{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T03:20:04Z","timestamp":1762917604537,"version":"build-2065373602"},"reference-count":65,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,9,18]],"date-time":"2015-09-18T00:00:00Z","timestamp":1442534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper discusses the results of computational fluid dynamics simulations carried out for rectangular cylinders with various side ratios of interest for many civil engineering structures. A bridge deck of common cross-section geometry was also considered. Unsteady Reynolds-averaged Navier\u2013Stokes (URANS) equations were solved in conjunction with either an eddy viscosity or a linearized explicit algebraic Reynolds stress model. The analysis showed that for the case studies considered, the 2D URANS approach was able to give reasonable results if coupled with an advanced turbulence model and a suitable computational mesh. The simulations even reproduced, at least qualitatively, complex phenomena observed in the wind tunnel, such as Reynolds number effects for a sharp-edged geometry. The study focused both on stationary and harmonically oscillating bodies. For the latter, self-excited forces and flutter derivatives were calculated and compared to experimental data. In the particular case of a benchmark rectangular 5:1 cylinder, 3D detached eddy simulations were also carried out, highlighting the improvement in the accuracy of the results with respect to both 2D and 3D URANS calculations. All of the computations were performed with the Tau code, a non-commercial unstructured solver developed by the German Aerospace Center.<\/jats:p>","DOI":"10.3390\/computation3030479","type":"journal-article","created":{"date-parts":[[2015,9,21]],"date-time":"2015-09-21T02:25:40Z","timestamp":1442802340000},"page":"479-508","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Applicability of URANS and DES Simulations of Flow Past Rectangular Cylinders and Bridge Sections"],"prefix":"10.3390","volume":"3","author":[{"given":"Claudio","family":"Mannini","sequence":"first","affiliation":[{"name":"CRIACIV\/Department of Civil and Environmental Engineering, University of Florence, Via S. Marta 3, Florence 50139, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2015,9,18]]},"reference":[{"key":"ref_1","unstructured":"Schwamborn, D., Gerhold, T., and Heinrich, R. (2006, January 5\u20138). The DLR-Tau code: Recent applications in research and industry. Proceedings of the European Conference on Computational Fluid Dynamics, Delft, The Netherlands."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Jameson, A., Schmidt, W., and Turkel, E. (1981, January 23\u201325). Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes. Proceedings of the AIAA 14th Fluid and Plasma Dynamics Conference, Palo Alto, CA, USA.","DOI":"10.2514\/6.1981-1259"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Mavriplis, D., Jameson, A., and Martinelli, L. (1989, January 9\u201312). Multigrid solution of the Navier-Stokes equations on triangular meshes. Proceedings of the 27th AIAA Aerospace Sciences Meeting, Reno, NV, USA.","DOI":"10.2514\/6.1989-120"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/3-540-32382-1_6","article-title":"Algorithmic Developments in TAU","volume":"Volume 89","author":"Kroll","year":"2005","journal-title":"MEGAFLOW\u2014Numerical Flow Simulation for Aircraft Design, Notes on Numerical Fluid Mechanics and Multidisciplinary Design"},{"key":"ref_5","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 AIAA Aerospace Sciences Meeting and Exhibit, NV, USA.","DOI":"10.2514\/6.1992-439"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"756","DOI":"10.2514\/3.13137","article-title":"Comparison of eddy viscosity-transport turbulence models for three-dimensional, shock-separated flowfields","volume":"34","author":"Edwards","year":"1996","journal-title":"AIAA J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"269","DOI":"10.2514\/3.12149","article-title":"Two-equation k-\u03c9 turbulence model for aerodynamic flows","volume":"32","author":"Menter","year":"1994","journal-title":"AIAA J."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Meier, G.E.A., and Sreenivasan, K.R. (2006). IUTAM Symposium on One Hundred Years of Boundary Layer Research, Springer.","DOI":"10.1007\/978-1-4020-4150-1"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1396","DOI":"10.2514\/2.2089","article-title":"Restatement of the Spalart\u2013Allmaras eddy-viscosity model in strain-adaptive formulation","volume":"41","author":"Rung","year":"2003","journal-title":"AIAA J."},{"key":"ref_10","unstructured":"Wilcox, D. (2006). Turbulence Modeling for CFD, DCW Industries, Inc.. [3rd ed.]."