RBF solution of MHD stokes flow and MHD flow in a constricted enclosure

This paper presents the radial basis function (RBF) approximation for the numerical solution of Stokes and Navier-Stokes equations in a constricted enclosure under the effect of magnetic field with different orientations. RBFs are used for the approximation of the particular solution which becomes also the approximate solution of the problem satisfying the boundary conditions. Numerical results are obtained for several values of Hartmann number and constriction ratio. As the strength of the horizontally applied magnetic field increases, Stokes flow extends covering the whole pipe. Applied magnetic field in the pipe-axis direction generates the electric potential exhibiting behavior similar to streamlines. When the constriction ratio increases, flow squeezes through the left wall regardless of the direction of the magnetic field.Publisher's Versio

MAGNETOHİDRODİNAMİK KANAL AKIŞLARININ KARŞILIKLI SINIR ELEMANLARI METODU İLE ÇÖZÜMÜ

In the thesis, four different MHD duct flow problems are solved by using the Dual Reciprocity Boundary Element Method (DRBEM) with the suitable boundary conditions according to the physics of the problem. The two-dimensional, steady or unsteady, fully-developed MHD flow of a viscous, incompressible and electrically conducting fluid is considered in a long pipe of rectangular cross-section (duct) under the effect of an externally applied magnetic field which is either uniform or time-dependent or axially changing. The inductionless MHD flow with temperature dependent viscosity and heat transfer is the first considered problem. In this problem, the induced magnetic field is neglected due to the small magnetic Reynolds number assumption. Secondly, the MHD duct flow under a time-varied external magnetic field is studied. Then, we turn our concern to MHD flow problems under an axial-dependent magnetic field varying in the streamwise direction (pipe-axis direction) in the third and the fourth problems. Specifically, the inductionless MHD flow with electric potential is considered under the effect of the axially-changing magnetic field as the third problem. Adding the induced magnetic field to the velocity and electric potential equations as a triple is the last MHD flow problem considered in the thesis. The parametrix BEM implementation is also presented for the solution of the variable coefficient convection-diffusion type equations. The influence of the magnetic fields on the MHD flows is investigated and simulated in terms of the velocity, temperature, induced magnetic field and electric potential contours for several values of physical parameters.Bu tezde, dört farklı Magnetohidrodinamik (MHD) kanal akış problemi, problemin fiziğine göre uygun sınır koşulları ile birlikte karşılıklı sınır elemanları metodu (DRBEM) kullanılarak çözülmüştür. Viskoz, sıkıştırılamaz ve elektrik ileten sıvının dikdörtgen kesitli bir kanal içerisindeki iki boyutlu, zamana bağlı veya zamandan bağımsız tam gelişmiş akışı dışarıdan uygulanan bir manyetik alan etkisinde incelenmiştir. Akışı etkileyen manyetik alan ya tek düzedir ya zamana bağlıdır ya da eksenel olarak değişmektedir. Ele alınan ilk problem, sıcaklığa bağlı viskoziteye ve ısı transferine sahip indüksiyonsuz MHD akışıdır. Bu problemde, indüklenen manyetik alan küçük manyetik Reynolds sayısı varsayımından dolayı ihmal edilmiştir. İkinci problem olarak, dışarıdan uygulanan ve zamana bağlı manyetik alan etkisindeki MHD akış çalışılmıştır. Daha sonra ise, üçüncü ve dördüncü problem olarak akım yönündeki eksen boyunca değişen bir manyetik alan etkisindeki MHD akış problemleri çözülmüştür. Üçüncü problemdeki MHD akışı elektrik potansiyeline sahip fakat indüksiyonsuz bir akıştır. Dördüncü problemde ise üçüncü problemdeki MHD akışa indüklenen manyetik alan eklenerek problem denklemleri hız, elektrik potansiyel ve indüklenen manyetik alan olarak üçlü çözülmüştür. Değişken katsayılı konveksiyon-difüzyon tipi denklemlerin çözümü için parametre sınır elemanı metodu (parametrix BEM) da kullanılmıştır. Uygulanan manyetik alanların MHD akışlarına etkisi, çeşitli fiziksel problem parametre değerleri için hız, sıcaklık, indüklenen manyetik alan ve elektrik potansiyeli açısından incelenmiş ve simülasyonları yapılmıştır.Ph.D. - Doctoral Progra

Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), 10-11 July 2017, Nottingham Conference Centre, Nottingham Trent University

This book contains the abstracts and papers presented at the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), held at Nottingham Trent University in July 2017. The work presented at the conference, and published in this volume, demonstrates the wide range of work that is being carried out in the UK, as well as from further afield

Isogeometric finite element methods for liquid metal magnetohydrodynamics

A fusion blanket is a key component in a fusion reactor which extracts heat energy, protects the surrounding structure and possibly produces tritium, one of the fuels required for the deuterium-tritium fusion reaction. Interest in magneto-hydrodynamic (MHD) effects in the fusion blanket has been growing due to the promising prospect of a liquid breeder blanket, due to its high power density and the possibility of sustainable production of tritium. However, MHD effects can significantly influence the operating performance of the fusion blanket and an accurate and reliable analysis of the MHD effects are critical in its design. Significant progress in the numerical study of MHD has been made recently, due in large part to the advancement in computing power. However, its maturity has not yet reached a point comparable with standard CFD solvers. In particular, complex domains and complex externally applied magnetic fields present additional challenges for numerical schemes in MHD. For that reason, the application of isogeometric analysis is considered in this thesis. Isogeometric Analysis (IGA) is a new class of numerical method which integrates Computer Aided Design (CAD) into Finite Element Analysis (FEA). In IGA, B-splines and NURBS, which are the building blocks used to construct a geometry in CAD, are also used to build the finite element spaces. This allows to represent geometries more accurately, and in some cases exactly. This may help advance the progress of numerical studies of MHD effects, not only in fusion blanket scenarios, but more widely. In this thesis, we develop and study a number of types of IGA based MHD solver; a fully-developed MHD flow solver, a steady-state MHD solver and a time-dependent MHD solver. These solvers are validated using analytical methods and methods of manufactured solution and are compared with other numerical schemes on a number of benchmark problems.Open Acces