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

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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.