Liquid metal flow behavior during vacuum consumable arc remelting process for titanium

Transcription

1 International Journal of Engineering & Technology IJET-IJENS Vol: 1 No: Liquid metal flow behavior during vacuum consumable arc remelting process for titanium Hongchao Kou, Yingjuan Zhang, Zhijun Yang, Pengfei Li, Jinshan Li, Lian Zhou Abstract To better understand the vacuum arc remelting (VAR) process, a 3D finite element model is established to analyzing the electromagnetic, temperature and flow fields of titanium alloy ingot during steady state melting process using ANSYS software. The research results show that the current flows from the crucible to consumable electrode. The magnetic field induced by current is rotary on axial line, which increases firstly and then decreases from the center to edge of crucible. The buoyancy, self-induced and stirring Lorentz forces are three main motion forces in molten pool. The molten pool is strongly influenced by fluid flows which in turn are driven by buoyancy and Lorentz force created by the melting current without stirring magnetic field. The flow velocity vectors resulted from buoyancy and self-induced Lorentz forces are opposite. The buoyancy dominates the liquid metal flow at lower current, but the self-induced Lorentz force becomes dominant with the increasing current. A transition from the buoyancy to self-induced Lorentz force dominant fluid flow occurs in the molten pool atop the ingot between 1.6 and.6 ka for size ingots. The stirring Lorentz force leads to a rotary flow of the molten pool in horizontal direction with stirring magnetic field. V Index Terms VAR, FEM, electromagnetic field, fluid field I. INTRODUCTION acuum arc remelting (VAR) is an important secondary melting process that is widely used for the industrial production of refractory metal ingots, such as titanium alloy and nickel alloy, which melt at high temperatures and are highly reactive in the liquid state [1-3]. The schematic of VAR process is shown in figure 1. A cylindrical electrode is loaded into the top of the water-cooled copper crucible. During remelting process, an electric arc is maintained between the tip of the electrode and the top of the secondary ingot, in order to heat the electrode sufficiently for melting. The liquid metal drops, which fall from the electrode, undergo solidification into the water-cooled crucible. The secondary ingot formed in this way is composed of three distinct zones, namely the liquid pool, fully solidified metal and intermediate mushy zone. The arc can be stabilized and confined with the aid of an axial magnetic field Manuscript received January 10, 011. This work was supported by National Basic Research Program of China (973 Project) (No. 011CB60550) and Program of introducing Talents of Discipline in the project of Advanced Materials and their Forming Technology. Hongchao Kou is with the State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi an 71007, China. Tel.: , address: hchkou@nwpu.edu.cn created by an external induction coil. This field is also used to create electromagnetic stirring of the liquid metal flow [4]. And the electrode is translated downward toward the molten pool to keep a constant mean distance between the electrode tip and the pool surface; this mean distance is called the arc gap. After a sufficient time elapses, a quasi-steady state is established in which relatively steady, molten pool and mushy zone sizes and shapes are maintained on the top of a solid ingot base [5]. Though VAR process is researched and developed for many years, there are still many challenges in making high quality ingots without LDI, HDI defects and macrosegregation which badly affect the quality of ingots [6-9]. Recently, Xu et al. [10] researched the formation of casting microstructure and estimated the casting defects, such as segregation and shrinkage by simulating. Hyun et al. [11] investigated the effect of VAR process parameters on the solidification behavior of titanium alloys and predicted the optimum VAR process by using the PROCAST software. In addition, P. Chapelle [1] studied the effect of electromagnetic stirring on melt pool free surface dynamics during VAR process. Although there were some researches for electromagnetic field and temperature field in the past, the investigation on coupling of electromagnetic, temperature and flow fields fluid field is not comprehensive in VAR process. Fig. 1 Schematic of the vacuum arc remelting process The performance of titanium alloy ingots depends largely on structure and chemical uniformity which is strongly influenced by the liquid metal flow behavior [13]. The Lorentz force resulted by electromagnetic fields influence macro fluid flow patterns in molten pool, which is typically as important as February 01 IJENS

