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arXiv 2002.05557physics.flu-dyncs.NAmath.NAmath.OC
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三维屈服应力流体绕沉降颗粒流动的屈服极限计算

Computing the Yield Limit in Three-dimensional Flows of a Yield Stress Fluid About a Settling Particle

José A. Iglesias, Gwenael Mercier, Emad Chaparian, Ian A. Frigaard

摘要:

计算粘塑性流体流动的屈服极限$Y_c$(屈服应力与驱动应力的临界比)是一个具有挑战性的问题,通常需要迭代流变参数以接近该极限,以及正确考虑屈服应力和潜在自适应网格的精确计算。对于颗粒沉降流,近年来,在二维(2D)或轴对称流动限制条件下,对许多反平面剪切流构型和许多几何形状,都已通过解析方法计算出了$Y_c$。在这里,我们接近3D颗粒沉降的问题,以及如何直接计算屈服极限,即无需迭代地改变流变学以接近屈服极限。所提出的方法开发工具,从优化理论,利用这一事实,即$Y_c$是通过一个最小化问题定义。我们重铸这个最小化的原始和对偶变分问题,发展必要的理论,最后实现一个基本的,但可行的算法。我们对准确的圆柱体和椭球体的轴对称流计算基准的结果,使用自适应网格计算。我们还比较了在可比的固定网格上计算$Y_c$的精度。这证明了在多个维度中直接计算$Y_c$的可行性和益处。最后,我们提出了一些复杂的3D粒子形状的示例计算。

英文摘要:

Calculating the yield limit $Y_c$ (the critical ratio of the yield stress to the driving stress), of a viscoplastic fluid flow is a challenging problem, often needing iteration in the rheological parameters to approach this limit, as well as accurate computations that account properly for the yield stress and potentially adaptive meshing. For particle settling flows, in recent years calculating $Y_c$ has been accomplished analytically for many antiplane shear flow configurations and also computationally for many geometries, under either two dimensional (2D) or axisymmetric flow restrictions. Here we approach the problem of 3D particle settling and how to compute the yield limit directly, i.e. without iteratively changing the rheology to approach the yield limit. The presented approach develops tools from optimization theory, taking advantage of the fact that $Y_c$ is defined via a minimization problem. We recast this minimization in terms of primal and dual variational problems, develop the necessary theory and finally implement a basic but workable algorithm. We benchmark results against accurate axisymmetric flow computations for cylinders and ellipsoids, computed using adaptive meshing. We also make comparisons of accuracy in calculating $Y_c$ on comparable fixed meshes. This demonstrates the feasibility and benefits of directly computing $Y_c$ in multiple dimensions. Lastly, we present some sample computations for complex 3D particle shapes.

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