As society evolves towards a green economy to face climate change, the combustion community is expected to develop new technologies and design low emission combustors for the aviation and energy sectors. In that respect, hydrogen is today a promising technical solution since it offers no direct CO2 production and even when it is mixed with classical fossil fuels it helps the stabilization of leaner and greener flames. However, the development of H2 combustion chamber is a technological challenge raising multiple questions in terms of reliability, efficiency and safety, especially for airplanes. When it comes to helicopter engines, there exists no specific pollutant emission regulation as of now and, due to their low power, helicopters are ideal testbed for new technologies. More specifically and to illustrate this ideal development context, Safran Helicopter Engines (SHE) has recently developed the Spinning Combustion Technology (SCT) gaining in engine operability and lean blow-out (LBO) capabilities. Due to its large potential in predicting complex reactive flows, Large Eddy Simulation (LES) has proven useful to support this design challenge, whether it is oriented toward a change in fuel (H2) or a change in combustor geometry (SCT). However, since engine operability is a very fine phenomenon given its multi-physics nature, large efforts and attention should be paid on the proper modeling of the different physics coexisting in these systems. In this work, a full assessment of Conjugate Heat Transfer based high-fidelity LES models is proposed and organized in three parts. First, main modeling challenges are addressed. As H2-enrichment and real engine conditions yield reduced flame thickness and more stringent requirements in terms of domain discretization, a physics-based Static Mesh Refinement (SMR) approach is derived and validated on different configurations. In parallel and since real flow prediction will depend on the applied thermal boundaries, Conjugate Heat Transfer (CHT) based LES simulations are validated and assessed compared to simpler strategies for a partially premixed swirled flame, the right dynamics being correctly predicted only with a correct estimation of the heat transfer at the walls. Finally, the effect of variable transport properties, typical of H2 mixture flows, on a swirled premixed flame is analyzed, confirming that a proper description of the chemistry and transport properties are needed when dealing with notconventional fuel mixtures.Second, the effects of H2-enrichment and elevated pressure (up to 5 bar) are investigated for a swirled CH4 flame. Both drastic changes on the flame shape and its dynamics are observed, eventually triggering thermoacoustic oscillations. Third, the flame stabilization and the LBO dynamics in the SCT are specifically studied. CHT-LES is able to retrieve the experimentally observed dynamics when decreasing the equivalence ratio and provides better results than typical adiabatic simulations. To finish, LES is used as an industrial tool to design a new burner closer to real SCT engines. By addressing these challenges, this work demonstrates the assessment of LES, in a CHT context, for predicting engine operability when dealing with innovative technologies and therefore highlights the central role of High Power Computing (HPC) and high-fidelity LES in the transition towards a decarbonized future.