ANALYSIS OF METALLURGICAL MELTING PROCESSES USING NUMERICAL SIMULATION

Transcription

1 ANALYSIS OF METALLURGICAL MELTING PROCESSES USING NUMERICAL SIMULATION E. Baake Institute of Electrotechnology, Leibniz University of Hannover Hannover, Wilhelm Busch Str. 4, Germany phone: +49 (0) , fax: +49 (0) Key words: metallurgical processes, induction melting, numerical simulation, large eddy simulation, heat and mass transfer Abstract -,. -, LES (Large Eddy Simulation) -.. Introduction Industrial metallurgical processes like melting of alloys in induction furnaces has become a subject of numerical modelling since many years. A wide range of different modelling approaches for the simulation of the turbulent melt flow and the heat and mass transfer processes have been developed. But up to now the question about an universal and always reliable modelling approach, which can be used for the development and design of industrial metallurgical applications, remains open. Melting of alloys in induction crucible furnaces can be mentioned as a wide spread example of numerical modelling, because this process can be approximated with two-dimensional (2D) axialsymmetric model. The flow pattern in these installations is formed by the influence of electromagnetic forces and usually comprises of two or more toroidal dominating recirculating vortices. Flow patterns obtained with two-dimensional solvers based on Reynolds Averaged Navier-Stokes (RANS) equations usually are in good agreement with estimated and measured time-averaged flow velocity values. The resulting spatial distribution of the temperature and alloys compound concentration depends strongly on the heat and mass exchange between vortices of mean flow. Numerical investigations show that two-dimensional turbulence models, e.g. k- and others, fail to describe correctly the heat and mass transfer processes between the main vortices. At the present time, different modelling techniques are being used to achieve better agreement with the experiment [1-3]. Our own engineering approach developed for this problem is described in [4], however, it is necessary to investigate advanced simulation methods for more generic and therefore universal flexible solutions. Due to the permanent growth of accessible high powerful computational resources, nowadays, it is possible to run more complicated transient and three-dimensional (3D) numerical calculations of fluid dynamic problems using advanced turbulent models with higher time and volume resolution requirements and to get reliable results in reasonable time. Concluding all these preconditions the calculations presented in this paper are devoted to the application of Large Eddy Simulation (LES) method for turbulent recirculating flows. The flows of this character often occur in various industrial processes where liquid metal is driven by electromagnetic forces. 59

2 1 Experimental set-up and measurement results The experimental investigations of the melt flow velocities and temperature distributions in the melt are carried out in different laboratory induction furnaces like an induction crucible furnace (ICF), shown in Picture 1, where Wood s metal is used as the model melt. Picture 1 Laboratory induction crucible furnace with sketch of typical Lorentz force distribution and vortexes of mean flow The particular experimental ICF shown in the Picture 1 has a radius of 158 mm and a height of 756 mm, where the inductor height is 570 mm. Wood's metal, which has a melting point of 72 C, and a dynamic viscosity of kg/m s, a density of 9,700 kg/m 3 and a conductivity of S/m serves as a model melt. Potential difference velocity probe with incorporated permanent magnet [5] is used to measure simultaneously two of three velocity s components with scanning rate from 20 up to 100 Hz. The water-cooled crucible wall keeps the melt temperature at the constant level slightly above 80 C, therefore thermal gradients are negligible and have no influence on the melt properties. The flow pattern measured consists of two typical toroidal vortexes of the mean flow. But, in the same time, velocity measurements revealed, that the melt flow is turbulent with Re = v ch R/ ~ 10 5 and the amplitude of velocity oscillations is comparable with the time averaged flow velocity magnitude v max v ch. Also, the presence of low-frequency flow oscillations was exposed: most intensive of them are located close to the crucible wall between the main vortexes and have the characteristic time period about 8-12 seconds depending on inductor current (Picture 2). Pulsations with shorter period (about 1-2 seconds) can be observed as well. The major oscillation frequency f increases in dependence on the time-averaged velocity: f ~ v ch ~ I ind. 60

