Experimental and CFD investigation on the solidification process in a co-rotating twin screw melt conditioner

Journal of Materials Processing Technology 210 (2010) 1464–1471

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Experimental and CFD investigation on the solidification process in a co-rotating twin screw melt conditioner R. Haghayeghi a,∗ , V. Khalajzadeh b , M. Farmahini Farahani b , H. Bahai a a b

Howell Building, School of Design and Engineering, Brunel University, Uxbridge, Middlesex UB8 3PH, UK Department of Mechanical Engineering, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 11 November 2009 Received in revised form 6 April 2010 Accepted 8 April 2010

Keywords: Computational fluid dynamic Solidification Co-rotating twin screw melt conditioner Grain size

a b s t r a c t Twin screw melt conditioners are used for mixing purposes and are mainly used for polymer processing. These conditioners (extruders) can be used for liquid metal processing in which liquid metal/slurry is subjected to high shear stress. This process results in grain refinement of structure. In this article, in a co-rotating twin screw melt conditioner, the solidification process of a liquid along with temperature variations of the melt with regard to the complexity of the flow has been examined. With the aid of dynamic mesh scheme, a Computational Fluid Dynamic (CFD) simulation was performed. The achieved results were in good agreement with values based on the experimental measurements. It was concluded that shearing and pouring temperatures play important roles in solidification progression and the main reason of surviving nuclei is heat dissipation from the barrel. Also, the main factor affecting the grain size is the temperature differences between the pouring and the setting temperature. It was observed that, the twin screw melt conditioner can decrease the temperature gradient and with the help of turbulence, providing appropriate conditions for formation of fine and equiaxed grains. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The co-rotating twin screw conditioners, have been widely used in polymer processing, reactive systems and mixing purposes. Due to their advantages, such as flexible screws and barrel configurations, low energy consumption as well as an excellent feeding capacity, the usage of these machines has increased. Designing an optimal window includes not only screw speed or barrel temperature, but also screws and barrel configurations are important. Melting is an essential mechanism in casting products. However, shearing the melt and its solidification process in a twin screw conditioner, is still not well understood; although few studies have been carried out in recent years (Gogos et al., 1998; Maier, 1996). Research, on the melting process of a liquid metal, involves two steps: (1) understanding the mechanism of melting by experiments and (2) prediction of melting/solidification progression by modeling. Currently, research is mostly focused on the first (Fan and Liu, 2005; Haghayeghi et al., 2009a,b) and no potent investigations have been carried out on the second. For example, Fan and Liu (2005) or Haghayeghi et al. (2008) have focused on the effect of intensive shearing on the magnesium and aluminium melts but no

∗ Corresponding author at: H106, Howell Building, School of Design and Engineering, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK. Tel.: +44 01895 265773. E-mail address: [email protected] (R. Haghayeghi). 0924-0136/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2010.04.004

investigations have been carried out to explain the melting mechanism inside the twin screw melt conditioner. Potente and Melisch (1996) were conducted an experiment on a laboratory extruder, in order to establish the parameters which influence the melting process. They showed the temperature increment that occurs in the conveying section of the screws is the main factor for melting process. However, their theories are based on the great assumptions and approximations. For example, in their model, temperature is considered constant or keeps it as injection temperature; whilst shearing would alter it. The complexity of the flow in addition to the friction of the screws can make the temperature results beyond expectations (Varela et al., 1996). Another complexity of the modeling is due to domain changes by rotation of the screws. In fact, because the screws interact with each other, hence the computational domain changes with time continuously. Therefore, flow modeling in a twin screw, is an important part of simulation due to its complexity. Several numerical and analytical models have been reported by some researchers like Lawal et al. (1999) that have concentrated on the geometry of twin screws and used finite element method. Further, Wilson et al. (1996) to account for the 3D time-dependent motion of the screws, have simulated a sequence of several instantaneous positions. However, small-scale features were blurred mainly to coarse grids; so, their results were not verified with experimental results. Also, radial spreading of flow has not been considered in their models. Vergnes et al. (1998) just had concentrated on mixing process of twin screw and no considerations on the parameters such as screw–barrel configuration

