Optimal design and decision making of an air cooling channel with hybrid ribs based on RSM and NSGA-II

The channels roughed by ribs have been widely applied in turbine blade internal cooling. A new concept of cooling channels with hybrid ribs (the combination arrangement of rectangular and semicircular ribs) is proposed in this paper. The optimal design and decision making of the new channels are performed to gain the optimal design variables and corresponding heat transfer and flow performance, combining response surface methodology and non-dominated sorting genetic algorithm II. The objective functions (Nu¯/Nu¯s,f¯/f¯s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{{\text{Nu}}}} {/}\overline{{{\text{Nu}}}}_{{\text{s}}} ,\overline{f}/\overline{f}_{{\text{s}}}$$\end{document}, and η) corresponding to the optimized design variables (Re, p/e, e/D) are obtained by a series of numerical simulation calculations. The surrogate models are obtained in quadratic polynomial forms, and then, the analysis of variance is utilized to assess the statistical significance of each term in the surrogate models. Pareto-optimal fronts are obtained by NSGA-II, and the Technique for Order Preference by Similarity to Ideal Situation is used to determine the better Pareto-optimal solution. The results indicate that the quadratic term (p/e)2, linear term Re, and linear term Re are the most significant terms for Nu¯/Nu¯s,f¯/f¯s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{{\text{Nu}}}} {/}\overline{{{\text{Nu}}}}_{{\text{s}}} ,\overline{f}/\overline{f}_{{\text{s}}}$$\end{document}, and η, respectively. That the optimum objective functions are Nu¯/Nu¯s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{{\text{Nu}}}} {/}\overline{{{\text{Nu}}}}_{{\text{s}}}$$\end{document} = 2.07 and f¯/f¯s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{f}/\overline{f}_{{\text{s}}}$$\end{document} = 4.00, corresponding design variables are Re = 20,571, p/e = 11.43, and e/D = 0.051. The optimal design variables along for various Re are also gained, which possesses guiding significance for cooling channels optimization design.