Turbulence topology evolution in weakly turbulent two-phase flows

Abstract

In turbulent two-phase flows, not only the isotropy of velocity fluctuations can be altered by the presence of liquid blobs, ligaments, or pockets, the structure of the turbulent flow field and associated flow topology may also be significantly modified. In this respect, the small-scale wrinkling and curvature of the liquid–gas interface, which is associated with sharp and large density variations, impact turbulence in the gas phase. In the present study, the joint probability density function of the second and third invariants of the velocity gradient tensor (VGT)—and especially its traceless counterpart—is considered so as to scrutinize how the turbulent flow topology in the gas may be altered. These quantities are analyzed on the basis of direct numerical simulation databases of two-phase flows evolution in homogeneous isotropic turbulence. Statistics of the invariants of the VGT are gathered at various distances to the interface so that the gas phase is divided into three sub-regions according to the values of the level-set G, i.e., the signed distance to the liquid/gas interface. The analysis of the VGT invariants shows that turbulent small-scale structures and associated flow topology are modified in the vicinity of the liquid–gas interface. Lagrangian evolution equations of the VGT and its invariants are thus studied to get a refined view of the corresponding changes. To the best of the authors' knowledge, this is first time that these budgets are scrutinized in such conditions. Special emphasis is placed on conditional mean rates of change of the VGT invariants in the plane of the second and third invariants. In the corresponding set of coordinates, the obtained trajectories are found to be mainly driven by (i) mutual interactions between invariants and (ii) pressure Hessian contributions, thus confirming the importance of the latter for the dynamics and structure of turbulent two-phase flows.