Using direct numerical simulation (DNS) in combination with the volume of fluid method (VoF), we investigate the influence of the density ratio between the carrier and dispersed phase on emulsions, ...where the baseline simulation approximately corresponds to the ratio of water-in-gasoline emulsions. For this purpose, homogeneous isotropic turbulence (HIT) is generated using a linear forcing method, enhanced by a proportional–integral–derivative (PID) controller, ensuring a constant turbulent kinetic energy (TKE) for two-phase flows, where the TKE balance equation contains an additional term due to surface tension. Then, the forcing is stopped, and gravitational acceleration is activated. The proposed computational setup represents a unique and well-controlled configuration to study emulsification and segregation. We consider four different density ratios, which are applied in industrial processes, to investigate the influence of the density ratio on the statistically steady state of the emulsions, and their segregation under decaying turbulence and constant gravitational acceleration. At the statistically steady state, we hold the turbulence constant and study the effects of the density ratio ρd/ρc, on the interface area, the Sauter mean diameter (SMD), and the statistical droplet size distribution. We find that all are affected by the density ratio, and we observe a relation between the SMD and ρd/ρc. Furthermore, we assume a dependence of the critical Weber number on the density ratio. In the second part of our work, we study the segregation process. To this end, we consider the change in the center of mass of the disperse phase and the energy release, to analyze the dependence of segregation on the density difference Δρ/ρd. We show that segregation scales with the density difference and the droplet size, and a segregation time scale has been suggested that collapses the height of the center of mass for different density ratios.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
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 Reτ≈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.
This study proposes two different strategies to enforce accurate volume conservation in volume‐of‐fluid (VOF)‐based simulations of turbulent bubble‐laden flows on coarse grids. It is demonstrated ...that, without a correction, minimal volume errors on a time‐step level, caused by the under‐resolution of the interface, can accumulate to significant deviations from the intended flow conditions despite the comparably good volume conservation properties of the geometric VOF method. In particular, large volume errors are observed for challenging setups combining coarse grid resolutions and comparably high Reynolds and Eötvös numbers. The problem is reinforced for long‐term simulations in periodic domains, which are often performed to collect flow statistics of bubbly flows. The first proposed volume conservation method simply corrects the volume error of a bubble by uniformly adding or removing the respective amount of gas volume in the interface cells. The second proposed method performs an additional reconstruction and advection step of the VOF field using a non‐divergence‐free velocity field, which can be interpreted as a slight dilatation or contraction of the bubble. A comparison between the global flow statistics as well as the individual bubble dynamics for both volume conservation methods reveals that the results are quasi‐identical for a number of challenging test cases, while the gas volume is accurately conserved. The proposed methods allow to perform numerical simulations of freely deformable bubbles in turbulent flows for setups that have previously been out of reach for this numerical framework.
For challenging volume‐of‐fluid based simulations of turbulent bubbly flows characterized by high Reynolds numbers, significant bubble deformations and large‐eddy‐simulation‐like grid resolutions, severe volume errors for the gas phase can accumulate. To avoid this, two methods to accurately conserve the gas volume are proposed, which allow to perform numerical simulations that have previously been out of reach for this numerical framework. Their reliability is demonstrated based on an investigation of global flow characteristics and individual bubble dynamics.
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
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.
Turbulent emulsion.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
We study the segregation of emulsions in decaying turbulence using direct numerical simulations (DNS) in combination with the volume of fluid method (VOF). To this end, we generate emulsions in ...forced homogeneous isotropic turbulence and then turn the forcing off and activate gravitational acceleration. This allows us to study the segregation process in decaying turbulence and under gravity. We consider non-iso-density emulsions, where the dispersed phase is the lighter one. The segregation process is driven by both the minimization of the potential energy achieved by the sinking of the heavier phase, as well as the minimization of the surface energy achieved by coalescence. To study these two processes and their impacts on the segregation progress in detail, we consider different buoyancy forces and surface tension coefficients in our investigation, resulting in five different configurations. The surface tension coefficient also alters the droplet size distribution of the emulsion. Using the three-dimensional simulation results and the monitored data, we analyze the driving mechanisms and their impact on the segregation progress in detail. We propose a dimensionless number that reflects the energy release dominating the segregation. Moreover, we evaluate the time required for the rise of the lighter phase and study correlations with the varied parameters gravitational acceleration and surface tension coefficient.
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