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首页> 外文会议>Eighth International Conference on Computational Fluid Dynamics >Entry u001dow computations of shear-thinning and viscoelastic liquids with the LS-STAG immersed boundary method
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Entry u001dow computations of shear-thinning and viscoelastic liquids with the LS-STAG immersed boundary method

机译：用LS-STAG浸入边界法计算剪切稀化和粘弹性液体的入口

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摘要

This communication presents a progress report on an ongoing project aiming at the computation of rheolog-rnically complex u001duid u001dows with a realistic constitutive law, which would take into account the pseudoplastic,rnviscoelastic and thixotropic behavior of the materials. The u001dow solver is based on the LS-STAG method,rnwhich is an immersed boundary (IB)/cut-cell method that allows the computation of u001dows in irregular orrnmoving geometries on u001cxed Cartesian meshes, reducing thus the bookkeeping of body-u001ctted methods. Therndiscretization in the cut-cells (i.e., the computational cells which are cut by the irregular boundary) is achievedrnby requiring that the global conservation properties of the Navier-Stokes equations are satisu001ced at the dis-rncrete level, resulting in a stable and accurate method and, thanks to the level-set representation of the IBrnboundary, at low computational costs [1].In a previous work [2] we have applied the LS-STAG method to viscoelastic u001dows, for which accuraterndiscretization of the viscous stresses up to the cut-cells is of paramount importance for stability and accuracy.rnFor this purpose, the LS-STAG discretization of the Newtonian stresses has been extended to the transportrnequation of the elastic stresses (whose prototype is the Oldroyd-B model), such that the node-to-node oscilla-rntions of the stress variables are prevented by using a velocity-pressure-stress (v−p−τu001c ) staggered arrangementrn(see Fig. 1). The discretization of the viscoelastic constitutive equation was performed by constructing spe-rncial quadratures for the volumic terms which yield a globally conservative discretization up to the cut-cells.rnResults on popular benchmarks for viscoelastic u001dows show that our IB method demonstrates an accuracyrnand robustness comparable to body-u001ctted methods up to large levels of elasticity.The next step was to incorporate the non-Newtonian (or pseudoplastic) behavior in the LS-STAG code,rnby considering that the stress tensor takes the form τu001c =η(r)D, where the shear viscosity η(γ) is modelled byrnpopular non-Newtonian laws such as the power-law, Carreau or Cross models. The crucial part for taking intornaccount shear-thinning or shear-thickening eu001bects is the computation of the rate-of-strain tensor D and theshear rate rγ=√1/2D in the cut-cells and at the immersed boundary. We have been able to achieve an accuraterndiscretization that u001cts elegantly in the framework of the v-p -τ u001c arrangement and the special quadraturesrndeveloped previously for viscoelastic u001dows. Preliminary LS-STAG computations of shear-thinning u001dows inrnCouette