Research ArticleEffects of Low Incoming Turbulence on the Flow arounda 5 1 Rectangular Cylinder at Non-Null-Attack Angle

M Ricci L Patruno S de Miranda and F Ubertini

DICAM University of Bologna Viale Risorgimento 2 40136 Bologna Italy

Correspondence should be addressed to L Patruno lucapatrunouniboit

Received 3 January 2016 Revised 22 June 2016 Accepted 21 July 2016

Academic Editor Manfred Krafczyk

Copyright copy 2016 M Ricci et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The incompressible high Reynolds number flow around the rectangular cylinder with aspect ratio 5 1 has been extensivelystudied in the recent literature and became a standard benchmark in the field of bluff bodies aerodynamics The majority of theproposed contributions focus on the simulation of the flow when a smooth inlet condition is adopted Nevertheless even whennominally smooth conditions are reproduced inwind tunnel tests a low turbulence intensity is present together with environmentaldisturbances and model imperfections Additionally many turbulence models are known to be excessively dissipative in laminar-to-turbulent transition zones generally leading to overestimation of the reattachment length In this paper Large Eddy Simulationsare performed on a 5 1 rectangular cylinder at non-null-attack angle aiming at studying the sensitivity of such flow to a low levelof incoming disturbances and compare the performance of standard Smagorinsky-Lilly and Kinetic Energy Transport turbulencemodels

1 Introduction

Thanks to the increase in the computer power the researchin the field of Wind Engineering is more and more makinguse of Computational Fluid Dynamics techniques in order toassess the effects of wind loading on structures

In fact a number of flows usually encountered aroundstructures relevant to Civil Engineering applications likebridge decks and buildings are characterized by the presenceof shear layers and separation bubbles which render theirprediction by means of CFD an extremely challenging task

Due to their special geometric simplicity prismaticshapes have been deeply investigated in the literature andhave been often adopted as a prototype of fully detached andreattached flowsAnumber of experimental studies identifiedthe main mechanisms involved in the definition of theflow field around such simple nominally two-dimensionalshapes and highlighted the fundamental role played by thestability conditions of the shear layers detached from theleading edges especially for shapes whose aspect ratio ishigher than three which approximately corresponds to thethreshold separating fully detached and reattached flows[1ndash4] In particular Nakamura and Ohya focused on the

effects of incoming turbulence showing that the reattach-ment point migrates upstream with increasing turbulencelevels [1] Subsequently it was clarified that Kelvin-Helmholtzinstabilities appear in the detached shear layers due toincoming disturbances destabilizing them and thus causingthe reattachment point upstream migration This result wasalso highlighted byHillier andCherry [5] andKiya and Sasaki[6] that investigated the effects of free-stream turbulenceon the topology of separation bubbles Their experimentsshowed that the incoming flow turbulence deeply influencespressure distributions in terms of both mean and standarddeviation Due to these considerations it appears that theincoming flow turbulence should be accurately taken intoaccount when dealing with wind loading problems for bothexperimental and numerical investigations

With regard to numerical studies several research workshave been proposed aiming at reproducing the flow fieldaround bluff bodies Among themYu andKareemperformedLarge Eddies Simulations (LES) around rectangular cylinderswith varying aspect ratio at null-attack angle in a two-and three-dimensional framework [7] Sohankar et al [8]proposed simulations of rectangular cylinders at non-null-attack angle focusing on very low Reynolds numbers for

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 2302340 12 pageshttpdxdoiorg10115520162302340

2 Mathematical Problems in Engineering

which the flow is expected to be mainly laminar Such simu-lations showed good results in terms of bulk parameters andhighlighted that when using the standard deviation of the liftcoefficient as an indicator the simulation appears to be verysensitive to the adopted numerical setups Shimada proposeda detailed validation of a two-layer 119896-120576 model with a modi-fication on the turbulent kinetic energy production term byanalyzing the flowfield around awide selection of rectangularcylinders at null-attack angle [9] while Noda and Nakayamaproposed LES including the effect of incoming turbulence(a turbulence intensity equal to 5 was considered) show-ing that the standard Smagosinsky model is suitable forreproducing the effects induced by incoming turbulence forengineering purposes [10] Moreover a wide number ofexperimental and computational studies have been also pro-posed in order to study the aeroelastic behavior of such bodiesin smooth [11] and turbulent conditions [12] In particularDaniels et al [13] performed LES on an elastically mountedrectangular cylinder in smooth and turbulent inflow condi-tions showing that increasing the turbulence intensity candiminish significantly the amplitude of oscillations

In all it appears that while all computational modelsare able to approximately reproduce some characteristicsof the flow field their accuracy strongly depends on theadopted numerical setups and on the quantities taken intoconsideration Indeed if on one hand the mean flow charac-teristics are generally reproduced by numerical simulations ina satisfactoryway on the other hand the standard deviation ofvelocity and pressure fields is often predicted with much lessaccuracy [14] It also emerged that due to the large numberof parameters whichmight affect the flow topology a detailedmapping of the prisms aerodynamic behavior has not beenyet achieved

Recently the BARC project focused on the simulationof the turbulent flow around a 5 1 rectangular cylinderand became a standard benchmark for comparison betweenexperimental data and numerical simulations [15] Theoverview of the first four years of activity of the BARC project[16] highlighted that even experimental results extracted byvarious research groups show a remarkable variability whosecauses are currently not completely clear When numericalsimulations are considered Bruno et al [16] observed thatresults are even more dispersed showing great sensitivity tothe adopted numerical schemes turbulencemodel andmeshsize while their relative importance is difficult to be evaluatedat the current stage In this context uncertainty studies canplay a fundamental role In particular Witteveen et al [17]showed that the flowfield around the 5 1 rectangular cylinderis very sensible to setup parameters as small variations of theangle of attack the incoming turbulence intensity and theincoming turbulence length scales

It is also noticed that while disturbances are alwayspresent in experimental conditions when numerical simu-lations are performed a fictitious environment is producedwhere imperfections are introduced only by the differen-tial problem discretization and by the numerical solutionitself Beside the absence of incoming disturbances manyturbulence models are known to be excessively dissipative inlaminar-to-turbulent transition zones [18] Thus numerical

simulations can be considered as a limit case expected toproduce excessively stable shear layers and thus generallyoverestimating the reattachment length

In this paper the performances of the standardSmagorinsky-Lilly [19 20] model and the Kinetik EnergyTransport [21] model are tested when the incoming flowis characterized by a very low turbulence intensity To thispurpose the flow around a fixed 5 1 rectangular cylinder isconsidered at 4∘ attack angle In fact the mismatch betweenexperimental and numerical results has been found toincrease with the attack angle when perfectly smooth inletconditions are adopted together with a standard SM turbu-lence model [22]

The paper is organized as follows In Section 2 the experi-mental setup adopted in the wind tunnel tests is briefly des-cribed while in Section 3 the numerical features of the com-putational model are discussed Numerical results obtainedfrom simulations are presented in Section 4 and comparedwith the experimental data Finally in Section 5 some con-clusions are drawn

2 Experimental Setup

In this section the setup used to extract the experimentalresults used for comparison with numerical simulations isdescribed The experimental study was performed in theopen-circuit boundary layer wind tunnel of CRIACIV labo-ratory located in Prato Italy [23]

An aluminium model characterized by width 119861 equalto 300mm depth 119863 equal to 60mm and length 119871 equalto 2380mm was employed in the experimental tests andequipped with 62 pressure taps monitored by two 32-channelPSI miniaturized piezoelectric scanners at a sampling rate of500Hz [24] The wind tunnel test section is 242m large and160m high so that the resulting blockage ratio was 375The Reynolds number based on 119863 was varied from 22 times 10

4

to 112times 105 while incoming turbulence intensity was variedfrom 07 to 136

In the present study the experimental configuration withnose-up angle equal to 4∘ at Reynolds number based on119863 equal to 55 times 104 has been used as a reference for thenumerical simulations

3 Computational Model

In this section the characteristics of the computationalmodelare reported and compared with other studies together withthe description of the adopted boundary conditions andnumerical setups

According to the aim of this study the lowest turbu-lence intensity recorded in the available wind tunnel testsrepresenting the experimental approximation of the smoothflow condition is adopted so that the incoming turbulenceintensity is set to be equal to 07 The inflow turbulent fieldis synthetically generated by using the Modified Discretizingand Synthesizing Random Flow Generator method proposedby Castro et al [25 26] which guarantees the divergence-free condition and is able to satisfy prescribed turbulencespectrum and spatial correlations It is worth noting that if

Mathematical Problems in Engineering 3

Periodic

Periodic

Outlet boundaryInlet boundary

Lx

x

z

D

yy

Symmetry

s

Dx

Dy

DzB = 5D

Symmetry

Λx

Figure 1 Model and computational domain geometries [15]

(a) (b)

Figure 2 Mesh adopted for the LES simulation detail of the mesh close to the solid boundary (a) and mesh in proximity of the body andwake (b)

the fluctuation field is introduced at the inlet boundary largepressure fluctuations are generated due to the violation of theNavier-Stokes equations In order to avoid this phenomenonfluctuations are introduced in the computational domain bymodifying the velocity-pressure coupling algorithm follow-ing the procedure reported by Kim et al [27]

The computational domain size and the grid resolutionhave been defined according to the guidelines provided byBruno et al [16] and the BARC main setup [15] As showedin Figure 1 the domain dimensions are such that 119863

119909= 40119861

and 119863119910= 30119861 while 119863

119911= 20119861 The resultant blockage

ratio is 067 and therefore blockage ratio effects can beneglected In order to avoid boundary effects on the solutionthe distance between the prism leading edge and the inletboundary is set to be equal to Λ

119909= 16119861

As showed in Figure 2(a) a structured mesh is adoptedin the boundary layer close to the wall with along-winddimension 120575

119909119861 = 25 times 10

minus3 and crosswind dimension120575119910119861 = 15 times 10

minus3 The maximum 119910+ recorded during all

simulations is found to be equal to 661 while the meanone equals 202 Outside the boundary layer the mesh isunstructured and quad dominated and its size is slowlycoarsened up to approximately 120575

119909119861 = 120575

119910119861 = 18 times 10

minus2

in the wake (see Figure 2(b)) where the cells aspect ratio isapproximately one In order to limit the numerical dissipation

and to propagate the fluctuation field minimizing the energyloss the mesh sizing in front of the rectangular cylinder hasdimensions 120575

119909119861 = 120575

119910119861 = 5times10

minus2 and ismaintained almostconstant and structured until the inlet boundary is reached

In 119911 direction the cell dimension is 120575119911119861 = 002The final

resultant mesh is composed of about 160119872 finite volumes Acomparison between the domain size and themesh resolutionadopted in the present study and similar ones is reported inTables 1 and 2

With respect to turbulence modeling two subgridscales models have been considered namely the standardSmagorisnky-Lilly (SM)model and theKinetic EnergyTrans-port (KET) model The fluid flow governing equations arereported in

120597119906119894

120597119909119894

= 0

120597120588119906119894

120597119905+120597120588119906119894119906119895

120597119909119895

= minus120597119901

120597119909119894

+120597120591119894119895

120597119909119895

minus

120597120591sgs119894119895

120597119909119895

(1)

where the overbar denotes the spatially filtered quantities and119906119894represents the velocity in the 119894th direction while 119901 is the

pressure 120591119894119895is the resolved viscous stress tensor and 120591sgs

119894119895

is

4 Mathematical Problems in Engineering

Table 1 Parameters of the computational domain as reported byBruno et al [16]

Source 119863119909

119861 119863119910

119861 119863119911

119861 Λ119909

119861

Present simulation 40 30 2 16

Bruno et al [30 32] 41 302 1 2 4 15

Grozescu et al [33] 41 302 1 15

Mannini et al [34] 200 200 1 2 100

the subgrid stress tensor The resolved viscous stress tensor120591119894119895can be written as

120591119894119895= 2120583 [119878

119894119895minus1

3120575119894119895119878119896119896] (2)

where 119878119894119895represents the resolved strain rate tensor whose

expression is reported below

119878119894119895=1

2(120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (3)

By assuming Boussinesqrsquos hypothesis the subgrid stresstensor 120591sgs

119894119895

can be written as

120591sgs119894119895

= 120588 (119906119894119906119895minus 119906119894119906119895)

= minus2120588]119905(119878119894119895minus1

3120575119894119895119878119896119896) +

2

3120588120575119894119895119896sgs

(4)

where 119896sgs is the subgrid kinetic energy

119896sgs=1

2(119906119894119906119894minus 119906119894119906119894) (5)

and ]119905is the turbulent eddy viscosity When the SMmodel is

adopted ]119905is expressed as

]119905= (119862119904Δ)2

radic2119878119894119895119878119894119895 (6)

where 119862119904is the Smagorinsky constant set to be equal to 012

whileΔ is the local grid spacing Conversely if theKETmodelis adopted the transport equation for the subgrid kineticenergy is considered in addition to equations reported in (1)

120597

120597119905(120588119896

sgs) +

120597

120597119909119894

(120588119896sgs119906119894)

=120597

120597119909119894

(120588]119905

120597119896sgs

120597119909119894

) minus 120591sgs119894119895

120597119906119895

120597119909119894

minus 120588119888120598

(119896sgs)32

Δ

(7)

and the turbulent eddy viscosity ]119905is calculated as

]119905= 119888]radic119896

sgsΔ (8)

where 119888120598and 119888] are model constants set to be equal respec-

tively to 105 and 0094With respect to the numerical scheme a centered second-

order accurate scheme is adopted to discretize the spatialderivatives exception made for the nonlinear convective

Table 2 Grid resolution in the boundary layer comparison withmeshes adopted by other authors as reported by Bruno et al [16]

Source 119899119908

119861 120575119909

119861 120575119911

119861

Presentsimulation 50 times 10

minus4

25 times 10minus3

002

Bruno et al[30 32] 50 times 10

minus4

20 times 10minus3 0042ndash001

Grozescu etal [33] 5 times 10

minus4 25 times 10minus4 10 times 10minus2 5 times 10minus3 0042 001

Mannini etal [34] 50 times 10

minus5

14 times 10minus2

00156

term For this term the Linear Upwind Stabilized Transportscheme is used which proved to be particularly successful forLES in complex geometries [28]

Time integration is performed by using the the two-step second-order Backward Differentiation Formulae inaccordance with Bruno et al [29] The solution at eachtime step is obtained by means of the well known PressureImplicit with Splitting of Operator algorithm The adoptednondimensional time step (based on 119863) is Δ119905lowast = 50 times 10minus3leading to amaximumCourant number in all the simulationsequal to 39

Symmetry boundary conditions are imposed at the topand bottom surfaces while periodic conditions are adoptedon the faces normal to the spanwise direction (see Figure 1)At the outlet boundary zero pressure is imposed while at theinlet the null normal gradient of pressure is prescribed

The generated fluctuation field is introduced in thecomputational domain in a plane shifted with respect to theinlet boundary of approximately 50 times 10minus1119861 while the meanvelocity is prescribed at the inlet The power spectral densityof the velocity components along 119909 119910 and 119911 directionsindicated respectively as 119906 V and 119908 is reported in Figure 3for two different points located near the inlet boundary at(minus15119861 0 0) and just upstream the rectangular cylinder at(minus15119861 0 0) As it can be seen the high frequency contentof the spectra appears to be slightly damped proceeding fromthe inlet towards the rectangular cylinderWith respect to thealong-wind turbulent length scale 119871

119906 it is found to be equal

to 119861 for both of the aforementioned locationsThe prism has been equipped with 2500 pressure moni-

tors and data are acquired at each time step leading to 200samples for one nondimensional time unit All simulationshave been run by using the open source finite volumesoftware119874119901119890119899119865119874119860119872 on 160CPUs atCINECAon theGalileocluster (516 nodes 2 eight-core Intel Haswell 240GHzprocessors with 128GB RAM per node)

4 Numerical Results

In this section numerical results obtained for each turbulencemodel with smooth and turbulent inflow condition arereported and systematically compared with experimentaldata In particular the flow bulk parameters obtained fromeach simulation together with a discussion of the resultingflow topology are reported in Section 41 The pressure

Mathematical Problems in Engineering 5

KET I = 07 xB = minus150

KET I = 07 xB = minus15

KET I = 07 xB = minus150

KET I = 07 xB = minus15

KET I = 07 xB = minus150

KET I = 07 xB = minus15

10minus1 10010minus2

fDU

10minus1 10010minus2

fDU

10minus1 10010minus2

fDU

10minus810minus710minus610minus510minus410minus310minus2

S wfU

2

10minus810minus710minus610minus510minus410minus310minus2

S fU

2

10minus810minus710minus610minus510minus410minus310minus2

S ufU

2

Figure 3 Spectra of the velocity time series obtained from the KETsimulation with incoming flow turbulence at different locations

coefficient statistics on the central section are showed inSection 42 while Section 43 focuses on the spanwise-averaged pressure distributions Then in Section 44 corre-lations in the spanwise direction are discussed

Numerical results have been obtained by considering asimulation time of 119905lowast = 1000 119905lowast being the nondimensionaltime unit The postprocessing of data has been carried outconsidering only the last 700 nondimensional time units inorder to avoid flow initialization effects [30]

In order to check the convergence of the recordedstatistics the time-history of the lift coefficient has beensubdivided into ten segments and first- and second-orderstatistics were extracted by incrementally extending the partof the signal considered in the postprocessing Despite therelatively long simulation time (longer than the minimumrequirements [30]) in the worst case a plateau has beenreached for second-order statistics only when 90of the totaltime-history has been used

41 Flow Topology and Bulk Parameters In order to have aqualitative view of the turbulent structures obtained from thenumerical analyses the flow topology in terms of isosurfacesof the invariant 120582

2[31] coloured with pressure is reported

in Figure 4 for the two investigated turbulence models insmooth and turbulent inflow conditions The instantaneousisosurfaces are plotted to correspond with maximum lift Asit can be seen when the inflow turbulence is considered the

Table 3 Reattachment point and main vortex core position

Source 119909119903

down 119909119888

up 119909119888

down 119910119888

up 119910119888

downSM(smooth) 116 054 minus049 096 minus078

SM 119868 = 07 001 091 minus081 091 minus063KET(smooth) 005 109 minus065 101 minus054

