scholarly journals Multiscale Simulation of Non-Metallic Inclusion Aggregation in a Fully Resolved Bubble Swarm in Liquid Steel

Metals ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 517
Author(s):  
Jean-Sébastien Kroll-Rabotin ◽  
Matthieu Gisselbrecht ◽  
Bernhard Ott ◽  
Ronja May ◽  
Jochen Fröhlich ◽  
...  
Keyword(s):  
Particle Size ◽  
Shear Flow ◽  
Initial Conditions ◽  
Bubbly Flow ◽  
Multiscale Simulation ◽  
Particle Collision ◽  
Immersed Boundary ◽  
Collision Dynamics ◽  
Plane Shear ◽  
Boltzmann Method

Removing inclusions from the melt is an important task in metallurgy with critical impact on the quality of the final alloy. Processes employed with this purpose, such as flotation, crucially depend on the particle size. For small inclusions, the aggregation kinetics constitute the bottleneck and, hence, determine the efficiency of the entire process. If particles smaller than all flow scales are considered, the flow can locally be replaced by a plane shear flow. In this contribution, particle interactions in plane shear flow are investigated, computing the fully resolved hydrodynamics at finite Reynolds numbers, using a lattice Boltzmann method with an immersed boundary method. Investigations with various initial conditions, several shear values and several inclusion sizes are conducted to determine collision efficiencies. It is observed that although finite Reynolds hydrodynamics play a significant role in particle collision, statistical collision efficiency barely depends on the Reynolds number. Indeed, the particle size ratio is found to be the prevalent parameter. In a second step, modeled collision dynamics are applied to particles tracked in a fully resolved bubbly flow, and collision frequencies at larger flow scale are derived.

scholarly journals Aggregation kernel of globular inclusions in local shear flow: application to aggregation in a gas-stirred ladle

2019 ◽  
Vol 116 (5) ◽  
pp. 512 ◽  
Author(s):  
Matthieu Gisselbrecht ◽  
Jean-Sébastien Kroll-Rabotin ◽  
Jean-Pierre Bellot
Keyword(s):  
Particle Size ◽  
Shear Flow ◽  
Inclusion Size ◽  
Numerical Approach ◽  
Collision Kernel ◽  
Immersed Boundary ◽  
Inclusion Removal ◽  
Local Shear ◽  
Lagrangian Tracking ◽  
Hydrodynamic Effects

The control of metal cleanliness has always been a concern for metallurgists since inclusions directly influence the mechanical properties of alloys. In most metallurgical routes, a refining treatment of the liquid alloy is performed, in particular with the aim of improving the metal cleanliness that is achieved via a better control of particle contents and particle size. Since the efficiencies of inclusion removal mechanisms increase with inclusion size, the turbulent aggregation process plays a major role in all refining treatments. Interaction between particles such as aggregation is usually modelled through kinetics kernels which may be difficult to estimate. This paper contributes to express turbulent aggregation kernel taking into account the hydrodynamic effects at the inclusion scale. The numerical approach combines three numerical techniques, a Lattice Boltzmann Method to resolve the flow, an immersed boundary method for the particle-fluid interactions and a Lagrangian tracking for the motion of individual particles. Deterministic simulations of spherical particle pair trajectories leading to collision or avoidance allow us to calculate statistical kernels in a shear flow. The results show a strong influence of the short distance hydrodynamic effects on the collision kernel, particularly when the diameter ratio of the two interacting particles is far from unity. An application of this new aggregation kernel is applied to simulate the time evolution of the particle size distribution in a typical steel gas-stirred ladle.

scholarly journals Deformation of a Capsule in a Power-Law Shear Flow

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Fang-Bao Tian
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Shear Flow ◽  
Lattice Boltzmann Method ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Immersed Boundary ◽  
Power Law Fluid ◽  
Boltzmann Method ◽  
Power Law Index

An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.

scholarly journals Simulation of Particle-Fluid Interaction in Fractal Fractures Based on the Immersed Boundary-Lattice Boltzmann Method

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Shenggui Liu ◽  
Songlei Tang ◽  
Jinkuang Huang ◽  
Mindong Lv ◽  
Yingjun Li
Keyword(s):  
Particle Size ◽  
Fractal Dimension ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Flow Characteristics ◽  
Immersed Boundary ◽  
Fluid Viscosity ◽  
Lower Permeability ◽  
Negative Exponential ◽  
Boltzmann Method

