Browsing by Author "Orhan, Mehmet."

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    Numerical investigation of convective-diffusive transport using the smoothed particle hydrodynamics technique
    (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2012., 2012.) Danış, Mustafa Engin.; Ecder, Ali.; Orhan, Mehmet.
    In this thesis, Incompressible Smoothed Particle Hydrodynamics (ISPH) technique is implemented to analyze various convective-diffusive transport problems numerically. First of all, a brief summary of applications and developments in SPH is given. Then, SPH methodology is presented. A detailed discussion on frequently used high order SPH approximation schemes is made and an expansion of existing projection methods developed for isothermal flow to non-isothermal and double-diffusive flows is introduced. The code developed during this thesis study is validated for isothermal problems such as lid-driven cavity and vortex spin-down. Furthermore, in order to test the upper limit of accuracy of SPH computations, a grid-based ISPH approach is proposed. Grid-based ISPH is applied to natural convection in a square cavity problem and the results are compared to the data available in the literature. Similar to gridbased ISPH code, meshless ISPH code is used to solve natural convection problems. Rayleigh-B́enard convection is studied and multiple states of the solutions are obtained. Moreover, natural convection is investigated at the onset of instability in which multicellular and oscillatory flow patterns are observed. Apart from natural convection, ISPH code also introduced to double-diffusive transport problems. In terms of doublediffusion, ISPH performance in aiding and opposing flows are provided. Furthermore, ISPH code is also implemented to two-phase flows. In the context of two-phase flows, topological changes of the interfaces and Rayleigh-Taylor instability problems are simulated. ISPH results for two-phase flow are compared to results obtained by Level Set Method.
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    Numerical investigation of high Knudsen number flow in rectangular enclosures
    (Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2006., 2006.) Orhan, Mehmet.; Ecder, Ali.; Tezel, Akın.
    Nowadays, enlightening unknown aspects of rarefied gas flow is one of the critical issues of fluid dynamic research to ensure correct and proper operations of manyMicro- Electro-Mechanical-Systems (MEMS). Thermally driven motion of rarefied gases is gaining in importance to develop Knudsen compressors having better performance or to improve single crystal growth processes. Therefore, accurate prediction of the physics lying behind the thermal creep in the transition regime as well as slip flow regime is one of the main motivations of this study. The other emphasis is possible flow instability of the rarefied gases in enclosures. For this purpose, an asymptotic approximation has been performed in the first part of the study to find analytical solutions. In the second one, linear disturbance theory of hydrodynamic stability has been applied to the problem to determine bounds of instabilities. Analytical solutions of two-dimensional stability analysis have been introduced. Critical states have been identified for different models and for varying Knudsen numbers. More generally, eigen-spectrum of the perturbation equations has been identified in three-dimensions. At the last part, by applications of an artificial viscosity scheme, a computer program has been constructed to solve Burnett and also Navier-Stokes equations. Mechanisms of the thermal creep flow have also been verified by inspecting stress tensors of Burnett equations. Most importantly, the insufficiency and the failure of Navier-Stokes equations for the creeping flows have been proved. Moreover, it has been shown that Burnett equations can correctly model such creeping flows.