EXAMPLE 115 NON-ISOTHERMAL FLOW IN A SINGLE SCREW EXTRUDER DESCRIPTION KEYWORDS FILENAMES. Example 115

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1 EXAMPLE 115 NON-ISOTHERMAL FLOW IN A SINGLE SCREW EXTRUDER DESCRIPTION In this example, we evaluate the flow in the last part of a single screw extruder, including the last few conveying screw elements, followed by the head of the extruder and the channel leading to the die. As the barrel wall has an axial symmetry, we can use a moving frame of reference. With such a moving frame, the screws appears to be fixed, while the barrel wall is in rotation. We assume the flow to be non -isothermal. For simplicity, we define the screw has an overlapping part: by the use of the Mesh Superposition Technique, all nodes of the flow domain inside the screw will be constrained ; their velocity and temperature will be imposed. The geometry can be seen in (fig. 1). Fig. 1. Flow domain. KEYWORDS mesh superposition technique, non-isothermal flow, single screw extruder, temperature imposed in the screw, inflow with free tangential velocities, library of material data, Picard and secant solver, resolution strategy for complex non-isothermal flows. FILENAMES sse_aniso.msh, sse_init.dat, sse_init.cons, sse_init.res, sse_aniso.dat, sse_aniso.cons, sse_ aniso.lst, sse_aniso.res,... January Version

2 N EW CONCEPTS Temperature imposed in the moving part, with mesh superposition technique (MST) Contrary to example 47, we will not evaluate a heat conduction inside the screw, but impose directly a temperature distribution. By this way, we fix the temperature distribution for all nodes of the flow domain that are located inside the screw. If the scre w is rotating (not the case here), the prescribed temperature field will follow the motion of the screw. Inflow with free tangential velocities At the inlet of the flow domain, we want to prescribe a volumetric flow rate. Usually, the boundaries adjacent to the inlet are fixed, and the methods used to evaluate the velocity distribution in the inlet impose the tangential velocities to be zero. In this case, however, as the barrel wall is in rotation, we cannot use the usual method : we will use the method named constant normal force with free Vs. Indeed, with this method, we search the normal force to the inlet that must be set in order to get the prescribed volumetric flow rate. However, we do not constrain tangential velocities. Library of material data A library of standard materials is available to the users. This library is located in:../ ansys_inc/ v150/ polyflow/ polyflow16.0.0/ Material_Data. In this case, we choose a rubber in the Extrusion sub-directory. Its name is Extrusion_FilledRubber_nonisoth_373K.mat. Let us note that this path will change with the successive releases of Polyflow software. More generally, if the latest installed release is XYZ, you should find the library in../ ansys_inc/ vxyz/ polyflow/ polyflowxyz/ Material_Data. As the system of units of this example (mm-g-s-kelvin) is different from the one found in the material data file (m-kg-s- Kelvin), we have to perform a change of system of units! Picard and secant solver As the fluid is a filled rubber with a low power law index, Polydata warns the user to use a Picard scheme or to define an evolution scheme. In this case, we choose to use the Picard scheme. Moreover, it appears that using the Algebraic Multi-frontal Direct solver + Secant iterations accelerate significantly the computation when Picard is chosen; that is why, we use this technique in this example. Indeed, the secant iterations use more memory than the simple Algebraic Multi-frontal Direct solver, but the CPU (Computer time) is significantly reduced: a secant iteration is solved almost instantly compared to the resolution of a system with all unknowns. Resolution strategy for complex non-isothermal flows In this case, w e ad op t the follow ing strategy: in a first stead y ru n, w e solve a nonisothermal flow problem, with a prescribed temperature defined everywhere (by the use of a January Version

3 sub-model of type temperature imposed ). The advantage of using a sub-model is the following: you can just define your complete setup as if it was non -isothermal, and thus use without any change the material data loaded from the library, and eventually add a submodel to freeze the temperature. Next, in a second run (in this case of the evolution type), starting from the solution of the first run, we solve the actual non -isothermal flow problem (without the sub-model!); in order to reach the solution, we perform an evolution on the viscous dissipation term. SYSTEM OF UNITS Millimeter-gram-second-Kelvin. GEOMETRY AND MESH Fig. 2. Main dimensions of the flow domain and the screw. The flow domain has an outer diameter of 42 mm, and a full length of 140 mm. From entry to exit, we have successfully (as can be seen in fig. 2): 1. a cylindrical domain (where no screw is located) of 20 mm length, 2. a first conveying element of 40 mm length (pitch = 40mm), January Version

4 3. two successive conveying elements of 20 mm length each (pitch = 20mm), 4. a conic screw head of 15 mm height., 5. eventually, the diameter of the barrel reduces to 20 mm. The clearance between screw and barrel is 1 mm, and the fligh t depth of the screw is 7.3 mm. The mesh of the flow domain (57404 cells) and the screw (5156 cells) can be seen in fig. 3 and fig. 4 respectively. Fig Two views of the mesh of the flow domain. Fig. 4. Screw mesh. MATERIAL PROPERTIES Material data file: Extrusion_FilledRubber_nonisoth_373K.mat in (m-kg-s-kelvin) After a change of units, into (mm -g-s-kelvin), the material properties are: January Version

