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Soc. Mech. Sci. Eng."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Conventional De Laval nozzles reliably produce thrust, but their divergent section poses the major design challenge. The contour of a bell nozzle can be traced with several philosophies such as thrust optimization parabolas (TOP) or truncated ideal compressed (TIC) nozzles. The major difference between the two enunciated contours lies on transient effects in overexpanding operation. In this study, the performance of the two contours and exhaust plume structures are compared for several pressure ratios simulating the operating conditions of an ascending vehicles. A high divergent angle at the exit is imposed at design and the results are compared to those of a cone nozzle, isentropic and Quasi-1D cases, showing that contoured bell nozzles suffer specific impulse losses due to a thicker boundary layer. Nonetheless, a lower than expected average angle allows that, near design conditions, the contoured nozzles have a higher specific impulse then if an isentropic expansion occurred, with the entire flow exiting with the design exit angle. The exhaust plumes show close resemblance to literature description, with the Mach disk concavity relating to oblique shocks and their interaction within the nozzle. The two contours show similar performances, with the TIC nozzle overperforming the TOP nozzle in overexpanding conditions near the design point, but with neither ever surpassing the cone nozzle performance.<\/jats:p>","DOI":"10.1007\/s40430-025-05759-8","type":"journal-article","created":{"date-parts":[[2025,7,6]],"date-time":"2025-07-06T23:12:15Z","timestamp":1751843535000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-altitude performance evaluation of axisymmetric propulsive nozzles with high divergence angles"],"prefix":"10.1007","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-0397-4589","authenticated-orcid":false,"given":"Jo\u00e3o C.","family":"Silva","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6992-5835","authenticated-orcid":false,"given":"Francisco","family":"Br\u00f3jo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,7]]},"reference":[{"key":"5759_CR1","doi-asserted-by":"publisher","unstructured":"El-Sayed, A. 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