Numerical simulation of droplets, bubbles and waves: state of the art

Abstract

Abstract. This work present current advances in the numerical simulation of twophase flows using a VOF method, balanced-force surface tension and quad/octree adaptive mesh refinement. The simulations of the atomization of a liquid sheet, the capillary retraction of a liquid sheet and two-and three-dimensional wave breaking all for air/water systems, are used to show the potential of the numerical techniques. New simulations of atomization processes for air/water conditions are allowing to investigate the processes leading to the appearance of instabilities in the primary atomization zone in real conditions. For the retracting liquid sheet, the new simulations show that two different regimes can be encountered as a function of the Ohnesorge number. For large values, a laminar flow is encountered inside the rim and a steady state is reached after a quick transient state. For small values, a turbulent flow is generated inside the rim which is responsible of large oscillations in the rim size and neck thickness. The breaking wave case study demonstrates the orders-of-magnitude efficiency gains of the adaptive mesh refinement method.

Droplets in turbulence: a new perspective

“…DF use a form of immersed interface method with a fixed numerical mesh and a volume of fluid scheme, taking care in evaluating the forces due to surface tension, the droplet shape and handling the rapid changes in fluid density and viscosity across the droplet interface. Fuster et al (2009) describe the technical challenges of computing these two-phase flows. Figure 1 shows a sample of the droplets for case C from DF, We rms = 1, soon after they are introduced into the flow.…”

“…Many questions remain open for both droplet and bubble flows. One of these is the evolution of the droplet spectrum and the observation by Lasheras & Hopfinger (2000) that in a stationary flow a balance between breakup and coalescence results in an equilibrium size distribution independent of the initial spectrum. The experiments by Bateson & Aliseda (2012) address this for small droplets (D η K ) at very low volume fractions for conditions relevant to atmospheric clouds.…”

“…Atomization of a liquid jet with a coaxial gas stream will rapidly generate a fine spray of droplets with a range of sizes depending on the Reynolds number of the flow and the Weber number (Lasheras & Hopfinger 2000). Individual droplets in an air flow can undergo oscillations in shape and may fragment via different modes, again depending on We and γ (Flock et al 2012).…”

Numerical modelling of diesel spray using the Eulerian multiphase approach

“…It is reasonable to use the diesel engines as the internal combustion engine power source due to their more efficient energy conversion and higher safety factor when compared to the spark ignition engines [6]. In internal combustion diesel engines there is mostly diffusion combustion present, meaning that the spray characteristics have the direct influence on the fuel energy conversion and the formation of harmful substances [7][8][9][10][11]. There are challenges associated with having a very short amount of time available for the fuel spray to atomise and form an adequate mixture for quality combustion.…”

An unconditionally stable uncoupled scheme for a triphasic Cahn–Hilliard/Navier–Stokes model

“…This system is a gradient flow for the following energy functional under the constraint of volume conservation: We introduce the hyperplane S = (c 1 , c 2 , c 3 ) ∈ R 3 ; c 1 + c 2 + c 3 = 1 of R 3 , to simplify notation in the sequel. The expressions of the triphasic Cahn-Hilliard potential F and of the constant triplet Σ = (Σ 1 , Σ 2 , Σ 3 ) was derived in [4], so that the model can correctly take into account the surface tensions values σ 12 , σ 13 and σ 23 prescribed between the different pairs of phases and so that it is consistent with the two-phase situations: the triphasic model has to exactly reproduce diphasic situations when one of the three phases is not present. The coefficient Σ i is given as a function of the surface tensions:…”