| Περίληψη: | Τhe aim of the present thesis is to study and compare algorithms for both hydrodynamic and magnetohydrodynamic incompressible internal flows. The study of magnetohydrodynamics is one of the most complicated fields of fluid dynamics because it is governed not only by the laws of classical fluid mechanics, but also of electromagnetism. That alone makes the flow equations more complicated and greater in number. It is obvious, then, that in order for a scientist to model and study a problem like this, there is a need of efficient computational power and deep understanding of the natural laws that govern the flow.
The first half of the thesis deals with the calculation of the incompressible hydrodynamic flows and the comparison of the well established PISO pressure-velocity coupling algorithm with the IPOT algorithm. The IPOT method has been used successfully in the past for calculating both external and internal flow problems, but with the disadvantage that oscillations are generated in the flowfield due to the method. In the present thesis the Rhie-Chow interpolation has been successfully implemented in the algorithm in order to address the previous problem. It will be shown that not only the IPOT method with the Rhie-Chow interpolation produces accurate ρesults, but it converges faster that the PISO algorithm.
The second half of the present thesis studies the engineering application of the magnetohydrodynamic flow of a conductive fluid through both a two and three dimensional channel. Once the specific boundary and initial conditions of the problem are set, the results for the axial velocity, the pressure drop and the induced magnetic field are presented for the cases of electrically insulating and conducting pipe walls, for a wide range of the parameters of the flow. The flow is considered laminar and the results correspond to developing flow. The results show that when the Hartmann number is increased, the axial velocity changes throughout the cross section, whereas the pressure drop increases along the pipe. The conductivity of the wall increases dramatically the pressure drop and the induced magnetic field, which can have a great effect on certain technological applications.
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