Turbomachine nozzle with an airfoil having a curvilinear trailing edge

A turbomachine defining an axial direction, a radial direction perpendicular to the axial direction, and a circumferential direction extending concentrically around the axial direction, the turbomachine comprising:

• a compressor;
• a combustor disposed downstream from the compressor;
• and
• a turbine disposed downstream from the combustor, the turbine including a stator vane having an inner platform, an outer platform, and an airfoil, the airfoil of the stator vane comprising:
• a leading edge extending across the airfoil from the inner platform to the outer platform;
• a trailing edge downstream of the leading edge along a flow direction, the trailing edge extending across the airfoil from the inner platform to the outer platform;
• a pressure side surface extending between the inner platform and the outer platform and extending between the leading edge and the trailing edge;
• and
• a suction side surface extending between the inner platform and the outer platform and extending between the leading edge and the trailing edge, the suction side surface opposing the pressure side surface;
• wherein the trailing edge intersects the inner platform at a first point and intersects the outer platform at a second point, wherein the trailing edge is orthogonal with the outer platform at the second point in an axial-radial plane and the trailing edge is oblique to the inner platform at the first point in the axial-radial plane, wherein the trailing edge defines an S-shape within a radial-circumferential plane, and wherein the S-shape comprises a compound curvature such that an outer portion of the trailing edge is concave at the pressure side surface and an inner portion of the trailing edge is convex at the pressure side surface, the outer portion extending from the outer platform to an inflection point at about a midspan of the trailing edge, the inner portion extending from the inflection point to the inner platform.