Turbine engine with a nozzle having cooling features

A turbine engine, comprising:

• an engine core including a combustor for generating hot combustion gases having an exhaust gas temperature (EGT) downstream of the combustor in a range of 980° C. to 1,170° C., inclusive of endpoints, the engine core further including a shaft for rotating about an engine centerline at a core speed (CORE Speed) in a range of 166 Hz to 209 Hz, inclusive of endpoints;
• and
• a nozzle downstream of the combustor for receiving the hot combustion gases at the EGT, the nozzle including a plurality of vanes that extend circumferentially about the engine centerline, individual vanes of the plurality of vanes including:
• an airfoil including an outer surface defining a leading edge, a trailing edge, a suction side, and a pressure side, the outer surface forming an internal cavity of the airfoil, the airfoil further including slots extending along the trailing edge in a generally radial direction, the slots defining a total slot flow area (SFA) between 0.0000160 m2 and 0.0000581 m2, inclusive of endpoints;
• and
• a baffle insert extending within the internal cavity, the baffle insert including baffle walls and cooling holes formed in the baffle walls, the cooling holes defining a total cooling hole area (CHA) between 0.0001060 m2 and 0.0001940 m2, inclusive of endpoints,
• wherein:
• 0.
• 9
• ≤
• (
• CHA
• ⁢
• (
• m
• 2
• )
• -
• 0
• .
• 0
• ⁢
• 0
• ⁢
• 0103
• ⁢
• m
• 2
• 0.000103
• m
• 2
• )
• ⁢
• (
• SFA
• ⁢
• (
• m
• 2
• )
• 0
• .
• 0
• ⁢
• 0004
• ⁢
• m
• 2
• )
• ⁢
• (
• EGT
• ⁢
• °
• ⁢
• C
• .
• 1000
• ⁢
• °
• ⁢
• C
• .
• )
• ⁢
• (
• Core
• ⁢
• Speed
• ⁢
• (
• Hz
• )
• 208
• ⁢
• Hz
• )
• ≥
• 1.509
• .