Nonlinear superposition of double-row film cooling effectiveness. I. Theoretical analysis

Full-coverage film cooling is commonly adopted in gas turbines to guarantee operating reliability. Due to the row-to-row dynamic interactions, nonnegligible errors are observed when using the linear Sellers model for multi-row cooling effectiveness predictions. The main target of Paper I of this two-part paper is to reveal the underlying nonlinear interaction mechanisms. In the current study, a decomposition theory is proposed and validated both experimentally and numerically. The multi-row cooling effectiveness can be divided into parts contributed by individually rows. In this way, the error source can be tracked separately. The cooling performance of double-row configurations arranged in four pitchwise spacings is analyzed. It is revealed that the vortical interaction between kidney vortices from adjacent rows plays the most important role by determining intensified or weakened vortical entrainment. It is found that the error distribution along the row centerline is much lower than the averaged error over the two-dimensional superposition domain. The conclusions provide solid guidance for the development of a novel nonlinear superposition method in Paper II.