A fundamental mathematical model of the flow field and surface deformation caused by an impinging jet in a top blown reactor has been developed. The results have been validated against water model experiments. More specifically, the predicted penetration depth has been found to agree well with surface deformation measurements and predictions using analytical equations. Furthermore, the predictions of the location of a vortex have been found to agree fairly well with PIV measurements. Calculations were also done to compare the widely used standard k-e model against the realizable extension of the standard k-e model to calculate the turbulent conditions of the flow. It was found that the penetration depth caused by the impinging jet on the liquid surface is relatively unaffected by the choice of turbulence model employed. However, when the main re-circulation loop in the bath was investigated there was a clear distinction in the flow fields produced when the two different turbulence models were used.

A novel mathematical model of gas injection in the AOD converter process has been developed. The model is based on fundamental transport equations and includes separate solutions of both the steel and the gas phases and their coupling by friction. The inlet boundary conditions at the nozzle are predicted using a separate fundamental mathematical model of an AOD nozzle. This approach, together with the two phase solution, avoids the need to guess the inlet boundary conditions. The predicted gas plume has been compared to a plume from a scaled down water model of an AOD nozzle in a qualitative manner. The plume shapes are very similar, which indicates that the model predictions are of the right order of magnitude. The AOD model has also been used to predict fluid flow patterns, turbulence characteristics and bubble diameters.KEY WORDS: AOD; modeling; steel; fluid flow; gas injection; two-phase; CFD; simulation; nozzle.Finally, the results from the comparison of the predicted and experimentally determined gas plumes as well as other model predictions are presented and discussed. Theoretical Model Mathematical Formulation of the AOD ConverterThe mathematical model of gas injection in an AOD converter is three-dimensional (3-D) and accounts for both the steel and gas phases. The calculation domain is described using non-linear coordinates, i.e. so called Body Fitted Coordinates (BFC). The fluid flow model is based on the following assumptions: ∑ The AOD converter is calculated using only a half a 3-D BFC grid due to symmetry along the middle plane. ∑ The free surface is frictionless and flat. The gas bubbles are allowed to leave the domain through the surface. ∑ The gas bubbles are introduced through a nozzle located in the side of the wall. The gas flow rate is 13.75 Nm 3 /min. ∑ The injected gas adopts the steel temperature momentarily. ∑ An interface-friction coefficient is used to describe the force between the gas phase and the steel phase. ∑ The transport equations for the enthalpies of the gas and steel are not solved. Therefore, the steel temperature is set to 1 873 K during the calculation period. ∑ No reactions or slag is accounted for. Transport Equations General EquationsBased on the above mentioned assumptions the following equations are solved in the three-dimensional two-phase fluid flow model of gas injection in the AOD converter:∑ Mass conservation for both the steel and gas phases. ∑ Conservation of momentum for x, y and z directions, both for the steel and the gas phases. Frictional Forces between the Gas and Steel PhasesThe friction forces cause the transfer of momentum from the slower moving steel phase to the faster moving gas phase. The friction force per unit volume that the steel exerts upon the gas at the interface is given by:........... (1) where C D is the drag coefficient for a spherical gas bubble, a g is the gas fraction, a l is the steel fraction, r l is the steel density, x rel, i is the absolute value of relative velocity difference between the gas and steel phase in the i-axis dire...

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The primary energy consumption and greenhouse gas emissions from nickel smelting products have been assessed through case studies using a process model based on mass and energy balance. The required primary energy for producing nickel metal, nickel oxide, ferronickel, and nickel pig iron is 174 GJ/t alloy (174 GJ/t contained Ni), 369 GJ/t alloy (485 GJ/t contained Ni), 110 GJ/t alloy (309 GJ/t contained Ni), and 60 GJ/t alloy (598 GJ/t contained Ni), respectively. Furthermore, the associated GHG emissions are 14 tCO2-eq/t alloy (14 tCO2-eq/t contained Ni), 30 t CO2-eq/t alloy (40 t CO2-eq/t contained Ni), 6 t CO2-eq/t alloy (18 t CO2-eq/t contained Ni), and 7 t CO2-eq/t alloy (69 t CO2-eq/t contained Ni). A possible carbon emission reduction can be observed by comparing ore type, ore grade, and electricity source, as well as allocation strategy. The suggested process model overcomes the limitation of a conventional life cycle assessment study which considers the process as a ‘black box’ and allows for an identification of further possibilities to implement sustainable nickel production.

