{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,4]],"date-time":"2026-07-04T14:57:04Z","timestamp":1783177024563,"version":"3.54.6"},"reference-count":27,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,13]],"date-time":"2021-01-13T00:00:00Z","timestamp":1610496000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The flow and heat transfer characteristics of a film jet inclined to different supersonic situations with a varying Mach number of the main flow were numerically investigated. In supersonic situations, complicated waves are generated by the obstacle of the film jet. In this work, extra pressure is exerted onto the film jet, causing better film attachment to the wall. The strengthening of attachment decreases mixing between the main flow and film jet, causing better film cooling. We observed multi-interfacial layered structures caused by the film jet under the complicated effect of shock waves. At the interfaces of the film jet and shock waves, additional pressure is exerted on the film towards the wall. The pressure increases as the Mach number of the main flow increases and contributes to the increased adhesion of the gas film, which causes the cooling enhancement under a supersonic condition. In the vicinity of the film hole exit, a local low pressure region is formed under the influence of the supersonic main flow. An aerodynamic convergent\u2013divergent state was formed in the film hole, devastating the state of supersonic congestion of the film hole and further enhancing the film cooling effect.<\/jats:p>","DOI":"10.3390\/sym13010127","type":"journal-article","created":{"date-parts":[[2021,1,13]],"date-time":"2021-01-13T21:50:54Z","timestamp":1610574654000},"page":"127","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["Influence of Mach Number of Main Flow on Film Cooling Characteristics under Supersonic Condition"],"prefix":"10.3390","volume":"13","author":[{"given":"Bo","family":"Zhang","sequence":"first","affiliation":[{"name":"Jiangsu Province Key Laboratory of Aerospace Power System, College of Energy and Power, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan-Xiang","family":"Chen","sequence":"additional","affiliation":[{"name":"Jiangsu Province Key Laboratory of Aerospace Power System, College of Energy and Power, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhi-guo","family":"Wang","sequence":"additional","affiliation":[{"name":"Jiangsu Province Key Laboratory of Aerospace Power System, College of Energy and Power, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ji-Quan","family":"Li","sequence":"additional","affiliation":[{"name":"Jiangsu Province Key Laboratory of Aerospace Power System, College of Energy and Power, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hong-hu","family":"Ji","sequence":"additional","affiliation":[{"name":"Jiangsu Province Key Laboratory of Aerospace Power System, College of Energy and Power, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,13]]},"reference":[{"key":"ref_1","unstructured":"Hartnett, J.P., Birkebak, R.C., and Eckert, E.R.G. (1961). Velocity distributions, temperature distributions effectiveness and heat transfer in cooling of a surface with a pressure gradient. Int. Dev. Heat Transf., 682\u2013689."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1115\/1.3230284","article-title":"Double-row discrete holes cooling: An experimental and numerical study","volume":"102","author":"Bergeles","year":"1980","journal-title":"ASME J. Eng. Power"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1115\/1.2840939","article-title":"The effect of high freestream turbulence on film cooling effectiveness","volume":"118","author":"Bons","year":"1996","journal-title":"ASME J. Turbo Mach."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1080\/10407789608913842","article-title":"Fluid flow and convective heat transfer in a vertical porous annulus","volume":"30","author":"Jiang","year":"1996","journal-title":"Numer. Heat Transf."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1115\/1.1459736","article-title":"A converging slot-hole file-cooling geometry-part 2: Transonic nozzle guide vane heat transfer and loss","volume":"124","author":"Goldfield","year":"2002","journal-title":"ASME J. Turbo-Mach."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1016\/j.ijheatfluidflow.2008.02.007","article-title":"Effect of coolant-mainstream blowing ratio on leading edge film cooling flow and heat transfer-LES investigation","volume":"120","author":"Rozati","year":"2008","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S1000-9361(08)60109-0","article-title":"Numerical study of flow and heat transfer characteristics of impingement\/effusion cooling","volume":"22","author":"Zhang","year":"2009","journal-title":"Chin. J. Aeronaut."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/978-94-017-9747-4_7","article-title":"Airfoil Aerodynamics","volume":"Volume 110","author":"Vos","year":"2015","journal-title":"Introduction to Transonic Aerodynamics"},{"key":"ref_9","unstructured":"Seddon, J. (1967). The Flow Produced by Interaction of a Turbulent Boundary Layer with a Normal Shock Wave of Strength Sufficient to Cause Separation, Her Majesty\u2019s Stationery Office."