Accurate description of stratified flow morphologies – the AIAD model
CFD simulations of stratified flows are often conducted on the basis of the homogeneous model-based approach in which only one set of balance equations is considered. The different phases are taken into account by different material properties. Since only a velocity field is calculated leads to problems if the phases are not clearly separated, for example, if there is bubble entrainment in a wave or slug flow regime. The separation of the phases can then not be described properly.
To overcome this problem HZDR uses the Euler-Euler two-fluid approach for industrial macro-scale multiphase flow modeling. On both sides of the free surface, shear layers are expected which require a specific attention since complex phenomena with turbulent transfers coupled to possible interfacial waves take place. It was found necessary to be able to track the interface position in order to treat this zone in a similar way as a wall boundary layer using wall functions. When trying to use a two-fluid approach, the development of a morphology detection method was found necessary.
Therefore the Algebraic Interfacial Area Density (AIAD) model has been developed in close cooperation with ANSYS CFX. The model detects the local flow pattern, such as the local phase content and switches to a transition algorithm to the valid correlations for example for the interfacial area density, the drag coefficient, or the local characteristic length scale. Now it can be distinguished between areas where droplets or bubbles are present and the region of the free surface. An important goal of the description of two-phase flows is the correct determination of turbulence parameters. These have for example a decisive influence on the generation of surface instabilities. Without special treatment of the free surface resulting from the use of two-equation turbulence models (k-e; k-w), the high velocity of the gas phase, particularly leads to high turbulence at the phase interface. In the new approach, the calculation of the turbulence now is done separately for each phase of the k-w turbulence model. An additional function similar to the wall damping function for the turbulent diffusion is introduced on the free surface.
A further step of improvement of modeling the turbulence at the free surface is the consideration of sub-grid wave turbulence (SWT) that means waves created by Kelvin-Helmholtz instabilities that are smaller than the grid size. In fact, the influence on the turbulence kinetic energy of the liquid side can be significantly large.
Also an improved description of the drag coefficient on the free surface on the basis of the surface shear stress is built into the model.
CFD calculations were validated for co- and counter-current flow experiments at the hot leg model (Fig. 2) and WENKA test facility (Fig. 3) and for slugs and the stationary hydraulic jump in the channel HAWAC. They showed consistently good results.
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The work is carried out in the frame of a current research project funded by the German Federal Ministry of Economics and Labour, project number 150 1265.