1. Design of Scintillator Die Fermi National Accelerator Laboratory Department of Mechanical Engineering Northern Illinois University

2. Ø 1.1 Front & Top Views of the Model Domain (All dimensions are in mm).

3. Density:882 kg/m 3 Shear-rate Dependent Viscosity (Carreau-Yasuda Law) Transition Parameter (expoa or e oa ) 0.5 Infinite Shear Rate Viscosity (facinf or   )0 Pa-s Zero Shear Rate Viscosity (fac or  o )200,000 Pa-s Exponent (expo or e o )0.252 Time Constant (tnat or  )4.6337 Temperature Dependent ViscosityNo BOUNDARY CONDITIONS  The flow inlet is given by volumetric flow rate Q = 1.287e-5 m 3 /s or 180 lb/hr. (Uniform mass flow rate).  All the walls are given as zero velocity, i.e. v s = v n = 0  A symmetry plane with zero tangential forces and zero normal velocity, f s = v n =0 are applied at half plane of the geometry.  Free surface is specified for the moving boundary conditions of the die with atmospheric pressure, p = p .  Exit for the flow is specified as, f s = f n = 0 MATERIAL DATA

4. Figure 1.1. Pressure Contours for Case 1. CASE 1. FULL MODEL Figure 1.2. Velocity Contours for Case 1. Figure 1.3. Velocity contours on different surfaces along Z-direction for Case 1 Figure 1.4. Swelling of the Extrudate for Case 1.

5. CASE 2 MODEL WITH SPIDER Figure 2.1. Pressure Contours for Case 2 Figure 2.2. Velocity Contours for Case 2. Figure 2.4. Swelling of the Extrudate for Case 2.Figure 2.3. Velocity contours on different surfaces along Z-direction for Case 2.

6. CASE 3 MODEL WITH/OUT SPIDER Figure 3.1. Pressure Contours for Case 3. Figure 3.2. Velocity Contours for Case 3. Figure 3.3. Velocity contours on different surfaces along Z-direction for Case 3. Figure 3.4. Swelling of the Extrudate for Case 3.

7. CASE 4RECTANGULAR SECTION Figure 4.1. Pressure Contours for Case 4.Figure 4.2. Velocity Contours for Case 4. Figure 4.4. Swelling of the Extrudate for Case 4. Figure 4.3. Velocity contours on different surfaces along Z-direction for Case 4.

9. TABLE 1 Comparison of Volumetric Flow rates, Average Velocities, and Average Inlet Pressures for Uniform Mass Flow at different sections Sections Volumetric Flow Rate (m 3 /s) Average Velocity (mm/s) Average Inlet Pressure (MPa) Inlet Outlet Case 1 Full Die1.286 x 10 -5 10.8 138.5 12.72 Case 2 With inlet as Spider 1.286 x 10 -5 38.85 138.5 8.79 Case 3 With inlet as Converging section(w/o spider) 1.286 x 10 -5 39.09 138.5 6.0053 Case 4 Rectangular section 1.286 x 10 -5 112.7 138.6 2.675

10. The reasons for the discrepancies may be one of the following:  There were some technical problems experienced in Polyflow. The values for pressure and velocity are supposed to change with change in the value of the density of the polymer. But running two simulations, one with 1 and the other with 882, the values for the pressure and velocity came out to be same. We are communicating with the Polyflow technicians about this problem from past one month and still waiting to hear from them.  The numerical analyses run for all these cases are based on the material properties of the polymer Styron 685d. But we are skeptical whether the results will be similar if we use the actual polymer Styron 663, for which the operating conditions were given.  One of the constraints that are imposed in the above analyses is “ No Temperature Dependence ”, i.e. the results are based on the assumption that the temperature is uniform throughout the process. To overcome this drawback, another simulation with temperature dependence is run and results show that the average Inlet Pressure and Exit velocity are the same which were earlier. DISCUSSIONS  From the data given by FNAL, it is known that for mass flow rate of 180,  The average operating pressure for the extrusion process is 1000 – 1200 psi 6.894 MPa – 8.2737 MPa.  The velocity with which the extrudate is pulled out is 12 60.96.  Now for this mass flow rate which is halved equivalent to a volumetric flow rate of 1.286 x 10 -5 m 3 /s, the average inlet pressure is found to be 12.72 MPa and the average exit velocity is 138.5 which is very high compared to current operating conditions.

11.  The shape of the die lip is similar for all the cases discussed.  The uniform average velocity at the exit is nearly 138.5, which is same for all the cases.  The Inlet pressure changes at the entry of different sections. For the whole die, the inlet pressure is 12.7 MPa.  The above three conclusions show that running the analyses for either the whole die or the die with different sections results in same exit velocity for a uniform mass flow rate. CONCLUSIONS

12.  To overcome the drawback of no temperature dependence, another simulation with temperature dependence is run and the results show that the values for Inlet pressure and Exit velocity do not change much. THERMAL BOUNDARY CONDITIONS Temperature imposed along the inlet and the walls of the die = 466K Along the symmetry planes, the condition imposed is Insulated/Symmetry along the boundaries. Flux density is imposed on the free surfaces as convection boundaries. The condition is as follows: Outflow condition is selected at the outlet for a vanishing conductive heat flux.

13. CASE 5. FULL MODEL (Temperature Dependence) Figure 5.1. Pressure Contours for Case 5.Figure 5.2. Velocity Contours for Case 5. Figure 5.3. Temperature Contours for Case 5. Figure 5.4. Swelling of the Extrudate for Case 5.

14.  The uniform average velocity at the exit is nearly 138.5.  The Inlet pressure changes at the entry of different sections. For the whole die, the inlet pressure is 12.7 MPa.  The Average Static temperature at the outlet is 374.681 K. though somewhere in the die,there is a maximum temperature point reaching 469.9693 K.  The above three conclusions show that running the analyses for either the whole die or the die with different sections results in same exit velocity for a uniform mass flow rate. CONCLUSIONS