Turbine engine having a fuel nozzle including a curvilinear structure

A turbine engine comprising:

• a compression section, a combustion section, and a turbine section in serial flow arrangement, the combustion section comprising:
• a wall at least partially forming a combustion chamber, the wall having a fuel nozzle opening;
• and
• a fuel nozzle extending through the fuel nozzle opening, the fuel nozzle comprising:
• a fuel nozzle body having a centerline and a continuous curvilinear structure bounding an open interior, the open interior opening to the combustion chamber at an outlet, the continuous curvilinear structure terminating at a distal end and having a curvilinear centerline-along the distal end;
• and
• a set of fuel injection channels provided within the fuel nozzle body and opening into the open interior at a set of fuel injection orifices that are spaced axially about the fuel nozzle body relative to the curvilinear centerline;
• and
• wherein the curvilinear centerline defines [is] a spiral formation disposed within a plane at the distal end of the continuous curvilinear structure and extending between a first circumferential end and a second circumferential end, wherein the first circumferential end is greater than 2π radians and less than or equal to 20π radians from the second circumferential end.