Revisiting Dimensionless Parameters Quantifying Film Cooling

Effectiveness of film cooling (η) has been characterized by the density (DRh) and blowing (BRh) ratios. In this study, a dimensional analysis and a computational study, based on steady RANS with and without conjugate heat transfer, were performed to identify and examine parameters needed to quantify η, where film cooling is crossflow fed instead of plenum fed. The test problem studied is film cooling of a flat plate, where the cooling air, issuing through 30-degree inclined circular holes, is fed from a cooling channel with a flow direction that is perpendicular to the direction of the hot-gas flow. For this test problem, dimensional analysis shows an additional blowing ratio is needed, denoted as BRc, to quantify η, and BRc is the ratio of the mass flux through the film-cooling hole to the mass flux in the cooling channel upstream of the film-cooling hole. CFD results obtained by varying the mass-flow rate in the cooling channel, while keeping the DRh and BRh constant (DRh = 1.9 and BRh = 0.75 or 1.0), show reducing the mass-flow rate in the cooling channel by one half, which doubles BRc (from 2.6 to 5.2) to slightly affect the discharge coefficient (< 5%) but up to 25% on overall cooling effectiveness and up to 85% on laterally-averaged adiabatic effectiveness. Results are presented that show the flow mechanisms induced by BRc. This computational study was validated by comparing with experimental data generated at the National Energy Technology Laboratory.