Solidification front shape control through modulating the traveling magnetic field

Solidification front shape control through modulating the traveling magnetic field

Journal of Crystal Growth 528 (2019) 125249 Contents lists available at ScienceDirect Journal of Crystal Growth journal homepage: www.elsevier.com/l...

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Journal of Crystal Growth 528 (2019) 125249

Contents lists available at ScienceDirect

Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro

Solidification front shape control through modulating the traveling magnetic field

T

G. Losev, I. Kolesnichenko Institute of Continuous Media Mechanics of the Ural Branch, RAS Laboratory of Technological Hydrodynamics, Perm, Russia

A R T I C LE I N FO

A B S T R A C T

Communicated by Peter Galenko

This paper is concerned with studying the process of indirect control of the molten metal solidification front by means of modulating power supply of a linear induction machine (LIM). The influence of the LIM power supply mode on the flow in the molten metal is considered. The structure of the flow and the position of the solidification front are determined by a noninvasive method using an ultrasonic Doppler velocimeter. The obtained experimental data are used to determine the shape of solidification front profiles for four LIM power supply modes, and to establish the dependence of the shape of the front profiles on the characteristics of the supply current (magnitude and period of low-frequency modulation). A comparative analysis of the interphase boundary smoothing is carried out for different power supply modes of the LIM.

Keywords: Fluid flows Heat transfer Mass transfer Solidification Stirring Industrial crystallization 2010 MSC: 00-02 99-00

1. Introduction In metallurgical technologies, stirring of metals during solidification is widely used to improve the quality of ingots, the uniformity of impurity distribution and the degree of metal grain refinement [1,2]. Due to high temperature and chemical activity of most liquid metals and molten salts the contact stirring methods cannot be applied to melts. Therefore, the electromagnetic stirring techniques based on the application of alternating magnetic fields have gained wide recognition as a reliable and effective means of noncontact controlling a melt flow both in the crystal growth and metal manufacturing processes [3]. In conductive media, the application of an alternating magnetic field leads to excitation of eddy currents. The interaction between these currents and the external magnetic field creates an electromagnetic force, which in the liquid medium acts as an excitation force of vortex flows. In turn, the vortex flows increase the intensity of heat transfer in melts [4,5], smooth the solidification front [6] and increase the energy efficiency of operations [7]. Therefore, the method of electromagnetic stirring of liquid metal under the action of externally applied rotating and travelling magnetic fields during solidification of ingots has found wide industrial application [8]. By virtue of the relation between the power supply process, electromagnetic field, liquid metal flow and solidification front shape, the latter can be controlled by changing (including magnitude, frequency

and signal output control) the value of the supply current [4,5,9,10]. The results of numerical simulations can be brought into agreement with the results of experimental modelling on the basis of small-scale models. However, in larger setups this correlation involves considerable difficulties, especially when upscaling them to industrial installations [3]. Thus, there is a strong need for experimental data obtained on industrial installations or pilot models. The above cited works have focused on studying the influence of flows generated by the travelling magnetic field (TMF) on the solidification process in a small-size layer (with regard to the size of the TMF inductor and characteristic dimensions of real technological installations). Such problem formulation implies that in the layer of current conducting liquid, the TMF generates only one large-scale vortex, which provides the main convective heat/mass transfer. However, an increase in the layer size and dimensions of the linear induction machine (LIM) changes the structure of the flow, which in this case includes two vortices differing in size and intensity [11,12]. A qualitative change in the flow structure and the resulting heat transfer leads to a change in the condition of the liquid-tosolid phase transition. Therefore, we should take into account a qualitative change in the behavior of the physical system caused by its size variation. This work is concerned with the experimental modelling of the process of liquid metal solidification under the action of modulated

E-mail addresses: [email protected] (G. Losev), [email protected] (I. Kolesnichenko). https://doi.org/10.1016/j.jcrysgro.2019.125249 Received 22 August 2019; Received in revised form 2 September 2019; Accepted 19 September 2019 Available online 23 September 2019 0022-0248/ © 2019 Elsevier B.V. All rights reserved.

