Session X08: Multiphase Flows: Turbulence (10:45am - 11:30am CST)

Global and local statistics in turbulent emulsions

Turbulent emulsions are complex systems characterized by a coupling between small-scale droplets and large-scale rheology. By using a specifically designed Taylor-Couette shear flow system, we can characterize the statistical properties of a turbulent emulsion made of oil droplets dispersed in an ethanol-water solution, at the oil volume fraction up to 40{\%}. We find that the dependence of the droplet size on the Reynolds number of the flow at the volume fraction of 1{\%} can be well described by Hinze's criterion. The droplet sizes are found to have a log-normal distribution, hinting at a fragmentation process in the droplet formation. Additionally, the effective viscosity of the turbulent emulsion increases with the volume fraction of the dispersed oil phase, and decreases with increasing shear strength. We find that the dependence of the effective viscosity on the shear rate can be described by the Herschel-Bulkley model, with a flow index decreasing with increasing the oil volume fraction. This finding indicates that the degree of shear thinning increases with the volume fraction of the dispersed phase. The current findings have important implications for bridging the knowledge on turbulence and low-Reynolds-number emulsion flows to turbulent emulsion flows.   

Sub-Hinze scale bubble production in turbulent bubble break-up

Through direct numerical simulations we study the dynamic of bubble break-up under isotropic and homogeneous turbulence. We create the turbulent flow by forcing in physical space and inject a bubble of initial radius $d_0$ once a stationary state is reached. We investigate the effect of the Weber number (ratio of turbulent and surface tension forces) on the break-up dynamics and statistics from large ensemble of simulations. We identify three regimes depending on the bubble size: below the critical size, $d_H$, the Hinze scale, bubbles are stable; close to the critical conditions $d_0 \approx d_H$ we observe binary and tertiary break-ups, leading to bubbles mostly between $0.5d_H$ and $d_H $, a signature of a production process local in scale. Finally for bubbles much larger than $d_H$ numerous bubbles much smaller than the critical size are produced: typically between $0.1 d_H$ and $0.3d_H$. We show that their formation relates to rapid large deformations and successive break-ups: the first break-up in a sequence leaves highly deformed bubbles which will break again, without recovering a spherical shape and creating an array of much smaller bubbles.   

Multi-scale characterization of the effect of gas swirl on two-fluid coaxial atomization.

This work aims at developing a better mechanistic understanding of the processes that control the instabilities leading to spray formation in coaxial two-fluid atomization. The goal is to characterize the near-field of the spray, where a dense multiscale turbulent multiphase flow evolves from the nozzle exit as the liquid break-up progresses and the formed inclusions interacts with the turbulent gas jet. We conduct experimental measurements in the optically dense region of the spray created by a canonical two-fluid atomizer, using Synchrotron high-speed radiography at the Advanced Photon Source of Argonne National Lab. We retrieve not only the statistics of the liquid core length, as has been done in previous studies of atomization in a narrower range of spray parameters, but also its characteristic timescales, with the goal of providing a better picture of the dynamic processes that control this important spray metric. This work, together with a complementary study using shadowgraphy at overlapping swirl and gas-to-liquid momentum ratios, yields a complete description of the spray near-field, over a wide range of parameters that are relevant for a broad scope of applications.   

Breakage, coalescence and droplet size distribution of surfactant-laden droplets

The effects of surface tension modifications on the dynamics of surfactant-laden droplets in wall-bounded turbulence are numerically investigated: direct numerical simulations of the Navier-Stokes equations are used to compute the flow field, while a phase-field method in a two-order-parameter formulation is adopted to track the interface (first-order parameter) and the surfactant concentration (second-order parameter). The surfactant acts on the interface reducing the local surface tension according to its strength and local concentration. To investigate surface tension effects, here we change the reference value of the surface tension (i.e. that of a surfactant-free interface) and the strength of the surfactant. Enhancement of both the coalescence and breakage rate is observed as the average surface tension over the interface is reduced. We also compute the droplet size distribution and find a fair agreement with available analytic scaling laws and experimental measurements in the breakage-dominated regime.   

