Derivation of 2-D empirical correlations for film-cooling effectiveness and heat transfer augmentation from spanwise averaged data and correlations

In existing gas turbine heat transfer literature, there are several correlations developed for the spanwise-averaged film-cooling effectiveness and heat transfer augmentation for inline injection on flat plates. More accurate and detailed predictions of film-cooling performance, particularly 3-D solid temperatures are needed for design purposes. 2-D correlations where effectiveness and heat transfer augmentation are functions of streamwise and spanwise directions are necessary to satisfy this need. Previously developed 2-D correlations for single row of cylindrical holes with inline injection have been improved to include the effects of shaped holes such as hole breakthrough width (t/D) and area ratio (AR). The correlations are improved to better match spanwise effectiveness of a single row of shaped cooling holes using data and spanwise-averaged correlations. Modifications to the correlations to improve application to compound injection (ß) have been implemented. The blowing ratio is modified to account for the compound angle effect. The spanwise location of maximum film-cooling effectiveness and heat transfer augmentation are obtained as functions of the streamwise coordinate. Iterative Conjugate Heat Transfer Reduced Order Film Model (ICHT-ROFM) was used to obtain 3-D conjugate temperature distribution in film cooled solids. The developed correlations predicted a relative cooling effect in the near hole region for shaped holes (24 K) and for compound angle injection (20K) compared to cylindrical holes. Spanwise variations in the solid temperature in the near hole region are between 40-50K for a temperature difference of 250K between the surface and the main stream and are quite significant, showing the need for 3-D simulations. Shaped and compound angle holes increase this temperature difference due to the increased cooling. The comparisons of solid temperatures for conjugate and non-conjugate heat transfer cases show about 13-18K or 8-10% of the local temperature difference of 180K. Therefore it can be concluded that the calculations of 3-D temperature distributions using conjugate heat transfer are very important for design purposes.