{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T17:59:06Z","timestamp":1771005546245,"version":"3.50.1"},"reference-count":23,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2015,11,30]],"date-time":"2015-11-30T00:00:00Z","timestamp":1448841600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Basic Research Program of China","doi-asserted-by":"publisher","award":["2012CB026002"],"award-info":[{"award-number":["2012CB026002"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51305355"],"award-info":[{"award-number":["51305355"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key Technology Research and Development Program of the Ministry of Science and Technology of China","award":["2013BAF01B02"],"award-info":[{"award-number":["2013BAF01B02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Based on phase space reconstruction and fractal dynamics in nonlinear dynamics, a method is proposed to extract and analyze the dynamics of the rotating stall in the impeller of centrifugal compressor, and some numerical examples are given to verify the results as well. First, the rotating stall of an existing low speed centrifugal compressor (LSCC) is numerically simulated, and the time series of pressure in the rotating stall is obtained at various locations near the impeller outlet. Then, the phase space reconstruction is applied to these pressure time series, and a low-dimensional dynamical system, which the dynamics properties are included in, is reconstructed. In phase space reconstruction, C\u2013C method is used to obtain the key parameters, such as time delay and the embedding dimension of the reconstructed phase space. Further, the fractal characteristics of the rotating stall are analyzed in detail, and the fractal dimensions are given for some examples to measure the complexity of the flow in the post-rotating stall. The results show that the fractal structures could reveal the intrinsic dynamics of the rotating stall flow and could be considered as a characteristic to identify the rotating stall.<\/jats:p>","DOI":"10.3390\/e17127848","type":"journal-article","created":{"date-parts":[[2015,11,30]],"date-time":"2015-11-30T10:57:24Z","timestamp":1448881044000},"page":"7888-7899","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Identify the Rotating Stall in Centrifugal Compressors by Fractal Dimension in Reconstructed Phase Space"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0445-0629","authenticated-orcid":false,"given":"Le","family":"Wang","sequence":"first","affiliation":[{"name":"School of Energy and Power Engineering, Xi\u2019an Jiaotong University, 710049 Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiazhong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Xi\u2019an Jiaotong University, 710049 Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenfan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Energy and Power Engineering, Xi\u2019an Jiaotong University, 710049 Xi\u2019an, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"65","DOI":"10.2514\/2.5532","article-title":"Computational Analysis of Stall and Separation Control in Centrifugal Compressors","volume":"16","author":"Stein","year":"2000","journal-title":"J. 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