The heating and explosive boiling leading to fragmentation of immiscible heavy fuel oil-water droplets, termed as W/HFO emulsions, is predicted numerically by solving the incompressible Navier-Stokes and energy equations alongside with a set of three VoF transport equations separating the interface of co-existing HFO, water liquid and water vapour fluid phases. Model predictions suggest that explosive boiling of the water inside the surrounding HFO, ought to their different boiling points, accelerates droplet breakup; this process is termed as either puffing or micro-explosion. In contrast to past studies which predefine the presence of vapor bubbles inside the water droplet, this is predicted here with a phenomenological model based on local temperature and superheat degree. Following their formation, the growth rate of the bubbles is computed with OCASIMAT phase-change algorithm. Moreover, the fuel droplet is simultaneously subjected to convective air flow which further contributes to its deformation. As a result, the performed simulations quantify the relative time scales of the aerodynamic-induced and the emulsioninduced breakup mechanisms. The conditions examined refer to a highly viscous emulsified heavy fuel oil droplet in a gas phase having fixed temperature and pressure equal to 1000 K and 30 bar, respectively. Initially, a benchmark case demonstrates the detailed mechanisms taking place, concluding that droplet fragmentation occurs only at a part of the fuel-air interface, resembling characteristics similar to puffing. Next, a parametric study with Weber number ( ℎ = 0.9, < 200) shows that puffing process can speed up to 10 times the breakup of the droplet relative to aerodynamic breakup.

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.

Bubble dynamics is generally described by the well-known Rayleigh-Plesset (R-P) equation in which the bubble pressure (or equivalently the bubble density) is predefined by assuming a polytropic gas equation of state with common assumptions to include either isothermal or adiabatic bubble behaviour. The present study examines the applicability of this assumption by assuming that the bubble density obeys the ideal gas equation of state, while the heat exchange with the surrounding liquid is estimated as part of the numerical solution. The numerical model employed includes the solution of the Navier-Stokes equations along with the energy equation, while the liquidgas interface is tracked using the Volume of Fluid (VOF) methodology; phase-change mechanism is assumed to be insignificant compared to bubble heat transfer mechanism. To assess the effect of heat transfer and gas equation of state on bubble behaviour, simulations are also performed for the same initial conditions by using a polytropic equation of state for the bubble phase without solving the energy equation. The accuracy of computations is enhanced by using a dynamic local grid refinement technique which reduces the computational cost and allows for the accurate representation of the interface for the whole duration of the phenomenon in which the bubble size changes significantly. A parametric study performed for various initial bubble sizes and ambient conditions reveals the cases for which the bubble behaviour resembles that of an isothermal or the adiabatic one. Additional to the CFD simulations, a 0-D model is proposed to predict the bubble dynamics. This combines the solution of a modified R-P equation assuming ideal gas bubble content along with an equation for the bubble temperature based on the 1 st law of thermodynamics; a correction factor is used to represent accurately the heat transfer between the two phases. KeywordsBubble dynamics, heat transfer, CFD-VOF model, 0-D model. IntroductionThe need for the inclusion of thermal effects in bubble dynamics was first addressed in [1] among others; it was shown that the polytropic gas assumption may provide inaccurate predictions of the bubble behaviour when thermal processes are taken into consideration. Since then, the effect of heat and mass transfer on bubble dynamics were examined in a large number of studies, either by CFD numerical models that are capable of solving the complex equations that characterize the physical processes of the bubble motion, or by reduced order models which include various assumptions but are computationally more efficient. In the framework of the CFD studies, the effect of heat transfer by solving the equation of gas-vapour bubble including variation of liquid temperature and assuming liquid incompressibility was examined in [2]. The main assumption in this study, was that the temperature distribution inside the bubble to be uniform, which allowed the authors to integrate analytically the continuity and momentum equations inside the bubble. In [3], the motion ...