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Nomenclature liquid fraction temperature (K) specific heat (J/kg K) velocity (m/s) time (s) turbulent kinetic energy (J/kg) Thermal conductivity (W/m K) one-dimensional pull U¯ p velocity (m/s) Pr Prandtl number of laminar flow Prt Prandtl number of turbulent flow Cε1 , Cε1 , C empirical constant h enthalpy (kJ/kg K) Al aluminium

fl T Cp u t k K

Greek symbols  density (kg/m3 )  dynamic viscosity (kg/m s) T turbulence eddy viscosity (kg/m s) ˇT expansion coefficient (1/K) ε turbulent kinetic energy dissipate rate (m2 /s3 )  phase change latent heat content (J/kg) empirical constant k, ε Subscripts l liquidus S solidus t turbulence ref reference

had been made. Avalosse et al. (2000) has discussed the different types of twin screw extruders i.e. co-rotating and counter-rotating screws. But they have assumed that the twin screw is fully filled and 2D simulation has been performed, although a large fraction of the twin screw operates in starvation mode and 3D model must be considered. In fact, most researches have focused on 2D simulation and have concentrated on one or two parameters, whilst all should be considered conclusively. In addition, most of the presented models cannot be applied with reality or have not been validated. Also, several numerical simulations of solidification processes had been done earlier. For example, Saitoh et al. (1989) concentrated on the two-dimensional modeling of solidification process in twin-roll casting by the full explicit-type, finite difference method. Tavares and Guthrie (1998) focused their numerical simulation on different metal delivery systems for twin-roll casting. Buechner (2004) suggested a new model to investigate the relations between feeding system and strip quality. Ohler (2005) has done a CFD simulation on free surface waves using a volume of fluid (VOF) model. However, none of these models cover the solidification at full length (process and parameters). In general, four parameters might be considered in twin screw melt conditioners: (1) (2) (3) (4)

Pouring temperature Shearing rate Shearing time Shearing temperature

Some researchers have suggested various methods for achieving fine and uniform microstructure, applying grain refiners and/or stirring with high shear rate (Flemings, 1974).However, there is no

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Table 1 The chemical composition of 5754 aluminium alloy (wt.%). Mg

Fe

Mn

Cr

Zn

Cu

Ti

Si

Al

3

0.25

0.25

0.11

0.06

0.05

0.01

0.08

Bal.

priority in choosing the best factor for achieving fine and uniform structure. In this article, bearing a novel approach in reality in which, turbulence, temperature gradient, shear rate and time, have all in all been presented. In addition, the most important factor for acquiring fine structure through experiment and modeling has been identified. Further, the variation of temperature in a turbulence condition was inspected. Following, the solidification phenomenon, inside the twin screw melt conditioner has been explained. Finally, through experimental and modeling approaches, the optimization for operational parameters for acquiring fine grain size has been offered. 2. Experimental 2.1. Material and machine Around 6 kg 5754 aluminium alloy with the following chemical composition given in Table 1 was prepared in a graphite crucible. Then the alloy was melted at 750 ◦ C in an electrical resistance furnace. After melting, the alloy was fed into a co-rotating twin screw conditioner and sheared at 630 ◦ C (melting point: 643 ◦ C) at shear rate of 1423 s−1 and cast into a die. The twin screw conditioner is a pair of co-rotating, self-wiping screws that applies intensive shear stress on the liquid metal; Table 2 and Fig. 1 show the machine’s specifications. 2.2. Temperature sensing system The principle of the design of temperature sensors in the barrel was similar to the ones originally developed by Wood et al. (1996). The design of temperature sensors consists of four inter-connected series of thermocouples, each inserted inside the barrel with a defined distance from each other, as well as from the screws. In this work, Alumel–Chromel (K-type) thermocouples were used. Determination of the temperature at the various junctions, involved the measurement of the voltage collected from each thermocouple and changing its data to temperature by an analogue to digital converter. Also, at the exit of the machine, an R-type thermocouple (with ±1 K error) was proposed to monitor the temperature of the melt at the exit of the barrel properly. 2.3. Solidification progression With regard to the Al–3%Mg phase diagram, Fig. 2 (Brandes, 1983) and Scheil equation (Scheil, 1942), the expected amount of solid fraction with respect to the experimental temperature Table 2 Geometry specifications. Screw root radius (mm) Screw tip radius (mm) Screw length (mm) Barrel radius (mm) Centerline distance of two screws (mm) Clearance of screw and barrel (mm) Inlet diameter (mm) Outlet diameter (mm)

