A Discontinuous Galerkin Method for Transcritical Multicomponent Flows with Phase Transition

Beschreibung

The simulation of multi-phase and multi-component flows under extreme ambient conditions places high demands on the numerical methods and the thermodynamic modelling. On the one hand, this is due to the compressible treatment of both phases. On the other hand, the consistent approximation of the entire multi-component system is of great importance. The numerical evaluation of real equations of state in the vicinity of the critical point, which allows the exact description of the liquid as well as the gaseous phase in a single formulation, is complex. This becomes even more difficult by considering the molar compositions of different individual components. With regard to an application of the numerical methods to rocket combustion engines, the exact local description of physical processes, such as surface tension effects at the phase boundary, is not of critical importance. A consistent description that allows the influence of the physical effects on the overall system is to be preferred. Therefore, the focus of this thesis is on near-critical multi-component systems, in which the phase transition is described as a thermodynamic equilibrium process. Here the transition from a liquid to a gaseous state is often not always sharply separated and therefore described by liquid-like and gas-like states. Extreme conditions are understood to be high temperatures and high pressures at which the compressibility of both phases can no longer be neglected. Incompressible approaches to describe the multi-phase region are no longer sufficient here. The basic motivation of the thesis is derived from the challenges mentioned above. Therefore, the aim of this thesis is the derivation of a numerical framework which is able to describe compressible multi-phase flows for binary multi-component systems near the critical point. The focus is on a thermodynamically consistent modelling which enables large scale simulations in rocket combustion engines.

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Fabian Föll

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Discontinuous Galerkin Multi-phase Transcritical Flows

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