Journal of Crystal Growth 528 (2019) 125249

G. Losev and I. Kolesnichenko

the temperature difference was of low intensity (the maximum flow velocity did not exceed 5·10−3 m/s). In the second mode, the liquid metal was stirred by applying a steady TMF. The horizontal component of electromagnetic force Fx generated by TMF was directed opposite to the x-axis. In the reverse modulation mode, the direction of the Fx was changed at the prescribed periods. In the last mode, the Fx direction was kept constant but the magnitude of the TMF was varied in compliance with the periodic law. Each of the forced stirring modes corresponded to the flow velocities of order of 0.1 m/s. The stirring flow had a twovortex structure. A larger vortex occupied the central region of the cell. A smaller vortex was formed in the near-wall region. Its formation was associated with the influx of fluid to the near-wall region and the curvature of the streamlines. The low-frequency modulations of the TMF resulted in the flow restructuring. The average profiles given above underwent qualitative changes: the average component of the flow decreases (up to complete disappearance due to small-period reverse modulations), while the pulsating component tends to repeat the velocity distribution characteristic of the unmodulated force action. Processing of the ultrasonic echo profiles allowed us to determine the positions and velocities of the metal solidification front at four points along the entire vertical layer extent. The shape of the profile of the crystalline phase was obtained by performing spline interpolation of experimentally obtained points. Figs. 2 and 4 show the profiles of the average solidification front velocity. In the absence of stirring, the solid phase has an S-shaped profile. A weak advective flow carries the cooled fluid into the bottom region of the layer before the solidification front and the heated metal behind the front. Hence, the velocity of solidification front is higher in the bottom region of the cell. The reversal flow, which is enriched with heated metal, increases the temperature in upper region of the cell and decreases the solidification front velocity (Fig. 2). The application of the TMF initiates a large-scale flow in the bulk of the metal. Under this formulation the effect of the forced convection on the process of solidification of the metal is ambiguous. Depending on the intensity of the flow, the heat transfers along with the layer changes (both in value and topology), which is accompanied by the variation in the temperature distribution at the interface and in the rate of phase transition at each point. The flow of low intensity (generating LIM supply current of 2–3 A) increases the heterogeneity of the solidification profile throughout the layer height (in the lower part of the layer, the solidification rate decreases, while in the upper part it increases). In this case, a slow large-scale vortex is topologically similar to the advective flow and plays a similar role in the heat transfer process. With increasingly growing effect of electromagnetic action on the metal, the intensity of the flow increases and, as a result, the conditions of heat transfer change. A rapidly rotating vortex does not allow the heated fluid to be held within the region of phase transition for a long time. However, the velocity of interface movement is 20% lower. At the stirring of highest intensity (generating the LIM supply current of 6 A) there is an intense outflow of the cooled fluid from the bottom area to the zone heated by the heater. As regards the front smoothing, the best flow modes are those occurring at the supply currents of 4.0 and 5.0 A.

Fig. 1. The schematic diagram of the experimental setup: 1. – channel filled with liquid metal, 2. – heat exchanger, 3. – criothermostats, 4. – LIM, 5. – power supply source, 6. – UDV, 7. – UDV sensors.

travelling magnetic field. Different types of TMF modulation are considered as indirect mechanisms for controlling the shape of solidification front. A distinguishing feature of this study is upscaling of the model setup to the prototype installation, which allows us to detect effects associated with the installation imperfection. 2. Methods An experimental setup (Fig. 1) consists of a vertical cell 1, which is made from plexiglass. The cell is filled with liquid alloy Ga90.15Sn6.64Zn3.21 (at.%). The physical properties of the alloy at the working temperature are density 6256 kg/m3, kinematic viscosity 3·10−7 m2/s, and conductivity 3.56·106 Sm·m. The cell dimensions are 450 × 20 × 75 mm3. The top surface of the metal is covered by a thick layer of 10% solution of chloride hydrogen acid in isopropanol to prevent the oxidation of the melt. Two copper heat exchangers 2 are placed at the thin walls of the cell. The temperature control is carried out by means of two cryo-thermostats 3 CRIO-VT-01 with precession of ± 0.5 °C. The cell is placed on the top surface of the linear inductor of the TMF 4 with dimensions of 480 × 350 mm3. The TMF is induced by six coils (170 turns in one coil). The coils are connected to a three-phase programmable current source 5 Pacific Smart Source 360 ASX-UPC3. This power supply unit makes it possible to specify the shape of the output signal and to modulate the TMF. The carrier frequency of the supplied current is 50 Hz. The position of the solidification front and the velocity of the flows in the liquid metal phase are measured by the ultrasonic Doppler velocimeter 6 (UDV) DOP 2000, Signal Processing. The four sensors 7 of the UDV are placed on the thin wall of the cell. The ultrasonic rays pass through the ports of the heater. The position of the solidification front is also determined with the UDV based on the level of the reflected ultrasound signal. At the interface, a significant part of the energy of the ultrasonic is reflected. This is manifested in the formation of the peak of the echo-signal. The peak position on the coordinate axis corresponds to the position of the solidification front. So the solid/liquid interface position is determined by the UDV sensor without coming into contact with the medium or distorting the shape of the solidification front [13,14]. The peak on the ultrasonic echo profiles is associated with the passage of ultrasound through the interface. The process of solidification is accompanied by the interface displacement, which results in a shift of the peak on the echo profile. The peak positions on the echo spatial-map have been determined based on the wavelet analysis. The obtained time dependencies of the solidification front have been approximated by the linear functions. The average velocity of solidification front motion has been evaluated analytically by calculating the average value of the approximating function. The parameter of the solidification front roughness has been used to characterize the influence of electromagnetic effects on the solidification process. It was defined as the RMS (root mean square) of the front position. 3. Results We considered four modes of solidification depending on the method of external action. In the first mode, the process of solidification of the metal occurred without stirring. The advective flow initiated by

