Physique des milieux granulaires, ségrégation, écoulements
Gaz de Boltzmann sur réseaux
Calcul parallèle en mécanique des fluides
Publications scientifiques au M2P2
Gang Wang, Umberto d'Ortona, Pierrette Guichardon. Improved partially saturated method for the lattice Boltzmann pseudopotential multicomponent flows. Physical Review E , 2023, 107 (3), pp.035301. ⟨10.1103/PhysRevE.107.035301⟩. ⟨hal-04307425⟩ Plus de détails...
This paper extends the partially saturated method (PSM), used for curved or complex walls, to the lattice Boltzmann (LB) pseudopotential multicomponent (MC) model and adapts the wetting boundary condition to model the contact angle. The pseudopotential model is widely used for various complex flow simulations due to its simplicity. To simulate the wetting phenomenon within this model, the mesoscopic interaction force between the boundary fluid and solid nodes is used to mimic the microscopic adhesive force between the fluid and the solid wall, and the bounceback (BB) method is normally adopted to achieve the no-slip boundary condition. In this paper, the pseudopotential interaction forces are computed with eighth-order isotropy since fourth-order isotropy leads to the condensation of the dissolved component on curved walls. Due to the staircase approximation of curved walls in the BB method, the contact angle is sensitive to the shape of corners on curved walls. Furthermore, the staircase approximation makes the movement of the wetting droplet on curved walls not smooth. To solve this problem, the curved boundary method may be used, but due to the extrapolation process, most curved boundary conditions suffer from massive mass leakage when applied to the LB pseudopotential model. Through three test cases, it is found that the improved PSM scheme is mass conservative, that nearly identical static contact angles are observed on flat and curved walls under the same wetting condition, and that the movement of a wetting droplet on curved and inclined walls is smoother compared to the usual BB method. The present method is expected to be a promising tool for modeling flows in porous media and in microfluidic channels.
Gang Wang, Umberto d'Ortona, Pierrette Guichardon. Improved partially saturated method for the lattice Boltzmann pseudopotential multicomponent flows. Physical Review E , 2023, 107 (3), pp.035301. ⟨10.1103/PhysRevE.107.035301⟩. ⟨hal-04307425⟩
Antoine Galko, Simon Gsell, Umberto d'Ortona, Laurent Morin, Julien Favier. Pulsated Herschel-Bulkley flows in two-dimensional channels: A model for mucus clearance devices. Physical Review Fluids, 2022, 7 (5), pp.053301. ⟨10.1103/PhysRevFluids.7.053301⟩. ⟨hal-03863329⟩ Plus de détails...
Umberto d'Ortona, Nathalie Thomas, Richard M Lueptow. Mechanisms for recirculation cells in granular flows in rotating cylindrical rough tumblers. Physical Review E, 2022. ⟨hal-03431772v2⟩ Plus de détails...
Friction at the endwalls of partially-filled horizontal rotating tumblers induces curvature and axial drift of particle trajectories in the surface flowing layer. Here we describe the results of a detailed discrete element method study of the dry granular flow of monodisperse particles in threedimensional cylindrical tumblers with endwalls and cylindrical wall that can be either smooth or rough. Endwall roughness induces more curved particle trajectories, while a smooth cylindrical wall enhances drift near the endwall. This drift induces recirculation cells near the endwall. The use of mixed roughness (cylindrical wall and endwalls having different roughness) shows the influence of each wall on the drift and curvature of particle trajectories as well as the modification of the free surface topography. The effects act in opposite directions and have variable magnitude along the length of the tumbler such that their sum determines both direction of net drift and the recirculation cells. Near the endwalls, the dominant effect is always the endwall effect, and the axial drift for surface particles is toward the endwalls. For long enough tumblers, a counter-rotating cell occurs adjacent to each of the endwall cells having a surface drift toward the center because the cylindrical wall effect is dominant there. These cells are not dynamically coupled with the two endwall cells. The competition between the drifts induced by the endwalls and the cylindrical wall determines the width and drift amplitude for both types of cells.
