Radiation effect on thermal explosion in a gas containing evaporating fuel droplets

Abstract

The dynamics of thermal explosion in a fuel droplets/hot air mixture is investigated using the geometrical version of the method of integral manifolds. The results are applied to the modelling of the ignition process in diesel engines. Effects of the thermal radiation, semi-transparency of droplets and oxidizer are taken into account. In contrast to the previous studies, the difference between gas temperature (responsible for convective heating of droplets) and external temperature (responsible for radiative heating of droplets) is taken into account. The dynamics of the explosion is presented in terms of the dynamics of a multi-scale, singularly perturbed system. The relevant parametric regions of this system are analyzed. Explicit analytical formulae for the ignition delay in the presence of thermal radiation are derived. It is shown that the effect of thermal radiation can lead to considerable reduction (up to about 30%) of the total ignition delay time.

Mathematical Modelling of Spray Combustion-Numerical and Analytical Analysis with application to Engineering Science

“…This generalization have been done by the authors of (Goldfarb, Sazhin, & Zinoviev, 2004;Goldfarb, Gol'dshtein, Katz, & Sazhin, 2007 the radiation effect on thermal explosion in a gas containing evaporating fuel monodisperse spray. The physical assumptions of the model are as follows: the difference between gas temperature (responsible for convective heating of droplets) and external temperature (responsible for radiative heating of droplets) is taken into account, the droplets are regarded as the source of endothermicity, the medium is modeled as a spatially homogeneous mixture of an optically thin, combustible gas with monodisperse spray of evaporating fuel droplets, the distortion of the incident radiation by surrounding droplets is ignored, the effects of droplet movement and the effect of temperature gradient inside the droplets are ignored, the incident radiation has a black-body spectrum, the system is adiabatic, the gas pressure is constant, convective and radiative heating of droplets are taken into account, the thermal conductivity of the liquid phase is assumed to be infinity large, the volume fraction of the liquid phase is assumed to be much less than that of the gaseous phase (hence, the heat transfer coefficient of the mixture is controlled by the thermal properties of the gaseous component), the burning process described by a first order exothermic reaction and takes place in the gaseous phase only, the velocity of the droplets and the effects of natural convection are neglected (hence, the effects of the Stefan flow are neglected), Nusselt and Sherwood numbers are taken equal to 2, Reynolds number is less than 1 (Re << 1).…”

“…Here, q heat flux (c for convective and r for radiative), a, a 0 , a 1 , a 2 , b, b 0 , b 1 and b 2 are coefficients introduced in Goldfarb, Gol'dshtein, Katz, and Sazhin (2007).…”

“…1;2017 The analysis of the model 180-184 is based on the geometrical version of the method of integral manifold (MIM). In order to apply the MIM method the authors of (Goldfarb, Gol'dshtein, Katz, & Sazhin, 2007) transform the Equations 180-184 to the SPS form (singular perturbed system). The non-dimensional model is…”

“…The authors of (Goldfarb, Gol'dshtein, Katz, & Sazhin, 2007) investigated the parameters given in tables 9 for the model 180-184 and found that the only possible dynamical scenarios, when the MIM can be applied, are those when the fast dimensionless variables are gas temperature θ g and droplet temperature θ d . Scenario 1: The gas temperature is the fas variable.…”

“…In this scenario, the thermal explosion process should be divided into two separate consecutive sub-processes: A-The heat-up and evaporation (time) process and, B-the induction (time) process. Let us review these two processes as presented in (Goldfarb, Gol'dshtein, Katz, & Sazhin, 2007). Case A: Heat-up and evaporation time: during the heat-up and evaporation time the dimensionless droplet temperature rises from its initial value θ d0 to its boiling point θ b and the droplets evaporate (during this time the fuel droplets evaporate completely).…”