Dikdörtgensel, sektörel ve eğrisel bölgelerde iki boyutlu Stokes akış problemlerinin analitik çözümü verildi. Tez beş bölümden oluşmakta olup birinci bölümde tez çalışmasında kullanılacak temel kavramlar, denklemler ve tanımlar verildi. İkinci bölümde, bir ya da iki duvarının hareketli ve karşılıklı yan duvarların birer serbest yüzey olduğu dikdörtgensel bölgedeki akış probleminin çözümü analiz edildi. Üçüncü bölümde kapalı dikdörtgensel bölgedeki Stokes akış probleminin analitik çözüm mekanizması verildi. Dördüncü bölümde ise eğrisel bir bölgedeki akışı yöneten kısmi diferansiyel denklem verilen sınır koşulları altında çözüldü. Böylece eğrisel bir bölgedeki akış hareketi için bilgiler elde edildi. Beşinci ve son bölümde elde edilen bulgular ve öneriler verildi.
In this study, some of cavity flow problems which are used in many areas of the industry are discussed. Two-dimensional Stokes flow in rectangular, sectorial and curved shaped cavity are considered. The thesis consists of five sections. In the first section, general concepts, equations and definitions which will be used in thesis, are introduced. In the second section, flow structures are analyzed in a rectangular cavity formed by a pair free surface and one or two moving lids. In the third section, analytical solution mechanism of Stokes flow problem in a closed rectangular region is given. In the fourth section, the governing partial differential equations for the flow in a curved region were solved under given boundary conditions. Thus, information was obtained for flow movement in a curved region. In the fifth and last section, the conclusions and recommendations were given.
In this study, some of cavity flow problems which are used in many areas of the industry are discussed. Two-dimensional Stokes flow in rectangular, sectorial and curved shaped cavity are considered. The thesis consists of five sections. In the first section, general concepts, equations and definitions which will be used in thesis, are introduced. In the second section, flow structures are analyzed in a rectangular cavity formed by a pair free surface and one or two moving lids. In the third section, analytical solution mechanism of Stokes flow problem in a closed rectangular region is given. In the fourth section, the governing partial differential equations for the flow in a curved region were solved under given boundary conditions. Thus, information was obtained for flow movement in a curved region. In the fifth and last section, the conclusions and recommendations were given.
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Keywords
Stokes Akış, Akış Fonksiyonu, Analitik Çözüm, Kavite Biortagonallik, Stokes Flow, Stream Function, Analytical Solution, Cavity, Biorthogonality
