{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T19:14:09Z","timestamp":1773256449133,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T00:00:00Z","timestamp":1488153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China under Grants","award":["11402024"],"award-info":[{"award-number":["11402024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The intent of shielding functions in delayed detached-eddy simulation methods (DDES) is to preserve the wall boundary layers as Reynolds-averaged Navier\u2013Strokes (RANS) mode, avoiding possible modeled stress depletion (MSD) or even unphysical separation due to grid refinement. An entropy function fs is introduced to construct a DDES formulation for the k-\u03c9 shear stress transport (SST) model, whose performance is extensively examined on a range of attached and separated flows (flat-plate flow, circular cylinder flow, and supersonic cavity-ramp flow). Two more forms of shielding functions are also included for comparison: one that uses the blending function F2 of SST, the other which adopts the recalibrated shielding function fd_cor of the DDES version based on the Spalart-Allmaras (SA) model. In general, all of the shielding functions do not impair the vortex in fully separated flows. However, for flows including attached boundary layer, both F2 and the recalibrated fd_cor are found to be too conservative to resolve the unsteady flow content. On the other side, fs is proposed on the theory of energy dissipation and independent on from any particular turbulence model, showing the generic priority by properly balancing the need of reserving the RANS modeled regions for wall boundary layers and generating the unsteady turbulent structures in detached areas.<\/jats:p>","DOI":"10.3390\/e19030093","type":"journal-article","created":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T11:00:20Z","timestamp":1488193220000},"page":"93","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["An Entropy-Assisted Shielding Function in DDES Formulation for the SST Turbulence Model"],"prefix":"10.3390","volume":"19","author":[{"given":"Ling","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Energy and Power Engineering, Huazhong University of Science &amp; Technology, Wuhan 430074, China"}]},{"given":"Rui","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Xiao-Pan","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/S0142-727X(02)00180-7","article-title":"Comparison of numerical methods applied to the flow over wall-mounted cubes","volume":"23","author":"Stefan","year":"2002","journal-title":"Int. J. Heat Fluid Flow"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.compfluid.2016.01.008","article-title":"Assessment of RANS and DES methods for realistic automotive models","volume":"128","author":"Ashton","year":"2016","journal-title":"Comput. Fluids"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.buildenv.2015.11.007","article-title":"CFD simulation of the wind environment around an isolated high-rise building: An evaluation of SRANS, LES and DES model","volume":"95","author":"Liu","year":"2016","journal-title":"Build. Environ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2377","DOI":"10.2514\/1.J054438","article-title":"Zonal detached-eddy simulation applied to the tip-clearance flow in an axial compressor","volume":"54","author":"Marty","year":"2016","journal-title":"AIAA J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"244","DOI":"10.2514\/1.C032678","article-title":"Hybrid Reynolds-Averaged Navier\u2013Stokes\/Large-Eddy simulation models for flow around an iced wing","volume":"52","author":"Alam","year":"2015","journal-title":"J. Aircr."},{"key":"ref_6","first-page":"625","article-title":"Ten years of industrial experience with the SST turbulence model","volume":"4","author":"Menter","year":"2003","journal-title":"Turbul. Heat Mass Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s00162-006-0015-0","article-title":"A new version of detached-eddy simulation, resistant to ambiguous grid densities","volume":"20","author":"Spalart","year":"2006","journal-title":"Theor. Comput. Fluid Dyn."},{"key":"ref_8","unstructured":"Menter, F.R., and Kuntz, M. (2004). Lecture Notes in Applied and Computational Mechanics, Springer."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1598","DOI":"10.2514\/3.12149","article-title":"Two-equation eddy-viscosity turbulence models for engineering applications","volume":"32","author":"Menter","year":"1994","journal-title":"AIAA J."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Spalart, P.R., and Allmaras, S.R. (1992, January 6\u20139). A one-equation turbulence model for aerodynamic flows. Proceedings of the 30th Aerospace Sciences Meeting & Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.1992-439"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1007\/s10494-011-9378-4","article-title":"Development of DDES and IDDES formulations for the k-\u03c9 shear stress transport model","volume":"88","author":"Gritskevich","year":"2012","journal-title":"Flow Turbul. Combust."