3 Picture 2 Axial component of the melt flow velocity oscillations measured in experimental ICF in the region between the dominating flow eddies near the crucible wall (P ~ 55 KW) 2 Numerical Modelling For the numerical investigations of the turbulent melt flow as well as the heat and mass transfer two turbulence models were applied. The first was the well-known k-ε model, which has relatively low mesh requirements and is widely used and verified in various numerical engineering applications. This model usually produces fast good quantitative results for the time-averaged velocity distribution in case of stationary two dimensional calculations, but fails to describe correctly the heat and mass transfer quantities in the melt when the system contains at least two dominating recirculating flow eddies. Picture 3 Axial velocity oscillations in the ICF calculated with LES turbulence model 61

4 The main reason is that k-ε equations are unable to describe low-frequency pulsations, which arise due to the large scale flow dynamics. Furthermore, the discussed k-ε model is based on the hypothesis of isotropic turbulence, but experiments show, that significant anisotropy takes place not only close to the crucible walls, where axial oscillations are dominating, but also at the symmetry axis, where radial oscillations are prevalent. Relative isotropy can be observed only in the centres of large eddies. The Reynolds stress model can be applied in order to take into account local flow anisotropy at the cost of additional equations to be solved. The unsteady modification of this approach (URANS) allows to perform transient investigations of the flow [3]. Numerical investigations with 3D LES turbulence model revealed flow instabilities similar to those observed in the experimental induction crucible furnace (Picture 2). In order to investigate the reliability of these results, up to two minutes of the flow development were calculated after refining the mesh. Examining results, it was found out that axial flow velocity component oscillates with the amplitude of approximately 20 cm/s near the crucible wall in the region of vortexes interaction (Picture 2), but at the half-radius of the crucible these oscillations are approximately two times less intensive. The main oscillations, which have period about 10 seconds, are combined with less intensive high frequency ones, like in the experiment. The amplitude of these oscillations remains the same for different mesh resolution levels and coincides with experimental data. Comparing the graphs with the Fourier analysis of the experimental and numerical data, one can see that the calculated results include not only the main frequency, but they also show several additional pulsations with higher and lower frequencies. The presented graph shows that the spectrum of the numerical results is shifted in the direction of the lower frequencies in comparison with the experimental data. This tendency remains when spatial grid resolution is decreased. Unfortunately, further experiments with mesh refinement are confronted with too high consumption of calculation time and computational resources. The transient eddies dynamics can be examined on the animated sequence with vertical crosssection of the crucible. It becomes clear, that the melt flow looses any symmetry in phase of fully developed oscillations. Main vortexes of the mean flow break up into smaller ones, which move between different regions and therefore providing the intensive heat and mass exchange in the entire melt. The discrete particle tracing approach has been carried out to investigate convective scalar transport mechanism in the considered flow. In the very beginning virtual particles are placed on the top of computational domain. These particles are assumed to have the same density as the fluid and this leads to the expectation that their path will coincide with the streamlines of the flow. When the 62 Picture 4 Results of particle tracing a, b) in transient simulation and c) in long time period averaged flow

