Resumen vii 1 Optimum Grids for Finite Difference Methods The second fluid-dynamic combustion problem deals with the vaporization and subsequent combustion of fuel droplets immersed in slowly convective flows. For small values of v Abstract the Peclet number Pe, the convection associated with the velocity of the oxidizer stream is in first approximation negligible at distances to the droplet of the order of the droplet radius a. Only in the Oseen region, located at distances of the order of

more »

... , do the convective effects become as important as the diffusive ones. For typical hydrocarbon fuels, where the overall stoichiometric ratio S is large compared to unity, the flame is located in the very same region if the distinguished limit of Pe ∼ 1/S is considered, inducing temperature and density variations of order unity, which require the use of numerical techniques for the description of the resulting fluid-dynamic problem. The overall analysis of this multiscale problem is carried out using matched asymptotic expansions between the different regions of the flow, where the matching has to be done between the semi-analytical solutions obtained for the inner region and the numerical solutions obtained for the Oseen region. The presented analysis reveals the non-dimensional parameters that are relevant in each of the regions and shows that the presence of the flame significantly modifies the convective velocity felt by the droplet, thus altering its vaporization rate and drag. vi