KET 119868 =07 004 110 minus063 100 minus051

Table 4 Statistics of the flow bulk parameters

Source 119862119863

1198621015840

119863

119862119871

1198621015840

119871

StSM (smooth) 126 0056 144 057 0116SM 119868 = 07 128 0064 156 061 0115KET (smooth) 137 0079 227 076 0117KET 119868 = 07 13 0080 226 081 0115Pigolotti et al [23] (Exp) 163 mdash 202 mdash 0126Schewe [35] (Exp) 138 mdash 252 mdash 0115

topology showed by the SM model appears to be quite inaccordance with that obtained by means of the KET modelFurthermore both of them comply well with the topologyshowed by theKETmodel in smooth inflow conditions whilein this case the topology obtained by using the SM modelshows a narrower wake

The different behavior of the two turbulence models isalso reflected in Table 3 which shows that the reattachmentpoint at the bottom surface moves from 119909

119903= 116 to

119909119903= 001 when turbulence is introduced and the SM

model considered while no significant differences betweenturbulent and smooth inlet are observed if the KET model isanalyzed

The effect of incoming turbulence can be also appreciatedby observing the streamlines of the time-averaged flow fieldsreported in Figure 5 In particular the SM model appearsto be significantly affected by the presence of incomingturbulence while the KET model appears to be rather stableIt is also noticed that all considered models apart from theSM in smooth flow predict the creation of a small elongatedvortex at the leading edge in correspondence with the topside whose core is located at approximately 119909

119888= minus15

The statistics of the flow bulk parameters are reported inTable 4 (results are made nondimensional with respect to119863)and referred to the global reference system In particular 119862

119863

and119862119871are the drag and the lift coefficients respectively while

their root mean square values are indicated as 1198621015840119863

and 1198621015840119871

respectively Again the results obtained by the two turbulencemodels are in good agreement when a low level of incomingturbulence is considered while remarkable differences areobserved in perfectly smooth flow Furthermore it should benoticed that 119862

119863and 119862

119871 together with the Strouhal number

(St) obtained by taking into account the incoming turbulenceagree quite well with experimental measurements In orderto provide a clearer picture of the obtained results in thefollowing pressure field statistics distributions are analyzed

6 Mathematical Problems in Engineering

minuspdyn pdynminuspdyn pdyn

minuspdyn pdyn minuspdyn pdyn

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 4 Isosurfaces of 1205822

coloured with pressure for the two analyzed turbulence models

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 5 Time-averaged streamlines for the two analyzed turbulence models

42 Central Section Statistics In this section the pressurecoefficient statistics on the prism central section are analyzedData are presented by adopting the curvilinear abscissa 119904as reported in Figure 1 The upwind face of the prism isidentified by 00 le 119904119863 le 05 and the along-wind surfacesare identified by 05 le 119904119863 le 50 while the downwind face isidentified by 55 le 119904119863 le 60

Figure 6 shows the distribution of the pressure statisticsobtained by means of the present simulations and compari-son with experimental results As it can be noticed if the topsurface is considered the time-averaged pressure coefficient119862119901 distribution predicted by the KET model is almost

in perfect accordance with the experimental data for both

smooth and turbulent inflow conditions Contrarily the SMmodel approaches experimental results only when turbulentinlet conditions are adopted Observing 1198621015840

119901

on the samesurface the KET model always complies with experimentalmeasurements with the peak position and the experimentaltrends being reproduced with good accuracy Generally theSM model appears to be unable to correctly reproduce theshape of the pressure recovery not catching the change ofsteepness that occurs at about 119904119863 = 3 in correspondencewith the separation between the vortex shedding and thevortex coalescing zones as individuated in [30]

When 119862119901distribution on the bottom surface is analyzed

the SMmodel appears to be very sensitive to small turbulence

Mathematical Problems in Engineering 7

Cp

Cp

Cp

Cp

SM KET

SM KET

SM KET

SM KET

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

1 2 3 4 5 60sD

minus10

minus05

00

05

10

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

1 2 3 4 5 60sD

60 3 4 51 2

sD

1 2 3 4 5 60sD

minus10

minus05

00

05

10

1 2 3 4 5 60sD

Top surface

Bottom surface

Figure 6 Distribution of 119862119901

statistics on the central alignment

8 Mathematical Problems in Engineering

00

01

02

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

543 60 1 2

sD

543 60 1 2

sD

00

01

02

C998400 p

00

01

02

C998400 p

Top surface

Bottom surface

SM

SM KET

KETSM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

SM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

Figure 7 Comparison between 119911-averaged and central section statistics for the SM and KET turbulence models

intensities in the incoming flow In fact the distributionobtained in smooth flow conditions clearly changes whenthe inflow turbulence is considered the reattachment pointmigrates upstream and the distribution shifts approachingthe experimental dataTheKETmodel instead shows again alower sensitivity to the incoming turbulence results obtainedin both configurations being approximately the same TheSM model is very accurate when turbulence is taken intoaccount and shows better performances if compared with theKET model which slightly overestimates the reattachmentlength and underestimates suctions at the leeward edge Theimprovement of the SM model with turbulent inlet observedfor mean values can be noticed also by considering 119862

1015840

119901

distribution on the bottom surface In this case the modelcorrectly predicts the peak position and the trend observedexperimentally even if the peak value is clearly overestimatedThe KET model correctly predicts the peak position and thetrend in particular at the trailing edge where an increment inrms is experimentally observed

The improvement of performances showed by the SMmodel when the incoming turbulence is taken into accountcan be due to the fact that the SM model is too dissipativein laminar and transitional regions [18] Indeed the SM

model predicts a nonvanishing eddy viscosity when the flowis laminar and this results in more stable shear layers whenthe incoming flow is smooth Conversely the KET model isable to adjust the eddy viscosity basing on the subgrid kineticenergy leading to an overall less dissipative behavior Whenthe incoming flow turbulence is considered the SM modelperforms better In fact the laminar-to-turbulent transitionis driven by disturbances introduced by the explicitly sim-ulated incoming flow turbulence This different behavior inperfectly smooth and low turbulence inflow conditions is notobserved when the KETmodel is considered Indeed the lessdissipative behavior of the KET model with respect to theSM model allows correctly predicting the destabilization ofthe shear layers without triggering it explicitly by introducingdisturbances

43 Spanwise-Averaged Quantities 119911-avg distributions of1198621015840119901

denoted as 119862

119901(119911-avg)1015840 are reported in Figure 7 for each case

Data concerning the central section statistics (see Figure 6)are repeated in this figure in order to better highlightdifferences with respect to the corresponding 119911-avg valuesFocusing on the top surface the SM model shows that thegap between 1198621015840

119901

and 119862119901(119911-avg)1015840 increases proceeding from

Mathematical Problems in Engineering 9

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

Top surface

Bottom surface

minus1 0 1 2minus2

zD

1 2minus1 0minus2

zD

minus1minus2 1 20zD

minus1minus2 1 20zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

Figure 8 Correlation functions for the SM model in smooth and turbulent inflow condition

the leading edge to the trailing one where the peak value of119862119901(119911-avg)1015840 is radically decreased with respect to the central

alignment for both smooth and turbulent inlet conditionThe flow two-dimensionality is dominant close to the leadingedge where 119911-avg statistics are identical to the central sectionones while the flow three-dimensional mechanisms prevaildownwind This trend is confirmed by the KET model evenif in this case the gap between1198621015840

119901

and119862119901(119911-avg)1015840 is reduced if

compared with the SM model suggesting that the predictedflow is more correlated in the spanwise direction

Considering results of the SM model on the bottomsurface the reduction between 119911-avg and central sectionstatistics is higher when the inflow turbulence is consideredIn fact while for the smooth inlet condition 119911-avg peak valueis roughly 66 of the central section one when turbulenceis taken into account the peak of 119862

119901(119911-avg)1015840 is only 44 of

the corresponding 1198621015840119901

value Therefore the SM model showsthat the inflow turbulence contributes to decreasing the flowcorrelation in the spanwise direction to a great extent

In agreement with the previously reported results theKET model does not show such a high sensitivity differ-ences between 119862

119901(119911-avg)1015840 and 1198621015840

119901

in smooth and turbulentcondition being almost identical Qualitatively by observing

the rms distributions in terms of both peak amplitude andposition results obtained by using the KET model appear tobe intermediate between the ones obtained in smooth andturbulent flow by using the SM model

44 Correlations This section reports 119862119901correlations along

the spanwise direction for three different sections locatedat 119904119863 = 175 300 and 425 Data acquired on probesclose to the edges in the spanwise direction can be affectedby the prescribed boundary conditions therefore results arepresented disregarding part of the rectangular cylinder nearto the boundary 119911119863 ranging from minus25 to 25 Figure 8shows the correlation of 119862

119901 indicated as 119877

119862119901 obtained for

the SM model on top and bottom surfaces for smooth andturbulent inlet while results obtained by using the KETmodel are reported in Figure 9

Interestingly in this case the correlation appears to behigher when a small incoming turbulence level is con-sidered The authors conjecture that this behavior mightbe related to the fact that when perfectly smooth con-ditions are considered the flow impinges on the trailingedge as it can be deduced from time-averaged streamlinesreported in Figure 5 Contrarily when incoming turbulence is

10 Mathematical Problems in Engineering

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

0 1 2minus1minus2

zD

0 21minus1minus2

zD

0 1 2minus1minus2

zD

0 21minus1minus2

zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

Top surface

Bottom surface

Figure 9 Correlation functions for the KET model in smooth and turbulent inflow condition

considered a higher level of entrapment of the separationbubble is observed probably leading to higher along-spancorrelations Regarding the bottom surface and focusing onresults obtained by means of the SM model an oppositebehavior is recorded This fact might be due to the develop-ment of spanwise vortical structures that decrease the flowcorrelation (see eg Sasaki and Kiya [36])

Also in this case results predicted by using the KETmodel are qualitatively intermediate between the onesobtained by using the SM model in smooth and turbulentconditions and a good stability with respect to the incomingturbulence level is observed

5 Conclusions

In this paper Large Eddy Simulations have been performedaiming at studying the unsteady flow field around a rectan-gular cylinder with aspect ratio 5 1 at 4∘ attack angle when asmall level of incoming turbulence is taken into account Twodifferent turbulence models have been considered namelythe classical Smagorinsky-Lillymodel and the Kinetic EnergyTransport model Both of them have been studied by adopt-ing perfectly smooth and turbulent inlet conditions with

turbulence intensity set to be equal to 07 The inflow tur-bulence has been synthetically generated with the MDSRFGmethod and introduced in the computational domain bymodifying the velocity-pressure coupling algorithm Resultsin terms of flow bulk parameters time-average and rms ofthe pressure coefficient distributions in correspondence withthe prism central section have been compared to availableexperimental data It appears that when the Smagorinsky-Lilly model is adopted the modeling of a realistic turbulentinflow is important in order to obtain accurate results sinceeven small values of the incoming flow turbulence intensitycan deeply affect resultsTheKinetic Energy Transportmodelproved to be less sensitive to the low inflow turbulenceand provided results qualitatively intermediate between theSmagorinsky-Lilly models adopted with perfectly smoothand turbulent inflow conditions The different behavior ofthe two considered models can be due to the fact that theSmagorinsky-Lilly model is not able to make the turbulenteddy viscosity null appearing to be too dissipative and failingin accurately predicting the laminar-to-turbulent transitionOn the contrary the Kinetic Energy Transport model canadjust the turbulent eddy viscosity depending on the subgridkinetic energy showing satisfactory results for both smooth

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical PhysicsAdvances in

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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Discrete Dynamics in Nature and Society

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Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

which the flow is expected to be mainly laminar Such simu-lations showed good results in terms of bulk parameters andhighlighted that when using the standard deviation of the liftcoefficient as an indicator the simulation appears to be verysensitive to the adopted numerical setups Shimada proposeda detailed validation of a two-layer 119896-120576 model with a modi-fication on the turbulent kinetic energy production term byanalyzing the flowfield around awide selection of rectangularcylinders at null-attack angle [9] while Noda and Nakayamaproposed LES including the effect of incoming turbulence(a turbulence intensity equal to 5 was considered) show-ing that the standard Smagosinsky model is suitable forreproducing the effects induced by incoming turbulence forengineering purposes [10] Moreover a wide number ofexperimental and computational studies have been also pro-posed in order to study the aeroelastic behavior of such bodiesin smooth [11] and turbulent conditions [12] In particularDaniels et al [13] performed LES on an elastically mountedrectangular cylinder in smooth and turbulent inflow condi-tions showing that increasing the turbulence intensity candiminish significantly the amplitude of oscillations

In all it appears that while all computational modelsare able to approximately reproduce some characteristicsof the flow field their accuracy strongly depends on theadopted numerical setups and on the quantities taken intoconsideration Indeed if on one hand the mean flow charac-teristics are generally reproduced by numerical simulations ina satisfactoryway on the other hand the standard deviation ofvelocity and pressure fields is often predicted with much lessaccuracy [14] It also emerged that due to the large numberof parameters whichmight affect the flow topology a detailedmapping of the prisms aerodynamic behavior has not beenyet achieved

Recently the BARC project focused on the simulationof the turbulent flow around a 5 1 rectangular cylinderand became a standard benchmark for comparison betweenexperimental data and numerical simulations [15] Theoverview of the first four years of activity of the BARC project[16] highlighted that even experimental results extracted byvarious research groups show a remarkable variability whosecauses are currently not completely clear When numericalsimulations are considered Bruno et al [16] observed thatresults are even more dispersed showing great sensitivity tothe adopted numerical schemes turbulencemodel andmeshsize while their relative importance is difficult to be evaluatedat the current stage In this context uncertainty studies canplay a fundamental role In particular Witteveen et al [17]showed that the flowfield around the 5 1 rectangular cylinderis very sensible to setup parameters as small variations of theangle of attack the incoming turbulence intensity and theincoming turbulence length scales

It is also noticed that while disturbances are alwayspresent in experimental conditions when numerical simu-lations are performed a fictitious environment is producedwhere imperfections are introduced only by the differen-tial problem discretization and by the numerical solutionitself Beside the absence of incoming disturbances manyturbulence models are known to be excessively dissipative inlaminar-to-turbulent transition zones [18] Thus numerical

simulations can be considered as a limit case expected toproduce excessively stable shear layers and thus generallyoverestimating the reattachment length

In this paper the performances of the standardSmagorinsky-Lilly [19 20] model and the Kinetik EnergyTransport [21] model are tested when the incoming flowis characterized by a very low turbulence intensity To thispurpose the flow around a fixed 5 1 rectangular cylinder isconsidered at 4∘ attack angle In fact the mismatch betweenexperimental and numerical results has been found toincrease with the attack angle when perfectly smooth inletconditions are adopted together with a standard SM turbu-lence model [22]

The paper is organized as follows In Section 2 the experi-mental setup adopted in the wind tunnel tests is briefly des-cribed while in Section 3 the numerical features of the com-putational model are discussed Numerical results obtainedfrom simulations are presented in Section 4 and comparedwith the experimental data Finally in Section 5 some con-clusions are drawn

2 Experimental Setup

In this section the setup used to extract the experimentalresults used for comparison with numerical simulations isdescribed The experimental study was performed in theopen-circuit boundary layer wind tunnel of CRIACIV labo-ratory located in Prato Italy [23]

An aluminium model characterized by width 119861 equalto 300mm depth 119863 equal to 60mm and length 119871 equalto 2380mm was employed in the experimental tests andequipped with 62 pressure taps monitored by two 32-channelPSI miniaturized piezoelectric scanners at a sampling rate of500Hz [24] The wind tunnel test section is 242m large and160m high so that the resulting blockage ratio was 375The Reynolds number based on 119863 was varied from 22 times 10

4

to 112times 105 while incoming turbulence intensity was variedfrom 07 to 136

In the present study the experimental configuration withnose-up angle equal to 4∘ at Reynolds number based on119863 equal to 55 times 104 has been used as a reference for thenumerical simulations

3 Computational Model

In this section the characteristics of the computationalmodelare reported and compared with other studies together withthe description of the adopted boundary conditions andnumerical setups

According to the aim of this study the lowest turbu-lence intensity recorded in the available wind tunnel testsrepresenting the experimental approximation of the smoothflow condition is adopted so that the incoming turbulenceintensity is set to be equal to 07 The inflow turbulent fieldis synthetically generated by using the Modified Discretizingand Synthesizing Random Flow Generator method proposedby Castro et al [25 26] which guarantees the divergence-free condition and is able to satisfy prescribed turbulencespectrum and spatial correlations It is worth noting that if

Mathematical Problems in Engineering 3

Periodic

Periodic

Outlet boundaryInlet boundary

Lx

x

z

D

yy

Symmetry

s

Dx

Dy

DzB = 5D

Symmetry

Λx

Figure 1 Model and computational domain geometries [15]

(a) (b)

Figure 2 Mesh adopted for the LES simulation detail of the mesh close to the solid boundary (a) and mesh in proximity of the body andwake (b)

the fluctuation field is introduced at the inlet boundary largepressure fluctuations are generated due to the violation of theNavier-Stokes equations In order to avoid this phenomenonfluctuations are introduced in the computational domain bymodifying the velocity-pressure coupling algorithm follow-ing the procedure reported by Kim et al [27]

The computational domain size and the grid resolutionhave been defined according to the guidelines provided byBruno et al [16] and the BARC main setup [15] As showedin Figure 1 the domain dimensions are such that 119863

119909= 40119861

and 119863119910= 30119861 while 119863

119911= 20119861 The resultant blockage

ratio is 067 and therefore blockage ratio effects can beneglected In order to avoid boundary effects on the solutionthe distance between the prism leading edge and the inletboundary is set to be equal to Λ

119909= 16119861

As showed in Figure 2(a) a structured mesh is adoptedin the boundary layer close to the wall with along-winddimension 120575

119909119861 = 25 times 10

minus3 and crosswind dimension120575119910119861 = 15 times 10

minus3 The maximum 119910+ recorded during all

simulations is found to be equal to 661 while the meanone equals 202 Outside the boundary layer the mesh isunstructured and quad dominated and its size is slowlycoarsened up to approximately 120575

119909119861 = 120575

119910119861 = 18 times 10

minus2

in the wake (see Figure 2(b)) where the cells aspect ratio isapproximately one In order to limit the numerical dissipation

and to propagate the fluctuation field minimizing the energyloss the mesh sizing in front of the rectangular cylinder hasdimensions 120575

119909119861 = 120575

119910119861 = 5times10

minus2 and ismaintained almostconstant and structured until the inlet boundary is reached

In 119911 direction the cell dimension is 120575119911119861 = 002The final

resultant mesh is composed of about 160119872 finite volumes Acomparison between the domain size and themesh resolutionadopted in the present study and similar ones is reported inTables 1 and 2

