Numerical investigation of reacting droplets in homogeneous shear turbulence

Numerical simulations are performed of a compressible oxidizer gas laden wi th fuel droplets. The carrier phase is considered in the Eulerian context a nd is simulated via direct numerical simulation (DNS). The fuel droplets ar e tracked in the Lagrangian frame and interactions between the two phases a re taken into account in a realistic two-way coupled formulation. It is ass umed that combustion takes place in the vapour phase, resulting in a 'homog eneous' reaction described by fuel + oxidizer --> products + energy. Severa l simulations are performed within the configuration of low-Mach-number hom ogeneous shear turbulence to investigate the effects of the mass loading ra tio, the droplet time constant, the Damkohler number, and the heat release coefficient, Initial mass loading ratios up to 0.8 and initial Stokes numbe rs (based on the Kolmogorov time scale) of 1.23 and 2.46 are considered. Th e results of these simulations along with those from non-reacting cases are utilized to analyse the droplet size distribution, the fuel vapour, the ox idizer, and the reaction rate and zone. An analysis of the statistics of th e two-phase flow indicates that various fields are accurately resolved and the assumptions invoked in the formulation of the problem are satisfied. Th e mean evaporation rate (normalized with the initial mass of the droplets) decreases with the increase of either the mass loading ratio or the droplet time constant, It is shown that the droplet size distribution can be reaso nably approximated by a Gaussian probability density function (p.d.f.) for all of the cases. The joint p.d.f. of the fuel vapour and the oxidizer mass fractions exhibits the features of a premixed reaction. The values of the Taylor microscale of the fuel vapour and the oxidizer are closer in the pre sence of the chemical reaction than in the evaporating but non-reacting cas e. The reaction rate exhibits higher values in the regions of the flow cont aining the droplets while experiencing moderate increase in the high-strain -rate regions. The evaporation rate (per mass of the droplet) is smaller fo r larger droplets but an opposite trend is observed for the reaction rate. The reaction zone tends to align with the streamwise direction due to the e ffects of the mean flow on the droplets. The alignment is enhanced with eit her the increase of the mass loading ratio or the decrease of the droplet t ime constant, or the decrease of the Damkohler number. The alignment of the fuel vapour and the oxidizer with the mean flow direction decreases and in creases, respectively, as a result of the chemical reaction.