The Effectiveness of Film Cooling of a Flat Surface in an Accelerated Flow with Air Injection Through Fan-Shaped Holes

In an accelerating flow, the effectiveness of film cooling by injecting air through cylindrical holes at the initial mixing section increases in comparison with a zero-pressure-gradient flow. This is caused by a decrease in the separation of the air jets injected through the holes from the cooled wall. With distance from the injection section, the cooling effectiveness of coolant injection through cylindrical holes decreases in comparison with a zero-pressure-gradient flow. The cause is the enhancement of rotation of large-scale paired vortex structures called kidney vortices. Comparative experimental studies into the effectiveness of film cooling with air injection through fan-shaped or cylindrical holes in an accelerating flow have demonstrated that different mechanisms of interaction between the secondary and main flows exist in the entrance and main mixing sections in both cases. In the performed experiments, single-row belts of both types of holes had five holes in a row. A dimensionless complex of film-cooling effectiveness in an accelerating flow was used for a comparative analysis of the relative film-cooling effectiveness on a flat surface with injection through fan-shaped and cylindrical holes. At angles of secondary air injection into the main flow of α = 30°, 45°, and 75°, the acceleration of the main flow has a different effect on the relative value of the film-cooling effectiveness for a flat surface, \({{\bar {\bar {\eta }}}}\), with injection through fan-shaped or cylindrical holes at the best (m = 0.5) or high (m = 2.5) blowing ratio. Thus, for m = 0.5, the value of \({{\bar {\bar {\eta }}}}\) in the entrance mixing section at α = 30° is 0.3, but the cooling effectiveness is hardly affected by it when α = 45° and 75°. For m = 2.5, the values of \({{\bar {\bar {\eta }}}}\) at α = 30°, 45°, and 75° are, respectively, 1.35, 1.15, and 2.15. In the main mixing section, for m = 0.5, the value of \({{\bar {\bar {\eta }}}}\) increases (1.0, 1.15, and 1.6) when the injection angle increases; for m = 2.5, it decreases in comparison to the zero-pressure-gradient value from 1.6 at α = 30° to 0.72–0.82 at α = 45° and 75°.