Coalescence and breakup of large droplets in turbulent channel flow

Abstract

Coalescence and breakup of large deformable droplets dispersed in a wall-bounded turbulent flow are investigated. Droplets much larger than the Kolmogorov length scale and characterized by a broad range of surface tension values are considered. The turbulent field is a channel flow computed with pseudo-spectral direct numerical simulations, while phase interactions are described with a phase field model. Within this physically consistent framework, the motion of the interfaces, the capillary effects, and the complex topological changes experienced by the droplets are simulated in detail. An oil-water emulsion is mimicked: the fluids are considered of same density and viscosity for a range of plausible values of surface tension, resulting in a simplified system that sets a benchmark for further analysis. In the present conditions, the Weber number (W e), that is, the ratio between inertia and surface tension, is a primary factor for determining the droplets coalescence rate and the occurrence of breakups. Depending on the value of W e, two different regimes are observed: when W e is smaller than a threshold value (W e < 1 in our simulations), coalescence dominates until droplet-droplet interactions are prevented by geometric separation; when W e is larger than the threshold value (W e > 1), a permanent dynamic equilibrium between coalescence and breakup events is established.

Direct Numerical Simulation of Turbulent Flows Laden with Droplets or Bubbles

“…Coalescence and breakup of large droplets in turbulent channel flow using PFM. Scarbolo et al (2015) used the above described PFM in simulating droplets with initial number N0 = 256, and volume fraction Φv = 0.054, in a DNS of a fully developed turbulent channel flow at Reτ = 150. The objective was to study the interactions between the droplets.…”

“…This is followed at large t + by a dynamic equilibrium state at which the number of droplets reaches an asymptotic value which is about an order of magnitude larger than that for the case of W e < 1. Scarbolo et al (2016) performed DNS with the same flow conditions and fluid properties of the above described study of Scarbolo et al (2015) to investigate turbulence modification by dispersed deformable droplets. The results show that for W e > 1 the normalized wall shear stress or friction coefficient, C f , for the channel flow is not affected by the deformed droplets and its temporal development is nearly the same as that of the single-phase flow.…”

Coalescence of surfactant-laden drops by Phase Field Method

“…The dynamics of a multiphase flow with surfactant is modeled coupling direct numerical simulations of the Navier-Stokes equations with a phase field method to compute the interface dynamics and the surfactant concentration. The phase field method, which we previously used to study the dynamics of large and deformable droplets in turbulent flows [52,55], is here used in a twoorder-parameter formulation to describe interfacial flows with surfactants. In the following, the governing equations of the two order parameters, phase field φ and surfactant concentration ψ, will be derived and then coupled with continuity and Navier-Stokes (NS) equations to describe the hydrodynamics of the system.…”

“…Interface-capturing methods are based on the use of an indicator function to represent implicitly the interface on an Eulerian grid; this greatly simplifies the discretization and the handling of topological changes. Among the interface capturing methods, we can find the more commonly used Volume-Of-Fluid (VOF) [27,57] and Level-Set (LS) [46,59], and the relatively newer Phase Field Method (PFM) [52,55,56]. In the frame of VOF, approaches initially developed for insoluble surfactants [7,18,32,51] have been then extended to soluble surfactants and 3D flows [3].…”

Phase-field simulation of core-annular pipe flow

“…Note that C also enters the Navier-Stokes equations through the variable density and viscosity of the mixture (1). The CHNS have been long used to simulate binary fluid flows [2] and more recently to investigate turbulent multiphase flows [25,1]. Their ability to deal with topological changes and their thermodynamic consistency make them an appealing alternative to other methods.…”