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/S0376-0421(98)00011-6","article-title":"Shock train and Pseudo-shock phenomena in internal gas flows","volume":"35","author":"Matsuo","year":"1999","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1017\/S0022112010001710","article-title":"Direct numerical simulation of transonic shock\/boundary layer interaction under conditions of incipient separation","volume":"657","author":"Pirozzoli","year":"2010","journal-title":"J. Fluid Mech."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Krause, E. (1981). High-Reynolds Number Boundary-Layer Shock-Wave Interaction in Transonic Flow. Advances in Fluid Mechanics, Springer. Lecture Notes in Physics.","DOI":"10.1007\/BFb0021328"},{"key":"ref_13","unstructured":"Holger, B. (2011). Shock Wave Boundary Layer Interactions. Shock Wave-Boundary-Layer Interactions, Cambridge University Press. Available online: https:\/\/assets.cambridge.org\/97805218\/48527\/frontmatter\/9780521848527_frontmatter.pdf."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2102","DOI":"10.2514\/1.J051405","article-title":"Large-eddy simulation of shock\/cooling-film interaction","volume":"50","author":"Konopka","year":"2012","journal-title":"AIAA J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/0376-0421(85)90001-6","article-title":"Shock Wave\/turbulent Boundary Layer Inter- action and Its Control","volume":"22","author":"Delery","year":"1985","journal-title":"Progress in Aerospace Sciences"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1517","DOI":"10.2514\/2.1476","article-title":"Fifty years of shock-wave\/boundary layer interaction research: What next?","volume":"39","author":"Dolling","year":"2001","journal-title":"AIAA J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/s00193-009-0220-z","article-title":"Some physical aspects of shock wave\/boundary layer interactions","volume":"19","author":"Delery","year":"2009","journal-title":"Shock Waves"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Dickmann, D.A., and Lu, F. (2006, January 5\u20138). Jet in Supersonic Crossflow on a Flat Plate. Proceedings of the 25th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, San Francisco, CA, USA.","DOI":"10.2514\/6.2006-3451"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"046101","DOI":"10.1063\/1.3112736","article-title":"Detailed Flow Physics of the Supersonic Jet Interaction Flow Field","volume":"21","author":"Viti","year":"2009","journal-title":"Phys. Fluids"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.ijrefrig.2013.11.008","article-title":"Experimental and numerical investigation of the effect of shock wave characteristics on the ejector performance","volume":"40","author":"Zhu","year":"2014","journal-title":"Int. J. Refrig."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2533","DOI":"10.1016\/j.enconman.2007.03.024","article-title":"Shock circle model for ejector performance evaluation","volume":"48","author":"Zhu","year":"2007","journal-title":"Energy Convers. Manag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2279","DOI":"10.2298\/TSCI190401310Z","article-title":"Numerical investigation of heat transfer in film layer under supersonic condition of convergent-divergent transition","volume":"24","author":"Zhang","year":"2020","journal-title":"Therm. Sci."},{"key":"ref_23","unstructured":"Hannemann, K., and Seiler, F. (2009). Experimental and numerical investigation of film cooling in hypersonic flows. Shock Waves, Springer."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1769","DOI":"10.2514\/3.49979","article-title":"Turbulent boundary layer shock interaction with and without injection","volume":"9","author":"Alzner","year":"1971","journal-title":"AIAA J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"265","DOI":"10.2514\/3.13060","article-title":"Experimental studies of supersonic film cooling with shock wave interaction","volume":"34","author":"Kanda","year":"1996","journal-title":"AIAA J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"578","DOI":"10.2514\/3.12024","article-title":"Flow field measurements in supersonic film cooling including the effect of shock-wave interaction","volume":"32","author":"Juhany","year":"1994","journal-title":"AIAA J."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1515\/phys-2020-0130","article-title":"Effect of forward expansion angle on film cooling characteristics of shaped holes","volume":"18","author":"Zhang","year":"2020","journal-title":"Open Phys."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/127\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:10:40Z","timestamp":1760159440000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,13]]},"references-count":27,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010127"],"URL":"https:\/\/doi.org\/10.3390\/sym13010127","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,13]]}}}