{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:55:06Z","timestamp":1777715706616,"version":"3.51.4"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T00:00:00Z","timestamp":1677196800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["52276031"],"award-info":[{"award-number":["52276031"]}]},{"name":"National Natural Science Foundation of China","award":["51876098"],"award-info":[{"award-number":["51876098"]}]},{"name":"National Natural Science Foundation of China","award":["J2019-III-0007-0050"],"award-info":[{"award-number":["J2019-III-0007-0050"]}]},{"name":"Tsinghua University Initiative Scientific Research Program","award":["52276031"],"award-info":[{"award-number":["52276031"]}]},{"name":"Tsinghua University Initiative Scientific Research Program","award":["51876098"],"award-info":[{"award-number":["51876098"]}]},{"name":"Tsinghua University Initiative Scientific Research Program","award":["J2019-III-0007-0050"],"award-info":[{"award-number":["J2019-III-0007-0050"]}]},{"name":"National Science and Technology Major Project","award":["52276031"],"award-info":[{"award-number":["52276031"]}]},{"name":"National Science and Technology Major Project","award":["51876098"],"award-info":[{"award-number":["51876098"]}]},{"name":"National Science and Technology Major Project","award":["J2019-III-0007-0050"],"award-info":[{"award-number":["J2019-III-0007-0050"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Film cooling is a major cooling technique used in modern gas turbines and air engines. The geometry of film-cooling holes is the fundamental aspect affecting the cooling performance. In this paper, a new cooling configuration called the double-expansion film-cooling hole has been put forward, which yields better performance than the widely used shaped holes and is easy to manufacture. The double-expansion holes at inclination angles of \u03b1=30\u2218, 45\u2218, and 60\u2218 are optimized using the genetic algorithm and the Kriging surrogate model, which is trained by CFD data randomly sampled using the Latin hypercube method. The numerically optimized double-expansion holes at different inclination angles were experimentally evaluated and compared with the optimized single-expansion laid-back fan-shaped holes, and the optimized double-expansion hole at \u03b1=30\u2218 was manually modified based on experiment results. Compared with the optimal single-expansion holes, the area-averaged cooling effectiveness of the double-expansion holes was increased by 34.5% at \u03b1=30\u2218, by 27.8% at \u03b1=45\u2218, and basically the same at \u03b1=60\u2218, showing the benefit of the double-expansion concept. The loss mechanism of film cooling was also analyzed in the perspective of the entropy generation rate, showing the optimal double-expansion holes have 21% less loss compared to a baseline narrow single-expansion hole. It was also found that CFD sometimes predicts a different trend from the experiment in optimization, and the experimental validation is necessary.<\/jats:p>","DOI":"10.3390\/e25030410","type":"journal-article","created":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T02:22:16Z","timestamp":1677464536000},"page":"410","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Optimization of the Double-Expansion Film-Cooling Hole Using CFD"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1559-625X","authenticated-orcid":false,"given":"Zhen","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Energy and Power Engineering, Tsinghua University, Haidian Distrct, Beijing 100084, China"}]},{"given":"Tianyu","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Energy and Power Engineering, Tsinghua University, Haidian Distrct, Beijing 100084, China"}]},{"given":"Xinrong","family":"Su","sequence":"additional","affiliation":[{"name":"Department of Energy and Power Engineering, Tsinghua University, Haidian Distrct, Beijing 100084, China"}]},{"given":"Xin","family":"Yuan","sequence":"additional","affiliation":[{"name":"Department of Energy and Power Engineering, Tsinghua University, Haidian Distrct, Beijing 100084, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"249","DOI":"10.2514\/1.18034","article-title":"Gas turbine film cooling","volume":"22","author":"Bogard","year":"2006","journal-title":"J. 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