Revisiting Dimensionless Parameters Quantifying Film Cooling

The adiabatic effectiveness of film cooling (eta) has been characterized by the density (DRh) and blowing (BRh) ratios. In this study, dimensional analysis and computations based on Reynolds-averaged Navier-Stokes (RANS) were performed to identify and examine parameters needed to quantify eta, 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-deg inclined circular holes, is fed from a cooling channel whose flow direction 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 eta, where 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. RANS results with and without conjugate heat transfer obtained by varying the mass flowrate in the cooling channel, while keeping DRh and BRh constant (DRh = 1.9 and BRh was either 0.75 or 1.0), show reducing mass flowrate in the cooling channel by one-half, which doubles BRc (from 2.6 to 5.2) to slightly affect the discharge coefficient through the film-cooling holes (<5%) but up to 85% on laterally averaged eta and up to 25% on overall cooling effectiveness. RANS results also show the flow mechanisms induced by BRc that affect eta. The RANS results of this study were validated by comparing with experimental data.