Toward a universal description of multiphase turbulence phenomena based on the vorticity transport equation

Understanding the evolution of turbulence in multiphase flows remains a challenge due to the complex inter-phase interactions at different scales. This paper attempts to enlighten the multiphase turbulence phenomenon from a new perspective by exploiting the classical concept of vorticity and its role in the evolution of the turbulent energy cascade. We start with the vorticity transport equations for two different multiphase flow formulations, which are one-fluid and two-fluid models. By extending the decaying homogeneous isotropic turbulence (HIT) problem to the multiphase flow context, we performed two highly resolved simulations of HIT in the presence of (i) a thin interface layer and (ii) homogeneously distributed solid particle. These two configurations allow for the investigation of interfacial turbulence and particulate turbulence, respectively. In addition to the analysis of the global flow characteristic in both cases, we evaluate the spectral contribution of each production/dissipation mechanism in the vorticity transport equation to the distribution of vortical energy (enstrophy) across the scales. We base our discussion on the role of the main inter-phase interaction mechanisms in vorticity transport (i.e., the surface tension for interfacial turbulence and drag force for particulate turbulence) and unveil a similar contribution from these mechanisms to the multiphase turbulence cascade. The results also explain the deviation of kinetic energy and enstrophy spectra of multiphase HIT problems from their single-phase similitudes, confirming the validity of this approach for establishing a universal description of multiphase turbulence.