{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T12:39:15Z","timestamp":1773837555701,"version":"3.50.1"},"reference-count":52,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2018,4,25]],"date-time":"2018-04-25T00:00:00Z","timestamp":1524614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The purpose of this study is the development of an automated two-dimensional airfoil shape optimization procedure for small horizontal axis wind turbines (HAWT), with an emphasis on high thrust and aerodynamically stable performance. The procedure combines the Computational Fluid Dynamics (CFD) analysis with the Response Surface Methodology (RSM), the Biobjective Mesh Adaptive Direct Search (BiMADS) optimization algorithm and an automatic geometry and mesh generation tool. In CFD analysis, a Reynolds Averaged Numerical Simulation (RANS) is applied in combination with a two-equation turbulence model. For describing the system behaviour under alternating wind conditions, a number of CFD 2D-RANS-Simulations with varying Reynolds numbers and wind angles are performed. The number of cases is reduced by the use of RSM. In the analysis, an emphasis is placed upon the role of the blade-to-blade interaction. The average and the standard deviation of the thrust are optimized by a derivative-free optimization algorithm to define a Pareto optimal set, using the BiMADS algorithm. The results show that improvements in the performance can be achieved by modifications of the blade shape and the present procedure can be used as an effective tool for blade shape optimization.<\/jats:p>","DOI":"10.3390\/computation6020034","type":"journal-article","created":{"date-parts":[[2018,4,25]],"date-time":"2018-04-25T11:15:39Z","timestamp":1524654939000},"page":"34","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Aerodynamic Optimization of Airfoil Profiles for Small Horizontal Axis Wind Turbines"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8642-2225","authenticated-orcid":false,"given":"Ali Cemal","family":"Benim","sequence":"first","affiliation":[{"name":"Center of Flow Simulation (CFS), Department of Mechanical and Process Engineering, D\u00fcsseldorf University of Applied Sciences, M\u00fcnsterstr. 156, D-40476 Germany"},{"name":"Institute of Thermal Power Engineering, Department of Mechanical Engineering, Cracow University of Technology, Al. Jana Paw\u0142a II 37, 31-864 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1325-8559","authenticated-orcid":false,"given":"Michael","family":"Diederich","sequence":"additional","affiliation":[{"name":"Center of Flow Simulation (CFS), Department of Mechanical and Process Engineering, D\u00fcsseldorf University of Applied Sciences, M\u00fcnsterstr. 156, D-40476 Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bj\u00f6rn","family":"Pfeiffelmann","sequence":"additional","affiliation":[{"name":"Center of Flow Simulation (CFS), Department of Mechanical and Process Engineering, D\u00fcsseldorf University of Applied Sciences, M\u00fcnsterstr. 156, D-40476 Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hau, E. (2013). Wind Turbines, Springer.","DOI":"10.1007\/978-3-642-27151-9"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Oyama, A., Liou, M.-S., and Obayashi, S. (2002, January 4\u20136). Transonic axial-flow blade shape optimization using evolutionary algorithm and three-dimensional Navier-Stokes solver. Proceedings of the 9th AIAA\/ISSMO Symposium on Multidisciplinary Analysis and Optimization (AIAA 2002-5642), Atlanta, GA, USA.","DOI":"10.2514\/6.2002-5642"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"012025","DOI":"10.1088\/1755-1315\/22\/1\/012025","article-title":"Multi-objective shape optimization of runner blade for Kaplan turbine","volume":"22","author":"Semenova","year":"2014","journal-title":"IOP Conf. Ser. Earth Environ. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1279","DOI":"10.1016\/j.renene.2008.09.017","article-title":"Optimal angle of attack for untwisted blade wind turbine","volume":"34","author":"Thumthae","year":"2009","journal-title":"Renew. Energy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.jmatprotec.2005.06.055","article-title":"Optimisation of wind turbine blades","volume":"167","author":"Jureczko","year":"2005","journal-title":"J. Mater. Process. Technol."},{"key":"ref_6","unstructured":"Mendez, J., and Greiner, D. (2006, January 12\u201315). Wind blade chord and twist angle optimization by using genetic algorithms. Proceedings of the 5th Conference on Engineering Computational Technology, Las Palmas de Gran Canaria, Spain."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Burger, C., and Hartfield, R. (2006, January 26\u201329). Wind turbine airfoil performance optimization using the vortex lattice method and a genetic algorithm. Proceedings of the 4th AIAA Energy Conversion Conference, San Diego, CA, USA.","DOI":"10.2514\/6.2006-4051"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"012017","DOI":"10.1088\/1742-6596\/75\/1\/012017","article-title":"Further dual purpose evolutionary optimization of small wind turbine blades","volume":"75","author":"Wood","year":"2007","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/s11465-007-0084-9","article-title":"Optimization model for rotor blades of horizontal axis wind turbines","volume":"2","author":"Liu","year":"2007","journal-title":"Front. Mech. Eng. China"},{"key":"ref_10","unstructured":"(2018, April 12). XFOIL Subsonic Airfoil Development System. Available online: http:\/\/web.mit.edu\/drela\/Public\/web\/xfoil\/."