The HF-10 test case, from the REST (Rocket Engine Stability Initiative) working group, is a typical injection element of LOX/CH4 liquid rocket engines. It is numerically studied with the AVBP solver from CERFACS, comparing two combustion models, either based on a beta-pdf equilibrium chemistry model or on reduced finite-rate chemistry. Both models lead to similar stable flame shapes, but locally higher temperatures and a shorter flame length are found with finite-rate chemistry. Phase-locked averages show that a pulsated inlet induces periodic oscillations of the heat release rate, which are however significant only at the lowest frequency.