Materials Science Forum Vols. 654-656 (2010) pp 1557-1560 © (2010) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/MSF.654-656.1557
Modeling Study of the Influence of Subflux Controller of Turbulence on the Molten Steel Flow in Tundish Tomasz Merder Silesian University of Technology,Department of Metallurgy, Krasińskiego 8, 40-019 Katowice, Poland
[email protected] Keywords: Steel, tundish, subflux controller of turbulence, residence time distribution
Abstract. The objective of the study is to diagnose the current condition of the two-strand tundish. The investigated object is a “T”-type tundish. The nominal capacity of the tundish is 7.5 tonne of liquid steel. By the mathematical simulation, fluid flow and heat transfer of molten-steel in a tundish of a billet caster under different conditions (bare tundish and tundish with flow control device) are analyzed. Three variants of subflux controller of turbulence configurations in the tundish are tested. Numerical simulations of are carried out with the finite-volume commercial code FLUENT using the realizable k-ε turbulence model. Liquid steel velocity, temperature, turbulent kinetic energy and Residence Time Distribution (RTD) characteristic have been obtained as a result of mathematical calculations. The RTD curve is used to estimate the different volumes such as plug volume, dead volume and mixed volume inside the tundish. The ratio of mixed to dead volume, which indicates the mixing capability of a tundish, is estimated. Introduction Because of the high cost of empirical investigation in steel plants, the economical and available tools are widely used in designing, trouble-shooting and optimizing the process. With the increasing power of computer hardware and software, mathematical modeling is becoming an important tool, which helps to understand all aspects of the process. Today there are many researchers who use mathematical tools to solve the problem of inclusion separation, bubble floatation, or thermal and composition homogenization in tundish. Considerable contribution to the modeling of steel flow in the tundish has been made by Szekely J. [1] and Roderick I.L Guthrie [2,3]. The numerical calculations were performed using the commercial software PHOENICS and computational codes (METFLO 3D) developed by individual authors. Noteworthy is the article published by Szekely in 1989 [4] which describes, in a concise form, the basic aspects of investigating and solving the problems of the construction optimization of the continuous steel casting tundish. The presented article includes an analysis of the working conditions of a real industrial facility, and modifications of the working space to improve these working conditions. The facility actually working in a steel plant is not equipped with any flow control device. The assessment made by the metallurgists and the author’s studies [5] showed that additional flow control devices should be installed in the tundish since they would positively improve the tundish working conditions. At the same time, due to financial outlays, the changes should be limited as far as possible. Therefore, studies were undertaken to select the best variant of subflux controller installed in of the tundish working space. In the author's studies, the mathematical modeling technique was used. Tundish Description The object of the study is a two-strand tundish designed for the continuous casting of slabs intended for small cross-section rolled products. The object taken for investigation is a typical T-type tundish, as used in the domestic metallurgical industry. The tundish is symmetrical relative to the transverse plane. The geometric dimensions and configuration of the industrial tundish are shown in Figure 1. The nominal capacity of the tundish is 7.5 Mg of liquid steel. Steel is poured into the All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 157.158.129.225-25/05/10,12:06:41)
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tundish through a ceramic shroud positioned in the device’s plane of symmetry (Figure 2 shows the location and geometry of the subflux controller of turbulence applied). For technological reasons, the installation of a subflux controller of turbulence was proposed. Three variants of turbulence inhibitor were considered in the studies, which differ in geometry.
Fig. 1 Geometry dimensions of industrial tundish [mm]
Fig. 2 Different tundish configurations studied in present work
umerical modeling The flow field in the tundish was computed with solving the mass, momentum, and energy conservation equations, which can be found in references [3,5]. They were solved together with the turbulence kinetic energy (k) and dissipation rate of the turbulence kinetic energy (ε). For the differential equation system being resolved it is assumed suitable initial and boundary conditions, corresponding to the model investigation conditions. Detailed boundary and operators conditions which correspond to the conditions of the industrial process can be found in other article [5]. The considered system is three-dimensional and symmetrical. Because of the plane of symmetry, only half of the tundish was considered in the numerical computation. The computational space discretization has been made with use of the computational mesh consisting of 550.000 control volumes. The mesh is denser in the inlet and outlets regions. For the computation of the velocity distribution in the liquid steel boundary condition of “no-slip” type were adopted for all walls, using the so called “wall function”. In the computations, the steel free surface it assumed as a flat surface – a wall with zero shear stresses. The SIMPLE numerical algorithm was used to solve those equations. During iteration, the convergence was assumed to reach a point where all the normalized residuals were smaller than 10-6. Computations were carried out for transient conditions. The time intervals of recorded concentration are constant in the entire testing range, being equal to ∆t=0.05s. The range in which continuous recording was performed is 2500 s. The mathematical simulations were run on a INTEL CORE i7 processor computer with the Computational Fluid Dynamics (CFD) software. Results and discussion The temperature fields and the distribution of velocity vectors and turbulence energy calculated for investigated tundish can be found in article [5]. These results give information abut flow field structure and casting conditions. However, these characteristics do not directly explain whether or not the tundish condition is suitable for nonmetallic inclusion removal or agitation processes in the sequential casting of different steel grades. The answer to this question is provided by Residence Time Distribution (RTD) curves. For this purpose, model tests on water model or numerical modelling are most often carried out. These involve the addition of an appropriate amount of a tracer at the tundish gate, followed by recording tracer concentration at the tundish strands during the
