Bionic crescent-shaped dune structure regulating turbine endwall film cooling: dynamic similarity and vortex inversion control mechanism based on Strouhal number

The key challenge faced by turbine endwall film cooling is that cooling jets are prone to detach from the wall surface induced by the mainstream kidney vortex pairs, resulting in uneven coverage and low effectiveness. Traditional bionic cooling studies are mostly limited to geometric shape imitation, lacking theoretical basis for establishing similarity correlations between natural organisms and engineering environments from the perspective of flow field dynamics. Breaking through the traditional method of geometric similarity, this paper introduces the Strouhal number ( St ) as the dynamic similarity criterion, and establishes for the first time the vortex shedding frequency matching relationship between natural crescent-shaped dunes and the high-speed flow field of turbine endwalls, providing a rigorous mathematical and physical foundation for the unsteady flow control of bionic structures. On this basis, a coupled theoretical model of vortex dynamics and thermal performance with the St number as the core is constructed. The overall cooling effectiveness is decomposed into the product of jet intrinsic effectiveness and adhesion effectiveness, revealing the time-scale competition mechanism between vortex shedding and lateral diffusion. A combined method of experiment and numerical simulation was employed to systematically investigate the cooling performance of different dune configurations in the turbine cascade environment. The results show that the streamwise-distributed crescent-shaped dune configuration achieved an overall cooling effectiveness 10.2% higher than that of the base model under the typical operating condition with a mass flow ratio of 2.33%. Flow field spectral analysis confirms that the vortex shedding frequency induced by this structure corresponds to St = 0.238, which is highly consistent with the dynamic characteristics of natural dunes, verifying the effectiveness of the “frequency locking” strategy from the mechanism level. The dynamic similarity design method based on the Strouhal number proposed in this paper provides theoretical support and quantitative tools for the transformation of bionic cooling structures from “shape imitation” to “dynamic mapping”.