Study on flow and heat transfer characteristics in rectangular channels with lantern-shaped pin fin array: Part II—Global sensitivity analysis and optimization

Abstract

Increasing gas turbine inlet temperatures are placing more stringent requirements on the efficiency of internal cooling. Pin fin arrays are a common tool for cooling electronic components or trailing edge cooling channels of gas turbine blades. A crucial concern for researchers is how to achieve a higher Nusselt number with constrained pressure loss to guarantee that the efficiency of the gas turbine will not be impacted by the power dissipation generated by the driving flow passing through the internal cooling loops. In Part I of this study, a lantern-shaped pin is proposed. To seek a more efficient design solution for the pin fin shape, the second part combines the surrogate model, Sobol’s method, and NSGA-II optimization method to perform the overall and spatial sensitivity analysis and optimization for the shape variables on the generatrix of different pin rows. The first-order and total-order sensitivity indices of different variables to Nu T and f are calculated using the surrogate model-based Sobol’s method. The variables that significantly affect the channel performance are identified. The overall and spatial sensitivity analysis results indicate that the variable X 3 i -1 contributes the most to Nu T and f, with total-order sensitivity indices of 70.59–64.26 and 58.16–59.09%, respectively. The overall optimization increases the Nu T and f by 6.95 and 9.91%, respectively, while the spatial optimization leads to an increase in the Nu T by 2.29% and a decrease in the f by 4.56%. Correspondingly, the two optimizations resulted in an increase in the TPI by 3.61 and 3.89%, respectively. The Pareto front solution obtained by the spatial optimization has a more concentrated distribution. Although the TPI obtained by the spatial optimization is only 0.21% higher than that of the overall optimization, it provides designers with a strategy considering the Nusselt number and pressure loss.