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Kenway, G., and Martins, J.R.R.A. (2008, January 10\u201312). Aerostructural shape optimization of wind turbine blades considering site-specific winds. Proceedings of the AIAA\/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, BC, Canada.","DOI":"10.2514\/6.2008-6025"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1002\/we.335","article-title":"Shape optimization of wind turbine blades","volume":"12","author":"Xudong","year":"2009","journal-title":"Wind Energy"},{"key":"ref_13","unstructured":"Ceyhan, O., Sezer-Uzol, N., and Tuncer, I. (2009, January 17\u201319). Optimization of horizontal axis wind turbines by using BEM theory and genetic algorithm. Proceedings of the 5th Ankara International Aerospace Conference, METU, Ankara, Turkey."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1243\/09576509JPE888","article-title":"Aerodynamic optimization of wind turbine airfoils using response surface techniques","volume":"224","author":"Li","year":"2010","journal-title":"Proc. Inst. Mech. Eng. Part A J. Power Energy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1007\/s11665-010-9596-2","article-title":"Multidisciplinary design optimization for glass-fibre epoxy-matrix composite 5 MW horizontal-axis wind-turbine blades","volume":"19","author":"Grujicic","year":"2010","journal-title":"J. Mater. Eng. Perform."},{"key":"ref_16","unstructured":"Bottasso, C., Campagnolo, F., and Croce, A. (2010). Computational Procedures for the Multidisciplinary Constrained Optimization of Wind Turbines, Scientific Report DIA-SR; Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.1016\/j.energy.2009.11.015","article-title":"Optimization of wind turbine energy and power factor with an evolutionary computation algorithm","volume":"35","author":"Kusiak","year":"2010","journal-title":"Energy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.proeng.2011.08.1097","article-title":"Optimization design, modeling and dynamic analysis for composite wind turbine blade","volume":"16","author":"Song","year":"2011","journal-title":"Procedia Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1007\/s10483-011-1453-x","article-title":"Improved non-dominated sorting genetic algorithm (NSGA)-II in multi-objective optimization studies of wind turbine blades","volume":"32","author":"Wang","year":"2011","journal-title":"Appl. Math. Mech. Engl. Ed."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Grasso, F. (2012, January 23\u201326). Hybrid optimization for wind turbine thick airfoils. Proceedings of the 53rd AIAAJASME\/ASCE\/AHS\/ASC Structures, Structural Dynamics and Materials Conference, Honolulu, HI, USA. AIAA Paper AIAA-2012.","DOI":"10.2514\/6.2012-1354"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"622","DOI":"10.2514\/1.C031614","article-title":"Optimization of flatback airfoils for wind-turbine blades using a genetic algorithm","volume":"49","author":"Chen","year":"2012","journal-title":"J. Aircr."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4898","DOI":"10.1016\/j.apm.2011.12.026","article-title":"An airfoil optimization technique for wind turbines","volume":"36","author":"Ribeiro","year":"2012","journal-title":"Appl. Math. Model."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1007\/s12206-011-1106-4","article-title":"Design optimization of a wind turbine blade to reduce the fluctuating unsteady aerodynamic load in turbulent wind","volume":"26","author":"Jeong","year":"2012","journal-title":"J. Mech. Sci. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1177\/0957650911426540","article-title":"Multi-point robust design optimization of wind turbine airfoil under geometric uncertainty","volume":"226","author":"Ju","year":"2012","journal-title":"Proc. Inst. Mech. Eng. Part A J. Power Energy"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.renene.2011.08.011","article-title":"Blade layers optimization of wind turbines using FAST and improved PSO algorithm","volume":"42","author":"Liao","year":"2012","journal-title":"Renew. Energy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.proeng.2013.07.088","article-title":"Aerodynamic shape optimization of wind turbine blades using a parallel genetic algorithm","volume":"61","author":"Polat","year":"2013","journal-title":"Procedia Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1080\/0305215X.2014.941532","article-title":"A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization","volume":"47","author":"Sessarego","year":"2015","journal-title":"Eng. Optim."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1016\/j.energy.2015.06.062","article-title":"Multi-objective optimization of wind turbine blades using lifting surface method","volume":"90","author":"Shen","year":"2015","journal-title":"Energy"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2035","DOI":"10.1016\/j.aej.2016.07.008","article-title":"Aerodynamic shape optimization and analysis of small wind turbine blades employing the Viterna approach for post-stall region","volume":"55","author":"Hassanzadeh","year":"2016","journal-title":"Alex. Eng. J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1016\/j.renene.2015.09.002","article-title":"Aero-structural design optimization of a small wind turbine blade","volume":"87","author":"Pourrajabian","year":"2016","journal-title":"Renew. Energy"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/j.compstruct.2016.09.042","article-title":"Proposal for a coupled aerodynamic-structural wind turbine blade optimization","volume":"159","author":"Castelli","year":"2017","journal-title":"Compos. Struct."