Convection in fluid overlying porous layer : an application to Hall-Heroult cell

Finite-element method is used to predict the buoyancy-driven convection in a horizontal layer of fluid (aluminum melt) overlying a porous layer (cathode) saturated with the same fluid. This work aims to compare the Hall–Héroult process in electrolytic cell, where a layer of molten aluminum is reduced over the porous cathode surface. In this study, the physical system of the aluminum melt (fluid) and cathode (porous) together is considered as a composite system of fluid overlying porous layer. The main objective of this study to analyse the velocity components in thin fluid layer and its impact on a porous cathode surface if there is any. In addition, an externally imposed time-independent uniform magnetic field is used to analyse its influence on natural convective forces. The physical system of fluid overlying porous layer is analysed at different Hartmann, Darcy, and fluid-Rayleigh numbers for a fixed Prandtl number (Pr = 0.014). The predicted data show that the convective forces, caused by buoyancy-driven flow, are significant. It is shown that the velocity peaks moves toward the solid wall because of the presence of a magnetic field creating a stronger boundary-layer growth over the permeable cathode surface. The predicted results are plotted in terms of average Nusselt number and Darcy number to indicate the influence of pores and permeability on overall convective heat-transfer characteristics.

Mixing layer oscillations for a submerged horizontal wall-jet

Measurements of the horizontal velocity component were made for a horizontal wall-jet emanating from a submerged sluice gate forming one side of a large flow compartment. The existence of large-scale vortex structures was quantified by spectral analysis of the velocity measurements taken at various distances from the floor of the flow compartment, for different measurement stations from the jet exit. Close to the jet exit, the spectra of the velocity measurements within the potential core exhibit multiple peaks. Further downstream, the spectra are more defined and peak at the same frequency, irrespective of whether the measurements were made within the potential core or the mixing layer. The spectral peak corresponds to the passage frequency of large-scale vortex structures. Downstream of the potential core, the peak frequencies of the velocity spectra increase as the measurement location was moved towards the floor of the flow compartment. The increase in peak frequencies is attributed to fluctuations associated with the wall boundary layer. Predictions of the mixing layer instabilities were made using linear stability analysis. The predictions are in good agreement with the observed vortex shedding frequencies in the mixing layer