2 International Journal of Engineering & Technology IJET-IJENS Vol: 1 No: buoyancy in creating the pool profile. In VAR ingots solidification, the molten metal through their part of the macro flow realize heat transfer process. At the same time, there is a much smaller interdendritic fluid flow in the mushy zone responsible for the transport of solute, which can cause the formation of macrosegregation and structure defects [14]. Therefore, to obtain a sound ingot, it is required to studying the electromagnetic, temperature and flow fields during VAR process. Actually, the direct measurement is extremely difficult due to the aggressive environment in VAR vacuum chamber. So it s very effective to understand and optimize the VAR process by computational model. The present study describes a comprehensive computational 3D-FE model of the VAR process that considers the electromagnetic field, temperature field and flow field within the ingots for axisymmetric conditions. The model performs the analysis of ingot in the steady state melting process. And the movement of molten metals under multi-field coupling and its effect on solidification behavior of ingot during VAR process are discussed in this paper. A. Electromagnetic field II. PHYSICS MATHEMATICS MODEL All practical ingot remitting processes constitute magnetic field systems induced by the imposed current. Therefore, Maxwell s equations accurately describe the behavior of the electromagnetic phenomena that occur in these processes. The electromagnetic field is described by vector potential A and scalar potential φ [15-17]. The relationship is as follows B = A (1) E = da / dt ϕ () Where, B is the magnetic induction intensity, E is the electric field intensity. The partial differential equation of magnetic field and electric field is deduced by Maxwell s equations. It follows that A A µε = µ J ϕ ϕ µε = ρ / ε Where, J is the current density, t is the time, ρ is the charging density, µ represents the magnetic permeability and ε represents the dielectric constant. The distributing value of magnetic vector A and electric potential φ are solved by finite-element method through Equations (3) and (4). Then, the various physical quantity of electromagnetic field is obtained. The Lorentz force F (3) (4) is computed from electrical current density J and the magnetic induction vector B as follow 1 1 F = J B = ( B ) B B µ µ The analysis of electromagnetic field is made by means of indirect coupling method. The followings are the procedure: First, based on electric field analysis, the current distribution of VAR process is obtained. Then, the magnetic field resulting from melting and stirring current is computed by electric field. In the end, on the basis of electromagnetic field, the electromagnetic force in ingot is analyzed. B. Fluid field The macro-scale fluid motion that occurs in the molten pool and the outer mushy region during VAR process is governed by mass and momentum conservation equations. Since the motion is turbulent in the molten pool, time-averaged forms of the Navier-Stokes equations are used to describe the mean flow velocity field [18]. Governing equation is derived from Navier Stokes equation: (1) Continuity Equation: ρv ) ρv ) x y ρvz ) = 0 ρ (6) Where, ρ denotes the fluid density; v x, v y and v z represent the velocity vector in the x, y and z directions, respectively; t stands for time. () Incompressible energy equation: ( ρ C pt ) + ( ρvxc pt) + ( ρvyc pt ) + ( ρvyc pt ) = (7) T T T ( K ) + ( K ) + ( K ) + Qv Where, K is thermal conductivity, T is temperature, C p is the specific heat and Qv is the volumetric heat source. (3) Momentum equation: ρu ρuu) ρvu) ρwu) P = Fx + µ e u ρv ρuv) ρvv) ρwv) P = Fy + µ e v ρ w ρuw) ρvw) ρww) P = ρg + Fz + µ e w (10) where x,y and z are coordinate of a point in a solving regional heat, m; u,v and w are the flow velocity in x,y and z direction, respectively; µ e represents the effective viscosity; ρ denotes the density; Q V denotes the volumetric heat source; T is temperature; t is time; P represents the pressure. F x, F y and F z are the body force in x,y and z direction, respectively; g is gravitational acceleration, equal to 9.8m s here; µ e represents effective viscosity. C. Establishment of FE model (1) Geometric model (5) (8) (9) February 01 IJENS

