Thèse Mad-Sim Modélisation des Poudres Agitées en Écoulement Dense des Études Rhéologiques à la Simulation Prédictive à l'Échelle des Procédés H/F - Doctorat.Gouv.Fr

Établissement : IMT Mines Albi École doctorale : MEGEP - Mécanique, Energétique, Génie civil, Procédés Laboratoire de recherche : RAPSODEE - Centre de Recherche d'Albi en Génie des Procédés, des Solides Divisés, de l'Energie et de l'Environnement Direction de la thèse : Cendrine GATUMEL ORCID 0000000292764002 Début de la thèse : 2027-09-01 Date limite de candidature : 2026-11-16T23:59:59 Ce projet vise à combler le « fossé d'échelle » dans le domaine du traitement et de l'ingénierie des poudres, de l'échelle des particules à celle des procédés industriels, ainsi que dans de nombreux autres domaines tels que la recherche environnementale ou l'exploration extraterrestre, où la rhéologie des poudres à l'échelle macroscopique en conditions de faible confinement reste un défi. L'objectif est donc de mettre en évidence les processus mécaniques fondamentaux impliqués dans l'agitation convective des poudres, d'identifier une loi rhéologique appropriée à l'aide d'expériences et de simulations numériques (DEM), puis de l'intégrer dans un modèle issu de la mécanique des milieux continus afin de réduire le temps de calcul pour les simulations à plus grande échelle. La nouveauté réside dans l'extension du cadre rhéologique (I), validé pour des écoulements simples, à des systèmes agités complexes, où des transitions solide-fluide-gaz peuvent se produire. Un partenariat multidisciplinaire a été mis en place pour relever ce défi scientifique multi-échelle. La méthodologie développée devrait servir de démonstrateur pour d'autres applications à l'échelle pilote et industrielle. Ce projet de recherche devrait également permettre de concevoir un prototype de rhéomètre à l'échelle du laboratoire capable de caractériser les poudres agitées, répondant ainsi à un besoin jusqu'alors non satisfait. Cela ouvrira la voie à une nouvelle approche intégrée de la caractérisation des poudres et de la simulation des écoulements à l'échelle macroscopique. Cela ouvrira la voie à un large éventail d'applications, telles que le développement de jumeaux numériques pour optimiser l'éco-conception des équipements et le choix des paramètres de fonctionnement pour les opérations industrielles impliquant l'agitation de poudres, ainsi que pour prédire le comportement des matériaux granulaires dans un large éventail de situations à faible confinement. Every second, approximately sixty kilograms of infant milk powder are produced worldwide, every year EDF nuclear reactors consume 120 tons of MOX, a powder mixture of uranium and recycled plutonium oxides, to generate electricity [1]. This is a brief illustration of the ubiquity of powder in industry. Handling powders often involves a mixing operation, which is essential as it directly affects the quality of the final product and can lead to considerable material waste if not properly controlled. As an example, in pharmaceutical production, the equivalent of tens of thousands of non-conform tablets may been destroyed during the starting time of continuous mixing operations. In addition, for convective mixing that is of common use in manufacturing industries, understanding the powder flow behaviour when agitated mechanically is crucial as some powders require significant energy to initiate motion and impose substantial loads on the paddles, which can lead to blockages and cause serious damage to the equipment. The way powders flow under agitation depends not only on the operating conditions such as agitation speed, filling ratio and mixer geometry, but also on both their intrinsic and extrinsic properties. Free-flowing powders, despite being perceived as easier to handle compared to cohesive powders, can present challenges in predicting their flow behaviour. They interact mainly through frictional contacts that impact their flow properties. These interactions arise differently depending on whether the material is in a static, solid-like state, or in a dynamic state when subjected to shear forces, e.g. when the powder bed is agitated by paddles. Whether behaving as a solid, fluid or gas, powder is a state of matter that is difficult to model on a large scale, in which these three states may co-exist. In industry, the sizing of powder agitation devices, and the choice of operating parameters are often carried out by trial-and-error test at full scale that are tedious, time-consuming and costly. Rationalising these operations, using adapted laws and methods is a challenge in ensuring product quality and process safety. In addition, reducing the number of trials required for these designs will help to reduce the product-related waste.
As regards powder rheology most studies have been conducted under quasi-static conditions as research was driven by storage-related issues. Existing characterisation equipment is often associated with these operating conditions and fails to represent the levels of speed and confinement that are found in convective mixers or situations like the displacement of an extraterrestrial rover. More generally, characterising the rheology of powders in dense flow under low confinement is a major challenge, not only in industry but also for environmental research [2], and extraterrestrial exploration. To give just an example, understanding the rheology of powders in low-gravity conditions, which causes them to behave in ways that are difficult to predict from existing characterization methods, is not only essential for planning the landing and movement of planetary exploration rovers, but also crucial for the use of regolith in extraterrestrial construction projects necessary for space exploration [3].
Two approaches based on completely different concepts that are dimensional analysis and digital simulations are possible. Based on small-scale experiments, dimensional analysis requires establishing a basis for extrapolation according to the principle of geometric similarity and the choice of an invariant. It is an alternative to solving constitutive equations, widely used in fluid mechanics for example, which simplifies the study of experimentally observed phenomena while retaining their physical meaning [4]. These methods make it possible to calculate macroscopic quantities very quickly and thus to size installations. However, they do not provide access to local compositions and velocity fields inside the mixer, which is essential for studying the mixture. Nonetheless, using dimensionless analysis therefore requires precise knowledge of the phenomena involved. As concerns digital simulation, discrete and continuum models have been explored to study particles flow. Discrete Elements Methods based on identification and modelling of each contact between particles among the time, provide accurate access to particles scale information as trajectories and velocities [5]. However their use requires significant computing time, which makes their direct deployment unrealistic for simulating a pilot-scale or industrial mixer with real powders [6]. Furthermore, these high-performance models require a delicate calibration step in order to be used for numerical experiments. To the opposite, continuum models and CFD-type simulation methods [7] might be developed for larger scale flow simulation with reduced computational time [8]. These continuum mechanics models need to resolve the underlying conservation equations of the media, thus requiring the constraint-deformation relationships specific to the powder to be known [9]. Some attempts have been made recently showing their efficiency on inclined plans and rotation drum geometries [10][11][12].
Focusing on physical approaches, since the 1960s, flow patterns generated around agitation paddles have been investigated, always near the free surface, in 2-D experiments [13][14][15][16]. These studies overlooks the powders flow in the immersed low-confined region. Actually, when the blade rotates within the powder bed, two distinct flow patterns can be observed: one at the surface, thoroughly studied and generally described by the Froude number and the second in the immersed region where friction forces prevail, described by the Inertial number. Dense flow regime is generally used to unify the descriptions of powder flows among a wide range of solicitation stresses, by means of the rheology (I) [17][18][19][20] that reveals the transition between frictional and pre-collisional regimes and account for particles characteristics. There again, configurations described in the scientific literature are mostly flows out of storages, inclined plans and rotating drums [18]. Recently, from systemic torque recording during agitation of a powder we have built an empirical law based on the (I)-rheology framework and observed a dense-phase flow in an horizontal powder mixer agitated by blade-equipped devices [21]. This relationship has proved to be an invariant basis for scaling up agitation [22]. While this work represents a fundamental advance in understanding the mechanisms at play in agitated devices, the underlying model still needs to be supplemented by the knowledge of particles scale flow pattern.
Thus, the study of dense powder flow and its application to design and scale-up of relevant industrial devices remains a scientific multi-scale and multidisciplinary challenge, at the crossroads of physics, applied mathematics and process engineering research, which generally have little interaction with each other. Given the complementary nature of our backgrounds and approaches our partnership is an undeniable asset and will make it a unique working group to take on this challenge, positioning us as the future leaders in this area.
The aim of the thesis is (i) to explore rheological approaches by means of experiments and Discrete Element Modelling in order to identify a mesoscale constitutive law and draw the lines of a new characterization device (ii) and implement it in a continuum mechanics model, in the objective to simulate powder flows in convective mixers agitated with stirring devices. Methodologies and work process
(i) Constitutive law identification
The instrumented horizontal mixer in which the initial observations were made [21] will be used as a systemic rheometer. Physical and digital experiments will be carried out to refine our understanding of the phenomena involved, in particular to identify the geometry of the shear zone within the powder in the surroundings of the paddles, and the physical mechanisms that cause it to form [35][36], in relation to particles characteristics and agitator geometry. The start-up phase and the role of powder compressibility will also be explored. In a first instance, free-flowing particles will be used, the influence of particle size and shape might be studied. The DEM model of a restricted volume close to the agitated zone of the mixer will be developed, paying attention to determine properly its inputs, contact model and solids characteristics. The experimental validation of the model will be done by comparison with in-situ torque measurement, complemented by image analysis of observation of the flow at the wall (PIV) [16]. It is expected to reveal details that might be impossible to measure in a laboratory environment and help to identify the (I)-type constitutive law for the powder flow [37].
Scientific challenge: elaborate a mesoscopic constitutive law from a particle's scale method
Deliverables: DEM model of the system, refined rheological model, shear zone measurement protocol, and a publication on fundamental mechanisms.
Impact: drawing the outlines of laboratory-scale rheometer prototype capable of characterising agitated powders, filling a current market gap.

