Dimensional analysis of vapor bubble growth considering bubble–bubble interactions in flash boiling microdroplets of highly volatile liquid electrofuels

Abstract

Electrofuels (e-fuels) produced from renewable electricity and carbon sources have gained significant attention in recent years as promising alternatives to fossil fuels for the transportation sector. However, the highly volatile e-fuels, such as short-chain oxymethylene ethers (OMEx) are prone to flash vaporization phenomena, which is associated with the formation and growth of vapor bubbles, followed by explosive bursting of the liquid jet. This phenomenon is important in many practical applications, for example, superheated liquid sprays in gasoline direct injection engines as well as cryogenic engines. The simulation of a flash boiling spray of such highly volatile liquid fuels is numerically challenging due to several reasons, including (1) the complexity of the bubble growth process in the presence of multiple vapor bubbles and (2) the need to use an extremely small time step size to accurately capture the underlying physics associated with the flash boiling process. In this paper, we first present a bubble growth model in flash boiling microdroplets considering bubble–bubble interactions along with the finite droplet size effects. A dimensional analysis of the newly derived Rayleigh–Plesset equation (RPE) with bubble–bubble interactions is then performed for Reynolds numbers of different orders of magnitude to estimate the relative importance of different forces acting on the bubble surface. Based on this analysis, a simplified nondimensional semi-analytical solution for bubble growth, which also includes the bubble–bubble interactions, is derived to estimate the bubble growth behavior with reasonable accuracy using the larger time step sizes for a wide range of operating conditions. The derived semi-analytical solution is shown to be a good approximation for describing the bubble growth rate over the whole lifetime of the bubble, thus making it useful for simulations of superheated sprays with large numbers of droplets and even more bubbles. The bubble–bubble interactions are found to have a significant impact on the bubble growth dynamics and result in delaying the onset of droplet bursting due to the slower growth of the vapor bubble compared to the bubble growth without bubble–bubble interactions. Furthermore, in a comparison with DNS results, the proposed bubble growth model is shown to reasonably capture the impact of bubble interactions leading to smaller volumetric droplet expansion.