The development and implementation of algorithms to investigate drop fragmentation under shear for viscoelastic liquids with surfactant

研究含表面活性剂的粘弹性液体在剪切作用下液滴破碎的算法的开发和实施

• 批准号: 0456086
• 负责人: Yuriko Renardy
• 金额: --
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-06-15 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0456086&HistoricalAwards=false
• 关键词: development; implementation; algorithms; investigate; drop

The proposed research concerns the development and implementation of new algorithms for the numerical investigation of drop breakup under shear. The investigator has used thevolume-of-fluid (VOF) approach to simulate Newtonian liquids, including the effect of inertia, and insoluble surfactants at low concentration. A fixed regular grid is used. The motion of fluid interfaces is tracked by means of a color function, which represents the volume fraction for a fluid in a grid cell. At each time step of the numerical simulation, the color function is advected with the flow, and gradients of it are used to reconstruct the position of the interface and to compute the interfacial tension force. In prior work, the first and second derivatives of the color function have been approximated by finite differences. However, since the color function is actually a step function, the use of finitedifferences for derivatives in nonlinear combinations such as curvature is problematic. The conventional remedy is to use a smoothed color function. This, on the other hand, requires a length scale of smoothing which is small relative to physical scales but still large relativeto the mesh size. In practice, smoothing introduces numerical diffusion into the interfacial tension force. In drop breakup simulations, for instance, smoothing on the order of two or three times the mesh size still leads to non-convergence of satellite drop volumes with spatial mesh refinement. The investigator has recently developed the method PROST, which is aparabolic representation of the interface in the surface tension force and which requires nosmoothing. The interface is reconstructed from a least square fit of a paraboloid to the values of the color function in a given cell and its neighbors, and the curvature and normalare retrieved from this paraboloid. This leads to convergence of daughter drop volumes with mesh refinement. The objective of the proposed research is to develop algorithms with the VOF- PROST framework to simulate viscoelastic liquids with surfactants, and to implement the codeon large-scale parallel processing systems. The mathematical model allows the liquids to havememory, first and second normal stress differences, and shear-thinning. A nonlinear constitutive model is used for soluble surfactants, with advection along the interface and exchange with the bulk.The breakup of liquid drops suspended in another liquid occurs in a number of chemical processes, such as the commercial mixing of molten plastics to form new materials in the recycling industry. Upon mixing, the size and distribution of the daughter drops influence the quality of the product, and therefore it is important to be able to control these outcomes. This is difficult to predict for a commercial mixer because of the complexity of thefluid flow, resulting in a trial and error approach. The investigator's starting point for a theoretical prediction is to study the deformation of a single droplet in a well-defined flowfield. Numerical algorithms are devised to track the history of drop deformation and breakup,which is an important contribution to the fundamental knowledge base of manufacturing processes that involve mixing two immiscible liquids. The success of this work depends on thephysical modeling of the liquids to compare with available experimental data, the accuracy ofthe algorithms to solve the equations, the implementation on high-performance computing platforms, and established collaborations with engineers who perform controlled experiments. Abroader impact is that the algorithms apply to a wider class of fluid-fluid systems, such asthe processing of physiological fluids. The participation of a postdoctoral research associate and a graduate student is an essential educational component of the project.

提出的研究涉及开发和实现新的算法，用于剪切作用下液滴破碎的数值研究。研究人员使用流体体积（VOF）方法来模拟牛顿液体，包括惯性的影响，以及低浓度的不溶性表面活性剂。使用固定的规则网格。通过颜色函数跟踪流体界面的运动，颜色函数表示网格单元中流体的体积分数。在数值模拟的每个时间步，将颜色函数与流动平流，利用颜色函数的梯度重建界面位置并计算界面张力。在以前的工作中，颜色函数的一阶和二阶导数已经用有限差分近似。然而，由于颜色函数实际上是阶跃函数，在非线性组合（如曲率）中对导数使用有限差分是有问题的。传统的补救方法是使用平滑的色彩功能。另一方面，这需要平滑的长度尺度，相对于物理尺度较小，但相对于网格尺寸仍然较大。实际上，平滑将数值扩散引入到界面张力中。例如，在雨滴破碎模拟中，按网格尺寸的两到三倍进行平滑处理仍然会导致卫星雨滴体积在空间网格细化时不收敛。研究者最近开发了PROST方法，它是表面张力界面的抛物线表示，不需要平滑。从抛物面到给定单元及其相邻单元的颜色函数值的最小二乘拟合重构界面，并从该抛物面检索曲率和法线。这导致子下降体与网格细化的收敛。提出的研究目标是利用VOF- PROST框架开发算法来模拟具有表面活性剂的粘弹性液体，并实现codeon大规模并行处理系统。该数学模型允许液体具有记忆、第一和第二正应力差以及剪切变薄。可溶性表面活性剂采用非线性本构模型，沿界面平流并与本体交换。悬浮在另一种液体中的液滴的破裂发生在许多化学过程中，例如在回收工业中熔融塑料的商业混合以形成新材料。混合后，子滴的大小和分布影响产品的质量，因此能够控制这些结果是很重要的。由于流体流动的复杂性，这对于商业混合器来说很难预测，从而导致尝试和错误的方法。研究者进行理论预测的出发点是研究一个明确定义的流场中单个液滴的变形。设计了数值算法来跟踪液滴变形和破碎的历史，这是对涉及混合两种不混相液体的制造过程的基础知识库的重要贡献。这项工作的成功取决于液体的物理建模与现有实验数据的比较，求解方程的算法的准确性，在高性能计算平台上的实现，以及与执行控制实验的工程师建立的合作。更广泛的影响是，该算法适用于更广泛的流体-流体系统，例如生理流体的处理。博士后研究助理和研究生的参与是该项目必不可少的教育组成部分。