Analysis of columnar crystals growth during the solidification in magnetic field J. Szajnar

Transcription

1 Analysis of columnar crystals growth during the solidification in magnetic field J. Szajnar Foundry Institute, Silesian Technical University, Gliwice, Towarowa 7, Poland ABSTRACT Interaction of rotational magnetic field on molten metal solidifying in a mould causes an intensive motion of liquid material. In these conditions a crystallization process and primary structure of casting is generated. In this paper the investigations concerning experimental and numerical analysis of Al 99.7 primary structure formation are presented. First of all conditions of columnar crystals formation have been taken into account. The crystals come into existence in molten metal being in rotational constrained motion and the direction of their growth is a result of asymmetrical heat flux distribution on the surface of crystal front. The numerical computations confirmed that a changeable heat transfer coefficient on the crystal front surface causes the aberration of crystal growth direction in comparison with typical conditions of crystallization. INTRODUCTION In the area of casting solidifying in typical conditions it means withoutless the forced convection of molten metal the columnar crystals growth comes into being from heterogenous nuclei formed on the mould internal surface. The columnar crystals zone is a result of continuous competitive growth of individual crystals and the structure character is determined by these crystals grains whose main direction of crystallographic axis is the most close to heat flux direction Figure la. One of the methods of casting structure improvement is the realization of crystallization process in conditions of changeable magnetic field action. The typical feature of this technology is a fact that solidification process proceeds in forced motion of molten metal [1, 2, 3, 4].

2 320 Free and Moving Boundary Problems Up to now the results of investigations concerning the influence of molten metal motion on its crystallization allow to distinguish three basic phenomena associated with the process - dynamic activation of nuclei generation, thermal processes changing temperature field and kinetics of casting solidification, mechanical phenomena forming in a certain way the solidification front. Theoretical investigations associated with discussed problem first of all concern the final effect of refinement of structure [5, 6, 7] and in this paper these problems are not taken into account. The experiments realized by the author show that the direction of columnar crystal growth does not coincide with normal vector at considered point of casting-mould surface. It can be noticed that columnar crystals growth in rotating magnetic field changes according to direction of its motion and the axis of crystals are oppositely directed in relation to molten metal movement Figure Ib. Fig. 1. Macrostructure of unstirred casting (a), stirred (b), pure Al GROWTH OF COLUMNAR CRYSTALS SOLIDIFYING IN FLOWING MELT A crystal growth can be considered as a process in atomic scale or microscopic one [9]. The first process depends on the addition of liquid atoms to crystal lattice of solid phase (nucleus). Crystal growth is determined at least by two phenomena it means atoms diffusion to crystallization front and their addition to the lattice. Intensity of this process depends on the kind of crystallization front. Metals and alloys solidified with atomic-coarse crystallization front which has a very big number of convenient positions of liquid atoms addition. A crystal growth as a process of atoms addition (in typical conditions) is presented schematically in Figure 2a.

3 Free and Moving Boundary Problems 321 If the atoms flux;, shifts in parallel to crystallization front forced by magnetic field then on the surface of growing crystal from the side of this flux appear conditions assuring the bigger intensity of addition process (Figure 2b). mould <p-deflection angle molten metal v direction of crystal growth Fig. 2. Atoms addition Additional atoms flux j\ changes direction of columnar crystal growth (ye[0, TT]) according to the growth rate u and molten metal velocity v [8]. Microscopic growth can be treated as an increment of solid phase being a result of casting cooling in particular the Stefan condition should be taken into account. The natural trend of the process is a crystal growth in the direction corresponding to resultant heat flux neglecting the certain aberrations caused by agent of crystallographic nature. In static conditions of crystallization the heat 11 ux is oriented perpendicular to casting surface and the same is columnar crystals direction (Figure la). Forced by magnetic field the motion of molten metal caused the essential asymmetry in heat transfer process in the region of growing crystals. Above phenomena is a result of better intensity of heat exchange on this part of crystal surface which is under the direct influence of molten metal flux. In theoretical part of investigations it was assumed that columnar crystals in pure Al can be approximated by superposition of cylinder and hemisphere (Kurz-Fisher model [9]). In conditions of working magnetic field the motion of melt caused the equalization of temperature field in liquid sub-domain [5J. On the basis of above considerations deflected crystals growth can be presented schematically as in Figure 3.

4 322 Free and Moving Boundary Problems a) mould Fig. 3. Heat transfer on the crystal end face a) typical conditions b) forced motion of melt MATHEMATICAL MODEL OF COLUMNAR CRYSTALS SOLIDIFICATION IN MAGNETIC FIELD A characteristic feature of crystallization in rotating magnetic field is waving structure of columnar crystals. The crystals generating from molten metal are deflected in this way that a crystal axis are oriented upstream of liquid metal shifting in mould domain and the direction of growth do not coincide with normal vector to contact surface casting-mould. After a change of magnetic field direction the repeated axis deflection takes place and as a result of this process the waving structure can be observed. The aim of presented fragment of above paper was a numerical verification of proposition concerning the thermal mechanism of this phenomena. The following mathematical model of columnar crystal growth has been proposed. At the initial moment of time (/=0) on the mould surface (the real shape of sample casting was cylindrical one) semicircular nuclei with radius 0.1 mm are generated. A temperature in nuclei domain corresponds to solidification point 7* whereas temperature of internal mould surface results from formulae

