• Citer

Stability and Transition in MHD Pipe Flows

par Velizhanina, Yelyzaveta
Président du jury Rongy, Laurence
Promoteur Knaepen, Bernard
Publication Non publié, 2024-09-26

Thèse de doctorat

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

The phenomena associated with laminar-turbulent transition in magnetohydrodynamic (MHD) flows are important for both theoretical understanding and practical applications. The electromagnetic effects can dramatically alter the stability the flow by introducing additional damping, as well as inducing flow instabilities. In this dissertation, we examine the stability of two types of canonical MHD flows: liquid-metal MHD pipe flow with a uniform transverse magnetic field and axisymmetric MHD flow in cylindrical geometry with a helical magnetic field.In contrast to its non-magnetic counterpart, liquid-metal flow in a circular pipe with transverse magnetic field lacks axial symmetry and is characterized by the presence of thin boundary layers and, in some regimes, sidewall regions of velocity overspeed with inflection points. Here, we address the problem of laminar-turbulent transition in this flow. Our study consists of two stages. First, we conduct a linear modal stability analysis of MHD pipe flow. Upon exploring a wide range of flow parameters, we demonstrate that a sufficiently strong magnetic field may render the flow linearly unstable to three-dimensional disturbances in the presence of an electrically conducting wall. We further investigate the nature and characteristics of the most unstable mode and find that they vary significantly with the wall conductance ratio. The global critical Reynolds number of 45 230 occurs for a perfectly conducting pipe wall and a Hartmann number of 19.7.In the second stage of our study, we consider the influence of a transverse magnetic field on the transient growth of perturbations in MHD pipe flow. The analysis is performed for Reynolds numbers of 5 000 and 10 000, close to the subcritical transitional regime for moderate Hartmann numbers. Aside from a slight modification of hydrodynamic optimal perturbations at low Hartmann numbers, we observe three other characteristic topologies of optimal perturbations depending on the intensity of the magnetic field. Their growth mechanisms differ, with the lift-up effect dominating at low Hartmann numbers and the Orr-mechanism becoming increasingly important as the magnetic field intensity is increased. We conclude our study by addressing the nonlinear evolution of optimal perturbations, illustrating their nonlinear growth and eventual breakdown to a sustained turbulent state or the return of the system to a laminar state.A third question we address in this thesis concerns the formulation of the MHD linear stability equations in general axisymmetric geometries. We propose a novel velocity-vorticity formulation that applies for example to the historically important MHD Taylor-Couette flow--the flow of an electrically conducting fluid between two concentric rotating cylinders subject to an axial, azimuthal or helical magnetic field. Our formulation generally resembles the classical Orr-Sommerfeld-Squire problem, is valid also for finite magnetic Reynolds numbers, and can be easily adapted to a circular pipe geometry with coordinate singularity.