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

在聚光太阳能发电厂(CSP)中，浓密颗粒悬浮液被用作热传递流体(HTF)，用于太阳能的收集、运输和存储。该项目的目标是对这种悬浮液进行流变学建模。利用直接数值模拟和最小二乘拟合法，离线计算了有效粘度随体积分数和剪切速率变化的多项式近似。对于每种基本流型，不可压缩Navier-Stokes方程的任意拉格朗日-欧拉(ALE)形式在单元立方体中使用有限元离散在演化的块结构网格上进行求解。将运动粒子放置在粗网格的顶点，通过求解小的局部优化问题，为每个宏元素生成贴体的子网格。粒子(和粗网格节点)的运动由一个由离散网络近似(DNA)导出的常微分方程组控制。这种方法使所提出的算法比ALE和虚拟区域方法要高效得多，后者需要在线计算和建模作用于粒子的力。此外，由于子网格节点的演化是由主网格的变形决定的，因此可以高效地更新计算网格。该项目的计算挑战包括为DNA模型的线性系统开发稳健的Schur补预处理子，以及ale Navier-Stokes求解器的离散鞍点问题。典型简单流动的离线模拟结果将被用来提取有效粘度的拟合闭合。这些封闭器描述稠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态化太阳能接收器，在文献中广泛使用PEPT(正电子发射粒子跟踪)测量和数值模拟，并对动力学、碰撞和摩擦粒子应力进行简化建模。将曝气面以上不同高度的固体体积分数分布与实验数据进行比较，以验证新模型在较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.