Numerical Simulation of MHD Processes in the Technology of Non-crucible Induction Melting of Titanium Alloys V Demidovich, M Khatsayuk, V Timofeev, A Maksimov, I Rastvorova To cite this version: V Demidovich, M Khatsayuk, V Timofeev, A Maksimov, I Rastvorova. Numerical Simulation of MHD Processes in the Technology of Non-crucible Induction Melting of Titanium Alloys. 8th International Conference on Electromagnetic Processing of Materials (EPM 2015), Oct 2015, Cannes, France. EPM2015. <hal-01332605> HAL Id: hal-01332605 https://hal.archives-ouvertes.fr/hal-01332605 Submitted on 16 Jun 2016 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Numerical Simulation of MHD Processes in the Technology of Non-crucible Induction Melting of Titanium Alloys V. Demidovich 1, M. Khatsayuk 2, V. Timofeev 2, A. Maksimov 2, I. Rastvorova 3 1 Saint-Petersburg Electrotechnical University, St. Petersburg, Russia 2 Department Electrotechnologies and Electrotechnics, Siberian federal university, Krasnoyarsk, Russia 3 Department Electronics system, National mineral resources university, St. Petersburg, Russia Corresponding authors: vbdemidovich@mail.ru, maxhac@ya.ru Abstract By means of ANSYS and Fluent coupling, a numeric model for melting of a cylindrical bar in an alternate electromagnetic field has been made. The calculation of the melting process has been carried out by the method enthalpy-porosity with application of models of turbulent currents k-ω SST in a non-static setting. Electromagnetic motion and heat sources have been defined by solving a harmonic task by the method of finite elements on a vector magnetic potential in the system inductor bar for each iteration of the hydrodynamic task. The calculation on the basis of the model and the analysis of physical processes with non-crucible melting of titanium alloy ВТ6 have also been carried out. Key words: non-crucible melting; titanium alloy; MHD; numerical modelling Introduction A unique opportunity to obtain a liquid phase of a titanium alloy inside cylindrical bars with induction heating reveals prospects for development of ultimately new technology for non-vacuum melting of titanium alloys. Such a technology looks competitive and energy-efficient compared to the existing technology of induction melting in a cold crucible due to the fact that no additional equipment is used for formation of vacuum and the process of obtaining titanium melt inside of the ingot by induction method requires much less time and energy consumption. Fig. 1 shows the dynamics of temperature field changes along the bar cross-section in the process of induction heating and formation of the melt inside of the ingot. Before the moment of time t 1 there is intensive heating of the bar surface with the constant supplying power value, the surface temperature significantly exceeds the core temperature (T SURFCE > T CORE ). Further the power value decreases, due to thermal losses from the bar surface the temperature maximum starts to shift to some depth from the surface and the temperature drop between the surface and the core starts to even. At the moment of time t 2 the temperatures on the surface and core are equal (T SURFCE = T CORE ) and consequently ΔТ 2 = 0. This effect takes place with induction heating of all metals however it shows itself more for titanium alloys due to low thermal conductivity and high melting temperature. Overheating of inner layers of metal can finally lead to the beginning of their melting at the moment of time t 3. The melting process takes place before there appears thermodynamic balance between energy coming into the bar and thermal losses from its surface when there is a melt zone inside of the bar separated from the external environment by a layer of protective skull ΔХ (moment of time t 4 ). Implementation of the offered technology requires careful choice of geometric and energetic parameters of the system inductor bar as well as Fig. 1: Temperature field changes dynamics around the bar radius.
