ISBN 978-3-8439-3523-4

978-3-8439-3523-4, Reihe Ingenieurwissenschaften

Fabian Hempert
Simulation of Multiphase Flows with Multiparameter Equations of State and the Discontinuous Galerkin Method

163 Seiten, Dissertation Universität Stuttgart (2017), Softcover, A5

Zusammenfassung / Abstract

Numerical simulations of multiphase flows for industrial applications have become increasingly complex. The demand on the resolution of temporal and spatial scales has increased and more complex and numerically demanding thermodynamic states of the fluid are required. The aim of this study is to demonstrate the applicability of a high order method, i.e., the discontinuous Galerkin spectral element method, with an accurate equation of state, valid for a wide range of pressures and temperatures, e.g., the Helmholtz energy formulation. Although these two aspects have been intensely investigated separately, a combination of both in an efficient manner remains challenging for complex applications, e.g., cavitational flows or real gas jets. The present work presents the application of a novel approach, which uses a dense gas approach with a discontinuous Galerkin method with a tabulated equation of state including the gaseous, liquid and two-phase states of the fluid. This new approach allows for detailed investigations of flow phenomena, which require accurate fluid properties and have been unfeasible to simulate in the past. The investigated cases include supersonic real gas jets and cavitational flows.

The simulation results for the supersonic real gas jet suggest large differences for the applied cases between the real gas and ideal gas approximation. A difference are the shock structures which might lead to differences in acoustics and mixing. Further, the mass flow rates show significant differences. Further, a micro channel flow simulation is conducted for water for many known effects could be reproduced by the simulation. An example is the shock propagation within the wet steam area, which is very slow compared to the mean flow velocities and is traveling in the upstream direction.

For both the real gas and cavitating flow, using the low dissipation discontinuous Galerkin scheme shows superior results compared to a second order finite volume scheme used in this work. The proposed framework shows great potential for the simulation of flows, that require an accurate representation of small spatial and temporal scales and multiparameter equation of states. First simulation results of industrially relevant flows are presented for both single and multiphase application. However, to fully exploit the potential of the combination high order methods with accurate equation of states further development is necessary, e.g., stability and sub-grid scale models.