Modelling of interfacial area and turbulence in two-phase flow

Full text of publication follows: Computational Two-Fluid Dynamics (CTFD) modelling is still under development. The single pressure two-fluid model is widely used as a model basis for the multidimensional simulation of typical two-phase flow phenomena, e.g. void and pressure wave propagation, phase transitions, sharp interface movements, thermal and mechanical non-equilibrium /1/. The conservation equations based on an averaging procedure are written for each phase allowing both phases to co-exist at any point in space. The local volumetric fraction alone, one of the solution variables of the two-fluid model, is not sufficient to describe the topology of the two phases and consequently the flow regime can not be determined by the two-fluid model. A determination of the flow situation requires additional knowledge of the interface. The concentration of the interfacial area is one of the key parameters that gives information of the flow pattern. It is also an important parameter for the modelling of interfacial friction forces and interfacial transfer terms. The modelling of a transport equation for the interfacial area concentration covering the whole two-phase flow range is outlined in this paper. In this transport equation the forces acting on the interface and mass transfer are modelled. Observed phenomena, e.g. bubble coalescence or disintegration, are not explicitly modelled, they are the result of the interacting forces on bubble interface. Thus the modelling is mainly based on first principles and is largely free from empiricism /2/. First validation calculations will be presented. For the modelling of turbulence in two-phase flows new transport equations for the turbulent kinetic energy and its dissipation are proposed, where turbulent shear stress for two-phase flows will be modelled. Beyond this the new turbulence model differentiates between turbulent scales and the usual constants of the dissipation rate equation are modelled /2/. A first verification calculation of a shear flow of two differently tempered streams show the bandwidth of the physical turbulent diffusion and additionally that the new proposed turbulence model is less energetic than the Standard k-ε model. References: 1 - U. Graf, P. Papadimitriou, Status of Development and Verification of the CTFD Code FLUBOX, NUTHOS-6, Japan, Oct. 4-8, 2004. 2 - P.Papadimitriou, Interfacial Area Transport and Turbulence Modelling in Two-Phase Flows, International ASTAR Workshop on Advanced Numerical Methods for Multidimensional Simulation of Two-phase Flow, September 15-16, GRS Garching, Germany 2003. (authors)