Mass transfer between solid and liquid in a gas-stirred vessel
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INTRODUCTION
MASS transfer between solid and liquid is an essential and integral feature of many pyrometallurgical operations carried out in metallurgical furnaces, ladles, etc. As examples of this, processes such as alloying and powder injection can be readily visualized. The large size of metallurgical reactors (i.e., today’s refining and holding vessels often contain as much as 500 tonnes of hot metal) coupled with the high intensity of agitation (e.g., large specific gas flows associated with near sonic velocities are often applied to stir melts) often preclude low Reynolds number flows in metal processing units. Thus, many investigations carried out so far[1–8] have indicated that in typical material processing operations, the intensity of turbulence is very often appreciable, and therefore, classical correlations for translatory flows are insufficient to realistically connect the hydrodynamic phenomena to transport rates. This, reproduced from the work of Taniguchi et al.,[2] is illustrated in Figure 1. There, the classical Ranz–Marshall correlation[9] is seen to underestimate heat transfer rates of ice spheres in an aqueous gas bubble driven system by about 40 to 50 pct. Consequently, to simulate the melting phenomena realistically, Taniguchi et al.[2] considered a modified version of the Ranz–Marshall correlation applicable to the turbulent flow situation.[6] AMARENDRA K. SINGH, Scientist, is with the Tata Research, Development and Design Centre, Pune, Maharashtra, 411001 India. DIPAK MAZUMDAR, Professor, is with the Department of Materials and Metallurgical Engineering, Indian Institute of Technology, Kanpur, UP, 208016 India. Manuscript submitted December 20, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS B
In turbulent metal processing operations, the combined influence of flow and turbulence on heat and mass transfer is generally well recognized, and accordingly, several new transport correlations have been proposed in recent years. A summary of these is presented in Table I. In developing or adapting[1,2,8] these correlations to infer melting and/or dissolution rates, practically in all the studies[1,4,8] reported to date, theoretically estimated velocity and turbulence kinetic energy fields were embodied in the various dimensionless groups, viz., Reloc,r, Ret, Tu, etc. (the List of Symbols provides explanation). To this end, while Szekely et al.[3] as well as Mazumdar et al.[4] applied a computational procedure based on the numerical solution of turbulent Navier–Stokes equations, Taniguchi et al.[2] and Koria[8] applied a macroscopic energy balance. No attempt has yet been made to assess the predictive capabilities of these correlations with reference to experimentally determined flow and turbulence kinetic energy fields. This is of concern since numerical simulation of flow phenomena is known to provide only approximate distributions of the turbulence characteristics (k, ε, mt, etc.) in gas bubble driven systems.[10,11,12] The purpose of the present work, consequently, has been to ass
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