An official website of the United States government
We propose a novel framework for simulating ink as a particle-laden flow using particle flow maps. Our method addresses the limitations of existing flow-map techniques, which struggle with dissipative forces like viscosity and drag, thereby extending the application scope from solving the Euler equations to solving the Navier-Stokes equations with accurate viscosity and laden-particle treatment. Our key contribution lies in a coupling mechanism for two particle systems, coupling physical sediment particles and virtual flow-map particles on a background grid by solving a Poisson system. We implemented a novel path integral formula to incorporate viscosity and drag forces into the particle flow map process. Our approach enables state-of-the-art simulation of various particle-laden flow phenomena, exemplified by the bulging and breakup of suspension drop tails, torus formation, torus disintegration, and the coalescence of sedimenting drops. In particular, our method delivered high-fidelity ink diffusion simulations by accurately capturing vortex bulbs, viscous tails, fractal branching, and hierarchical structures.
more »
« less
Clustering in Euler–Euler and Euler–Lagrange simulations of unbounded homogeneous particle-laden shear
Particle-laden flows of sedimenting solid particles or droplets in a carrier gas have strong inter-phase coupling. Even at low particle volume fractions, the two-way coupling can be significant due to the large particle to gas density ratio. In this semi-dilute regime, the slip velocity between phases leads to sustained clustering that strongly modulates the overall flow. The analysis of perturbations in homogeneous shear reveals the process by which clusters form: (i) the preferential concentration of inertial particles in the stretching regions of the flow leads to the formation of highly concentrated particle sheets, (ii) the thickness of the latter is controlled by particle-trajectory crossing, which causes a local dispersion of particles, (iii) a transverse Rayleigh–Taylor instability, aided by the shear-induced rotation of the particle sheets towards the gravity normal direction, breaks the planar structure into smaller clusters. Simulations in the Euler–Lagrange formalism are compared to Euler–Euler simulations with the two-fluid and anisotropic-Gaussian methods. It is found that the two-fluid method is unable to capture the particle dispersion due to particle-trajectory crossing and leads instead to the formation of discontinuities. These are removed with the anisotropic-Gaussian method which derives from a kinetic approach with particle-trajectory crossing in mind.
more »
« less
- Award ID(s):
- 1505795
- PAR ID:
- 10095329
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 859
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 174 to 203
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Structured bubbling with a triangular lattice pattern has been demonstrated previously to form in fluidized beds with oscillated gas injection velocity. Here, we demonstrate using two‐fluid model simulations that dividing the gas distributor into slices and oscillating gas flow with a phase offset between consecutive slices enables structured bubbling to form with a wider range of bubble sizes and lattice configurations. Local particle solidification below bubbles leads to the formation of these structures, as manifested in high particle pressures in simulations. Varying the number of slices and phase offset enables a number of configurations that mix particles faster than cases with conventional structured bubbling or unstructured bubbling with the same overall gas flow rate.more » « less
-
null (Ed.)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.more » « less
-
We study the instability of a dusty simple shear flow where the dust particles are distributed non-uniformly. A simple shear flow is modally stable to infinitesimal perturbations. Also, a band of particles remains unaffected in the absence of any background flow. However, we demonstrate that the combined scenario – comprising a simple shear flow with a localized band of particles – can exhibit destabilization due to their two-way interaction. The instability originates solely from the momentum feedback from the particle phase to the fluid phase. Eulerian–Lagrangian simulations are employed to illustrate the existence of this instability. Furthermore, the results are compared with a linear stability analysis of the system using an Eulerian–Eulerian model. Our findings indicate that the instability has an inviscid origin and is characterized by a critical wavelength below which it is not persistent. We have observed that increasing particle inertia dampens the unstable modes, whereas the strength of the instability increases with the strength of the coupling between the fluid and particle phases.more » « less
-
A computational study was performed both of a single agglomerate and of the collision of two agglomerates in a shear flow. The agglomerates were extracted from a direct numerical simulation of a turbulent agglomeration process, and had the loosely packed fractal structure typical of agglomerate structures formed in turbulent agglomeration processes. The computation was performed using a discrete-element method for adhesive particles with four-way coupling, accounting both for forces between the fluid and the particles (and vice versa ) as well as force transmission directly between particles via particle collisions. In addition to understanding and characterizing the particle dynamics, the study focused on illuminating the fluid flow field induced by the agglomerate in the presence of a background shear and the effect of collisions on this particle-induced flow. Perhaps the most interesting result of the current work was the observation that the flow field induced by a particle agglomerate rotating in a shear flow has the form of two tilted vortex rings with opposite-sign circulation. These rings are surrounded by a sea of stretched vorticity from the background shear flow. The agglomerate rotates in the shear flow, but at a slower rate than the ambient fluid elements. In the computations with two colliding agglomerates, we observed cases resulting in agglomerate merger, bouncing and fragmentation. However, the bouncing cases were all observed to also result in an exchange of particles between the two colliding agglomerates, so that they were influenced both by elastic rebound of the agglomerate structures as well as by tearing away of particulate matter between the agglomerates. Overall, the problems of agglomerate–flow interaction and of the collision of two agglomerates in a shear flow are considerably richer in physical phenomena and more complex than can be described by the common approximation that represents each agglomerate by an ‘equivalent sphere’.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2018.796