3 /(kg at/(jichepecify/(kgensit3/m)k))temperature/k(w/(mtion/onducmalck) her48ty/(kgcosits)/(m is700vinternational Journal of Engineering & Technology IJET-IJENS Vol: 1 No: 01 5 The 3D finite element model of VAR is showed as figure. It consists of a cylindrical copper crucible containing liquid metal pool, though which a DC electric current is flowing. The crucible is surrounded by an electromagnetic coil, which produces an external magnetic field across the liquid metal. In order to simplify calculation, the model is based on the following assumptions. 1) Molten metal is incompressible Newtonian fluid and turbulent flow. ) Surface arc pressure and metal steam pressure are neglected. 3) The chemical reactions in the molten pool are neglected. 4) Heat radiation is neglected at the surface of the VAR molten pool. Stirring magnetic field (T) Crucible outer diameter (mm) Temperat100 ure/ K )S )D Fig. 3 Thermal physical properties of the Ti-6Al-4V alloy Fig. The 3D FE model of VAR process The fluid14 is selected for finite mesh elements of flow field in the model. First, the electromagnetic fields and temperature field are computed by the VAR model, respectively. And the applied load in flow field simulation comes from the result of electromagnetic field and temperature field. ()Physical parameters Thermal conduction and specific heat of Cu are 390 W/m K and 383 J/kg K, respectively. Electrical resistivity of Ti-6Al-4V and Cu are and Ω m, respectively. The arc zone is considered to be a high resistance conductor. Due to the electric current varies directly as voltage, the electrical resistivity of the arc zone is calculated by the current and voltage of the arc zone in the experiment and it is Ω m. The relative permeability of all materials is set to be 1. The settings of VAR and geometry parameters in the model are listed in Table 1. The thermophysical parameters of Ti-6Al-4V alloy are showed in figure. 3 [1-3]. TABLE 1 TECHNOLOGY OF VAR AND GEOMETRY PARAMETERS Parameters Value Geometry Value Steady state Volt.(v) 8 Ingot diameter (mm) 100 Arc current (ka) Ingot height (mm) 180 Ingot growth rate (mm/s) 0.5 Electrode diameter(mm) 60 (3)Boundary conditions In VAR, the only source of heat is electric arc from VAR power. The temperature on molten pool surface located under the tip of the consumable is determined by the overheat value above the alloy liquidus temperature [19]: T = T + T J, D ) (11) L ( i Where, T L is the alloy liquidus temperature, K; T is the overheat of the metal above the liquidus temperature, K. The melt overheat T (J, D c ) is described by Belyanchikov s formula [0]: i Di 1 J T ( J, D ) = 400e (1) Where, J is the current, ka; and D i is the diameter of the ingot, m. According to calculating, the overheat T is about 3K and the alloy liquidus temperature is 1933K. So the temperature on molten pool surface is about 165K in simulation. The heat transfer coefficient between copper crucible and cooling water is defined as 5000 W/m K in this simulation. And the heat transfer between the ingot and the copper crucible is modelled as follows: there is a contact boundary condition at the top, where the ingot touches the mould. In the case of contact the crucible and the ingot are ideal heat conductions. After gap formation, the heat transfer coefficient is set to 80 W/m K February 01 IJENS

