Optimization of an Extrusion Die for Polymer

Optimization of an Extrusion Die for Polymer Flow Y. Chahbani Ridenea,b*, D. Graeblinga, M. Boujelbenec a

Université de Pau et des Pays de l’Adour, IPREM/EPCP UMR CNRS 5154 & INRIA Bordeaux-SudOuest EPI Concha, France b National Engineering School of Tunisia c Handibio, laboratory of University of the South Toulon-Var, La Garde, France

Abstract. In this work, we used the CFD software PolyFlow to optimize the extrusion process of polystyrene flow. In this process, the flow of the molten polymer through the die can be viewed as a critical step for the material in terms of shear rate, self heating by viscous dissipation and temperature reached. The simulation is focused on the flow and heat transfer in the die to obtain a uniform velocity profile and a uniform temperature profile. The rheological behavior of polymer melt was described by the nonlinear Giesekus model. The dependence of the viscosity has also to be taken into account for a correct description of the flow. The design of the die has been validated by our numerical simulation. Keywords: Extrusion die, polymer flow, Non-Newtonian flow, Velocity. PACS: 47.11.-j

INTRODUCTION Insuring uniform material flow in the cross section of the extrusion die exit in a polymer extrusion process is extremely important for getting high quality products. In polymer extrusion manufacturing, the flow velocity of the melt in the crosssection of the die exit should be uniform for getting satisfactory products. Understanding of flow velocity and heat-transfer-related problems during polymer extrusion is one of the very fundamental steps to control the polymer final product. If the repartition channel in a flat die is not designed properly, the velocity at the exit of the flat die may not be uniform and leads to a variation in the sheet thickness across the width of the die [1]. Usually, to get the best extrusion tool and cycle, process and die designers make many trials and repair tasks. By using numerical simulation, costly experiment can be avoided. Numerical simulation allows us to fit the urgent demand for short cycle and low cost of product development in modern industrial market. This practice is widely adopted in modern manufacturing industry development [2, 3]. To simulate the polymer and other non Newtonians flows, computational fluids dynamics software (CFD) are widely used [4, 5]. The present work is aiming at verifying the correctness of an extrusion die exit already designed. Hence, our concern is the outlet velocity profile. Many studies have CREDIT LINE (BELOW) TO BE INSERTED ON THE FIRST PAGE OF EACH PAPER been devoted to similar subjects [6-9]. CP1315, International Conference on Advances in Materials and Processing Technologies (AMPT2010) Edited by F. Chinesta, Y. Chastel, and M. El Mansori © 2010 American Institute of Physics 978-0-7354-0871-5/10/$30.00

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EXPERIMENTAL DEVICE: EXTRUSION DIE The extrusion die, subject of numerical simulation is described as follow (FIG. 1): To make polystyrene foam sheets with different thickness l and a fixed width W = 50mm, the extrusion die is composed of 4 prismatic blocks made of steel. Two blocks represent the top and bottom, and two fasteners. The upper and lower parts (90mm*50mm*25mm) of the die are symmetrical and are normally mounted to form a flow channel for the molten polymer. To ensure a uniform transfer of the polymer melt (constant flow at the outlet of the die), a channel was machined on the inner sides of the die. It contains a geometry for flow distribution: a “fish-tail” channel. It consists of two identical cylindrical channels, discarded with an angle of 120 ° (thus forming an angle of 30 ° horizontal). This distribution channel is connected to the extruder outlet through a threaded hole. This threaded hole with a nominal diameter of 10mm and a pitch of 1mm represents the input section of the molten polymer in the chain. To ensure a uniform velocity at the outlet of the distribution channel, the channels have a radius which varies with to the length according to the following law: 1

 2 Lh03 z cos α  4 (1) (1 − R( z ) =   L   3π sin α A relaxation channel (radius= 2mm) is also machined on the inner faces parallel to the width of the die. The flat triangular area between the portmanteau channel and the relaxation channel has 3mm in depth and 25 mm in length. The sheet thickness is adjustable with a set of wedges.

FIGURE 1. Different views of the extrusion die designed for the study.

RHEOLOGICAL MODEL Polymer flows are characterized by a particular rheological behavior: • Viscosity is dependent on the shear rate. Thus, polymer flows are non Newtonian. • The evolution of viscosity as a function of strain rate depends on the nature of flow (shear, elongational flow ...) • They have a viscoelastic nature [10-14], i.e they have an intermediate behavior between an elastic solid and a viscous liquid. For example, a polymer liquid

