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Title: A high order Discontinuous Galerkin - Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes for simulating cross-flow turbines
Author: Ferrer, Esteban
ISNI:       0000 0004 2738 8033
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2012
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This thesis details the development, verification and validation of an unsteady unstructured high order (≥ 3) h/p Discontinuous Galerkin - Fourier solver for the incompressible Navier-Stokes equations on static and rotating meshes in two and three dimensions. This general purpose solver is used to provide insight into cross-flow (wind or tidal) turbine physical phenomena. Simulation of this type of turbine for renewable energy generation needs to account for the rotational motion of the blades with respect to the fixed environment. This rotational motion implies azimuthal changes in blade aero/hydro-dynamics that result in complex flow phenomena such as stalled flows, vortex shedding and blade-vortex interactions. Simulation of these flow features necessitates the use of a high order code exhibiting low numerical errors. This thesis presents the development of such a high order solver, which has been conceived and implemented from scratch by the author during his doctoral work. To account for the relative mesh motion, the incompressible Navier-Stokes equations are written in arbitrary Lagrangian-Eulerian form and a non-conformal Discontinuous Galerkin (DG) formulation (i.e. Symmetric Interior Penalty Galerkin) is used for spatial discretisation. The DG method, together with a novel sliding mesh technique, allows direct linking of rotating and static meshes through the numerical fluxes. This technique shows spectral accuracy and no degradation of temporal convergence rates if rotational motion is applied to a region of the mesh. In addition, analytical mappings are introduced to account for curved external boundaries representing circular shapes and NACA foils. To simulate 3D flows, the 2D DG solver is parallelised and extended using Fourier series. This extension allows for laminar and turbulent regimes to be simulated through Direct Numerical Simulation and Large Eddy Simulation (LES) type approaches. Two LES methodologies are proposed. Various 2D and 3D cases are presented for laminar and turbulent regimes. Among others, solutions for: Stokes flows, the Taylor vortex problem, flows around square and circular cylinders, flows around static and rotating NACA foils and flows through rotating cross-flow turbines, are presented.
Supervisor: Houlsby, Guy T. ; Willden, Richard H. J. Sponsor: John Fell Fund Oxford University Press
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Engineering & allied sciences ; Aerodynamics and heat transfer ; Aeronautical research ; Civil engineering ; Dynamics and ocean and coastal engieneering ; Mathematical modeling (engineering) ; Ocean and coastal engineering ; Applications and algorithms ; Computing ; Program development and tools ; Physical Sciences ; Partial differential equations ; Numerical analysis ; Fluid mechanics (mathematics) ; Functional analysis (mathematics) ; Computer science (mathematics) ; Mathematics ; Mathematics ; High order discontinuous Galerkin ; Incompressible Navier-Stokes ; sliding meshes ; cross-flow turbines (wind and tidal turbines) ; turbulence ; Large Eddy Simulation (LES) ; Direct Numerical Simulation (DNS) ; Arbitrary Lagrangian-Eulerian