4 International Journal of Engineering & Technology IJET-IJENS Vol: 1 No: The crucible wall and crucible bottom are no slip wall boundary. The flow velocity of crucible wall is zero in X and Y direction and the flow velocity of crucible bottom is zero in Z direction. So we assume boundary conditions for the momentum equations as follows: u r =0. 05 = 0, v r =0. 05 = 0, w r =0. 05 = 0 (13) u z = 0 = 0, v z = 0 = 0, w z = 0 = 0 (14) where u,v and w are velocities in X, Y and Z directions, respectively. (4)Initial conditions The initial temperature of VAR chamber is set to be 300K. III. RESULTS AND DISCUSSION simulation result agrees with the previous conclusion obtained by Ward et al [4]. The current density at the molten pool surface in different directions is shown in figure 5. It can be seen that the current density becomes strong gradually from the crucible wall to the electrode edge in X direction, and the change is very small in Y direction. The vector distribution of magnetic field induced by remelting current in the mold is seen in figure 6. It can be seen that the self-induced magnetic field is revolving on axial line. Figure 7 shows the magnetic flux of the molten pool surface from the symmetry axis to the crucible edge. The magnetic density increases firstly and then decreases from the symmetry axis to the crucible edge and gets a maximum value at the electrode edge. The current flow out through the crucible and its return the electrode are axisymmetric, so it is shown that the resultant magnetic field external to the crucible will be zero according to Ampere s law. A. Distribution of the electromagnetic field during VAR process Fig. 6 The vector distribution of the magnetic field during VAR Fig. 4 The distribution of the remelting current during VAR Fig. 7 The magnetic flux of the molten pool sueface Fig. 5 The current density at the surface of the molten pool The distribution of the remelting current and the corresponding magnetic fields during VAR can affect the temperature and flow velocity distributions in molten pool [4]. Figure 4 shows the distribution of the current among the electrode, ingot and crucible at steady state melting. The current flows from the crucible to consumable electrode. It is radial distribution at the ingot top and axial direction in both the arc zone and electrode, and tiny current flows out from the crucible bottom. This Figure 8 shows the vector distribution of self-induced Lorentz force of molten pool in different directions. The Lorentz forces come from the vertical remelting current and the revolving electromagnetic field in a horizontal direction. When the current passes through the melting ingot, it produces a significant revolving electromagnetic field, which induces self-induced Lorentz force that has important effects on the molten liquid fluid flow. The self-induced Lorentz force field is radial inwards (figure 8a) and axial downwards which give rise to an axisymmetric recirculation in the molten pool (figure 8b) February 01 IJENS

5 International Journal of Engineering & Technology IJET-IJENS Vol: 1 No: Further study shows that the remelting current is very small at the bottom of the molten pool, while it is larger at the top of the molten pool. As a result, the azimuthal distribution of the Lorentz forces is not uniform, the Lorentz forces is bigger at the top of the molten pool than that at the bottom of the molten pool. With magnetic stirring in VAR process, there will be a vertical magnetic field which is introduced to stabilize the arc and it about 0.004T. Fig. 8 Vector distribution of the self-induced Lorentz force in molten pool: (a) cross section and (b) Longitudinal section B. The liquid metal flow behavior during VAR process Fig. 10 Flow field in molten pool during stead state melting process without magnetic stirring: (a) velocity resulting from buoyancy, (b) velocity Lorentz force and (c) velocity resulting from buoyancy coupled Lorentz force Fig. 9 The molten pool profile of titanium alloy ingots: (a) simulation results and (b) experimental results Liquid metal flow comes from buoyancy and Lorentz force that affects the melting in VAR process and the current in the stirring coils [14]. Figure 8a shows the temperature field and flow field in titanium alloy ingots during VAR steady state melting process, which are calculated by the 3D FEM. The boundary between the isotherm of 1877K and 1933K is regarded as the mushy region [5]. In order to validate VAR model, a tungsten block was dropped into the molten pool during a melt. And the macrostructure of φ mm ingots was observed after melting. The calculated molten pool profile is in good agreement with its measured value in the same process, as shown in Figure 9a and 9b. Figure 10 shows the flow field in molten pool during VAR steady state melting process without magnetic stirring. Flow velocity of molten metal resulting from buoyancy is shown in figure 10a. The buoyancy tends to drive hot metal up along the axis of the ingot and