Block-Spectral Approach to Film-Cooling Modeling

Gas turbine performance improvement requires efficient and accurate prediction tools for film-cooling of high pressure turbine blades. Use of computational fluid dynamics in the cooling design faces a challenge due to a wide range of length scales to be resolved. The difficulty is also seriously compounded by the basic feature that each blade has a large number of cooling holes. In the present paper, a new spectral approach is proposed to address this modeling difficulty. The motivation is to resolve the aerothermal flow field and mixing process of film-cooling by the numerical solution to the first principle based governing equations while avoiding large computational resources required in directly solving a large number of cooling holes. By using a spectral representation for each corresponding mesh point, the block-to-block (hole-to-hole) variation can be accurately and efficiently modeled. The number of mesh blocks (cooling holes) to be solved is then dictated by the number of unknowns required to determine the spectrum. Consequently, the aerothermal field for a large number of cooling hole blocks can be obtained by solving a much smaller set of blocks. The modeling consideration, method formulation, validation, and demonstration results will be presented.