In our everyday life, turbulence is an omnipresent phenomenon and yet remains poorly understood. Its random and chaotic nature makes it a subject almost impossible to treat from the mathematical point of view and, at present, there
is no real prospect of a simple analytic theory. Scientists have therefore regarded the numerical simulation as an alternative to compute the relevant properties of turbulent flows. In this context, our thesis aims at developing and using accurate computational methods, namely pseudo-spectral methods, for studying hydrodynamic (1st part) and magnetohydrodynamic (2nd part) turbulence.
In the hydrodynamic part, Chapter I introduces the governing equations of fluid mechanics as well as the main issues related to the numerical study of turbulent flows. In particular, the Direct Numerical Simulations (DNS) of turbulence, in which accurate numerical solutions of the Navier-Stokes equations are obtained, are shown to be limited to moderately turbulent flows.
Chapter II introduces the Large Eddy Simulation (LES) technique which aims at simulating highly turbulent flows and which is based on a separation of scales.
In practice, it consists of simulating the large - resolved - scales of the flow explicitly while modelling the small - unresolved - scales. Two different approaches for modelling the kinetic energy of the unresolved scales are proposed and their respective advantages and drawbacks are discussed.
Chapter III is devoted the study of the mixing-layer using both DNS and LES. It consists of an inhomogeneous turbulent flow which has been studied experimentally and for which well-documented measurements are available. A highly accurate DNS mimicking the same experiment has been produced. It allows to study the inhomogeneity and anisotropy properties of this flow. Also, LES of the same flow, using different models, have been evaluated. In Chapter IV, we explore a pseudo-spectral method to investigate turbulence in a pipe. In this case, the method has to take into account two additional difficulties: i) the presence of the boundary and ii) the axis singularity. We detail how to circumvent these issues.
The second part of the thesis is devoted to magnetohydrodynamic (MHD) turbulence. It concerns phenomena where electrically conducting flows interact with electromagnetism and for which governing equations are derived in Chapter V. In Chapter VI, a detailed analysis of the energy transfers between the magnetic and velocity fields is performed thanks to a high resolution database of homogeneous MHD turbulence. It provides some insights to understand the physics of the nonlinear interactions and is also a valuable diagnostic in the framework of LES modelling. Finally, the inhomogeneous configuration studied in Chapter III has been extended to MHD. Several statistics related to the kinetic and magnetic energies are measured and LES of this flow are performed and presented in Chapter VII.
| Identifer | oai:union.ndltd.org:BICfB/oai:ulb.ac.be:ETDULB:ULBetd-12022004-110536 |
| Date | 23 December 2004 |
| Creators | Debliquy, Olivier |
| Contributors | Carati, Daniele, Weyssow, Boris, Degrez, Gérard, Knaepen, Bernard, Mareschal, Michel, Sagaut, Pierre, Winckelmans, Grégoire, Malek-Mansour, Mohammad-Ali |
| Publisher | Universite Libre de Bruxelles |
| Source Sets | Bibliothèque interuniversitaire de la Communauté française de Belgique |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://theses.ulb.ac.be/ETD-db/collection/available/ULBetd-12022004-110536/ |
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