Large Eddy Simulations of recessed central-duct coaxial injectors under transcritical and two-phase conditions are detailed in this paper, with the objective of assessing the ability of recently develop models [1, 2] to recover the experimental observations of an augmentation of the flame expansion rate and its dynamics due to the recess. The simulated cases correspond to the LOx/GH2 Mascotte A10 and C10, both operating at 10 bar with two-phase flow conditions, and Mascotte C60, injected under transcritical conditions in a chamber at 60 bar [3]. Cases A10 and C10 qualitatively reproduce the experimental visualizations. However, the simulation with recess for case C60 produces a more disrupted inner jet and a shorter flame than in the experiment. In addition, a fine grid resolution is necessary to capture the absolute instability in this case. Case C60 is then examined. It is observed in particular that heat release rate distribution is importantly modified once the LOx injector is recessed, nearly doubled up to 10 LOx injector diameters. This huge increase of heat release has two origins: 1) an enhanced turbulent mixing in the near injector region due to an increased injector exit velocity because of the thermal expansion in the recessed part, in line with the model proposed by Kendrick et al. [4] ; 2) a larger flame surface because of the quicker destabilization and larger spreading rate of the flame at the injector exit.