Engine with rotating detonation combustion system

An engine, the engine comprising:

• a longitudinal wall extended along a lengthwise direction, wherein the longitudinal wall defines a gas flowpath of the engine and a combustion section, the gas flowpath having a gas flowpath depth perpendicular to the longitudinal wall;
• an inner wall assembly extendable from the longitudinal wall into the gas flowpath, wherein the inner wall assembly includes a concave upstream face that defines a rotating detonation combustion region at an upstream side of the inner wall assembly and adjacent to the longitudinal wall, and the inner wall assembly includes a first actuator configured to actuate the inner wall assembly to extend the inner wall assembly into the gas flowpath depth;
• and
• an upstream wall assembly coupled to the longitudinal wall upstream of the inner wall assembly, wherein a second actuator is coupled to the upstream wall assembly, the second actuator configured to actuate the upstream wall assembly to extend the upstream wall assembly into the gas flowpath depth;
• and
• wherein the engine is configured to perform operations comprising;
• flowing an oxidizer through the gas flowpath into the combustion section, wherein the flow of oxidizer includes a first portion and a second portion;
• capturing the first portion of the flow of oxidizer at the rotating detonation combustion region via the concave upstream face of the inner wall assembly being extended into the gas flowpath a depth;
• adjusting an amount and flow direction of the first portion of the flow of oxidizer provided to the concave upstream face of the inner wall assembly via actuating the upstream wall assembly via the second actuator to adjust the depth of the upstream wall assembly extended into the gas flowpath and to adjust the flow direction of the first portion of the flow of oxidizer;
• flowing a first flow of fuel to the first portion of the flow of oxidizer at the rotating detonation combustion region;
• producing, via a first mixture of the first flow of fuel and the first portion of the flow of oxidizer, a rotating detonation wave of detonation gases at the rotating detonation combustion region;
• adjusting a size of the rotating detonation wave at the rotating detonation combustion region by adjusting a depth of the inner wall assembly extended into the gas flowpath via the first actuator;
• mixing at least a portion of the detonation gases from the rotating detonation combustion region with a second flow of fuel and the second portion of the flow of oxidizer in the gas flowpath;
• and
• burning a second mixture comprising the second flow of fuel, at least a portion of the detonation gases, and the second portion of the flow of oxidizer, wherein burning the second mixture is downstream of the rotating detonation wave of detonation gases relative to the gas flowpath.