{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:45:25Z","timestamp":1760402725379,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,13]],"date-time":"2020-01-13T00:00:00Z","timestamp":1578873600000},"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>A two-dimensional numerical study was conducted for flow past a square rod in the presence of two control rods. One is placed vertically in the upstream direction and the second one is placed horizontally in the downstream direction of the square rod. The influence of gap spacing was studied by taking g1 = 1\u20135 and g2 = 0.5\u20135 (where g1 is the gap between the upstream control rod and the main rod, and g2 is the space between the main rod and the downstream control rod) at Re = 160. The simulation results were obtained in the form of vorticity contour, drag and lift coefficients, Strouhal number, and force statistics. Under the effect of gap spacing, three different flow modes were found and named according to their behavior. It was found that the mean drag coefficient showed decreasing behavior by increasing the value of g2 continually at a fixed value of g1. The largest value of     C d m e a n     was found at (g1, g2) = (1, 1) and the greatest percentage reduction in     C d m e a n     was obtained at (g1, g2) = (1, 3), which is 139.72%. The effect of thrust was also noticed for all selected values of g1 and g2. Furthermore, it was noticed that the Strouhal number and the root mean square values of the drag and lift coefficients smaller values than the single rod values, except for the Clrms value of (g1, g2) = (1, 3) and (1, 4).<\/jats:p>","DOI":"10.3390\/sym12010159","type":"journal-article","created":{"date-parts":[[2020,1,13]],"date-time":"2020-01-13T04:05:51Z","timestamp":1578888351000},"page":"159","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Numerical Analysis of Fluid Forces for Flow Past a Square Rod with Detached Dual Control Rods at Various Gap Spacing"],"prefix":"10.3390","volume":"12","author":[{"given":"Raheela","family":"Manzoor","sequence":"first","affiliation":[{"name":"Mathematics Department, SBK Women\u2019s University, Quetta 87300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5994-8440","authenticated-orcid":false,"given":"Abdul","family":"Ghaffar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, BUITEMS, Quetta 87300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cankaya University, Anakara 06790, Turkey"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan"},{"name":"Institute of Space Sciences, 077125 Magurele-Bucharest, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5769-4320","authenticated-orcid":false,"given":"Kottakkaran Sooppy","family":"Nisar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1006\/jfls.2000.0354","article-title":"Flow past a bluff body with a wavy stagnation face","volume":"15","author":"Darekar","year":"2001","journal-title":"J. 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