Turbine engine with a blade

A turbine engine, comprising:

• an engine core extending along an engine centerline and including a compressor section, a combustor, and a turbine section in serial flow arrangement;
• a temperature sensor within the engine and configured to detect an exhaust gas temperature (EGT) within the engine core;
• a set of nozzles circumferentially arranged in the turbine section and defining a number of nozzles (NN);
• and
• a set of blades circumferentially arranged in the turbine section adjacent to, and downstream of, the set of nozzles, with the set of blades defining a number of blades (NB);
• wherein a blade in the set of blades comprises:
• an outer wall bounding an interior and having an exterior surface, with the outer wall defining a pressure side and a suction side and extending between a leading edge and a trailing edge to define a chord-wise direction, and also extending between a tip and a root to define a span-wise direction;
• a cooling conduit within the interior;
• a plurality of film holes comprising a corresponding plurality of passages extending between a corresponding plurality of inlets and a corresponding plurality of outlets, with the plurality of inlets fluidly coupled to the cooling conduit and the plurality of outlets located on the exterior surface, wherein the plurality of outlets comprises a first subset of outlets at least partially extending along the chord-wise direction proximate the tip, and also comprises a second subset of outlets extending at least partially along the span-wise direction and intersecting the first subset of outlets;
• a tip radius (TR) defined between the engine centerline and the tip under standard day conditions of 15° C. at mean sea level altitude and 101.3 kPa atmospheric pressure;
• a radial length (R) defined by a span-wise line extending between a first location on the outer wall and a second location on the outer wall, with the first location and the second location having a common chord-wise position;
• a surface length (Lmax) defined by a contour line along the outer wall between the first location and the second location at the common chord-wise position;
• and
• a blade parameter (BP) defined as a ratio of the surface length to the radial length (BP=Lmax/R);
• wherein the engine exhaust gas temperature EGT, the number of blades NB, the number of nozzles NN, the tip radius TR, and the blade parameter BP define a blade tip durability factor (BTDF) by the following expression:
• BTDF
• =
• (
• TR
• EGT
• )
• ×
• (
• NB
• NN
• )
• ×
• BP
• ;
• wherein the blade tip durability factor BTDF is between 0.020-0.033 in/° C., and the blade parameter BP is between 1-1.234.