Journal of Crystal Growth 528 (2019) 125249
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Solidiﬁcation front shape control through modulating the traveling magnetic ﬁeld
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 . 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  and increase the energy eﬃciency of operations . 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 . 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 . 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  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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