Umberto d'Ortona, Nathalie Thomas, Richard M Lueptow. Mechanisms for recirculation cells in granular flows in rotating cylindrical rough tumblers. Physical Review E, 2022. ⟨hal-03431772v2⟩
Simon Gsell, Umberto d'Ortona, Julien Favier. Lattice-Boltzmann simulation of creeping generalized Newtonian flows: theory and guidelines. Journal of Computational Physics, 2021, 429, pp.109943. ⟨10.1016/j.jcp.2020.109943⟩. ⟨hal-03166492⟩ Plus de détails...
The accuracy of the lattice-Boltzmann (LB) method is related to the relaxation time controlling the flow viscosity. In particular, it is often recommended to avoid large fluid viscosities in order to satisfy the low-Knudsen-number assumption that is essential to recover hydrodynamic behavior at the macroscopic scale, which may in principle limit the possibility of simulating creeping flows and non-Newtonian flows involving important viscosity variations. Here it is shown, based on the continuous Boltzmann equations, that a two-relaxation-time (TRT) model can however recover the steady Navier-Stokes equations without any restriction on the fluid viscosity, provided that the Knudsen number is redefined as a function of both relaxation times. This effective Knudsen number is closely related to the previously-described parameter controlling numerical errors of the TRT model, providing a consistent theory at both the discrete and continuous levels. To simulate incompressible flows, the viscous incompressibility condition M a 2 /Re 1 also needs to be satisfied, where M a and Re are the Mach and Reynolds numbers. This concept is extended by defining a local incompressibility factor, allowing one to locally control the accuracy of the simulation for flows involving varying viscosities. These theoretical arguments are illustrated based on numerical simulations of the two-dimensional flow past a square cylinder. In the case of a Newtonian flow, the viscosity independence is confirmed for relaxation times up to 10 4 , and the ratio M a 2 /Re = 0.1 is small enough to ensure reliable incompressible simulations. The Herschel-Bulkley model is employed to introduce shear-dependent viscosities in the flow. The proposed numerical strategy allows to achieve major viscosity variations, avoiding the implementation of artificial viscosity cutoff in high-viscosity regions. Highly non-linear flows are simulated over ranges of the Bingham number Bn ∈ [1, 1000] and flow index n ∈ [0.2, 1.8], and successfully compared to prior numerical works based on Navier-Stokes solvers. This work provides a general framework to simulate complex creeping flows, as encountered in many biological and industrial systems, using the lattice-Boltzmann method.
Simon Gsell, Umberto d'Ortona, Julien Favier. Lattice-Boltzmann simulation of creeping generalized Newtonian flows: theory and guidelines. Journal of Computational Physics, 2021, 429, pp.109943. ⟨10.1016/j.jcp.2020.109943⟩. ⟨hal-03166492⟩
Dry granular material flowing on rough inclines can experience a self-induced Rayleigh-Taylor (RT) instability followed by the spontaneous emergence of convection cells. For this to happen, particles are different in size and density, the larger particles are the denser but still segregate toward the surface. When the flow is, as usual, initially made of two layers, dense particles above, a Rayleigh-Taylor instability develops during the flow. When the flow is initially made of one homogeneous layer mixture, the granular segregation leads to the formation of an unstable layer of large-dense particles at the surface which subsequently destabilizes in a RT plume pattern. The unstable density gradient has been only induced by the motion of the granular matter. This self-induced Rayleigh-Taylor instability and the two-layer RT instability are studied using two different methods, experiments and simulations. At last, contrarily to the usual fluid behavior where the RT instability relaxes into two superimposed stable layers of fluid, the granular flow evolves to a pattern of alternated bands corresponing to recirculation cells analogous to Rayleigh-Bénard convection cells where segregation sustains the convective motion.
