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首页> 外文期刊>Journal of the Brazilian Society of Mechanical Sciences and Engineering >Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids
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Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids

机译：稀疏剪切流体和规则屈服应力流体的纯粘性流的Galerkin最小二乘解

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This paper aims to present Galerkin Least-Squares approximations for flows of Bingham plastic fluids. These fluids are modeled using the Generalized Newtonian Liquid (GNL) constitutive equation. Their viscoplastic behavior is predicted by the viscosity function, which employs the Papanastasiou's regularization in order to predict a highly viscous behavior when the applied stress lies under the material's yield stress. The mechanical modeling for this type of flow is based on the conservation equations of mass and momentum, coupled to the GNL constitutive equation for the extra-stress tensor. The finite element methodology concerned herein, the well-known Galerkin Least-Squares (GLS) method, overcomes the two greatest Galerkin shortcomings for mixed problems. There is no need to satisfy Babu?ka-Brezzi condition for velocity and pressure subspaces, and spurious numerical oscillations, due to the asymmetric nature of advective operator, are eliminated. Some numerical simulations are presented: first, the lid-driven cavity flow of shear-thinning and shear-thickening fluids, for the purpose of code validation; second, the flow of shear-thinning fluids with no yield stress limit, and finally, Bingham plastic creeping flows through 2:1 planar and axisymmetric expansions, for Bingham numbers between 0.2 and 133. The numerical results illustrate the arising of two distinct unyielded regions: one near the expansion corner and another along the flow centerline. For those regions, velocity and pressure fields are investigated for the various Bingham numbers tested.
机译：本文旨在提出宾汉塑性流体流动的Galerkin最小二乘近似。使用广义牛顿液体（GNL）本构方程对这些流体进行建模。它们的粘塑性行为是由粘度函数预测的，该函数利用Papanastasiou的正则化来预测当施加的应力处于材料的屈服应力之下时的高粘性行为。这种类型的流动的机械建模基于质量和动量守恒方程，再加上超应力张量的GNL本构方程。本文涉及的有限元方法，即众所周知的Galerkin最小二乘（GLS）方法，克服了混合问题的两个最大的Galerkin缺点。不需要满足速度和压力子空间的Babu？ka-Brezzi条件，并且消除了由于对流算子的非对称性质而引起的虚假数值振荡。提出了一些数值模拟：首先，为了代码验证的目的，剪切稀化和剪切稠化流体的盖驱动腔流动。其次，剪切稀化流体的流动没有屈服应力极限，最后，宾厄姆塑性蠕变流经2：1的平面和轴对称膨胀，宾厄姆数在0.2和133之间。数值结果说明了两个明显的非屈服区域的产生：一个靠近膨胀角，另一个沿流中心线。对于这些区域，研究了各种宾汉数的速度和压力场。

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