What is the most commonly used method for cooling and relieving thermal stresses on a turbine?

The method of using bleed air from the high-pressure compressor for cooling and relieving thermal stresses on a turbine is favored for several reasons. Bleed air is taken from the compressor stage of the engine, which operates at relatively high pressures and temperatures, and this air can be used effectively to cool the turbine components.

Utilizing bleed air allows for controlled thermal management as it enables the engine to regulate the temperature of critical components like the turbine blades. This process helps to prevent excessive thermal gradients that can induce mechanical stresses, thus prolonging the life of the turbine materials and enhancing operational reliability.

In comparison, direct water injection is less common because it can complicate the engine's operation and affect combustion characteristics. Radiator cooling systems, while effective in other applications, are typically not practical for turbine engines due to their design and operational requirements. Low-pressure air ducts do not provide the same level of cooling effectiveness or control as bleed air from the high-pressure compressor.

Therefore, the use of bleed air is a well-established method to ensure efficient cooling while minimizing stresses, essential for maintaining the performance and integrity of turbine engines.