The lattice Boltzmann method often involves small numerical time steps due to the acoustic scaling (i.e., scaling between time step and grid size) inherent to the method. In this work, a second-order dual-time-stepping lattice Boltzmann method is proposed in order to avoid any time-step restriction. The implementation of the dual time stepping is based on an external source in the lattice Boltzmann equation, related to the time derivatives of the macroscopic flow quantities. Each time step is treated as a pseudosteady problem. The convergence rate of the steady lattice Boltzmann solver is improved by implementing a multigrid method. The developed solver is based on a two-relaxation time model coupled to an immersed-boundary method. The reliability of the method is demonstrated for steady and unsteady laminar flows past a circular cylinder, either fixed or towed in the computational domain. In the steady-flow case, the multigrid method drastically increases the convergence rate of the lattice Boltzmann method. The dual-time-stepping method is able to accurately reproduce the unsteady flows. The physical time step can be freely adjusted; its effect on the simulation cost is linear, while its impact on the accuracy follows a second-order trend. Two major advantages arise from this feature. (i) Simulation speed-up can be achieved by increasing the time step while conserving a reasonable accuracy. A speed-up of 4 is achieved for the unsteady flow past a fixed cylinder, and higher speed-ups are expected for configurations involving slower flow variations. Significant additional speed-up can also be achieved by accelerating transients. (ii) The choice of the time step allows us to alter the range of simulated timescales. In particular, increasing the time step results in the filtering of undesired pressure waves induced by sharp geometries or rapid temporal variations, without altering the main flow dynamics. These features may be critical to improve the efficiency and range of applicability of the lattice Boltzmann method.
Simon Gsell, Umberto d'Ortona, Julien Favier. Multigrid dual-time-stepping lattice Boltzmann method. Physical Review E , 2020, 101 (2), ⟨10.1103/PhysRevE.101.023309⟩. ⟨hal-02573156⟩
The coordinated beating of epithelial cilia in human lungs is a fascinating problem from the hydrodynamics perspective. The phase lag between neighboring cilia is able to generate collective cilia motions, known as metachronal waves. Different kinds of waves can occur, antiplectic or symplectic, depending on the direction of the wave with respect to the flow direction. It is shown here, using a coupled lattice Boltzmann-immersed boundary solver, that the key mechanism responsible for their transport efficiency is a blowing-suction effect that displaces the interface between the periciliary liquid and the mucus phase. The contribution of this mechanism on the average flow generated by the cilia is compared to the contribution of the lubrication effect. The results reveal that the interface displacement is the main mechanism responsible for the better efficiency of antiplectic metachronal waves over symplectic ones to transport bronchial mucus. The conclusions drawn here can be extended to any two-layer fluid configuration having different viscosities, and put into motion by cilia-shaped or comb-plate structures, having a back-and-forth motion with phase lags.
Sylvain Chateau, Julien Favier, Sébastien Poncet, Umberto d'Ortona. Why antiplectic metachronal cilia waves are optimal to transport bronchial mucus. Physical Review E , 2019, 100 (4), pp.042405. ⟨10.1103/PhysRevE.100.042405⟩. ⟨hal-02468006⟩
Simon Gsell, Umberto d'Ortona, Julien Favier. Explicit and viscosity-independent immersed-boundary scheme for the lattice Boltzmann method. Physical Review E , 2019, 100 (3), ⟨10.1103/PhysRevE.100.033306⟩. ⟨hal-02339475⟩ Plus de détails...
Viscosity independence of lattice-Boltzmann methods is a crucial issue to ensure the physical relevancy of the predicted macroscopic flows over large ranges of physical parameters. The immersed-boundary (IB) method, a powerful tool that allows one to immerse arbitrary-shaped, moving, and deformable bodies in the flow, suffers from a boundary-slip error that increases as a function of the fluid viscosity, substantially limiting its range of application. In addition, low fluid viscosities may result in spurious oscillations of the macroscopic quantities in the vicinity of the immersed boundary. In this work, it is shown mathematically that the standard IB method is indeed not able to reproduce the scaling properties of the macroscopic solution, leading to a viscosity-related error on the computed IB force. The analysis allows us to propose a simple correction of the IB scheme that is local, straightforward and does not involve additional computational time. The derived method is implemented in a two-relaxation-time D2Q9 lattice-Boltzmann solver, applied to several physical configurations, namely, the Poiseuille flow, the flow around a cylinder towed in still fluid, and the flow around a cylinder oscillating in still fluid, and compared to a noncorrected immersed-boundary method. The proposed correction leads to a major improvement of the viscosity independence of the solver over a wide range of relaxation times (from 0.5001 to 50), including the correction of the boundary-slip error and the suppression of the spurious oscillations. This improvement may considerably extend the range of application of the IB lattice-Boltzmann method, in particular providing a robust tool for the numerical analysis of physical problems involving fluids of varying viscosity interacting with solid geometries.
