Fuel staging for rotating detonation combustor

A combustion system comprising:

• an annular tube disposed between an inner wall and an outer wall, the annular tube extending from an inlet end to an outlet end;
• at least one fluid inlet disposed in the annular tube proximate the inlet end, the at least one fluid inlet providing a conduit through which fluid flows into the annular tube;
• at least one outlet disposed in the annular tube proximate the outlet end;
• at least one primary fuel injector configured to disperse fuel into a fluid stream entering the annular tube via the at least one fluid inlet, the at least one primary fuel injector being configured to disperse the fuel into the annular tube in an orthogonal orientation to the fluid entering the annular tube via the at least one fluid inlet;
• at least one secondary fuel injector disposed in the annular tube;
• at least one tertiary fuel injector disposed in the annular tube axially aft of the at least one primary fuel injector, the at least one tertiary fuel injector comprising multiple tertiary fuel injectors spaced circumferentially around the annular tube;
• a first fuel line fluidly coupled upstream of the at least one primary fuel injector, the first fuel line configured to deliver the fuel to the at least one primary fuel injector;
• a first fuel control valve fluidly coupled upstream of the first fuel line, the first fuel control valve configured to control a first flow of the fuel to the first fuel line;
• a fuel supply fluidly coupled upstream of the first fuel control valve;
• a second fuel line fluidly coupled downstream of the first fuel control valve, the first fuel control valve configured to control a second flow of the fuel to the second fuel line;
• a second fuel control valve fluidly coupled downstream of the second fuel line, the second fuel control valve configured to control a third flow of the fuel to the at least one secondary fuel injector;
• a third fuel line fluidly coupled downstream of the second fuel control valve, the third fuel line fluidly coupled upstream of the at least one tertiary fuel injector, the third fuel line configured to deliver a fourth flow of the fuel to the at least one tertiary fuel injector;
• at least one hood portion disposed at the inlet end of the annular tube, the at least one hood portion comprising:
• a hood outer wall disposed radially outward of the outer wall;
• and
• a hood taper portion coupled to an aft end of the hood outer wall and extending axially aft and radially inward from the hood outer wall to the outer wall;
• and
• a fluid inlet plenum fluidly coupled upstream of the at least one fluid inlet, the fluid inlet plenum comprising a contoured plenum backwall that curves from an axial alignment to radial alignment with respect to a central axis of the annular tube.