5 flow in closed domain without inlets and outlets is stationary, the streamlines are also closed and particle trajectories should be looped. In this case it is improbable that particle will penetrate into the neighbouring flow region if the turbulent transfer is neglected. Therefore, transport processes between the main flow eddies generally would have diffusive character in steady-state flow. In this case scalar exchange intensity will strongly depend on the semi-empiric turbulent parameters such as turbulent viscosity and turbulent Prandtl ( t = c p t / t ) or Schmidt (Sc t = t / D t ) number. Both latter parameters magnitude often depends on the type of fluid and flow properties and has to be determined experimentally. The flexibility of using such approach for different industrial installations is rather low. The sub-grid viscosity models seem to have more universal character. Transient simulations with a small time step and appropriate meshing allow resolving the wide range of flow formations involved in scalar transport. Particle trajectories, traced in such instationary simulations, show that estimated convective mass exchange between the main flow eddies is quite intensive (Picture 5 a, b). Four particles were launched simultaneously at z = H, r = R/2, = /2 and traced for 20 seconds (about 5-6 eddy turnover times). The choice of starting position was caused by conformity with industrial alloying process, when additional components are added on the melt surface. The typical tracing result states, that most particles don't stay in one eddy longer than two or three turnover times. Hence, it is possible to come to the conclusion that convective transport mechanism plays significant role in the heat and mass exchange between the main flow eddies. The same tracing procedure was used with the time-averaged velocity field from transient LES calculations. As it was expected, all particles rotated in the initial eddy with relatively small azimuthally drift (Picture 5c). Probably, if longer time for averaging would be taken the trajectories would converge to those in steady-state flow pattern. 3 Industrial Applications The simulation of the turbulent melt flow in an industrial crucible furnace is presented here as the first example of our LES numerical investigations. This furnace has a melt volume of about 0.9 m 3 at 100% filling level. The radius of the crucible furnace is about 0.49 m and the height of the inductor is 1.34 m. The furnace is used for melting grey cast iron, which has a density of 6,800 kg/m 3. The three-dimensional hydrodynamic model consisted of about elements and the time step in the transient calculations was 10-2 s. Industrial crucible furnace differs from the experimental installa- Picture 5 Velocity distribution [m/s] in the industrial furnace calculated three dimensional instationary with LES after 20 (left), 21 (centre) and 22 seconds 63

6 tion with significantly larger linear dimensions, higher EM forces density and noticeable free surface deformation (meniscus). The comparative analysis of LES and experimental data from model furnace allows applying this numerical method also for industrial scale installations, and qualitatively similar phenomena is achieved. The period of the low-frequency oscillations become smaller 2 seconds because of significant increase of the rotational velocity of the flow eddies. Initially axial symmetrical flow pattern becomes fully three-dimensional, but the symmetry remains in the time-averaging of the fluctuating flow. furnace vessel thermal isolation refractory magnetic yoke induction coil inductor channel The second example presented here is devoted to the induction channel furnace (ICF), which is used for holding and casting of ferrous and non-ferrous metals and due to its good efficiency for melting of non-ferrous metals. Picture 6 shows the principle design of a one loop ICF, which is typically used for holding and casting of grey cast iron. The ICF basically consist of a ceramic lined furnace vessel and one or several inductors. In principle, the inductor can be regarded as a transformer with iron yoke, where the induction coil is the primary circuit and the melt filled inductor channel represents the secondary short-circuited loop. For the safety and efficient operation of the ICF the heat transport from the channel, where the Joule heat is generated, to the melt bath in the furnace vessel is important in order to avoid a local overheating in the channel. The melt flow in the channel itself and in the transition zone between the channel and the bath, the so-called inductor-throat, is very complex, highly turbulent and influenced mainly by electromagnetic forces but additionally by buoyancy forces. In order to investigate the operation behaviour of the ICF heat and mass transfer processes in the melt have been analysed applying the Large Eddy Simulation (LES) approach. The simulation results are verified by already existing data of melt flow velocity and temperature measurements [7]. The simulation results presented here are carried out for an industrial sized experimental furnace running with Wood metal as a model melt. The results are obtained using the two parameter or LES model show highly turbulent 3D dynamic flow vortex structures, with flow velocities up to 70 cm/s. The steady state velocity distribution in the symmetry plane calculated with the k- model (Picture 7 left) shows, that the flow is directed radial outwards in the channel and there is up-flow just above the channel forming two vortex loops in the bath. These loops have complex structure and are closed on front wall of the bath. Instantaneous velocity pattern calculated with the LES model (Picture 7 right) shows highly turbulent structure of the flow. However even here the regions of more or less symmetric structures and constant direction flow can be observed. 64 Picture 6 Principle design of an one loop induction channel furnace [6]