With respect to turbulence modeling two subgridscales models have been considered namely the standardSmagorisnky-Lilly (SM)model and theKinetic EnergyTrans-port (KET) model The fluid flow governing equations arereported in

120597119906119894

120597119909119894

= 0

120597120588119906119894

120597119905+120597120588119906119894119906119895

120597119909119895

= minus120597119901

120597119909119894

+120597120591119894119895

120597119909119895

minus

120597120591sgs119894119895

120597119909119895

(1)

where the overbar denotes the spatially filtered quantities and119906119894represents the velocity in the 119894th direction while 119901 is the

pressure 120591119894119895is the resolved viscous stress tensor and 120591sgs

119894119895

is

4 Mathematical Problems in Engineering

Table 1 Parameters of the computational domain as reported byBruno et al [16]

Source 119863119909

119861 119863119910

119861 119863119911

119861 Λ119909

119861

Present simulation 40 30 2 16

Bruno et al [30 32] 41 302 1 2 4 15

Grozescu et al [33] 41 302 1 15

Mannini et al [34] 200 200 1 2 100

the subgrid stress tensor The resolved viscous stress tensor120591119894119895can be written as

120591119894119895= 2120583 [119878

119894119895minus1

3120575119894119895119878119896119896] (2)

where 119878119894119895represents the resolved strain rate tensor whose

expression is reported below

119878119894119895=1

2(120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (3)

By assuming Boussinesqrsquos hypothesis the subgrid stresstensor 120591sgs

119894119895

can be written as

120591sgs119894119895

= 120588 (119906119894119906119895minus 119906119894119906119895)

= minus2120588]119905(119878119894119895minus1

3120575119894119895119878119896119896) +

2

3120588120575119894119895119896sgs

(4)

where 119896sgs is the subgrid kinetic energy

119896sgs=1

2(119906119894119906119894minus 119906119894119906119894) (5)

and ]119905is the turbulent eddy viscosity When the SMmodel is

adopted ]119905is expressed as

]119905= (119862119904Δ)2

radic2119878119894119895119878119894119895 (6)

where 119862119904is the Smagorinsky constant set to be equal to 012

whileΔ is the local grid spacing Conversely if theKETmodelis adopted the transport equation for the subgrid kineticenergy is considered in addition to equations reported in (1)

120597

120597119905(120588119896

sgs) +

120597

120597119909119894

(120588119896sgs119906119894)

=120597

120597119909119894

(120588]119905

120597119896sgs

120597119909119894

) minus 120591sgs119894119895

120597119906119895

120597119909119894

minus 120588119888120598

(119896sgs)32

Δ

(7)

and the turbulent eddy viscosity ]119905is calculated as

]119905= 119888]radic119896

sgsΔ (8)

where 119888120598and 119888] are model constants set to be equal respec-

tively to 105 and 0094With respect to the numerical scheme a centered second-

order accurate scheme is adopted to discretize the spatialderivatives exception made for the nonlinear convective

Table 2 Grid resolution in the boundary layer comparison withmeshes adopted by other authors as reported by Bruno et al [16]

Source 119899119908

119861 120575119909

119861 120575119911

119861

Presentsimulation 50 times 10

minus4

25 times 10minus3

002

Bruno et al[30 32] 50 times 10

minus4

20 times 10minus3 0042ndash001

Grozescu etal [33] 5 times 10

minus4 25 times 10minus4 10 times 10minus2 5 times 10minus3 0042 001

Mannini etal [34] 50 times 10

minus5

14 times 10minus2

00156

term For this term the Linear Upwind Stabilized Transportscheme is used which proved to be particularly successful forLES in complex geometries [28]

Time integration is performed by using the the two-step second-order Backward Differentiation Formulae inaccordance with Bruno et al [29] The solution at eachtime step is obtained by means of the well known PressureImplicit with Splitting of Operator algorithm The adoptednondimensional time step (based on 119863) is Δ119905lowast = 50 times 10minus3leading to amaximumCourant number in all the simulationsequal to 39

Symmetry boundary conditions are imposed at the topand bottom surfaces while periodic conditions are adoptedon the faces normal to the spanwise direction (see Figure 1)At the outlet boundary zero pressure is imposed while at theinlet the null normal gradient of pressure is prescribed

The generated fluctuation field is introduced in thecomputational domain in a plane shifted with respect to theinlet boundary of approximately 50 times 10minus1119861 while the meanvelocity is prescribed at the inlet The power spectral densityof the velocity components along 119909 119910 and 119911 directionsindicated respectively as 119906 V and 119908 is reported in Figure 3for two different points located near the inlet boundary at(minus15119861 0 0) and just upstream the rectangular cylinder at(minus15119861 0 0) As it can be seen the high frequency contentof the spectra appears to be slightly damped proceeding fromthe inlet towards the rectangular cylinderWith respect to thealong-wind turbulent length scale 119871

119906 it is found to be equal

to 119861 for both of the aforementioned locationsThe prism has been equipped with 2500 pressure moni-

tors and data are acquired at each time step leading to 200samples for one nondimensional time unit All simulationshave been run by using the open source finite volumesoftware119874119901119890119899119865119874119860119872 on 160CPUs atCINECAon theGalileocluster (516 nodes 2 eight-core Intel Haswell 240GHzprocessors with 128GB RAM per node)

4 Numerical Results

In this section numerical results obtained for each turbulencemodel with smooth and turbulent inflow condition arereported and systematically compared with experimentaldata In particular the flow bulk parameters obtained fromeach simulation together with a discussion of the resultingflow topology are reported in Section 41 The pressure

Mathematical Problems in Engineering 5

KET I = 07 xB = minus150

KET I = 07 xB = minus15

KET I = 07 xB = minus150

KET I = 07 xB = minus15

KET I = 07 xB = minus150

KET I = 07 xB = minus15

10minus1 10010minus2

fDU

10minus1 10010minus2

fDU

10minus1 10010minus2

fDU

10minus810minus710minus610minus510minus410minus310minus2

S wfU

2

10minus810minus710minus610minus510minus410minus310minus2

S fU

2

10minus810minus710minus610minus510minus410minus310minus2

S ufU

2

Figure 3 Spectra of the velocity time series obtained from the KETsimulation with incoming flow turbulence at different locations

coefficient statistics on the central section are showed inSection 42 while Section 43 focuses on the spanwise-averaged pressure distributions Then in Section 44 corre-lations in the spanwise direction are discussed

Numerical results have been obtained by considering asimulation time of 119905lowast = 1000 119905lowast being the nondimensionaltime unit The postprocessing of data has been carried outconsidering only the last 700 nondimensional time units inorder to avoid flow initialization effects [30]

In order to check the convergence of the recordedstatistics the time-history of the lift coefficient has beensubdivided into ten segments and first- and second-orderstatistics were extracted by incrementally extending the partof the signal considered in the postprocessing Despite therelatively long simulation time (longer than the minimumrequirements [30]) in the worst case a plateau has beenreached for second-order statistics only when 90of the totaltime-history has been used

41 Flow Topology and Bulk Parameters In order to have aqualitative view of the turbulent structures obtained from thenumerical analyses the flow topology in terms of isosurfacesof the invariant 120582

2[31] coloured with pressure is reported

in Figure 4 for the two investigated turbulence models insmooth and turbulent inflow conditions The instantaneousisosurfaces are plotted to correspond with maximum lift Asit can be seen when the inflow turbulence is considered the

Table 3 Reattachment point and main vortex core position

Source 119909119903

down 119909119888

up 119909119888

down 119910119888

up 119910119888

downSM(smooth) 116 054 minus049 096 minus078

SM 119868 = 07 001 091 minus081 091 minus063KET(smooth) 005 109 minus065 101 minus054

KET 119868 =07 004 110 minus063 100 minus051

Table 4 Statistics of the flow bulk parameters

Source 119862119863

1198621015840

119863

119862119871

1198621015840

119871

StSM (smooth) 126 0056 144 057 0116SM 119868 = 07 128 0064 156 061 0115KET (smooth) 137 0079 227 076 0117KET 119868 = 07 13 0080 226 081 0115Pigolotti et al [23] (Exp) 163 mdash 202 mdash 0126Schewe [35] (Exp) 138 mdash 252 mdash 0115

topology showed by the SM model appears to be quite inaccordance with that obtained by means of the KET modelFurthermore both of them comply well with the topologyshowed by theKETmodel in smooth inflow conditions whilein this case the topology obtained by using the SM modelshows a narrower wake

The different behavior of the two turbulence models isalso reflected in Table 3 which shows that the reattachmentpoint at the bottom surface moves from 119909

119903= 116 to

119909119903= 001 when turbulence is introduced and the SM

model considered while no significant differences betweenturbulent and smooth inlet are observed if the KET model isanalyzed

The effect of incoming turbulence can be also appreciatedby observing the streamlines of the time-averaged flow fieldsreported in Figure 5 In particular the SM model appearsto be significantly affected by the presence of incomingturbulence while the KET model appears to be rather stableIt is also noticed that all considered models apart from theSM in smooth flow predict the creation of a small elongatedvortex at the leading edge in correspondence with the topside whose core is located at approximately 119909

119888= minus15

The statistics of the flow bulk parameters are reported inTable 4 (results are made nondimensional with respect to119863)and referred to the global reference system In particular 119862

119863

and119862119871are the drag and the lift coefficients respectively while

their root mean square values are indicated as 1198621015840119863

and 1198621015840119871

respectively Again the results obtained by the two turbulencemodels are in good agreement when a low level of incomingturbulence is considered while remarkable differences areobserved in perfectly smooth flow Furthermore it should benoticed that 119862

119863and 119862

119871 together with the Strouhal number

(St) obtained by taking into account the incoming turbulenceagree quite well with experimental measurements In orderto provide a clearer picture of the obtained results in thefollowing pressure field statistics distributions are analyzed

6 Mathematical Problems in Engineering

minuspdyn pdynminuspdyn pdyn

minuspdyn pdyn minuspdyn pdyn

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 4 Isosurfaces of 1205822

coloured with pressure for the two analyzed turbulence models

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 5 Time-averaged streamlines for the two analyzed turbulence models

42 Central Section Statistics In this section the pressurecoefficient statistics on the prism central section are analyzedData are presented by adopting the curvilinear abscissa 119904as reported in Figure 1 The upwind face of the prism isidentified by 00 le 119904119863 le 05 and the along-wind surfacesare identified by 05 le 119904119863 le 50 while the downwind face isidentified by 55 le 119904119863 le 60

Figure 6 shows the distribution of the pressure statisticsobtained by means of the present simulations and compari-son with experimental results As it can be noticed if the topsurface is considered the time-averaged pressure coefficient119862119901 distribution predicted by the KET model is almost

in perfect accordance with the experimental data for both

smooth and turbulent inflow conditions Contrarily the SMmodel approaches experimental results only when turbulentinlet conditions are adopted Observing 1198621015840

119901

on the samesurface the KET model always complies with experimentalmeasurements with the peak position and the experimentaltrends being reproduced with good accuracy Generally theSM model appears to be unable to correctly reproduce theshape of the pressure recovery not catching the change ofsteepness that occurs at about 119904119863 = 3 in correspondencewith the separation between the vortex shedding and thevortex coalescing zones as individuated in [30]

When 119862119901distribution on the bottom surface is analyzed

the SMmodel appears to be very sensitive to small turbulence

Mathematical Problems in Engineering 7

Cp

Cp

Cp

Cp

SM KET

SM KET

SM KET

SM KET

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

1 2 3 4 5 60sD

minus10

minus05

00

05

10

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

1 2 3 4 5 60sD

60 3 4 51 2

sD

1 2 3 4 5 60sD

minus10

minus05

00

05

10

1 2 3 4 5 60sD

Top surface

Bottom surface

Figure 6 Distribution of 119862119901

statistics on the central alignment

8 Mathematical Problems in Engineering

00

01

02

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

543 60 1 2

sD

543 60 1 2

sD

00

01

02

C998400 p

00

01

02

C998400 p

Top surface

Bottom surface

SM

SM KET

KETSM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

SM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

Figure 7 Comparison between 119911-averaged and central section statistics for the SM and KET turbulence models

intensities in the incoming flow In fact the distributionobtained in smooth flow conditions clearly changes whenthe inflow turbulence is considered the reattachment pointmigrates upstream and the distribution shifts approachingthe experimental dataTheKETmodel instead shows again alower sensitivity to the incoming turbulence results obtainedin both configurations being approximately the same TheSM model is very accurate when turbulence is taken intoaccount and shows better performances if compared with theKET model which slightly overestimates the reattachmentlength and underestimates suctions at the leeward edge Theimprovement of the SM model with turbulent inlet observedfor mean values can be noticed also by considering 119862

1015840

119901

distribution on the bottom surface In this case the modelcorrectly predicts the peak position and the trend observedexperimentally even if the peak value is clearly overestimatedThe KET model correctly predicts the peak position and thetrend in particular at the trailing edge where an increment inrms is experimentally observed

The improvement of performances showed by the SMmodel when the incoming turbulence is taken into accountcan be due to the fact that the SM model is too dissipativein laminar and transitional regions [18] Indeed the SM

model predicts a nonvanishing eddy viscosity when the flowis laminar and this results in more stable shear layers whenthe incoming flow is smooth Conversely the KET model isable to adjust the eddy viscosity basing on the subgrid kineticenergy leading to an overall less dissipative behavior Whenthe incoming flow turbulence is considered the SM modelperforms better In fact the laminar-to-turbulent transitionis driven by disturbances introduced by the explicitly sim-ulated incoming flow turbulence This different behavior inperfectly smooth and low turbulence inflow conditions is notobserved when the KETmodel is considered Indeed the lessdissipative behavior of the KET model with respect to theSM model allows correctly predicting the destabilization ofthe shear layers without triggering it explicitly by introducingdisturbances

43 Spanwise-Averaged Quantities 119911-avg distributions of1198621015840119901

denoted as 119862

119901(119911-avg)1015840 are reported in Figure 7 for each case

Data concerning the central section statistics (see Figure 6)are repeated in this figure in order to better highlightdifferences with respect to the corresponding 119911-avg valuesFocusing on the top surface the SM model shows that thegap between 1198621015840

119901

and 119862119901(119911-avg)1015840 increases proceeding from

Mathematical Problems in Engineering 9

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

Top surface

Bottom surface

minus1 0 1 2minus2

zD

1 2minus1 0minus2

zD

minus1minus2 1 20zD

minus1minus2 1 20zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

Figure 8 Correlation functions for the SM model in smooth and turbulent inflow condition

the leading edge to the trailing one where the peak value of119862119901(119911-avg)1015840 is radically decreased with respect to the central

alignment for both smooth and turbulent inlet conditionThe flow two-dimensionality is dominant close to the leadingedge where 119911-avg statistics are identical to the central sectionones while the flow three-dimensional mechanisms prevaildownwind This trend is confirmed by the KET model evenif in this case the gap between1198621015840

119901

and119862119901(119911-avg)1015840 is reduced if

compared with the SM model suggesting that the predictedflow is more correlated in the spanwise direction

Considering results of the SM model on the bottomsurface the reduction between 119911-avg and central sectionstatistics is higher when the inflow turbulence is consideredIn fact while for the smooth inlet condition 119911-avg peak valueis roughly 66 of the central section one when turbulenceis taken into account the peak of 119862

119901(119911-avg)1015840 is only 44 of

the corresponding 1198621015840119901

value Therefore the SM model showsthat the inflow turbulence contributes to decreasing the flowcorrelation in the spanwise direction to a great extent

In agreement with the previously reported results theKET model does not show such a high sensitivity differ-ences between 119862

119901(119911-avg)1015840 and 1198621015840

119901

in smooth and turbulentcondition being almost identical Qualitatively by observing

the rms distributions in terms of both peak amplitude andposition results obtained by using the KET model appear tobe intermediate between the ones obtained in smooth andturbulent flow by using the SM model

44 Correlations This section reports 119862119901correlations along

the spanwise direction for three different sections locatedat 119904119863 = 175 300 and 425 Data acquired on probesclose to the edges in the spanwise direction can be affectedby the prescribed boundary conditions therefore results arepresented disregarding part of the rectangular cylinder nearto the boundary 119911119863 ranging from minus25 to 25 Figure 8shows the correlation of 119862

119901 indicated as 119877

119862119901 obtained for

the SM model on top and bottom surfaces for smooth andturbulent inlet while results obtained by using the KETmodel are reported in Figure 9

Interestingly in this case the correlation appears to behigher when a small incoming turbulence level is con-sidered The authors conjecture that this behavior mightbe related to the fact that when perfectly smooth con-ditions are considered the flow impinges on the trailingedge as it can be deduced from time-averaged streamlinesreported in Figure 5 Contrarily when incoming turbulence is

10 Mathematical Problems in Engineering

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

0 1 2minus1minus2

zD

0 21minus1minus2

zD

0 1 2minus1minus2

zD

0 21minus1minus2

zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

Top surface

Bottom surface

Figure 9 Correlation functions for the KET model in smooth and turbulent inflow condition

considered a higher level of entrapment of the separationbubble is observed probably leading to higher along-spancorrelations Regarding the bottom surface and focusing onresults obtained by means of the SM model an oppositebehavior is recorded This fact might be due to the develop-ment of spanwise vortical structures that decrease the flowcorrelation (see eg Sasaki and Kiya [36])

Also in this case results predicted by using the KETmodel are qualitatively intermediate between the onesobtained by using the SM model in smooth and turbulentconditions and a good stability with respect to the incomingturbulence level is observed

5 Conclusions

In this paper Large Eddy Simulations have been performedaiming at studying the unsteady flow field around a rectan-gular cylinder with aspect ratio 5 1 at 4∘ attack angle when asmall level of incoming turbulence is taken into account Twodifferent turbulence models have been considered namelythe classical Smagorinsky-Lillymodel and the Kinetic EnergyTransport model Both of them have been studied by adopt-ing perfectly smooth and turbulent inlet conditions with

turbulence intensity set to be equal to 07 The inflow tur-bulence has been synthetically generated with the MDSRFGmethod and introduced in the computational domain bymodifying the velocity-pressure coupling algorithm Resultsin terms of flow bulk parameters time-average and rms ofthe pressure coefficient distributions in correspondence withthe prism central section have been compared to availableexperimental data It appears that when the Smagorinsky-Lilly model is adopted the modeling of a realistic turbulentinflow is important in order to obtain accurate results sinceeven small values of the incoming flow turbulence intensitycan deeply affect resultsTheKinetic Energy Transportmodelproved to be less sensitive to the low inflow turbulenceand provided results qualitatively intermediate between theSmagorinsky-Lilly models adopted with perfectly smoothand turbulent inflow conditions The different behavior ofthe two considered models can be due to the fact that theSmagorinsky-Lilly model is not able to make the turbulenteddy viscosity null appearing to be too dissipative and failingin accurately predicting the laminar-to-turbulent transitionOn the contrary the Kinetic Energy Transport model canadjust the turbulent eddy viscosity depending on the subgridkinetic energy showing satisfactory results for both smooth

