A simple model for breakup time prediction of water-heavy fuel oil emulsion droplets

Abstract

Immiscible heavy fuel-water (W/HFO) emulsion droplets inside combustion chambers are subjected to explosive boiling and fragmentation due to the different boiling point between the water and the surrounding host fuel. These processes, termed as either puffing or micro-explosion, are investigated with the aid of a CFD model that solves the Navier-Stokes and energy conservation equations alongside with three sets of VoF transport equations resolving the formed interfaces. The model is applied in 2-D axisymmetric configuration and it is valid up to the time instant of HFO droplet initiation of disintegration, referred to as breakup time. Model predictions are obtained for a wide range of pressure, temperature, water droplet surface depth and Weber number; these are then used to calibrate the parameters of a fitting model estimating the initiation breakup time of the W/HFO droplet emulsion with a single embedded water droplet. The model assumes that the breakup time can be split in two distinct temporal stages. The first one is defined by the time needed for the embedded water droplet to heat up and reach a predefined superheat temperature and a vapor bubble to form; while the succeeding stage accounts for the time period of vapor bubble growth, leading eventually to emulsion droplet break up. It is found that the fitting parameters are ±10% accurate in the examined range of 𝑊𝑒 <220, 𝑇 <2000 K, 𝑃 <140 bar and 𝛿 < 0.15.

Puffing/micro-explosion in composite multi-component droplets

“…The analytical solution to Equation (7) subject to Conditions (8), (9), and (11) was obtained as (see Appendix 1 for the details):…”

“…Calculations were performed using Matlab R2020a. One hundred terms were used in series (13) and 200 terms were used in the corresponding series in the analytical solution for temperature (see Expression (11) in [2]); no difference in the results was noticed when these numbers of terms increased further. Time steps 50 µs and 0.1 s were used for the smallest and largest droplets, respectively; 10,000 cells along the droplet radius were used to calculate integrals for the parameters in (13) and Expression (11) in [2].…”

“…The most advanced models of these processes suggested so far are based on high-fidelity direct numerical simulations (DNS) from first principles [4,5,6,7]. These models were supplemented by several simplified models of the phenomena [8,2,9,10,11]. Without discussing the details of these models, we mention that in all of them fuel was assumed to be mono-component; the limitations of this approximation have been widely discussed [12].…”

Micro-explosions in composite droplets: experimental observations and modelling

“…In the model described in [10], the contribution of time required for bubble formation at the water-fuel interface to time to puffing/micro-explosion was taken into account alongside the contribution of the heating time of the composite droplet. The results of the experimental and theoretical investigations of the mutual effect on their puffing/micro-explosion of droplets in a flow, using an example of two closely spaced droplets in tandem, are presented in [11].…”

Temperature measurements in a string of three closely spaced droplets before the start of puffing/micro-explosion: Experimental results and modelling

“…The most advanced models of puffing and micro-explosion developed so far are based on Direct Numerical Simulation [10][11][12] . These were complemented by several simplified models of the phenomena [13][14][15][16][17] . The latter model and its recent modifications (e.g.…”