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1016\/S0167-6105(01)00134-9","article-title":"Comparison of LES and RANS in bluff-body flows","volume":"89","author":"Schmidt","year":"2001","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Rung, T., L\u00fcbcke, H., Franke, M., Xue, L., Thiele, F., and Fu, S. (1999, January 24\u201326). Assessment of Explicit Algebraic Stress Models in transonic flows. Proceedings of the 4th International Symposium on Engineering Turbulence Modeling and Experiments, Ajaccio, France.","DOI":"10.1016\/B978-008043328-8\/50063-1"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1017\/S0022112093002034","article-title":"On explicit algebraic stress models for complex turbulent flows","volume":"254","author":"Gatski","year":"1993","journal-title":"J. Fluid Mech."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.2514\/3.10041","article-title":"Reassessment of the scale-determining equation for advanced turbulence models","volume":"26","author":"Wilcox","year":"1988","journal-title":"AIAA J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1007\/978-3-540-39507-2_21","article-title":"Non linear eddy viscosity models and explicit algebraic Reynolds stress models","volume":"Volume 94","author":"Haase","year":"2006","journal-title":"FLOMANIA\u2014A European Initiative on Flow Physics Modeling"},{"key":"ref_16","unstructured":"Spalart, P.R., Jou, W.H., Strelets, M.K., and Allmaras, S.R. (1997, January 4\u20138). Comments on the feasibility of LES for wings, and on a hybrid RANS\/LES approach. Advances in DNS\/LES, Proceedings of the First AFOSR International Conference on DNS\/LES, Louisiana Tech University, Ruston, LA, USA."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Shur, M.L., Spalart, P.R., Strelets, M.K., and Travin, A. (1999, January 24\u201326). Detached-Eddy Simulation of an airfoil at high angle of attack. Proceedings of the 4th International Symposium on Engineering Turbulence Modeling and Experiments, Ajaccio, France.","DOI":"10.1016\/B978-008043328-8\/50064-3"},{"key":"ref_18","unstructured":"Spalart, P.R. (2001). Young-Person\u2019s Guide to Detached-Eddy Simulation Grids, NASA Langley Research Center. Technical Report; CR-2001-211032."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Strelets, M.K. (2001, January 8\u201311). Detached Eddy Simulation of massively separated flows. Proceedings of the 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA.","DOI":"10.2514\/6.2001-879"},{"key":"ref_20","unstructured":"Soda, A. (2006). Numerical Investigation of Unsteady Transonic Shock\/Boundary-Layer Interaction for Aeronautical Applications. [PhD Thesis, RWTH Aachen University]."},{"key":"ref_21","unstructured":"Weinman, K., van der Ven, H., Mockett, C., Knopp, T., Kok, J., Perrin, R., and Thiele, F. (2006, January 5\u20138). A study of grid convergence issues for the simulation of the massively separated flow around a stalled airfoil using DES and related methods. Proceedings of the European Conference on Computational Fluid Dynamics, Delft, The Netherlands."},{"key":"ref_22","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_23","unstructured":"Travin, A.K., Shur, M.L., Spalart, P.R., and Strelets, M.K. (2006, January 5\u20138). Improvement of Delayed Detached-Eddy Simulation for LES with wall modeling. Proceedings of the European Conference on Computational Fluid Dynamics, Delft, The Netherlands."},{"key":"ref_24","first-page":"341","article-title":"Contributions of DLR in DESider","volume":"Volume 103","author":"Haase","year":"2009","journal-title":"DESider\u2014A European Effort on Hybrid RANS-LES Modelling"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1006\/jcph.1996.5597","article-title":"On the effect of numerical errors in Large Eddy Simulations of turbulent flow","volume":"131","author":"Kravchenko","year":"1997","journal-title":"J. Comput. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Whitfield, D.L., and Janus, J.M. (1984, January 25\u201327). Three-dimensional Unsteady Euler equations solution using flux vector splitting. Proceedings of the 17th AIAA Fluid Dynamics, Plasma Dynamics, and Lasers Conference, Snowmass, CO, USA.","DOI":"10.2514\/6.1984-1552"},{"key":"ref_27","first-page":"11","article-title":"Investigation of unsteady air flow around two-dimensional rectangular cylinders","volume":"35","author":"Mannini","year":"2011","journal-title":"Trans. Famena"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1002\/fld.1650210702","article-title":"Simulations of the unsteady separated flow past a normal flat plate","volume":"21","author":"Najjar","year":"1995","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1230","DOI":"10.2514\/1.9694","article-title":"Three dimensionality in Reynolds-Averaged Navier-Stokes solutions around two-dimensional geometries","volume":"43","author":"Shur","year":"2005","journal-title":"AIAA J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1017\/S0022112084002640","article-title":"The effects of turbulence on the mean flow past two-dimensional rectangular cylinders","volume":"149","author":"Nakamura","year":"1984","journal-title":"J. Fluid Mech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1006\/jfls.2001.0433","article-title":"Application of a modified k-\u03f5 model to the prediction of aerodynamic characteristics of rectangular cross-section cyliders","volume":"16","author":"Shimada","year":"2002","journal-title":"J. Fluids Struct."