APPLICATION OF THE COMBINED REACTORS METHOD FOR ANALYSIS OF STEELMAKING PROCESS

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1 APPLICATION OF THE COMBINED REACTORS METHOD FOR ANALYSIS OF STEELMAKING PROCESS Simon N. Lekakh and D. G. C. Robertson Missouri University of Science and Technology, 14 N. Bishop, Rolla, MO 6549 Keywords: Steelmaking, Ladle metallurgy, Ar-mixing, Melt flow, Combined reactors Abstract A new integrated CFD-combined reactors approach is proposed for the description of processes in metallurgical vessels. CFD simulations were used to obtain the melt flow pattern in the vessels (ladle, tundish, and continuous caster mold). From these simulations, the characteristic curves were derived: (i) the residence time distribution curves (RTD) for flow-through systems (at tundish exit or at dendrite coherency surface in the mold) and (ii) the mixing curves for closed systems (ladle). In the next step, the melt flow was represented in a combined reactors system consisting of a combination of unit reactors (Plug Flow, Mixer, and Recirculated Volume). An inverse simulation was used to define the volumes of the reactor units and the melt flow rates between them by fitting to the characteristic curves from both methods (CFD and combined reactors). The suggested approach is demonstrated for multiple designs of Ar-stirred ladles, tundish, and SEN. This methodology can be used to enhance traditional post-processing CFD analysis and also as a tool for on-line process control. Introduction Physical modeling and CFD simulation of liquid metal processing are both carried out in order to achieve several major objectives, which can be classified into three levels: Level 1: to understand the process, for example, the melt flow pattern, inclusion separation, and refining (chemical reaction) kinetics in metallurgical vessels; Level 2: to optimize existing and design new processes and equipment, for example, to optimize the dam and weir geometry of an industrial tundish; Level 3: to control the entire steelmaking process on-line, when several models need to be integrated in a fast-working algorithm, communicating with sensors and process control devices. Knowledge of the melt flow phenomena is essential to meet these objectives. A broad review of the methods used to understand the nature of melt flow in the ladle, the tundish, and the mold (Level 1) can be found elsewhere [1-3]. For example, CFD simulations are used for visualization of melt flow; however this method alone is not effective in achieving Level 2 objectives and very complicated and time-consuming for on-line process control (Level 3 objectives). The combined reactors (CR) method was originally developed by Levenspiel [4] to analyze continuous chemical engineering processes as a set of interconnected unit reactors such as Continuous- Stirred-Tank Reactor (Mixer) and Plug Flow Reactor (PF). By solving the mass conservation equations, the flow can be characterized in the terms of the residence-time distribution (RTD) for continuous processes. The RTD curve in an actual process or simulations is obtained by short time dye injection into the in-flow stream and measuring the dye concentration in the out-flow stream. The combined reactors method was used by Sahai and Emi [5] for description of melt

2 Melt flow Inclusion separation Refining Optimization New design Process control flow in a continuous casting tundish. The capabilities of different methods to solve different objective levels are ranked as high (H), low (L) or not applicable (N) in Table 1. Table 1. Ranking the capabilities of the different methods Objectives Methods Levels CFD + CR H H H H H H Combined Reactors (CR) N N H L L N CFD simulation H H L H H L Physical modeling H H L L L N Industrial measurements H H H L L N In this paper, a new approach to analyze processes in metallurgical vessels is developed. The suggested method is based on CFD modeling of general melt flow in the real 3D-metallurgical vessel followed by inverse simulations using a virtual architecture of combined reactors to achieve a good match between the CFD and the CR characteristic curves (RTD or Mixing) by varying the volume of the unit reactors and the flow rates between them. This approach has a high capability to solve the different objectives shown in Table 1 and can combine high complexity with short simulation time (Figure 1). Figure 1. Complexity of methods versus simulation time. Combined reactor design based on inverse optimization CFD FLUENT 12. software [6] was used to solve 3-dimensional transient multiphase turbulent melt flow in a ladle with bottom Ar-plugs, tundish, and mold. Species transport was included to allow the derivation of the characteristic curves. A strategy of combined reactors (CR) design is suggested below for the achievement of a reasonable similarity between the CFD simulated

