Nonlinear superposition of double-row film cooling effectiveness. II. Analytical model and prediction

In the modern gas turbine film cooling design scheme, the classic linear Sellers model is commonly adopted for multi-row effectiveness predictions. However, the prediction accuracy can hardly satisfy the demand in the layout design of the full coverage film cooling. The main target of Part II of this two-part paper is to develop a superposition method considering the nonlinear effect of the row-to-row interaction based on the conclusions in Part I. Lateral distributions of the cooling effectiveness are modeled using the scalar transport equation, where effects of the vortical entrainment and the turbulent diffusion are included. The row-to-row vortical interaction is quantified by superposing the induced velocity by kidney vortices of injections from adjacent rows. Then, the two-dimensional (2D) multi-row effectiveness can be obtained based on the assumption that the partial effectiveness distributions along the row centerline obeys the linear superposition relation. The currently proposed nonlinear superposition method is proved to be simple, accurate, and efficient, well satisfying the industrial demand in full-coverage film cooling design. No extra model parameter is needed when extending the 2D model from the single-row film cooling to the multi-row. The averaged relative prediction error is reduced to 7.18%, almost on the same level as the experimental uncertainty. The prediction accuracy is insensitive to changes in the blowing ratio and the main-flow turbulence intensity, with the maximum error smaller than 13% compared with over 27% of the 2D Sellers model. The time consumption of a double-row effectiveness distribution calculation is on the magnitude of 0.1 s.