A discrete differential geometric framework for scalable coupled multiphase simulations using hybrid Lagrange-Eulerian methods in mesoporous systems

• Applicant: Professor Dr.-Ing. Lutz Mädler
• Subject Area: Mechanical Process Engineering
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 536406449

Many important processes in chemical engineering require a deep understanding of multiscale-, multiphase systems in order to develop novel processing routes, simulate product properties, as well as to develop accurate models for control and maintenance during normal operation. Porous materials and particle layers fundamentally involve interactions between moving solid phases such as particles or fibres with two or more fluid phases (liquid(-liquid)-gas) at meso- and macroscale which have phenomenological effects that change their macroscopic properties. Such porous particle based materials or films are finding increasing use in industrial products and processes such as solar cells, batteries, catalysts, sensors and coating processes. Accurate direct numerical simulation of these systems is challenging due to the multiphase physics involving surface tension at the interfaces and viscous effects in the liquid and/or gas phase in order to compute particle film properties and device characteristics. The focus of this project is on improving current models and methods in CFD-DEM (computational fluid dynamics-discrete element method) frameworks with a particular focus on rigorous, mesh-independent formulations of hybrid Lagrange-Eulerian models and simulation methods for coupled three-phase simulations. In particular, recent advancements in the field of discrete differential geometry are applied to develop new operators for velocity, pressure and surface tension computations in a unified fluid-solid momentum balance framework. The advantages of the proposed method are the use of tensor operations in a single timestep, the ability to utilze other well-established ordinary differential equation integrators without relying on an iterative coupling between the fluid and solid solvers-, and to possibility of rigorous error estimates for phase interface discretisation. This would allow for significantly faster direct numerical simulations of multiscale-, multiphase systems without sacrificing accuracy by using lumped models or mesh dependent grid refinements. The research focusses on fundamental test cases that demonstrate the fundamental physics being modelled in order to validate the new framework and methods. These cases aim for validating our method with respect to simple incompressible flow, compressible shock flow and three-phase surface tension interactions in particle-particle liquid bridges. All developments will be implemented in high performance open-source software libraries available to the general public which can be used in scalable simulation of practical multiphase CFD-DEM systems.

• DFG Programme: Research Grants