Session D12: Multiphase Flows: Turbulence

On the effects of density ratio on droplet-laden isotropic turbulence

Our objective is to determine the effects of varying the droplet- to carrier-fluid density ratio ($\rho_d/\rho_c$) on the interaction of droplets with turbulence. We performed DNS of 3130 finite-size, non-evaporating droplets of diameter approximately equal to the Taylor lengthscale and with 5~\% droplet volume fraction in decaying isotropic turbulence at initial Taylor-scale Reynolds number Re$_\lambda=83$. We varied $\rho_d/\rho_c$ from 1 to 100 while keeping the Weber number and dynamic viscosity ratio constant, We$_\mathrm{rms}$=1 and $\mu_d/\mu_c$=1. We derived the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. These equations allow us to explain the pathways for TKE exchange between the carrier turbulent flow and the flow inside the droplet. We show that increasing $\rho_d/\rho_c$ increases the decay rate of TKE in the two-fluid flow. The TKE budget shows that this increase is caused by an increase in the dissipation rate of TKE and a decrease in the power of the surface tension. The underlying physical mechanisms for these behaviors will be presented.   

On the effects of isotropic turbulence on the evaporation rate of a liquid droplet

Our objective is to explain the effects of isotropic turbulence on the vaporization rate of a liquid droplet in conditions that are relevant to spray combustion applications. To this end, we have performed direct numerical simulation (DNS) of a single droplet in homogeneous isotropic turbulence using the volume-of-fluid method for resolving fully the process of momentum, heat, and mass transfer between the liquid droplet and the gas. The simulations were performed using $1024^3$ grid points. The effect of turbulence on the droplet vaporization rate is investigated by varying the gas-phase Reynolds number based on the Taylor microscale, Re$_\lambda$. Re$_\lambda$ is increased from 0 to 75 by increasing the r.m.s. velocity of the gas phase while keeping all other physical properties constant. We will present the droplet evaporation rate as a function of turbulence Reynolds number and investigate the physical mechanisms.   

On the dispersion of finite-size droplets in isotropic turbulence.

The paper presents a comparison between the dispersion characteristics of finite size liquid droplets and finite size solid particles in isotropic turbulence at initial R$_{\mathrm{\lambda \thinspace \thinspace }}=$75$_{\mathrm{\thinspace }}$. The droplets and particles have equal diameters (about 15 times the initial Kolmogorov length scale) and equal densities. The immersed boundary method is used for direct numerical simulations (DNS) of the solid particles case. The level set method is used for DNS of the droplet-laden turbulence where a variable-density projection method is used to impose the incompressibility constraint. We discuss the effects of varying the surface tension (Weber number) of the liquid droplets on their dispersion and acceleration characteristics.   

Angular dynamics of a small particle in turbulence

We compute the angular dynamics of a neutrally buoyant nearly spherical particle immersed in an unsteady fluid. We assume that the particle is small, that its translational slip velocity is negligible, and that unsteady and convective inertia are small perturbations. We derive an approximation for the torque on the particle that determines the first inertial corrections to Jeffery's equation. These corrections arise as a consequence of local vortex stretching, and can be substantial in turbulence where local vortex stretching is strong and closely linked to the irreversibility of turbulence.   

Entrainment at a sediment concentration interface in turbulent channel flow

In this work we address the role of turbulence on entrainment at a sediment concentration interface. This process can be conceived as the entrainment of sediment-free fluid into the bottom sediment-laden flow, or alternatively, as the entrainment of sediment into the top sediment-free flow. We have performed direct numerical simulations for fixed Reynolds and Schmidt numbers while varying the values of Richardson number and particle settling velocity. The analysis performed shows that the ability of the flow to pick up a given sediment size decreases with the distance from the bottom, and thus only fine enough sediment particles are entrained across the sediment concentration interface. For these cases, the concentration profiles evolve to a final steady state in good agreement with the well-known Rouse profile. The approach towards the Rouse profile happens through a transient self-similar state. Detailed analysis of the three dimensional structure of the sediment concentration interface shows the mechanisms by which sediment particles are lifted up by tongues of sediment-laden fluid with positive correlation between vertical velocity and sediment concentration. Finally, the mixing ability of the flow is addressed by monitoring the center of mass of the sediment-laden layer.   

