Revisiting Dimensionless Parameters Quantifying Film Cooling

The adiabatic effectiveness of film cooling (η) has been characterized by the density (DR_h) and blowing (BR_h) 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 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-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 BR_c, to quantify η, where BR_c 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 DR_h and BR_h constant (DR_h = 1.9 and BR_h was either 0.75 or 1.0), show reducing mass flowrate in the cooling channel by one-half, which doubles BR_c (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 η and up to 25% on overall cooling effectiveness. RANS results also show the flow mechanisms induced by BR_c that affect η. The RANS results of this study were validated by comparing with experimental data.