Multiphase flow problems are ubiquitous in many engineering disciplines like in chemical and process engineering, where the interaction of different phases such as liquids or gases strongly influences system performance. Accurate modeling of multiphase flow phenomena therefore is a crucial cornerstone for optimizing system design and control. A widely recognized modeling approach are diffuse interface approaches, which combine the Navier-Stokes equations – the fundamental governing equations of fluid dynamics – with phase-field models like the Cahn-Hilliard equations, allowing to capture fluid mixtures of different densities or viscosities.
Over the last decades, many different variants of the coupled Cahn-Hilliard Navier-Stokes (CH-NS) equations for fluids with non-matching densities have surfaced, including transformation of variables (volume- vs. mass-averaged velocity formulations), degenerate phase-field mobilities, or capillary tension models.
The topic of this thesis is to extend and implement a consistent and flexible framework for different variants of CH-NS systems, investigate their thermodynamic consistency, and thoroughly study their (physical and numerical) performance for a variety of benchmark cases, with the aim of carving out best practices and recommendations for formulating, implementing, and solving of these equation systems.
Description of Task:
- Literature review on formulations and thermodynamic consistency of Cahn-Hilliard Navier-
Stokes systems - Implementation of mass-averaged velocity formulations into an existing (FEniCSx-based) CH-NS finite element environment, along with common variants regarding constitutive equations for the diffusive flux and surface tensions
- Testing formulations across (2D and 3D) benchmarks of a rising fluid bubble under gravitiy
Desirable Knowledge and Skills:
- Familiarity with computational fluid dynamics, ideally two-phase flow
- Conceptual understanding of the finite element method
- Knowledge of continuum mechanics and basic continuum thermodynamics
- Programming experience, ideally Python
In division 2.2, research focuses on the development of dynamic process models to describe all system states from start-up to shutdown, supported by an open library of dynamic, pressure-driven models. The division uses machine learning, uncertainty quantification and hybrid modeling methods to drive forward real-time application and plant monitoring. For the comprehensive digitalization of process engineering, the division is also researching information and data modelling as well as process models from engineering to the operation of chemical plants. This is supplemented by the development of methods for the safe and optimal transformation of chemical plants.
Start: Immediately
Contact person:
Dr.-Ing. Marc Hirschvogel
marc.hirschvogel@bam.de