(ii) Continuum mechanic modelling and simulation
The so-called effective viscosity thus identified might mimic the microscopic behaviour of a fluid. It can also lead to other type of multi-phase flow models. Initially, the continuous model will be applied to simulate the pilot mixer. Once this has been done, the model can be used to simulate the agitation of a 3-litre device available at RAPSODEE, stirred by several agitation mobiles mounted in series on a horizontal shaft. As this device is transparent and equipped with a torque meter, it will also be possible to carry out experimental validation. Finally, the continuous macroscopic mechanical model will be implemented in versatile CFD software used in industry, enabling large-scale simulations. A partnership with an industrial company will be sought to develop applications at a larger pilot scale (several dozens of litres), taking advantages of the Finnish supercomputers. Macroscopic validation of the model may consist in comparing the torque exerted on the stirring device obtained from simulations with the torque forecasted by means of a non-dimensional method-based scale-up built on the knowledge of the (I) rheology. Looking ahead to this doctoral work, the model could be adapted to different geometries, ultimately resulting in volumes of several hundred or thousand litres.
Scientific challenge: implement the constitutive law in a continuum model, fixing numerical issues of transitions between different states of the matter in the mixer
Deliverables: continuum model, flow simulations at lab and pilot scales, publication
Impact: a step towards the development of large scale simulations digital twins to optimise the eco-design of equipment ; lay the foundations for partnerships with companies.

- Diplôme d'ingénieur ou master en génie chimique ou des procédés, physique appliquée, mécanique, mathématiques appliquées, mécanique des fluides ou calcul scientifique.
- Candidats motivés, possédant un intérêt, des connaissances et des compétences en physique et en mécanique : modélisation et calcul numérique, ainsi que dans le domaine des travaux expérimentaux.
- Les candidats doivent également faire preuve d'un esprit d'équipe, de flexibilité, d'autonomie, d'initiative, d'un sens de l'organisation et de curiosité intellectuelle.