Direct numerical simulation (DNS) of heptane reacting sprays in a slab region is performed to investigate the effects of turbulence and droplet size on the evolutions of spray combustion. The gas phase is simulated using an Eulerian approach; while the droplets are treated with a Lagrangian method. The coupling between the two phases is considered. It is shown that the mean normalized squared droplet diameter decreases linearly for the cases studies, featuring the d(2) law. Turbulence is proved to be of advantage to evaporation while droplet diameter greatly affects the evaporating rate and the evaporation lifetime. The conditional evaporating rate is found to increase linearly with the mixture fraction. The log-normal distribution for the scalar dissipation rate is examined, and reasonably good agreements are obtained between the DNS results and the model predictions. A parameter characterizing the amount of burning in premixed regime, W-p, is analyzed. Two stages of combustion are identified for the base case: most of the burning occurs in a non-premixed fashion following auto-ignition, and then premixed combustion becomes prevalent. It is shown that the fraction of premixed combustion generally increases with turbulent intensity and decreases with droplet diameter. (C) 2014 Elsevier Ltd. All rights reserved.