Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions

The complexity of the interactions between the constituent granular and liquid phases of a suspension requires an adequate treatment of the constituents themselves. A promising way for numerical simulations of such systems is given by hybrid computational frameworks. This is naturally done, when the Lagrangian description of particle dynamics of the granular phase finds a correspondence in the fluid description. In this work we employ extensions of the Lattice-Boltzmann Method for non-Newtonian rheology, free surfaces, and moving boundaries. The models allows for a full coupling of the phases, but in a simplified way. An experimental validation is given by an example of gravity driven flow of a particle suspension

A quantification of hydrodynamical effects on protoplanetary dust growth

Context. The growth process of dust particles in protoplanetary disks can be modeled via numerical dust coagulation codes. In this approach, physical effects that dominate the dust growth process often must be implemented in a parameterized form. Due to a lack of these parameterizations, existing studies of dust coagulation have ignored the effects a hydrodynamical gas flow can have on grain growth, even though it is often argued that the flow could significantly contribute either positively or negatively to the growth process. Aims. We intend to provide a quantification of hydrodynamical effects on the growth of dust particles, such that these effects can be parameterized and implemented in a dust coagulation code. Methods. We numerically integrate the trajectories of small dust particles in the flow of disk gas around a proto-planetesimal, sampling a large parameter space in proto-planetesimal radii, headwind velocities, and dust stopping times. Results. The gas flow deflects most particles away from the proto-planetesimal, such that its effective collisional cross section, and therefore the mass accretion rate, is reduced. The gas flow however also reduces the impact velocity of small dust particles onto a proto-planetesimal. This can be beneficial for its growth, since large impact velocities are known to lead to erosion. We also demonstrate why such a gas flow does not return collisional debris to the surface of a proto-planetesimal. Conclusions. We predict that a laminar hydrodynamical flow around a proto-planetesimal will have a significant effect on its growth. However, we cannot easily predict which result, the reduction of the impact velocity or the sweep-up cross section, will be more important. Therefore, we provide parameterizations ready for implementation into a dust coagulation code.Comment: 9 pages, 6 figures; accepted for publication in A&A; v2 matches the manuscript sent to the publisher (very minor changes

Homogeneous equilibrium model for geomechanical multi-material flow with compressible constituents

Multi-material flow generally describes a situation where several distinct materials separated by sharp material interfaces undergo large deformations. In order to model such flow situations in the context of geomechanics and geotechnical engineering, a theoretical framework is presented which introduces a possible two-phase coupled saturated granular material behavior among the different materials. This is achieved by extending the technique of local volume averaging to a hierarchy of three spatial scales, based on a product of two indicator functions. A homogeneous equilibrium mixture model is subsequently derived for an example flow consisting of bulk solid, bulk fluid, and undrained granular material with compressible constituents. The closure relations are provided at the macroscale, including those describing granular behavior covering the full frictional-collisional flow regime and bulk material volume fraction evolution. The paper discusses the advantages and restrictions of the proposed mixture model and addresses its application and full-scale numerical implementation.DFG, FOR 1136, Modellierung von geotechnischen Herstellungsvorgängen mit ganzheitlicher Erfassung des Spannungs-Verformungs-Verhaltens im Boden (GeoTech)DFG, SA 310/26-1, Numerische Modellierung der Herstellung von RüttelinjektionspfählenDFG, SA 310/26-2, Numerische Modellierung der Herstellung von Rüttelinjektionspfähle

Theory and Numerical Modeling of Geomechanical Multi-material Flow

Multi-material flow describes a situation where several distinct materials separated by sharp material interfaces undergo large deformations. The research presented in this paper addresses a particular class of multi-material flow situations encountered in geomechanics and geotechnical engineering which is characterized by a complex coupled behavior of saturated granular material as well as by a hierarchy of distinct spatial scales. Examples include geotechnical installation processes, liquefaction-induced soil failure, and debris flow. The most attractive numerical approaches to solve such problems use variants of arbitrary Lagrangian–Eulerian descriptions allowing interfaces and free surfaces to flow through the computational mesh. Mesh elements cut by interfaces (multi-material elements) necessarily arise which contain a heterogeneous mixture of two or more materials. The heterogeneous mixture is represented as an effective single-phase material using mixture theory. The paper outlines the specific three-scale mixture theory developed by the authors and the MMALE numerical method to model and simulate geomechanical multi-material flow. In contrast to traditional flow models which consider the motion of multiple single-phase materials or single multi-phase mixture, the present research succeeds in incorporating both the coupled behavior of saturated granular material and its interaction with other (pure) materials.DFG, 76838227, Numerische Modellierung der Herstellung von Rüttelinjektionspfähle

