一种热力学一致的约翰逊-塞加曼-吉塞库斯模型：杆攀爬效应的数值模拟
A thermodynamically consistent Johnson-Segalman-Giesekus model: numerical simulation of the rod climbing effect
AI总结：
本文提出了一种热力学一致的约翰逊-塞加曼-吉塞库斯模型，通过数值模拟展示了其在描述杆攀爬效应方面的优越性能。
摘要：
粘弹性速率型流体因其能够描述应力松弛、非线性蠕变和法向应力差等现象而成为非牛顿流体模型中的一大类。在简单剪切流中正常应力差的存在会导致作用于主流动方向垂直方向上的力。杆攀爬效应，即流体沿旋转轴的杆上升，与这一现象有关。在包括Oldroyd-B模型和Giesekus模型以及Gordon--Schowalter卷积导数的粘弹性速率型流体类中，我们通过热力学分析和数值模拟表明，约翰逊-塞加曼模型的一个热力学一致变种能够极好地捕捉实验数据，并因此优于该类中的其他模型，包括标准的约翰逊-塞加曼模型，该模型在工程应用中被广泛使用，但在此被证明与热力学第二定律不一致。我们发布了一个稳健且计算高效的高阶有限元实现作为开源软件在GitHub上。该实现基于任意拉格朗日-欧拉（ALE）公式来表述控制方程，并使用Firedrake库开发。
英文摘要：
Viscoelastic rate-type fluids represent a popular class of non-Newtonian fluid models due to their ability to describe phenomena such as stress relaxation, non-linear creep, and normal stress differences. The presence of normal stress differences in a simple shear flow gives rise to forces acting in directions orthogonal to the primary flow direction. The rod climbing effect, i.e. the rise of a fluid along a rod rotating about its axis, is associated with this phenomenon. Within the class of viscoelastic rate-type fluids that includes the Oldroyd-B and Giesekus models with Gordon--Schowalter convected derivatives, we show -- by means of thermodynamical analysis and numerical simulations -- that a thermodynamically consistent variant of the Johnson--Segalman model captures experimental data exceedingly well and is therefore superior to other models in this class, including the standard Johnson--Segalman model, which is widely used in engineering applications but is shown here to be incompatible with the second law of thermodynamics. We release a robust and computationally efficient higher-order finite-element implementation as open-source software on GitHub. The implementation is based on an arbitrary Lagrangian--Eulerian (ALE) formulation of the governing equations and is developed using the Firedrake library.
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