},{"key":"ref_32","unstructured":"Schewe, G. (1984). Untersuchung der aerodynamischen Kr\u00e4fte, die auf stumpfe Profile bei gro\u00dfen Reynolds-Zahlen wirken, Institut f\u00fcr Aeroelastik. (In German)."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1017\/S0022112095004435","article-title":"A laser Doppler velocimetry study of ensemble-averaged characteristics of the turbulent flow near wake of a square cylinder","volume":"304","author":"Lyn","year":"1995","journal-title":"J. Fluid Mech."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/S0167-6105(97)00147-5","article-title":"Comparison of LES and RANS calculations of the flow around bluff bodies","volume":"69\u201371","author":"Rodi","year":"1997","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1017\/S0022112082003115","article-title":"Strouhal numbers of rectangular cylinders","volume":"123","author":"Okajima","year":"1982","journal-title":"J. Fluid Mech."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/S0167-6105(02)00342-2","article-title":"Spanwise coherence characteristics of surface pressure field on 2-D bluff bodies","volume":"91","author":"Matsumoto","year":"2003","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.jfluidstructs.2013.02.013","article-title":"Reynolds-number-effects in flow around a rectangular cylinder with aspect ratio 1:5","volume":"39","author":"Schewe","year":"2013","journal-title":"J. Fluids Struct."},{"key":"ref_38","unstructured":"Mannini, C., Marra, A.M., Pigolotti, L., and Bartoli, G. (2015, January 21\u201326). Unsteady pressure and wake characteristics of a benchmark rectangular section in smooth and turbulent flow. Proceedings of the 14th International Conference on Wind Engineering, Porto Alegre, Brazil."},{"key":"ref_39","unstructured":"Bartoli, G., Bruno, L., Buresti, G., Ricciardelli, F., Salvetti, M.V., and Zasso, A. BARC Overview Document. Available online: http:\/\/www.aniv-iawe.org\/barc."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1016\/j.compfluid.2010.05.014","article-title":"Unsteady RANS modeling of flow past a rectangular cylinder: Investigation of Reynolds number effects","volume":"39","author":"Mannini","year":"2010","journal-title":"Comput. Fluids"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Tropea, C., Jakirlic, S., Heinemann, H.J., Henke, R., and H\u00f6nlinger, H. (2008). New Results in Numerical and Experimental Fluid Mechanics VI, Springer.","DOI":"10.1007\/978-3-540-74460-3"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/S0022-460X(78)80028-5","article-title":"The action of flexible bridges under wind, I: Flutter theory","volume":"60","author":"Scanlan","year":"1978","journal-title":"J. Sound Vib."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0167-6105(96)00005-0","article-title":"Aerodynamic damping of prisms","volume":"59","author":"Matsumoto","year":"1996","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_44","unstructured":"Righi, M. (1996). Aeroelastic Stability of Long Span Suspended Bridges: Flutter Mechanism on Rectangular Cylinders in Smooth and Turbulent Flow. [Ph.D. Thesis, University of Florence]."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/j.jweia.2010.12.016","article-title":"Numerical investigation on the three-dimensional unsteady flow past a 5:1 rectangular cylinder","volume":"99","author":"Mannini","year":"2011","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_46","unstructured":"Mannini, C., and Schewe, G. (2011, January 12\u201315). Detached-eddy simulations of a Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder. Proceedings of the 20th Congress of the Italian Association of Theoretical and Applied Mechanics, Bologna, Italy."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1016\/j.compfluid.2003.10.002","article-title":"A low-diffusion MUSCL scheme for LES on unstructured grids","volume":"33","author":"Camarri","year":"2004","journal-title":"Comput. Fluids"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.jweia.2009.10.005","article-title":"3D flow around a rectangular cylinder: A computational study","volume":"98","author":"Bruno","year":"2010","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_49","unstructured":"Matsumoto, M. Personal communication."