FOR 563:  Micro-Macro Modelling and Simulation of Liquid-Vapour Flows

• Subject Area: Mathematics ; Thermal Engineering/Process Engineering
• Term: from 2005 to 2009
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5471371

In this Research Unit we will study the modelling, analytical and computational aspects of liquid-vapour flow with phase transition. The most basic experiment on liquid-vapour flows considers the dynamics of a single vapour bubble in a container filled with a liquid fluid. If the outer pressure of the liquid is decreased to vapour pressure then the liquid-vapour interface starts to move: We have a dynamic phase boundary with mass transfer. In more complex settings this occurs during the process of cavitation. Lord Rayleigh discovered that pressure waves emitted during the process of cavitation near rigid walls may cause damage on the surface. This can be observed on the surface of ship propellers. We are going to investigate the mathematical modelling and simulation of the dynamics of a bubble within the surrounding fluid. Although ensembles of bubbles will appear and are important for real applications we will also concentrate on the treatment of a single bubble in order to understand the elementary processes. The main difference between existing mathematical models for phase transition consists in a sharp and diffusive resolution of the interfaces. In the first case, the interface is modelled by a hypersurface and the density is discontinuous across the phase boundary. The relation between pressure, surface tension and curvature is given by an additional boundary condition on the interface. In the second case, the interface will be modelled by a thin layer with steep density gradients. For the treatment of large ensembles of bubbles a homogenised model will be used. The basic underlying mathematical models are given by the compressible or incompressible Navier-Stokes equations, which will be completed by special expressions and equations (van der Waals, Korteweg, equations for the mass fractions) for the phase transition. The numerical tools will be based on Finite Volume and Discontinuous Galerkin schemes of higher order. In order to obtain efficient numerical tools local grid adaption and parallelisation of the code will be necessary. Special physical experiments for the dynamical fluid-vapour interaction will be performed for the validation of the different mathematical models and the numerical schemes. Within this Research Unit German and French research groups will cooperate.

• DFG Programme: Research Units
• International Connection: France

Projects

• Dynamics of cavitation bubbles in compressible two-phase fluid flow (Applicant Müller, Siegfried )
• Dynamics of cavitation bubbles in compressible two-phase fluid flow (Applicant Lauterborn, Werner )
• Experimental Investigation of the Interface Dynamics and Phase Transition of Growing Bubbles in a Gravitational Field (Applicant Peters, Norbert )
• Homogenized systems for liquid-vapour transition in unsteady compressible two-phase flow (Applicant Warnecke, Gerald )
• Koordinatorprojekt (Applicant Kröner, Dietmar )
• Numerical Solution of the Navier-Stokes-Korteweg System (Applicant Kröner, Dietmar )
• Numerical Solution of the Navier-Stokes-Korteweg System (Applicant Rohde, Christian )

• Spokesperson: Professor Dr. Dietmar Kröner