geometries were presented in [3].The aim of this presentation is twofold. First, we intent to give a thorough examination on the globalrnaccuracy of the LS-STAG method, and especially the computation of the stresses and non-Newtonian viscosityrnat the IB where the shear is maximal. For this purpose, we will consider the steady 2D Taylor-Couette u001dow forrnwhich an analytical solution can be obtained for the cases of Newtonian, shear-thinning (power-law model) andrnelastic (Oldroyd-B model) u001duids. In a second part, we intent to perform numerical simulations of contractionrnu001dows of dilute polymer solutions that display both shear-thinning and elastic behaviour. In the vicinityrnof contractions such as the one displayed in Fig. 2, polymer u001dows undergo large extensional deformationsrnwhich pose a numerical and modelling challenge to traditional diu001berential constitutive equations [4]. Forrnaddressing this issue, a hierarchy of constitutive equations is implemented in the LS-STAG code (Oldroyd-B,rnWhite-Metzner and Giesekus models, including multi-mode versions). The robustness and the validity of ourrnnumerical predictions will be evaluated for contraction u001dows for which experimental results are available [4, 5].
机译：这份通讯提供了一个正在进行中的项目的进度报告，该项目旨在利用现实的本构定律来计算流变-复杂的u001duid u001dows，其中应考虑材料的假塑性，粘弹弹性和触变性。 u001dow解算器基于LS-STAG方法，这是一种浸入边界（IB）/切割单元方法，允许在u001固定的笛卡尔网格上以不规则或不规则运动的几何形状计算u001dows，从而减少了对人体方法的记账。通过要求Navier-Stokes方程的全局守恒性质在离散水平上得到满足，从而实现了切割单元（即被不规则边界切割的计算单元）的离散化，从而获得了一种稳定而准确的方法并且，由于使用了IBrnboundary的水平集表示形式，因此计算成本较低[1]。在先前的工作[2]中，我们将LS-STAG方法应用于粘弹性u001dows，为此，粘滞应力的精确离散化达到了切单元对于稳定性和准确性至关重要。为此，牛顿应力的LS-STAG离散化已扩展到弹性应力的传递方程（其原型为Oldroyd-B模型），因此该节点通过使用速度-压力-应力（v-p-τu001c）交错排列来防止应力变量的节点间振荡（见图1）。粘弹性本构方程的离散化是通过构造体积项的专业正交函数来进行的，从而对切割单元产生全局保守的离散化。粘弹性u001dow的流行基准测试结果表明，我们的IB方法证明了精度与鲁棒性相当下一步是将非牛顿（或假塑性）行为纳入LS-STAG代码中，考虑到应力张量采用τu001c=η（r）D的形式，其中剪切粘度η（γ）由非牛顿定律建模，例如幂律，Carreau或Cross模型。考虑剪切变稀或剪切变厚eu001bects的关键部分是计算剪切单元中和浸入边界处的应变率张量D和剪切率rγ=√1/ 2D。我们已经能够在v-p-τu001c排列和先前为粘弹性u001dows开发的特殊正交框架内实现优雅的精确离散化。 [0013]提出了剪切稀化u001dows inrnCouette几何形状的LS-STAG的初步计算。该演示的目的是双重的。首先，我们打算对LS-STAG方法的整体精度进行彻底检查，尤其是在剪切最大的IB处的应力和非牛顿粘度的计算。为此，我们将考虑稳态二维Taylor-Couette u001dow形式，对于牛顿，剪切稀化（幂律模型）和弹性（Oldroyd-B模型）u001duid情况，可以得到解析解。在第二部分中，我们打算对显示剪切稀化和弹性行为的稀聚合物溶液的contractrnu001dows进行数值模拟。在如图2所示的附近收缩中，聚合物udows经历了大的拉伸变形，这对传统的双微分本构方程[4]提出了数值上和模型上的挑战。为了解决这个问题，在LS-STAG代码（Oldroyd-B，rnWhite-Metzner和Giesekus模型，包括多模式版本）中实现了本构方程的层次结构。我们的数值预测的鲁棒性和有效性将针对可得到实验结果的收缩率进行评估[4，5]。

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  • 会议地点 Chengdu(CN)
  • 作者

    Olivier Botella; Farhad Nikfarjam; Marcela Stoica; Yoann Cheny;

  • 作者单位

    LEMTA, Université de Lorraine, CNRS2 avenue de la Forêt de Haye - TSA 60604 - 54518 Vandoeuvre Cedex, France olivier.botella@univ-lorraine.fr;

    LEMTA, Université de Lorraine, CNRS2 avenue de la Forêt de Haye - TSA 60604 - 54518 Vandoeuvre Cedex, France;

    LEMTA, Université de Lorraine, CNRS2 avenue de la Forêt de Haye - TSA 60604 - 54518 Vandoeuvre Cedex, France;

    LEMTA, Université de Lorraine, CNRS2 avenue de la Forêt de Haye - TSA 60604 - 54518 Vandoeuvre Cedex, France;

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