},{"key":"ref_50","unstructured":"Galli, F. (2005). Comportamento Aerodinamico di Strutture Snelle Non Profilate: Approccio Sperimentale e Computazionale. [Master\u2019s Thesis, Politecnico di Torino]. (In Italian)."},{"key":"ref_51","unstructured":"Bronkhorst, A.J., Geurts, C.P.W., and van Bentum, C.A. (2011, January 10\u201315). Unsteady pressure measurements on a 5:1 rectangular cylinder. Proceedings of the 13th International Conference on Wind Engineering, Amsterdam, The Netherlands."},{"key":"ref_52","unstructured":"Lander, D.C., Baker, J., Letchford, C.W., Amitay, M., and Kopp, G.A. (2015, January 21\u201326). The effect of freestream turbulence on vortex formation in the wake of a square cylinder. Proceedings of the 14th International Conference on Wind Engineering, Porto Alegre, Brazil."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.jweia.2012.03.018","article-title":"Simulated flow around a rectangular 5:1 cylinder: Spanwise discretisation effects and emerging flow features","volume":"104\u2013106","author":"Bruno","year":"2012","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_54","unstructured":"Ricciardelli, F., and Marra, A.M. (2008, January 20\u201324). Sectional aerodynamic forces and their longitudinal correlation on a vibrating 5:1 rectangular cylinder. Proceedings of the 6th International Colloquium on Bluff Body Aerodynamics and Applications, Milan, Italy."},{"key":"ref_55","unstructured":"Mannini, C. (2008). Flutter Vulnerability Assessment of Flexible Bridge Decks. [Ph.D. Thesis, Verlag Dr. M\u00fcller]."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"399","DOI":"10.12989\/was.2001.4.5.399","article-title":"Pressure distribution and aerodynamic forces on stationary box bridge sections","volume":"4","author":"Ricciardelli","year":"2001","journal-title":"Wind Struct."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1016\/j.jweia.2010.06.010","article-title":"Unsteady RANS simulations of flow around a bridge section","volume":"98","author":"Mannini","year":"2010","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1016\/j.jweia.2008.02.015","article-title":"Prediction of aerodynamic characteristics of a box girder bridge section using the LES turbulence model","volume":"96","author":"Sarwar","year":"2008","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.1016\/j.compfluid.2010.05.005","article-title":"Three dimensional numerical simulations of long-span bridge aerodynamics, using block-iterative coupling and DES","volume":"39","author":"Bai","year":"2010","journal-title":"Comput. Fluids"},{"key":"ref_60","first-page":"141","article-title":"Bridge flutter derivatives based on computed, validated pressure fields","volume":"104\u2013106","author":"Fisch","year":"2012","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jweia.2013.05.002","article-title":"On the evaluation of bridge deck flutter derivatives using RANS turbulence models","volume":"119","author":"Brusiani","year":"2013","journal-title":"J. Wind Eng. Ind. Aerodyn."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.strusafe.2014.07.005","article-title":"Aerodynamic uncertainty propagation in bridge flutter analysis","volume":"52","author":"Mannini","year":"2015","journal-title":"Struct. Saf."},{"key":"ref_63","unstructured":"Mannini, C., Sbragi, G., Schewe, G., and Borri, C. (2011, January 4\u20136). Determination of flutter derivatives for a box-girder bridge deck through URANS simulations. Proceedings of the 8th International Conference on Structural Dynamics, Leuven, Belgium."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Mannini, C., Sbragi, G., and Schewe, G. (2015). Analysis of self-excited forces for a box-girder bridge deck through unsteady RANS simulations. J. Fluids Struct., submitted.","DOI":"10.1016\/j.jfluidstructs.2016.02.007"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.1016\/j.jweia.2003.09.011","article-title":"On the wind loading mechanism of long-span bridge deck box sections","volume":"91","author":"Ricciardelli","year":"2003","journal-title":"J. Wind Eng. Ind. Aerodyn."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/3\/3\/479\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:48:55Z","timestamp":1760215735000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/3\/3\/479"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,18]]},"references-count":65,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,9]]}},"alternative-id":["computation3030479"],"URL":"https:\/\/doi.org\/10.3390\/computation3030479","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2015,9,18]]}}}