Theoretical insights into transient gas and liquid phase effects on the evaporation and autoignition of stationary droplets

Abstract

Droplet evaporation and autoignition are considerably influenced by transient gas-phase diffusion and variations in droplet temperature during the initial stage, especially under elevated pressure conditions and when substantial differences exist between the initial and equilibrium droplet temperatures. In this paper, we present a theoretical analysis of the combined transient effects of gas-phase diffusion (GT) and droplet temperature variation (DT) on the pure evaporation and autoignition of individual, stationary fuel droplets. Asymptotic solutions reveal that the evolution of droplet surface temperatures consists of two phases: an initial rapid response followed by a more gradual variation. By investigating the development of the evaporating boundary layer and droplet temperature, we derive the transient correction factors for both GT and DT effects, accounting for the impact of non-unity Lewis numbers. Due to the GT effect, evaporation accelerates under conditions of a reduced liquid–gas density ratio (e.g., elevated ambient pressure) and increased evaporation intensity (e.g., higher ambient temperature). Meanwhile, a larger deviation between the initial droplet temperature and the equilibrium temperature results in a more pronounced DT effect. Beyond pure evaporation, this paper also analyzes the autoignition of droplets under the combined impact of both transient effects, employing large-activation-energy asymptotics. The ignition delay time and critical conditions for droplet ignition are theoretically established. Analysis indicates that the GT effect exerts a greater influence on the critical ignition temperature than both the DT and non-unity Lewis number effects. A comprehensive comparison of the current theory with transient numerical simulations reveals its ability to accurately address both GT and DT effects on droplet evaporation and autoignition processes. Consequently, this paper successfully extends the classical theory on droplet evaporation and autoignition through an intuitive and physically meaningful analysis.

Novelty and significance statement

The novelty of this research stems from its detailed theoretical exploration of the concurrent transient impacts of gas-phase diffusion (GT) and droplet temperature variation (DT) on the evaporation and autoignition of individual fuel droplets. Through the development of asymptotic solutions and transient correction factors for GT and DT effects, this paper constructs a comprehensive framework that effectively refines classical theory. This work is significant for bridging a crucial gap in understanding droplet evaporation and ignition behaviors under conditions that mirror real-world scenarios, especially under elevated system pressures and notable deviations between initial and equilibrium droplet temperatures, where transient effects are prominent. This enhanced theoretical basis holds promise for advancing the design and optimization of innovative combustion systems, fostering the development of technologies that are more efficient and environmentally friendly.