{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T05:07:11Z","timestamp":1770527231459,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2015,8,3]],"date-time":"2015-08-03T00:00:00Z","timestamp":1438560000000},"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>Fluid machinery operating in the supersonic regime unveil avenues towards more compact technology. However, internal supersonic flows are associated with high aerodynamic and thermal penalties, which usually prevent their practical implementation. Indeed, both shock losses and the limited operational range represent particular challenges to aerodynamic designers that should be taken into account at the initial phase of the design process. This paper presents a design methodology for supersonic passages based on direct evaluations of the velocity field using the method of characteristics and computation of entropy generation across shock waves. This meshless function evaluation tool is then coupled to an optimization scheme, based on evolutionary algorithms that minimize the entropy generation across the supersonic passage. Finally, we assessed the results with 3D Reynolds Averaged Navier Stokes calculations.<\/jats:p>","DOI":"10.3390\/e17085593","type":"journal-article","created":{"date-parts":[[2015,8,5]],"date-time":"2015-08-05T03:18:55Z","timestamp":1438744735000},"page":"5593-5610","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":51,"title":["Entropy Minimization Design Approach of Supersonic Internal Passages"],"prefix":"10.3390","volume":"17","author":[{"given":"Jorge","family":"Sousa","sequence":"first","affiliation":[{"name":"Von Karman Institute, Chaussee de Waterloo 72, Rhode Saint Genese 1640, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guillermo","family":"Paniagua","sequence":"additional","affiliation":[{"name":"Zucrow Laboratories, Purdue University, 500 Allison Road, West Lafayette, IN 47907, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,8,3]]},"reference":[{"key":"ref_1","unstructured":"Kantrowitz, A., and Donaldson, C. 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