Fluidization of irregular particles - Part II: A particle-resolved simulation method to model hydrodynamic interactions

Irregular particle shapes are ubiquitous in many real-life systems and in particular in the chemical engineering industry. Most of the corresponding numerical simulations are carried out using spherical particles due to the lack of appropriate numerical methods at the particle level or appropriate closure laws for hydrodynamic and collisional interactions in Euler-Lagrange and Euler-Euler models. Since in Part I, we presented a numerical technique implemented in our granular code Grains3D to treat the collisional behaviour of particles of (almost) arbitrary shape, we are now in a favourable position to suggest a corresponding Particle-Resolved Simulation (PRS) method to which Grains3D is coupled to (1,2,3). It is based on a Distributed Lagrange Multiplier/Fictitious Domain technique combined with Finite Volume/Staggered Grid discretization (2,3), that supplies solutions of satisfactory accuracy. This study aims to go one step further and to extend our numerical method to non-convex particles. This extension is implemented in our parallel numerical platform PeliGRIFF (4) . We illustrate the novel simulation capabilities of PeliGRIFF on the problem of the fluidization of trilobic/quadrilobic particles encountered in Oil & Gas catalytic reactors. First, we assess the space convergence and overall accuracy of the computed solution in the case of the flow past an infinite array of trilobes/quadrilobes. Then, we show results of the flow through a fixed bed made of trilobes/quadrilobes at random loose packing. Finally, we present preliminary results relevant to an actual fluidization. In conclusion, we discuss the computing challenges of these simulations and the integration of their results in a comprehensive multi-scale approach. REFERENCES A. Wachs. A DEM-DLM/FD method for direct numerical simulation of particulate flows: Sedimentation of polygonal isometric particles in a Newtonian fluid with collisions. Computers & Fluids, 38, 1608-1628, 2009. A. Wachs, A. Hammouti, G. Vinay, M. Rahmani. Accuracy of Finite Volume/Staggered Grid Distributed Lagrange Multiplier/Fictitious Domain simulations of particulate flows. Computers & Fluids, 115, 154-172, 2015. F. Dorai, C. Moura Teixeira, M. Rolland, E. Climent, M. Marcoux, A. Wachs. Fully resolved simulations of the flow through a packed bed of cylinders: Effect of size distribution. Chemical Engineering Science, 129, 180-192, 2015. PeliGRIFF, A multi-scale numerical modeling tool for fluid/particles flows. http://www.peligriff.co

Direct numerical simulation of reactive flow through a fixed bed of catalyst particles

Many catalytic refining and petrochemical processes involve two-phase reactive systems in which the continuous phase is a fluid and the porous phase consists of rigid particles randomly stacked. Improving both the design and the operating conditions of these processes represents a major scientific and industrial challenge in a context of sustainable development. Thus, it is above all important to better understand all the intricate couplings at stake in these flows: hydrodynamic, chemical and thermal contributions. The objective of our work is to build up a multi-scale modelling approach of reactive particulate flows and at first to focus on the development of a microscopic-scale including heat and mass transfers and chemical reactions for the prediction of reactive flows through a dense or dilute fixed bed of catalyst particles. Please download the full abstract below

Fluidization of irregular particles - Part I: A discrete element method to model collisions between non-convex particles

The flow dynamics of a fluidized bed can be very complicated. As the solid volume fraction is generally high, particle-particle collisions cannot be ignored. Many studies in the literature deal with perfectly spherical particles while very few deal with non-spherical ones and even less with angular or non-convex particles. However, these irregularly shaped particles are not uncommon in chemical engineering. Among others, Escudié et al (1) showed that the particle shape influences markedly the dynamics of such a system. We suggest an accurate and efficient way to model collisions between particles of (almost) arbitrary shape, that can be integrated into a comprehensive modeling of a fluidized bed. For that purpose, we develop a Discrete Element Method (DEM) combined with a soft particle contact model that treats the contact between bodies of various shape and size (2). In particular, for non-convex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones (3). Therefore, our novel method can be called “glued convex method”, as an extension of the popular “glued-spheres” method (4). It hence uses all the features involved in DEM simulations of convex bodies, such as the contact detection strategy based on a Gilbert-Johnson-Keerthi algorithm (5) and the linked-cell spatial sorting which accelerates the contact resolution (6). The problem of multiple contact requires a particular attention (4,7). The method is implemented in our granular dynamics code Grains3D. As an illustration of the powerful modelling capabilities of Grains3D, we show results of simulation of settling non-convex catalytic pellets in a cylindrical chemical reactor. REFERENCES R. Escudié, N. Epstein, J.R. Grace, H.T. Bi, Effect of particle shape on liquid-fluidized beds of binary (and ternary) solids mixtures: segregation vs. mixing. Chemical Engineering Science, 61(5): 1528, 2006. A. Wachs, L. Girolami, G. Vinay, and G. Ferrer. Grains3D, a flexible DEM approach for particles of arbitrary convex shape - Part I: Numerical model and validations. Powder Technology, 224:374-389, 2012. A. D. Rakotonirina, A. Wachs, J.-Y. Delenne, F. Radjai. Grains3D, a flexible DEM approach for particles of arbitrary convex shape - Part III: extension to non convex particles, submitted to Powder Technology, 2015. D. Höhner, S. Wirtz, H. Kruggel-Emden, and V. Scherer. Comparison of the multi-sphere and polyhedral approach to simulate non-spherical particles within the discrete element method: Influence on temporal force evolution for multiple contacts. Powder Technology, 208(3):643-656, 2011. Elmer G. Gilbert, Daniel W. Johnson, and S. Sathiya Keerthi. A fast procedure for computing the distance between complex objects in three-dimensional space. Robotics and Automation, IEEE Journal of Robotics and Automation, 4(2):193-203, 1988. Gary S. Grest, Burkhard Dünweg, and Kurt Kremer. Vectorized link cell Fortran code for molecular dynamics simulations for a large number of particles. Computer Physics Communications, 55(3):269-285, 1989. H. Kruggel-Emden, S. Rickelt, S. Wirtz, and V. Scherer. A study on the validity of the multi-sphere discrete element method. Powder Technology, 188(2):153-165, 2008