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Periodic

Periodic

Outlet boundaryInlet boundary

Lx

x

z

D

yy

Symmetry

s

Dx

Dy

DzB = 5D

Symmetry

Λx

Figure 1 Model and computational domain geometries [15]

(a) (b)

Figure 2 Mesh adopted for the LES simulation detail of the mesh close to the solid boundary (a) and mesh in proximity of the body andwake (b)

the fluctuation field is introduced at the inlet boundary largepressure fluctuations are generated due to the violation of theNavier-Stokes equations In order to avoid this phenomenonfluctuations are introduced in the computational domain bymodifying the velocity-pressure coupling algorithm follow-ing the procedure reported by Kim et al [27]

The computational domain size and the grid resolutionhave been defined according to the guidelines provided byBruno et al [16] and the BARC main setup [15] As showedin Figure 1 the domain dimensions are such that 119863

119909= 40119861

and 119863119910= 30119861 while 119863

119911= 20119861 The resultant blockage

ratio is 067 and therefore blockage ratio effects can beneglected In order to avoid boundary effects on the solutionthe distance between the prism leading edge and the inletboundary is set to be equal to Λ

119909= 16119861

As showed in Figure 2(a) a structured mesh is adoptedin the boundary layer close to the wall with along-winddimension 120575

119909119861 = 25 times 10

minus3 and crosswind dimension120575119910119861 = 15 times 10

minus3 The maximum 119910+ recorded during all

simulations is found to be equal to 661 while the meanone equals 202 Outside the boundary layer the mesh isunstructured and quad dominated and its size is slowlycoarsened up to approximately 120575

119909119861 = 120575

119910119861 = 18 times 10

minus2

in the wake (see Figure 2(b)) where the cells aspect ratio isapproximately one In order to limit the numerical dissipation

and to propagate the fluctuation field minimizing the energyloss the mesh sizing in front of the rectangular cylinder hasdimensions 120575

119909119861 = 120575

119910119861 = 5times10

minus2 and ismaintained almostconstant and structured until the inlet boundary is reached

In 119911 direction the cell dimension is 120575119911119861 = 002The final

resultant mesh is composed of about 160119872 finite volumes Acomparison between the domain size and themesh resolutionadopted in the present study and similar ones is reported inTables 1 and 2

With respect to turbulence modeling two subgridscales models have been considered namely the standardSmagorisnky-Lilly (SM)model and theKinetic EnergyTrans-port (KET) model The fluid flow governing equations arereported in

120597119906119894

120597119909119894

= 0

120597120588119906119894

120597119905+120597120588119906119894119906119895

120597119909119895

= minus120597119901

120597119909119894

+120597120591119894119895

120597119909119895

minus

120597120591sgs119894119895

120597119909119895

(1)

where the overbar denotes the spatially filtered quantities and119906119894represents the velocity in the 119894th direction while 119901 is the

pressure 120591119894119895is the resolved viscous stress tensor and 120591sgs

119894119895

is

4 Mathematical Problems in Engineering

Table 1 Parameters of the computational domain as reported byBruno et al [16]

Source 119863119909

119861 119863119910

119861 119863119911

119861 Λ119909

119861

Present simulation 40 30 2 16

Bruno et al [30 32] 41 302 1 2 4 15

Grozescu et al [33] 41 302 1 15

Mannini et al [34] 200 200 1 2 100

the subgrid stress tensor The resolved viscous stress tensor120591119894119895can be written as

120591119894119895= 2120583 [119878

119894119895minus1

3120575119894119895119878119896119896] (2)

where 119878119894119895represents the resolved strain rate tensor whose

expression is reported below

119878119894119895=1

2(120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (3)

By assuming Boussinesqrsquos hypothesis the subgrid stresstensor 120591sgs

119894119895

can be written as

120591sgs119894119895

= 120588 (119906119894119906119895minus 119906119894119906119895)

= minus2120588]119905(119878119894119895minus1

3120575119894119895119878119896119896) +

2

3120588120575119894119895119896sgs

(4)

where 119896sgs is the subgrid kinetic energy

119896sgs=1

2(119906119894119906119894minus 119906119894119906119894) (5)

and ]119905is the turbulent eddy viscosity When the SMmodel is

adopted ]119905is expressed as

]119905= (119862119904Δ)2

radic2119878119894119895119878119894119895 (6)

where 119862119904is the Smagorinsky constant set to be equal to 012

whileΔ is the local grid spacing Conversely if theKETmodelis adopted the transport equation for the subgrid kineticenergy is considered in addition to equations reported in (1)

120597

120597119905(120588119896

sgs) +

120597

120597119909119894

(120588119896sgs119906119894)

=120597

120597119909119894

(120588]119905

120597119896sgs

120597119909119894

) minus 120591sgs119894119895

120597119906119895

120597119909119894

minus 120588119888120598

(119896sgs)32

Δ

(7)

and the turbulent eddy viscosity ]119905is calculated as

]119905= 119888]radic119896

sgsΔ (8)

where 119888120598and 119888] are model constants set to be equal respec-

tively to 105 and 0094With respect to the numerical scheme a centered second-

order accurate scheme is adopted to discretize the spatialderivatives exception made for the nonlinear convective

Table 2 Grid resolution in the boundary layer comparison withmeshes adopted by other authors as reported by Bruno et al [16]

Source 119899119908

119861 120575119909

119861 120575119911

119861

Presentsimulation 50 times 10

minus4

25 times 10minus3

002

Bruno et al[30 32] 50 times 10

minus4

20 times 10minus3 0042ndash001

Grozescu etal [33] 5 times 10

minus4 25 times 10minus4 10 times 10minus2 5 times 10minus3 0042 001

Mannini etal [34] 50 times 10

minus5

14 times 10minus2

00156

term For this term the Linear Upwind Stabilized Transportscheme is used which proved to be particularly successful forLES in complex geometries [28]

Time integration is performed by using the the two-step second-order Backward Differentiation Formulae inaccordance with Bruno et al [29] The solution at eachtime step is obtained by means of the well known PressureImplicit with Splitting of Operator algorithm The adoptednondimensional time step (based on 119863) is Δ119905lowast = 50 times 10minus3leading to amaximumCourant number in all the simulationsequal to 39

Symmetry boundary conditions are imposed at the topand bottom surfaces while periodic conditions are adoptedon the faces normal to the spanwise direction (see Figure 1)At the outlet boundary zero pressure is imposed while at theinlet the null normal gradient of pressure is prescribed

The generated fluctuation field is introduced in thecomputational domain in a plane shifted with respect to theinlet boundary of approximately 50 times 10minus1119861 while the meanvelocity is prescribed at the inlet The power spectral densityof the velocity components along 119909 119910 and 119911 directionsindicated respectively as 119906 V and 119908 is reported in Figure 3for two different points located near the inlet boundary at(minus15119861 0 0) and just upstream the rectangular cylinder at(minus15119861 0 0) As it can be seen the high frequency contentof the spectra appears to be slightly damped proceeding fromthe inlet towards the rectangular cylinderWith respect to thealong-wind turbulent length scale 119871

119906 it is found to be equal

to 119861 for both of the aforementioned locationsThe prism has been equipped with 2500 pressure moni-

tors and data are acquired at each time step leading to 200samples for one nondimensional time unit All simulationshave been run by using the open source finite volumesoftware119874119901119890119899119865119874119860119872 on 160CPUs atCINECAon theGalileocluster (516 nodes 2 eight-core Intel Haswell 240GHzprocessors with 128GB RAM per node)

4 Numerical Results

In this section numerical results obtained for each turbulencemodel with smooth and turbulent inflow condition arereported and systematically compared with experimentaldata In particular the flow bulk parameters obtained fromeach simulation together with a discussion of the resultingflow topology are reported in Section 41 The pressure

Mathematical Problems in Engineering 5

KET I = 07 xB = minus150

KET I = 07 xB = minus15

KET I = 07 xB = minus150

KET I = 07 xB = minus15

KET I = 07 xB = minus150

KET I = 07 xB = minus15

10minus1 10010minus2

fDU

10minus1 10010minus2

fDU

10minus1 10010minus2

fDU

10minus810minus710minus610minus510minus410minus310minus2

S wfU

2

10minus810minus710minus610minus510minus410minus310minus2

S fU

2

10minus810minus710minus610minus510minus410minus310minus2

S ufU

2

Figure 3 Spectra of the velocity time series obtained from the KETsimulation with incoming flow turbulence at different locations

coefficient statistics on the central section are showed inSection 42 while Section 43 focuses on the spanwise-averaged pressure distributions Then in Section 44 corre-lations in the spanwise direction are discussed

Numerical results have been obtained by considering asimulation time of 119905lowast = 1000 119905lowast being the nondimensionaltime unit The postprocessing of data has been carried outconsidering only the last 700 nondimensional time units inorder to avoid flow initialization effects [30]

In order to check the convergence of the recordedstatistics the time-history of the lift coefficient has beensubdivided into ten segments and first- and second-orderstatistics were extracted by incrementally extending the partof the signal considered in the postprocessing Despite therelatively long simulation time (longer than the minimumrequirements [30]) in the worst case a plateau has beenreached for second-order statistics only when 90of the totaltime-history has been used

41 Flow Topology and Bulk Parameters In order to have aqualitative view of the turbulent structures obtained from thenumerical analyses the flow topology in terms of isosurfacesof the invariant 120582

2[31] coloured with pressure is reported

in Figure 4 for the two investigated turbulence models insmooth and turbulent inflow conditions The instantaneousisosurfaces are plotted to correspond with maximum lift Asit can be seen when the inflow turbulence is considered the

Table 3 Reattachment point and main vortex core position

Source 119909119903

down 119909119888

up 119909119888

down 119910119888

up 119910119888

downSM(smooth) 116 054 minus049 096 minus078

SM 119868 = 07 001 091 minus081 091 minus063KET(smooth) 005 109 minus065 101 minus054

KET 119868 =07 004 110 minus063 100 minus051

Table 4 Statistics of the flow bulk parameters

Source 119862119863

1198621015840

119863

119862119871

1198621015840

119871

StSM (smooth) 126 0056 144 057 0116SM 119868 = 07 128 0064 156 061 0115KET (smooth) 137 0079 227 076 0117KET 119868 = 07 13 0080 226 081 0115Pigolotti et al [23] (Exp) 163 mdash 202 mdash 0126Schewe [35] (Exp) 138 mdash 252 mdash 0115

topology showed by the SM model appears to be quite inaccordance with that obtained by means of the KET modelFurthermore both of them comply well with the topologyshowed by theKETmodel in smooth inflow conditions whilein this case the topology obtained by using the SM modelshows a narrower wake

The different behavior of the two turbulence models isalso reflected in Table 3 which shows that the reattachmentpoint at the bottom surface moves from 119909

119903= 116 to

119909119903= 001 when turbulence is introduced and the SM

model considered while no significant differences betweenturbulent and smooth inlet are observed if the KET model isanalyzed

The effect of incoming turbulence can be also appreciatedby observing the streamlines of the time-averaged flow fieldsreported in Figure 5 In particular the SM model appearsto be significantly affected by the presence of incomingturbulence while the KET model appears to be rather stableIt is also noticed that all considered models apart from theSM in smooth flow predict the creation of a small elongatedvortex at the leading edge in correspondence with the topside whose core is located at approximately 119909

119888= minus15

The statistics of the flow bulk parameters are reported inTable 4 (results are made nondimensional with respect to119863)and referred to the global reference system In particular 119862

119863

and119862119871are the drag and the lift coefficients respectively while

their root mean square values are indicated as 1198621015840119863

and 1198621015840119871

respectively Again the results obtained by the two turbulencemodels are in good agreement when a low level of incomingturbulence is considered while remarkable differences areobserved in perfectly smooth flow Furthermore it should benoticed that 119862

119863and 119862

119871 together with the Strouhal number

(St) obtained by taking into account the incoming turbulenceagree quite well with experimental measurements In orderto provide a clearer picture of the obtained results in thefollowing pressure field statistics distributions are analyzed

6 Mathematical Problems in Engineering

minuspdyn pdynminuspdyn pdyn

minuspdyn pdyn minuspdyn pdyn

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 4 Isosurfaces of 1205822

coloured with pressure for the two analyzed turbulence models

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 5 Time-averaged streamlines for the two analyzed turbulence models

42 Central Section Statistics In this section the pressurecoefficient statistics on the prism central section are analyzedData are presented by adopting the curvilinear abscissa 119904as reported in Figure 1 The upwind face of the prism isidentified by 00 le 119904119863 le 05 and the along-wind surfacesare identified by 05 le 119904119863 le 50 while the downwind face isidentified by 55 le 119904119863 le 60

Figure 6 shows the distribution of the pressure statisticsobtained by means of the present simulations and compari-son with experimental results As it can be noticed if the topsurface is considered the time-averaged pressure coefficient119862119901 distribution predicted by the KET model is almost

in perfect accordance with the experimental data for both

smooth and turbulent inflow conditions Contrarily the SMmodel approaches experimental results only when turbulentinlet conditions are adopted Observing 1198621015840

119901

on the samesurface the KET model always complies with experimentalmeasurements with the peak position and the experimentaltrends being reproduced with good accuracy Generally theSM model appears to be unable to correctly reproduce theshape of the pressure recovery not catching the change ofsteepness that occurs at about 119904119863 = 3 in correspondencewith the separation between the vortex shedding and thevortex coalescing zones as individuated in [30]

When 119862119901distribution on the bottom surface is analyzed

the SMmodel appears to be very sensitive to small turbulence

Mathematical Problems in Engineering 7

Cp

Cp

Cp

Cp

SM KET

SM KET

SM KET

SM KET

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

1 2 3 4 5 60sD

minus10

minus05

00

05

10

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

1 2 3 4 5 60sD

60 3 4 51 2

sD

1 2 3 4 5 60sD

minus10

minus05

00

05

10

1 2 3 4 5 60sD

Top surface

Bottom surface

Figure 6 Distribution of 119862119901

statistics on the central alignment

8 Mathematical Problems in Engineering

00

01

02

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

543 60 1 2

sD

543 60 1 2

sD

00

01

02

C998400 p

00

01

02

C998400 p

Top surface

Bottom surface

SM

SM KET

KETSM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

SM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

Figure 7 Comparison between 119911-averaged and central section statistics for the SM and KET turbulence models

intensities in the incoming flow In fact the distributionobtained in smooth flow conditions clearly changes whenthe inflow turbulence is considered the reattachment pointmigrates upstream and the distribution shifts approachingthe experimental dataTheKETmodel instead shows again alower sensitivity to the incoming turbulence results obtainedin both configurations being approximately the same TheSM model is very accurate when turbulence is taken intoaccount and shows better performances if compared with theKET model which slightly overestimates the reattachmentlength and underestimates suctions at the leeward edge Theimprovement of the SM model with turbulent inlet observedfor mean values can be noticed also by considering 119862

1015840

119901

distribution on the bottom surface In this case the modelcorrectly predicts the peak position and the trend observedexperimentally even if the peak value is clearly overestimatedThe KET model correctly predicts the peak position and thetrend in particular at the trailing edge where an increment inrms is experimentally observed

The improvement of performances showed by the SMmodel when the incoming turbulence is taken into accountcan be due to the fact that the SM model is too dissipativein laminar and transitional regions [18] Indeed the SM

model predicts a nonvanishing eddy viscosity when the flowis laminar and this results in more stable shear layers whenthe incoming flow is smooth Conversely the KET model isable to adjust the eddy viscosity basing on the subgrid kineticenergy leading to an overall less dissipative behavior Whenthe incoming flow turbulence is considered the SM modelperforms better In fact the laminar-to-turbulent transitionis driven by disturbances introduced by the explicitly sim-ulated incoming flow turbulence This different behavior inperfectly smooth and low turbulence inflow conditions is notobserved when the KETmodel is considered Indeed the lessdissipative behavior of the KET model with respect to theSM model allows correctly predicting the destabilization ofthe shear layers without triggering it explicitly by introducingdisturbances

43 Spanwise-Averaged Quantities 119911-avg distributions of1198621015840119901

denoted as 119862

119901(119911-avg)1015840 are reported in Figure 7 for each case

Data concerning the central section statistics (see Figure 6)are repeated in this figure in order to better highlightdifferences with respect to the corresponding 119911-avg valuesFocusing on the top surface the SM model shows that thegap between 1198621015840

119901

and 119862119901(119911-avg)1015840 increases proceeding from

Mathematical Problems in Engineering 9

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

Top surface

Bottom surface

minus1 0 1 2minus2

zD

1 2minus1 0minus2

zD

minus1minus2 1 20zD

minus1minus2 1 20zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

Figure 8 Correlation functions for the SM model in smooth and turbulent inflow condition

the leading edge to the trailing one where the peak value of119862119901(119911-avg)1015840 is radically decreased with respect to the central

alignment for both smooth and turbulent inlet conditionThe flow two-dimensionality is dominant close to the leadingedge where 119911-avg statistics are identical to the central sectionones while the flow three-dimensional mechanisms prevaildownwind This trend is confirmed by the KET model evenif in this case the gap between1198621015840

119901

and119862119901(119911-avg)1015840 is reduced if

compared with the SM model suggesting that the predictedflow is more correlated in the spanwise direction

Considering results of the SM model on the bottomsurface the reduction between 119911-avg and central sectionstatistics is higher when the inflow turbulence is consideredIn fact while for the smooth inlet condition 119911-avg peak valueis roughly 66 of the central section one when turbulenceis taken into account the peak of 119862

119901(119911-avg)1015840 is only 44 of

the corresponding 1198621015840119901

value Therefore the SM model showsthat the inflow turbulence contributes to decreasing the flowcorrelation in the spanwise direction to a great extent

In agreement with the previously reported results theKET model does not show such a high sensitivity differ-ences between 119862

119901(119911-avg)1015840 and 1198621015840

119901

in smooth and turbulentcondition being almost identical Qualitatively by observing

the rms distributions in terms of both peak amplitude andposition results obtained by using the KET model appear tobe intermediate between the ones obtained in smooth andturbulent flow by using the SM model

