A reactor for reforming a liquid hydrocarbon fuel, and associated processes and systems, are described herein. In one example, a two stage process is disclosed in which a first reactor is coupled to a second stage reactor having a reaction volume greater than the first reactor. In the first reactor, the liquid hydrocarbon fuel is partially reformed and thereafter is inputted into the second stage reactor for complete partial oxidation. The reaction product is at last partially synthesis gas, a mixture of carbon monoxide, hydrogen, as well as other low hydrocarbons such as methane, ethylene, ethane, and acetylene. The low hydrocarbons can be reformed further in a solid oxide fuel cell. A portion of the gaseous, rotating contents of the second stage reactor may be input into the first reactor to help generate and sustain rotation within the first reactor.