Kinematic Optimization of Energy Extraction Efficiency for Flapping Airfoil by using Response Surface Method and Genetic Algorithm

Document Type : Regular Article


1 Aeronautics and Propulsive Systems Laboratory, Faculty of Mechanical Engineering, Department of Mechanics, University of Sciences and Technology of Oran Mohamed Boudiaf, BP. 1505 Oran El M'Naouer, 31000 Oran, Algeria

2 LMF, Ecole Militaire Polytechnique (EMP), B.P 17 Bordj-el-Bahri, 16111, Algiers, Algeria

3 IUSTI Laboratory, UMR 7343 CNRS-University of Aix-Marseille Technopole de Chateau-Gombert, 5 rue Enrico Fermi 13453 MARSEILLE, Cedex 13, France



In this paper, numerical simulations have been performed to study the performance of a single fully activated flapping wing serving as energy harvester. The aims of the paper are predicting and maximizing the energy extraction efficiency by using optimization methodology. The metamodeling and the genetic algorithms are applied in order to find the optimal configuration improving the efficiency. A response surface method (RSM) based on Box–Behnken experimental design and genetic algorithm has been chosen to solve this problem. Three optimization factors have been manipulated, i.e. the dimensionless heaving amplitude h0, the pitching amplitude θ0 and the flapping frequency f. The ANSYS FLUENT 14 commercial software has been used to compute the governing flow equations at a Reynolds number of 1100, while the flapping movement combined from heaving and pitching of the NACA0015 foil has been carried out by using an in house user-defined function (UDF). A maximum predicted efficiency of 34.02% has been obtained with high accuracy of optimal kinematic factors of dimensionless heaving amplitude around the chord, high pitching amplitude and low flapping frequency of 0.304 hertz. Results have also showed that the interaction effect between optimization factors is important and the quadratic effect of the frequency is strong confirming the great potential of the applied optimization methodology.


Anderson, J. M., K. Streitlien, D. S. Barrett and M. S. Triantafyllou (1998). Oscillating foils of high propulsive efficiency. Journal of Fluid Mechanics 360, 41-72.##
Betiku, E., V. O. Odude, N. B. Ishola, A. Bamimore, A. S. Osunleke and A. A. Okeleye (2016). Predictive capability evaluation of RSM, ANFIS and ANN : A case of reduction of high free fatty acid of palm kernel oil via esterification process. Energy Conversion and Management 124, 219-230.##
Boudis, A., H. Oualli, A. Benzaoui, O. Guerri, A. C. Bayeul-Lainé and O. Coutier-Delgosha (2021). Effects of non-sinusoidal motion and effective angle of attack on energy extraction performance of a fully activated flapping foil. Journal of Applied Fluid Mechanics 14(2), 485-498.##
Box, G. E. P. and D. W. Behnken (1960). Some new three level desing for study of quantitative variables box. Technometrics 2(4), 455-475.##
Dharma, S. M. H. H., H. H. Masjuki, H. C. Ong, A. H. Sebayang, A. S. Silitonga, F. Kusumo and T. M. I. Mahlia (2016). Optimization of biodiesel production process for mixed Jatropha curcas – Ceiba pentandra biodiesel using response surface methodology. Energy Conversion and Management 115,178-190.##
Goldberg, D. E. (2000). The Design of Innovation: Lessons from and for Competent Genetic Algorithms. Technological Forecasting & Social Change 64(1), 7-12.##
Haftka, R. T. (1996). Response surface approximations for structural optimization W. J. Roux AIAA, NASA, and ISSMO. In Symposium on Multidisciplinary Analysis and Optimization.##
Holland, J. H. (1992). Genetic Algorithms. Scientific American. 267(1), 66-73.##
Ji, T., F. Jin, F. Xie, H. Zheng, X. Zhang and Y. Zheng (2022). Active learning of tandem flapping wings at optimizing propulsion performance. Physics of Fluids 34, 047117.##
Kinsey, T. and G. Dumas (2008). Parametric study of an oscillating airfoil in a power-extraction regime. AIAA Journal 46(6), 1318-1330.##
Li, Y., T. Liu, Y. Wang and Y. Xie (2022). Deep learning based real-time energy extraction system modeling for flapping foil. Energy 246, 123390.##
Liu, Z., K. S. Bhattacharjee, F. Tian, J. Young, T. Ray and J. C. S. Lai (2018). Kinematic optimization of a flapping foil power generator using a multi-fidelity evolutionary algorithm. Renewable Energy 132, 543-557.##
Ma, P., Y. Wang, Y. Xie and J. Zhang (2018). Analysis of a hydraulic coupling system for dual oscillating foils with a parallel configuration. Energy 143, 273–283.##
McKinney, W. and J. DeLaurier (1980). Wingmill: an oscillating-wing windmill. J. Energy 5(2), 109-115.##
Myers, R. H., D. C. Montgomery, G. Geoffrey Vining, C. M. Borror and S. M. Kowalski (2004). Response surface methodology: a retrospective and literature survey. Journal of Quality Technology 36(1), 53-78.##
Park, H. S. and X. P. Dang (2010). Structural optimization based on CADCAE integration and metamodeling techniques. Computer-Aided Design 42(10), 889-902.##
Platzer, M. F., M. A Ashraf, J. Young and J. Lai (January 2009). Development of a New Oscillating-Wing Wind and Hydropower Generator, AIAA -1211. 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition.##
Shukla, L. and A. Nishkam (2014). Performance optimization, prediction, and adequacy by response surfaces methodology with allusion to drf technic. International Scholarly Research Notices Text 1-12.##
Xiao, Q., W. Liao, S. Yang and Y. Peng (2012). How motion trajectory affects energy extraction performance of a biomimic energy generator with an oscillating foil. Renew Energy 37(1), 61-75.##
Xu, B., Q. Ma and D Huang (2021). Research on energy harvesting properties of a diffuser-augmented flapping wing. Renew. Energy 180, 271-280.##
Zheng, H., F. Xie, T. Ji, Z. Zhu and Y. Zheng (2020a). Multifidelity kinematic parameter optimization of a flapping airfoil. Physical Review E 101, 013107.##
Zheng, H., F. Xie, T. Ji and Y. Zheng (2020b). Kinematic parameter optimization of a flapping ellipsoid wing based on the datainformed self-adaptive quasi-steady model. Physics of Fluids 32, 041904.##
Zhu, B. (2019). Energy extraction properties of a flapping wing with an arc-deformable airfoil. Journal of Renewable Sustainable Energy 11, 023302.##
Zhu, B., Y. Huang and Y. Zhang (2018). Energy harvesting properties of a flapping wing with an adaptive Gurney flap. Energy 152, 119-128.##
Zhu, J. and T. Tian (2017). The time asymmetric pitching effects on the energy extraction performance of a semi-active flapping wing power generator. European Journal of Mechanics -B/Fluids 66, 92-101.##