A study of Reynolds-stress closure model

A hybrid model of the Reynolds stress closure was developed. This model was tested for various sizes of step flow, and the computed Reynolds stress behavior was compared with experimental data. The third order closure model was reviewed. Transport equations for the triple velocity correlation were developed and implemented in a numerical code to evaluate the behavior of the triple velocity products in various regions of the flow field including recirculating, reattaching, and redeveloping flow domains

Third-moment closure of turbulence for predictions of separating and reattaching shear flows: A study of Reynolds-stress closure model

A numerical study of computations in backward-facing steps with flow separation and reattachment, using the Reynolds stress closure is presented. The highlight of this study is the improvement of the Reynold-stress model (RSM) by modifying the diffusive transport of the Reynolds stresses through the formulation, solution and subsequent incorporation of the transport equations of the third moments, bar-u(i)u(j)u(k), into the turbulence model. The diffusive transport of the Reynolds stresses, represented by the gradients of the third moments, attains greater significance in recirculating flows. The third moments evaluated by the development and solution of the complete transport equations are superior to those obtained by existing algebraic correlations. A low-Reynolds number model for the transport equations of the third moments is developed and considerable improvement in the near-wall profiles of the third moments is observed. The values of the empirical constants utilized in the development of the model are recommended. The Reynolds-stress closure is consolidated by incorporating the equations of k and e, containing the modified diffusion coefficients, and the transport equations of the third moments into the Reynolds stress equations. Computational results obtained by the original k-e model, the original RSM and the consolidated and modified RSM are compared with experimental data. Overall improvement in the predictions is seen by consolidation of the RMS and a marked improvement in the profiles of bar-u(i)u(j)u(k) is obtained around the reattachment region

Numerical study of a separating and reattaching flow by using Reynolds-stress tubulence closure

The numerical study of the Reynolds-stress turbulence closure for separating, reattaching, recirculating and redeveloping flow is summarized. The calculations were made for two different closure models of pressure - strain correlation. The results were compared with the experimental data. Furthermore, these results were compared with the computations made by using the one layer and three layer treatment of k-epsilon turbulence model which were developed. Generally the computations by the Reynolds-stress model show better results than those by the k-epsilon model, in particular, some improvement was noticed in the redeveloping region of the separating and reattaching flow in a pipe with sudden expansion

Improvement of the second- and third-moment modeling of turbulence: A study of Reynolds-stress closure model

Four parts of the Reynolds-stress closure modeling are reported: (1) improvement of the k and epsilon equaitons; (2) development of the third-moment transport equation; (3) formulation of the diffusion coefficient of the momentum equation by using the algebraic-stress model of turbulence; and (4) the application of the Reynolds-stress model to a heat exchanger problem. It was demonstrated that the third-moment transport model improved the prediction of the triple-velocity products in the recirculating and reattaching flow regions in comparison with the existing algebraic models for the triple-velocity products. Optimum values for empirical coefficients are obtained for the prediction of the backward-facing step flows. A functional expression is derived for the coefficient of the momentum diffusion by employing the algebraic-stress model. The second-moment closure is applied to a heat transfer problem. The computations for the flow in a corrugated-wall channel show that the second-moment closure improves the prediction of the heat transfer rates by 30% over the k - epsilon model

Slag formation and control in electric furnace steel making

Because of their fusibility, low density, chemical activity and dissolving capacity, slags provide an effective means for separating impurities from liquid metal in steel making processes. As poor conductor of heat, slags also help to thermally insulate the bath

A Mathematical Description of the Thermodynamic Behaviour of Multi-Component Slag Systems with the use of Solution Species

For a better understanding and control of the chemistry of smelting processes, the importance of adequate descript-ion of the thermodynamic behaviour of slag, metal and matte solutions has been increasingly realized. In this regard, the concept of associated solution species has gained wide acceptance over the past two decades for its efficacy and flexibility in representing the properties of complex slag and matte solutions. This paper reviews the highlights of this approach and the author's experience in applying it for describing the thermodynamic properties of iron silicate slag systems wherein the hypothetical chemical species are considered to behave in a non-ideal manner. The activity coefficients of the solution species are described with the help of three-suffix Margules equations with zero ternary inter-actions which correspond, in the author's opinion, to a generalized form of the regular solution behaviour. Examp-les from the lime containing iron silicate quaternary and the nickel containing quinary and their subsystems are examined briefly

Thermodynamic Considerations in Metal Extraction

Chemical thermodynamics can be used to ascertain the feasibility of a given chemical reaction. It permits quantitative calculation to the state of equilibrium of a system. Conversely, the concepts of chemical equilibria can be used to find out conditions for making a desired reaction feasible

Smelting Technologies for Ferrochromium Production - Recent Trends

The conventional process for producing high carbon ferrochromium by smelting chromite ore in a submerged arc furnace is reviewed and its limitations highlighted with regard to (a) product quality through impurity removal, and (b) high power consumption for a given raw materials supply. The trends towards (i) utilization of medium grade ore fines by agglomeration, and (ii) pre-reduction of chromite ore prior to arc smelting are examined in terms of their effectiveness in accomplishing substantial savings in power consumption. A technoeconomic evaluation of the conventional smelting practice in the Indian context makes obvious the need for adopting improved technologies for better cost-competitiveness and survival in this era of economic liberalization

Thermodynamic Considerations in the production of Bulk Ferro Alloys (Fe-Mn, Fe-Cr and Fe-Si

The above mentioned ferro alloys are produced commercially by reduction smelting of their oxide minerals with, coke or charcoal in a submerged arc furnace and, to a lesser extent, by a metallic reductant such as aluminium. In general, the overall reduction reactions are highly endothermic, thus, requiring large thermal energy inputs. In this paper, the thermodynamic principles. underlining reduction smelting of oxides are discussed with the help of free energy-temperature (Ellingham), diagram with a focus on the role of direct reduction, the smelting temp-eratures required for a given oxide mineral, the thermal energy requirements, the suitability of carbon as redu-ctant, the alloy grade and inpurity levels, the slag- metal equilibria and the formation of carbides

A transport model of the turbulent scalar-velocity

Performance tests of the third-order turbulence closure for predictions of separating and recirculating flows in backward-facing steps were studied. Computations of the momentum and temperature fields in the flow domain being considered entail the solution of time-averaged transport equations containing the second-order turbulent fluctuating products. The triple products, which are responsible for the diffusive transport of the second-order products, attain greater significance in separating and reattaching flows. The computations are compared with several algebraic models and with the experimental data. The prediction was improved considerably, particularly in the separated shear layer. Computations are further made for the temperature-velocity double products and triple products. Finally, several advantages were observed in the usage of the transport equations for the evaluation of the turbulence triple products; one of the most important features is that the transport model can always take the effects of convection and diffusion into account in strong convective shear flows such as reattaching separated layers while conventional algebraic models cannot account for these effects in the evaluation of turbulence variables