44 Correlations This section reports 119862119901correlations along

the spanwise direction for three different sections locatedat 119904119863 = 175 300 and 425 Data acquired on probesclose to the edges in the spanwise direction can be affectedby the prescribed boundary conditions therefore results arepresented disregarding part of the rectangular cylinder nearto the boundary 119911119863 ranging from minus25 to 25 Figure 8shows the correlation of 119862

119901 indicated as 119877

119862119901 obtained for

the SM model on top and bottom surfaces for smooth andturbulent inlet while results obtained by using the KETmodel are reported in Figure 9

Interestingly in this case the correlation appears to behigher when a small incoming turbulence level is con-sidered The authors conjecture that this behavior mightbe related to the fact that when perfectly smooth con-ditions are considered the flow impinges on the trailingedge as it can be deduced from time-averaged streamlinesreported in Figure 5 Contrarily when incoming turbulence is

10 Mathematical Problems in Engineering

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

0 1 2minus1minus2

zD

0 21minus1minus2

zD

0 1 2minus1minus2

zD

0 21minus1minus2

zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

Top surface

Bottom surface

Figure 9 Correlation functions for the KET model in smooth and turbulent inflow condition

considered a higher level of entrapment of the separationbubble is observed probably leading to higher along-spancorrelations Regarding the bottom surface and focusing onresults obtained by means of the SM model an oppositebehavior is recorded This fact might be due to the develop-ment of spanwise vortical structures that decrease the flowcorrelation (see eg Sasaki and Kiya [36])

Also in this case results predicted by using the KETmodel are qualitatively intermediate between the onesobtained by using the SM model in smooth and turbulentconditions and a good stability with respect to the incomingturbulence level is observed

5 Conclusions

In this paper Large Eddy Simulations have been performedaiming at studying the unsteady flow field around a rectan-gular cylinder with aspect ratio 5 1 at 4∘ attack angle when asmall level of incoming turbulence is taken into account Twodifferent turbulence models have been considered namelythe classical Smagorinsky-Lillymodel and the Kinetic EnergyTransport model Both of them have been studied by adopt-ing perfectly smooth and turbulent inlet conditions with

turbulence intensity set to be equal to 07 The inflow tur-bulence has been synthetically generated with the MDSRFGmethod and introduced in the computational domain bymodifying the velocity-pressure coupling algorithm Resultsin terms of flow bulk parameters time-average and rms ofthe pressure coefficient distributions in correspondence withthe prism central section have been compared to availableexperimental data It appears that when the Smagorinsky-Lilly model is adopted the modeling of a realistic turbulentinflow is important in order to obtain accurate results sinceeven small values of the incoming flow turbulence intensitycan deeply affect resultsTheKinetic Energy Transportmodelproved to be less sensitive to the low inflow turbulenceand provided results qualitatively intermediate between theSmagorinsky-Lilly models adopted with perfectly smoothand turbulent inflow conditions The different behavior ofthe two considered models can be due to the fact that theSmagorinsky-Lilly model is not able to make the turbulenteddy viscosity null appearing to be too dissipative and failingin accurately predicting the laminar-to-turbulent transitionOn the contrary the Kinetic Energy Transport model canadjust the turbulent eddy viscosity depending on the subgridkinetic energy showing satisfactory results for both smooth

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

Table 1 Parameters of the computational domain as reported byBruno et al [16]

Source 119863119909

119861 119863119910

119861 119863119911

119861 Λ119909

119861

Present simulation 40 30 2 16

Bruno et al [30 32] 41 302 1 2 4 15

Grozescu et al [33] 41 302 1 15

Mannini et al [34] 200 200 1 2 100

the subgrid stress tensor The resolved viscous stress tensor120591119894119895can be written as

120591119894119895= 2120583 [119878

119894119895minus1

3120575119894119895119878119896119896] (2)

where 119878119894119895represents the resolved strain rate tensor whose

expression is reported below

119878119894119895=1

2(120597119906119894

120597119909119895

+120597119906119895

120597119909119894

) (3)

By assuming Boussinesqrsquos hypothesis the subgrid stresstensor 120591sgs

119894119895

can be written as

120591sgs119894119895

= 120588 (119906119894119906119895minus 119906119894119906119895)

= minus2120588]119905(119878119894119895minus1

3120575119894119895119878119896119896) +

2

3120588120575119894119895119896sgs

(4)

where 119896sgs is the subgrid kinetic energy

119896sgs=1

2(119906119894119906119894minus 119906119894119906119894) (5)

and ]119905is the turbulent eddy viscosity When the SMmodel is

adopted ]119905is expressed as

]119905= (119862119904Δ)2

radic2119878119894119895119878119894119895 (6)

where 119862119904is the Smagorinsky constant set to be equal to 012

whileΔ is the local grid spacing Conversely if theKETmodelis adopted the transport equation for the subgrid kineticenergy is considered in addition to equations reported in (1)

120597

120597119905(120588119896

sgs) +

120597

120597119909119894

(120588119896sgs119906119894)

=120597

120597119909119894

(120588]119905

120597119896sgs

120597119909119894

) minus 120591sgs119894119895

120597119906119895

120597119909119894

minus 120588119888120598

(119896sgs)32

Δ

(7)

and the turbulent eddy viscosity ]119905is calculated as

]119905= 119888]radic119896

sgsΔ (8)

where 119888120598and 119888] are model constants set to be equal respec-

tively to 105 and 0094With respect to the numerical scheme a centered second-

order accurate scheme is adopted to discretize the spatialderivatives exception made for the nonlinear convective

Table 2 Grid resolution in the boundary layer comparison withmeshes adopted by other authors as reported by Bruno et al [16]

Source 119899119908

119861 120575119909

119861 120575119911

119861

Presentsimulation 50 times 10

minus4

25 times 10minus3

002

Bruno et al[30 32] 50 times 10

minus4

20 times 10minus3 0042ndash001

Grozescu etal [33] 5 times 10

minus4 25 times 10minus4 10 times 10minus2 5 times 10minus3 0042 001

Mannini etal [34] 50 times 10

minus5

14 times 10minus2

00156

term For this term the Linear Upwind Stabilized Transportscheme is used which proved to be particularly successful forLES in complex geometries [28]

Time integration is performed by using the the two-step second-order Backward Differentiation Formulae inaccordance with Bruno et al [29] The solution at eachtime step is obtained by means of the well known PressureImplicit with Splitting of Operator algorithm The adoptednondimensional time step (based on 119863) is Δ119905lowast = 50 times 10minus3leading to amaximumCourant number in all the simulationsequal to 39

Symmetry boundary conditions are imposed at the topand bottom surfaces while periodic conditions are adoptedon the faces normal to the spanwise direction (see Figure 1)At the outlet boundary zero pressure is imposed while at theinlet the null normal gradient of pressure is prescribed

The generated fluctuation field is introduced in thecomputational domain in a plane shifted with respect to theinlet boundary of approximately 50 times 10minus1119861 while the meanvelocity is prescribed at the inlet The power spectral densityof the velocity components along 119909 119910 and 119911 directionsindicated respectively as 119906 V and 119908 is reported in Figure 3for two different points located near the inlet boundary at(minus15119861 0 0) and just upstream the rectangular cylinder at(minus15119861 0 0) As it can be seen the high frequency contentof the spectra appears to be slightly damped proceeding fromthe inlet towards the rectangular cylinderWith respect to thealong-wind turbulent length scale 119871

119906 it is found to be equal

to 119861 for both of the aforementioned locationsThe prism has been equipped with 2500 pressure moni-

tors and data are acquired at each time step leading to 200samples for one nondimensional time unit All simulationshave been run by using the open source finite volumesoftware119874119901119890119899119865119874119860119872 on 160CPUs atCINECAon theGalileocluster (516 nodes 2 eight-core Intel Haswell 240GHzprocessors with 128GB RAM per node)

4 Numerical Results

In this section numerical results obtained for each turbulencemodel with smooth and turbulent inflow condition arereported and systematically compared with experimentaldata In particular the flow bulk parameters obtained fromeach simulation together with a discussion of the resultingflow topology are reported in Section 41 The pressure

Mathematical Problems in Engineering 5

KET I = 07 xB = minus150

KET I = 07 xB = minus15

KET I = 07 xB = minus150

KET I = 07 xB = minus15

KET I = 07 xB = minus150

KET I = 07 xB = minus15

10minus1 10010minus2

fDU

10minus1 10010minus2

fDU

10minus1 10010minus2

fDU

10minus810minus710minus610minus510minus410minus310minus2

S wfU

2

10minus810minus710minus610minus510minus410minus310minus2

S fU

2

10minus810minus710minus610minus510minus410minus310minus2

S ufU

2

Figure 3 Spectra of the velocity time series obtained from the KETsimulation with incoming flow turbulence at different locations

coefficient statistics on the central section are showed inSection 42 while Section 43 focuses on the spanwise-averaged pressure distributions Then in Section 44 corre-lations in the spanwise direction are discussed

Numerical results have been obtained by considering asimulation time of 119905lowast = 1000 119905lowast being the nondimensionaltime unit The postprocessing of data has been carried outconsidering only the last 700 nondimensional time units inorder to avoid flow initialization effects [30]

In order to check the convergence of the recordedstatistics the time-history of the lift coefficient has beensubdivided into ten segments and first- and second-orderstatistics were extracted by incrementally extending the partof the signal considered in the postprocessing Despite therelatively long simulation time (longer than the minimumrequirements [30]) in the worst case a plateau has beenreached for second-order statistics only when 90of the totaltime-history has been used

41 Flow Topology and Bulk Parameters In order to have aqualitative view of the turbulent structures obtained from thenumerical analyses the flow topology in terms of isosurfacesof the invariant 120582

2[31] coloured with pressure is reported

in Figure 4 for the two investigated turbulence models insmooth and turbulent inflow conditions The instantaneousisosurfaces are plotted to correspond with maximum lift Asit can be seen when the inflow turbulence is considered the

Table 3 Reattachment point and main vortex core position

Source 119909119903

down 119909119888

up 119909119888

down 119910119888

up 119910119888

downSM(smooth) 116 054 minus049 096 minus078

SM 119868 = 07 001 091 minus081 091 minus063KET(smooth) 005 109 minus065 101 minus054

KET 119868 =07 004 110 minus063 100 minus051

Table 4 Statistics of the flow bulk parameters

Source 119862119863

1198621015840

119863

119862119871

1198621015840

119871

StSM (smooth) 126 0056 144 057 0116SM 119868 = 07 128 0064 156 061 0115KET (smooth) 137 0079 227 076 0117KET 119868 = 07 13 0080 226 081 0115Pigolotti et al [23] (Exp) 163 mdash 202 mdash 0126Schewe [35] (Exp) 138 mdash 252 mdash 0115

topology showed by the SM model appears to be quite inaccordance with that obtained by means of the KET modelFurthermore both of them comply well with the topologyshowed by theKETmodel in smooth inflow conditions whilein this case the topology obtained by using the SM modelshows a narrower wake

The different behavior of the two turbulence models isalso reflected in Table 3 which shows that the reattachmentpoint at the bottom surface moves from 119909

119903= 116 to

119909119903= 001 when turbulence is introduced and the SM

model considered while no significant differences betweenturbulent and smooth inlet are observed if the KET model isanalyzed

The effect of incoming turbulence can be also appreciatedby observing the streamlines of the time-averaged flow fieldsreported in Figure 5 In particular the SM model appearsto be significantly affected by the presence of incomingturbulence while the KET model appears to be rather stableIt is also noticed that all considered models apart from theSM in smooth flow predict the creation of a small elongatedvortex at the leading edge in correspondence with the topside whose core is located at approximately 119909

119888= minus15

The statistics of the flow bulk parameters are reported inTable 4 (results are made nondimensional with respect to119863)and referred to the global reference system In particular 119862

119863

and119862119871are the drag and the lift coefficients respectively while

their root mean square values are indicated as 1198621015840119863

and 1198621015840119871

respectively Again the results obtained by the two turbulencemodels are in good agreement when a low level of incomingturbulence is considered while remarkable differences areobserved in perfectly smooth flow Furthermore it should benoticed that 119862

119863and 119862

119871 together with the Strouhal number

(St) obtained by taking into account the incoming turbulenceagree quite well with experimental measurements In orderto provide a clearer picture of the obtained results in thefollowing pressure field statistics distributions are analyzed

6 Mathematical Problems in Engineering

minuspdyn pdynminuspdyn pdyn

minuspdyn pdyn minuspdyn pdyn

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 4 Isosurfaces of 1205822

coloured with pressure for the two analyzed turbulence models

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 5 Time-averaged streamlines for the two analyzed turbulence models

42 Central Section Statistics In this section the pressurecoefficient statistics on the prism central section are analyzedData are presented by adopting the curvilinear abscissa 119904as reported in Figure 1 The upwind face of the prism isidentified by 00 le 119904119863 le 05 and the along-wind surfacesare identified by 05 le 119904119863 le 50 while the downwind face isidentified by 55 le 119904119863 le 60

Figure 6 shows the distribution of the pressure statisticsobtained by means of the present simulations and compari-son with experimental results As it can be noticed if the topsurface is considered the time-averaged pressure coefficient119862119901 distribution predicted by the KET model is almost

in perfect accordance with the experimental data for both

smooth and turbulent inflow conditions Contrarily the SMmodel approaches experimental results only when turbulentinlet conditions are adopted Observing 1198621015840

119901

on the samesurface the KET model always complies with experimentalmeasurements with the peak position and the experimentaltrends being reproduced with good accuracy Generally theSM model appears to be unable to correctly reproduce theshape of the pressure recovery not catching the change ofsteepness that occurs at about 119904119863 = 3 in correspondencewith the separation between the vortex shedding and thevortex coalescing zones as individuated in [30]

When 119862119901distribution on the bottom surface is analyzed

the SMmodel appears to be very sensitive to small turbulence

Mathematical Problems in Engineering 7

Cp

Cp

Cp

Cp

SM KET

SM KET

SM KET

SM KET

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

1 2 3 4 5 60sD

minus10

minus05

00

05

10

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

1 2 3 4 5 60sD

60 3 4 51 2

sD

1 2 3 4 5 60sD

minus10

minus05

00

05

10

1 2 3 4 5 60sD

Top surface

Bottom surface

Figure 6 Distribution of 119862119901

statistics on the central alignment

8 Mathematical Problems in Engineering

00

01

02

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

543 60 1 2

sD

543 60 1 2

sD

00

01

02

C998400 p

00

01

02

C998400 p

Top surface

Bottom surface

SM

SM KET

KETSM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

SM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

Figure 7 Comparison between 119911-averaged and central section statistics for the SM and KET turbulence models

intensities in the incoming flow In fact the distributionobtained in smooth flow conditions clearly changes whenthe inflow turbulence is considered the reattachment pointmigrates upstream and the distribution shifts approachingthe experimental dataTheKETmodel instead shows again alower sensitivity to the incoming turbulence results obtainedin both configurations being approximately the same TheSM model is very accurate when turbulence is taken intoaccount and shows better performances if compared with theKET model which slightly overestimates the reattachmentlength and underestimates suctions at the leeward edge Theimprovement of the SM model with turbulent inlet observedfor mean values can be noticed also by considering 119862

1015840

119901

distribution on the bottom surface In this case the modelcorrectly predicts the peak position and the trend observedexperimentally even if the peak value is clearly overestimatedThe KET model correctly predicts the peak position and thetrend in particular at the trailing edge where an increment inrms is experimentally observed

The improvement of performances showed by the SMmodel when the incoming turbulence is taken into accountcan be due to the fact that the SM model is too dissipativein laminar and transitional regions [18] Indeed the SM

model predicts a nonvanishing eddy viscosity when the flowis laminar and this results in more stable shear layers whenthe incoming flow is smooth Conversely the KET model isable to adjust the eddy viscosity basing on the subgrid kineticenergy leading to an overall less dissipative behavior Whenthe incoming flow turbulence is considered the SM modelperforms better In fact the laminar-to-turbulent transitionis driven by disturbances introduced by the explicitly sim-ulated incoming flow turbulence This different behavior inperfectly smooth and low turbulence inflow conditions is notobserved when the KETmodel is considered Indeed the lessdissipative behavior of the KET model with respect to theSM model allows correctly predicting the destabilization ofthe shear layers without triggering it explicitly by introducingdisturbances

43 Spanwise-Averaged Quantities 119911-avg distributions of1198621015840119901

denoted as 119862

119901(119911-avg)1015840 are reported in Figure 7 for each case

Data concerning the central section statistics (see Figure 6)are repeated in this figure in order to better highlightdifferences with respect to the corresponding 119911-avg valuesFocusing on the top surface the SM model shows that thegap between 1198621015840

119901

and 119862119901(119911-avg)1015840 increases proceeding from

Mathematical Problems in Engineering 9

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

Top surface

Bottom surface

minus1 0 1 2minus2

zD

1 2minus1 0minus2

zD

minus1minus2 1 20zD

minus1minus2 1 20zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

Figure 8 Correlation functions for the SM model in smooth and turbulent inflow condition

the leading edge to the trailing one where the peak value of119862119901(119911-avg)1015840 is radically decreased with respect to the central

alignment for both smooth and turbulent inlet conditionThe flow two-dimensionality is dominant close to the leadingedge where 119911-avg statistics are identical to the central sectionones while the flow three-dimensional mechanisms prevaildownwind This trend is confirmed by the KET model evenif in this case the gap between1198621015840

119901

and119862119901(119911-avg)1015840 is reduced if

compared with the SM model suggesting that the predictedflow is more correlated in the spanwise direction

Considering results of the SM model on the bottomsurface the reduction between 119911-avg and central sectionstatistics is higher when the inflow turbulence is consideredIn fact while for the smooth inlet condition 119911-avg peak valueis roughly 66 of the central section one when turbulenceis taken into account the peak of 119862

119901(119911-avg)1015840 is only 44 of

the corresponding 1198621015840119901

value Therefore the SM model showsthat the inflow turbulence contributes to decreasing the flowcorrelation in the spanwise direction to a great extent

In agreement with the previously reported results theKET model does not show such a high sensitivity differ-ences between 119862

119901(119911-avg)1015840 and 1198621015840

119901

in smooth and turbulentcondition being almost identical Qualitatively by observing

the rms distributions in terms of both peak amplitude andposition results obtained by using the KET model appear tobe intermediate between the ones obtained in smooth andturbulent flow by using the SM model

