Turbine engine including a combustor

A turbine engine comprising:

• a combustor comprising:
• a main combustion chamber including an outer liner and an inner liner, the main combustion chamber defining a radial direction, an axial direction, and a circumferential direction;
• an annular dome coupled to the outer liner and the inner liner at a forward end of the main combustion chamber;
• and
• a secondary combustion chamber formed in at least one of the outer liner or the inner liner and positioned downstream of the annular dome, wherein the secondary combustion chamber is a cavity in the outer liner or the inner liner, and the outer liner and the inner liner extend aft of the secondary combustion chamber and forward of the secondary combustion chamber, and wherein the secondary combustion chamber is defined by a forward wall, an aft wall, and an axial wall that extends from the forward wall to the aft wall, the forward wall being positioned forward of the axial wall, the aft wall extending substantially perpendicular along the radial direction from a downstream portion of the outer liner to the axial wall or substantially perpendicular along the radial direction from a downstream portion of the inner liner to the axial wall;
• a plurality of first mixing assemblies each having a pilot mixer, the plurality of first mixing assemblies disposed through the annular dome, the pilot mixer configured to inject a pilot mixer fuel-air mixture axially into the main combustion chamber to generate a first recirculation zone within the main combustion chamber;
• and
• a plurality of second mixing assemblies each having a main mixer, the plurality of second mixing assemblies disposed through the outer liner or the inner liner at the secondary combustion chamber and axially aft of the plurality of first mixing assemblies, the main mixer configured to inject a main mixer fuel-air mixture into the secondary combustion chamber to produce combustion gases and to generate a second recirculation zone within the secondary combustion chamber, the second recirculation zone being axially aft of, and separate from, the first recirculation zone, and the secondary combustion chamber configured to inject the combustion gases into the main combustion chamber.