A numerical study has been conducted to investigate the effects of surface curvature on cooling effectiveness using three-dimensional film cooling geometries that included the mainflow, injection hole, and supply plenum regions. Three surfaces were considered in this study, namely, convex, concave, and flat surfaces. The fully elliptic, three-dimensional Navier–Stokes equations were solved over a body-fitted grid. The effects of streamline curvature were taken into account by using algebraic relations for the turbulent viscosity and the turbulent Prandtl number in a modified k–ε turbulence model. Computations were performed for blowing ratios of 0.5, 1.0, and 1.5 at a density ratio of 2.0. The computed and experimental cooling effectiveness results were compared. For the most part, the cooling effectiveness was predicted quite well. A comparison of the cooling performances over the three surfaces reveals that the effect of streamline curvature on cooling effectiveness is very significant. For the low blowing ratios considered, the convex surface resulted in a higher cooling effectiveness than both the flat and concave surfaces. The flow structures over the three surfaces also exhibited important differences. On the concave surface, the flow involved a stronger vorticity and greater mixing of the coolant jet with the mainstream gases. On the convex surface, the counterrotating vortices were suppressed and the coolant jet pressed to the surface by a strong cross-stream pressure gradient.
Numerical Study of a Vortex Ring Interacting with a Three-dimensional Convex Surface