3 characteristic curves with the characteristic curves from CR models. To represent the melt flow patterns, the CR architectures consist of combination of one plug flow reactor and two or three mixers, each loop-connected with recirculated volumes (RV). The specific architectures will be described below for ladle, tundish and mold. Mass conservation simulation tests showed [7] that these architectures were more suitable when compared to the set of unit reactors with dead volume [5]. In the CR architecture several parameters, such as the reactor volumes and the flow rates between mixers and recirculated volumes, needed to be calculated. The CR method used to represent true characteristic curves works as follows: (i) defining the architecture of the combined reactors by trial and error, based on general analysis of the CFD simulated melt flow pattern; (ii) building a CR mass conservation flow sheet with calculation of the characteristic curve for an arbitrary set of parameters of reactor volumes and flow rates; (iii) finding the best values of these parameters by fitting the calculated curve to the true curve by inverse optimization. The flow process mass conservation equations for the different CR architectures were solved using Microsoft EXCEL. A function (φ) was minimized (Eq. 1) with the built-in EXCEL Solver: φ = (C i true C i calc ) 2 min (1) Combined Reactors Method for Different Metallurgical Vessels Ar-Stirred Ladle. CFD FLUENT 12. software was used to solve isothermal transient multiphase turbulent melt flow in 1 ton ladle (2. m bottom and 2.4 m top diameters and 3.4 m height) with bottom Ar-plugs. Only the results for the central plug location are discussed here for reasons of brevity. To obtain the general geometry of the melt streams and their flow rate, isovalues of vertical (Z-direction) velocity were plotted at different levels from the bottom. Fig. 2a presents the negative (downward) melt Z-velocity and geometry of the rising plume (empty area). The Ar-flow rate affected the average downward vertical melt velocity (V z ) at different horizontal levels: increasing Ar-flow intensified melt downward flow at deep locations. The downward flow rate (tonne/s) was calculated based on the average V z value over the area of downward flow (filled sections in Fig. 2a) and melt density. Downward flow intensity decreased from the top to the bottom of the ladle. The generalized design of the architecture of the combined reactors for the ladle was chosen as follows: the CFD simulation melt flow pattern was subdivided into four regions: the Ar-gas driven rising plume (V), top horizontal layer (V3), central recirculated region (V2), and slow flow bottom layer (V1), as shown in Fig. 2b. The bottom volume (V1) was assumed to be plug flow and the others were assumed to be perfect mixers. The small top volume V3 was assumed as 4% of the total ladle volume, the volumes V1 and V2 were included in the inverse simulation and volume V was calculated as the remainder. Flow rates between reactors V2 and V1 (F21) and in the top of the rising plume V (F3) were included in the inverse simulation based on the CFD data; all other flow rates were calculated based on mass conservation equations. The values of the four independent parameters included in the inverse simulation were varied to achieve similarity of mixing time between the CFD and the combined reactors.

4 Relative concentration Relative concentration a) b) c) Figure 2. Vertical velocity (V z ) values at different horizontal levels (a), vector velocity flow pattern from CFD simulation (b) and combined reactors architecture (c). In the CFD simulation, a tracer was injected at four symmetrical points near the top of the melt surface of the Ar-stirred ladle. The relative tracer concentration was plotted as a function of time. Figure 3 illustrates CFD-simulated dye concentration curves for the bottom volume V1 and the rising plume V. The concentration curve in the bottom volume had a delay period - which is typical for plug flow. The mixing time was calculated based on 95% criterion. The Ar-flow rate affected the mixing time: 35 sec at 4 CFM and 22 sec at 2 CFM of Ar flow. The similarity of melt flow in the CFD modeled Ar-stirred ladle and combined reactors was achieved by inverse simulation. The concentration curves in the bottom reactor V1 were used for the inverse simulation. This region has a mixing delay when compared to the other ladle regions. Comparisons of the CFD and combined reactor mixing curves are given in Figure 3 for Arstirred ladle at 4 CFM and 2 CFM. After inverse simulation of the reactor volumes and flows between them, the combined reactors representation delivered identical to CFD mixing curve in the bottom volume V1. The agreement was not as good in other ladle regions, for example, in the rising plume (Figure 3); however, the mixing curves from both methods had similar averaged trends Reactor V1 CFD V1 Reactor V CFD V Time, sec Time, sec a) b) Figure 3. CFD simulated and combined reactor modeled tracer concentration in the bottom region and plume stream of 1 t Ar-stirred ladle at 4 CFM (a) and 2 CFM (b). Arrows show mixing time. Using the suggested combined reactors design (Figure 2c) the inverse simulation delivered a unique set of reactor parameters, including reactor volumes and melt flow rates. The results of inverse simulations are shown in Figure 4 for the centrally located Ar-plug at different Ar flow rates. Increasing Ar flow rate significantly decreased the bottom plug volume V1, had a minor Reactor V1 CFD V1 Reactor V CFD V