16.25 23 750 24 43 1 28 12

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(630 ◦ C) was calculated and compared with the CFD modeling results. 3. CFD simulation 3.1. Governing equations Governing equations include the time averaged continuity, momentum, energy and turbulence model equations. The interface conditions between the solid and the liquid phase are accounted for by incorporating a suitable source term in the governing equations. In addition, the total solid fraction and the heat content (enthalpy) are defined by a unique set of equations: Solid fraction fs is a function of temperature which varies from 0 (complete liquid) to 1 (complete solid) and defines volumetric ratio of the solid phase in a computational cell and calculated by Eq. (1): fSSch = 1 −

 T − T −1/(1−Kp ) M

(1)

TM − Tl

In which, TM is the melting point, Tl is the liquidus temperature, T is the working temperature and Kp is the partition coefficient. Using the definition of liquid fraction, the total heat content for a fluid (the enthalpy function), can be expressed as:



T

h(T ) =

Cp dT + fl 

(2)

Tref

where  denotes latent heat required for a phase change and Cp presents specific heat content. By foregoing discussions, the model equations are given as follows: The continuity equation: ∂ (u¯ i ) = 0 ∂xi

(3)

The momentum equations: Fig. 1. The schematic picture of (a) co-rotating twin screw melt conditioner, (b) its screws and (c) inside the barrel.

D ∂P ∂ (u¯ i ) = − + Dt ∂xi ∂xj −C

(1 − fl ) fl3





∂u¯ i − ui uj ∂xj

 − pgi ˇT (T − T∞ )

2

+ı

(u¯ i − U¯ pi )

(4)

Eq. (4) describes an implementation of Darcy’s law (Darcy, 1856) for flow in a porous medium (so called mushy zone). In fact, for a temperature greater than Tl , source terms in momentum equations disappear, and the equation describes pure fluid flow. When the local temperature is less than TS the source terms become dominant and it suppresses velocity in the solid phase. In the region where local temperature is between TS and Tl , flow in the porous medium is simulated. Therefore, the source terms have been fit for the mushy zone state which is applied in this article (Barman et al., 2009). In Eq. (4), C is a constant of the liquid phase value between 104 and 107, U¯ pi is a one-dimensional pull velocity, ˇT is the volumetric thermal expansion coefficient, ı is a small number to avoid division by zero when the bulk temperature is equal to solidus temperature or when the liquid fraction is equal to zero (Zeng et al., 2009). Also, for calculating energy, the following equation is applied: D ∂ (Cp T ) = Dt ∂xj

Fig. 2. Al–Mg phase diagram (Brandes, 1983).



K

∂T − ui T ∂xj

  −



∂ − (fl ) ∂t

(5)

The Reynolds averaged Eqs. (3)–(5) introduce some higher-order unknowns: ui uj , ui T , called Reynolds stress and turbulent heat flux, respectively. Attempts to derive accurate transport equations of these unknowns, give rise to some higher-order ones. This is

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Table 3 Thermo-physical properties. Properties