7 In comparison to these high local melt flow velocities, which are driven by EM-forces, the integral transition flow through the channel, caused mainly by buoyancy forces, is very small in the range of 5 cm/s and therefore only secondarily responsible for the heat transfer processes from the channel into the bath Picture 7 Melt flow velocity distribution on symmetry plane of the ICF. Left: steady-state distribution with k-ε model, right: intermediate situation at 9 sec with LES-model The velocity distribution in the cross-section inside the channel is represented by two-vortex structurewhich also is in accordance with Lorentz force distribution and experimental measurements. Characteristic velocity magnitudes in the channel are approximately the same for both simulation models ( m/s in maximum). The distance between the vortex centres is about channel radius. Results of the simulation of the temperature distribution in the symmetry plane of the channel furnace are shown in Picture 8. The initial state with the channel maximal temperature in the bottom point is unstable and small velocity fluctuations can shift it to the left hand or right hand side on the channel, where it becomes stable corresponding to the transit convectional flow. Our still running investigations have shown, that the position of the magnetic yoke, which leads to unsymmetrical electromagnetic field and Joule heat distribution in the channel, influences the shift of the temperature maximum to the left hand or right hand side. Due to the dynamic interaction of the turbulent vortexes the heat and mass exchange along the channel is well developed. The dynamic flow structure in the throat of the channel inductor leads to a smooth temperature gradient in the transition zone between the channel and the bath, which is shown as a result of the LES model (Picture 8 middle). But the results of the steady state temperature distribution, calculated with the k-ε model (Picture 8 right) show a precipitous temperature gradient at the exit of channel, because the interactions between the flow vortexes in this region, which are characterized by low frequency oscillations, are not taken into account according to the real situation with the two parameter turbulence models. 65

8 Picture 8 Temperature distribution in the channel furnace. Left: intermediate distribution after 45 sec (LES), middle: time averaged over 60 sec (LES), right: steady-state (k-ε model) Conclusion By Intensive numerical studies concentrated on applying the Large Eddy Simulation (LES) model for recirculating melt flows in induction furnaces were done together with experimental investigations in a model induction crucible furnace. The comparative analysis shows a good coincidence between the numerical and experimental results not only in terms of mean flow, but also for the turbulent fluctuations and their kinetic energy. The studies reveal that the low-frequency velocity oscillations play a main role in convective heat and mass transfer when flow structure contains two or more large vortexes of the mean flow. The modelling results show, that only the 3D transient LES is able to model correctly the heat and mass transfer processes in these recirculating flows. Therefore, the correct estimation of the characteristic parameters of these oscillations applying the LES method leads to creation of a universal and reliable numerical method, which can be used for solving fluid dynamics and thermal problems in practical metallurgical applications. Literature [1] B.G. Thomas, Q. Yuan, S. Sivaramakrishnan, T. Shi, S.P. Vanka, and M.B. Assar: Iron Steel Inst. Jpn. Int., 2001, vol. 41, pp [2] V. Bojarevics, G. Djambazov, R.A. Harding, K. Pericleous, M. Wickins: Magnetohydrodynamics, 2003, no. 4. pp [3] R. Schwarze, F. Obermeier: Modelling and simulation in materials science and engineering, 2004, vol. 12, pp [4] E. Baake, B. Nacke, A. Jakovics, A. Umbrashko: Magnetohydrodynamics, 2001, vol. 37, no. 1-2, pp [5] T. Weissenfluh: Int. J. Heat Mass Transf., 1985, vol. 28, no 8, pp [6] Fasholz, J.; Orth. G.: Induktive Erwärmung. Verfahrensinformation, RWE-Energie, Essen 1991 [7] Eggers, A.: Untersuchungen der Schmelzenströmung und des Wärmetransports im Induktions-Rinnenofen. Fortschritt-Berichte VDI, Reihe 19, Nr. 63, Düsseldorf