{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T03:01:34Z","timestamp":1777604494639,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,18]],"date-time":"2019-06-18T00:00:00Z","timestamp":1560816000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Rapid aerodynamic design and optimization is essential for the development of future turbomachinery. The objective of this work is to demonstrate a methodology from 1D mean-line-design to a full 3D aerodynamic optimization of the turbine stage using a parameterization strategy that requires few parameters. The methodology is tested by designing a highly loaded and efficient turbine for the Purdue Experimental Turbine Aerothermal Laboratory. This manuscript describes the entire design process including the 2D\/3D parameterization strategy in detail. The objective of the design is to maximize the entropy definition of efficiency while simultaneously maximizing the stage loading. Optimal design trends are highlighted for both the stator and rotor for several turbine characteristics in terms of pitch-to-chord ratio as well as the blades metal and stagger angles. Additionally, a correction term is proposed for the Horlock efficiency equation to maximize the accuracy based on the measured blade kinetic losses. Finally, the design and performance of optimal profiles along the Pareto front are summarized, featuring the highest aerodynamic performance and stage loading.<\/jats:p>","DOI":"10.3390\/e21060604","type":"journal-article","created":{"date-parts":[[2019,6,19]],"date-time":"2019-06-19T02:42:46Z","timestamp":1560912166000},"page":"604","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Turbine Passage Design Methodology to Minimize Entropy Production\u2014A Two-Step Optimization Strategy"],"prefix":"10.3390","volume":"21","author":[{"given":"Paht","family":"Juangphanich","sequence":"first","affiliation":[{"name":"School of Aeronautical Engineering, Purdue University, West Lafayette, IN 47906, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cis","family":"De Maesschalck","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2437-4045","authenticated-orcid":false,"given":"Guillermo","family":"Paniagua","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Juangphanich, P., De Maesschalck, C.G., and Paniagua, G. (2017, January 9\u201313). From Conceptual 1D Design Towards Full 3D Optimization of a Highly Loaded Turbine Stage. Proceedings of the 55th AIAA Aerospace Sciences Meeting, Grapevine, TX, USA.","DOI":"10.2514\/6.2017-0110"},{"key":"ref_2","unstructured":"Denton, J. (2019, June 02). The Evolution of Turbomachinery Design Methods. Available online: https:\/\/www.pcaeng.co.uk\/library\/PCA_20th_JDDenton.pdf."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Farin, G. (1988). Curves and Surfaces for Computer Aided Geometric Design, Academic Press.","DOI":"10.1016\/B978-0-12-460515-2.50020-2"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Shelton, M.L., Gregory, B.A., Lamson, S.H., Moses, H.L., Doughty, R.L., and Kiss, T. (1993, January 24\u201327). Optimization of a Transonic Turbine Airfoil Using Artificial Intelligence, CFD and Cascade Testing. Proceedings of the ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition, Cincinnati, OH, USA. 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