5 Relative volume S, wt.% [S], wt.% Flow rate, t/s (S), wt.% effect on rising plume volume V, and increased recirculated (F2) and plume (F3) melt flow rates. The combined reactor parameters describe the effect of increased Ar-flow rate by simultaneously increasing the overall melt recirculation flow rate and the volume of ladle regions involved in intensive mixing Bottom plug volume Plume volume Plume flow rate Ar flow rate, CFM Figure 4. Effect of Ar-flow rate on the volumes of bottom plug reactor and plume mixer reactor and flow rate in plume. Once the flow in the ladle is described then this can be used with a description of the kinetics of the metal-slag-gas reactions to calculate the refining and mixing in the ladle [8]. Figure 5 illustrates the predicted sulfur concentrations in the ladle in comparison to the experimentally measured values at the start and finish of refining [9]. There are large gradients in sulfur concentration in the metal between the different ladle regions initially, but these slowly disappear until the metal is more or less homogeneous at the end of the refining period Measured Top Middle Bottom Bulk Slag Time, sec Figure 5. Comparison of predicted sulfur concentration in in the slag (right axis) and in the different ladle regions (left axis) with experimentally measured in the bulk steel at starting and finishing refining [9]. Tundish. The CR method is illustrated for one case: a single-strand tundish of 14 metric ton liquid steel capacity without flow control devices. The tundish had a trapezoidal shape with 1 degree vertical walls incline and 3 m long, 1 m wide and.8 m melt level (Figure 6a). The melt flow rate was varied from 2 t/min (slow) to 2.6 t/min (medium) and to 3.2 t/min (high). This gave 446, 34 and 27 seconds for the mean residence time values respectively. The tundish had a submerged entry nozzle (SEN) of 25 mm OD, and 15 mm ID submerged 3 mm into the melt, and a 2 mm OD stopper rod above a 7 mm diameter exit nozzle. CFD FLUENT 12. software was used to solve isothermal transient turbulent melt flow (Figure 6b); species transport was included to allow the derivation of the RTD curve (Figure 6c).

6 C Low flow Medium flow High flow a) b) c) Figure 6. Tundish design (a), vector velocity in central vertical section (b), RTD curves (c). In the combined reactors architecture (insert in Figure 7 a), used by Sahai abd Emi [5] a plug flow reactor was followed by a mixer directly connected to dead volume. It can be seen that this simplified architecture of combined reactors was not in agreement with CFD simulated flow and the RTD CFD curve at any combination of variables (reactor volumes and internal flow rate) θ a) b) Figure 7. Comparison of CFD simulated RTD CFD curves with RTD CR curves: a) obtained from the simplified combined reactor approach, and b) using the plug plus 3-mixers-RV loops architecture and inverse optimization. Visual analysis of CFD simulated flow pattern (Figure 6b) indicated the existence of multiple recalculated zones in the tundish without flow control devices. To better represent this flow pattern, the combined reactor architecture contained a set of mixer reactors (Mixer) connected to recirculated volumes (RV) was suggested and optimized using inverse simulation (Figure 7b). Inverse simulation delivered a combination of the variables (Table 2) which indicated that RV volumes are negligible and can be omitted in this tundish design. The optimized structure consisted of a small plug volume connected to two or three in-line ideal mixers. This is a reasonable CR representation of the CFD-visualized flow pattern in the case of the tundish without flow control devices. The melt flow in tundish could be also characterized as an eddy diffusion or dispersed plug flow pattern [1]. In the case of a tundish with flow control devices and Ar-stirring, the CR approach well-represented the real flow pattern [7].

7 Table 2. Optimized parameters of combined reactors representing the tundish without flow control devices. Reactor volume, part from tundish volume Plug Mix 1 RV 1 Mix 2 RV 2 Mix 3 RV Continuous casting mold. The SEN design, casting mold geometry, and casting speed all have a significant influence on steel quality through their effect on the flow pattern. The integrated CR approach was used to describe the melt flow in the mold. CFD simulations were performed to solve coupled transient multiphase turbulent melt flow and heat transfer in continuous casting. Modeling was done for a simplified geometry (½ of 15 mm x 225 mm slab domain with square outport located on a central symmetry plane (Figure 8a). The parameter chosen to characterize the melt flow in liquid pool in the mold was the evolution of tracer concentration on the dendrite coherency surface (Figure 8b) assuming that mixing takes place only in the liquid pool. Inverse simulation was used to calculate the combined reactors volumes and flow rates by matching the residence time curves obtained from CFD simulation to those for the chosen combined reactors architecture (Figures 8c,d). Applying this approach, the effect of SEN design and casting speed on the melt flow and recirculation in the liquid pool was analyzed. 1.2 C i CFD CR a) b) c) d) Figure 8. Continuous casting mold: a) CFD simulated vector velocity, b) dendrite coherency isosurface, c) combined reactor architecture, and c) CFD simulated and inverse optimized RTD curves for combined reactor at dendrite coherency surface. Conclusions θ A combined reactors method is suggested for the fast and adequate representation of melt flow in metallurgical vessels. The examples described were the Ar-stirred ladle, the tundish and the continuous casting mold in steelmaking. CFD-modeling results were converted into melt flow in combined reactors, the architecture of which represented the different characteristic zones in the reactor. The flows between the zones were also specified. Similarity of melt flow between the CFD and combined reactors methods was achieved by matching the characteristic curves for: (i) melt mixing kinetics in the ladle, (ii) RTD curve at tundish exit and (iii) RTD curve at dendrite coherency iso-surface of the mold. The suggested combined reactors approach can be used for the description of the high level of complexity of pyrometallurical processes and implemented in an on-line fast-running algorithm for the control of such operations..4.2

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