Numerical modelling and simulation of multiphase flows : applications to granular materials and heat transfer
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Date
2026-09-25
Authors
Μπαλαχτσής, Αθανάσιος
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Abstract
Rotary kilns are critical high-temperature reactors used in a wide range of industrial processes, including cement production, mineral calcination, waste incineration, biomass pyrolysis, and solid-state reactions. Their ability to process heterogeneous granular materials under extreme conditions makes them essential in process industries. However, the physics governing their operation remains only partially understood due to strongly coupled, multiscale transport phenomena involving granular flow, heat transfer, phase change, and chemical reactions. Consequently, kiln operation is still largely guided by empirical knowledge and reduced-order models that do not fully resolve the underlying multiphysics behaviour. This thesis develops a unified continuum computational framework for rotary kiln processes, enabling a rigorous description of dense granular flow, thermal transport, phase change, viscoplastic melt rheology, and the melting of granular beds and their transition into cohesive aggregates within a multiphase finite element formulation. A central objective is to enhance predictive capability by resolving the transition from granular to partially or fully molten regimes, with particular emphasis on melting dynamics as previously underrepresented aspects of kiln modelling. The proposed framework provides a structured foundation for future extensions toward fully coupled multiphysics simulations of industrial pyroprocessing systems.The first part of the thesis addresses granular flow using a pressure-dependent () rheology. Benchmark simulations of granular column collapse reveal mesh-dependent instabilities in the computed fields, associated with the ill-posed character of the constitutive model under certain flow regimes. These numerical difficulties are addressed through partial rheological regularization combined with shock-capturing stabilization terms in the momentum equation. The stabilized formulation accurately reproduces collapse dynamics across all stages (free fall, spreading, and arrest), while distinguishing between yielded regions, where the material flows, and unyielded regions, where it exhibits solid-like behaviour. Building on this foundation, the framework is extended to simulate dense granular flow in the transverse cross-section of a partially filled rotating cylinder. The model reproduces experimentally observed flow structures and captures the formation of characteristic regions, including an active layer (with intense shear deformation) and a passive layer undergoing near-solid-body rotation. Extensive parametric studies quantify the influence of angular velocity, filling degree, friction coefficient, and particle size on flow topology, active layer thickness, and dynamic angle of repose, as well as the transition from rolling to cascading regimes. The second stage of the thesis extends beyond isothermal mechanical processes by incorporating thermal transport and phase change. A single-domain enthalpy formulation is employed in the energy equation, combined with a temperature-dependent viscosity model, allowing the solid–liquid transition to be captured implicitly. This approach avoids mesh deformation and explicit interface tracking, as the solid–liquid boundary is represented through the temperature field. Initially, the melt is approximated as a Newtonian fluid. The simulations show that melting kinetics are governed by the balance between buoyancy-driven natural convection and rotation-induced forced convection. Subsequently, to represent more accurately partially molten clinker agglomerates, the melt is modelled as a viscoplastic Bingham fluid using Papanastasiou regularization. The introduction of yield stress modifies the flow structure by promoting yielded and unyielded regions, thereby altering mixing behaviour within the melt. Higher yield stress leads to increased adherence of the fluid to the rotating wall, which enhances local heat transfer and can reduce the overall melting time compared to the Newtonian case. While this viscoplastic fluid model captures the non-Newtonian dynamics of the liquid phase, a complete representation of the physical process requires a more rigorous description of the solid state, which up to this point had been simplified as an extremely viscous Newtonian fluid limit. To address this limitation and provide a dedicated rheological description of the granular medium under thermal transition, the final stage of the thesis unifies dense granular mechanics and phase-change thermodynamics through a cohesive granular analogy. Utilizing an empirical melt-fraction-dependent yield stress function integrated into the original ()-model, the framework captures the progressive transformation of the dry powder into cohesive, partially molten aggregates. Crucially, the liquid phase acts as a rheological binder rather than a heat-transfer medium, creating a thermal bottleneck that dampens convective recirculation. This framework provides a useful starting point for developing future predictive tools that aim to integrate coupled chemical reactions and phase-change dynamics in high-temperature industrial processing.
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Keywords
Viscoplastic materials, Finite element method (FEM), Simulation of melting, Multiphase flows, Phase field, Heat transfer, Rotary Kiln, Granular materials