A new approach to modelling micro-explosions in composite droplets

• Published in: International journal of heat and mass transfer 2020-11, Vol.161, p.120238, Article 120238
• Main Authors: Sazhin, Sergei S., Bar-Kohany, Tali, Nissar, Zuhaib, Antonov, Dmitrii, Strizhak, Pavel A., Rybdylova, Oyuna D.
• Format: Article
• Language: English
• Subjects: Boundary conditions; Composite water/fuel droplets; Conduction heating; Conductive heat transfer; Dodecane; Droplet heating/evaporation; Droplets; Evolution; Exact solutions; Explosions; Fuels; Micro-explosions; Nucleation; Nucleation temperature; Robin boundary conditions; Temperature
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2020.120238

•A new approach to the mathematical modelling of puffing/micro-explosions.•The heat conduction equation inside a composite spherical water/fuel droplet.•Effects of droplet evaporation and swelling on times to puffing/micro-explosion.•Approximations of the dependence of the nucleation temperature on the heating rate.•The effect of the nucleation temperature on times to puffing/micro-explosion. A new approach to modelling puffing and micro-explosion in composite water/fuel droplets is proposed. This approach is based on the assumption previously made that a spherical water sub-droplet is located in the centre of a spherical fuel (n-dodecane) droplet. The heating of a fuel droplet is described by the heat conduction equation with the Robin boundary condition at its surface and continuity conditions at the fuel-water interface. The analytical solution to this equation, obtained at each time step, is incorporated into the numerical code and used for the analysis of droplet heating and evaporation. The effects of droplet thermal swelling are taken into account. The results of calculations using this code allowed us to obtain the time evolution of the temperature at the water/fuel interface and the evolution of time derivative of this temperature (T˙) with time in the same location. Using the original and previously published experimental data, two new correlations for the nucleation temperatures TN as functions of T˙, valid in the range 0≤T˙≤106 K/s, are suggested. Using these correlations and the values of T˙ inferred from the analysis, the time evolutions of the nucleation temperatures TN at the water-fuel interface are obtained. The predicted values of TN are compared with the values of temperature at this interface Tw. The time instant when Tw=TN is associated with the time instant when puffing/micro-explosion starts.