Thermal explosion characteristics of a combustible gas containing fuel droplets Saad A. El-Sayed 1 Abstract This paper investigated the critical ignition conditions of combustible gas containing liquid fuel droplets. The analysis is done based on the criteria of the thermal explosion theory. It includes analytical and numerical solutions of modeling equations of fuel droplets heating and evaporation by convection and radiation from the surrounding reactive hot gas. The exothermic reaction is usually modeled as a single-step reaction obeying an Arrhenius temperature dependence. The thermal conductivity of the fuel droplet is dependent on temperature. The analytical solution produced relations between the main critical characteristic parameters in all planes of the solution. The results obtained from investigating the effect of the characteristic parameters on the explosion behavior of gas and fuel droplets and the thermal radiation proved that both of them are significant. The study proved that the criticality definitions of the thermal explosion of a single-phase system can be used effectively and efficiently to determine the critical conditions of a multi-phase system. Finally, the application of the numerical solutions of the modeling equations was used to analyze the explosion character- istics of a diesel fuel spray system. Keywords Thermal explosion, combustible gas, fuel droplets, critical conditions for ignition, numerical analysis Date received: 10 March 2021; accepted: 04 October 2021 Introduction The thermal explosion of a reactive gas containing fuel droplets is a significant problem because it has many indus- trial applications such as in furnaces, boilers, gas turbines, internal combustion engines, and rocket engines where it is considered a critical state in these systems’ operations. Combustion of liquid fuel droplets spray in a reactive gaseous mixture (two-phase reaction) can be described as a different form of an identical pure reactive gaseous mixture (single-phase combustion). The previous experi- mental work showed that the addition of fuel droplets increased the flammable pre-gaseous mixture burning velo- city, which in turn increased the combustion efficiency, but on the other hand, the combustion hazards also increased. 1–4 The use of liquid fuel droplets, rather than pre-vaporized ones, produced an explicit oscillation during the combustion at a frequency of about 1–5 MHz. 5 The thermal explosion of stationary exothermic chemical reaction with heat loss (Newton’s cooling law) has first been established and solved analytically in. 6 In reality, the assumption of uniform temperature, neglecting reactant consumption, mea- suring ignition temperature, simple thermal reaction, and others raise criticisms and limitations on applications of the theory. After that, different treatments and applications of the theory were handled in 7–11 and so many others. Analytical and numerical solutions to the critical ignition and transition conditions of a dust cloud of carbon particles were obtained. 12 The critical conditions of a gas-solid mixture in an adiabatic confined vessel was investigated. 13 A mathematical model for the thermal explosion in a combust- ible dusty gas containing fuel droplets with general Arrhenius reaction-rate laws and convective and radiative heat losses considering the interphase heat exchange between the gas and inert solid particles was investigated in ref. 14 The effects of liquid droplets on reactive gas combustion behavior have less concern in their work. The effect of a liquid fuel spray on the thermal explosion of a combustible droplet-gas cloud 1 Mechanical Power Engineering Dept., Zagazig University, Zagazig, Egypt Corresponding author: Saad A. El-Sayed, Mechanical Power Engineering Dept., Zagazig University, Alsharkia, Zagazig, Egypt. Email: shamad53@hotmail.com Original Research Article International Journal of Spray and Combustion Dynamics 2021, Vol. 13(2–3) 124–145 © The Author(s) 2021 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/17568277211057360 journals.sagepub.com/home/scd