Toward large eddy simulation of shear-thinning liquid jets: <i>A priori</i> analysis of subgrid scale closures for multiphase flows

While direct numerical simulation (DNS) of multiphase flows has been the focus of many research investigations in recent years, large eddy simulation (LES) of multiphase flows remains a challenge. There is no standardized set of governing equations for multiphase LES. Different approaches and formulations have been discussed in the literature, each with its own advantages and disadvantages. In this paper, the conventional (non-weighted) filtering approach is compared with the density-weighted Favre filtering method by evaluating the subgrid scale (SGS) energy transfer for a simple test case of a shear-thinning droplet in air. The findings reveal that, unlike the Favre filtering approach, the conventional filtering method results in a notable amount of nonphysical backward scatter in the flow. Based on these results, the Favre filtering method appears preferable and is applied to the a priori analysis of shear-thinning liquid jets, where the viscosity has been modeled using the Carreau–Yasuda model. First, by explicitly filtering existing DNS data of shear-thinning jet breakup into stagnant air, the order of magnitude of different SGS terms is evaluated using the Favre filtering method. Consistent with earlier studies on Newtonian jets, the present study indicates that the diffusive term remains negligible, while the convective term plays a dominant role. Functional and structural models for the closure of the convective SGS term are assessed by means of a correlation analysis and an order of magnitude study. Existing structural models provide good results for both Newtonian and shear-thinning cases. Promising a posteriori model candidates are discussed.