Discrete networks and finite element approaches to rheological modeling of dense suspensions of particles via direct numerical simulations

密集颗粒悬浮液在聚光太阳能（CSP）电厂中用作传热流体（HTF），用于收集、运输和储存太阳能。这个项目的目标是这种悬浮液的流变学建模。使用直接数值模拟（DNS）和最小二乘拟合程序，离线计算有效粘度作为体积分数和剪切速率的函数的多项式近似。对于每一种基本流型，在单元立方体中采用演化块结构网格的有限元离散方法求解不可压缩Navier-Stokes方程的任意拉格朗日-欧拉（ALE）形式。将运动粒子放置在粗主网格的顶点上，通过求解小的局部优化问题，为每个宏元生成贴体子网格。粒子（和粗网格节点）的运动由一个由斯托克斯问题的离散网络近似（DNA）导出的常微分方程系统控制。这种方法使得所提出的算法比需要在线计算和模拟作用在粒子上的力的ALE和虚拟域方法要有效得多。此外，由于子网格节点的演化取决于主网格的变形，因此可以有效地更新计算网格。本项目的计算挑战包括开发DNA模型线性系统的鲁棒Schur补预条件和ALE Navier-Stokes解算器的离散鞍点问题。对典型简单流动的离线模拟结果将用于提取有效粘度的拟合闭包。这些闭包描述致密颗粒流的非牛顿流动行为的能力将在四个阶段的验证过程中得到证明。在最后阶段，开发的模拟工具将应用于流化床太阳能接收器，该接收器在文献中使用PEPT（正电子发射粒子跟踪）测量和数值模拟进行了广泛的研究，并简化了动力学，碰撞和摩擦粒子应力的建模。将曝气水平以上不同高度的固体体积分数分布与实验数据进行比较，以验证新模型在更大体积分数范围内准确预测有效粘度的能力。

Dense particle suspensions are used in Concentrated Solar Power (CSP) plants as heat transfer fluids (HTF) for collection, transport, and storage of solar energy. The objective of this project is rheological modeling of such suspensions. Using direct numerical simulations (DNS) and least-squares fitting procedures, polynomial approximations to the effective viscosity as a function of the volume fraction and shear rate are calculated off-line. For each basic flow pattern, the arbitrary Lagrangian-Eulerian (ALE) form of the incompressible Navier-Stokes equations is solved in a unit cube using a finite element discretization on an evolving block-structured mesh. The moving particles are placed at the vertices of a coarse master mesh, and a body-fitted submesh is generated for each macroelement by solving small local optimization problems. The motion of particles (and coarse mesh nodes) is governed by a system of ordinary differential equations derived from the discrete network approximation (DNA) to a Stokes problem. This approach makes the proposed algorithm far more efficient than ALE and fictitious domain methods that require online calculation and modeling of forces acting on the particles. Moreover, the computational mesh can be updated efficiently because the evolution of submesh nodes is determined by the deformation of the master mesh. The computational challenges of this project include the development of robust Schur complement preconditioners for the linear system of the DNA model and the discrete saddle point problem of the ALE Navier-Stokes solver. The results of offline simulations for typical simple flows will be used to extract fitted closures for the effective viscosity. The ability of these closures to describe the non-Newtonian flow behavior of dense particulate flows will be demonstrated in the process of a four-stage validation. At the final stage, the developed simulation tool will be applied to a fluidized bed solar receiver which was extensively studied in the literature using PEPT (positron emission particle tracking) measurements and numerical simulations with simplified modeling of kinetic, collisional, and frictional particle stresses. A comparison of solid volume fraction distributions at different heights above the aeration level to experimental data will be used to verify the ability of the new models to accurately predict effective viscosity for a wider range of volume fractions.