Energy-efficient thermal protection for aero-engine supersonic nozzles by anti-kidney vortices in shaped film cooling systems

Thermal management of aero-engine supersonic convergent–divergent nozzles under extreme flow conditions remains a critical challenge. This study investigates the flow interactions and cooling performance of novel expanding and branching film hole configurations in a two-dimensional supersonic nozzle using Reynolds-Averaged Navier–Stokes and Delayed Detached Eddy Simulation (DDES) methods, and anti-kidney vortices are identified as an effective cooling mechanism. A baseline cylindrical hole is compared against three expanding holes (forward-inclined, fan-shaped, and dust-pan) and three branching holes (backward-bending, forward-bending, and dumbbell) under a low coolant-to-mainstream mass flow ratio of 0.0079%. Results reveal that shock/expansion waves induced by coolant injection exhibit limited propagation due to low secondary flow rates. Branching holes generate anti-kidney vortices that suppress traditional kidney vortex dominance, enhancing cooling effectiveness by up to 28.65% and improving spanwise uniformity by 47.74% compared to cylindrical holes. Expanding holes, particularly the fan-shaped design, increase cooling uniformity by 19.86% but exhibit shorter high-effectiveness regions. Transient DDES analyses highlight coherent vortex structures (e.g., hairpin vortices) and asymmetrical coolant distribution influenced by vortex evolutions. Despite minor reductions in discharge coefficient by 0.12% and thrust coefficient by 0.01%, all configurations introduce negligible aerodynamic losses. This work provides critical insights into vortex-driven cooling mechanisms and establishes design guidelines for high-efficiency supersonic nozzle thermal protection systems.