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process. The description of RTD curves, the method of their determination, and implementation to the numerical model are covered in work [4]. For estimating the character of flow in an actual reactor (tundish) in terms of its suitability for refining purposes, it is usually refer to idealized reactors, or those characterized by solely one type of flow. Such assessment is largely qualitative only, but it gives information on the hydrodynamic conditions prevailing in the facility under examination to be obtained in the most expeditious manner. Figure 3 illustrates the shape of the RTD (E) curves recorded for the examined tundish furnishing configurations. The presented curves indicate a similar steel flow for particular configurations (A, C and D). The curve obtained for configuration B shows a similar tendency of the flow to the short circuited flow. The appearance of the short circuited flow is a disadvantageous phenomenon in the tundish, as it makes the free flotation of non-metallic inclusions difficult (because the residence time is too short). Moreover, steel leaving the tundish is recirculated (the marker concentration is increase again). Using a developed RTD curve, based on model tests, and taking an appropriate theoretical description of liquid flow, individual flow shares or their ratio can be estimated for a based tundish configuration. For the purposes of this analysis, three different theoretical models are used: the mixed model [6], the modified mixed model [3] and the so called combined mixed model [7,8]. It is hard to categorically judge of which of them is the most suitable for the analysis of flow, as each of them assumes a certain level of idealization. For the purpose of own analysis, the mixed model was used, whereby three flow zones are distinguished in the tundish volume, namely: a stagnant (dead) flow (Vd), a dispersion plug flow (Vdp) and an (ideal) mixing flow (Vm), whose volumetric shares can be estimated from the RTD curve according to the following relationships: Vd = 1 −
Vdp =
Va Θ av V
(Θ
min
+ Θ peak ) 2
Vm = 1 − Vd − Vdp
(1)
(2)
(3)
The stagnant (dead) region is the one, in which fluid liquid moves very slowly and the time spent in this region by the liquid is at least twice the mean residence time. Therefore, the fraction of this flow is calculated according to [7], where the ratio Va /V is defined as a part of the area under curve C which is contained in the range from θ=0 to θ=2. Table 1 presents the computed percentage shares of dead, plug and mixed flows for the analyzed configurations respectively. From the data shown in Table 1, one can notice an increase in dispersion plug flow share (configurations C & D). The largest increase of 32.1% occurs for configuration D. This is the expected effect of tundish working space modification, since the increase in dispersion of the plug flow promotes the flotation of non-metallic inclusions. It follows from Table 1 that the use of subflux controllers of turbulence has a negligible effect on the share of mixed flow, which equal approx. 45% for the facilities examined. The presented values of particular flow shares show that in all configurations with the subflux controller of turbulence, the share of dead flow has markedly decreased. Steel stays in this particular tundish region for double mean residence time, which is an unfavorable parameter. In configuration A (basic configuration - a bare industrial) under consideration, the share of dead flow is 35.6%, and is the largest. The smallest share of this flow (24.7%) is found for configuration D of the examined tundish subflux controller of turbulence, which again confirms its advantageous technological features. The most unfavorable contribution of flow shares exist for configuration B, where the mixed flow share has increased at the cost of a reduction in the plug flow share. From the analysis of the presented results it can be concluded, that it is useful to install the appropriate regulator of flow (subflux controllers of turbulence) in the investigated tundish.
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Table 1 Residence Time Distribution parameters and volume fraction of flow Volume fraction, [%] Dispersed Well mixed Dead Conf. plug volume volume volume (Vdp) (Vm) (Vd) A 18.8 45.6 35.6 B 17.2 52.4 30.4 C 25.9 43.9 30.2 D 32.1 43.2 24.7 Fig. 3 RTD curves for the four configurations studied
Conclusions The numerical computations of the commercial facility's operation have provided significant information on the structure of steel flow, and by that on the operation conditions of the “T”-type tundish equipped with subflux controllers of turbulence of different geometries. The analysis of results of computations and numerical simulations enables the following conclusions to be drawn: 1) The use of turbulence controllers (with different geometries) in the working space of the facility under consideration significantly influences the values of particular steel flow shares within the whole tundish volume. 2) The proposed configurations of tundish working space furnishing result in a reduction of the liquid steel residence time, which positively develops the casting conditions. 3) An optimal tundish configuration is characterized by an increasing plug flow, with a decreasing dead flow. In the above context, the tundish with configuration D should be considered as the optimal tundish configuration examined.
References [1] [2] [3] [4] [5] [6] [7] [8]
J. Szekely, O.J. Illegbussi, N. El-Kaddah: PCH Physic. Hydrodynamics 39 vol. 3-4 (1987), p. 453 S. Joo, R.I.L. Guthrie: Metall. Trans. B Vol. 24B (1993), p. 755 D. Mazumdar, G. Yamanoglu, R.I.L. Guthrie: Steel Res. Vol.68 7 (1997), p. 293 J. Szekely: The physical and mathematical modeling of tundish operations, Springer-Verlag, New York, USA (1989). T. Merder, J. Pieprzyca, Z. Kudliński, L. Bulkowski, U. Galisz, H. Kania: Wiadomości Hutnicze Vol. 3 (2009), p.178 S. Singh, K.M. Godiwalla, D.K. Shaw: Scan. J. of Metall. Vol. 30 (2001), p. 103 Y. Sahai, T. Emi: ISIJ Intern Vol. 36 (1996), p. 667 J. Palafox, J.D.J. Barreto, S. Lopez–Ramirez, R.D. Morales: Ironmaking Steelmaking Vol. 28 (2001), p. 101