down along the side wall. As a result, they bring cool molten metal to the bottom of the pool, resulting in clockwise flow in the right half of the molten pool. The maximum velocity distribute along the ingot vertical axis. On the other hand, it can be seen that the self-induced Lorentz force drives the molten metal down along the axis and up along the side wall from figure 10b. Thus, they drive hot molten metal to the bottom, leading to an anticlockwise flow in the right half of the molten pool. Figure 10c shows that the fluid flow pattern of molten metal is the result of interaction between the buoyancy and self-induced Lorentz force. At the top of the molten pool, where the current density is very big, the flow velocity of molten metal resulting from self-induced Lorentz force is much stronger than that buoyancy, which causes an anticlockwise recirculation, while it is reverse at the bottom of the molten pool. In other words, considering the mushy zone is far away the February 01 IJENS IJENS

6 International Journal of Engineering & Technology IJET-IJENS Vol: 1 No: electrode tip, the effects of self-induced Lorentz force on the interdendritic fluid flow are considered to be much weaker than buoyancy in the molten pool. This conclusion agrees well with the simulation results obtained by Reiter et al [3]. Fig. 1 The comparing the simulations with the experiments: (a) flow velocity resulting from string coil and (b) macrostructure of ingot in cross section Fig. 11 The variation of flow velocity resulting from the buoyancy and self-induced Lorentz force with the increasing remelting current The flow pattern resulting from buoyancy and self-induced Lorentz force effects on the interdendritic fluid flow, which has strong influences on the structure of the ingots [6, 7]. The variation of maximum flow velocity resulting from buoyancy and self-induced Lorentz force with increasing remelting current is illustrated in figure 11. It manifests that the flow velocity resulting from buoyancy dominates at low current operation. As the current increased, the self-induced Lorentz force increases rapidly and overpower the buoyancy, so that it becomes dominant in the molten pool. The value of flow velocity resulting from the buoyancy and self-induced Lorentz force is very close at. ka melting current for φ100 mm diameter titanium alloy ingots, which is considered to be the optimal remelting current. Under the circumstances, since the effects of buoyancy and self-induced Lorentz forces are close and opposite, their impact on the flow velocity in molten pool are both decreasing. For example, take Ti-10V-Fe-3Al alloy, this case makes the Fe element macrosegregation degree decrease, which improves the quality of ingot. Furthermore, Zanner [9] finds that when the melting current changes from 6.6KA to 7.6KA for remelting 508mm diameter INCOEL718 alloy, the flow pattern between the thermal buoyancy forces and the electromagnetic Lorentz force has transformed in VAR. Davidson [30] studies that the flow pattern has transformed for remelting 50mm diameter nickel alloy by numerical experiments. At melting current is 3.6KA, the buoyancy dominates flow pattern, but melting current reaches 10KA, the buoyancy driven motion has completely disappeared and the electromagnetic Lorentz force dominates flow pattern. When a stirring magnetic field is applied for VAR process, it will generate a stirring Lorentz force in the molten pool. The current in the stirring coils creates a magnetic field parallel to the axis. The interaction of the radial remelting current and the vertical magnetic field gives rise to a rotating Lorentz force which leads to a rotary flow in the molten pool horizontal direction, as shown in Figure 1a, which are in good agreement with the experimental results (Figure 1b). IV. CONCLUSIONS The computational model predicts the electromagnetic, temperature and flow fields of the titanium ingot during VAR process. To better understand the physical phenomena that govern the flow fields, the distribution of electromagnetic field is analyzed and the temperature field is obtained. Further, the liquid metal flow behavior is studied in this paper. In longitudinal section direction, the flow velocity vectors resulting from buoyancy and self-induced Lorentz force are opposite. The buoyancy dominates the liquid metal flow at lower