28,685 research outputs found
Diffusion-Based Coarse Graining in Hybrid Continuum-Discrete Solvers: Theoretical Formulation and A Priori Tests
Coarse graining is an important ingredient in many multi-scale
continuum-discrete solvers such as CFD--DEM (computational fluid
dynamics--discrete element method) solvers for dense particle-laden flows.
Although CFD--DEM solvers have become a mature technique that is widely used in
multiphase flow research and industrial flow simulations, a flexible and
easy-to-implement coarse graining algorithm that can work with CFD solvers of
arbitrary meshes is still lacking. In this work, we proposed a new coarse
graining algorithm for continuum--discrete solvers for dense particle-laden
flows based on solving a transient diffusion equation. Via theoretical analysis
we demonstrated that the proposed method is equivalent to the statistical
kernel method with a Gaussian kernel, but the current method is much more
straightforward to implement in CFD--DEM solvers. \textit{A priori} numerical
tests were performed to obtain the solid volume fraction fields based on given
particle distributions, the results obtained by using the proposed algorithm
were compared with those from other coarse graining methods in the literature
(e.g., the particle centroid method, the divided particle volume method, and
the two-grid formulation). The numerical tests demonstrated that the proposed
coarse graining procedure based on solving diffusion equations is theoretically
sound, easy to implement and parallelize in general CFD solvers, and has
improved mesh-convergence characteristics compared with existing coarse
graining methods. The diffusion-based coarse graining method has been
implemented into a CFD--DEM solver, the results of which are presented in a
separate work (R. Sun and H. Xiao, Diffusion-based coarse graining in hybrid
continuum-discrete solvers: Application in CFD-DEM solvers for particle laden
flows)
Characterisation of global flow and local fluctuations in 3D SPH simulations of protoplanetary discs
A complete and detailed knowledge of the structure of the gaseous component
in protoplanetary discs is essential to the study of dust evolution during the
early phases of pre-planetesimal formation. The aim of this paper is to
determine if three-dimensional accretion discs simulated by the Smoothed
Particle Hydrodynamics (SPH) method can reproduce the observational data now
available and the expected turbulent nature of protoplanetary discs. The
investigation is carried out by setting up a suite of diagnostic tools
specifically designed to characterise both the global flow and the fluctuations
of the gaseous disc. The main result concerns the role of the artificial
viscosity implementation in the SPH method: in addition to the already known
ability of SPH artificial viscosity to mimic a physical-like viscosity under
specific conditions, we show how the same artificial viscosity prescription
behaves like an implicit turbulence model. In fact, we identify a threshold for
the parameters in the standard artificial viscosity above which SPH disc models
present a cascade in the power spectrum of velocity fluctuations, turbulent
diffusion and a mass accretion rate of the same order of magnitude as measured
in observations. Furthermore, the turbulence properties observed locally in SPH
disc models are accompanied by meridional circulation in the global flow of the
gas, proving that the two mechanisms can coexist.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical
Society. 21 pages, 25 figure
Diffusion-Based Coarse Graining in Hybrid Continuum-Discrete Solvers: Applications in CFD-DEM
In this work, a coarse-graining method previously proposed by the authors in
a companion paper based on solving diffusion equations is applied to CFD-DEM
simulations, where coarse graining is used to obtain solid volume fraction,
particle phase velocity, and fluid-particle interaction forces. By examining
the conservation requirements, the variables to solve diffusion equations for
in CFD-DEM simulations are identified. The algorithm is then implemented into a
CFD-DEM solver based on OpenFOAM and LAMMPS, the former being a
general-purpose, three-dimensional CFD solver based on unstructured meshes.
Numerical simulations are performed for a fluidized bed by using the CFD-DEM
solver with the diffusion-based coarse-graining algorithm. Converged results
are obtained on successively refined meshes, even for meshes with cell sizes
comparable to or smaller than the particle diameter. This is a critical
advantage of the proposed method over many existing coarse-graining methods,
and would be particularly valuable when small cells are required in part of the
CFD mesh to resolve certain flow features such as boundary layers in wall
bounded flows and shear layers in jets and wakes. Moreover, we demonstrate that
the overhead computational costs incurred by the proposed coarse-graining
procedure are a small portion of the total costs in typical CFD-DEM simulations
as long as the number of particles per cell is reasonably large, although
admittedly the computational overhead of the coarse graining often exceeds that
of the CFD solver. Other advantages of the present algorithm include more
robust and physically realistic results, flexibility and easy implementation in
almost any CFD solvers, and clear physical interpretation of the computational
parameter needed in the algorithm. In summary, the diffusion-based method is a
theoretically elegant and practically viable option for CFD-DEM simulations
River-bed armoring as a granular segregation phenomenon
Gravel-river beds typically have an "armored" layer of coarse grains on the
surface, which acts to protect finer particles underneath from erosion. River
bed-load transport is a kind of dense granular flow, and such flows are known
to vertically segregate grains. The contribution of granular physics to
river-bed armoring, however, has not been investigated. Here we examine these
connections in a laboratory river with bimodal sediment size, by tracking the
motion of particles from the surface to deep inside the bed, and find that
armor develops by two distinct mechanisms. Bed-load transport in the
near-surface layer drives rapid segregation, with a vertical advection rate
proportional to the granular shear rate. Creeping grains beneath the bed-load
layer give rise to slow but persistent segregation, which is diffusion
dominated and insensitive to shear rate. We verify these findings with a
continuum phenomenological model and discrete element method simulations. Our
results suggest that river beds armor by granular segregation from below ---
rather than fluid-driven sorting from above --- while also providing new
insights on the mechanics of segregation that are relevant to a wide range of
granular flows
Inertial Coupling Method for particles in an incompressible fluctuating fluid
We develop an inertial coupling method for modeling the dynamics of
point-like 'blob' particles immersed in an incompressible fluid, generalizing
previous work for compressible fluids. The coupling consistently includes
excess (positive or negative) inertia of the particles relative to the
displaced fluid, and accounts for thermal fluctuations in the fluid momentum
equation. The coupling between the fluid and the blob is based on a no-slip
constraint equating the particle velocity with the local average of the fluid
velocity, and conserves momentum and energy. We demonstrate that the
formulation obeys a fluctuation-dissipation balance, owing to the
non-dissipative nature of the no-slip coupling. We develop a spatio-temporal
discretization that preserves, as best as possible, these properties of the
continuum formulation. In the spatial discretization, the local averaging and
spreading operations are accomplished using compact kernels commonly used in
immersed boundary methods. We find that the special properties of these kernels
make the discrete blob a particle with surprisingly physically-consistent
volume, mass, and hydrodynamic properties. We develop a second-order
semi-implicit temporal integrator that maintains discrete
fluctuation-dissipation balance, and is not limited in stability by viscosity.
Furthermore, the temporal scheme requires only constant-coefficient Poisson and
Helmholtz linear solvers, enabling a very efficient and simple FFT-based
implementation on GPUs. We numerically investigate the performance of the
method on several standard test problems...Comment: Contains a number of corrections and an additional Figure 7 (and
associated discussion) relative to published versio
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