44 Correlations This section reports 119862119901correlations along

the spanwise direction for three different sections locatedat 119904119863 = 175 300 and 425 Data acquired on probesclose to the edges in the spanwise direction can be affectedby the prescribed boundary conditions therefore results arepresented disregarding part of the rectangular cylinder nearto the boundary 119911119863 ranging from minus25 to 25 Figure 8shows the correlation of 119862

119901 indicated as 119877

119862119901 obtained for

the SM model on top and bottom surfaces for smooth andturbulent inlet while results obtained by using the KETmodel are reported in Figure 9

Interestingly in this case the correlation appears to behigher when a small incoming turbulence level is con-sidered The authors conjecture that this behavior mightbe related to the fact that when perfectly smooth con-ditions are considered the flow impinges on the trailingedge as it can be deduced from time-averaged streamlinesreported in Figure 5 Contrarily when incoming turbulence is

10 Mathematical Problems in Engineering

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

0 1 2minus1minus2

zD

0 21minus1minus2

zD

0 1 2minus1minus2

zD

0 21minus1minus2

zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

Top surface

Bottom surface

Figure 9 Correlation functions for the KET model in smooth and turbulent inflow condition

considered a higher level of entrapment of the separationbubble is observed probably leading to higher along-spancorrelations Regarding the bottom surface and focusing onresults obtained by means of the SM model an oppositebehavior is recorded This fact might be due to the develop-ment of spanwise vortical structures that decrease the flowcorrelation (see eg Sasaki and Kiya [36])

Also in this case results predicted by using the KETmodel are qualitatively intermediate between the onesobtained by using the SM model in smooth and turbulentconditions and a good stability with respect to the incomingturbulence level is observed

5 Conclusions

In this paper Large Eddy Simulations have been performedaiming at studying the unsteady flow field around a rectan-gular cylinder with aspect ratio 5 1 at 4∘ attack angle when asmall level of incoming turbulence is taken into account Twodifferent turbulence models have been considered namelythe classical Smagorinsky-Lillymodel and the Kinetic EnergyTransport model Both of them have been studied by adopt-ing perfectly smooth and turbulent inlet conditions with

turbulence intensity set to be equal to 07 The inflow tur-bulence has been synthetically generated with the MDSRFGmethod and introduced in the computational domain bymodifying the velocity-pressure coupling algorithm Resultsin terms of flow bulk parameters time-average and rms ofthe pressure coefficient distributions in correspondence withthe prism central section have been compared to availableexperimental data It appears that when the Smagorinsky-Lilly model is adopted the modeling of a realistic turbulentinflow is important in order to obtain accurate results sinceeven small values of the incoming flow turbulence intensitycan deeply affect resultsTheKinetic Energy Transportmodelproved to be less sensitive to the low inflow turbulenceand provided results qualitatively intermediate between theSmagorinsky-Lilly models adopted with perfectly smoothand turbulent inflow conditions The different behavior ofthe two considered models can be due to the fact that theSmagorinsky-Lilly model is not able to make the turbulenteddy viscosity null appearing to be too dissipative and failingin accurately predicting the laminar-to-turbulent transitionOn the contrary the Kinetic Energy Transport model canadjust the turbulent eddy viscosity depending on the subgridkinetic energy showing satisfactory results for both smooth

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical PhysicsAdvances in

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International Journal of

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Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Discrete Dynamics in Nature and Society

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Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

KET I = 07 xB = minus150

KET I = 07 xB = minus15

KET I = 07 xB = minus150

KET I = 07 xB = minus15

KET I = 07 xB = minus150

KET I = 07 xB = minus15

10minus1 10010minus2

fDU

10minus1 10010minus2

fDU

10minus1 10010minus2

fDU

10minus810minus710minus610minus510minus410minus310minus2

S wfU

2

10minus810minus710minus610minus510minus410minus310minus2

S fU

2

10minus810minus710minus610minus510minus410minus310minus2

S ufU

2

Figure 3 Spectra of the velocity time series obtained from the KETsimulation with incoming flow turbulence at different locations

coefficient statistics on the central section are showed inSection 42 while Section 43 focuses on the spanwise-averaged pressure distributions Then in Section 44 corre-lations in the spanwise direction are discussed

Numerical results have been obtained by considering asimulation time of 119905lowast = 1000 119905lowast being the nondimensionaltime unit The postprocessing of data has been carried outconsidering only the last 700 nondimensional time units inorder to avoid flow initialization effects [30]

In order to check the convergence of the recordedstatistics the time-history of the lift coefficient has beensubdivided into ten segments and first- and second-orderstatistics were extracted by incrementally extending the partof the signal considered in the postprocessing Despite therelatively long simulation time (longer than the minimumrequirements [30]) in the worst case a plateau has beenreached for second-order statistics only when 90of the totaltime-history has been used

41 Flow Topology and Bulk Parameters In order to have aqualitative view of the turbulent structures obtained from thenumerical analyses the flow topology in terms of isosurfacesof the invariant 120582

2[31] coloured with pressure is reported

in Figure 4 for the two investigated turbulence models insmooth and turbulent inflow conditions The instantaneousisosurfaces are plotted to correspond with maximum lift Asit can be seen when the inflow turbulence is considered the

Table 3 Reattachment point and main vortex core position

Source 119909119903

down 119909119888

up 119909119888

down 119910119888

up 119910119888

downSM(smooth) 116 054 minus049 096 minus078

SM 119868 = 07 001 091 minus081 091 minus063KET(smooth) 005 109 minus065 101 minus054

KET 119868 =07 004 110 minus063 100 minus051

Table 4 Statistics of the flow bulk parameters

Source 119862119863

1198621015840

119863

119862119871

1198621015840

119871

StSM (smooth) 126 0056 144 057 0116SM 119868 = 07 128 0064 156 061 0115KET (smooth) 137 0079 227 076 0117KET 119868 = 07 13 0080 226 081 0115Pigolotti et al [23] (Exp) 163 mdash 202 mdash 0126Schewe [35] (Exp) 138 mdash 252 mdash 0115

topology showed by the SM model appears to be quite inaccordance with that obtained by means of the KET modelFurthermore both of them comply well with the topologyshowed by theKETmodel in smooth inflow conditions whilein this case the topology obtained by using the SM modelshows a narrower wake

The different behavior of the two turbulence models isalso reflected in Table 3 which shows that the reattachmentpoint at the bottom surface moves from 119909

119903= 116 to

119909119903= 001 when turbulence is introduced and the SM

model considered while no significant differences betweenturbulent and smooth inlet are observed if the KET model isanalyzed

The effect of incoming turbulence can be also appreciatedby observing the streamlines of the time-averaged flow fieldsreported in Figure 5 In particular the SM model appearsto be significantly affected by the presence of incomingturbulence while the KET model appears to be rather stableIt is also noticed that all considered models apart from theSM in smooth flow predict the creation of a small elongatedvortex at the leading edge in correspondence with the topside whose core is located at approximately 119909

119888= minus15

The statistics of the flow bulk parameters are reported inTable 4 (results are made nondimensional with respect to119863)and referred to the global reference system In particular 119862

119863

and119862119871are the drag and the lift coefficients respectively while

their root mean square values are indicated as 1198621015840119863

and 1198621015840119871

respectively Again the results obtained by the two turbulencemodels are in good agreement when a low level of incomingturbulence is considered while remarkable differences areobserved in perfectly smooth flow Furthermore it should benoticed that 119862

119863and 119862

119871 together with the Strouhal number

(St) obtained by taking into account the incoming turbulenceagree quite well with experimental measurements In orderto provide a clearer picture of the obtained results in thefollowing pressure field statistics distributions are analyzed

6 Mathematical Problems in Engineering

minuspdyn pdynminuspdyn pdyn

minuspdyn pdyn minuspdyn pdyn

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 4 Isosurfaces of 1205822

coloured with pressure for the two analyzed turbulence models

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 5 Time-averaged streamlines for the two analyzed turbulence models

42 Central Section Statistics In this section the pressurecoefficient statistics on the prism central section are analyzedData are presented by adopting the curvilinear abscissa 119904as reported in Figure 1 The upwind face of the prism isidentified by 00 le 119904119863 le 05 and the along-wind surfacesare identified by 05 le 119904119863 le 50 while the downwind face isidentified by 55 le 119904119863 le 60

Figure 6 shows the distribution of the pressure statisticsobtained by means of the present simulations and compari-son with experimental results As it can be noticed if the topsurface is considered the time-averaged pressure coefficient119862119901 distribution predicted by the KET model is almost

in perfect accordance with the experimental data for both

smooth and turbulent inflow conditions Contrarily the SMmodel approaches experimental results only when turbulentinlet conditions are adopted Observing 1198621015840

119901

on the samesurface the KET model always complies with experimentalmeasurements with the peak position and the experimentaltrends being reproduced with good accuracy Generally theSM model appears to be unable to correctly reproduce theshape of the pressure recovery not catching the change ofsteepness that occurs at about 119904119863 = 3 in correspondencewith the separation between the vortex shedding and thevortex coalescing zones as individuated in [30]

When 119862119901distribution on the bottom surface is analyzed

the SMmodel appears to be very sensitive to small turbulence

Mathematical Problems in Engineering 7

Cp

Cp

Cp

Cp

SM KET

SM KET

SM KET

SM KET

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

1 2 3 4 5 60sD

minus10

minus05

00

05

10

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

1 2 3 4 5 60sD

60 3 4 51 2

sD

1 2 3 4 5 60sD

minus10

minus05

00

05

10

1 2 3 4 5 60sD

Top surface

Bottom surface

Figure 6 Distribution of 119862119901

statistics on the central alignment

8 Mathematical Problems in Engineering

00

01

02

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

543 60 1 2

sD

543 60 1 2

sD

00

01

02

C998400 p

00

01

02

C998400 p

Top surface

Bottom surface

SM

SM KET

KETSM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

SM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

Figure 7 Comparison between 119911-averaged and central section statistics for the SM and KET turbulence models

intensities in the incoming flow In fact the distributionobtained in smooth flow conditions clearly changes whenthe inflow turbulence is considered the reattachment pointmigrates upstream and the distribution shifts approachingthe experimental dataTheKETmodel instead shows again alower sensitivity to the incoming turbulence results obtainedin both configurations being approximately the same TheSM model is very accurate when turbulence is taken intoaccount and shows better performances if compared with theKET model which slightly overestimates the reattachmentlength and underestimates suctions at the leeward edge Theimprovement of the SM model with turbulent inlet observedfor mean values can be noticed also by considering 119862

1015840

119901

distribution on the bottom surface In this case the modelcorrectly predicts the peak position and the trend observedexperimentally even if the peak value is clearly overestimatedThe KET model correctly predicts the peak position and thetrend in particular at the trailing edge where an increment inrms is experimentally observed

The improvement of performances showed by the SMmodel when the incoming turbulence is taken into accountcan be due to the fact that the SM model is too dissipativein laminar and transitional regions [18] Indeed the SM

model predicts a nonvanishing eddy viscosity when the flowis laminar and this results in more stable shear layers whenthe incoming flow is smooth Conversely the KET model isable to adjust the eddy viscosity basing on the subgrid kineticenergy leading to an overall less dissipative behavior Whenthe incoming flow turbulence is considered the SM modelperforms better In fact the laminar-to-turbulent transitionis driven by disturbances introduced by the explicitly sim-ulated incoming flow turbulence This different behavior inperfectly smooth and low turbulence inflow conditions is notobserved when the KETmodel is considered Indeed the lessdissipative behavior of the KET model with respect to theSM model allows correctly predicting the destabilization ofthe shear layers without triggering it explicitly by introducingdisturbances

43 Spanwise-Averaged Quantities 119911-avg distributions of1198621015840119901

denoted as 119862

119901(119911-avg)1015840 are reported in Figure 7 for each case

Data concerning the central section statistics (see Figure 6)are repeated in this figure in order to better highlightdifferences with respect to the corresponding 119911-avg valuesFocusing on the top surface the SM model shows that thegap between 1198621015840

119901

and 119862119901(119911-avg)1015840 increases proceeding from

Mathematical Problems in Engineering 9

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

Top surface

Bottom surface

minus1 0 1 2minus2

zD

1 2minus1 0minus2

zD

minus1minus2 1 20zD

minus1minus2 1 20zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

Figure 8 Correlation functions for the SM model in smooth and turbulent inflow condition

the leading edge to the trailing one where the peak value of119862119901(119911-avg)1015840 is radically decreased with respect to the central

alignment for both smooth and turbulent inlet conditionThe flow two-dimensionality is dominant close to the leadingedge where 119911-avg statistics are identical to the central sectionones while the flow three-dimensional mechanisms prevaildownwind This trend is confirmed by the KET model evenif in this case the gap between1198621015840

119901

and119862119901(119911-avg)1015840 is reduced if

compared with the SM model suggesting that the predictedflow is more correlated in the spanwise direction

Considering results of the SM model on the bottomsurface the reduction between 119911-avg and central sectionstatistics is higher when the inflow turbulence is consideredIn fact while for the smooth inlet condition 119911-avg peak valueis roughly 66 of the central section one when turbulenceis taken into account the peak of 119862

119901(119911-avg)1015840 is only 44 of

the corresponding 1198621015840119901

value Therefore the SM model showsthat the inflow turbulence contributes to decreasing the flowcorrelation in the spanwise direction to a great extent

In agreement with the previously reported results theKET model does not show such a high sensitivity differ-ences between 119862

119901(119911-avg)1015840 and 1198621015840

119901

in smooth and turbulentcondition being almost identical Qualitatively by observing

the rms distributions in terms of both peak amplitude andposition results obtained by using the KET model appear tobe intermediate between the ones obtained in smooth andturbulent flow by using the SM model

44 Correlations This section reports 119862119901correlations along

the spanwise direction for three different sections locatedat 119904119863 = 175 300 and 425 Data acquired on probesclose to the edges in the spanwise direction can be affectedby the prescribed boundary conditions therefore results arepresented disregarding part of the rectangular cylinder nearto the boundary 119911119863 ranging from minus25 to 25 Figure 8shows the correlation of 119862

119901 indicated as 119877

119862119901 obtained for

the SM model on top and bottom surfaces for smooth andturbulent inlet while results obtained by using the KETmodel are reported in Figure 9

Interestingly in this case the correlation appears to behigher when a small incoming turbulence level is con-sidered The authors conjecture that this behavior mightbe related to the fact that when perfectly smooth con-ditions are considered the flow impinges on the trailingedge as it can be deduced from time-averaged streamlinesreported in Figure 5 Contrarily when incoming turbulence is

10 Mathematical Problems in Engineering

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

0 1 2minus1minus2

zD

0 21minus1minus2

zD

0 1 2minus1minus2

zD

0 21minus1minus2

zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

Top surface

Bottom surface

Figure 9 Correlation functions for the KET model in smooth and turbulent inflow condition

considered a higher level of entrapment of the separationbubble is observed probably leading to higher along-spancorrelations Regarding the bottom surface and focusing onresults obtained by means of the SM model an oppositebehavior is recorded This fact might be due to the develop-ment of spanwise vortical structures that decrease the flowcorrelation (see eg Sasaki and Kiya [36])

Also in this case results predicted by using the KETmodel are qualitatively intermediate between the onesobtained by using the SM model in smooth and turbulentconditions and a good stability with respect to the incomingturbulence level is observed

5 Conclusions

In this paper Large Eddy Simulations have been performedaiming at studying the unsteady flow field around a rectan-gular cylinder with aspect ratio 5 1 at 4∘ attack angle when asmall level of incoming turbulence is taken into account Twodifferent turbulence models have been considered namelythe classical Smagorinsky-Lillymodel and the Kinetic EnergyTransport model Both of them have been studied by adopt-ing perfectly smooth and turbulent inlet conditions with

turbulence intensity set to be equal to 07 The inflow tur-bulence has been synthetically generated with the MDSRFGmethod and introduced in the computational domain bymodifying the velocity-pressure coupling algorithm Resultsin terms of flow bulk parameters time-average and rms ofthe pressure coefficient distributions in correspondence withthe prism central section have been compared to availableexperimental data It appears that when the Smagorinsky-Lilly model is adopted the modeling of a realistic turbulentinflow is important in order to obtain accurate results sinceeven small values of the incoming flow turbulence intensitycan deeply affect resultsTheKinetic Energy Transportmodelproved to be less sensitive to the low inflow turbulenceand provided results qualitatively intermediate between theSmagorinsky-Lilly models adopted with perfectly smoothand turbulent inflow conditions The different behavior ofthe two considered models can be due to the fact that theSmagorinsky-Lilly model is not able to make the turbulenteddy viscosity null appearing to be too dissipative and failingin accurately predicting the laminar-to-turbulent transitionOn the contrary the Kinetic Energy Transport model canadjust the turbulent eddy viscosity depending on the subgridkinetic energy showing satisfactory results for both smooth

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

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Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

minuspdyn pdynminuspdyn pdyn

minuspdyn pdyn minuspdyn pdyn

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 4 Isosurfaces of 1205822

coloured with pressure for the two analyzed turbulence models

SM smooth

KET I = 07SM I = 07

KET smooth

Figure 5 Time-averaged streamlines for the two analyzed turbulence models

42 Central Section Statistics In this section the pressurecoefficient statistics on the prism central section are analyzedData are presented by adopting the curvilinear abscissa 119904as reported in Figure 1 The upwind face of the prism isidentified by 00 le 119904119863 le 05 and the along-wind surfacesare identified by 05 le 119904119863 le 50 while the downwind face isidentified by 55 le 119904119863 le 60

Figure 6 shows the distribution of the pressure statisticsobtained by means of the present simulations and compari-son with experimental results As it can be noticed if the topsurface is considered the time-averaged pressure coefficient119862119901 distribution predicted by the KET model is almost

in perfect accordance with the experimental data for both

smooth and turbulent inflow conditions Contrarily the SMmodel approaches experimental results only when turbulentinlet conditions are adopted Observing 1198621015840

119901

on the samesurface the KET model always complies with experimentalmeasurements with the peak position and the experimentaltrends being reproduced with good accuracy Generally theSM model appears to be unable to correctly reproduce theshape of the pressure recovery not catching the change ofsteepness that occurs at about 119904119863 = 3 in correspondencewith the separation between the vortex shedding and thevortex coalescing zones as individuated in [30]

