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The behaviour of second phase particles in molten steel processing vessels was investigated, using the E.S.Z. (Electric Sensing Zone) method, in conjunction with aqueous modelling and molten steel systems. / 1. Slag droplet entrainment/dispersion is an axisymmetric gas injection stirred system was investigated: A tank containing a water-olive oil simulation of stirred ladles of molten steel was used. Extensive numerical predictions of the oil (slag) droplet population distributions within the vessel were also carried out, and reasonable agreement with the experimental data achieved. Droplet dispersions were shown to be time and spatially dependent. / 2. Inclusion separation characteristics in tundishes of continuous steel casting operations were investigated. The mixed reactor model proved to be adequate for predicting particle separation behaviour, proved that the effective upper surface area of the dispersed plug flow region is known, a priori. / 3. An on-line method for the detection and measurement of inclusions in molten steel systems was developed. Inclusion removal rates within an induction furnace, as well as inclusion separation behaviour in a commercial scale tundish for continuous billet casting, were measured.

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A Fourier transform for a finite group G is an isomorphism from the complex group algebra CG to a direct product of complex matrix algebras, which are determined beforehand by the structure of G. Given such an isomorphism, naive application of that isomorphism to an arbitrary element of CG takes time proportional to |G|2. A fast Fourier transform for some (family of) groups is an algorithm which computes the Fourier transform of a group G of the family in less than O(|G|2) time, generally O(|G| log |G|) or O(|G|(log |G|)2). I describe the construction of a fast Fourier transform for the special linear groups SL(q) with q = 2n.

The present work was to study the population and chemicalcharacterization of the inclusions at different steps of thetool steel making process based on industrial trialexperiments. The inclusion populations were found to increasewith ladle age (number of heats ladle being used) beforealuminium deoxidation and before casting. A substantialincrease in inclusion population was noticed after a certainladle age. The analyses of the steel samples from thesolidified ingot revealed a non-uniform distribution ofinclusions. The inclusion populations in the final productswere also found to increase with the ladle age. Totally four types of inclusions, viz. Type-1 (MgO), Type-2(an oxide solution), Type-3 (spinel), and Type-4 (spinel in thecenter surrounded by the oxide solution of Type-2) wereobserved before deoxidation. Thermodynamic calculation revealedthat the Type-2 and Type-4 inclusions were generated by thereactions between EAF slag and ladle glaze. Three types ofinclusions were found before casting, viz. Type-6 (spinel inthe center surrounded by the oxide solution of Type-7), Type-7(oxide solution with low contents of MgO and SiO2), and Type-8 (small MgO islands embedded in anoxide solution). Inclusions of both Type-6 and Type-7 were theproducts of the reaction between inclusions of Type-3 and theliquid metal. On the other hand, the occurrence of pieces ofMgO having sharp edges in the oxide solution suggested that theType-8 inclusions were generated by the ladle glaze. In thesteel samples during mould fillings, totally three types ofinclusions namely, Type-6, Type-7, and Type-9 (alumina basedinclusions) were found. The Type-9 inclusions were originatedfrom the erosion of the nozzles and the closing gates duringthe mould filling. The steel samples after casting were foundto contain inclusions of Type-6, Type-7, Type-9, Type-10(alumina-silicate oxide solution), and Type-11 (spinel phasewith calcium sulphide). The types of inclusions were found tovary with the position in the ingot. In the final productsType-6, Type-7, and Type-11 inclusions were found. While almostall the inclusions in the final products were originated in theladle before casting, sulphur was detected in all types ofinclusions. The increase in the sulphur activity of the steelmelt during casting was the cause of the formation ofoxide-sulphide and calcium sulphide phases in the inclusionsdetected after casting and in the final products. A preliminary examination on the possibility of inclusionseparation by bubble floatation using cold models was alsocarried out. Deionised water and silicon oil were used as thebulk phase. Charcoal particles of different size ranges wereemployed as the dispersed phase. The examination of thecharcoal-water-gas system indicated that the positivefloatation coefficient was not a sufficient condition for theinclusion separation. The experimental results were found to bein contradiction with the prediction of a typical model thatconsiders interfacial energies. The omitting of the drag forcewas believed to be the reason causing the failure of the modelprediction in the charcoal-water-gas system. The failure of themodel prediction suggested a need of a new model taking intoaccount interfacial energies, drag force, buoyancy force andgravity force. <b>Key words:</b>non-metallic inclusions, ladle metallurgy,ladle glaze, inclusion population, ladle age, ingot casting,interfacial tension, inclusion separation

<p>The present work was to study the population and chemicalcharacterization of the inclusions at different steps of thetool steel making process based on industrial trialexperiments. The inclusion populations were found to increasewith ladle age (number of heats ladle being used) beforealuminium deoxidation and before casting. A substantialincrease in inclusion population was noticed after a certainladle age. The analyses of the steel samples from thesolidified ingot revealed a non-uniform distribution ofinclusions. The inclusion populations in the final productswere also found to increase with the ladle age.</p><p>Totally four types of inclusions, viz. Type-1 (MgO), Type-2(an oxide solution), Type-3 (spinel), and Type-4 (spinel in thecenter surrounded by the oxide solution of Type-2) wereobserved before deoxidation. Thermodynamic calculation revealedthat the Type-2 and Type-4 inclusions were generated by thereactions between EAF slag and ladle glaze. Three types ofinclusions were found before casting, viz. Type-6 (spinel inthe center surrounded by the oxide solution of Type-7), Type-7(oxide solution with low contents of MgO and SiO₂), and Type-8 (small MgO islands embedded in anoxide solution). Inclusions of both Type-6 and Type-7 were theproducts of the reaction between inclusions of Type-3 and theliquid metal. On the other hand, the occurrence of pieces ofMgO having sharp edges in the oxide solution suggested that theType-8 inclusions were generated by the ladle glaze. In thesteel samples during mould fillings, totally three types ofinclusions namely, Type-6, Type-7, and Type-9 (alumina basedinclusions) were found. The Type-9 inclusions were originatedfrom the erosion of the nozzles and the closing gates duringthe mould filling. The steel samples after casting were foundto contain inclusions of Type-6, Type-7, Type-9, Type-10(alumina-silicate oxide solution), and Type-11 (spinel phasewith calcium sulphide). The types of inclusions were found tovary with the position in the ingot. In the final productsType-6, Type-7, and Type-11 inclusions were found. While almostall the inclusions in the final products were originated in theladle before casting, sulphur was detected in all types ofinclusions. The increase in the sulphur activity of the steelmelt during casting was the cause of the formation ofoxide-sulphide and calcium sulphide phases in the inclusionsdetected after casting and in the final products.</p><p>A preliminary examination on the possibility of inclusionseparation by bubble floatation using cold models was alsocarried out. Deionised water and silicon oil were used as thebulk phase. Charcoal particles of different size ranges wereemployed as the dispersed phase. The examination of thecharcoal-water-gas system indicated that the positivefloatation coefficient was not a sufficient condition for theinclusion separation. The experimental results were found to bein contradiction with the prediction of a typical model thatconsiders interfacial energies. The omitting of the drag forcewas believed to be the reason causing the failure of the modelprediction in the charcoal-water-gas system. The failure of themodel prediction suggested a need of a new model taking intoaccount interfacial energies, drag force, buoyancy force andgravity force.</p><p><b>Key words:</b>non-metallic inclusions, ladle metallurgy,ladle glaze, inclusion population, ladle age, ingot casting,interfacial tension, inclusion separation</p>