Numerical evaluation of heat/mass transfer analogy for leading edge showerhead film cooling on a first-stage vane

A numerical study was conducted to evaluate the applicability of the heat/mass transfer analogy to leading edge film cooling on a first-stage vane. A typical showerhead configuration was taken into account, thus including four staggered rows of evenly spaced cylindrical holes, angled at 45° towards the tip. The investigation was carried out at low speed (isentropic exit Mach number of Ma2is = 0.2), inlet turbulence intensity of Tu1 = 1.6% and 13%, and three different blowing ratios (BR = 2.0, 3.0 and 4.0). Steady-state simulations were conceived to mimic the pressure sensitive paint (PSP) technique aiming to measure the adiabatic film cooling effectiveness (η) in the leading edge region, under a density ratio of DR = 1 and 1.5. With the mainstream flow assumed to be air at ambient temperature, the desired DR was obtained by injecting coolant as air at different temperature from the mainstream (namely, heat transfer approach) or as isothermal foreign gas (namely, mass transfer approach). Despite the dominant effect of the DR on η, results indicated that the heat/mass transfer properties of the coolant are to be considered when comparing film cooling performance, at matched BR conditions. At low inlet turbulence intensity, the heat/mass transfer analogy was found to be applicable only to the lowest BR of 2.0. Its validity was extended to the medium BR of 3.0, in case of DR = 1.5, provided that the leading edge is approached by high turbulence intensity flow.