Non-isothermal Polymer Filling Process via Phase Field Method in Three Dimensions

doi:10.19596/j.cnki.1001-246x.8659

Abstract

Abstract:

We investigate the non-isothermal non-Newtonian filling process according to the phase field method in three dimensions. The moving interface between the Newtonian and non-Newtonian fluid is captured by the Cahn-Hilliard equation. Based on phase field parameters, the governing equations of the flow field could be written in a unified form. After that, the Navier-Stokes equations are split into several sub-equations and the FEM and SUPG will be used to handle the appropriate equations. The variation of the viscosity of the polymer melt is described via the Cross-WLF model. The thin wall rectangular cavities with and without obstacles are considered to illustrate the convergence, robustness and accuracy of the numerical algorithm. The influences of the inlet velocity and the size of the injection gate on the filling process are analyzed. The numerical results agree well with the experimental data and also exhibit good mass conservation properties.

Key words: non-isothermal, filling process, Cross-WLF model, phase field method, finite element method

CLC Number:

O242.1

Puyang GAO. Non-isothermal Polymer Filling Process via Phase Field Method in Three Dimensions[J]. Chinese Journal of Computational Physics, 2023, 40(6): 689-698.

Figures/Tables 16

Fig.1 Schematic diagram of the whole calculation process

Table 1 Several parameters for the polypropylene (PP) and its Cross-WLF model

Parameter	Value	Parameter	Value
ρ_l/(kg·m^-3)	0.96 × 10³	D₁/(Pa·s)	6.93 × 10¹¹
C_l/(J·kg^-1·K^-1)	2.0 × 10³	D₂/K	263.15
κ_l/(W·m^-1·K^-1)	0.19	D₃/(K·Pa^-1)	0
τ^*/Pa	30 354	A₁	26.5
n	0.21	A₂/K	51.6

Fig.2 Sketch map of the three dimensional rectangular cavity

Fig.3 Experimental data (left column) and numerical results (right column) of interface front development at different time instants (a) t=1.1 s; (b) t=1.9 s; (c) t=3.5 s

Fig.4 (a) Exact solution (red line) and numerical result (black line) of polymer melt volume; (b) variation of relative mass error of polymer melt

Fig.5 Distribution of temperature on the x-y plane with z=1.5 mm at different time instants (a) t=1.1 s; (b) t=1.9 s; (c) t=3.5 s

Fig.6 Three-dimensional view of distribution of temperature field at t=3.5 s

Fig.7 Temperature field distribution with velocities v1 and v2

Fig.8 Sketch of the rectangular cavity with a cylindrical obstacle

Fig.9 Experimental figures (left column) and numerical results (right column) of the free interface front at (a) t=0.8 s; (b) t=1.4 s

Fig.10 (a) Exact solution (red line) and numerical result (black line) of polymer melt volume; (b) variation of relative mass error of polymer melt

Fig.11 Distribution of temperature field at (a) t=0.6 s; (b) t=0.8 s; (c) t=1.4 s

Fig.12 Three-dimensional view of distribution of temperature field at t=1.4 s

Fig.13 (a) Interface front and (b) distribution of temperature at t=0.27 s

Fig.14 (a) Interface front and (b) distribution of temperature at t=0.275 s

Fig.15 (a) Interface front and (b) distribution of temperature field at t=0.525 s

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