When 119862119901distribution on the bottom surface is analyzed

the SMmodel appears to be very sensitive to small turbulence

Mathematical Problems in Engineering 7

Cp

Cp

Cp

Cp

SM KET

SM KET

SM KET

SM KET

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

1 2 3 4 5 60sD

minus10

minus05

00

05

10

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

1 2 3 4 5 60sD

60 3 4 51 2

sD

1 2 3 4 5 60sD

minus10

minus05

00

05

10

1 2 3 4 5 60sD

Top surface

Bottom surface

Figure 6 Distribution of 119862119901

statistics on the central alignment

8 Mathematical Problems in Engineering

00

01

02

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

543 60 1 2

sD

543 60 1 2

sD

00

01

02

C998400 p

00

01

02

C998400 p

Top surface

Bottom surface

SM

SM KET

KETSM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

SM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

Figure 7 Comparison between 119911-averaged and central section statistics for the SM and KET turbulence models

intensities in the incoming flow In fact the distributionobtained in smooth flow conditions clearly changes whenthe inflow turbulence is considered the reattachment pointmigrates upstream and the distribution shifts approachingthe experimental dataTheKETmodel instead shows again alower sensitivity to the incoming turbulence results obtainedin both configurations being approximately the same TheSM model is very accurate when turbulence is taken intoaccount and shows better performances if compared with theKET model which slightly overestimates the reattachmentlength and underestimates suctions at the leeward edge Theimprovement of the SM model with turbulent inlet observedfor mean values can be noticed also by considering 119862

1015840

119901

distribution on the bottom surface In this case the modelcorrectly predicts the peak position and the trend observedexperimentally even if the peak value is clearly overestimatedThe KET model correctly predicts the peak position and thetrend in particular at the trailing edge where an increment inrms is experimentally observed

The improvement of performances showed by the SMmodel when the incoming turbulence is taken into accountcan be due to the fact that the SM model is too dissipativein laminar and transitional regions [18] Indeed the SM

model predicts a nonvanishing eddy viscosity when the flowis laminar and this results in more stable shear layers whenthe incoming flow is smooth Conversely the KET model isable to adjust the eddy viscosity basing on the subgrid kineticenergy leading to an overall less dissipative behavior Whenthe incoming flow turbulence is considered the SM modelperforms better In fact the laminar-to-turbulent transitionis driven by disturbances introduced by the explicitly sim-ulated incoming flow turbulence This different behavior inperfectly smooth and low turbulence inflow conditions is notobserved when the KETmodel is considered Indeed the lessdissipative behavior of the KET model with respect to theSM model allows correctly predicting the destabilization ofthe shear layers without triggering it explicitly by introducingdisturbances

43 Spanwise-Averaged Quantities 119911-avg distributions of1198621015840119901

denoted as 119862

119901(119911-avg)1015840 are reported in Figure 7 for each case

Data concerning the central section statistics (see Figure 6)are repeated in this figure in order to better highlightdifferences with respect to the corresponding 119911-avg valuesFocusing on the top surface the SM model shows that thegap between 1198621015840

119901

and 119862119901(119911-avg)1015840 increases proceeding from

Mathematical Problems in Engineering 9

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

Top surface

Bottom surface

minus1 0 1 2minus2

zD

1 2minus1 0minus2

zD

minus1minus2 1 20zD

minus1minus2 1 20zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

Figure 8 Correlation functions for the SM model in smooth and turbulent inflow condition

the leading edge to the trailing one where the peak value of119862119901(119911-avg)1015840 is radically decreased with respect to the central

alignment for both smooth and turbulent inlet conditionThe flow two-dimensionality is dominant close to the leadingedge where 119911-avg statistics are identical to the central sectionones while the flow three-dimensional mechanisms prevaildownwind This trend is confirmed by the KET model evenif in this case the gap between1198621015840

119901

and119862119901(119911-avg)1015840 is reduced if

compared with the SM model suggesting that the predictedflow is more correlated in the spanwise direction

Considering results of the SM model on the bottomsurface the reduction between 119911-avg and central sectionstatistics is higher when the inflow turbulence is consideredIn fact while for the smooth inlet condition 119911-avg peak valueis roughly 66 of the central section one when turbulenceis taken into account the peak of 119862

119901(119911-avg)1015840 is only 44 of

the corresponding 1198621015840119901

value Therefore the SM model showsthat the inflow turbulence contributes to decreasing the flowcorrelation in the spanwise direction to a great extent

In agreement with the previously reported results theKET model does not show such a high sensitivity differ-ences between 119862

119901(119911-avg)1015840 and 1198621015840

119901

in smooth and turbulentcondition being almost identical Qualitatively by observing

the rms distributions in terms of both peak amplitude andposition results obtained by using the KET model appear tobe intermediate between the ones obtained in smooth andturbulent flow by using the SM model

44 Correlations This section reports 119862119901correlations along

the spanwise direction for three different sections locatedat 119904119863 = 175 300 and 425 Data acquired on probesclose to the edges in the spanwise direction can be affectedby the prescribed boundary conditions therefore results arepresented disregarding part of the rectangular cylinder nearto the boundary 119911119863 ranging from minus25 to 25 Figure 8shows the correlation of 119862

119901 indicated as 119877

119862119901 obtained for

the SM model on top and bottom surfaces for smooth andturbulent inlet while results obtained by using the KETmodel are reported in Figure 9

Interestingly in this case the correlation appears to behigher when a small incoming turbulence level is con-sidered The authors conjecture that this behavior mightbe related to the fact that when perfectly smooth con-ditions are considered the flow impinges on the trailingedge as it can be deduced from time-averaged streamlinesreported in Figure 5 Contrarily when incoming turbulence is

10 Mathematical Problems in Engineering

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

0 1 2minus1minus2

zD

0 21minus1minus2

zD

0 1 2minus1minus2

zD

0 21minus1minus2

zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

Top surface

Bottom surface

Figure 9 Correlation functions for the KET model in smooth and turbulent inflow condition

considered a higher level of entrapment of the separationbubble is observed probably leading to higher along-spancorrelations Regarding the bottom surface and focusing onresults obtained by means of the SM model an oppositebehavior is recorded This fact might be due to the develop-ment of spanwise vortical structures that decrease the flowcorrelation (see eg Sasaki and Kiya [36])

Also in this case results predicted by using the KETmodel are qualitatively intermediate between the onesobtained by using the SM model in smooth and turbulentconditions and a good stability with respect to the incomingturbulence level is observed

5 Conclusions

In this paper Large Eddy Simulations have been performedaiming at studying the unsteady flow field around a rectan-gular cylinder with aspect ratio 5 1 at 4∘ attack angle when asmall level of incoming turbulence is taken into account Twodifferent turbulence models have been considered namelythe classical Smagorinsky-Lillymodel and the Kinetic EnergyTransport model Both of them have been studied by adopt-ing perfectly smooth and turbulent inlet conditions with

turbulence intensity set to be equal to 07 The inflow tur-bulence has been synthetically generated with the MDSRFGmethod and introduced in the computational domain bymodifying the velocity-pressure coupling algorithm Resultsin terms of flow bulk parameters time-average and rms ofthe pressure coefficient distributions in correspondence withthe prism central section have been compared to availableexperimental data It appears that when the Smagorinsky-Lilly model is adopted the modeling of a realistic turbulentinflow is important in order to obtain accurate results sinceeven small values of the incoming flow turbulence intensitycan deeply affect resultsTheKinetic Energy Transportmodelproved to be less sensitive to the low inflow turbulenceand provided results qualitatively intermediate between theSmagorinsky-Lilly models adopted with perfectly smoothand turbulent inflow conditions The different behavior ofthe two considered models can be due to the fact that theSmagorinsky-Lilly model is not able to make the turbulenteddy viscosity null appearing to be too dissipative and failingin accurately predicting the laminar-to-turbulent transitionOn the contrary the Kinetic Energy Transport model canadjust the turbulent eddy viscosity depending on the subgridkinetic energy showing satisfactory results for both smooth

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

Cp

Cp

Cp

Cp

SM KET

SM KET

SM KET

SM KET

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

SM smoothExperimental SM I = 07

KET smoothExperimental KET I = 07

1 2 3 4 5 60sD

minus10

minus05

00

05

10

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

minus10

minus05

00

05

10

00

01

02

03

04

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

1 2 3 4 5 60sD

60 3 4 51 2

sD

1 2 3 4 5 60sD

minus10

minus05

00

05

10

1 2 3 4 5 60sD

Top surface

Bottom surface

Figure 6 Distribution of 119862119901

statistics on the central alignment

8 Mathematical Problems in Engineering

00

01

02

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

543 60 1 2

sD

543 60 1 2

sD

00

01

02

C998400 p

00

01

02

C998400 p

Top surface

Bottom surface

SM

SM KET

KETSM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

SM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

Figure 7 Comparison between 119911-averaged and central section statistics for the SM and KET turbulence models

intensities in the incoming flow In fact the distributionobtained in smooth flow conditions clearly changes whenthe inflow turbulence is considered the reattachment pointmigrates upstream and the distribution shifts approachingthe experimental dataTheKETmodel instead shows again alower sensitivity to the incoming turbulence results obtainedin both configurations being approximately the same TheSM model is very accurate when turbulence is taken intoaccount and shows better performances if compared with theKET model which slightly overestimates the reattachmentlength and underestimates suctions at the leeward edge Theimprovement of the SM model with turbulent inlet observedfor mean values can be noticed also by considering 119862

1015840

119901

distribution on the bottom surface In this case the modelcorrectly predicts the peak position and the trend observedexperimentally even if the peak value is clearly overestimatedThe KET model correctly predicts the peak position and thetrend in particular at the trailing edge where an increment inrms is experimentally observed

The improvement of performances showed by the SMmodel when the incoming turbulence is taken into accountcan be due to the fact that the SM model is too dissipativein laminar and transitional regions [18] Indeed the SM

model predicts a nonvanishing eddy viscosity when the flowis laminar and this results in more stable shear layers whenthe incoming flow is smooth Conversely the KET model isable to adjust the eddy viscosity basing on the subgrid kineticenergy leading to an overall less dissipative behavior Whenthe incoming flow turbulence is considered the SM modelperforms better In fact the laminar-to-turbulent transitionis driven by disturbances introduced by the explicitly sim-ulated incoming flow turbulence This different behavior inperfectly smooth and low turbulence inflow conditions is notobserved when the KETmodel is considered Indeed the lessdissipative behavior of the KET model with respect to theSM model allows correctly predicting the destabilization ofthe shear layers without triggering it explicitly by introducingdisturbances

43 Spanwise-Averaged Quantities 119911-avg distributions of1198621015840119901

denoted as 119862

119901(119911-avg)1015840 are reported in Figure 7 for each case

Data concerning the central section statistics (see Figure 6)are repeated in this figure in order to better highlightdifferences with respect to the corresponding 119911-avg valuesFocusing on the top surface the SM model shows that thegap between 1198621015840

119901

and 119862119901(119911-avg)1015840 increases proceeding from

Mathematical Problems in Engineering 9

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

Top surface

Bottom surface

minus1 0 1 2minus2

zD

1 2minus1 0minus2

zD

minus1minus2 1 20zD

minus1minus2 1 20zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

Figure 8 Correlation functions for the SM model in smooth and turbulent inflow condition

the leading edge to the trailing one where the peak value of119862119901(119911-avg)1015840 is radically decreased with respect to the central

alignment for both smooth and turbulent inlet conditionThe flow two-dimensionality is dominant close to the leadingedge where 119911-avg statistics are identical to the central sectionones while the flow three-dimensional mechanisms prevaildownwind This trend is confirmed by the KET model evenif in this case the gap between1198621015840

119901

and119862119901(119911-avg)1015840 is reduced if

compared with the SM model suggesting that the predictedflow is more correlated in the spanwise direction

Considering results of the SM model on the bottomsurface the reduction between 119911-avg and central sectionstatistics is higher when the inflow turbulence is consideredIn fact while for the smooth inlet condition 119911-avg peak valueis roughly 66 of the central section one when turbulenceis taken into account the peak of 119862

119901(119911-avg)1015840 is only 44 of

the corresponding 1198621015840119901

value Therefore the SM model showsthat the inflow turbulence contributes to decreasing the flowcorrelation in the spanwise direction to a great extent

In agreement with the previously reported results theKET model does not show such a high sensitivity differ-ences between 119862

119901(119911-avg)1015840 and 1198621015840

119901

in smooth and turbulentcondition being almost identical Qualitatively by observing

the rms distributions in terms of both peak amplitude andposition results obtained by using the KET model appear tobe intermediate between the ones obtained in smooth andturbulent flow by using the SM model

44 Correlations This section reports 119862119901correlations along

the spanwise direction for three different sections locatedat 119904119863 = 175 300 and 425 Data acquired on probesclose to the edges in the spanwise direction can be affectedby the prescribed boundary conditions therefore results arepresented disregarding part of the rectangular cylinder nearto the boundary 119911119863 ranging from minus25 to 25 Figure 8shows the correlation of 119862

119901 indicated as 119877

119862119901 obtained for

the SM model on top and bottom surfaces for smooth andturbulent inlet while results obtained by using the KETmodel are reported in Figure 9

Interestingly in this case the correlation appears to behigher when a small incoming turbulence level is con-sidered The authors conjecture that this behavior mightbe related to the fact that when perfectly smooth con-ditions are considered the flow impinges on the trailingedge as it can be deduced from time-averaged streamlinesreported in Figure 5 Contrarily when incoming turbulence is

10 Mathematical Problems in Engineering

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

0 1 2minus1minus2

zD

0 21minus1minus2

zD

0 1 2minus1minus2

zD

0 21minus1minus2

zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

Top surface

Bottom surface

Figure 9 Correlation functions for the KET model in smooth and turbulent inflow condition

considered a higher level of entrapment of the separationbubble is observed probably leading to higher along-spancorrelations Regarding the bottom surface and focusing onresults obtained by means of the SM model an oppositebehavior is recorded This fact might be due to the develop-ment of spanwise vortical structures that decrease the flowcorrelation (see eg Sasaki and Kiya [36])

Also in this case results predicted by using the KETmodel are qualitatively intermediate between the onesobtained by using the SM model in smooth and turbulentconditions and a good stability with respect to the incomingturbulence level is observed

5 Conclusions

In this paper Large Eddy Simulations have been performedaiming at studying the unsteady flow field around a rectan-gular cylinder with aspect ratio 5 1 at 4∘ attack angle when asmall level of incoming turbulence is taken into account Twodifferent turbulence models have been considered namelythe classical Smagorinsky-Lillymodel and the Kinetic EnergyTransport model Both of them have been studied by adopt-ing perfectly smooth and turbulent inlet conditions with

turbulence intensity set to be equal to 07 The inflow tur-bulence has been synthetically generated with the MDSRFGmethod and introduced in the computational domain bymodifying the velocity-pressure coupling algorithm Resultsin terms of flow bulk parameters time-average and rms ofthe pressure coefficient distributions in correspondence withthe prism central section have been compared to availableexperimental data It appears that when the Smagorinsky-Lilly model is adopted the modeling of a realistic turbulentinflow is important in order to obtain accurate results sinceeven small values of the incoming flow turbulence intensitycan deeply affect resultsTheKinetic Energy Transportmodelproved to be less sensitive to the low inflow turbulenceand provided results qualitatively intermediate between theSmagorinsky-Lilly models adopted with perfectly smoothand turbulent inflow conditions The different behavior ofthe two considered models can be due to the fact that theSmagorinsky-Lilly model is not able to make the turbulenteddy viscosity null appearing to be too dissipative and failingin accurately predicting the laminar-to-turbulent transitionOn the contrary the Kinetic Energy Transport model canadjust the turbulent eddy viscosity depending on the subgridkinetic energy showing satisfactory results for both smooth

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

00

01

02

C998400 p

00

01

02

03

04

C998400 p

1 2 3 4 5 60sD

1 2 3 4 5 60sD

543 60 1 2

sD

543 60 1 2

sD

00

01

02

C998400 p

00

01

02

C998400 p

Top surface

Bottom surface

SM

SM KET

KETSM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

SM smoothSM smooth z-avg

SM I = 07SM I = 07 z-avg

KET smoothKET smooth z-avg

KET I = 07KET I = 07 z-avg

Figure 7 Comparison between 119911-averaged and central section statistics for the SM and KET turbulence models

intensities in the incoming flow In fact the distributionobtained in smooth flow conditions clearly changes whenthe inflow turbulence is considered the reattachment pointmigrates upstream and the distribution shifts approachingthe experimental dataTheKETmodel instead shows again alower sensitivity to the incoming turbulence results obtainedin both configurations being approximately the same TheSM model is very accurate when turbulence is taken intoaccount and shows better performances if compared with theKET model which slightly overestimates the reattachmentlength and underestimates suctions at the leeward edge Theimprovement of the SM model with turbulent inlet observedfor mean values can be noticed also by considering 119862

1015840

119901

distribution on the bottom surface In this case the modelcorrectly predicts the peak position and the trend observedexperimentally even if the peak value is clearly overestimatedThe KET model correctly predicts the peak position and thetrend in particular at the trailing edge where an increment inrms is experimentally observed

The improvement of performances showed by the SMmodel when the incoming turbulence is taken into accountcan be due to the fact that the SM model is too dissipativein laminar and transitional regions [18] Indeed the SM

model predicts a nonvanishing eddy viscosity when the flowis laminar and this results in more stable shear layers whenthe incoming flow is smooth Conversely the KET model isable to adjust the eddy viscosity basing on the subgrid kineticenergy leading to an overall less dissipative behavior Whenthe incoming flow turbulence is considered the SM modelperforms better In fact the laminar-to-turbulent transitionis driven by disturbances introduced by the explicitly sim-ulated incoming flow turbulence This different behavior inperfectly smooth and low turbulence inflow conditions is notobserved when the KETmodel is considered Indeed the lessdissipative behavior of the KET model with respect to theSM model allows correctly predicting the destabilization ofthe shear layers without triggering it explicitly by introducingdisturbances

43 Spanwise-Averaged Quantities 119911-avg distributions of1198621015840119901

denoted as 119862

119901(119911-avg)1015840 are reported in Figure 7 for each case

Data concerning the central section statistics (see Figure 6)are repeated in this figure in order to better highlightdifferences with respect to the corresponding 119911-avg valuesFocusing on the top surface the SM model shows that thegap between 1198621015840

119901

and 119862119901(119911-avg)1015840 increases proceeding from

Mathematical Problems in Engineering 9

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

Top surface

Bottom surface

minus1 0 1 2minus2

zD

1 2minus1 0minus2

zD

minus1minus2 1 20zD

minus1minus2 1 20zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

Figure 8 Correlation functions for the SM model in smooth and turbulent inflow condition

the leading edge to the trailing one where the peak value of119862119901(119911-avg)1015840 is radically decreased with respect to the central

alignment for both smooth and turbulent inlet conditionThe flow two-dimensionality is dominant close to the leadingedge where 119911-avg statistics are identical to the central sectionones while the flow three-dimensional mechanisms prevaildownwind This trend is confirmed by the KET model evenif in this case the gap between1198621015840

