{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T23:50:42Z","timestamp":1780098642890,"version":"3.54.0"},"reference-count":26,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,19]],"date-time":"2025-04-19T00:00:00Z","timestamp":1745020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Mississippi NASA EPSCoR program"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Micro-vortex generators (MVGs) are widely utilized as passive devices to control flow separation in supersonic boundary layers by generating ring-like vortices that mitigate shock-induced effects. This study employs large eddy simulation (LES) to investigate the flow structures in a supersonic boundary layer (Mach 2.5, Re = 5760) controlled by two MVGs installed in tandem, with spacings varying from 11.75 h to 18.75 h (h = MVG height), alongside a single-MVG reference case. A fifth-order WENO scheme and third-order TVD Runge\u2013Kutta method were used to solve the unfiltered Navier\u2013Stokes equations, with the Liutex method applied to visualize vortex structures. Results reveal that tandem MVGs produce complex vortex interactions, with spanwise and streamwise vortices merging extensively, leading to a significant reduction in vortex intensity due to mutual cancellation. A momentum deficit forms behind the second MVG, weakening that from the first, while the boundary layer energy thickness doubles compared to the single-MVG case, indicating increased energy loss. Streamwise vorticity distributions and instantaneous streamlines highlight intensified interactions with closer spacings, yet this complexity diminishes overall flow control effectiveness. Contrary to expectations, the tandem configuration does not enhance boundary layer control but instead weakens it, as evidenced by reduced vortex strength and amplified energy dissipation. These findings underscore a critical trade-off in tandem MVG deployment, suggesting that while vortex interactions enrich flow complexity, they may compromise the intended control benefits in supersonic flows, with implications for optimizing MVG arrangements in practical applications.<\/jats:p>","DOI":"10.3390\/computation13040101","type":"journal-article","created":{"date-parts":[[2025,4,20]],"date-time":"2025-04-20T20:15:06Z","timestamp":1745180106000},"page":"101","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Computational Analysis of Tandem Micro-Vortex Generators for Supersonic Boundary Layer Flow Control"],"prefix":"10.3390","volume":"13","author":[{"given":"Caixia","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistical Sciences, Jackson State University, Jackson, MS 39217, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4726-8998","authenticated-orcid":false,"given":"Yong","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, West Texas A&M University, Canyon, TX 79016, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yonghua","family":"Yan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistical Sciences, Jackson State University, Jackson, MS 39217, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.actaastro.2022.07.025","article-title":"Control Mechanism of Micro Vortex Generator and Secondary Recirculation Jet Combination in the Shock Wave\/Boundary Layer Interaction","volume":"200","author":"Wu","year":"2022","journal-title":"Acta Astronaut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"106111","DOI":"10.1063\/5.0170104","article-title":"Flow and Acoustic Fields Investigation of Noise Reduction by Micro Vortex Generators in Supersonic Nozzles","volume":"35","author":"Saleem","year":"2023","journal-title":"Phys. Fluids"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Liu, J., Khine, Y.Y., Saleem, M., Lopez Rodriguez, O., and Gutmark, E. (2021, January 2\u20136). Supersonic Jet Noise Reduction Using Micro Vortex Generators. Proceedings of the AIAA AVIATION 2021 FORUM, Virtual.","DOI":"10.2514\/6.2021-2183"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"116115","DOI":"10.1063\/5.0123541","article-title":"Study of the Streamwise Location of a Micro Vortex Generator for a Separation-Control Mechanism in Supersonic Flow","volume":"34","author":"Wu","year":"2022","journal-title":"Phys. Fluids"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Sajeev, S., Pal Singh Sandhu, J., Ghosh, S., and Edwards, J.R. (2020, January 15\u201319). Effectiveness of Micro-Vortex Generators in Tandem in High-Speed Flows. Proceedings of the AIAA AVIATION 2020 FORUM, Virtual.","DOI":"10.2514\/6.2020-2961"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.paerosci.2012.03.003","article-title":"Microvortex Generators in High-Speed Flow","volume":"53","author":"Lu","year":"2012","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.ast.2015.09.029","article-title":"An Improved Micro-Vortex Generator in Supersonic Flows","volume":"47","author":"Zhang","year":"2015","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Anderson, B., Tinapple, J., and Surber, L. (2006, January 5\u20138). Optimal Control of Shock Wave Turbulent Boundary Layer Interactions Using Micro-Array Actuation. Proceedings of the 3rd AIAA Flow Control Conference, San