Simon Gsell, Umberto d'Ortona, Julien Favier. Explicit and viscosity-independent immersed-boundary scheme for the lattice Boltzmann method. Physical Review E , 2019, 100 (3), ⟨10.1103/PhysRevE.100.033306⟩. ⟨hal-02339475⟩
Yongliang Feng, Pierre Boivin, Jérome Jacob, Pierre Sagaut. Hybrid recursive regularized lattice Boltzmann simulation of humid air with application to meteorological flows. Physical Review E , 2019. ⟨hal-02265484⟩ Plus de détails...
An extended version of the hybrid recursive regularized Lattice-Boltzmann model which incorporates external force is developed to simulate humid air flows with phase change mechanisms under the Boussinesq approximation. Mass and momentum conservation equations are solved by a regu-larized lattice Boltzmann approach well suited for high Reynolds number flows, whereas the energy and humidity related equations are solved by a finite volume approach. Two options are investigated to account for cloud formation in atmospheric flow simulations. The first option considers a single conservation equation for total water and an appropriate invariant variable of temperature. In the other approach, liquid and vapor are considered via two separated equations, and phase transition is accounted for via a relaxation procedure. The obtained models are then systematically validated on four well-established benchmark problems including a double diffusive Rayleigh Bénard convection of humid air, 2D and 3D thermal moist rising bubble under convective atmospheric environment as well as a shallow cumulus convection in framework of large-eddy simulation.
Yongliang Feng, Pierre Boivin, Jérome Jacob, Pierre Sagaut. Hybrid recursive regularized lattice Boltzmann simulation of humid air with application to meteorological flows. Physical Review E , 2019. ⟨hal-02265484⟩
To better understand the velocity field and flowing layer structure, we have performed a detailed discrete element method study of the flow of monodisperse particles in a partially filled three-dimensional cylindrical rotating tumblers. Similar to what occurs near the poles in spherical and conical tumblers, recirculation cells (secondary flows) develop near the flat endwalls of a cylindrical tumbler in which particles near the surface drift axially toward the endwall, while particles deeper in the flowing layer drift axially toward the midlength of the tumbler. Another recirculation cell with the opposite sense develops next to each endwall recirculation cell, extending to the midlength of the tumbler. For a long enough tumbler, each endwall cell is about one quarter of the tumbler diameter in length. Endwall cells are insensitive to tumbler length and relatively insensitive to rotation speed (so long as the flowing layer remains flat and continuously flowing) or fill level (from 25% to 50% full). However, for shorter tumblers (0.5 to 1.0 length/diameter aspect ratio) the endwall cell size does not change much, while center cells reduce their size and eventually disappear for the shortest tumblers. For longer tumblers (length/diameter aspect ratio larger than 2), a stagnation zone appears in between the central cells. These results provide insight into the mixing of monodisperse particles in rotating cylindrical tumblers as well as the frictional effects of the tumbler endwalls.
Umberto d'Ortona, Nathalie Thomas, Richard M. Lueptow. Recirculation cells for granular flow in cylindrical rotating tumblers. Physical Review E , 2018, 97 (5). ⟨hal-02001973⟩
Sylvain Chateau, Umberto d'Ortona, Sébastien Poncet, Julien Favier. Transport and Mixing Induced by Beating Cilia in Human Airways. Frontiers in Physiology, 2018, 9, pp.161. ⟨10.3389/fphys.2018.00161⟩. ⟨hal-01875672⟩ Plus de détails...