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1051\/eucass\/201305023","article-title":"Fine-tuning of DDES and IDDES formulations to the k-\u03c9 shear stress transport model","volume":"5","author":"Gritskevich","year":"2013","journal-title":"Prog. Flight Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4137","DOI":"10.1007\/s11434-014-0569-y","article-title":"Entropy and its application in turbulence modeling","volume":"59","author":"Zhao","year":"2014","journal-title":"Chin. Sci. Bull."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1970","DOI":"10.1007\/s11433-012-4976-2","article-title":"Towards an entropy-based detached eddy simulation","volume":"56","author":"Zhao","year":"2013","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3090","DOI":"10.2514\/1.36849","article-title":"Evaluation of two high-order weighted essentially nonoscillatory schemes","volume":"46","author":"Nichols","year":"2008","journal-title":"AIAA J."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8283","DOI":"10.1016\/j.jcp.2009.08.004","article-title":"High order conservative differencing for viscous terms and the application to vortex-induced vibration flows","volume":"228","author":"Shen","year":"2009","journal-title":"J. Comput. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.2514\/1.J051299","article-title":"Numerical dissipation effects on massive separation around tandem cylinders","volume":"50","author":"Xiao","year":"2012","journal-title":"AIAA J."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Strelets, M.K. (2001, January 8\u201311). Detached eddy simulation of massively separated flows. Proceedings of the 39th Aerospace Sciences Meeting & Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.2001-879"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"375","DOI":"10.3390\/e6040375","article-title":"On the use of entropy to predict boundary layer stability","volume":"6","author":"Walsh","year":"2004","journal-title":"Entropy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1115\/1.1845551","article-title":"Modeling of entropy production in turbulent flows","volume":"126","author":"Adeyinka","year":"2004","journal-title":"J. Fluids Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2306","DOI":"10.1063\/1.858537","article-title":"Generalized smagorinsky model for anisotropic grids","volume":"5","author":"Scotti","year":"1993","journal-title":"Phys. Fluids A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1023\/A:1009901401183","article-title":"Detached eddy simulation past a circular cylinder","volume":"63","author":"Travin","year":"2000","journal-title":"Flow Turbul. Combust."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Zhao, R., and Yan, C. (2012). Detailed investigation of detached-eddy simulation for the flow past a circular cylinder at Re = 3900. Appl. Mech. Mater. J., 401\u2013412.","DOI":"10.1007\/978-3-642-31818-4_35"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zdravkovich, M.M. (1997). Flow around Circular Cylinders, Oxford University Press.","DOI":"10.1093\/oso\/9780198563969.001.0001"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1017\/S0022112065000162","article-title":"Investigation of the flow behind a two-dimensional model with a blunt trailing edge and flitted with splitter plates","volume":"21","author":"Bearman","year":"1965","journal-title":"J. Fluid Mech."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"085101","DOI":"10.1063\/1.2957018","article-title":"Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900","volume":"20","author":"Philippe","year":"2008","journal-title":"Phys. Fluids"},{"key":"ref_27","unstructured":"Norberg, C. (1987). Effects of Reynolds Number, Low-Intensity Free-Stream Turbulence on the Flow around a Circular Cylinder, Chalmer University of Technology."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1063\/1.870318","article-title":"Numerical studies of flow over a circular cylinder at ReD = 3900","volume":"12","author":"Kravchenko","year":"2000","journal-title":"Phys. Fluids"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"60","DOI":"10.2514\/3.51047","article-title":"Reattachment of a compressible turbulent free shear layer","volume":"20","author":"Settles","year":"1982","journal-title":"AIAA J."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Fan, T.C., Tian, M., Edwards, J.R., and Hassan, H.A. (2001, January 11\u201314). Validation of a hybrid Reynolds-Averaged\/Large-Eddy simulation method for simulating cavity flameholder configurations. Proceedings of the 31st AIAA Fluid Dynamics Conference & Exhibit, Anaheim, CA, USA.","DOI":"10.2514\/6.2001-2929"},{"key":"ref_31","unstructured":"Wilcox, D.C. (2006). Turbulence Modeling for CFD, DCW Industries. [3rd ed.]."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/3\/93\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:29:18Z","timestamp":1760207358000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/3\/93"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,27]]},"references-count":31,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["e19030093"],"URL":"https:\/\/doi.org\/10.3390\/e19030093","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,27]]}}}