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1. Dense Discrete Phase Model Coupled with Kinetic Theroy of Granular Flow to Improve Predictions of Bubbling Fluidized Bed Hydrodynamics

   Hashemisohi, Abolhasan ( September 2018 , Kona powder and particle journal)

   Formation, expansion, and breakage of bubbles in single bubble and freely bubbling fluidized beds were studied using an improved hybrid Lagrangian-Eulerian computational fluid dynamics (CFO) approach. Dense Discrete Phase Model (DDPM) is a novel approach to simulate industrial scale fluidized bed reactors with polydispersed particles. The model uses a hybrid Lagrangian-Eulerian approach to track the particle parcels (lumping several particles in one computational cell) in a Lagrangian framework according to Newton's laws of motion. The interactions between particles are estimated by the gradient of solids stress solved in Eulerian grid. In this work. a single bubble fluidized bed and a freely bubbling fluidized bed were simulated using DDPM coupled with kinetic theory of granular flows (KTGF). The solid stress was improved to include both tangential and normal forces compared to current hybrid methods with the consideration of only normal stress or solid pressure. The results showed that solid pressure (normal forces) as the only contributor in solid stress would lead to over prediction of bubble size and overlooking of bubble breakage in a single bubble bed. Also, the results showed the improved model bad a good prediction of bubble path in a freely bubbling bed compared to solid pressure-based model.more »It was shown that increasing the restitution coefficient increased the particle content of the bubbles and it lead to less breakage during the formation of the bubble. The probability of formation of bubbles was compared with experimental results and solid stress model showed less discrepancies compared to the solid pressure-based model.« less
2. Sparse identification of multiphase turbulence closures for coupled fluid–particle flows

   https://doi.org/10.1017/jfm.2021.53  

   Beetham, S. ; Fox, R.O. ; Capecelatro, J. ( May 2021 , Journal of Fluid Mechanics)

   In this work, model closures of the multiphase Reynolds-averaged Navier–Stokes (RANS) equations are developed for homogeneous, fully developed gas–particle flows. To date, the majority of RANS closures are based on extensions of single-phase turbulence models, which fail to capture complex two-phase flow dynamics across dilute and dense regimes, especially when two-way coupling between the phases is important. In the present study, particles settle under gravity in an unbounded viscous fluid. At sufficient mass loadings, interphase momentum exchange between the phases results in the spontaneous generation of particle clusters that sustain velocity fluctuations in the fluid. Data generated from Eulerian–Lagrangian simulations are used in a sparse regression method for model closure that ensures form invariance. Particular attention is paid to modelling the unclosed terms unique to the multiphase RANS equations (drag production, drag exchange, pressure strain and viscous dissipation). A minimal set of tensors is presented that serve as the basis for modelling. It is found that sparse regression identifies compact, algebraic models that are accurate across flow conditions and robust to sparse training data.
3. An Efficient B-Spline Lagrangian/Eulerian Method for Compressible Flow, Shock Waves, and Fracturing Solids

   https://doi.org/10.1145/3519595  

   Cao, Yadi ; Chen, Yunuo ; Li, Minchen ; Yang, Yin ; Zhang, Xinxin ; Aanjaneya, Mridul ; Jiang, Chenfanfu ( October 2022 , ACM Transactions on Graphics)

   This study presents a new method for modeling the interaction between compressible flow, shock waves, and deformable structures, emphasizing destructive dynamics. Extending advances in time-splitting compressible flow and the Material Point Methods (MPM), we develop a hybrid Eulerian and Lagrangian/Eulerian scheme for monolithic flow-structure interactions. We adopt the second-order WENO scheme to advance the continuity equation. To stably resolve deforming boundaries with sub-cell particles, we propose a blending treatment of reflective and passable boundary conditions inspired by the theory of porous media. The strongly coupled velocity-pressure system is discretized with a new mixed-order finite element formulation employing B-spline shape functions. Shock wave propagation, temperature/density-induced buoyancy effects, and topology changes in solids are unitedly captured.
4. The power particle-in-cell method

   https://doi.org/10.1145/3528223.3530066  

   Qu, Ziyin ; Li, Minchen ; De Goes, Fernando ; Jiang, Chenfanfu ( July 2022 , ACM Transactions on Graphics)

   This paper introduces a new weighting scheme for particle-grid transfers that generates hybrid Lagrangian/Eulerian fluid simulations with uniform particle distributions and precise volume control. At its core, our approach reformulates the construction of Power Particles [de Goes et al. 2015] by computing volume-constrained density kernels. We employ these optimized kernels as particle domains within the Generalized Interpolation Material Point method (GIMP) in order to incorporate Power Particles into the Particle-In-Cell framework, hence the name the Power Particle-In-Cell method. We address the construction of volume-constrained density kernels as a regularized optimal transportation problem and describe an iterative solver based on localized Gaussian convolutions that leads to a significant performance speedup compared to [de Goes et al. 2015]. We also present novel extensions for handling free surfaces and solid obstacles that bypass the need for cell clipping and ghost particles. We demonstrate the advantages of our transfer weights by improving hybrid schemes for fluid simulation such as the Fluid Implicit Particle (FLIP) method and the Affine Particle-In-Cell (APIC) method with volume preservation and robustness to varying particle-per-cell ratio, while retaining low numerical dissipation, conserving linear and angular momenta, and avoiding particle reseeding or post-process relaxations.
5. Lagrangian vs. Eulerian: An Analysis of Two Solution Methods for Free-Surface Flows and Fluid Solid Interaction Problems

   https://doi.org/10.3390/fluids6120460  

   Rakhsha, Milad ; Kees, Christopher E. ; Negrut, Dan ( December 2021 , Fluids)

   As a step towards addressing a scarcity of references on this topic, we compared the Eulerian and Lagrangian Computational Fluid Dynamics (CFD) approaches for the solution of free-surface and Fluid–Solid Interaction (FSI) problems. The Eulerian approach uses the Finite Element Method (FEM) to spatially discretize the Navier–Stokes equations. The free surface is handled via the volume-of-fluid (VOF) and the level-set (LS) equations; an Immersed Boundary Method (IBM) in conjunction with the Nitsche’s technique were applied to resolve the fluid–solid coupling. For the Lagrangian approach, the smoothed particle hydrodynamics (SPH) method is the meshless discretization technique of choice; no additional equations are needed to handle free-surface or FSI coupling. We compared the two approaches for a flow around cylinder. The dam break test was used to gauge the performance for free-surface flows. Lastly, the two approaches were compared on two FSI problems—one with a floating rigid body dropped into the fluid and one with an elastic gate interacting with the flow. We conclude with a discussion of the robustness, ease of model setup, and versatility of the two approaches. The Eulerian and Lagrangian solvers used in this study are open-source and available in the public domain.