The use of shrouded supersonic jets for enhancing the performance of top blown metallurgical reactors has been studied using BOF pilot scale facilities set up in the MMPC's water modelling laboratory. The experimental results for three different designs of shrouded supersonic jet nozzles have demonstrated that greater depths of penetration and reduced mixing times can be achieved with co-axial sub and supersonic jets flow. Dimensional analysis indicates that the depth of penetration of a gas jet into a liquid bath depends on the height, H, of the lance tip from the quiescent bath, the liquid's Froude, Reynolds and Weber numbers, reflecting the ratios of gravity, viscous and surface tension forces to the jet's inertial, or momentum, forces. Good agreement between the mathematical model and experiments were obtained in terms of predicted and observed depths of penetration. Further efforts have been made to study jet penetration into liquid metals. The effects of density of liquid metal and a wide range of gas flow rates on the penetration depth were investigated theoretically. The results confirm that jet penetration depth can be increased with increasing shroud gas flow rate and decreased bath density.

After making the laboratory approximation of small magnetic Reynolds number, the steady, axisymmetric and purely azimuthal velocity profile that in principle can be generated in an incompressible viscous electrically conducting fluid contained in a fixed infinitely long circular cylinder by a magnetic field transverse to the cylinder axis and uniformly rotating with low frequency is subjected to infinitesimal axisymmetric perturbations. The principle of the exchange of stabilities is assumed to hold and the marginal-stability problem becomes a sixth-order eigenvalue problem involving the magnetic Taylor number and the axial wavenumber. An asymptotic analysis, based on the assumption that the magnetic Taylor number is large, and using solutions of the comparison equation d6y/dz6 = zy, is presented in order to obtain first approximations to the neutral-stability curves of the first and second eigenmodes, and compared with the results of direct numerical integration. It is found that at the onset of instability the secondary motions have a multi-cell structure, the motions in the region, near the cylinder wall, of adversely distributed angular momentum driving through weak viscous action the cells in the interior.

Experiments have demonstrated that a d-c voltage applied across a thermally stabilized plane layer of dielectric liquid can induce both stationary and oscillatory instabilities and thereby significantly augment heat transfer. While a unipolar charge injection model can explain both types of instability, the predictions of a conductivity model depend crucially upon the way the electrical conductivity varies with temperature. Here a conductivity model is derived from a dissociation and recombination model in an Ohmic limit, and its linear instabilities for linear, quadratic, and Arrhenius-type conductivity variations are investigated numerically. Oscillatory instability is usually predicted and an energy argument rules out stationary instability for the type of conductivity variation observed experimentally. This casts doubts on the experimental relevance of earlier quadratic conductivity models predicting stationary instability. The relative merits of conductivity and charge injection models are discussed in the light of empirical evidence.

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The nonlinear stability of a thermally stabilized horizontal plane layer of dielectric liquid subjected to unipolar charge injection at a voltage near the linear instability threshold is investigated using a normal-mode cascade analysis valid for small perturbation amplitudes. In this first analysis, the primary mode is chosen to be a system of parallel rolls whose amplitude varies aperiodically with time. The branching behaviour at the critical voltage is found to reflect the distinction, apparent in the linear instability problem, between an essentially isothermal space-charge instability and an instability dominated by the effects of an ion mobility varying with temperature. The effect of motion on heat and charge transfer through the system is also considered. Furthermore, in certain cases it appears that overstability is the preferred form of linear instability.