{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T19:49:32Z","timestamp":1770839372609,"version":"3.50.1"},"reference-count":63,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T00:00:00Z","timestamp":1674604800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Aeronautics and Astronautics Research Center (AEROG)","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}]},{"name":"Aeronautics and Astronautics Research Center (AEROG)","award":["SFRH\/BD\/136381\/477\/2018"],"award-info":[{"award-number":["SFRH\/BD\/136381\/477\/2018"]}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BD\/136381\/477\/2018"],"award-info":[{"award-number":["SFRH\/BD\/136381\/477\/2018"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Aerospace"],"abstract":"<jats:p>Supercritical nitrogen jet behavior is modeled using an incompressible but variable density approach developed for variable density jets. Following mechanical and thermal breakup concepts, several injection conditions relevant to liquid rocket propulsion are analyzed, considering heat transfer in the injector. Regarding axial density distributions, different levels of agreement with experimental data are encountered for potential core, subsided core, and plateau formations. Further comparisons with compressible formulations from the literature are a good indicator of the proposed methodology\u2019s suitability for the simulation of supercritical injection behavior.<\/jats:p>","DOI":"10.3390\/aerospace10020114","type":"journal-article","created":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T03:53:18Z","timestamp":1674618798000},"page":"114","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Supercritical Injection Modeling by an Incompressible but Variable Density Approach"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1256-9689","authenticated-orcid":false,"given":"Leandro B.","family":"Magalh\u00e3es","sequence":"first","affiliation":[{"name":"AEROG-LAETA, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"},{"name":"ISEC, ISEC Lisbon\u2014Institute for Higher Education, Alameda das Linhas de Torres 179, 1750-142 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4901-7140","authenticated-orcid":false,"given":"Andr\u00e9 R. R.","family":"Silva","sequence":"additional","affiliation":[{"name":"AEROG-LAETA, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9014-5008","authenticated-orcid":false,"given":"Jorge M. M.","family":"Barata","sequence":"additional","affiliation":[{"name":"AEROG-LAETA, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103023","DOI":"10.1016\/j.cryogenics.2019.103023","article-title":"Numerical Investigation of Supercritical Methane in Helically Coiled Tube on Regenerative Cooling of Liquid Rocket Electromechanical Actuator","volume":"106","author":"Gao","year":"2020","journal-title":"Cryogenics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"052101","DOI":"10.1063\/1.2912055","article-title":"Subcritical to Supercritical Mixing","volume":"20","author":"Segal","year":"2008","journal-title":"Phys. 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