Coupled Population Balance and Large Eddy Simulation model for Polydisperse Droplet Evolution in a Turbulent Round Jet

A population balance model coupled with large eddy simulations (LES) is adapted and applied to study the evolution of oil droplets in an axisymmetric turbulent jet including the effects of droplet breakup. We develop a hybrid approach where the inlet condition is prescribed using a one dimensional (1D) parcel model that accounts for the evolution of the dispersed phase along the jet centerline due to the combined effects of advection, radial turbulent transport and droplet breakup. LES results are compared to published experimental data, with good agreement and we examine the statistics of the velocity field and the concentration of the polydisperse oil droplet plumes for two droplet Weber numbers. We find that the centerline decay rate of the concentration for different droplet sizes is modified in the breakup dominated zone. Moreover, the transverse dispersion of larger droplets is suppressed due to trajectory crossing effects. Unlike Reynolds averaged approaches, LES also allows us to quantify size distribution variability due to turbulence. We quantify the radial and axial distributions and the variability of key quantities such as the Sauter mean diameter, total surface area and droplet breakup time-scale and explore their sensitivity to the Weber number.   

Rise Velocity of Bubbles in Turbulence

Turbulence in the liquid phase impacts the mean rate at which bubbles rise or heavy particles sink through the fluid, with practical relevance in environmental and industrial processes in which bubbles mediate mass transfer between liquid and gaseous phases. With a turbulent water flow generated in the laboratory, we show that air bubbles significantly smaller than the integral length scale of the turbulence experience a reduction in mean rise speed $\langle v_z \rangle$ by an amount approximately equal to the scale of the turbulent fluctuations $u'$ (that is, $\langle v_z \rangle \approx v_\mathrm{q} - u'$, where $v_\mathrm{q}$ is the bubble rise speed in a quiescent environment), when the dimensionless intensity of the turbulence $\beta = u' / v_\mathrm{q}$ is less than 1. Our experiment employs planar particle image velocimetry to characterize the turbulence throughout the measurement volume and a two-camera stereo vision system to track bubbles in three dimensions. We then utilize the homogeneous, isotropic turbulence simulation from the Johns Hopkins Turbulence Database to integrate the Maxey-Riley equation for a point-bubble in a carrier flow, revealing the mechanisms responsible for the turbulence's reduction of the bubbles' rise velocity.   

Phase-conditioned turbulent statistics of an immiscible buoyant jet in the near-field

Simultaneous applications of PIV and PLIF in a refractive index matched facility provide the velocity and phase distribution in the near-field of an immiscible buoyant oil jet in water. Close to the nozzle, vertical momentum exchange occurs as water is entrained and oil ligaments extend outward. Kevin-Helmholtz vortices form in the water with their centers located at the tip of oil ligaments. Further downstream, the momentum diffuses in both phases as the oil fragments into compound droplets. The spreading and decay rates of the centerline oil fraction are lower than those of the axial momentum. Comparison to a single-phase jet at the same Re shows that the transition from azimuthal shear layers to self-similar profiles of velocity and Reynolds stresses occur earlier in the oil jet. The phase-conditioned turbulence reveals differences in velocity and all Reynolds stress components. The peripheral turbulence in the water is higher near the jet exit, but lower at 6-7 diameters downstream, the latter owing to the intermittency of entrained water. Shear production dominants the turbulence production in the periphery of the jet fragmentation region. Near the centerline, the TKE production rate, hence the turbulent kinetic energy, is higher in in the water.   

LES of droplet-laden isotropic turbulence using artificial neural networks

Developing accurate SGS models for LES is important for making the simulation of high-Reynolds-number turbulence computationally feasible. We are particularly interested in the LES of decaying homogeneous isotropic turbulence laden with finite-size droplets. Only until recently has the DNS of such flows become possible (Dodd \& Ferrante, \textit{J.\@ Fluid Mech.\@} 806 (2016), 356--412), meaning that their LES is relatively unstudied. Part of the challenge of creating LES models for such flows is that their multiphase nature introduces additional closure terms besides just SGS stress. Using DNS data, we analyze these terms a priori to determine which are sufficiently significant to warrant modeling. We then employ artificial neural networks to develop models for these terms and show in our a posteriori analysis that our LES faithfully reproduces the decay of TKE seen in DNS.