The fluid transport and mixing induced by beating cilia, present in the bronchial airways, are studied using a coupled lattice Boltzmann-Immersed Boundary solver. This solver allows the simulation of both single and multi-component fluid flows around moving solid boundaries. The cilia aremodeled by a set of Lagrangian points, and Immersed Boundary forces are computed onto these points in order to ensure the no-slip velocity conditions between the cilia and the fluids. The cilia are immersed in a two-layer environment: the periciliary layer (PCL) and the mucus above it. The motion of the cilia is prescribed, as well as the phase lag between two cilia in order to obtain a typical collective motion of cilia, known as metachronal waves. The results obtained from a parametric study show that antiplectic metachronal waves are the most efficient regarding the fluid transport. A specific value of phase lag, which generates the larger mucus transport, is identified. The mixing is studied using several populations of tracers initially seeded into the pericilary liquid, in the mucus just above the PCL-mucus interface, and in the mucus far away from the interface. We observe that each zone exhibits different chaotic mixing properties. The larger mixing is obtained in the PCL layer where only a few beating cycles of the cilia are required to obtain a full mixing, while above the interface, the mixing is weaker and takes more time. Almost no mixing is observed within the mucus, and almost all the tracers do not penetrate the PCL layer. Lyapunov exponents are also computed for specific locations to assess how the mixing is performed locally. Two time scales are introduced to allow a comparison between mixing induced by fluid advection and by molecular diffusion. These results are relevant in the context of respiratory flows to investigate the transport of drugs for patients suffering from chronic respiratory diseases.
Sylvain Chateau, Umberto d'Ortona, Sébastien Poncet, Julien Favier. Transport and Mixing Induced by Beating Cilia in Human Airways. Frontiers in Physiology, 2018, 9, pp.161. ⟨10.3389/fphys.2018.00161⟩. ⟨hal-01875672⟩
Umberto d'Ortona, Nathalie Thomas, Richard M. Lueptow. Axial segregation in spherical and cylindrical rotating tumblers. EPJ Web of Conferences, 2017, Powders and Grains 2017 – 8th International Conference on Micromechanics on Granular Media, 140, pp.03011. ⟨10.1051/epjconf/201714003011⟩. ⟨hal-01671207⟩ Plus de détails...
Monodisperse and bidisperse granular flows are studied in rotating tumblers using DEM. In spherical tumblers, flowing particles’ trajectories do not follow straight lines but are curved. At the same time particles near the surface drift toward the pole, inducing two global recirculation cells. Combined with radial segregation, drift and curvature compete to impose the axial segregation pattern: Small-Large-Small (SLS) or Large-Small-Large (LSL). Fill level, rotation speed and wall roughness influence drift and curvature, and modify the resulting segregation pattern. In cylindrical tumblers, equivalent recirculation cells occur next to the end walls. A second pair of recirculation cells with a weak drift in the opposite direction appears at the center for long enough tumblers. Unlike the sphere case, curvature and drift in the primary cells combine to push large particles toward the end walls, explaining why large particle bands appear at the end walls for axial segregation in cylinder.
Umberto d'Ortona, Nathalie Thomas, Richard M. Lueptow. Axial segregation in spherical and cylindrical rotating tumblers. EPJ Web of Conferences, 2017, Powders and Grains 2017 – 8th International Conference on Micromechanics on Granular Media, 140, pp.03011. ⟨10.1051/epjconf/201714003011⟩. ⟨hal-01671207⟩
Umberto d'Ortona, Nathalie Thomas, Richard M. Lueptow. Influence of Rough and Smooth Walls on Macroscale Granular Segregation Patterns. Physical Review E , 2016, 93 (2), pp.022906. ⟨10.1103/PhysRevE.93.022906⟩. ⟨hal-01306600⟩ Plus de détails...
Size bidisperse granular materials in a spherical tumbler segregate into two different patterns of three bands with either small particles at the equator and large particles at the poles or vice versa, depending upon the fill level in the tumbler. Here we use discrete element method (DEM) simulations with supporting qualitative experiments to explore the effect of the tumbler wall roughness on the segregation pattern, modeling the tumbler walls as either a closely packed monolayer of fixed particles resulting in a rough wall, or as a geometrically smooth wall. Even though the tumbler wall is in contact with the flowing layer only at its periphery, the impact of wall roughness is profound. Smooth walls tend toward a small-large-small (SLS) band pattern at the pole-equator-pole at all but the highest fill fractions; rough walls tend toward a large-small-large (LSL) band pattern at all but the lowest fill fractions. This comes about because smooth walls induce poleward axial drift of small particles and an equator-directed drift for large particles, resulting in an SLS band pattern. On the other hand, rough walls result in both sizes of particles moving poleward at the surface of the flow, but due to radial segregation, small particles percolate lower in the flowing layer where there is a return drift toward the equator while large particles remain at the surface near the pole, resulting in an LSL band pattern. The tendency toward either of the two band patterns depends on the fill level in the tumbler and the roughness of the tumbler's bounding wall.
