The vortex-driven heat transfer coefficient of the inner surface of the inclined cylindrical holes under the influence of the length-to-diameter ratio

As a critical element of active cooling technology, the internal flow within film holes exhibits three-dimensional flow characteristics due to factors such as geometric configuration, wall effects, shear forces, velocity gradients, and pressure gradients. These complex flow behaviors significantly influence the distribution of the Nusselt number. In this study, thermochromic liquid crystal experiments were conducted to investigate the internal heat transfer characteristics of film holes, while numerical simulations were used to analyze the internal flow structures. The effects of Reynolds number, length-to-diameter ratio, and hole inclination angle were systematically explored, and incorporated as correction factors into conventional internal heat transfer correlations. The results indicated that the internal flow is dominated by a complex three-dimensional vortex system consisting of inlet separation vortices, shear layer vortices, and secondary counter-rotating vortices. Driven by these vortices, the streamwise Nusselt number distribution exhibits a rise-and-fall trend, with the peak appearing in the 0-1D entrance region, where the Nusselt number is approximately three times higher than in the fully developed region. Increasing the length-to-diameter ratio does not change the overall Nusselt number distribution pattern but enhances the extent of flow development, with full development occurring after about 5D. In contrast, variations in hole inclination angle introduce varying degrees of inlet effects.