Multi-scale interface modeling for multi-phase turbulent flows

Multi-phase turbulent flows are relevant to many industrial applications. One important issue associated with multi-phase turbulence is the broad range of length scales of the dynamically evolving material interface. For example, in the turbulent mixing process, though the interface is well resolved at the early stage, small unresolved interface structures are produced continuously. With a given spatial-temporal resolution limit these resolved and unresolved interface scales usually coexist. Therefore, an efficient numerical modeling method is required to cope both resolved and unresolved interface scales.

In this work, based on our previous developed conservative sharp-interface method (Hu and Khoo 2004, Hu et al. 2006, Hu et al. 2009), we propose an idea of a multi-scale two-phase method, which handles the resolved and unresolved interfaces in a different way, e.g. treat the flow region with resolved interface by the sharp-interface method and flow region with unresolved interface by coarse-graining methods. The first step of this approach is to identifying resolved and unresolved interface by a scale-separation scheme. We propose a scale-separation scheme, which is similar to that of Harten (1996) for calculating the scale coefficient, and is much simpler than previous methods, such as that of Hermann (2010), which are complicated in identifying and tagging separated small interfacial structures. It measures the difference between the volume fractions reconstructed on a refined-grid and a coarse-grid interface representations.  If the difference is larger than a threshold value,  the computational cell is considered has a unresolved interface patch.  The second step is handling the unresolved interface. If only numerical stability is considered, the simplest way is delete the unresolved interface. However, this is not desirable when the effects of the unresolved interface (sub-grid effects) are not negligible. For this, we include  the sub-grid effects by using a smeared interface model, in which the fluids near unresolved interface is considered as a mixture.

Figure 1 shows the preliminary results for the simulation of shock-bubble interaction. The Schlieren-type images of density at t=0.2 show the different results calculated with and  without the multi-scale model. By comparing the results at two resolutions considerably more detailed interface and flow structure are obtained for the multi-scale model. This is not unexpected since the multi-scale model includes the influence of the unresolved-interface interactions which are neglected by the single-scale model due to the loss of unresolved mass, momentum and energy, or due to the wrongly predicted interface interaction based on the ill-defined interface normal direction. These structures show very complex mixing behavior which is totally missing from a previous single-scale simulation at similar resolution (Hu et al. 2006).