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• A multi-parameter optimization method is developed based on the simplified conjugate-gradient algorithm. • Heights of perturbation ribs in turbine blade internal cooling are optimized at various conditions. • All of the optimal designs possess a hierarchically nonuniform characteristic. • The design direction is provided for perturbation elements involving turbulent flow heat transfer. Owing to the limited cold-air amount and pressure in supply systems, high-efficient heat transfer with low-level friction loss is highly desired for cooling units of a turbine blade. To exploit the potential improvement of hierarchically arranged ribs in cooling passages proposed previously, multi-parameter optimizations for rib arrangements are implemented by integrating the simplified conjugate-gradient algorithm with the turbulent flow and heat transfer model. Rib heights as design variables are optimized with various performance indices as objective functions at a fixed Re. The optimizations confirm that using the wall temperature difference and Nu as the objective function, respectively, a limited heat transfer improvement is achieved with a greatly increased friction loss. Taking the overall performance factor as the objective function, different optimal designs at different constraint conditions possess hierarchical characteristics. A significant friction loss reduction of 52.1%, 54.7%, and 54.8%, is achieved with a moderate heat transfer loss of 10.9%, 7.0%, and 2.3%. Despite different thermal and friction performances, their overall performances are consistent with a remarkable increase of 13.9%, 21.2%, and 27.3%. Finally, the optimization strategy coupling the multi-parameter optimization and hierarchical scheme is confirmed as effective for enhancing the thermohydraulic performance of convective heat transfer systems with perturbation elements. [ABSTRACT FROM AUTHOR]

• A novel hierarchical scheme of rib arrangements is proposed for turbine blade internal cooling. • Various representative rib configurations are considered to implement the hierarchical scheme. • The improvement achieves greatly-reduced friction loss and low-level heat transfer deterioration. • Heat transfer details and turbulent flow structures are analyzed to reveal the underlying physics. • The feasibility and generality of the hierarchical scheme are verified comprehensively. Turbulators, such as ribs, dimples, and pin-fins, play a vital role in the internal cooling efficiency of turbine blades. As a typical turbulator, various rib configurations using a uniform arrangement scheme have indicated high heat transfer enhancement but the friction loss is simultaneously subject to a great increase. In this work, a novel hierarchical arrangement scheme of ribs is developed aiming to improve the cooling efficiency. Adopting the uniform scheme as a baseline, the hierarchical scheme is implemented for six representative rib configurations (including transverse ribs, angled ribs, V-shaped ribs, inverted V-shaped ribs, M-shaped ribs, and inverted M-shaped ribs) and evaluated for its feasibility and generality. For different cooling designs, turbulent flow and heat transfer of the ribbed cooling channel are studied by three-dimensional numerical simulations based on the finite volume method with a constructed turbulence model. It is found that for all rib configurations, the hierarchical scheme can remarkably reduce the friction loss as desired, especially for the inverted V-shaped rib with a reduction of up to 50%. Due to the occurrence of flow separation, secondary flows offered by transverse ribs are characterized by a two-dimensional recirculation vortex behind the rib. For other rib configurations, secondary flows present a typical three-dimensional characteristic including the downwash flows along the inclined rib leg and the longitudinal vortices. The usage of the hierarchical scheme with small ribs strongly suppresses these secondary flows, which contributes to the significant decrease in form drag loss. Meanwhile, using the hierarchical scheme produces a slight heat transfer deterioration commonly, which is because the constrained secondary vortices weaken the turbulent mixing and convection heat transfer. Significantly, for the two W-shaped ribs, the limited secondary vortices but fully developed under the hierarchical scheme achieve a higher heat transfer enhancement. Finally, for all considered ribs, the hierarchical scheme can improve the overall performance factor of (Nu / Nu 0)/(f / f 0)1/3 by more than 10%, and up to 21.15% for the V-shaped rib. Adjusting design variables, including the decreasing ratio of the rib size and the initial rib size, the hierarchical scheme still provides even higher performance enhancement. [ABSTRACT FROM AUTHOR]