AI 中文总结
本文通过数值计算，探究新近提出的粘弹性流体对数应变张量模型中魏森贝格数与粘度比的作用，发现粘度比影响非牛顿流剖面，且流动类型依赖性在圆柱绕流中显著。
AI 中文摘要
本文开展计算研究，旨在探究粘弹性流体模型中魏森贝格数（Weissenberg number）与聚合物和溶剂粘度贡献比值的不同及独立作用。所研究的张量模型为新近提出，基于弹性（或可恢复）应变与弹性应力间的对数关系；该模型中，弹性应变充当构象张量，其演化方程固有地保持行列式与正定性，本研究采用的计算方法亦强制这些性质。时间采用有限差分离散，空间采用基于变分多尺度（Variational Multiscale）方法的稳定混合有限元格式，对流项采用广义李导数（generalized Lie derivative）方法。在典型压力驱动流中分析模型行为，发现粘度比值对魏森贝格数增大时非牛顿流剖面的出现程度至关重要；将对数应变张量模型的解与合适的广义牛顿流体（Generalized Newtonian Fluid）模型解对比，表明即使在简单的圆柱绕平面流中，流动类型依赖性也具有显著作用。
英文摘要
We present a computational study aimed at exploring the different and independent roles of the Weissenberg number and of the ratio between the polymeric and solvent viscosity contributions in a viscoelastic fluid model. The tensorial model under investigation, recently proposed, is based on a logarithmic relation between the elastic (or recoverable) strain and the elastic stress. In this model, the elastic strain plays the role of a conformation tensor and its evolution equation inherently preserves its determinant and positive definiteness. These properties are also enforced in the computational method employed in the study. A finite-difference discretization in time is combined with a stabilized mixed finite element formulation based on the Variational Multiscale method for the spatial discretization and with a generalized Lie derivative approach for the advection terms. The behavior of the model is analyzed in paradigmatic pressure-driven flows and we find that the value of the viscosity ratio is crucial in determining to which extent non-Newtonian flow profiles are observed upon increasing the Weissenberg number. By comparing the solutions of the log-strain tensorial model with those of a suitable Generalized Newtonian Fluid model, we show that flow-type dependence plays a significant role even in the simple planar flow past a cylinder.