Fig. 2: Results of electro-thermal calculation (left) and experiment (right). the parameters of heating modes and hold. Preliminary research of the system was carried out on a thermal model [1]. The results of theoretical research on the present model showed just a partial coincidence with the experiments (Fig. 2). There was a theory that in order to get a correct picture of the process it is necessary to complete the model taking into account magneto hydrodynamic (MHD) effects. At the initial stage it is enough to obtain a solution on a two-dimensional model. Mathematic model The system inductor bar has an axial symmetry and the electromagnetic task can be solved in an axis symmetrical 2D setting. Such systems usually have low values of the magnetic Reynolds number which helps to solve the electromagnetic task not taking into account the influence of velocity fields in the metal on an electromagnetic field. Thus to solve the electromagnetic task the following allowances have been made: electromagnetic field in a calculation area changes by the harmonic law and has an axial symmetry in a 2D setting, we neglect the influence of metal motion on electromagnetic field. The system of equations describing the electromagnetic field consists of equations for vector and scalar potentials and equations of continuity. A further stage of mathematic modelling is solving a thermal hydrodynamic task based on the results obtained during electromagnetic calculation. The system of equations describing thermal hydrodynamic processes consists of the equation of mass, motion and energy conservation. As we should anticipate appearance of free convection currents and their turbulization, it is necessary to introduce gravitation forces taking into account the difference of densities and application of turbulence models. For the account of free convection motions the Boussinesq-Oberbeck approximation is used. In this approximation the dependence of density on temperature gets linear and is only considered with volume forces. Thus, the liquid can be considered incompressible. To take account of the processes taking place during melting and freezing, the thermal hydrodynamic model is completed with a model of crystallization and melting based on the method enthalpy porosity. The influence of the electromagnetic field is taken into account by introduction of the corresponding source members into the equations of motion and energy which have been obtained during the electromagnetic calculation. The thermal hydrodynamic task can be solved in an axis symmetrical 2D setting. Today there are several approaches to solve a multi-phase MHD task and several ways of their implementation [2, 3, 4, 5]. An alternative algorithm of solving such tasks has been suggested on the basis of software products ANSYS and Fluent [6, 7]. Their peculiarity is transfer of full contribution of the demanded value in the calculation area of the thermal hydrodynamic part of the task. Such an approach can be applied for a broad spectrum of MHD tasks including distribution of various phases, the boundaries of which are located in the concentration area of an electromagnetic field and lead to its responsive distortion. Numerical calculation of the thermal hydrodynamic part of the task taking into account the phase transit and turbulent effects has been fulfilled in Fluent, an electromagnetic part in ANSYS Classic. To provide the transfer of source members of the motion and energy equations obtained as a result of solution of the electromagnetic part of the task from ANSYS into Fluent and transfer of the liquid phase distribution, obtained as a result of solving the thermal hydrodynamic part of the task from Fluent into ANSYS, data exchange algorithm has been developed and fulfilled. To fulfill the algorithm the following Copper inductor Bar made of alloy ВТ6 Fig. 3: Geometry and the adopted system dimensions. languages were used: a functional language Scheme, a structural language C with the library User defined function (UDF) based on the in-built compiler Fluent and a special Ansys parametric design language (APDL).
