聚合物充填过程中裹气现象的数值模拟

doi:10.19596/j.cnki.1001-246x.8327

摘要/Abstract

摘要：

针对聚合物充填过程中的裹气现象，采用一种有限元（FEM）-间断有限元（DG）耦合算法对其进行数值模拟。对于自由运动界面，采用水平集（Level Set）方法进行捕捉；用XPP（eXtended Pom-Pom）本构模型来描述黏弹性流体的流变行为。采用有限元-间断有限元耦合算法求解统一的流场方程，并采用隐式间断有限元求解XPP本构方程、Level Set及其重新初始化方程。数值结果与文献中的实验结果及模拟结果吻合较好，验证了数值方法的稳定性及准确性。分析带有非规则嵌件型腔内，注射速度及浇口尺寸对裹气现象的影响，裹气容易出现在较高注射速度及较小浇口的情形。

关键词: 裹气, 有限元, 间断有限元, XPP本构模型, 水平集方法

Abstract:

The complicated gas entrapment problem in polymer filling process is studied. The moving melt interface is captured with a level set method. An XPP (eXtended Pom-Pom) constitutive model is utilized for the description of viscoelastic fluid. The governing equations of flow field are solved with a coupled continuous and discontinuous Galerkin method. The XPP constitutive equation, level set and its re-initialization equations are solved with an implicit discontinuous Galerkin method. Good agreement between experimental and numerical results illustrates validity of the combined algorithm. Influence of injection velocity and gate size on gas entrapment in a cavity with irregular insert was investigated. Entrapped gas is easier to appear as the injection velocity is higher and the gate size is smaller.

Key words: gas entrapment, finite element, discontinuous Galerkin, XPP constitutive model, level set method

中图分类号:

O242.1

高普阳. 聚合物充填过程中裹气现象的数值模拟[J]. 计算物理, 2021, 38(6): 693-706.

Puyang GAO. Numerical Investigation of Gas Entrapment in Polymer Filling Process[J]. Chinese Journal of Computational Physics, 2021, 38(6): 693-706.

图/表 20

图1 非规则管道型腔示意图

Fig.1 A schematic of irregular channel cavity

图2 计算中用到的网格2

Fig.2 Mesh2 used in the computation

图3 不同时刻实验结果(左)和数值结果(右)的对比(a) t=2.48；(b) t=3.0；(c) t=3.4；(d) t=3.7

Fig.3 A comparison of experimental (left) and numerical (right) results at different time instants (a) t=2.48, (b) t=3.0, (c) t=3.4, (d) t=3.7

图4 不同计算网格下t=2.48时刻前沿界面形态

Fig.4 Interface front at t=2.48 on different meshes

图5 t=3.7时刻，沿着垂直线x=7.5，(a) τxx、(b) τxy、(c) τyy的分布

Fig.5 (a) τxx, (b) τxy, (c) τyy along a vertical line x=7.5 on different meshes at t=3.7

图6 带有菱形嵌件矩形腔的示意图

Fig.6 A schematic of rectangular cavity with a diamond insert

图7 不同时刻实验结果(左)和数值结果(右)(a) t=0.4；(b) t=0.7；(c) t=1.1；(d) t=1.33

Fig.7 Experimental (left) and numerical (right) results (a) t=0.4; (b) t=0.7; (c) t=1.1; (d) t=1.33

图8 带有非规则嵌件梯形腔的示意图

Fig.8 A schematic of trapezoidal cavity with an irregular insert

图9 计算中用的网格2

Fig.9 Mesh2 used in the computation

图10 u=2.0时不同时刻前沿界面形态(a)t=0.2；(b)t=0.7；(c)t=1.0；(d)t=1.15

Fig.10 Profiles of interface front with u=2.0 at different time (a) t=0.2; (b) t=0.7; (c) t=1.0; (d) t=1.15

图11 不同网格上计算得到t=0.7时刻的(a)前沿界面及(b) τxx、(c) τxy和(d) τyy

Fig.11 (a) Profiles of interface front and (b) τxx, (c) τxy, (d) τyy at t=0.7 on different meshes

图12 u=10时不同时刻前沿界面形态(a)t=0.09；(b)t=0.15；(c)t=0.19；(d)t=0.28

Fig.12 Profiles of interface front with u=10 at different time (a) t=0.09; (b) t=0.15; (c) t=0.19; (d) t=0.28

表1 中等尺寸浇口下τxx, τxy, τyy的最大、最小值

Table 1 The minimum and maximum of τxx, τxy, τyy for a injection gate with middle size

	τ_xx		τ_xy		τ_yy
	最小值	最大值	最小值	最大值	最小值	最大值
u=2	-1.8	2.3	-2.1	2.1	-0.95	-0.92
u=5	-3.7	5.9	-4.7	4.7	-3.1	2.4
u=10	-4.1	6.7	-5.3	5.3	-3.4	3.9

图13 u=2.0时不同时刻前沿界面形态(a) t=0.3；(b) t=1.5；(c) t=2.0；(d) t=2.5

Fig.13 The development of interface front with u=2.0 at (a) t=0.3; (b) t=1.5; (c) t=2.0; (d) t=2.5

图14 u=5.0时不同时刻前沿界面形态(a) t=0.3；(b) t=0.6；(c) t=0.8；(d) t=1.1

Fig.14 Free surfaces for u=5.0 at different time instants (a) t=0.3; (b) t=0.6; (c) t=0.8; (d) t=1.1

图15 u=10.0时不同时刻前沿界面形态(a) t=0.05；(b) t=0.15；(c) t=0.2；(d) t=0.3

Fig.15 The development of melt front with u=10.0 at (a) t=0.05; (b) t=0.15; (c) t=0.2; (d) t=0.3

表2 较小尺寸浇口下τxx, τxy, τyy的最大、最小值

Table 2 The minimum and maximum of τxx, τxy, τyy for a smaller injection gate

	τ_xx		τ_xy		τ_yy
	最小值	最大值	最小值	最大值	最小值	最大值
u=2	-1.9	2.2	-1.8	1.8	-0.86	1.1
u=5	-2.7	4.1	-4.7	4.7	-2.6	2.3
u=10	-3.7	5.7	-5.4	5.4	-2.9	2.7

图16 u=5.0时熔体前沿界面在不同时刻的形态(a) t=0.08；(b) t=0.18；(c) t=0.25；(d) t=0.4

Fig.16 Profiles of melt front with u=5.0 at four time instants (a) t=0.08; (b) t=0.18; (c) t=0.25; (d) t=0.4

图17 u=10.0时熔体前沿界面在不同时刻的形态(a) t=0.05；(b) t=0.1；(c) t=0.15；(d) t=0.25

Fig.17 Profiles of interface front with u=10.0 at different time instants (a) t=0.05; (b) t=0.1; (c) t=0.15; (d) t=0.25

表3 较大尺寸浇口下τxx, τxy, τyy的最大、最小值

Table 3 The minimum and maximum of τxx, τxy, τyy for a bigger injection gate

	τ_xx		τ_xy		τ_yy
	最小值	最大值	最小值	最大值	最小值	最大值
u=2	-1.7	2.8	-4.8	4.8	-0.95	1.05
u=5	-5.1	6.1	-6.3	6.3	-3.0	3.9
u=10	-5.6	6.2	-7.0	7.0	-4.1	4.6

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