Unsteady simulations of hydrazine (N2H4) sprays in nitrogen tetroxide (NTO, NO2-N2O4) streams were conducted to explore the hypergolic combustion in bipropellant thrusters. The Navier-Stokes equations were solved using a detailed chemical kinetics mechanism and dispersed droplets were modeled through direct numerical simulations. Auto-ignition occurred when the sum of the heat transfer from the ambient gas and the heat release from hydrogen abstraction reactions exceeded the latent heat of the droplets. Although the evaporation of the droplets was enhanced as the droplet size decreased, the ignition delay time increased due to the lower temperatures of the mixtures of the N2H4 vapor and nitrogen tetroxide. After the flames reached a steady state, a double flame structure appeared, comprised of outer diffusion and inner decomposition flames. The inner decomposition flame and N2H4 vapor flow exhibited a sinusoidal behavior at a certain droplet size. This behavior was initiated by the locally expanded decomposition gases and developed by the supply of N2H4 droplets to the decomposition gases at relatively high temperatures. In cases of larger and smaller droplet sizes, the sinusoidal behavior was not significant due to less evaporation of the N2H4 droplets and a lower temperature of the N2H4 vapor, respectively. The sinusoidal behavior of the decomposition flames enhanced the mixing and reactions of the fuel components (i.e., N2H4, NH3, and H-2). The present study demonstrated a large impact of droplet size on flame dynamics, suggesting that a fine spray is not always better for hypergolic propellant combustion to consume the fuel components quickly.