An efficient parallel flow solver for two-way coupled turbulent flows with deformable bodies

There are countless examples in Nature and technology in which a flow and a deformable structure interact dynamically and determine each other's behaviour. Among many, two contexts in which this is particularly relevant is in two-phase flows with finite size deformable bubbles or immiscible drops and in cardiovascular flows of heart valves and deformable vessels. Since the standard methods become terminally expensive when the number of deformable bodies become large or the set-up has a complex geometric configuration, in this work, we discuss a simple yet effective approach to cope with the above problems. The main ingredients are: i) an efficient Navier-Stokes solver, ii) an interaction potential approach for the dynamics of a deformable structure, iii) an immersed boundary procedure to deal with the geometrical complexity iv) a set of fluid/structure interaction approaches (strong or loose) and v) a simple and efficient parallelisation strategy to handle large-scale simulations. Several complex examples will be shown and discussed with the results validated either by ad-hoc experiments or by comparisons with results from the literature.   

Understanding the link between deformability and drag reduction in sheared turbulent flows

Injection of a small concentration of gas bubbles into a carrier fluid can result in significant drag reduction in wall bounded turbulent flows. While experimental studies have shown that deformability of the dispersed phase is crucial for strong drag reduction, measurement of local flow conditions to understand the governing mechanism is extremely challenging. In this work we attempt to understand the underlying physics between deformability and drag reduction across a regime of scales in a turbulent Taylor-Couette flow using Direct Numerical Simulations of the carrier flow while a mixture of approaches are used to simulate the dispersed phase (i) Euler-Lagrangian tracking of sub-Kolmogorov ellipsoidal bubbles with a sub-grid deformation model (ii) Fully resolved finite size bubbles with an interaction potential approach to capture the deformation dynamics. We will study and compare the boundary layer profiles, dispersion of the bubbles and shape oscillations of the bubbles as they are transported between the boundary layers and bulk back and forth to get a detailed understanding of the link between deformability and drag reduction.   

Parameter dependences of the onset location of turbulent liquid jet breakup

A previous study of primary breakup of turbulent liquid jets obtained a We$^{\mathrm{-0.67}}$ dependence of breakup onset location on jet Weber number We based on reasonable agreement with measurements and closeness to a theoretical prediction We$^{\mathrm{-2/5}}$ inferred from inertial-range phenomenology [1]. It is proposed that breakup onset is instead controlled by the residual presence of the boundary-layer structure of the nozzle flow in the near field of the jet. Assuming that the size of the breakup-inducing eddy is within the scale range of the log-law region, We$^{\mathrm{-1}}$ dependence is predicted. This dependence agrees with the measurements more closely than the We$^{\mathrm{-0.67}}$ dependence. To predict the dependence on Reynolds number Re, either the friction velocity based on the Blasius friction law or the bulk velocity can be used, where the former yields Re$^{\mathrm{3/8}}$ dependence and the latter implies no Re dependence. The latter result is consistent with measurements, but not with the boundary-layer interpretation of breakup onset, so the origin of the measured lack of Re dependence merits further investigation. A preliminary assessment has been made using a computational model of primary breakup. [1] P.-K. Wu, G. M. Faeth, Phys. Fluids 7, 2915 (1995).   

Experimental study on immiscible jet breakup using refractive index matched oil-water pair

A subsea oil well blowout creates an immiscible crude oil jet. This jet fragments shortly after injection, resulting in generation of a droplet cloud. Detailed understanding of the processes involved is crucial for modeling the fragmentation and for predicting the droplet size distribution. High density of opaque droplets near nozzle limits our ability to visualize and quantify the breakup process. To overcome this challenge, two immiscible fluids: silicone oil and sugar water with the same index of refraction (1.4015) are used as surrogates for crude oil and seawater, respectively. Their ratios of kinematic viscosity (5.64), density (0.83) and interfacial tension are closely matched with those of crude oil and seawater. Distribution of the oil phase is visualized by fluorescent tagging. Both phases are also seeded with particles for simultaneous PIV measurements. The measurements are performed within atomization range of Ohnesorge and Reynolds numbers. Index matching facilitates undistorted view of the phase distribution in illuminated section. Ongoing tests show that the jet surface initially rolls up into Kelvin-Helmholtz rings, followed by development of dispersed phase ligaments further downstream, which then break into droplets. Some of these droplets are re-entrained into the high momentum core, resulting in secondary breakup. As the oil layer and ligaments evolve, they often entrain water, resulting in generation of multiple secondary water droplets encapsulated within the oil droplets.