In order to reveal the influence of particles on fluid flow characteristics in rough fractures under fluid-solid coupling, a range of fracture systems with varying roughness were generated using the Weierstrass-Mandelbrot function. Fluid-particle interactions in rough fractal fractures were simulated using the immersed boundary-lattice Boltzmann method. In this paper, the effects of fluid viscosity, particle size, particle quantity, fracture fractal dimension, and particle grading composition are studied. Results illustrate that increasing fluid viscosity hinders the movement of particles, resulting in the decreasing of particle velocity. As particle size and particle quantity increase, the particle occupation of the channel area grows larger, which lead to lower permeability of the channel. Increasing fracture fractal dimension surges the curvature of the fluid channel, but permeability has a negative exponential correlation to fractal dimension. With increasing particle grading composition, the blocking effect of particles on fracture flow also increases with increasing particle proportion.

scholarly journals On the longitudinal optimal perturbations to inviscid plane shear flow: formal solution and asymptotic approximation

2013 ◽  
Vol 737 ◽  
pp. 387-411 ◽  
Author(s):  
C. Arratia ◽  
J.-M. Chomaz
Keyword(s):  
Shear Flow ◽  
Initial Conditions ◽  
Formal Solution ◽  
Base Flow ◽  
Flow Profile ◽  
Plane Shear ◽  
Optimal Perturbation ◽  
Energy Growth ◽  
Perturbation Problem ◽  
New Formulation

AbstractWe study the longitudinal linear optimal perturbations (which maximize the energy gain up to a prescribed time $T$) to inviscid parallel shear flow, which present unbounded energy growth due to the lift-up mechanism. Using the phase invariance with respect to time, we show that for an arbitrary base flow profile and optimization time, the computation of the optimal longitudinal perturbation reduces to the resolution of a single one-dimensional eigenvalue problem valid for all times. The optimal perturbation and its amplification are then derived from the lowest eigenvalue and its associated eigenfunction, while the remainder of the infinite set of eigenfunctions provides an orthogonal base for decomposing the evolution of arbitrary perturbations. With this new formulation we obtain, asymptotically for large spanwise wavenumber ${k}_{z} , $ a prediction of the optimal gain and the localization of inviscid optimal perturbations for the two main classes of parallel flows: free shear flow with an inflectional velocity profile, and wall-bounded flow with maximum shear at the wall. We show that the inviscid optimal perturbations are localized around the point of maximum shear in a region with a width scaling like ${ k}_{z}^{- 1/ 2} $ for free shear flow, and like ${ k}_{z}^{- 2/ 3} $ for wall-bounded shear flows. This new derivation uses the stationarity of the base flow to transform the optimization of initial conditions in phase space into the optimization of a temporal phase along each trajectory, and an optimization among all trajectories labelled by their intersection with a codimension-1 subspace. The optimization of the time phase directly imposes that the initial and final energy growth rates of the optimal perturbation should be equal. This result requires only time invariance of the base flow, and is therefore valid for any linear optimal perturbation problem with stationary base flow.

Rod-like colloids and polymers in shear flow: a multi-particle-collision dynamics study

2004 ◽  
Vol 16 (38) ◽  
pp. S3941-S3954 ◽  
Author(s):  
R G Winkler ◽  
K Mussawisade ◽  
M Ripoll ◽  
G Gompper
Keyword(s):  
Shear Flow ◽  
Particle Collision ◽  
Collision Dynamics

scholarly journals Waterfall Algorithm as a tool of investigation the geometrical features of granular porous media

2021 ◽  
Author(s):  
Wojciech Sobieski
Keyword(s):  
Particle Size ◽  
Porous Media ◽  
Lattice Boltzmann ◽  
Granular Media ◽  
Density Ratio ◽  
Geometrical Features ◽  
Granular Porous Media ◽  
Collision Density ◽  
Boltzmann Method ◽  
The Impact

AbstractThe paper describes the so-called Waterfall Algorithm, which may be used to calculate a set of parameters characterising the spatial structure of granular porous media, such as shift ratio, collision density ratio, consolidation ratio, path length and minimum tortuosity. The study is performed for 1800 different two-dimensional random pore structures. In each geometry, 100 individual paths are calculated. The impact of porosity and the particle size on the above-mentioned parameters is investigated. It was stated in the paper, that the minimum tortuosity calculated by the Waterfall Algorithm cannot be used directly as a representative tortuosity of pore channels in the Kozeny or the Carman meaning. However, it may be used indirect by making the assumption that a unambiguous relationship between the representative tortuosity and the minimum tortuosity exists. It was also stated, that the new parameters defined in the present study are sensitive on the porosity and the particle size and may be therefore applied as indicators of the geometry structure of granular media. The Waterfall Algorithm is compared with other methods of determining the tortuosity: A-Star Algorithm, Path Searching Algorithm, Random Walk technique, Path Tracking Method and the methodology of calculating the hydraulic tortuosity based on the Lattice Boltzmann Method. A very short calculation time is the main advantage of the Waterfall Algorithm, what meant, that it may be applied in a very large granular porous media.

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