Umberto d'Ortona, Nathalie Thomas, Richard M. Lueptow. Influence of Rough and Smooth Walls on Macroscale Granular Segregation Patterns. Physical Review E , 2016, 93 (2), pp.022906. ⟨10.1103/PhysRevE.93.022906⟩. ⟨hal-01306600⟩
Umberto d'Ortona, Nathalie Thomas, Zafir Zaman, Richard M. Lueptow. Influence of rough and smooth walls on macroscale flows in tumblers. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 92 (6), pp.062202. ⟨10.1103/PhysRevE.92.062202⟩. ⟨hal-01306604⟩ Plus de détails...
Walls in discrete element method simulations of granular flows are sometimes modeled as a closely packed monolayer of fixed particles, resulting in a rough wall rather than a geometrically smooth wall. An implicit assumption is that the resulting rough wall differs from a smooth wall only locally at the particle scale. Here we test this assumption by considering the impact of the wall roughness at the periphery of the flowing layer on the flow of monodisperse particles in a rotating spherical tumbler. We find that varying the wall roughness significantly alters average particle trajectories even far from the wall. Rough walls induce greater poleward axial drift of particles near the flowing layer surface but decrease the curvature of the trajectories. Increasing the volume fill level in the tumbler has little effect on the axial drift for rough walls but increases the drift while reducing curvature of the particle trajectories for smooth walls. The mechanism for these effects is related to the degree of local slip at the bounding wall, which alters the flowing layer thickness near the walls, affecting the particle trajectories even far from the walls near the equator of the tumbler. Thus, the proper choice of wall conditions is important in the accurate simulation of granular flows, even far from the bounding wall.
Umberto d'Ortona, Nathalie Thomas, Zafir Zaman, Richard M. Lueptow. Influence of rough and smooth walls on macroscale flows in tumblers. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 92 (6), pp.062202. ⟨10.1103/PhysRevE.92.062202⟩. ⟨hal-01306604⟩
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Zafir Zaman, Umberto d'Ortona, Paul B. Umbanhowar, Julio M. Ottino, Richard M. Lueptow. Slow axial drift in three-dimensional granular tumbler flow. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2013, 88 (1), pp.012208. ⟨10.1103/PhysRevE.88.012208⟩. ⟨hal-00905562⟩ Plus de détails...
Models of monodisperse particle flow in partially filled three-dimensional tumblers often assume that flow along the axis of rotation is negligible. We test this assumption, for spherical and double cone tumblers, using experiments and discrete element method simulations. Cross sections through the particle bed of a spherical tumbler show that, after a few rotations, a colored band of particles initially perpendicular to the axis of rotation deforms: particles near the surface drift toward the pole, while particles deeper in the flowing layer drift toward the equator. Tracking of mm-sized surface particles in tumblers with diameters of 8-14 cm shows particle axial displacements of one to two particle diameters, corresponding to axial drift that is 1-3% of the tumbler diameter, per pass through the flowing layer. The surface axial drift in both double cone and spherical tumblers is zero at the equator, increases moving away from the equator, and then decreases near the poles. Comparing results for the two tumbler geometries shows that wall slope causes axial drift, while drift speed increases with equatorial diameter. The dependence of axial drift on axial position for each tumbler geometry is similar when both are normalized by their respective maximum values.
Zafir Zaman, Umberto d'Ortona, Paul B. Umbanhowar, Julio M. Ottino, Richard M. Lueptow. Slow axial drift in three-dimensional granular tumbler flow. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2013, 88 (1), pp.012208. ⟨10.1103/PhysRevE.88.012208⟩. ⟨hal-00905562⟩
Journal: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics