论文标题
对等效GNF模型的制定，作为Fene-P所描述的聚合物溶液流的有效近似
Formulation of an equivalent GNF model as an efficient approximation for flow of polymer solutions described by FENE-P
论文作者
论文摘要
已知分子本构模型，例如用于聚合物溶液的Fene-P，在相对较大的流速下具有收敛性问题。在这项研究中，我们研究了基于数值有效的基于GNF的FENE-P近似值的可能性，该近似值将紧密近似流场。首先，我们比较Fene-P和等效GNF模型预测的流场。对于这些研究，我们考虑了球体周围的流量，并选择了Carreau-Yasuda模型作为代表性GNF。通过选择参数以均衡粘度剪切速率依赖性来使其等效于Fene-P。我们的结果显示了GNF模型的严重缺陷，这是由于无法解释链条拉伸，尤其是在停滞点附近。接下来，通过制定等效的GNF-X（流变学杂志64，493（2020）]模型，添加了扩展成分对局部粘度的影响。甚至这也未能捕获应力和流量曲线中的不对称性，并且相对于Fene-P，在两个停滞点上都会预测非常巨大的应力。因此，我们提出了一种新颖的修改形式主义（称为GNF-XM），能够成功捕获所有趋势。 GNF-XM的阻力系数与考虑所有流速的FENE-P预测非常吻合。值得注意的是，用GNF-XM解决流场所需的计算时间大约比Fene-P的数量级低，尤其是在较高的流速下。因此，我们成功地制定了高效的基于GNF的近似值，其形式主义可以扩展到其他类似复杂的本构模型。
The molecular constitutive models, like FENE-P for polymer solutions, are known to have convergence issues at relatively larger flow rates. In this study, we investigate the possibility of a numerically efficient GNF-based approximation of FENE-P, which would closely approximate the flow field. Firstly, we compare the flow fields predicted by FENE-P and an equivalent GNF model. For these studies, we considered the flow around a sphere and selected the Carreau-Yasuda model as the representative GNF. This is made equivalent to the FENE-P by selecting parameters to equalize the viscosity-shear rate dependence. Our results show severe deficiencies of the GNF model, owing to its inability to account for chain stretching, particularly near the stagnation points. Next, the effect of extensional components on the local viscosity was added by formulating an equivalent GNF-X [Journal of Rheology 64, 493 (2020)] model. Even this failed to capture the asymmetry in the stress and flow profiles and predicted very large stresses at both stagnation points, relative to FENE-P. Hence, we proposed a novel modified formalism (denoted as GNF-XM) that was able to capture all trends successfully. The drag coefficients from GNF-XM agreed well with FENE-P predictions for all flow rates considered. Significantly, the computational times required to solve the flow field with GNF-XM is about an order of magnitude lower than that of FENE-P, especially at higher flow rates. Thus, we have successfully formulated a highly efficient GNF-based approximation to the FENE-P, whose formalism can be extended to other similarly complicated constitutive models.