(a) Fig. 4: Dynamics of the liquid phase formation. (b) s Research on the dynamics of liquid phase creation Based on the created mathematic modelling there has been a numeric experiment carried out on formation of a liquid phase inside of a cylindrical bar of titanium alloy ВТ6 in an electromagnetic field of a 10-wind inductor with the current 2500 А with the frequency of 4 khz. The emissivity factor on the surface of the bar was taken as 0.5. The main geometrical dimensions of the system are shown in Fig. 3. To simulate the maintenance of the constant surface temperature in the model there is a control algorithm for supplied power. When the surface is heated above the temperature of 1407 С there is a smooth decrease of supplied power by 30% to the temperature of 1644 С. The function which controls the power is as follows: ( ) ( ( ( ( )))) (1) where P 0 base power; k fall = 0.3 coefficient of power decrease; T serf max maximum temperature on the surface; T S, T F temperature of the beginning and end of power decrease. The obtained distribution of the liquid phase concentration in the bar at different moments of time is shown in Fig. 4-a. Fig. 4-b shows the dynamics of the liquid phase percentage in the bar volume. The liquid phase percentage is defined from the equation: where V the bar volume. As it is seen from the pictures, the liquid phase formation takes place at a distance from the surface with the following distribution along the whole depth of the bar. The character of the liquid phase formation process at an initial melting stage is defined by distribution of enthalpy and the following mass transfer process. A condition necessary for the beginning of melt, when the temperature of solidus T SOL is reached, is sufficient power reserve to increase specific enthalpy by the value of metal L latent heat. The present power reserve is defined by the difference between active power, emitted in the bar due to eddy kw Fig. 5: Distribution dynamics of integral effective power and power losses in a bar. s currents running on it, and thermal losses from the bar surfaces which are mainly caused by thermal emissions. (Fig. 5). As electromagnetic efforts influence the bar, there are hydrodynamic currents appearing in the forming liquid phase. Heat and mass transfer taking place by means of those currents defines further dynamics of the liquid phase distribution. The distribution of the temperature field, velocity vector fields, specific electromagnetic force and power at different moments of time are shown in Fig. 6. As it is seen from the pictures, the currents character is a symmetrical two-contour toroidal circulation typical of classical systems inductor melt. As the liquid phase volume increases, the size and intensity of circulation increases. At once the square of the phase transition wetted border increases which speeds up melting of metal central (2)
Fig. 6: Distribution of the temperature field, vector velocity field, specific electromagnetic forces and power at different moments of time. layers. The bar surface layers retain their shape and a solid phase thickness providing its tightness and not allowing the melt to leak outside. Conclusion A coupled numerical model for non-vacuum melting process of titanium alloy ВТ6 has been made. The model takes into account MHD-effects and processes of phase transition with correction of the electromagnetic part of the task. The comparisons of the results obtained on the present model with the results obtained from a thermal electrical model has shown how important it is to consider latent melting heat and forced convection currents in a liquid phase due to the action of an electromagnetic field. These results showed better agreement with experiments presented in [8]. Further, this model will be used to find out key parameters and patterns for transformation of energy in the system. However, for a more detailed research of non-stationary turbulent MHD-effects and their influence on the process of liquid phase formation it is necessary to build a 3D model with the application of LES modelling of turbulence. Acknowledgment Financial support from Russian foundation for basic research under contract 15-38-50067 Mathematical modeling and research of physical processes during non-crucible melting of titanium alloys in electromagnetic field is gratefully acknowledged. References [1] V.B. Demidovich, P.А. Maslikov, D.А. Baranov, А.А. Kovinka (2012), Technologies to electromagnetically produce cast products of titanium and titanium alloys, Induction heating 2 (20), 14-18 [2] E. Baake, M. Langejuergen, M. Kirpo, A. Jakovics (2009), Analysis of transient heat and mass transfer processes in the melt of induction channel furnaces using LES, Magnetohydrodynamics 3, 385-392 [3] O. Pesteanu, E. Baake (2011), The Multicell Volume of Fluid (MC-VOF) Method for the Free Surface Simulation of MFD Flows. Part II: Experimental Verifications and Results, ISIJ International 5, 714 721 [4] V. Bojarevics, A. Roy, K. Pericleous (2010), Magnetic levitation of large liquid volume, Magnetohydrodynamics 4, 317 329 [5] S. Spitans, A. Jakovics, E. Baake, B. Nacke (2010), Numerical modelling of free surface dynamics of conductive melt in the induction crucible furnace, Magnetohydrodynamics 4, 425 436 [6] M.Yu.Khatsayuk (2013), Induction installation with MHD influence on high aluminum alloy during preparing and casting processes, candidate of technical science thesis: 05.09.01, Ekaterinburg [7] M. Khatsayuk, A. Minakov, V. Demidovich, M. Pervukhin (2015), Mathematical modeling of casting processes in electromagnetic field, Magnetohydrodynamics 1, 57-65. [8] P.A.Maslikov (2014), Research of obtaining liquid phase of titanium alloys in cylindrical bodies during induction heating, candidate of technical science thesis: 05.09.10, St. Petersburg