Chemical modification of polymers by acyloxyimide derivatives in reactive extrusion

La fonctionnalisation post-polymérisation ou post-fonctionnalisation est une technique qui permet d’apporter des propriétés spécifiques à des polymères dont les caractéristiques intrinsèques sont limitées pour une application donnée. Parmi les différentes stratégies de post-fonctionnalisation, une des plus courantes est le greffage radicalaire en milieu fondu par extrusion réactive (T > 160 °C). Dans ce type de procédé, un précurseur de radicaux appelé agent de greffage est utilisé afin de greffer des unités fonctionnelles sur les chaines de polymère. A ce jour, ce sont les radicaux à base de peroxydes qui sont employés. Cependant, ces derniers engendrent souvent des réactions de réticulation de chaines qui réduisent l’efficacité du processus. Afin de surmonter ces inconvénients, il est alors important de développer de nouvelles structures pertinentes. Dans ce contexte, les travaux de recherche que nous avons entrepris dans cette thèse concernent la conception et l’étude de nouveaux agents de greffage dérivés d’acétoxyphtalimide (NAPI) pour la post-fonctionnalisation de polymères. Afin d’atteindre ces objectifs, notre démarche a été basée sur une approche multidisciplinaire comportant une étude théorique par modélisation moléculaire et une approche expérimentale incluant la synthèse et l’étude de réactivité des nouvelles structures. Par la suite, des essais de post-fonctionnalisation de polyéthylène, de polyamide ainsi que de poly(acide lactique) par ces nouveaux agents de greffage ont été réalisés. Ces essais ont montré des résultats prometteurs à l’utilisation de ces nouveaux composés par rapport aux peroxydes dans les systèmes d’extrusion.Post-functionalization is a technique which allows to introduce specific properties to polymers whose intrinsic characteristics are limited for a defined application. It has become an appropriate tool to answer the strong demand for performance materials that is constantly growing. Among the post-functionalization methods, one of the most exploited is the radical grafting of the polymers in the molten state by reactive extrusion (T> 160 ° C). In this type of process, a radical precursor called grafting agent is used to graft functional units (monomers) onto the polymer backbone. In this context, the conventional grafting agents used in extrusion are peroxides. However, the radicals generated by peroxide compounds often lead to side reactions, particularly crosslinking reactions of the polymer chains which limit the efficiency of the process. Thus, finding a new family of grafting agents remains a challenge to optimize these extrusion systems. In this research work, the main objective is to use new grafting agents based on acetoxyphthalimide (NAPI) for extrusion. To reach this goal, our strategy is based on a multidisciplinary approach which presents a theoretical study by chemical modeling and an experimental approach by the synthesis and the reactivity study of the targeted structures. To validate the concept, polyethylene, polyamide and polylactic acid post-functionalization tests through these new grafting agents have been carried out. The results obtained have shown that these NAPI derivatives are efficient to graft monomers and to reduce the crosslinking reaction compared to peroxide agents

Grains3D, a flexible DEM approach for particles of arbitrary convex shape - Part II: Parallel implementation and scalable performance

International audienceIn [1] we suggested an original Discrete Element Method that offers the capability to consider non-spherical particles of arbitrary convex shape. We elaborated on the foundations of our numerical method and validated it on assorted test cases. However, the implementation was serial and impeded to examine large systems. Here we extend our method to parallel computing using a classical domain decomposition approach and inter-domain MPI communication. The code is implemented in C++ for multi-CPU architecture. Although object-oriented C++ offers high-level programming concepts that enhance the versatility required to treat multi-shape and multi-size granular systems, particular care has to be devoted to memory management on multi-core architecture to achieve reasonable computing efficiency. The parallel performance of our code Grains3D is assessed on various granular flow configurations comprising both spherical and angular particles. We show that our parallel granular solver is able to compute systems with up to a few hundreds of millions of particles. This opens up new perspectives in the study of granular material dynamics

A parallel Discrete Element Method to model collisions between non-convex particles

In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost) arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM) combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called “glued-convex method” (in the sense clumping convex bodies together), as an extension of the popular “glued-spheres” method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i) the collapse of a granular column made of convex particles and (i) the microstructure of a heap of non-convex particles in a cylindrical reactor

A parallel Discrete Element Method to model collisions between non-convex particles

In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost) arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM) combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called “glued-convex method” (in the sense clumping convex bodies together), as an extension of the popular “glued-spheres” method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i) the collapse of a granular column made of convex particles and (i) the microstructure of a heap of non-convex particles in a cylindrical reactor