To validate the concept of free oblique detonation waves (ODWs) induced by non-intrusive energy deposition applied in ODW engines (ODWEs), numerical simulations are performed by modeling the laser spark as a high-temperature and high-pressure zone embedding in the high-speed incoming flow and by solving the non-dimensional reactive Euler equations with one-step chemistry. The initiation process, flow structures, and self-adapted characteristics of such kinds of free ODWs in an open space are discussed with varying dimensionless source energy and inflow Mach number. The results show that free ODWs can be initiated successfully by local non-intrusive energy deposition. In particular, four ignition regimes, namely, the subcritical regime, the critical I regime, the critical II regime, and the supercritical regime, which are analogous to the one-dimensional direct initiation of detonation, are distinguished by varying the dimensionless source energy. However, the typical energy required by each ignition regime is higher than that in the one-dimensional case due to multi-dimensional energy transmission and instabilities. Moreover, the dimensionless source energy should be moderate to obtain a stable free ODW flow field because extremely low source energy leads to ignition failure, while extremely high source energy causes premature ignition. When the inflow Mach number varies, it is found that free ODWs can adjust automatically to a nearly Chapman-Jouguet state, indicating the self-sustaining nature of free detonation waves. Due to this feature, ODWE performance will be relatively stable despite the change in inflow Mach numbers if free ODWs are utilized in the combustor.