The local flow topology analysis of the primary atomization of liquid jets has been conducted using the invariants of the velocity-gradient tensor. All possible small-scale flow structures are categorized into two focal and two nodal topologies for incompressible flows in both liquid and gaseous phases. The underlying direct numerical simulation database was generated by the one-fluid formulation of the two-phase flow governing equations including a high-fidelity volume-of-fluid method for accurate interface propagation. The ratio of liquid-to-gas fluid properties corresponds to a diesel jet exhausting into air. Variation of the inflow-based Reynolds number as well as Weber number showed that both these non-dimensional numbers play a pivotal role in determining the nature of the jet break-up, but the flow topology behaviour appears to be dominated by the Reynolds number. Furthermore, the flow dynamics in the gaseous phase is generally less homogeneous than in the liquid phase because some flow regions resemble a laminar-to-turbulent transition state rather than fully developed turbulence. Two theoretical models are proposed to estimate the topology volume fractions and to describe the size distribution of the flow structures, respectively. In the latter case, a simple power law seems to be a reasonable approximation of the measured topology spectrum. According to that observation, only the integral turbulent length scale would be required as an input for the a priori prediction of the topology size spectrum.

This paper presents a detailed investigation of flow topologies in bubble-induced two-phase turbulence. Two freely moving and deforming air bubbles that have been suspended in liquid water under counterflow conditions have been considered for this analysis. The direct numerical simulation data considered here are based on the one-fluid formulation of the two-phase flow governing equations. To study the development of coherent structures, a local flow topology analysis is performed. Using the invariants of the velocity gradient tensor, all possible small-scale flow structures can be categorized into two nodal and two focal topologies for incompressible turbulent flows. The volume fraction of focal topologies in the gaseous phase is consistently higher than in the surrounding liquid phase. This observation has been argued to be linked to a strong vorticity production at the regions of simultaneous high fluid velocity and high interface curvature. Depending on the regime (steady/laminar or unsteady/turbulent), additional effects related to the density and viscosity jump at the interface influence the behaviour. The analysis also points to a specific term of the vorticity transport equation as being responsible for the induction of vortical motion at the interface. Besides the known mechanisms, this term, related to surface tension and gradients of interface curvature, represents another potential source of turbulence production that lends itself to further investigation.

The present study deals with the application of a sub-grid activity sensor to an eddy viscosity type base model in the context of Large Eddy Simulation (LES). The coherent structure function is used to build this sensor in combination with explicit test filtering. The proposed sensor features two main advantages: First, it attenuates the sub-grid scale dissipation of the base model for transitional flows. Depending on local conditions, the sensor is essentially blending the eddy viscosity between zero and the value resulting from the standard Smagorinsky model. Second, the sensor rectifies the incorrect near-wall scaling of the standard Smagorinsky model. Application of the sensor requires no averaging (in the homogeneous direction) and is easy to implement, and the additional computational cost is insignificant. In order to assess the model, three different configurations have been examined: laminar-to-turbulent transition in the Taylor–Green vortex, wall-dominated channel flows, and a free planar jet flow including passive scalar mixing. Based on a posteriori LES, it has been found that the new sensor-enhanced Smagorinsky model often outperforms established eddy viscosity models from the literature, such as the standard Smagorinsky model and the sigma model, as well as the LES without the explicit sub-grid model.

To investigate the coherent structures in turbulent wall-bounded bubbly flows, a local flow topology analysis has been performed in this work. Using the invariants of the velocity-gradient tensor, all possible small-scale flow structures can be categorized into two nodal and two focal topologies for incompressible flows. The analysed direct numerical simulation database of freely moving and deforming bubble swarms is based on a multi-marker geometrical volume-of-fluid method. It appears that bubbles are acting as mixing elements and fragmenting the large topology structures. Since the behaviour in both phases is quite different, key quantities were evaluated in a conditional manner, i.e. separately for the gaseous dispersed phase and the liquid carrier phase. Several similarities with an analytical solution for laminar creeping flows have been observed although the investigated channel flow is turbulent. It has been concluded that the inclusion of bubbles results in a partial shift from focal to nodal flow character whereas the share of stable and unstable flow types remains fairly constant at approximately 50 % in both phases. No clear analogy can be discerned in terms of the global effects of bubble inclusion and wall confinement on flow topologies. At least with respect to flow topologies, regions in the vicinity of the interface show a clearly different behaviour depending on the phase. The size distribution of coherent structures in the bubble-laden channel flow has also been analysed. The measured flow topology size spectrum in the liquid phase can be approximated by a simple model with reasonable accuracy.

We study turbulent emulsions and the emulsification process in homogeneous isotropic turbulence (HIT) using direct numerical simulations (DNS) in combination with the volume of fluid method (VOF). For generating a turbulent flow field, we employ a linear forcing approach augmented by a proportional‐integral‐derivative (PID) controller, which ensures a constant turbulent kinetic energy for two phase flow scenarios and accelerates the emulsification process. For the simulations, the density ratio of dispersed and carrier phases is chosen to be similar to that of oil and water (0.9), representing a typical application. We vary the turbulence intensity and the surface tension coefficient. Thus, we modulate those parameters that directly affect the Hinze scale, which is expected to be the most stable maximum droplet diameter in emulsions in HIT. The considered configurations can be characterized with Taylor Reynolds numbers in the range of 100–140 and Weber numbers, evaluated with the velocity fluctuations and the integral length scale, of 4–70. Using the 3‐D simulation results, we study the emulsification process as well as the emulsions at a statistically stationary state. For the latter, droplet size distributions are evaluated and compared. We observe a Hinze scale similarity of the size distributions considering a fixed integral length scale, that is, similar Hinze scales obtained at different turbulence intensities or for different fluid properties result in similar distributions.

The influence of non-Newtonian fluid behavior on the flow statistics of turbulent bubble-laden downflow in a vertical channel is investigated. A Direct Numerical Simulation (DNS) study is conducted for power-law fluids with power-law indexes of 0.7 (shear-thinning), 1 (Newtonian) and 1.3 (shear-thickening) in the liquid phase at a gas volume fraction of 6%. The flow is driven downward by a constant volumetric flow rate corresponding to a friction Reynolds number of $R{e}_{\tau }\approx 127.3$. The Eötvös number is varied between $Eo=0.3125$ and $Eo=3.75$ in order to investigate the influence of quasi-spherical as well as wobbling bubbles and thus the interplay of the bubble deformability with the power-law behavior of the liquid bulk. The resulting first- and second-order fluid statistics, i.e., the gas fraction, mean velocity and velocity fluctuation profiles across the channel, show clear trends in reply to varying power-law indexes. In addition, it was observed that the bubble oscillations increase with decreasing power-law index. In the channel core, the bubbles significantly increase the dissipation rate, which, in contrast to its behavior at the wall, shows similar orders of magnitude for all power-law indexes.