流动过程中聚合物动态结晶的数学建模与数值模拟

发布时间：2018-02-11 21:14

本文关键词： 相场数值模拟定向核串晶流场枝晶　出处：《太原科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：在凝固过程中,流动对晶体成核和晶体生长产生很大的影响。在晶体成核阶段,流动会影响成核形状;晶体生长阶段,流动影响结晶形态,晶体又影响流动。把流动考虑到微观组织模拟中,可以进一步了解材料的各种特性。在微观组织模拟方面,相场模型是一种有效的材料模拟方法,能够获取微观组织在空间和时间上的瞬时状态。论文运用相场方法模拟了聚合物串晶晶体和流动下的聚合物动态结晶过程中的晶粒生长形貌。论文主要研究的内容为:首先,建立耦合流场的相场模型。在已有的相场模型上,考虑流体流动对结晶过程的影响,重新构造温度场方程。根据能量守恒,将流动添加到温度控制方程中,从而得到耦合流场的温度方程。并在该方程中引入一个耦合系数,使得熔体为固相时,流体流速为零;熔体为液相时,流体流速不为零。通过一组实验获得的材料物理参数计算相场模型参数,计算出的模型参数能够呈现许多种晶体相貌。其次,离散相场模型。用有限差分方法对无量纲流动下的聚合物动态结晶模型进行求解,模型中出现的时间和空间导数分别用向前差分格式、中心差分格式,拉普拉斯算子用九点格式离散。通过FORTRAN计算机语言进行编程,利用可视化软件进行后处理,得到相应的结晶图像,并进行比较。再次,用相场方法分别模拟以棒状和螺纹状为初始核的串晶形貌。通过改变前者与方向轴的角度,发现界面的不连续是串晶形成的主要原因;形成的串晶的横向薄片相互平行,并等距离分布;随着定向核的角度不同,模拟出不同的串晶形貌,横向薄片的稠密程度也不相同。而模拟出的螺纹状串晶上的薄片分布不规律,定向角对薄片的密度影响不大。最后,通过改变流速、各性异性系数、温度、无量纲扩散率、驱动力参数的数值,研究了在流场下各因素对聚合物(ips)结晶形态的影响。通过实验比对,结果显示:在流场下,聚合物结晶形貌不对称;各项异性系数、过冷度、无量纲驱动力的增加,能够促进晶体上分枝的增加,晶体长的比较密;扩散系数的增加反而抑制了枝晶二次分枝的形成。而流动促进顺流方向枝晶的生长,抑制逆流方向枝晶的生长。
[Abstract]:In the solidification process, the flow has a great influence on the nucleation and growth of the crystal. In the nucleation stage, the flow will affect the nucleation shape, while in the crystal growth stage, the flow will affect the morphology of the crystal. When the flow is considered in the microstructure simulation, the properties of the material can be further understood. In the field of microstructure simulation, the phase field model is an effective material simulation method. The transient state of microstructure in space and time can be obtained. In this paper, the morphology of grain growth in the process of dynamic crystallization of polymer is simulated by using phase field method. The main contents of this paper are as follows: first of all, The phase field model of coupled flow field is established. In the existing phase field model, considering the effect of fluid flow on crystallization process, the temperature field equation is re-constructed. According to the conservation of energy, the flow is added to the temperature control equation. The temperature equation of the coupled flow field is obtained, and a coupling coefficient is introduced into the equation so that the flow velocity is zero when the melt is a solid phase, and the melt is a liquid phase. The flow velocity of the fluid is not zero. The parameters of the phase field model can be calculated by the physical parameters of the material obtained from a group of experiments, and the calculated model parameters can present many kinds of crystal features. Discrete phase field model. The dynamic crystallization model of polymer under dimensionless flow is solved by finite difference method. The time and space derivatives in the model are obtained by the forward difference scheme and the central difference scheme, respectively. Laplacian operator is discretized in nine-point format. It is programmed by FORTRAN computer language and processed by visualization software. The corresponding crystalline images are obtained and compared. The phase field method is used to simulate the morphology of strands and threaded nuclei respectively. By changing the angle between the former and the directional axis, it is found that the discontinuity of the interface is the main cause of the formation of the crystals, and the transverse slices of the formed crystals are parallel to each other. And isometric distribution; with the different angle of the directional nucleus, different crystal morphology is simulated, and the density of the transverse slice is not the same, while the distribution of the thin slice on the threaded string is not regular, and the thickness of the transverse slice is not the same. The orientation angle has little effect on the density of the sheet. Finally, by changing the velocity of flow, coefficient of heterogeneity, temperature, dimensionless diffusivity, driving force parameters, The effects of various factors under the flow field on the crystalline morphology of the polymer were studied. The experimental results show that the morphology of the polymer is asymmetric, the heterogeneity coefficient, the undercooling degree and the dimensionless driving force increase in the flow field. The increase of diffusion coefficient inhibited the formation of secondary branching of dendrite, while the flow promoted the growth of dendrite in downstream direction and inhibited the growth of dendrite in countercurrent direction.
【学位授予单位】：太原科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O631.1

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