A population balance model for large eddy simulation of polydisperse droplet evolution

Abstract

In the context of many applications of turbulent multi-phase flows, knowledge of the dispersed phase size distribution and its evolution is critical to predicting important macroscopic features. We develop a large eddy simulation (LES) model that can predict the turbulent transport and evolution of size distributions, for a specific subset of applications in which the dispersed phase can be assumed to consist of spherical droplets, and occurring at low volume fraction. We use a population dynamics model for polydisperse droplet distributions specifically adapted to a LES framework including a model for droplet breakup due to turbulence, neglecting coalescence consistent with the assumed small dispersed phase volume fractions. We model the number density fields using an Eulerian approach for each bin of the discretized droplet size distribution. Following earlier methods used in the Reynolds averaged Navier-Stokes framework, the droplet breakup due to turbulent fluctuations is modelled by treating droplet-eddy collisions as in kinetic theory of gases. Existing models assume the scale of droplet-eddy collision to be in the inertial range of turbulence. In order to also model smaller droplets comparable to or smaller than the Kolmogorov scale we extend the breakup kernels using a structure function model that smoothly transitions from the inertial to the viscous range. The model includes a dimensionless coefficient that is fitted by comparing predictions in a one-dimensional version of the model with a laboratory experiment of oil droplet breakup below breaking waves. After initial comparisons of the one-dimensional model to measurements of oil droplets in an axisymmetric jet, it is then applied in a threedimensional LES of a jet in crossflow with large oil droplets of a single size being released at the source of the jet. We model the concentration fields using N d = 15 bins of discrete droplet sizes and solve scalar transport equations for each bin. The resulting droplet size distributions are compared with published experimental data, and good agreement for the relative size distribution is obtained. The LES results also enable us to quantify size distribution variability. We find that the probability distribution functions of key quantities such as the total surface area and the Sauter mean diameter of oil droplets are highly variable, some displaying strong non-Gaussian intermittent behavior.

Material Transport in the Ocean Mixed Layer: Recent Developments Enabled by Large Eddy Simulations

“…One example of application of this coupled polydispersed approach is the study of gas bubbles by Liang et al (2011). For oil droplets, a recent application is found in Aiyer et al (2019).…”

Oil Droplet Dispersion under a Deep-Water Plunging Breaker: Experimental Measurement and Numerical Modeling

“…However, a more detailed numerical approach would consist of coupling a hydrodynamic model with the VDROP model to fully understand the temporal-spatial behavior of oil within a breaker. Advances in simulations of wave breaking [53,54] and the ensuring droplet transport [49,55] and breakup [56] have been achieved, and our group is building on these advances to allow the scaling-up of laboratory results to the sea-scale.…”

A Review on Multiphase Underwater Jets and Plumes: Droplets, Hydrodynamics, and Chemistry

“…Martínez‐Bazán et al (1999b) released bubbles in a water jet and observed that the breakup of the bubbles continued until around 40 diameters from the orifice. In fact, because turbulence is inhomogeneous, all works on the breakup of oil in systems (reactors, jets, and waves) relied on representing the breakup through a breakage frequency g ( d ) derived from fundamental principles with constants obtained by fitting to data (Aiyer et al, 2019; Tsouris & Tavlarides, 1994; Zhao, Boufadel, et al, 2014). The third mechanism that favors additional breakup at large distances from the orifice relates to the buoyancy of plumes from large orifices, such as the DWH, where a relatively large rise velocity and energy dissipation rate would persist for 100s of diameters from the jet (Zhao et al, 2015).…”

“…Recently, the Eulerian‐Eulerian LES modeling framework is further advanced with additional important features being incorporated. For example, Aiyer et al (2019) adopted the method of particle population balance model (Coulaloglou & Tavlarides, 1977; Prince & Blanch, 1990; Tsouris & Tavlarides, 1994; Wang & Wang, 2007; Zhao, Boufadel, et al, 2014; Zhao, Torlapati, et al, 2014) and developed a Eulerian‐Eulerian LES model for simulating polydisperse droplet evolution.…”