5 Free and Moving Boundary Problems 323 T" - T, On, (1) where T, is a contact temperature, 7^ - initial temperature of mould domain, bm, &2 - coefficients of mould and casting materials accumulation, #2 = ^2/02^2, ^2, P2, ^2 - thermal conductivity, mass density and specific heat of solid metal, K - solidification constant, L - latent heat. Equations (1) result from Schwarz solution (e.g. [10]) and for interval of time directly after pouring they are a good approximation of real heat transfer processes. The numerical computations concern the area of nine nuclei (comp. Figure 4). Di(x,0) r*(x,0) Figure 4. Nuclei domain They are in thermal contact with molten metal domain which temperature for r=0 TI(X, Q) = Tp (pouring temperature). So the following initial condition has been assumed 0)Ur*(*, 0) : 0), 0) = = r, (2) During the solidification and cooling process the crystallization front T*(x, t) displaces and after a certain time / achieves the position shown in Figure 5.

6 324 Free and Moving Boundary Problems DO(X, t) D2(X,t) n v Fig. 5. The shifting of solidification front m Now the boundary conditions of considered boundary initial problem will be formulated. Along the surface I\,(x) the condition of continuity of the form (%) :, t) = -X^n-, f) = 7^(%,, t), (4) can be assumed, at the same time n-gradt denotes a normal derivative. Condition (4) assuring the continuity of temperature on I\, is as a rule accepted in the case of computations concerning the problem of type "casting sand mould" or "casting shell mould" [11]. Along surface FQ conventionally limiting the analyzed area it was assumed that for t=q + dt (dt a certain interval of time after pouring into mould), f) = 0, (5) and next for t>bt the boundary condition (heat flux) corresponds to adequate heat fluxes calculated in numerical way for the surfaces limiting a central crystal of considered domain. This approach allows "to extend" the area of columnar crystals whose have been taken into account. For xef*(f) a generalized Stefan condition has been introduced, f) + a(x *er*(0 jc, f) f) =

7 Free and Moving Boundary Problems 325 In last equation v^ is a crystallization rate, «(*, t) - heat transfer coefficient, TO, temperature of molten metal in domain of forced convection. Coefficient a(x, t) is a function of position of considered point on the nucleus end face and the value of a(x, r) has been changed in wide limits. The problem of a determining was treated as an inverse one, but the method of proper choice of function describing the course a(x, t) = a(x) based on a traditional trial-and-error method. A temperature r«results from energy balance for molten metal domain and it was assumed that 7*,= const forxedo(f) at the same time D^t) correspond to the area of forced convection resulting from "work" of magnetic field. Close to surface T(0 the area of boundary layer DI(X t) has been assumed. The temperature field from the range <T\ T^> in this domain results from Fourier equation. Non-steady temperature field in domains D^(x), D,(x, f), D^(x, t) describes a system of equations,)] = 1, 2, m (7) supplemented by above presented boundary-initial conditions. Numerical model of columnar crystal growth has been constructed on the basis of control volume method (e.g. [11, 12]). The area has been divided into cylindrical elementary volumes (the end face of nuclei was approximated by "stepped figure"). Elementary balances for distinguished volumes allowed to determine a temperature field for successive levels of time (explicit differential scheme) and additionally to find the predominant direction of heat flux in the region of nuclei end face it means the direction of crystals growth. It turned out that during the time which was taken into account the predominant direction was practically the same. It should be pointed that the results of numerical computations were close to experimental data. In Figure 6 a temporary temperature field in parallel direction to molten metal motion in a section of columnar crystal is shown O.O < O.O1 / O.OO O.O Fig. 6. Temperature after s

8 326 Free and Moving Boundary Problems ACKNOWLEDGMENT This paper was prepared in the range of research work realized in project No sponsored by KBN REFERENCES 1. Lesoult, G., Neu, P. and BiratJ.P. Modeling of Equiaxed Solidification Induced by Electromagnetic Stirring on a Steel Continuous Caster, Pro. IUTAM Symposium on Metallurgical Applications of Magnetohydrodynamics, Cambridge, Szajnar, J. Doctor's thesis. Publ. of the Silesian Technical University, Gliwice, Poland, Sakwa, W., Gawroriski, J. and Szajnar, J/Effect of Rotating Reversing Magnetic Field on the Solidification of Aluminium Castings' Giessreiforschung, Vol.40, No.l, pp , Etienne, A/Columnar and Equiaxed Dendrite Growth in Continuosly Cast Products' Steel Research, T.61, No.10, pp , Fredriksson, H. et al/the Effect of Stirring on the Solidification Process in Metals' Scandinavian Journal of Metallurgy, Vol.15, pp , Miksch, E.S/Solidification of Ice Dendrites in Flowing Supercooled Water' Transactions of the Metallurgical Society ofaime, Vol.245, pp , Quenisset, J.M. and Naslain, R.'Effect of Forced Convection on Eutectic Growth' Journal of Crystal Growth, Vol.54, pp , Szajnar, J/Hypothesis of Columnar Crystals Growth in Electromagnetic Field' Solidification of Metals and Alloys, No. 16, pp , Kurz, W. and Fischer, D.J. Fundamentals of Solidification Trans Tech Publications, Switzerland-Germany-UK-USA, Longa, W. Solidification of Castings in Sand Molds, Slask, Katowice Mochnacki, B. and Suchy, J. Modeling and Simulation of Casting Solidification, PWN, Warsaw Szargut, J. Thermal Calculations of Industrial Furnaces, Slask, Katowice 1977.