AIAA JOURNAL Vol. 38, No. 3, March 2000 Large Eddy Simulations of the Flow Around a Square Prism C. Fureby, ¤ G. Tabor, † H. G. Weller, † and A. D. Gosman ‡ Imperial College, London, England SW7 2BX, United Kingdom The aim of this study is to examine unsteady wake ows by means of large eddy simulation (LES). In particular, the ow around a square prism in a channel at a prism-height Reynolds number of 2:14 £ 10 4 is studied using different subgrid scale (SGS) models and different grids. Results from rst- and second-order statistical moments of the velocity are validated against two sets of experimental data and compared with different Reynolds-average simulations. All LES models correctly reproduce the rst- and second-order statistical moments of the resolvable velocity, the global parameters, such as the lift and drag coefcients and their uctuations, and the Strouhal number, as well as the length of the recirculation region. However, a locally rened grid is necessary to reproduce the maximum velocity within the recirculation region. LES appears virtually independent of the details of the SGS model if it can correctly channel kinetic energy out of eddies close to the cutoff wave number to prevent aliasing provided that the resolution is ne enough to ensure that the cutoff wave number is within the inertial subrange. In addition, phase-averaged ow quantities are compared with experimental data; this comparison supports the belief in LES as a reliable and accurate model for studying unsteady ows. The LES results are subsequently used to analyze and describe the topology of the ow. I. Introduction T HE ow around bluff bodies is very complex and can involve regions of laminar, transitional, and turbulent ows, unsteady separation and reattachment associated with the obstacle, and the formation of coherent structures, particularly in the wake region of the ow. The wake is spatially complex, often consisting of curved shearlayersenclosinga regionof extremecomplexitycharacterized by the presence of intense vortices, but also including the entrain- ment of irrotationalow elements into the wake from the surround- ings. The vortices are generated by shear around the obstacle and are shed and convected down the wake. If the obstacle exhibits a degreeof bilateralsymmetry,thewakemay exhibitself-inducedpe- riodicity because of vortices being shed from alternate sides of the obstacle.The second effect of the vortex shedding is the generation of intense uctuating forces on the obstacle in the streamwise and spanwise directions.Many industrialapplicationsand environmen- tal situations including tall buildings and technical structures such as cooling towers, chimneys and suspension bridges, ame holders in combustionchambers,cooling of electronicequipmentand com- ponents and ow-metering devices require better predictionsof the ow characteristics. These demands, as well as the overall desire to increase our present understanding of the fundamental physical processesgoverningsuch ows, demonstratethe need for advanced ow modeling. In this study a square prism mounted in a rectilinear channel is chosen as a natural compactly characterized bluff body, the separation points of which are xed and known, unlike the case of a cylinder, where the separation points are known to wander in time. An additional advantage of this geometry, as observed in ex- perimental studies, 1,2 is the favorable pressure gradient just prior to separation,resultingin a very thin separatingshear layer; effects on shear-layer development caused by initial shear-layer thickness could therefore be neglected. Direct numerical simulation (DNS) of the Navier– Stokes equations 3 (NSE), in which all eddies down to the dissipationscales are properly simulated, is almost impossible because of the large computationaleffort in resolving all scales of motion. Thus, the ne- Received 29 January 1999; revision received 8 March 1999; accepted for publication 25 August 1999. Copyright c ° 1999 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. ¤ Research Associate, Department of Mechanical Engineering; currently Senior Researcher, Department of Warheads and Propulsion, FOA Defence Research Establishment, S-17200 Stockholm, Sweden. Member AIAA. † Research Associate, Department of Mechanical Engineering. ‡ Professor, Department of Mechanical Engineering. cessity for other, less computationally expensive but still accurate methods is apparent. In Reynolds-averagedsimulation 4 (RAS), all eddiesare averagedoverto giveequationsfor variablesrepresenting the mean ow. These equations are similar to the NSE but contain terms representing the effects of the turbulence on the mean ow that require modeling. The success of RAS is limited because the large eddies responsible for the primary transport are geometry de- pendent,and experienceindicates that RAS often break down when a variety of ows are considered. 5 Large eddy simulation 6 (LES) lies between the extremes of DNS and RAS in resolution and com- putational cost using modied NSE, in which eddies smaller than the grid spacing are eliminated from the dynamics by low-pass l- tering whereas their effect on the resolvable motion is provided by subgridscale (SGS) models. 7,8 It is clear from the wealth of simula- tions that the larger the part of the energy spectrum that is resolved the better the predictions.A recent alternative 9 involves solving the NSE by high-resolution monotone algorithms in which nonlinear high-frequency lters are built into the models providing implicit SGS models, and thus explicit SGS can be dispensed with. The aims of this study are to 1) analyse the predictivecapabilities of LES models based on the eddy-viscosityhypothesisin unsteady, isochoric,wake ows; 2) examinethe insensitivityof LES modelsto thespecics oftheSGS model;3)investigatethe physicsofunsteady wake ow involvingseparation,streamlinecurvature,recirculation, unsteady vortex shedding, and large-scale complex ow structures at a moderately high Reynolds number; and moreover 4) generate a database of rst- and second-orderstatistical moments of the ve- locity for the ow around a square prism at Re = 2.14 £ 10 4 , which can be used to examine and calibrate conventional RAS models. II. LES Model The uid dynamic model is based on the incompressible NSE (Ref. 3), i.e., conservation of mass and balance of momentum of a linear viscous uid. In LES the dependent variables are split into grid scale and SGS components f = ¯ f + f 0 , where ¯ f = G ¤ f and G = G( x, D ) is the lter kernel. The ltering is ideally required to be distributive, associative, and to commute with differentia- tion. Convolving the NSE with G, using the commutation rela- tions [r, G ¤ ] f = [( @G / @D ) ¤ f ] grad D + ( Gf n) @D , where n is the outward pointing unit normal to @D, and [@ t , G¤ ] f = 0, the LES equations results. The decit of commutation results in additional termsinthe LES equations;however,followingRef.10,anorder-of- magnitude analysis indicates that these are of ( D 2 ), whereas the unresolved transport terms are of ( D n ), where 4 3 < n < 2. Hence, to a rst-order approximation the LES equations are 442