Fig. 2. Distribution of the solidification front velocity through the depth of the layer depending on the value of the supply voltage of LIM. 2

Journal of Crystal Growth 528 (2019) 125249

G. Losev and I. Kolesnichenko

Fig. 3. Smoothing of the solidification front profiles: dependence on the value of the LIM supply current.

Fig. 6. The dependence of solidification front smoothing on the stirring mode: no stirring, steady stirring, reverse modulation stirring, modulation stirring.

this case, the voltage at each phase of the power supply of the LIM have varied by a harmonic law from zero to the maximum value corresponding to the current of 4.0 A. The modulation period was 20 s. The mechanism of the amplitude modulation of the flow is similar in nature to the reverse modulation mechanism. Heated metal is carried by the flow to the phase transition region, the flow decays as the intensity of the external force action decreases. In this case, the heated liquid metal releases excess heat to the environment. The main difference from the reverse modulation mode is that this portion of the liquid metal does not return to the zone of heating, but remains instead in the phase transition zone and pushes the cooled fluid from the bottom area to the heating region. This facilitates extra smoothing of the phase boundary through the layer height. Fig. 6 presents a comparative graph of the roughness parameter of the solidification front for different modes of liquid metal stirring.

Fig. 4. Distribution of solidification front velocity throughout the layer height as a function of the interval of the reverse TMF modulation.

4. Conclusions A change in the power supply characteristics of the TMF inductor leads to a change in the topology of the magnetic field. The latter changes the structure of the molten metal flow and, as a result, the efficiency of convective heat transfer along the entire interphase boundary. Finally, a change in the condition of heat exchange has a direct impact on the rate of the phase transition at each point of the interphase boundary. In the absence of forced stirring, heat supply to the interface is provided by the mechanisms of low intensity thermal convection. Application of the external TMF significantly increases the flow intensity, which results in smoothing the solidification front due to a more uniform distribution of heat throughout the height of the layer. TMF modulations produce an additional effect on smoothing the solidification front, due to changes in the velocity and structure of the metal flow in the liquid phase. Periodic pumping of additional portions of heated fluid positively effects smoothing of the interphase boundary. Thus, the results of this study allow us to reveal the dependence of the effective smoothing of the solidification front on the mode of LIM power supply, and to establish the physical mechanism responsible for the observed changes in the system behavior.

Fig. 5. Smoothing of the solidification front profile: dependence on the interval of TMF modulation.

(Fig. 3). Therefore, to investigate further the effect of flow modulation, we have used the supply current of 4.0 A. Due to periodic changes in the direction of the large-scale molten metal flow, the contribution of pulsations to the structure of the flow increases, which leads to an additional smoothing of temperature inhomogeneities in the bulk of the liquid phase. Fig. 4 shows the profiles of the metal solidification rate at different points along the full vertical extent of the layer, versus the period of reverse modulation. Small periods of flow modulation produce another negative effect on the process of smoothing the solidification profile, since at small times of changing the direction of the large-scale vortex rotation, its rate is also turns out to be small. This reduces the efficiency of convective heat transfer to the interface. An increase in the modulation period causes an increase in the maximum velocity of the large-scale flow, as the force action in one and the same direction continues for a longer time. In this case, the convective flow ensures a long-term inflow of the heated fluid into the upper part of the layer, which results in the distortion of the solidification profile shape (Fig. 4, the curve 80 s). The intermediate values of the reverse modulation period provide the best smoothing of the solidification front due to limitations on the rate of heated fluid supply (Fig. 5). The final stage of this study is concerned with the amplitude modulation of the LIM supply current. The variation of the supply current amplitude leads to a change in the quantity of the electromagnetic effect and, consequently, to a change in the liquid metal flow velocity. In

Declaration of Competing Interest None. Acknowledgments The work is supported by the RFBR grant 17-48-590539_r_a. References [1] S. Eckert, P.A. Nikrityuk, B. Willers, D. Räbiger, N. Shevchenko, H. NeumannHeyme, V. Travnikov, S. Odenbach, A. Voigt, K. Eckert, Electromagnetic melt flow

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