Performance analysis of three heuristic algorithms for airfoil design optimization

ABSTRACT

The airfoil design optimizations are often limited due to the high computational cost and complex algorithm selections. However, such computational requirement has not been fulfilled well because some major unpaired performances exist between the mathematical benchmarks and airfoil designs. In this study, we compared three heuristic optimization algorithms: hill-climbing algorithm (HC), simulated annealing algorithm (SA), and genetic algorithm (GA), using three test functions in the airfoil design optimization of the wind turbines. The results show that with functions representing relatively flat shape, the HC and the SA are faster to find the global optimum than the GA. Tested with multimodal functions such as Shubert function, however, it is found that the HC and SA failed to find the global optimum although the SA has better possibilities to jump out the local extremum than the HC. For the airfoil optimization of S809 and NACA64418, it is found that the SA is more efficient than the GA. After the optimization, the S809 airfoil noise is decreased more than 0.9 dB, and the lift-drag ratio is improved 6.96% compared to its baseline in the given working condition. Similarly, the performance of NACA64418 is also improved with the proposed optimization algorithms. However, when the computational cost is taken into account, the performance of the three widely used algorithms is different from that in the benchmark tests. Therefore, our findings provide important insights of the airfoil design optimization of wind turbines on how to select algorithms and trade-off between computational cost and efficiency.

KEYWORDS:

• Airfoil optimization
• heuristic algorithms
• airfoil design
• aerodynamic shape design

Acknowledgments

The authors would like to thank Globalink Research Internship of Mathematics of Information Technology and Complex Systems (MITACS) and China Scholarship Council (CSC) for the support. The data that support the findings of this study are openly available in [http://airfoiltools.com/airfoil/details?airfoil=naca643418-il], reference number [NACA64418] and in [http://airfoiltools.com/airfoil/details?airfoil=s809-nr], reference number [S809 Airfoil]

Additional information

Funding

This work was supported by the Mitacs [Globalink Research Internship].