Quantitative evaluation methodology for aerodynamic periodicity in variable geometry turbine sector cascades

• The periodicity of the blade passage of variable geometry turbine adjustable guide vane sector cascade is analyzed. • The periodic seven-dimensional evaluation index of the adjustable guide vane sector cascade blade passages is established. • The adjustable guide vane sector cascade of 9 blades is determined to ensure the optimal number of blades for two periodic blade channels. Given the current lack of quantitative metrics for the periodicity analysis of the flow field in variable-geometric turbine sector cascades, this study proposes a method for evaluating the flow field periodicity to enhance the consistency of blade passage periodicity and ensure the reliability of experimental research. In this paper, the influence of the number of blade passages on the periodicity of the flow field of the variable geometry turbine adjustable nozzle guide vane. Sector cascade is studied by the numerical simulation method verified by experiments. The periodicity distribution of outlet flow angles, endwall static pressure, total pressure loss coefficients, mass flow rate, Mach number and vane static torque at various locations is analyzed. A seven-dimensional evaluation metric for blade passage periodicity is established, aimed at determining the minimum number of blade passages necessary to satisfy different experimental conditions and requirements. The results indicate that under a periodicity criterion where the maximum and average relative errors of the outlet flow angle (measured at 10 %, 50 % and 90 % blade spans) are less than 0.30 % and 0.20 %, respectively, an 8 blade passages ensures periodicity for 2 blade passages, while a 10 blade passages achieves it for 3. When the number of blade passages increases to eight, the fifth and sixth passages exhibit the best periodicity, with the average relative errors of the seven periodicity parameters being below 0.50 %, and the standard deviation being below 0.80 %. Further increasing the number of passages results in a slower reduction of periodicity error, with eight blade passages being the optimal number to ensure the periodicity of two measurable blade passages.