Numerical simulation of mechanofusion system for dry particle coating process

A numerical simulation of the Meclianofusion device for dry particle coating is carried out using Discrete Element Method (DEM) technique. In dry particle coating, tiny sub-micron guest particles are coated onto larger micron sized host particles by using mechanical forces, which the Mechanofusion device provides. It consists of a rotating cylindrical chamber that contains the powder mixture, a stationary inner piece (which has a cylindrical surface at the end), and a fixed scraper blade, which prevents powder from caking against the chamber wall. The simulation studies are performed on two scales: system scale to investigate the particle-particle and particle system interactions, and micro scale to study the degradation of agglomerates prior to the dry particle coating process. The system-scale simulation is based on a mono-dispersed system where only host particles are taken into consideration. The particles are assumed to be frictional, elastic-plastic spheres. A widely used, non-adhesion Walton-Braun. contact model has been applied in two-dimensional configuration. Two simplified geometric models of the Mechanofusion chamber with and without the scraper have been studied. The visualization of the particulate patterns inside the system and the diagnostic analysis derived from the numerical simulations clearly demonstrate the effect of scraper on the system. The forces acting on the inner piece are calculated and compared with the experimental results available from the literature. Average forces on particles due to interactions with other particles and vessel parts are also calculated and categorized into four regions. The effect of particle properties on coating level is examined through a simple deformation analysis. In addition, minimum coating time is estimated. Furthermore, the important parameters that affect the system performance are studied. Another important contribution of the dissertation lies in the dimensional analysis of the Mechanofusion system carried out on the basis of kinetic theory under the assumption of collisional flow, verified qualitatively by simulations. An equation for average force on particles inside the system is derived to establish the correlation between a simulated system and a real system. Major kinetic theory modeling based similarity results, verified by simulations and in part from available experimental data, include: (1) Inter-particle (host-host) forces vary linearly with the rotation speed; (2) Force exerted on the particles within the inner-piece zone is inversely proportional to the gap-size; and (3) Force on the inner-piece varies linearly with the square of the rotation speed. Based on the results from system simulation, the fracture/ fragment at ion of ail agglomerate during normal interactions with host particle and with system wall is examined in detail by the micro-scale simulation. The numerical study is implemented using a DEM code (developed by Prof. Thornton\u27s group at Aston University) in two-dimensional mode, which enables the simulation of auto-adhesive particles. The study shows that single agglomerate may fracture or even shatter inside the system as a result of interactions with the host particles and system boundaries. The fracture pattern of the agglomerate is in agreement with reported three dimensional simulation results. Results show that higher impact velocities lead to higher local damage and debris formation. However, impact velocities as low as 0.1 m/s lead to fracture in some case. In most cases, impacts at velocities of I m/s and higher lead to shattering of the agglomerate. In summary, the work presented in this dissertation, which is one of the first reported work on DEM simulation of dry particle coating system, shows that DEM technique can be used to model important aspects of the Mechanofusion system, such as the salient pattern of particles inside the system and the overall system performance as well as the agglomerate fragmentation prior to the dry particle coating process

Modeling of debris flow depositional patterns according to the catchment and sediment source area characteristics

A method to predict the most probable flow rheology in Alpine debris flows is presented. The methods classifies outcropping rock masses in catchments on the basis of the type of resulting unconsolidated deposits. The grain size distribution of the debris material and the depositional style of past debris flow events are related to the dominant flow processes: viscoplastic and frictional/collisional. Three catchments in the upper Susa Valley (Western Alps), characterized by different lithologies, were selected for numerical analysis carried out with a Cellular Automata code with viscoplastic and frictional/collisional rheologies. The obtained numerical results are in good agreement with in site evidences in terms of depositional patterns, confirming the possibility of choosing the rheology of the debris flow based on the source material within the catchment

Cellular Automaton for Realistic Modelling of Landslides

A numerical model is developed for the simulation of debris flow in landslides over a complex three dimensional topography. The model is based on a lattice, in which debris can be transferred among nearest neighbors according to established empirical relationships for granular flows. The model is then validated by comparing a simulation with reported field data. Our model is in fact a realistic elaboration of simpler ``sandpile automata'', which have in recent years been studied as supposedly paradigmatic of ``self-organized criticality''. Statistics and scaling properties of the simulation are examined, and show that the model has an intermittent behavior.Comment: Revised version (gramatical and writing style cleanup mainly). Accepted for publication by Nonlinear Processes in Geophysics. 16 pages, 98Kb uuencoded compressed dvi file (that's the way life is easiest). Big (6Mb) postscript figures available upon request from [email protected] / [email protected]

Developing a mechanistic model for flow through a perforated plate with application to screening of particulate materials