Values 3

Alloy density of solid (kg/m ) Alloy density of liquid (kg/m3 ) Alloy thermal conductivity solid (W/m K) Alloy thermal conductivity liquid (W/m K) Thermal expansion coefficient (1/K) Molten alloy viscosity (kg/ms) Specific heat of solid (J/kg K) Specific heat of liquid (J/kg K) Solidus temperature (◦ C) Liquidus temperature (◦ C)

2654 2425 35.6 22.4 2.1 × 10−5 2.91 × 10−3 1200 1200 600 643

called the closure problem. To solve this problem, some approximations have to be introduced. An approximation proposed by Boussinesq is:



−ui uj = T

∂u¯ j ∂u¯ i + ∂xj ∂xi



−

2 ı k 3 ij

(6)

where T is called eddy viscosity and k denotes the turbulent kinetic energy (k = (1/2)u¯ i u¯ i ). Also, the turbulent heat flux can be expressed as: −ui T =

T ∂T Prt ∂xi

(7)

The eddy viscosity is calculated by: T = C

k2 ε

(8)

Indeed, in order to model the Reynolds stress components, the standard k–ε model was selected. The turbulent kinetic energy and turbulence dissipation rate equations are:

 ∂

D (k) = Dt ∂xi D ∂ (ε) = Dt ∂xi



+

  T ∂k k

T + ε

∂xi

 ∂ε  ∂xi

− ui uj

− Cε1

∂u¯ i − ε ∂xj

ε k

(9)

∂u¯ ui uj i − Cε2  ∂xj



ε2 k



(10) The model constants were assumed to have the following values: ε = 1.3

k = 1.0

Cε1 = 1.44

Cε2 = 1.92

C = 0.09(11)

At the most solidification processes the viscosity is variable. Due to having an accurate prediction of flow field characteristics, the non-linear viscosity is adopted as function of bulk temperature:

(T )

0

T ≥ Tl

0 eA(Tl −T )

T < Tl

(12)

where for the examined material 0 = 2.91 × 10−3 kg/ms, A = 100 and Tl = 916.15 K. Table 3 shows the thermo-physical properties of the examined alloy. In equations, velocity components, density, thermal conductivity and specific heat stand for a linear combination of the proper value for the solid and the liquid phases: u¯ i = fs (u¯ i )s + (1 − fs )(u¯ i )l

(13)

 = fs s + (1 − fs )l

(14)

K = fs Ks + (1 − fs )Kl

(15)

Cp = fs Cps + (1 − fs )Cpl

(16)

Fig. 3. (a) The geometry of the twin screw melt conditioner used in the CFD simulations; (b) cross section of the barrel; (c) mesh at cross section; (d) magnification of the mesh, adjacent to barrel wall.

3.2. Meshing scheme Fig. 3 shows the geometry of twin screw melt conditioner. It consists of two helical screws which are placed in an 8-shaped barrel. A boundary layer mesh was used adjacent to the barrel wall of the conditioner. It was extruded in an axial direction so the all clearance region is filled with boundary layer cells. The rest of the conditioner is meshed using an unstructured tetrahedral mesh, which can be adapted to the curvature regions in geometry. A grid independence study was performed with four different mesh densities with mesh quantities varying 2,250,000–3,000,000. Fluid distribution studies have indicated better predictions are obtained at higher mesh densities. A mesh density of 2,750,000 cells, as displayed in Fig. 3, has a reasonable computational simulation results. 3.3. Numerical simulation considerations A three-dimensional Cartesian system with double-precision unsteady segregated solver, is selected for simulation. The secondorder upwind differencing scheme is used to evaluate the advection terms in the Navier–Stokes equations, the energy equation and the turbulent transport equations. An initial velocity inlet, along with a constant temperature was used for the inlet boundary condition and a single outflow was applied to the conditioner outlet boundary. Indeed, no-slip condition is applied to the all-wall boundaries which have been joined into each other. The screws boundary conditions are set to a constant rotational speed with the adiabatic thermal condition and the barrel wall was set at a constant temperature. The boundary condition values are presented in Table 4.

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R. Haghayeghi et al. / Journal of Materials Processing Technology 210 (2010) 1464–1471 Table 4 Boundary conditions. Barrel temperature (◦ C) Inlet temperature (◦ C) Initial temperature (◦ C) Screw angular velocity (RPM) Velocity inlet (m/s)

630 700 700 800 0.25

The pressure–velocity coupling in the flow region is performed by using the Semi-Implicit Pressure Linked Equations (SIMPLE) algorithm scheme. Also, because the two rotating screws interact with each other, the computational domain is changed with time continuously. So, it is necessary to use the dynamic mesh scheme to predict the fluid behavior. The dynamic mesh scheme uses the re-meshing and smoothing procedures to update the grid at each time step (Fluent Inc., 2006). The convergence tolerance for the smoothening is set to 0.001 and the maximum iteration in each time step is equaled to 100. In order to reach the stable temperature along the conditioner, the unsteady simulation was carried out in 90 s. The unsteady simulations were performed with various time steps; the initial, was 0.00001 s, later 0.0001 s and finally 0.001 s. 4. Results and discussions 4.1. Temperature analysis The result of temperature characterization by Thermo-Calc analysis (Fig. 4) shows at 630 ◦ C, around 30% solid fraction is formed. In fact, by decreasing temperature from 643 ◦ C to 630 ◦ C, the liquid is transformed to mushy state; so the liquid consists of solid particles and liquid phase. By addition of stirring to the mushy state liquid, rheocasting is achieved. In fact, by stirring the melt in the twin screw in the mushy zone and casting the melt to the die, rheocasting is implied (Flemings, 1991). The solidification is initiated from the barrel, where the heat is extracted by conduction. In other words, in the twin screw, the machine is first set to the desired temperature and when it gains, the experiments begin. When the melt is poured into the barrel, screws and all its components are in the same temperature (630 ◦ C in this paper). Therefore, when the melt is poured from high temperature, in a fraction of second, it reaches

Fig. 4. Thermo-Calc prediction of the semi-solid transformation for the AA 5754 alloy.

below the melting point, thus solidification is occurred. The best place where the first nuclei can form is the barrel. If the nuclei are formed on the screws, they would melt due to friction and high intensity turbulence which increases the temperature locally. Then, the constituted nuclei, with the help of turbulence, would disperse uniformly in the slurry. By decreasing the temperature, the nuclei can grow, thus solidification is continued progressively. From metallurgical point of view, decreasing temperature is the main factor for crystallization and solidification. It is difficult to characterize the microstructure which is produced at 630 ◦ C. The reason is, as solidification continues, more than predicted solid fraction is formed. In other words, the 30% solid fraction is the survived crystals, which are available in the liquid at 630 ◦ C. Generally, for surviving a particle (crystal), few points need to be considered: (i) Crystals should have a particle size, in which are larger than the critical size (passing the energy barrier). (ii) Crystals should be able to initiate freezing at very small undercooling (larger particles are at priority), according to free growth model (Greer et al., 2000; Questeed, 2004).

Fig. 5. The temperature variation in twin screw melt conditioner: (a) continuous decrease in temperature, across the screws; (b) a general over-view of decreasing temperature in the barrel.

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(iii) The formation of crystals, should lead to decrease the surface energy and to increase the volumetric energy. (iv) The substrate that has lower mismatch with crystals is at priority. As observed, considerations (i) and (ii) directly depend on temperature and items (iii) and (iv), imply thermodynamic laws which indirectly depend on temperature. So, for investigating solidification, inspecting temperature variations inside the twin screw conditioner is necessary. When the melt at high temperature is poured into the barrel, the temperature drops slightly due to the barrel wall temperature. However, the screws rotation would increase the temperature dissipation by convection and conduction from the barrel wall. Fig. 5 shows the temperature variation in the machine. Fig. 5a shows the heat depletion with the aid of rotation of screws, and Fig. 5b implies the temperature variation across the barrel. It is observed that the heat is dissipated by rotation of screws across the length of barrel. Thus the temperature reaches a steady state after few rotations. In term of phenomenology in the machine, few occasions occur. When the melt is poured inside the machine is at 700 ◦ C and as it enters the machine its temperature may be dropped slightly. However, after each rotation of the screws the temperature is decreased. In other words, all the components of the twin screw machine including screws and barrel are at the set temperature. At each rotation, the temperature is decreased gradually and as it is seen in Fig. 5a, the melt is losing its temperature across the barrel. By dissipating heat from the wall of the barrel the first nuclei can be formed. As the temperature decreases gradually the nuclei can finally pass the energy barrier and grow. It is observed in Fig. 5b that at least half of machine takes the melt temperature and conduct it toward the set temperature. After 643 ◦ C (the liquidus temperature), nucleation and growth of nuclei occur. From 643 ◦ C to the desired temperature the process of breaking the dendrite and refinement of microstructure due to intense shearing is performed. In fact, heat conduction from the screws outward is the main reason for changing temperature and further crystallization. Concluded as in Fig. 5, after a period, the temperature gradient is depleted and further constant. 4.2. Solidification progression results The Al 5754 consists of Al–3%Mg; its phase diagram (Fig. 2) shows no intermetallic is formed at twin screw working temperature. Further analysis by Thermo-Calc, predicts 70% liquid fraction can form at 630 ◦ C. However, as solidification is a non-equilibrium phenomenon, Scheil equation is applied: Cs = KC0 (1 − fs )

(K−1)

(17)

where Cs is the solid fraction, K is the partition coefficient, and C0 is the average solute content. With respect to the diagram, by substituting values, fs can be retrieved as follows: 0.4 = 0.1 × 3 × (1 − fs )

−0.9

→ fs = 27%

Fig. 6. Formation of equiaxed grains via twin screw melt conditioner.

The achieved fs is very close to the Thermo-Calc analysis. Metallurgically, the 27% solid fraction contains particles submerged in liquid where their structure is close to the matrix. Therefore, the slurry can be considered as a homogenous solution. In fact, the temperature loss can be counted as solidification progression. By the decrease of temperature, heat is dissipated from the wall of the barrel and the first nuclei can be formed near the barrel. Then these nuclei are transferred into the nip section, where heat is generated due to friction of the screws. However, the rate of heat loss from the wall is more than the heat produced by the screws. So, since the temperature gradient is totally decreased, the nuclei are able to pass the energy barrier. As the temperature gradient reaches a steady state, the equiaxed grains are achieved. In other words, the equiaxed grains are produced in two ways: (1) Temperature gradient reaches a steady state. (2) The nuclei are hotter than the melt surrounded. In fact, by the effect of turbulence, the nuclei which have been formed near the barrel are distributed uniformly and grow in a dendritic/equiaxed shape. On the other hand, shearing provides the following advantages for acquiring equiaxed grains: (a) Helps temperature gradient reach a steady state faster. (b) Due to cavitation, the nuclei can form due to the explosion of bubbles, where the melt temperature has decreased locally. Therefore, the non-metallic particles which have dispersed in the melt are positioned in a colder temperature than the melt surrounded and can act as nuclei substrates. Thus, the exquiaxed growth is encouraged. (c) Dendritic grains which have been formed, can be broken by shearing and due to their surface energy, they tend to get an equiaxed shape. (d) Shearing due to grain multiplication, would increase the amount of nuclei, resulting in more equiaxed zone. Fig. 6 shows a sample of produced grains at experimental condition of 630 ◦ C at 1423 s−1 . The samples show equiaxed grains and further secondary grains due to solidification progression incurred in the die.

Fig. 7. The liquid fraction on the screws.