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.apenergy.2014.12.043","article-title":"Review of performance optimization applied to wind turbines","volume":"142","author":"Chehouri","year":"2015","journal-title":"Appl. Energy"},{"key":"ref_33","unstructured":"Myers, R.H., Montgomery, D.C., and Anderson-Cook, C.M. (2016). Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley. [4th ed.]."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Benim, A.C., Brillert, D., and Cagan, M. (2004, January 14\u201317). Investigation into the computational analysis of direct-transfer pre-swirl systems for gas turbine cooling. Proceedings of the ASME Turbo Expo 2004, Vienna, Austria. Paper No. GT2004-54151.","DOI":"10.1115\/GT2004-54151"},{"key":"ref_35","first-page":"343","article-title":"Modelling the Flow in the Exhaust Hood of Steam Turbines under Consideration of Turbine-Exhaust Hood Interaction","volume":"Volume 1185","author":"Benim","year":"1995","journal-title":"Proceedings of the 1st European Conference on Turbomachinery\u2014Fluid Dynamic and Thermodynamic Aspects: Computational Methods"},{"key":"ref_36","unstructured":"(2018, October 17). Engineering Simulations and 3-D Design Software. Available online: www.ansys.com."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Durbin, P.A., and Pettersson Reif, B.A. (2011). Statistical Theory and Modeling for Turbulent Flows, Wiley. [2nd ed.].","DOI":"10.1002\/9780470972076"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1504\/PCFD.2005.007680","article-title":"URANS and LES analysis of turbulent swirling flows","volume":"5","author":"Benim","year":"2005","journal-title":"Prog. Comput. Fluid Dyn. An Int. J."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1973","DOI":"10.1016\/j.ijthermalsci.2011.05.002","article-title":"Computational analysis of turbulent forced convection in a channel with a triangular prism","volume":"50","author":"Benim","year":"2011","journal-title":"Int. J. Therm. Sci."},{"key":"ref_40","unstructured":"Rodi, W., and Fueye, N. (2002, January 16\u201318). Transition modelling based on local variables. Proceedings of the Fifth International Symposium on Engineering Turbulence Modelling and Measurements, Mallorca, Spain. Engineering Turbulence Modelling and Experiments 5."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1016\/j.ijthermalsci.2004.02.012","article-title":"Computational analysis of transient heat transfer in turbulent pipe flow","volume":"43","author":"Benim","year":"2004","journal-title":"Int. J. Therm. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1108\/09615530710730157","article-title":"Computational investigation of turbulent jet impinging onto rotating disk","volume":"17","author":"Benim","year":"2007","journal-title":"Int. J. Numer. Methods Heat Fluid Flow"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.jbiomech.2011.09.021","article-title":"Pulsatile extracorporeal circulation during on-pump cardiac surgery enhances aortic wall shear stress","volume":"45","author":"Assmann","year":"2012","journal-title":"J. Biomech."},{"key":"ref_44","first-page":"191","article-title":"New fully coupled solutions of the Navier-Stokes equations","volume":"Volume 35","author":"Vos","year":"1992","journal-title":"Notes on Numerical Fluid Mechanics (NNFM), Proceedings of the 9th GAMM Conference on Numerical Methods in Fluid Mechanics, Lausanne, Switzerland, 25\u201327 September 1991"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/0045-7825(79)90034-3","article-title":"A stable and accurate convective modelling procedure based on quadratic upstream interpolation","volume":"19","author":"Leonard","year":"1979","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Barth, T.J., and Jespersen, D. (1989, January 9\u201312). The design and application of upwind schemes on unstructured meshes. Proceedings of the AIAA 27th Aerospace Sciences Meeting, Reno, NV, USA. Technical Report AIAA-89-0366.","DOI":"10.2514\/6.1989-366"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1504\/PCFD.2008.019483","article-title":"Modeling turbulent flow past a circular cylinder by RANS, URANS, LES and DES","volume":"8","author":"Benim","year":"2008","journal-title":"Prog. Computat. Fluid Dyn. An Int. J."},{"key":"ref_48","unstructured":"(2018, April 17). GNU Octave. Available online: https:\/\/www.gnu.org\/software\/octave\/."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Conn, A.R., Scheinberg, K., and Vincente, L.N. (2009). Introduction to Derivative-Free Optimization, SIAM.","DOI":"10.1137\/1.9780898718768"},{"key":"ref_50","first-page":"44","article-title":"Algorithm 909: NOMAD: Nonlinear Optimization with the MADS Algorithm","volume":"37","year":"2011","journal-title":"ACM Trans. Math. Softw."},{"key":"ref_51","unstructured":"Selig, M.S., Lyon, C.A., Gigu\u00e8re, P., Ninham, C.P., and Guglielmo, J.J. (1996). Summary of Low-Speed Airfoil Data, Soar Tech Publications."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Branke, J., Deb, K., Miettinen, K., and Slowinski, R. (2008). Multiobjective Optimization, Springer.","DOI":"10.1007\/978-3-540-88908-3"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/6\/2\/34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:02:08Z","timestamp":1760194928000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/6\/2\/34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,25]]},"references-count":52,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["computation6020034"],"URL":"https:\/\/doi.org\/10.3390\/computation6020034","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4,25]]}}}