Screening in mineral processing is the practice of separating granulated ore materials into multiple particle size fractions, and is employed in most mineral processing plants. Models of screening performance have been developed previously with the aim of improving process efficiency. Different methods have been used, such as physical modelling, empirical modelling, and mathematical modelling including the discrete element method (DEM). These methods have major limitations in practice, and experimental data to validate the models have been difficult to obtain. Currently, the design and scale-up of screens still relies on rules of thumb and empirical factor methods rather than a fundamentally based understanding of the behaviour of the granular system. To go beyond the current state-of-the-art in screen modelling requires a clear understanding of the particle motion along a dynamic (vibrating) inclined plane. Central to this understanding is the notion that granular systems exhibit a unique rheology that is not observed in fluids; i.e. neither Newtonian nor non-Newtonian. It is thus imperative to fully quantify the granular rheology, which is determined by the depth of the particle bed along the screen, the solids concentration, and the average velocity of the granular avalanche on the screen. The concept of granular rheology is important. Existing empirical models of vibrating screens tend to be extremely dependent on boundary conditions of a particular machine design. The concept of granular rheology is important because, akin to fluid flow, granular flow exhibits different flow regimes depending on the extent of energy input in the system. This work employed DEM to quantify the granular rheology of particles moving along a vibrating inclined screen in order to begin the development of a phenomenological model of screening. The model extends the visco-plastic rheology formation of Pouliquen et al. (2006) to capture the kinetic and turbulent stresses obtained in granular flow on an inclined vibrating screen. In general, DEM was employed to develop a mechanistic model of screening which includes a description of the rheology of granular flow on a vibrating screen. Microscopic properties of granular flow were used in DEM to simulate screening of particulate materials. Granular mixtures of two particle constituents (3 mm and 5 mm) were simulated on an inclined vibrating screen of 3.5 mm apertures. For the base case, frequency and amplitude are 4 Hz and 1 mm, respectively. While microscopic properties were employed for the simulation, the properties extracted from the simulations are macroscopic fields which are consistent with the continuum equations of mass, momentum and energy balance. From the continuum equations, a micro-macro transition method called the coarse-graining approach was employed to obtain the volume fraction and the tangential velocity as a function of the depth of flow along the inclined surface. This approach is suitable for this work because the produced fields satisfy the equations of continuum mechanics; even near the base of the flow. The continuum analysis of the flowing layer reveals a coexistence of flow regimes- (i) quasi-static, (ii) dense (liquid-like), and (iii) inertial. The regimes are consistent with the measured solids concentrations spanning these regimes on inclined vibrating screens. The quasi-static regime is dominated by frictional stress and corresponds to low inertial number (I). Beyond the quasi-static regime, the frictional stress chains break and the collisional-kinetic and turbulent stress begin to dominate. The variation of the effective frictional coefficient with the inertial number (I) characterises the flow. Finally, an effective frictional coefficient model that is based on frictional, collisionalkinetic and turbulent stress was developed. Data analyses for this model were done at a steady flow in the base case where a coexistence of three flow regimes were observed. It was observed that each regime of flow is dominated by corresponding shear stresses. While the quasi-static regime is dominated by frictional stress, the kinetic and the inertial regimes are dominated by kinetic and turbulent shear stresses, respectively. This model was tested by varying the intensity of vibration in the base case and it was observed that at higher frequencies and amplitudes, the quasi-static regime gradually disappeared. Furthermore, the inertial number at which transition occurs to different regimes varies in response to the intensity of vibration. This is an important step in developing a phenomenological model of screening. The model presents a fundamental understanding of the mechanisms governing transport of granular matter on an inclined vibrating screen

Multiphase debris flow simulations with the discrete element method coupled with a lattice-boltzmann fluid

Debris flows are dangerous natural hazards that occur mainly in mountainous terrains after heavy rainfall, responsible for casualties and damages reported yearly worldwide. Their heterogeneous composition, with a viscoplastic fluid and the presence of a relevant granular solid phase, leads to a non-trivial behaviour making them a challenging problem both for the physical description of the phenomena and for the design of effective protection measures. A numerical model is developed, fully coupling the two phases. A Discrete Element approach is used for the description of the solid phase, with a realistic particle size distribution, while the fluid phase is solved with a Lattice-Boltzmann Method. The effect of shape on the rolling mechanism is included with a simplified model, as well as the effects of non-Newtonian rheology and the presence of a free surface. The numerical results provide insight into complex segregation, transportation and sedimentation phenomena, essential for understanding and predicting the run-out mechanism of debris avalanches and their interaction with obstacles and retaining structures

Microgravity experiments on the collisional behavior of Saturnian ring particles

In this paper we present results of two novel experimental methods to investigate the collisional behavior of individual macroscopic icy bodies. The experiments reported here were conducted in the microgravity environments of parabolic flights and the Bremen drop tower facility. Using a cryogenic parabolic-flight setup, we were able to capture 41 near-central collisions of 1.5-cm-sized ice spheres at relative velocities between 6 and $22 \mathrm{cm s^{-1}}$. The analysis of the image sequences provides a uniform distribution of coefficients of restitution with a mean value of $\overline{\varepsilon} = 0.45$ and values ranging from $\varepsilon = 0.06$ to 0.84. Additionally, we designed a prototype drop tower experiment for collisions within an ensemble of up to one hundred cm-sized projectiles and performed the first experiments with solid glass beads. We were able to statistically analyze the development of the kinetic energy of the entire system, which can be well explained by assuming a granular `fluid' following Haff's law with a constant coefficient of restitution of $\varepsilon = 0.64$. We could also show that the setup is suitable for studying collisions at velocities of $< 5 \mathrm{mm s^{-1}}$ appropriate for collisions between particles in Saturn's dense main rings.Comment: Accepted for publication in the Icarus Special Issue "Cassini at Saturn