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CFD simulation also predicts 31% solid fraction, close to equilibrium condition. Although, CFD uses Scheil (non-equilibrium) equation but its low precision makes the calculations result near the equilibrium condition, as shown in Fig. 7. In Fig. 7, it is observed that after a few steps, the solid fraction reaches to 31%. 4.3. Effect of operating parameters on grain size There are four operating parameters in the melt conditioner technique may affect the grain size. Those parameters are shearing temperature, shearing rate, shearing time and pouring temperature. Shearing temperature just defines the solid fraction and does not contribute to the size of the grains. The only parameter which defines the solid fraction is temperature. So, 630 ◦ C was selected as the temperature in order to acquire 30% solid fraction with regard to the Thermo-Calc analysis. Shear rate plays a significant role in refinement of the structure. In fact, by increasing shear rate the intensity of turbulence would increase which results in breaking the dendrite to very small pieces and as the fluid has a vigorous agitation pattern even secondary dendrite arms may also break and contribute to the refinement. Consequently, the grain size decreases significantly as the shear rate increases. Shearing time just defines the period of time in which intense agitation occurs. However, as the shear rate increases the required time for achieving desired temperature is decreased. Pouring temperature would define the temperature gradient inside the machine and with respect to the applied shear rate and time achieving the set temperature is possible. But, pouring temperature cannot contribute to the refinement of the structure in the melt conditioner. However, it is important to mention that the grain size has an indirect relationship with temperature differences of pouring and shearing (Easton and St John, 2005). 4.4. Effect of flow pattern on the grain size Melt flow in the liquid and slurry determine the solute transport by the liquid and solid phases and the general structure distribution (e.g. floating grains). In fact, melt flow influence the grain structure in a way in which increasing melt flow promotes columnar to equiaxed transition in the agitated melt (Turchin et al., 2005). Turbulent flow by breaking the dendrite or floating grains encourage formation of fine structure. In addition, agitated flow would remove thermal discrepancies in the melt and promote equiaxed microstructure. In the melt conditioner, when the melt is poured inside the twin screw it agitated significantly in a way that after a few rotation the melt acquires the desired temperature. On passing the melting point, the slurry has already got a uniform temperature and chemical composition which both promote equiaxed grains. In fact, by agitation the nuclei which are formed at liquidus are distributed uniformly across the melt with consistent temperature. Hence, all the nuclei have opportunity to grow and can contribute to the refinement of the structure. Consequently, vigorous pattern of flow would help refinement of the grain structure by distributing nuclei, providing uniform temperature and chemical composition profile, breaking the dendrites and floating them inside the slurry. 4.5. Optimization of solidification parameters As mentioned, in twin screw melt conditioner following operational parameters need to be considered: pouring temperature, shearing rate, shearing time and shearing temperature. The importance of these parameters would lead to select the right one, in which by varying it, achieving fine microstructure is possible. Formerly, the tests were performed in an adiabatic temperature.

Fig. 8. The variation of the necessary time for achieving a set temperature vs. shearing rate by pouring at 700 ◦ C.

Whatever the other parameters may be, the shearing temperature would be constant at 630 ◦ C. So, shearing temperature just defines the amount of solid fraction and does not contribute to the size of the grains. But, temperature discrepancies between pouring and shearing may affect the grain size. The effect of various shearing time and rate on the temperature of the extracted melt has been shown in Fig. 8. Respectively, by the increase of shear rate, the required time for achieving the desired temperature (steady state), is decreased. The modeling results as shown in Fig. 8 are in good agreement with the experimental achievements. The small discrepancies between the model and experimental results rise from boundary conditions, equations and the constants which may vary by a small percent from the real numbers. However, all in all with considering all the affecting parameters the results are in good agreement with the experimental results. The above diagram can be explained physically. In the twin screw melt conditioner, the rate of heat dissipation is increased when the slurry is rotated rapidly, where it is in more contact with the barrel. Hence, the required time is decreased. The model has calculated the required time in which the temperature gradient reaches the steady state. It further validates the results presented in Fig. 8. For measuring the grain size in the modeling, the following equation is used (Easton and St John, 2005): d=a+

b T m Q

(18)

