Effects of Upstream Step Geometries on the Turbine Endwall Aerothermal Performance With Fan-Shaped Holes

Abstract Due to weaker coolant separation tendency and broader lateral dispersion capability, fan-shaped holes can significantly improve the endwall aerothermal performance at the desirable connection between the combustor lining and the nozzle guide vane (NGV) endwall, compared to cylindrical holes. Nevertheless, the misalignment between the two components, typically represented by the upstream step geometry, is common in realistic gas turbines, which is caused by component assembly errors, material corrosion, and discrepancies in thermal expansion. This study numerically investigated the film cooling benefits with the upstream purge flow from dual-row staggered fan-shaped holes compared to cylindrical holes at design operational conditions (inlet turbulence—Tu = 16%, outlet Mach number—Maex = 0.85, and outlet Reynolds number—Reex = 1.7 × 106). The numerical results were derived by solving steady Reynolds-averaged Navier–Stokes equations with a realizable k–ɛ turbulence model. This research encompassed three aspects: (1) a comparison of the aerothermal performance between cylindrical holes and fan-shaped holes with three coolant mass flow ratios (MFR = 1.5%, 1.9%, and 2.3%) at the baseline cascade; (2) a benefit evaluation of fan-shaped holes at three upstream step configurations (forward-facing step, baseline step, and backward-facing step); (3) a comprehensive analysis of endwall aerothermal performance with fan-shaped at various upstream step heights (HR = −0.16, −0.1, −0.06, 0, 0.06, 0.1, and 0.16). The results indicated that the adoption of fan-shaped holes can significantly enhance endwall film cooling effectiveness for the baseline case under high coolant flowrate (MFR = 2.3%) compared to cylindrical holes, particularly in the regions of the vane leading edge, vane suction and pressure sides, and downstream of the film holes, with an improvement of up to 35%. A reduction in the coolant MFR of fan-shaped holes will significantly compromise its film cooling benefits (with the benefit decreasing to −23.7% at MFR = 1.5% and 2.7% at MFR = 1.9%). Fan-shaped holes exhibit more stable aerodynamic performance compared to cylindrical holes as the coolant MFR varies, showing a minimum mass-averaged total pressure loss coefficient (TPLC) reduction of 0.2% at MFR = 1.9% and a maximum reduction of 1.2% at MFR = 2.3%. Furthermore, the variations in the upstream step configurations will influence the film cooling benefits of the fan-shaped hole. At coolant MFR = 2.3%, the maximum film cooling benefit decreases from 35% to 20% at the forward-facing step case, and from 35% to −80% in the region downstream of the vane passage throat at the backward-facing step case. With a reduction in coolant MFR (1.9%), fan-shaped holes exhibit more pronounced changes in the film cooling benefits range. For the forward-facing step (HR = −0.1), this area increases by 66%, whereas for the backward-facing step (HR = 0.1), it decreases by 75%. Fan-shaped holes exhibit lower mass-averaged TPLC than cylindrical holes across forward-facing (HR = −0.1) and backward-facing (HR = 0.1) step configurations. At MFR = 1.9%, TPLC reductions are 3.2% (forward) and 1.79% (backward), declining to 0.99% and 0.69% respectively at MFR = 2.3%. Regarding the film cooling performance of fan-shaped holes under various upstream step heights, under coolant MFR = 2.3%, the forward-facing step has a slight positive effect on film cooling effectiveness, with the maximum improvement being within 10% for all forward-facing step heights. Nevertheless, the backward-facing step has a negative effect, with film cooling effectiveness reductions of 20% at HR = 0.06, 80% at HR = 0.1, and nearly 100% at HR = 0.16. This suggests that the cooling scheme design of fan-shaped holes can further enhance the endwall film cooling effectiveness and aerodynamic performance robustness, but the inlet pressure of the coolant chamber needs to be augmented. Additionally, the negative effects of geometric deviation between the combustor and the NGV endwall should be taken into account in the cooling scheme design, otherwise, the film cooling benefits will be significantly diminished.