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首页> 外文会议>International Conference on Computational Fluid Dynamics >Entry ow computations of shear-thinning and viscoelastic liquids with the LS-STAG immersed boundary method
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Entry ow computations of shear-thinning and viscoelastic liquids with the LS-STAG immersed boundary method

机译：具有LS-STAG浸没边界法的剪切变薄和粘弹性液体的进入剪切和粘弹性液体

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This communication presents a progress report on an ongoing project aiming at the computation of rheolog- ically complex uid ows with a realistic constitutive law, which would take into account the pseudoplastic, viscoelastic and thixotropic behavior of the materials. The ow solver is based on the LS-STAG method, which is an immersed boundary (IB)/cut-cell method that allows the computation of ows in irregular or moving geometries on xed Cartesian meshes, reducing thus the bookkeeping of body- tted methods. The discretization in the cut-cells (i.e., the computational cells which are cut by the irregular boundary) is achieved by requiring that the global conservation properties of the Navier-Stokes equations are satis ed at the dis- crete level, resulting in a stable and accurate method and, thanks to the level-set representation of the IB boundary, at low computational costs [1].In a previous work [2] we have applied the LS-STAG method to viscoelastic ows, for which accurate discretization of the viscous stresses up to the cut-cells is of paramount importance for stability and accuracy. For this purpose, the LS-STAG discretization of the Newtonian stresses has been extended to the transport equation of the elastic stresses (whose prototype is the Oldroyd-B model), such that the node-to-node oscilla- tions of the stress variables are prevented by using a velocity-pressure-stress (v?p?τ ) staggered arrangement (see Fig. 1). The discretization of the viscoelastic constitutive equation was performed by constructing spe- cial quadratures for the volumic terms which yield a globally conservative discretization up to the cut-cells. Results on popular benchmarks for viscoelastic ows show that our IB method demonstrates an accuracy and robustness comparable to body- tted methods up to large levels of elasticity.The next step was to incorporate the non-Newtonian (or pseudoplastic) behavior in the LS-STAG code, by considering that the stress tensor takes the form τ =η(r)D, where the shear viscosity η(γ) is modelled by popular non-Newtonian laws such as the power-law, Carreau or Cross models. The crucial part for taking into account shear-thinning or shear-thickening e ects is the computation of the rate-of-strain tensor D and theshear rate γ=√1/2D in the cut-cells and at the immersed boundary. We have been able to achieve an accurate discretization that ts elegantly in the framework of the v-p -τ arrangement and the special quadratures developed previously for viscoelastic ows. Preliminary LS-STAG computations of shear-thinning ows in Couette geometries were presented in [3].The aim of this presentation is twofold. First, we intent to give a thorough examination on the global accuracy of the LS-STAG method, and especially the computation of the stresses and non-Newtonian viscosity at the IB where the shear is maximal. For this purpose, we will consider the steady 2D Taylor-Couette ow for which an analytical solution can be obtained for the cases of Newtonian, shear-thinning (power-law model) and elastic (Oldroyd-B model) uids. In a second part, we intent to perform numerical simulations of contraction ows of dilute polymer solutions that display both shear-thinning and elastic behaviour. In the vicinity of contractions such as the one displayed in Fig. 2, polymer ows undergo large extensional deformations which pose a numerical and modelling challenge to traditional di erential constitutive equations [4]. For addressing this issue, a hierarchy of constitutive equations is implemented in the LS-STAG code (Oldroyd-B, White-Metzner and Giesekus models, including multi-mode versions). The robustness and the validity of our numerical predictions will be evaluated for contraction ows for which experimental results are available [4, 5].
机译：该通信礼物上一个正在进行的项目，旨在rheolog- ically复杂UID OWS的与现实的本构关系，这将考虑到假塑性，材料的粘弹性和触变行为计算的进展报告。所述流解算器是基于LS-STAG方法，这是一种浸入边界（IB）/切割单元，其允许在固定的笛卡尔网格在不规则或移动的几何形状OWS的计算，从而减少身体 - 的方法tted簿记方法。在切割单元的离散化（即，计算单元，其由不规则边界切断）被要求实现了Navier-Stokes方程的全球保护的性能是在解散克里特水平SATIS版，从而得到稳定的而准确的方法及，由于IB边界的水平集表示，在低计算成本[1]。在一个以前的工作[2]我们已经应用了LS-STAG方法粘弹OWS，为的，其准确的离散化粘性应力高达切口细胞是对于稳定性和准确性最为重要的。为了这个目的，牛顿应力的LS-STAG离散一直延伸到弹性应力的输运方程（其原型的奥尔德罗伊德-B型），使得该节点到节点振上的应力变量的蒸发散通过使用速度 - 压力应力（v 2 p 3τ）防止交错排列（参照图1）。粘弹性构方程的离散化通过构建spe-官方求积为其产生一个全局保守离散可达切口细胞volumic条款进行。结果上流行的基准粘弹性OWS表明，我们的IB方法演示了精确度和耐用性堪比体佩tted方法达到大级别elasticity.The下一步就是将非牛顿（或假的）行为在LS-STAG码，通过考虑应力张量的形式为τ=η（r）的d，其中剪切粘度η（γ）由流行非牛顿法如幂律，或的Carreau Cross车型建模。用于考虑剪切稀化或剪切稠化Ê学分的关键部分是速率的应变张量d的计算，并在切割细胞中并在浸入边界theshear速率γ=√1/ 2D。我们已经能够实现精确的离散化是TS优雅在V-P-τ安排的框架和特殊求积粘弹性OWS以前开发。在库埃特几何剪切稀化OWS的初步LS-STAG计算在已提交[3] .The此介绍的目的是双重的。首先，我们打算给在LS-STAG方法的准确性全球彻底检查，尤其是应力和非牛顿粘度在IB其中剪切是最大的计算。为此目的，我们将考虑稳定2D泰勒-库埃特流动对于可以为牛顿，剪切稀化（幂律模型）和弹性（奥尔德罗伊德-B型）的UID的情况下获得的解析解。在第二部分中，我们的意图来执行同时显示剪切变稀和弹性行为稀聚合物溶液的收缩OWS的数值模拟。在收缩的附近，如一个在图2中显示的，聚合物OWS经历其构成数值和建模挑战传统二大的拉伸变形erential构方程[4]。为了解决这一问题，本构方程的层次结构在LS-STAG实现代码（奥尔德罗伊德-B，白METZNER和Giesekus模式，包括多模版本）。的鲁棒性和我们的数字预测的有效性将用于收缩OWS针对实验结果可用[4，5]进行评价。

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