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

在聚光太阳能发电（CSP）厂中，致密颗粒悬浮液用作传热流体（HTF），用于收集、运输和储存太阳能。该项目的目标是流变学建模的悬浮液。使用直接数值模拟（DNS）和最小二乘拟合程序，多项式近似的有效粘度作为体积分数和剪切速率的函数计算离线。对于每个基本的流动模式，任意拉格朗日-欧拉（ALE）形式的不可压缩的Navier-Stokes方程求解在一个单位立方体上使用有限元离散的块结构的网格。移动粒子被放置在一个粗糙的主网格的顶点，并通过求解小的局部优化问题为每个宏单元生成一个贴体子网格。粒子（和粗网格节点）的运动由从离散网络近似（DNA）导出的常微分方程系统控制到斯托克斯问题。这种方法使得所提出的算法比ALE和虚拟域方法更有效，这些方法需要在线计算和建模作用在粒子上的力。此外，由于子网格节点的演化由主网格的变形决定，因此可以有效地更新计算网格。该项目的计算挑战包括开发强大的舒尔补预条件的线性系统的DNA模型和ALE Navier-Stokes求解器的离散鞍点问题。典型简单流的离线模拟结果将用于提取有效粘度的拟合封闭。将在四阶段验证过程中证明这些密封件描述致密颗粒流的非牛顿流动行为的能力。在最后阶段，开发的模拟工具将被应用到流化床太阳能接收器，这是广泛研究的文献中使用PEPT（正电子发射粒子跟踪）测量和数值模拟与简化建模的动力学，碰撞和摩擦粒子应力。在不同的高度以上的曝气水平的实验数据的固体体积分数分布的比较将被用来验证新的模型，以准确地预测有效粘度的更广泛的体积分数的能力。

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.