Discrete networks and finite element approaches to rheological modeling of dense suspensions of particles via direct numerical simulations
Final Report Abstract
Dense particle suspensions are used in Concentrated Solar Power (CSP) plants as heat transfer fluids for collection, transport, and storage of solar energy. The objective of this project was the development of tailor-made numerical methods and subgrid scale models for computational studies of such suspensions. For coarse-grained simulations, we use an inexpensive mixture model that requires a closure for the effective viscosity as a function of the volume fraction. In this project, we construct such closures using the results of offline direct numerical simulations (DNS) on fine meshes. The main challenges of this endeavor include realistic modeling of lubrication forces and accurate calculation of hydrodynamic forces acting on the particles. Adopting the framework of fictitious domain finite element methods, we performed a major upgrade of the 3D simulation tools originally developed by our team for dilute particulate flows. For the finite element discretization of the macroscopic mixture model, we developed a new kind of monolithic convex limiting techniques that keep volume fractions in the physically admissible range. Lubrication forces and discrete network approximations were incorporated into the microscopic model of particle motion. In the context of DNS, we explored two approaches to achieve high precision at low cost by using Arbitrary Lagrangian-Eulerian (ALE) formulations and unstructured meshes fitted to the surface of moving particles. The first method places the particles at the vertices of a coarse master mesh, and a body-fitted submesh is generated for each macroelement. The second approach represents a Chimera domain decomposition method in which moving submeshes interact with a fixed background mesh. The main novelty of our new Chimera-ALE scheme lies in the weak imposition of Dirichlet-Robin coupling conditions, which enables us to suppress spurious oscillations of drag and lift forces. Validation of the developed simulation tools was performed for a numerical viscometer configuration, permitting direct comparison with theoretical predictions and established benchmark results. Subsequently, the viscometer arrangement was changed to a periodic cubic domain, serving as a representative volume element for CSP systems. In this numerical study, effective viscosities were quantified through wall force measurements and independent balancing of energy dissipation rates. The close agreement between the results obtained with the two approaches substantiates the reliability of numerical viscometry. Polynomial fitting to the data was used to extract DNS-based closures for the macroscopic model, and systematic validation was performed for typical CSP operating conditions. The validated closure was used to perform a macroscopic 3D simulation of a CSP configuration. This project has produced two research articles and a book (Property-Preserving Numerical Schemes for Conservation Laws, 470 pages, World Scientific, 2023).
Publications
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Property-Preserving Numerical Schemes for Conservation Laws. WORLD SCIENTIFIC.
Kuzmin, Dmitri & Hajduk, Hennes
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A Chimera domain decomposition method with weak Dirichlet-Robin coupling for őnite element simulation of particulate ŕows. Submitted to Computers and Mathematics in Simulation
R. Münster, O. Mierka, D. Kuzmin & S. Turek
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Effective viscosity closures for dense suspensions in CSP systems via lubrication-enhanced DNS and numerical viscometry. International Journal of Multiphase Flow, 197, 105618.
Münster, Raphael; Mierka, Otto; Kuzmin, Dmitri & Turek, Stefan
