A solution-propagation-based two-scale framework towards high-fidelity, low-computational-cost modelling of film cooling applications

• A solution-propagation-based two-scale framework is proposed to overcome the interface challenges. • The proposed framework is implemented within the open-source suite SU2, offering greater computational efficiency. • A novel boundary treatment is introduced to accurately reproduce coolant ejection in film cooling simulations using the two-scale method. • An application of the two-scale method to a film-cooled blade demonstrates its computational efficiency in a scenario of practical interest. The computational fluid dynamics (CFD) simulation for film cooling applications is a complex multi-scale problem that often requires substantial, if not prohibitive, computational resources. The mesh resolution in the cooling domain must be sufficiently refined to capture the high-gradient flow resulting from the interactions between the coolant and the main flow. To address the length-scale disparity inherent in such applications, a two-scale method has been proposed, demonstrating the potential for high-fidelity, low-computational-cost simulations, particularly in cases involving a large number of cooling holes. This method utilizes the source terms mapped from the fine mesh domain to augment the governing equations in the coarse mesh domain, thereby reproducing the well-resolved solution within the coarse domain. However, the original two-scale method relies on propagated source terms as mapped variables, which can encounter challenges at the interface. In this study, the spatially averaged solutions are propagated from the fine mesh domains to the coarse mesh domains. The source terms are then locally evaluated in the coarse mesh using these mapped solutions. The advantages of propagating solution over propagating source terms are analysed theoretically. The two-scale framework is implemented in the open-source code SU2, which is validated on different flat plate film cooling configurations and extended to the film-cooled high-pressure turbine vane C3X. It is also found that the present method can correctly reproduce the cooling flow injection without cooling holes when appropriate boundary treatment is specified. The relevant results show that the current two-scale method holds significant potential for film cooling applications, offering high fidelity at a substantially lower computational cost.