Fig. 12.Predicted radial steel velocity at the surface at different steel heights during the mold filling. Data are given for the reference case and the three cases with swirl blade at 250, 500 and 750 mm distance to the inlet, for the velocity of 1 m/s. The radial velocity for the flared inlet is also shown.

With increasingly more stringent requirements on steel quality and productivity in uphill teeming production, it is vital to attain more desirable fluid flow conditions in the filling of the mould. In this investigation, physical and mathematical modelling was carried out to study the effects of nozzle type and utilization of a swirl generator in the inlet nozzle on the flow pattern in the ingot mould during the initial filling period. Specific focus was on the effects on the resultant hump and axial velocities. Three cases were considered: 1) a straight nozzle, 2) a divergent nozzle, and 3) a divergent nozzle combined with a swirl generator. It was found that usage of the divergent nozzle, compared to the straight nozzle, resulted in a smaller hump and lower axial velocities in the bath. For the combination of divergent nozzle and swirl generator, these findings were even more pronounced, with the hump practically eliminated, and the axial velocities, as well as the turbulence at the meniscus, significantly lower. The findings of the study suggest that a divergent nozzle combined with a swirling flow generated in the nozzle could be used in the up‐hill teeming process in purpose to get calmer initial filling conditions.

3/s and 800 cm 3 /s as well as bath heights ranging from 106 to 314 mm. The mixing times were also calculated based on an expression involving the Strouhal and Reynolds numbers. The experimentally determined mixing times were found to be within Ϯ20 % of the theoretical values, which is considered to be good in physical modelling. Overall, the mixing time was found to be influenced by the gas flow rate and the vessel diameter, but not by the bath height.KEY WORDS: physical modeling; mixing time; converter; side-blown; conductivity measurements. 663© 2010 ISIJ used to simulate steel and air to simulate argon/oxygen. The gas flow rates were determined by using the Froude number to scale the rate from a full scale converter to a physical model.The different flow rates were calculated by using the Froude number similarity criteria: (2) where r g is the density of air, Q g is the gas flow rate, r l is the density of water, g is the gravitational constant and d i is the nozzle inner diameter. In addition the following Froude number was used to scale the gas flow rate: Equation (3) was used to scale the gas flow rate, compared to a real converter. When this is determined, Eq. (2) was used to scale the size of the nozzle. The size of the nozzle was determined to be 3.2 mm for the smaller physical model. From experience it was determined that the nozzle size has a very small influence on the mixing time in the same manner as observed in a bottom blown bath. The mixing time is mainly governed by the gas flow rate, although the penetration depth of bubbles in the horizontal direction is affected by the nozzle size as well as the gas flow rate. Thus, the same nozzle was used in the larger physical model.A mass flow controller was used to regulate the gas flow rate during the experiments. Also, a conductivity probe was used to measure the change in conductivity. The probe was placed 30 mm from the bottom of the bath and near the side wall, as illustrated in Fig. 1. The output of the probe was fed to a conductivity meter and provided a 0 to 1 V DC output to a computer interface. In addition, the fluid flow was fully developed before the tracer injection of the KCl-solution was made. The solution had a concentration of 1 M KCl, and the amount added was 1 mL solution per 1 000 mL of liquid in the bath. Furthermore, the injection was made by a syringe close to the wall of the vessel. The conductivity of the bath was measured with an interval of 100 ms.The experimental mixing time was defined as the period required for instantaneous tracer concentration to settle within Ϯ5 % deviation around the final tracer concentration in the bath. Results and DiscussionExperiments were done using two vessel diameters of 200 mm and 300 mm, respectively. In addition, experiments were done for bath heights varying from 106 to 314 mm.Air was injected at the bottom of a side wall, as illustrated in Fig. 1. Flow rates between 30 cm 3 /s and 800 cm 3 /s were tested during the trials. Based on Eq. (2) the inner diameter of the side nozzle was determi...

A mathematical model of gas injection in the AOD converter process has been developed by augmentation of an earlier developed three-dimensional two-phase model to the slag phase and an industrial relevant geometry including six nozzles. The model is based on fundamental transport equations and includes separate solution of the steel and the gas phases and their coupling by friction as well as the slag phase. The 3D 3-phase (steel, slag, and gas) AOD model has been used to predict fluid flow, turbulence, and bubble characteristics as well as fluid-slag dispersion. In addition, two different gas flow rates have been simulated which resulted in quite different flow pattern. This new findings opens up for future investigations of gas-metal reactions in the AOD converter, which are of key interest from an industrial point of view.