Vortex evolution and heat transfer enhancement in a quasi-two-dimensional magnetohydrodynamic duct flow

Abstract

The quest for cleaner, cheaper and reliable energy has motivated the development of magnetic confinement fusion reactor technology as a possible means of harnessing the energy produced by nuclear fusion for power generation. It is known that magnetohydrodynamic effects act to reduce the thermal-hydraulic performance of the duct flows within the cooling blankets by greatly increasing the pressure drop and reducing the heat transfer coefficient through Laminarisation of the flow. Despite the considerable efforts that have already been dedicated to the study of convective heat transfer in these flows, a further investigation for a more efficient and practical solution to the aforementioned issues is yet to be carried out. In this thesis, a numerical investigation of an electrically conducting fluid flowing in a heated duct under the influence of a strong magnetic field is presented. The major driving motivation of this work is to propose a better mechanism for improving convective heat transfer transversely from a hot wall into a cooler fluid flowing within the duct. The idea of heat-transfer enhancement from a duct wall is based on generating intensive vortices parallel to a magnetic field. As a prelude to the heat transfer analysis, the decay of these vortices has been quantified, whereby a vortex decay model has been proposed. The devised model describes the decay behaviour of the peak vorticity within stable wake vortices behind a circular cylinder under the influence of a strong magnetic field. Comparison with published data demonstrates remarkable consistency. The model suggests that the instantaneous spatial decay rate of vorticity is strongly dependent on friction parameter and Reynolds number at their higher and lower ranges, respectively. The model also proposes that far downstream, the vortex decay is mainly due to magnetic damping, where the decay rate asymptotes to the rate described by the Hartmann friction term, and that the viscous dissipation remain important only in the near wake. When the friction parameter is above the critical value, Hartman braking dominates the decay for the entire wake. Further analysis on the model also reveals that this critical friction parameter is dependent on Reynolds number and blockage ratio, and the dependency becomes more apparent at lower ranges of these parameters. However, these passively generated wake vortices tend to be suppressed by the strong magnetic damping. The potential of current injection to intensify these vortices is therefore explored. The derivation of an analytical solution of the electrical forcing velocity fields and the outcomes from the investigation are presented in Chapter 5. Electric current enters the flow through electrodes around the base of the cylinder, and radiates outward, imparting a rotational forcing around the electrode due to the Lorentz force. The results indicate that the employment of current injection as a vortex enhancer appears to be principally viable. The results indicate that the imposed magnetic field strength and current injection significantly alter the kinematic behaviour of the wake behind a cylinder. Spectral analysis of the response in the wake of the cylinder to the current injection revealed a distinct spectrum of cylinder lift coefficient in the unlock-in regime. A maximum Nusselt number improvement of almost twofold was observed, with a moderate additional pump power required to drive the flow in the presence of current injection (a maximum additional pressure drop of approximately 30% was recorded). Following this, the performance of electrically-driven vortex generator without the presence of the cylinder is then evaluated. The only source of vorticity that is responsible for the thinning of the thermal boundary layer is induced by the current injection. The aim is to investigate the sensitivity of the Nusselt number to the variations of the current injection parameters. Findings are presented in Chapter 6 and they revealed a gain in thermal-hydraulic performance over the case when the cylinder is present, particularly for cases with high current amplitude, long pulse widths, and strong magnetic field. This is likely due to the absence of the detrimental nonlinear interaction between the electrically generated vortices and the naturally shed vortices from the cylinder. The results also indicate a maximum pressure drop induced by the current injection of less than 2%, which is an order of magnitude less than the gain in pressure drop due to the employment of the current injection in the presence of a cylinder. Ultimately, this thesis has found that a perturbation system composed solely of electrically generated vorticity is far more effective for increasing heat transfer in high Hartmann number MHD duct flows than systems employing physical obstacles for vortex promotion.