current, but the self-induced Lorentz force becomes dominant with increasing current. A transition from the buoyancy to self-induced Lorentz force dominant fluid flow occurs in the molten pool atop the ingot about. ka for 100 mm diameter titanium alloy ingots. When bring to bear on a stirring magnetic field, the stirring Lorentz force leads to a rotary flow in the molten pool horizontal direction. Liquid metal flow behavior obtained from the model is of significant to optimize the operation process so as to produce sound ingots with the desired composition and microstructure. In the future work, we will study the solidification structure of the ingot, investigate the effect the fluid flow on the macrosegregation of the ingot and establish the relationship between the process parameters and solidification structure finally. ACKNOWLEDGMENT This work was supported by National Basic Research Program of China (973 Project) (No. 011CB60550) and Program of introducing Talents of Discipline in the project of Advanced Materials and their Forming Technology. REFERENCES [1] R. L. Williamson, J.J. Beaman, D.K. Melgaard, G.J. Shelmidine, A.D. Patel, and C.B. Adasczik: J. Mater. Sci., 004, vol. 39, pp [] R.L. Willamson, F.J. Zanner, and S.M. Grose: Metall Mater Trans B, 1997, vol.10, p.841 [3] R.C. Atwood, P.D. Lee, R.S. Minisandram, and R.M. Forbes Jones: J Mater Sci., 004, vol.39, p.7193 [4] T. Quatravaux, S. Ryberon, S. Hans, A. Jardy, B. Lusson and P.E. Richy: J. Mater. Sci., 004, vol. 39, pp [5] X. Xu, R.M. Ward, M.H. Jacobs, P.D. Lee and M. Mclean: Metall. Mater. Trans. A, 00, vol. 33, pp February 01 IJENS

7 International Journal of Engineering & Technology IJET-IJENS Vol: 1 No: [6] P.D. Lee, A. Mitchell, A. Jardy, and J.P. Bellot: J Mater Sci., 004, vol.39, p.7133 [7] A. Mitchell: Mater Sci Eng A,1998, vol.43, p.57 [8] J.P. Bellot, B. Foster, S. Hans, E. Hess, D. Ablitzer, and A. Mitchell: Metall Mater Trans B, 1997, vol.8, p.1001 [9] V.I. Dobatkin, and N.F. Anoshkin: Mater Sci Eng A., 1999, vol.63, p.4 [10] X. Xu, R.M. Ward, M.H. Jacobs, P.D. Lee, and M. Mclean: Metall Mater Trans B, 00, vol.33, pp [11] Y.T. Hyun, J.W. Kim, J.H. Lee, S.E. Kim, Y.T. Lee: in: Lütjering G, Albrecht J (Eds) Ti-003 Science and Technology. Wiley, Hamburg, 004, pp [1] P. Chapelle, A. Jardy, and J.P. Bellot: J Mater Sci., 008, vol.43, p.5746 [13] T. Quatravaux, S. Ryberon, S. Hans, A. Jardy, B. Lusson, and P.E. Richy: J Mater Sci., 004, vol.39, pp [14] L.A. Bertram, R.S. Minisandram: in: KO Yu (Ed) Modeling for casting and solidification processing. Marcel Dekker, Inc, New York, 00, pp [15] Z.W. Yan: Ansys10.0 engineering electromagnetic analysis and detailed interpretation of example, 3rd edn. China Water Power Press, Beijing, 00, pp (in chinese) [16] Q. Zhang, J.Z. Jin, T.M. Wang, T.J. Li, Q.T. Guo: Trans Nonferr Met Soc China, 007, vol.17, pp (in chinese) [17] K.H. Spitzer: Cryst Growth Charact Mater, 1999, pp [18] Y. Xu, S.S. Dang, and R.X. Hu: ANSYS11.0/FLOTRAN flow analysis example tutorial, Mechanical Industry Press, Beijing, 009 (in chinese) [19] A. Jardy, L. Falk,and D. Ablitzer: Iron making and Steelmaking, 199, vol.19, p.6 [0] A.L. Andreev, N.F. Anoshkin, and G.A. Bochvar: Melting and Casting of Titanium Alloys, Metallurgiya, Moscow, 1994 [1] Z.H. Huang: Material Datum Handbook for Aero engine Design. National defence Industry Press, Beijing, 1993(in Chinese) [] D. Rosenthal: Trans ASME, 1946, vol.43, pp [3] B.Y. Huang, and C.G. Li: China material engineering Canon Non ferrous metal material engineering, Chemistry Industry Press, Beijing, 006 (in Chinese) [4] R.M. Ward, and M.H. Jacobs: J Mater Sci., 004, vol.39, pp [5] H. Hayakawa, N. Fukada, T. Udagawa, M. Koizumi, H.G. Suzuki, and T. Fukuyama: ISIJ Int., 1991, vol.31, pp [6] D. Zagrebelnyy, M. Jone, and M. Krane: Metall Mater Trans B, 009, vol.40, pp [7] L.A. Bertram, C.B. Adasczik, D.G. Evans, R.S. Minisandram, P.A. Sackinger, D.D. Wegman, and R.L. Williamson: in: Mitchell A, Auburtin P (eds) Symposium on Liquid Metal Processing and Casting. American Vacuum Society, Santa Fe, NM, New York, 1997 [8] F.J. Zanner, R.L. Williamson, R.P. Harrison, H.D. Flanders, R.D. Thompson, and W.C. Szeto: in: E.A. Loria (eds) Superalloy 718-Metallurgy and Application. TMS, Warrendale, PA, 1989 [9] P.A. Davidson, X. He, and A.J. Lowe: J. Mater. Sci. Technol., 000, vol. 16, pp February 01 IJENS