Development of a numerical correlation for the discharge coefficient of round inclined holes with low crossflow

The estimation of the discharge coefficient is of paramount importance in gas turbine design as this parameter affects the actual mass flow rate through secondary air and cooling systems. The lack of confidence in the estimation of its value may entail a reduction in the engine performance as well as lifespan. The scope of this work is therefore still an object of study in the scientific community, mostly due to the complexity and the variety of phenomena involved. In an effort to provide a general characterization of the aerodynamic losses across round orifices, an extended numerical campaign was carried out to develop a correlation for the discharge coefficient. The investigation was focused on round, inclined holes at isothermal conditions, with limited crossflow on both mainstream and coolant sides. Exploiting CFD simulations validated against a literature test case, a Design of Experiments (DoE) was performed to assess the influence of length-to-diameter ratio (L/d), inclination angle with respect to the crossflow direction (α) and pressure ratio (β ). The large amount of data obtained were then correlated in order to provide an expression capable of predicting the discharge coefficient. The correlation is valid for round holes (α=20°−90°, L/d=1−10, β=1.01−2.0) with low crossflow on both mainstream and coolant sides (Mam=Mac=0.02). allowing to reproduce the CFD data set with a mean absolute error of 3.44% and a standard deviation of 1.81%.