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Design of Solid Hexagonal Scintillator Die

INTRODUCTION

The report is divided in several sections as:

  1. Problem Description
  2. Polymer Constitutive Models
  3. Material Properties, Boundary Conditions, and Other Conditions for Numerical Simulation
  4. Meshes
  5. Results
  6. Discussion

PROBLEM DESCRIPTION:

The problem deals with the flow of a polymer fluid through a three-dimensional hexagonal die. Due to the symmetry of the problem, the computational domain is defined for half geometry and a plane of symmetry is taken.

Figure 1 shows the model domain indicated with different sections. The desired final shape at end of extrudate was assumed to be a regular hexagon with dimensions given from NICADD. Further, the die length is assumed as 35 mm and the extrudate length is taken both as 70 mm. The melt enters at one end, flows through the solid die, and exits to the open atmosphere for extrudate. Figures 2 and 3 are the front and the top views for the model domain with the dimensions taken in mm.

Figure 1.Model Domain.

Figure 2.Front view of the Model

Figure 3.Model Domain.

POLYMER CONSTITUTIVE MODELS

In contrast to Newtonian fluid for which there exists a single constitutive model that can account for all Newtonian flows, there is no single model that can account for all polymer flows due to complexity of the polymer fluid. This leads to many suggested models for different flows. Though some are much more general than some others like co-rotational and co-deformational models, they are too complicated for ordinary implementation. Thus, simple but much practical models are more frequently found being used in industry. One extension of Newtonian model is called generalized Newtonian model. In this analysis this model is used with in different scenarios: (1) isothermal flow, (2) non-isothermal flow, and This model has been used in industry for more than a couple of decades and proved to quite accurately predict the flows in die design as in this study.

  • Generalized Newtonian Isothermal Flow
  • Generalized Newtonian Non-Isothermal Flow with Temperature dependence on Viscosity. (Viscous heating is not taken into account).

Even in the generalized Newtonian model there are various models. In this study the Carreau-Yasuda model was adopted as used in Altair’s report for Fermi Lab.

MATERIAL PROPERTIES, BOUNDARY CONDITIONS, AND OTHER CONDITIONS FOR NUMERICAL SIMULATION

Material properties used in the study are assumed same as in Altair’s report and are of Dow’s Styron 685d. This material is chosen because it has all the values necessary to run the POLYFLOW software and is the closest to the Styron 663 provided by Fermi Lab. It is also expected to yield very similar results to the Styron 663.

MODEL 1. GENERALIZED NEWTONIAN ISOTHERMAL FLOW

MATERIAL DATA

Density:882 kg/m3

(Here, the Boussinesq approximation is used instead of a constant density. This model treats density as a constant value in all solved equations, except for the buoyancy term in the momentum equation)

Shear-rate Dependent Viscosity (Carreau-Yasuda Law)

Zero Shear Rate Viscosity (fac or o)200,000 Pa-s

Infinite Shear Rate Viscosity (facinf or )0 Pa-s

Exponent (expo or eo)0.252 (evolution on this parameter)

Time Constant (tnat or )4.6337

Transition Parameter (expoa or eoa) 0.5

Temperature Dependent ViscosityNo
BOUNDARY CONDITIONS

The boundary sets for the problem and the conditions at the boundaries of the domains are specified as follows:

A) FLOW BOUNDARY CONDITIONS

The flow inlet is given by volumetric flow rate

a) Q = 1.66 x 10-6m3/s (i.e., uniform velocity = 1.4041 x 10-2 m/s) (from Altair’s report) and b) Q = 1.287e-5 m3/s or 180 lb/hr. (Uniform mass flow rate).

All the walls are given as zero velocity, i.e. vs = vn = 0

 A symmetry plane with zero tangential forces and zero normal velocity, fs=vn=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, fs = fn = 0

B) 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.

RESULTS

The general behaviors of the pressure, velocity and temperature are shown for the full model for isothermal and non-isothermal cases. The volumetric flow rate is calculated from uniform mass flow rate at the entry section.

With volumetric flow rate calculated from mass flow rate ( = 180lb/hr). The mass flow rate of 180 lb/hr is taken and halved to input the volumetric flow rate for the model with plane of symmetry taken at half of the geometry.

In Figures 4 & 5, the velocity contours and pressure contours are shown along the whole die to predict the behavior of the polymer flow for Isothermal case. Swelling of the extrudate is shown in Figure 6. In Figures 7, 8 & 9 pressure, velocity and temperature contours are shown for Non-Isothermal case. Figure 10 shows the profile of the die, which is the desired shape to be designed for a Non-Isothermal case. The swelling of the extrudate clearly shows that the required dimensions of the scintillator are obtained if the die is manufactured with the profile modeled.

FOR FULL MODEL (Q = 1.287 x 10-5m3/s)

Figure 4.Pressure Contours for Isothermal Case.

Figure 5.Velocity Contours for Isothermal Case.

Figure 6.Swelling of the Extrudate for Isothermal Case.

Non Isothermal Case(Case 2) (Q = 1.287 x 10-5m3/s)

Figure 7.Pressure Contours for Non Isothermal Case.

Figure 8.Velocity Contours for Non Isothermal Case.

Figure 9.Temperature contours for Non Isothermal Case.

Figure 10. Swelling of the Extrudate for Non Isothermal Case.

COMPARISON OF DIE LIP SHAPES FOR ISOTHERMAL AND NON-ISOTHERMAL CASES

In Figure 11, the profiles of the die for both Isothermal and Non-Isothermal cases are compared. It shows that they are almost similar for equal and uniform mass flow rate at the entry section.

Figure 11.Comparison of Die Inlet Profile for Isothermal and Non Isothermal cases with uniform mass flow rate

CONCLUSIONS

The shape of the die lip is similar for both the cases discussed.

The uniform average velocity at the exit is nearly 28.33 mm /sec for Isothermal case and 28.355for Non-Isothermal case, which is almost same for both cases.

The Inlet pressure for the whole die is 1.81 MPa for both cases.

The Average Static temperature at the outlet is 465.72 K.

DISCUSSIONS

All the results obtained are to be checked by comparing them with the experimental simulations.

The mass flow rate can be increased since the exit velocity is smaller when compared to previous simulations.

All the dimensions of the geometry are assumed except the dimensions of the outlet shape, which is given by NICADD.