Ph.D. Theses
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Browsing Ph.D. Theses by Author "Atalık, Salim Kunt."
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Item A deterministic approach to transition to turbulance in plane shear flows(Thesis (Ph.D.)- Bogazici University. Institute for Graduate Studies in Science and Engineering, 1999., 1999.) Atalık, Salim Kunt.; Tezel, Akın.In this work, a parametrical study of the transition to turbulence in two-dimensional shear flows has been conducted. For this purpose, the solutions of the full two-dimensional Navier-Stokes equations have been investigated numerically using spectral methods. In parallel, a new spectral integration algorithm, called the Nonlinear Galerkin Method, stemming from dynamical systems theory and developed for the integration of dissipative evolution equations such as Navier-Stokes equations, has been tested and applied for the study cases. Different nonlinear Galerkin methods have been compared for this purpose with respect to each other in terms of convergence and efficiency and the improvements on the classical Galerkin spectral method have been shown numerically. Transition to turbulence has been analyzed by the parametrical investigation of qualitatively different solutions in the phase space of two-dimensional Navier-Stokes equations for bounded and unbounded shear flows with one nonhomogeneous direction. The applications were plane channel (Poiseuille) flow and oscillatory plane Poiseuille flow for the bounded flow case, and temporally growing mixing layer and plane jet flows for the unbounded flow case. With this work, we aim to contribute to the enlightening of the structure of the phase space of two-dimensional Navier-Stokes equations as well as to the testing of a new integration algorithm which seems to be promising in the direct numerical simulation of Navier-Stokes equations.Item Numerical analysis of surface-driven non-isothermal viscoelastic flow(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2010., 2010.) Kaptan, Yalın.; Ecder, Ali.; Atalık, Salim Kunt.The numerical investigations of the moving edge non-isothermal viscoelastic flows are simulated by using two example problems (lid driven cavity (LDC) and rotating disc in a cylindrical enclosure (RDCE) flows) in this study. The viscoelastic behavior of the fluids is modeled by adopting three differential constitutive relations namely Upper Convected Maxwell (UCM), Oldroyd B and Giesekus models. The comparisons reveal that the Giesekus model is the most realistic one and the maximum Weissenberg number limit is higher compared to the others. Two separate solvers are used in the simulations; PETSc and IN-GMRES solvers. PETSc code is used as a solver for the Newtonian flows and a benchmark tool for the Krylov subspace methods and preconditioners. PETSc analyses reveal that BiCGStab with ILU(5) preconditioning is the most effective solver in the simulations of the Newtonian flows. IN-GMRES solver is used to simulate the non-isothermal viscoelastic flows and it is based on the matrix free preconditioned inexact Newton-Krylov methods. To obtain higher Weissenberg number limits in the simulations, the numerical tools such as the continuation, the upwind differencing scheme, the higher order discretization schemes, the slanted stencils and similar others are implemented in the IN-GMRES algorithm. In the non-isothermal part of the study, besides the advection and diffusion, the viscous dissipation is also included and it is understood that the viscous dissipation is very important in simulations of non-Newtonian flows. The viscosity is modeled as temperature dependent by adopting the approximate Arrhenius formulation and it is realized that the viscosity changes can alter the flow field. The effects of the Reynolds number, the Weissenberg number, the Prandtl number, the Brinkman number, aspect ratio and some of the material parameters are documented within this study.Item Numerical investigation of isothermal and non-isothermal viscoelastic flow in lid-driven polar cavity(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2012., 2012.) Mercan, Hatice.; Atalık, Salim Kunt.The isothermal and non-isothermal viscoelastic ow of Phan-Thien-Tanner (PTT) uids is considered in lid-driven polar cavity geometry, with stationary and oscillatory lid motion, using a numerical solution method with parameter continuation technique. Thermoelastic e ects, in terms of elastic/elongational e ects and viscous dissipation, are demonstrated by the changes in vortical structure, temperature/stress distributions and heat transfer characteristics in the curved cavity. Central vortex location shifts are observed under elastic and elongational (strain hardening and strain softening/shear thinning) e ects for isothermal and non-isothermal conditions. The growth in size and strength of a secondary vortex is denoted in the downstream stationary corner of the cavity for the viscoelastic uid under strain hardening e ects which also introduce an increase in stress gradients. Decrease in both stress values and their gradients are observed under viscous dissipation. The changes in temperature eld and heat transfer properties are revealed. The oscillatory response of the viscoelastic Phan-Thien-Tanner model for isothermal and non-isothermal cases is examined. The Fourier transform rheology technique is used to understand the frequency spectrum of the response. The results are shown as phase diagrams and Fourier spectrums of the time variations of the shear stress, rst normal stress di erence, and dimensionless Nusselt modulus, which is an indication of the heat transfer rate.