Multi-parameter cross-condition scaling of adiabatic film-cooling effectiveness on a turbine vane

Existing film-cooling scaling studies are mostly based on single-parameter scaling for flat plates and simple hole geometries, which limits their direct applicability to complex vane-passage flows and shaped-hole configurations under gas turbine conditions. Therefore, the present study considers cylindrical holes and 7–7-7 laidback fan-shaped holes at four representative locations on a turbine vane, and employs an experimentally validated CFD approach to investigate the effects of coolant thermophysical properties, momentum ratio (IR), density ratio (DR), and mainstream Reynolds number (Re) on the scaling of adiabatic film-cooling effectiveness. The results show that thermal conductivity and viscosity have minor effects on film-cooling effectiveness, whereas specific heat capacity noticeably affects temperature-based effectiveness (η_t). In contrast, concentration-based effectiveness (η_c) is nearly insensitive to coolant thermophysical properties and serves as a robust similarity metric for scaling engine-condition film-cooling distributions. For flow-parameter matching, IR captures cooling-effectiveness trends and lift-off/reattachment features at low blowing ratio (MR), but its accuracy decreases as MR increases; DR yields the closest agreement with engine-condition η_c distributions, particularly when the coolant film remains attached. Owing to reduced wall-normal momentum and enhanced spanwise spreading, 7–7-7 holes suppress lift-off and show better scaling stability than cylindrical holes. With matched MR and DR, no clear Re self-similar region is identified, and Re mainly affects the intensity of local lift-off/reattachment-related flow-state transitions rather than area-averaged cooling effectiveness. These findings identify the relative roles of coolant properties, hole geometry, and scaling parameters, supporting scaled turbine-vane film-cooling experiments and engine-condition thermal driving-temperature estimation.