Energy transfer mechanisms in compressible two-phase turbulent flows*

Compressible two-phase turbulent flows play a fundamental role in many different fields of engineering interest from aeronautical to marine applications. Within this regime, the inter-scale and inter-phase mechanisms to transfer kinetic energy through the cascade can be linked to the effects of compressibility and surface tension. We propose a simple benchmark problem based on decaying homogeneous isotropic turbulence which is used to study these different mechanisms of energy transfers. In particular, explicit filtering is applied to DNS data to investigate the different terms that appear in the filtered kinetic energy equation, namely the pressure-dilatation, resolved surface tension power, and sub-grid scale production. We seek correlations between sub-grid terms with resolved scale terms. Filter widths are varied to capture the contribution of different scales. For instance, at large filter widths, where full bubbles represent under-resolved features, backscatter is observed due to the effect of surface tension. This work not only proposes a benchmark case, but also provides useful scale-by-scale analyses with the goal of optimizing sub-grid scales closure models, to be ultimately tested in a-posteriori Large-Eddy Simulations.