Modelling of heating, evaporation and ignition of fuel droplets: combined analytical, asymptotic and numerical analysis
Abstract.The paper discusses recent progress in the development of a combined analytical, asymptotic and numerical approach to modelling of heating and evaporation of fuel droplets and ignition of a fuel vapour/ air mixture. This includes a new approach to combined analytical and numerical modelling of droplet heating and evaporation by convection and radiation from the surrounding hot gas. The relatively small contribution of thermal radiation to droplet heating and evaporation allows us to take it into account using a simplified model, which does not consider the variation of radiation absorption inside droplets. The results of the analysis of the simplified problem of heating and evaporation of fuel droplets and ignition of fuel vapour/ air mixture based on the asymptotic method of integral manifolds are discussed. The semi-transparency of droplets was taken into account in this analysis, and a simplified model for droplet heat-up was used. The results of investigations of the effect of the temperature gradient inside fuel droplets on droplet evaporation, break-up and the ignition of fuel vapour/ air mixture based on a new zero-dimensional code are reviewed. The convection heating of droplets is described in this code based on a combined analytical and numerical approach. A new decomposition technique for a system of ordinary differential equations, based on the geometrical version of the integral manifold method is discussed. This is based on comparing the values of the right hand sides of these equations, leading to the separation of the equations into 'fast' and 'slow' variables. The hierarchy of the decomposition is allowed to vary with time. The application of this technique to analyse the explosion of a polydisperse spray of diesel fuel is presented. It is pointed out that this approach has clear advantages from the point of view of accuracy and CPU efficiency when compared with the conventional approach widely used in CFD codes.
IntroductionThe problems of droplet heating, evaporation and ignition of fuel vapour/ air mixture have been widely discussed in the literature [1] - [10]. However, the models used in most practical engineering applications tend to be rather simple. This is due to the fact that droplet heating and evaporation have to be modelled alongside the effects of turbulence, combustion, droplet breakup and related phenomena in realistic 3D enclosures. Hence, finding a compromise between the complexity of the models and their computational efficiency is the essential precondition for successful modelling. In a series of our recent papers [11] -[25] an attempt was made to develop simplified models for droplet heating, evaporation and ignition of fuel vapour/air mixture;