where d is the grain size and a is a constant which relates to the density of particles and the fraction of those which are active and can nucleate a grain. b is also a constant and depends on nucleation undercooling, cooling rate and potency of particles for nucleation. Q describes the growth restriction factor that depends on alloy elements, T is the temperature difference between the pouring temperature and the set temperature, and m varies from 1 to 2 depending on the alloy. In this article, as no grain refiner has been used, a equals zero. As observed, the T is the only factor that can be changed and as it decreases, the grain size is decreased. Table 5 presents the results of various parameters and their effects on the final grain size. The effect of pouring temperature and shearing rate on the grain size is performed through experiments and validated by modeling (the grain size in the experimental method has been calculated via ASTM E 112-96) (ASTM International, 1996). It is clear from Table 5 and the experimental results no shearing rate neither shearing time can affect the grain size, whilst T changes the grain size more significantly. Lower T would lead to finer grain size. So, if the melt is poured at high temperature, the grain size would be larger than the low pouring temperature.

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Table 5 The results of experiments and modeling on the final grain size. Test number

Pouring temperature (◦ C)

Shearing rate (RPM)

1 2 3 4 5 6 7 8 9

700 650 645 700 650 645 700 650 645

100 500 800 500 800 100 800 100 500

Indeed, higher shear rate can decrease the grain size; however, its importance is not as great as temperature differences. 5. Conclusions From metallurgical point of view, the temperature reduction would decrease the energy barrier for the formation of nuclei and can be counted as one of the main factors for solidification progression. Using co-rotating twin screw would help temperature distribute uniformly across the barrel and the temperature gradient reach a steady state condition more rapidly. It was proved that shearing and pouring temperature are the most important parameters for acquiring the right solid fraction and fine grain size, respectively. Therefore, the formation of equiaxed grains can be facilitated by low temperature gradient or cavitation. It was also evidenced that turbulent flow would help the transfer of nuclei from hot zones to warm zones where solidification can take place through the survived crystals and grains multiplication. Modeling results demonstrated that solid fraction is in direct relationship with shearing and pouring temperature that would furnish the final grain size, the results of which are in good agreement with the experimental achievements. Validation of solid fraction, temperature variations across the barrel and the required time for achieving steady state temperature in the machine, were also validated properly. Further the analysis of the geometry of screws, their effects on shear rate and on solidification progression, along with achieved understanding, can provide greater knowledge of solidification in twin screw melt conditioner. Acknowledgements The authors would like to express special thanks to BCAST team for their great collaboration in the experimental section. Also, we would like to deliver their great acknowledgements to CFD labs of Brunel and Tarbiat Modares universities for their great cooperations. References ASTM International., 1996. Standard Test Methods for Determining Average Grain Size E 112–96. Avalosse, T., Rubin, Y., Fondin, L., 2000. Non-isothermal modelling of co-rotating and contra-rotating twin screw extruders. In: Proceeding ANTEC XLVI, vol. 1, Brookfield, CT. Society of Plastics Engineers, Orlando, USA, pp. 19–23. Barman, N., Kumar, P., Dutta, P., 2009. Studies on transport phenomena during solidification of an aluminum alloy in the presence of linear electromagnetic stirring. Journal of Materials Processing Technology 209, 5912–5923. Brandes, E.A., 1983. Smith’s Metals Hand Book, 6th ed. Butterworth, ISBN 0-40871053-5. Buechner, A.R., 2004. Thin strip casting of steel with a twin-roll caster correlations between feeding system and strip quality. Journal of Steel Research 75, 5–12.

Steady state time (s)

T (K)

Grain size (␮m) (Eq. (18))

CFD

EXP

CFD

EXP

CFD

EXP

73 36 14 46 26 38 40 51 23

70 35 15 45 23 38 20 47 21

71.2 19.4 15.3 71.1 20.5 16.7 69.8 21.5 14.8

70 20 15 70 20 15 70 20 15

163.8 130.1 93.6 136.4 117.2 145.8 130.1 159.3 99.6

164 130 92 137 118 145 132 158 100

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