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subjected to the action of gravity will have a viscous behavior. On the other side, if it undergoes an impact his behavior is elastic. • The viscoelastic nature led to the emergence of particular behavior as the Weisenberg effect [15], the swelling at the outlet of the die … Therefore, it seems impossible to describe the rheological behavior of a liquid polymer with a simple law of Newton. Hence, we must adopt either a quasi-linear model or a non linear model. The non Newtonian non linear Giesekus model reflects the realistic rheological behavior of polymer flow for both shear flow and elongational flow. The constitutive equation of this model is written as follow: ∇ α τ + τ .τ + λ τ = 2η D (2) G τ is the deviator stress tensor, α a coefficient between 0 and 1, G is the torsion module, D is the strain rate tensor or the Oldroyd tensor, λ is the relaxation time, η is the ∇

viscosity, τ is the contravariant convected derivative which have the following expression: ∇ D τ = τ − τ .Lt + L.τ (3) Dt where L represents the variation of velocity in the vicinity of a point M. This model gives a realistic description of polymer flow with a value of α = 1 / 2. For Giesekus flow subjected to a simple shear flow, the viscosity is expressed by the following relation: . 2η 0 η (γ ) = . (4) 1 + 1 + 4λ 2 γ 2

{

}

Besides its Non-Newtonien property (viscosity dependant on the shear rate), polymer flow is characterized by the dependence of the viscosity on the temperature. In fact, the viscosity drops when the temperature increases. This behavior could be described by a semi empirical equation: the WLF law [16], valid between Tg (glass transition temperature) and Tg + 100 ° C:  η (T )  − C1 (T − Tg ) log  = (5) η (Tg )  C 2 + (T − Tg ) with C1 and C2 universal constants empirically found for differents polymers, η(T) the viscosity at a temperature T, η(Tg) viscosity at the glass transition temperature Tg.

NUMERICAL SIMULATION OF THE POLYMER FLOW ON THE EXTRUSION DIE The CFD software Polyflow version 3.10.2 is used to simulate the behavior of the polymer flow as it enters the die until its exit as a thin plate. At a first step, we simulate the flow on the die by considering an isothermal condition on the distribution channel. The result shows that the velocity profile is uniform thanks to the form of the distribution channel (FIGURE 2).

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FIGURE 2. Velocity profile at different zones of the die

To take into account the temperature impact on the flow distribution, we have to represent the metallic bloc of the die in addition of its distribution geometry. The following material characteristics are adopted: For the polystyrene: the thermal conductivity is k = 0,5 W.K-1.m-1; the heat capacity is Cp = 2500 J.kg-1.K-1, the viscosity is η0 = 3939 Pa.s ; the relaxation time is λ = 0,288 s. Boundary conditions are classified into two categories (FIGURE 2): 1. Boundary conditions related to the fluid mechanics: The inlet flow is 5,2.10-7 m3/s. Indeed, it is the flow delivered by the extruder. On the side walls of the distribution geometry, taking into account the assumption of no wall slip (adhesion of the polymer), the tangential and normal velocities are zero. 2. Thermal boundary conditions: A free convection on the front and back sides of the metal block. For the free convection parameters, 293K was chosen as room temperature and 3W.m2.K-1 as a coefficient of heat transfer. An interface condition, i.e continuity of the field of temperature and the thermal flow at the contact surface polymer / metal block. A constant temperature is fixed (by the resistors flat) on the outer surfaces of the upper and lower block, the temperature imposed is 413K, it is also the temperature of the molten polymer as it enters the die from the extruder.

FIGURE 3. Boundary conditions adopted for the numerical simulation.

After 17 days and 12 hours of calculation, we could see the results only after 60 seconds of flowing on the die.

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FIGURE 3 shows that there is no difference between the two simulations (Giesekus model, Newtonien model) and the change in temperature is still quite small, hence we can consider that we are on isothermal conditions where the velocity profile is uniform at the exit. The lack of self-heating is explained by the drop in viscosity, characteristic of non-Newtonian behavior. Now, if we compare the results after 60s of flowing to 25s seconds, it is clear that there are no changes: the system is quickly established (FIGURE 4-5).

(a) (b) FIGURE 4. Temperature field at the die after a simulation of 60s of flowing: (a) Giesekus model (b) Newtonien model.

(a) (a) FIGURE 5. Temperature field at the die after a simulation of 20s of flowing (a) Giesekus model, (b) Newtonien model.

FIGURE 6. Curves Pressure = f(y) for Newtonien and Giesekus model.

However, the curves on FIGURE 6 show that the pressure decreases in the case of non-Newtonian behavior. This decrease reflects the decrease in viscosity which is inversely proportional to shear rate in the non-Newtonian Giesekus model (EQ. 4, 6).

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∆p =

12η LQ e3

(6)

CONCLUSION This study focuses on the optimization of polymer extrusion at the die. An engineering work has been performed for the mechanical design of the extrusion die specific. It has a “fish-tail” geometry for the flow distribution. A study of the flow allowed us to determine the characteristics of this geometry in order to obtain a flat exit velocity profile. A rheological study of the polymer flow led us to define the model better adapted to our case namely the nonlinear model of Giesekus. This model describes realistically the non-Newtonian behavior of viscoelastic polymers in the molten state. We have used the platform of the software Polyflow to simulate the flow. Initially, we studied the case of Newtonian liquid to validate the “fish-tail” geometry of the die. Thus, we confirmed that the velocity profile was flat at the exit. Then, we verified our approach for the Giesekus model. We have shown that taking into account the liquid polymer pseudoplasticity and viscoelasticity does not alter the temperature field at the die. The little difference observed between the simulations is explained by the relatively low flow rate.

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