5 Fluid model: Gen. Newtonian non-isothermal flow problem. - Viscosity = F(g). H(T) F(g) = Bird-Carreau law: Fac = [g/ mm s] Facinf = 0 [g/ mm s] Tnat = 100 [s] Expo = 0.2 [-] H(T) = Arrhenius law: Alfa = 1400 [K] Talfa = [K] - Density = [g/ mm 3 ] - Conductivity = [g mm/ s 3 K] - Heat capacity = [mm 2 /s 2 K] - Inertia taken into account (*) - Viscous dissipation taken into account (*) (*) These two parameters must be activated by the user, because they were not set in the material data file. OPERATING CONDITIONS Flow boundary conditions for the flow d omain: - inlet_1: inflow, with a volumetric flow rate = 3000 mm 3 / s, with the method Constant normal force with free Vs - innerwall_2: zero wall velocity (vn=vs=0) - outerwall_3: Cartesian velocities imposed (vx,vy,vz), First point on rotation axis = (0, 0, 0), Second point on rotation axis = (0, 0, 1), angular velocity = rad/ s (=30rpm) - outlet_4: normal and tangential forces vanish (fn=fs=0) Thermal boundary conditions for the flow domain : - inlet_1: temperature imposed: T = K (= 80 C) - innerwall_2: temperature imposed : T = K (= 90 C) - outerwall_3: flux density imposed Q = * ( T T ), with = [g s -3 K -1 ] and T = K (= 110 C) - outlet_4: outflow Moving parts: January Version

6 - Moving part #1: domain = screw_2, angular velocity = 0 rpm, fluid sticks to the screw surface, temperature imposed condition, with T = K (= 90 C) POLYDATA SESSION #0 - read a mesh file: sse_aniso.msh - create a new task: F.E.M., steady state type - create a sub-task of type: Gen. Newt. non-isothermal flow problem - domain: flowdomain_1 - material data - read an old material data file: Browse in material data library; in directory Extrusion, select file Extrusion_FilledRubber_nonisoth_373K.mat Next, accept to change the system of units. Modify the new system of units into (mm-g-s-kelvin) Select RUN item. After conversion, accept the new data and the new units. - inertia terms taken into account - viscous heating taken into account - average temperature: T = K - flow boundary conditions - inlet_1: Inflow, with a volumetric flow rate = 3000 mm 3 / s, with the method "Constant normal force with free Vs" - innerwall_2: zero wall velocity (vn=vs=0) - outerwall_3: Cartesian velocities imposed (vx,vy,vz), First point on rotation axis = (0, 0, 0), Second point on rotation axis = (0, 0, 1), angular velocity = rad/ s (=30rpm). - outlet_4: normal and tangential forces vanish (fn=fs=0) - temperature boundary conditions - inlet_1: temperature imposed: T = K - innerwall_2: temperature imposed: T = K - outerwall_3: flux density imposed Q = * ( T - T ), with = [g s -3 K -1 ] and T = K. - outlet_4: outflow - interpolation - linear velocities - linear temperature - add upwinding on energy equation - Picard iteration on viscosity(g) - define moving parts - moving part #1 - domain: Screw_2 January Version

7 - motion: point of rotation axis: ( 0, 0, 0) orientation of axis: (0, 0, 1) angular velocity: 0 rpm. moving part coordinates are NOT updated. - thermal boundary condition: Switch to temperature imposed condition Temperature distribution: T = K. - Define sub-models: - create a sub-model of type: Temperature imposed - domain: flowdomain_1 - Temperature imposed: T = K. - Numerical parameters - numerical parameters for iterations - solver aggressivity = 3 ( AMF direct solver + secant) - filename syntax: - prefix: sse_init - outputs: - System of units for CFD-POST: mm-g-s-kelvin - save and exit: - data file: sse_init.dat - result file: sse_init.res - CFD-Post: sse_init.cfx.res POLYFLOW RUN #0 polyflow < sse_init.dat > sse_ini.lst & POLYDATA SESSION #1 - read a mesh file: sse_aniso.msh - read an old data file: sse_init.dat - redefine global parameter of a task: F.E.M., evolution type - in F.E.M. Task - Define sub-models - Redefine global parameters of a sub-model - Delete sub-model #1 - in F.E.M. Task 1 Sub-Task 1 - Material Data - viscous heating - EVOL on - scaling factor = 1, with f(s) = s on this parameter - EVOL off - Numerical parameters January Version

8 - start from an old result file: sse_init.res - evolution parameters - initial value of S = 0 - final value of S = 1 - initial value of delta-s = filename syntax: - prefix: sse_aniso - save and exit: - data file: sse_aniso.dat - result file: sse_aniso.res - CFD-Post: sse_aniso.cfx.res POLYFLOW RUN #1 polyflow < sse_aniso.dat > sse_aniso.lst & Thanks to the use of the algebraic multi-frontal (AMF) direct solver + secant and thanks to the chosen evolution strategy, the cost of this run is as follows: 3.2 Gb of Virtual Memory and 6800 seconds of CPU on a Linux 64 bit machine, on a single processor. If we keep the setup identical, except the kind of solver (one selects now the AMF direct solver), we get the following performances on the same computer: 2.5 Gb of Virtual Memory and seconds of CPU. By looking at these numbers, we can see the big interest of the secant option: despite a higher memory requirement (+ 33% here), we divided by slightly more than two the CPU time! GRAPHIC POST-PROCESSING In fig. 5, 6 and 7, we can see successively the pressure, the temperature and the viscous heating in half the geometry x 0: the barrel wall/ screw clearance experiences the highest shear and thus the greatest temperature rise. We observe that the heat generated increases the temperature from inlet to outlet of the flow domain (Fig 6), almost exclusively in this thin layer adjacent to the barrel wall. It seems that it is essentially the screw (maintained in this simulation at 90 C) that heats the main stream of fluid. As the temperature is only linear per element, some oscillations are observed; these should be avoided with a richer element for the interpolation of the temperature, 2x2 sub-linear for example (but with a significant higher CPU and memory costs). January Version

9 Fig. 5. Pressure distribution in half the geometry x 0. January Version

10 Fig. 6. Temperature distribution in half the geometry x 0. January Version

11 Fig. 7. Viscous heating distribution in half the geometry x 0 (Log scale). January Version

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