Film hole arrangement criterions along coupled temperature gradient based on the superellipse

Abstract

An optimization criteria for film hole arrangements based on superellipse theory was established. And these criteria was evaluated using conjugate heat transfer computational methods. The temperature field and flow field structure of the endwall was analyzed, and the patterns of enhanced cooling and reduced heat transfer associated with optimized film hole configurations was clarified. This criterion employs superellipse curves to define the temperature gradients between rows of film holes. And according to the distribution of the temperature field, the design of the film hole arrangement is obtained by changing the hyperelliptic parameters. Arranging film holes along a gradually expanding temperature gradient reduces the temperature difference between the upstream and downstream sections of the endwall, diminishes the intensity of channel vortices, and suppresses the cross-migration of cooling jets. And transforms continuous vorticity into discrete vorticity. Informed by superellipse theory, the optimization criterion regulates the distribution of cooling air, resulting in a more uniform cooling film while minimizing shear between the cooling jet and the mainstream, thereby reducing mixing. In terms of momentum, this optimization criteria modifies the near-wall boundary layer, alters disturbances across different regions, and adjusts the distribution of heat transfer coefficients on the endwall surface, ultimately reducing heat transfer. From an energy perspective, it mitigates the interference and mixing of upstream and downstream cooling jets, addresses severe pressure fluctuations within the coolant chamber, and alleviates uneven outflow from film holes, thereby resulting energy losses. Overall, the optimal arrangement criterion provides a methodological basis for solving the problem that the layout design of turbine endwall film holes mainly relies on experience and lacks the guidance of design criteria.