{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T12:53:53Z","timestamp":1775825633780,"version":"3.50.1"},"reference-count":57,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T00:00:00Z","timestamp":1690848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51925603"],"award-info":[{"award-number":["51925603"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52206177"],"award-info":[{"award-number":["52206177"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22PJ1412800"],"award-info":[{"award-number":["22PJ1412800"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Pujiang Talents Plan","award":["51925603"],"award-info":[{"award-number":["51925603"]}]},{"name":"Pujiang Talents Plan","award":["52206177"],"award-info":[{"award-number":["52206177"]}]},{"name":"Pujiang Talents Plan","award":["22PJ1412800"],"award-info":[{"award-number":["22PJ1412800"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This article focuses on entropy generation in the combustion field, which serves as a useful indicator to quantify the interaction between turbulence and combustion. The study is performed on the direct numerical simulations (DNS) of high pressure non-premixed and premixed swirling flames. By analyzing the entropy generation in thermal transport, mass transport, and chemical reactions, it is found that the thermal transport, driven by the temperature gradient, plays a dominant role. The enstrophy transport analysis reveals that the responses of individual terms to combustion can be measured by the entropy: the vortex stretching and the dissipation terms increase monotonically with the increasing entropy. In high entropy regions, the turbulence behaves as the \u201ccigar shaped\u201d state in the non-premixed flame, while as the axisymmetric state in the premixed flame. A substantial increase in the normal Reynolds stress with the entropy is observed. This is due to the competition between two terms promoted by the entropy, i.e., the velocity\u2013pressure gradient correlation term and the shear production term. As a result, the velocity\u2013pressure gradient correlation tends to isotropize turbulence by transferring energy increasingly from the largest streamwise component to the other smaller normal components of Reynolds stress and is dominated by the fluctuating pressure gradient that increases along the entropy. The shear production term increases with the entropy due to the upgrading alignment of the eigenvectors of strain rate and Reynolds stress tensors.<\/jats:p>","DOI":"10.3390\/e25081151","type":"journal-article","created":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T09:06:44Z","timestamp":1690880804000},"page":"1151","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Entropy: An Inspiring Tool for Characterizing Turbulence\u2013Combustion Interaction in Swirling Flames via Direct Numerical Simulations of Non-Premixed and Premixed Flames"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5133-6741","authenticated-orcid":false,"given":"Jingke","family":"Su","sequence":"first","affiliation":[{"name":"State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anxiong","family":"Liu","sequence":"additional","affiliation":[{"name":"Shanghai Institute for Advanced Study, Zhejiang University, Shanghai 200000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hualin","family":"Xiao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kun","family":"Luo","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianren","family":"Fan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.expthermflusci.2015.07.023","article-title":"Review of laboratory swirl burners and experiments for model validation","volume":"69","author":"Masri","year":"2015","journal-title":"Exp. 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