Francisco, CA, USA.","DOI":"10.2514\/6.2006-3197"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"668","DOI":"10.2514\/1.38022","article-title":"Microramp Control of Supersonic Oblique Shock-Wave\/Boundary-Layer Interactions","volume":"47","author":"Babinsky","year":"2009","journal-title":"AIAA J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1518","DOI":"10.2514\/1.J052649","article-title":"Numerical and Experimental Investigations of the Supersonic Microramp Wake","volume":"52","author":"Sun","year":"2014","journal-title":"AIAA J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"055110","DOI":"10.1063\/1.4719146","article-title":"Experimental Investigation of the Micro-Ramp Based Shock Wave and Turbulent Boundary Layer Interaction Control","volume":"24","author":"Wang","year":"2012","journal-title":"Phys. Fluids"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2283","DOI":"10.2514\/2.1266","article-title":"Large-Eddy Simulation of Supersonic Compression-Ramp Flow by High-Order Method","volume":"39","author":"Rizzetta","year":"2001","journal-title":"AIAA J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2516","DOI":"10.2514\/1.6002","article-title":"Large-Eddy Simulation of Shock-Turbulence Interaction","volume":"42","author":"Kaenel","year":"2004","journal-title":"AIAA J."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Li, Q., Yan, Y., Wang, X., and Liu, C. (2011, January 4\u20137). The Interaction between Vortex Rings and Oblique Shocks by the MVG Controlled Ramp Flow at M = 2.5. Proceedings of the 49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, FL, USA.","DOI":"10.2514\/6.2011-861"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"015505","DOI":"10.1088\/0169-5983\/46\/1\/015505","article-title":"Numerical Investigations on the Wake Structures of Micro-Ramp and Micro-Vanes","volume":"46","author":"Xue","year":"2014","journal-title":"Fluid Dyn. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3777","DOI":"10.2514\/1.J054074","article-title":"Fluid Redistribution in the Turbulent Boundary Layer Under the Microramp Control","volume":"53","author":"Wang","year":"2015","journal-title":"AIAA J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.euromechflu.2022.04.010","article-title":"Control of Flow Separation over an Axisymmetric Flared Body Using Ramped Vanes","volume":"95","author":"Nilavarasan","year":"2022","journal-title":"Eur. J. Mech. B\/Fluids"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"023328","DOI":"10.1063\/5.0252143","article-title":"Tip Vortex Cavitation Control by the Micro Vortex Generator","volume":"37","author":"Wang","year":"2025","journal-title":"Phys. Fluids"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s00193-016-0633-4","article-title":"Numerical Study of Micro-Ramp Vortex Generator for Supersonic Ramp Flow Control at Mach 2.5","volume":"27","author":"Yan","year":"2017","journal-title":"Shock Waves"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Yang, Y., Yan, Y., Chen, C., Wu, Q., Kwembe, T.A., and Wu, R. (2022). Modal Analysis on MVG Controlled Supersonic Flow at Different Mach Numbers. Processes, 10.","DOI":"10.3390\/pr10081456"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s13160-021-00484-w","article-title":"Numerical Study on the Ring-like Vortex Structure Generated by MVG in High-Speed Flows with Different Mach Numbers","volume":"39","author":"Yan","year":"2022","journal-title":"Jpn. J. Indust. Appl. Math."},{"key":"ref_22","unstructured":"Lu, F., Pierce, A., and Shih, Y. (July, January 28). Experimental Study of near Wake of Micro Vortex Generators in Supersonic Flow. Proceedings of the 40th Fluid Dynamics Conference and Exhibit, Chicago, IL, USA."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1016\/j.euromechflu.2018.09.003","article-title":"Structures and Aero-Optical Effects of Supersonic Flow over a Backward Facing Step with Vortex Generators","volume":"74","author":"Zhu","year":"2019","journal-title":"Eur. J. Mech. B\/Fluids"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3481","DOI":"10.2514\/1.J054947","article-title":"Mach and Reynolds Number Effects on the Wake Properties of Microramps","volume":"54","author":"Giepman","year":"2016","journal-title":"AIAA J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"055105","DOI":"10.1063\/1.4711372","article-title":"The Three-Dimensional Flow Organization Past a Micro-Ramp in a Supersonic Boundary Layer","volume":"24","author":"Sun","year":"2012","journal-title":"Phys. Fluids"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/978-981-97-8608-4_2","article-title":"Comparison of Liutex and Other Vortex Identification Methods Based on Vortex Models","volume":"Volume 309","author":"Wang","year":"2024","journal-title":"Proceedings of the Vortex Workshop"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/4\/101\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:18:04Z","timestamp":1760030284000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/13\/4\/101"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,19]]},"references-count":26,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,4]]}},"alternative-id":["computation13040101"],"URL":"https:\/\/doi.org\/10.3390\/computation13040101","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,19]]}}}