119901

and119862119901(119911-avg)1015840 is reduced if

compared with the SM model suggesting that the predictedflow is more correlated in the spanwise direction

Considering results of the SM model on the bottomsurface the reduction between 119911-avg and central sectionstatistics is higher when the inflow turbulence is consideredIn fact while for the smooth inlet condition 119911-avg peak valueis roughly 66 of the central section one when turbulenceis taken into account the peak of 119862

119901(119911-avg)1015840 is only 44 of

the corresponding 1198621015840119901

value Therefore the SM model showsthat the inflow turbulence contributes to decreasing the flowcorrelation in the spanwise direction to a great extent

In agreement with the previously reported results theKET model does not show such a high sensitivity differ-ences between 119862

119901(119911-avg)1015840 and 1198621015840

119901

in smooth and turbulentcondition being almost identical Qualitatively by observing

the rms distributions in terms of both peak amplitude andposition results obtained by using the KET model appear tobe intermediate between the ones obtained in smooth andturbulent flow by using the SM model

44 Correlations This section reports 119862119901correlations along

the spanwise direction for three different sections locatedat 119904119863 = 175 300 and 425 Data acquired on probesclose to the edges in the spanwise direction can be affectedby the prescribed boundary conditions therefore results arepresented disregarding part of the rectangular cylinder nearto the boundary 119911119863 ranging from minus25 to 25 Figure 8shows the correlation of 119862

119901 indicated as 119877

119862119901 obtained for

the SM model on top and bottom surfaces for smooth andturbulent inlet while results obtained by using the KETmodel are reported in Figure 9

Interestingly in this case the correlation appears to behigher when a small incoming turbulence level is con-sidered The authors conjecture that this behavior mightbe related to the fact that when perfectly smooth con-ditions are considered the flow impinges on the trailingedge as it can be deduced from time-averaged streamlinesreported in Figure 5 Contrarily when incoming turbulence is

10 Mathematical Problems in Engineering

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

0 1 2minus1minus2

zD

0 21minus1minus2

zD

0 1 2minus1minus2

zD

0 21minus1minus2

zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

Top surface

Bottom surface

Figure 9 Correlation functions for the KET model in smooth and turbulent inflow condition

considered a higher level of entrapment of the separationbubble is observed probably leading to higher along-spancorrelations Regarding the bottom surface and focusing onresults obtained by means of the SM model an oppositebehavior is recorded This fact might be due to the develop-ment of spanwise vortical structures that decrease the flowcorrelation (see eg Sasaki and Kiya [36])

Also in this case results predicted by using the KETmodel are qualitatively intermediate between the onesobtained by using the SM model in smooth and turbulentconditions and a good stability with respect to the incomingturbulence level is observed

5 Conclusions

In this paper Large Eddy Simulations have been performedaiming at studying the unsteady flow field around a rectan-gular cylinder with aspect ratio 5 1 at 4∘ attack angle when asmall level of incoming turbulence is taken into account Twodifferent turbulence models have been considered namelythe classical Smagorinsky-Lillymodel and the Kinetic EnergyTransport model Both of them have been studied by adopt-ing perfectly smooth and turbulent inlet conditions with

turbulence intensity set to be equal to 07 The inflow tur-bulence has been synthetically generated with the MDSRFGmethod and introduced in the computational domain bymodifying the velocity-pressure coupling algorithm Resultsin terms of flow bulk parameters time-average and rms ofthe pressure coefficient distributions in correspondence withthe prism central section have been compared to availableexperimental data It appears that when the Smagorinsky-Lilly model is adopted the modeling of a realistic turbulentinflow is important in order to obtain accurate results sinceeven small values of the incoming flow turbulence intensitycan deeply affect resultsTheKinetic Energy Transportmodelproved to be less sensitive to the low inflow turbulenceand provided results qualitatively intermediate between theSmagorinsky-Lilly models adopted with perfectly smoothand turbulent inflow conditions The different behavior ofthe two considered models can be due to the fact that theSmagorinsky-Lilly model is not able to make the turbulenteddy viscosity null appearing to be too dissipative and failingin accurately predicting the laminar-to-turbulent transitionOn the contrary the Kinetic Energy Transport model canadjust the turbulent eddy viscosity depending on the subgridkinetic energy showing satisfactory results for both smooth

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

SM smooth sD = 175

SM smooth sD = 300

SM smooth sD = 425

Top surface

Bottom surface

minus1 0 1 2minus2

zD

1 2minus1 0minus2

zD

minus1minus2 1 20zD

minus1minus2 1 20zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

SM I = 07 sD = 175SM I = 07 sD = 300SM I = 07 sD = 425

Figure 8 Correlation functions for the SM model in smooth and turbulent inflow condition

the leading edge to the trailing one where the peak value of119862119901(119911-avg)1015840 is radically decreased with respect to the central

alignment for both smooth and turbulent inlet conditionThe flow two-dimensionality is dominant close to the leadingedge where 119911-avg statistics are identical to the central sectionones while the flow three-dimensional mechanisms prevaildownwind This trend is confirmed by the KET model evenif in this case the gap between1198621015840

119901

and119862119901(119911-avg)1015840 is reduced if

compared with the SM model suggesting that the predictedflow is more correlated in the spanwise direction

Considering results of the SM model on the bottomsurface the reduction between 119911-avg and central sectionstatistics is higher when the inflow turbulence is consideredIn fact while for the smooth inlet condition 119911-avg peak valueis roughly 66 of the central section one when turbulenceis taken into account the peak of 119862

119901(119911-avg)1015840 is only 44 of

the corresponding 1198621015840119901

value Therefore the SM model showsthat the inflow turbulence contributes to decreasing the flowcorrelation in the spanwise direction to a great extent

In agreement with the previously reported results theKET model does not show such a high sensitivity differ-ences between 119862

119901(119911-avg)1015840 and 1198621015840

119901

in smooth and turbulentcondition being almost identical Qualitatively by observing

the rms distributions in terms of both peak amplitude andposition results obtained by using the KET model appear tobe intermediate between the ones obtained in smooth andturbulent flow by using the SM model

44 Correlations This section reports 119862119901correlations along

the spanwise direction for three different sections locatedat 119904119863 = 175 300 and 425 Data acquired on probesclose to the edges in the spanwise direction can be affectedby the prescribed boundary conditions therefore results arepresented disregarding part of the rectangular cylinder nearto the boundary 119911119863 ranging from minus25 to 25 Figure 8shows the correlation of 119862

119901 indicated as 119877

119862119901 obtained for

the SM model on top and bottom surfaces for smooth andturbulent inlet while results obtained by using the KETmodel are reported in Figure 9

Interestingly in this case the correlation appears to behigher when a small incoming turbulence level is con-sidered The authors conjecture that this behavior mightbe related to the fact that when perfectly smooth con-ditions are considered the flow impinges on the trailingedge as it can be deduced from time-averaged streamlinesreported in Figure 5 Contrarily when incoming turbulence is

10 Mathematical Problems in Engineering

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

0 1 2minus1minus2

zD

0 21minus1minus2

zD

0 1 2minus1minus2

zD

0 21minus1minus2

zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

Top surface

Bottom surface

Figure 9 Correlation functions for the KET model in smooth and turbulent inflow condition

considered a higher level of entrapment of the separationbubble is observed probably leading to higher along-spancorrelations Regarding the bottom surface and focusing onresults obtained by means of the SM model an oppositebehavior is recorded This fact might be due to the develop-ment of spanwise vortical structures that decrease the flowcorrelation (see eg Sasaki and Kiya [36])

Also in this case results predicted by using the KETmodel are qualitatively intermediate between the onesobtained by using the SM model in smooth and turbulentconditions and a good stability with respect to the incomingturbulence level is observed

5 Conclusions

In this paper Large Eddy Simulations have been performedaiming at studying the unsteady flow field around a rectan-gular cylinder with aspect ratio 5 1 at 4∘ attack angle when asmall level of incoming turbulence is taken into account Twodifferent turbulence models have been considered namelythe classical Smagorinsky-Lillymodel and the Kinetic EnergyTransport model Both of them have been studied by adopt-ing perfectly smooth and turbulent inlet conditions with

turbulence intensity set to be equal to 07 The inflow tur-bulence has been synthetically generated with the MDSRFGmethod and introduced in the computational domain bymodifying the velocity-pressure coupling algorithm Resultsin terms of flow bulk parameters time-average and rms ofthe pressure coefficient distributions in correspondence withthe prism central section have been compared to availableexperimental data It appears that when the Smagorinsky-Lilly model is adopted the modeling of a realistic turbulentinflow is important in order to obtain accurate results sinceeven small values of the incoming flow turbulence intensitycan deeply affect resultsTheKinetic Energy Transportmodelproved to be less sensitive to the low inflow turbulenceand provided results qualitatively intermediate between theSmagorinsky-Lilly models adopted with perfectly smoothand turbulent inflow conditions The different behavior ofthe two considered models can be due to the fact that theSmagorinsky-Lilly model is not able to make the turbulenteddy viscosity null appearing to be too dissipative and failingin accurately predicting the laminar-to-turbulent transitionOn the contrary the Kinetic Energy Transport model canadjust the turbulent eddy viscosity depending on the subgridkinetic energy showing satisfactory results for both smooth

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Mathematical Problems in Engineering

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET smooth sD = 175

KET smooth sD = 300

KET smooth sD = 425

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

KET I = 07 sD = 175

KET I = 07 sD = 425

KET I = 07 sD = 300

0 1 2minus1minus2

zD

0 21minus1minus2

zD

0 1 2minus1minus2

zD

0 21minus1minus2

zD

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

00

02

04

06

08

10

RC119901

Top surface

Bottom surface

Figure 9 Correlation functions for the KET model in smooth and turbulent inflow condition

considered a higher level of entrapment of the separationbubble is observed probably leading to higher along-spancorrelations Regarding the bottom surface and focusing onresults obtained by means of the SM model an oppositebehavior is recorded This fact might be due to the develop-ment of spanwise vortical structures that decrease the flowcorrelation (see eg Sasaki and Kiya [36])

Also in this case results predicted by using the KETmodel are qualitatively intermediate between the onesobtained by using the SM model in smooth and turbulentconditions and a good stability with respect to the incomingturbulence level is observed

5 Conclusions

In this paper Large Eddy Simulations have been performedaiming at studying the unsteady flow field around a rectan-gular cylinder with aspect ratio 5 1 at 4∘ attack angle when asmall level of incoming turbulence is taken into account Twodifferent turbulence models have been considered namelythe classical Smagorinsky-Lillymodel and the Kinetic EnergyTransport model Both of them have been studied by adopt-ing perfectly smooth and turbulent inlet conditions with

turbulence intensity set to be equal to 07 The inflow tur-bulence has been synthetically generated with the MDSRFGmethod and introduced in the computational domain bymodifying the velocity-pressure coupling algorithm Resultsin terms of flow bulk parameters time-average and rms ofthe pressure coefficient distributions in correspondence withthe prism central section have been compared to availableexperimental data It appears that when the Smagorinsky-Lilly model is adopted the modeling of a realistic turbulentinflow is important in order to obtain accurate results sinceeven small values of the incoming flow turbulence intensitycan deeply affect resultsTheKinetic Energy Transportmodelproved to be less sensitive to the low inflow turbulenceand provided results qualitatively intermediate between theSmagorinsky-Lilly models adopted with perfectly smoothand turbulent inflow conditions The different behavior ofthe two considered models can be due to the fact that theSmagorinsky-Lilly model is not able to make the turbulenteddy viscosity null appearing to be too dissipative and failingin accurately predicting the laminar-to-turbulent transitionOn the contrary the Kinetic Energy Transport model canadjust the turbulent eddy viscosity depending on the subgridkinetic energy showing satisfactory results for both smooth

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 11

and turbulent inlet conditions Indeed the less dissipativebehavior of the Kinetic Energy Transport model with respectto the Smagorinsky-Lilly model allows the shear layer insta-bilities to develop even without directly triggering them withincoming disturbances In all when incoming turbulence isconsidered a good agreement between numerical results andexperimental data is observed in particular in terms of time-averaged pressure distributions Moreover the differencesbetween the flow fields obtained by the two consideredmodels significantly reduce

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors are grateful to CRIACIV for providing theexperimental results and CINECA for providing the HPCfacilities needed to accomplish the present research workIn particular they would like to thank Ivan Spisso for hisinvaluable constant support

References

[1] Y Nakamura and Y Ohya ldquoThe effects of turbulence on themean flow past two-dimensional rectangular cylindersrdquo Journalof Fluid Mechanics vol 149 pp 255ndash273 1984

[2] R Mills J Sheridan and K Hourigan ldquoResponse of base suc-tion and vortex shedding from rectangular prisms to transverseforcingrdquo Journal of Fluid Mechanics vol 461 pp 25ndash49 2002

[3] R Mills J Sheridan and K Hourigan ldquoParticle image veloci-metry and visualization of natural and forced flow around rec-tangular cylindersrdquo Journal of FluidMechanics no 478 pp 299ndash323 2003

[4] H Noda and A Nakayama ldquoFree-stream turbulence effectson the instantaneous pressure and forces on cylinders of rec-tangular cross sectionrdquo Experiments in Fluids vol 34 no 3 pp332ndash344 2003

[5] R Hillier and N J Cherry ldquoThe effects of stream turbulence onseparation bubblesrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 8 no 1-2 pp 49ndash58 1981

[6] M Kiya and K Sasaki ldquoFree-stream turbulence effects on aseparation bubblerdquo Journal of Wind Engineering and IndustrialAerodynamics vol 14 no 1ndash3 pp 375ndash386 1983

[7] D Yu and A Kareem ldquoParametric study of flow around rec-tangular prisms using LESrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 77-78 pp 653ndash662 1998

[8] A Sohankar C Norberg and L Davidson ldquoNumerical simula-tion of unsteady low-Reynolds number flow around rectangularcylinders at incidencerdquo Journal of Wind Engineering and Indus-trial Aerodynamics vol 69ndash71 pp 189ndash201 1997

[9] K Shimada and T Ishihara ldquoApplication of a modified k-120576model to the prediction of aerodynamic characteristics of rec-tangular cross-section cylindersrdquo Journal of Fluids and Struc-tures vol 16 no 4 pp 465ndash485 2002

[10] H Noda and A Nakayama ldquoReproducibility of flow past two-dimensional rectangular cylinders in a homogeneous turbulentflow by LESrdquo Journal of Wind Engineering and Industrial Aero-dynamics vol 91 no 1-2 pp 265ndash278 2003

[11] S de Miranda L Patruno F Ubertini and G Vairo ldquoOnthe identifcation of futter derivatives of bridge decks viaRANS-based numerical models benchmarking on rectangularprismsrdquo Engineering Structures vol 76 pp 359ndash370 2013

[12] T Tamura and Y Ono ldquoLES analysis on aeroelastic instabilityof prisms in turbulent flowrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 91 no 12ndash15 pp 1827ndash1846 2003

[13] S J Daniels I P Castro and Z T Xie ldquoNumerical analysis offreestream turbulence effects on the vortex-induced vibrationsof a rectangular cylinderrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 153 pp 13ndash25 2016

[14] S deMiranda L PatrunoM Ricci and FUbertini ldquoNumericalstudy of a twin box bridge deck with increasing gap ratio byusing RANS and LES approachesrdquo Engineering Structures vol99 pp 546ndash558 2015

[15] G Bartoli L Bruno G Buresti F Ricciardelli M V Salvettiand A Zasso ldquoBARC overview documentrdquo 2008 httpwwwaniv-iaweorgbarc

[16] L Bruno M V Salvetti and F Ricciardelli ldquoBenchmark on theaerodynamics of a rectangular 51 cylinder an overview afterthe first four years of activityrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 126 pp 87ndash106 2014

[17] J A S Witteveen P S Omrani A Mariotti and M V SalvettildquoUncertainty quantification of a rectangular 51 cylinderrdquo inProceedings of the 17th AIAA Non-Deterministic ApproachesConference AIAA 2015-0663 American Insitute of Aeronauticsand Astronautics Kissimmee Fla USA January 2015

[18] A W Vreman ldquoAn eddy-viscosity subgrid-scale model forturbulent shear flow algebraic theory and applicationsrdquo Physicsof Fluids vol 16 no 10 pp 3670ndash3681 2004

[19] MGermanoU Piomelli PMoin andWHCabot ldquoA dynamicsubgrid-scale eddy viscosity modelrdquo Physics of Fluids A vol 3no 7 pp 1760ndash1765 1991

[20] D K Lilly ldquoA proposed modification of the Germano subgrid-scale closure methodrdquo Physics of Fluids A vol 4 no 3 pp 633ndash635 1992

[21] A Yoshizawa and K Horiuti ldquoA statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation ofturbulent flowsrdquo Journal of the Physical Society of Japan vol 54no 8 pp 2834ndash2839 1985

[22] L PatrunoM Ricci S deMiranda and FUbertini ldquoNumericalsimulation of a 5 1 rectangular cylinder at non-null angles ofattackrdquo Journal of Wind Engineering and Industrial Aerodynam-ics vol 151 pp 146ndash157 2016

[23] Personal Communication from CRIACIV University of Flo-rence Florence Italy 2015

[24] CMannini AMMarra L Pigolotti andG Bartoli ldquoUnsteadypressure and wake characteristics of a benchmark rectangularsection in smooth and turbulent flowrdquo in Proceedings of the 14thInternational Conference on Wind Engineering Porto AlegreBrazil June 2015

[25] H G Castro and R R Paz ldquoA time and space correlated tur-bulence synthesis method for Large Eddy Simulationsrdquo Journalof Computational Physics vol 235 pp 742ndash763 2013

[26] A Smirnov S Shi and I Celik ldquoRandom flow generation tech-nique for large eddy simulations and particle-dynamics model-ingrdquo Journal of Fluids Engineering vol 123 no 2 pp 359ndash3712001

[27] Y Kim I P Castro and Z-T Xie ldquoDivergence-free turbulenceinflow conditions for large-eddy simulations with incompress-ible flow solversrdquoComputers and Fluids vol 84 pp 56ndash68 2013

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

12 Mathematical Problems in Engineering

[28] H Weller ldquoControlling the computational modes of the arbi-trarily structured C gridrdquoMonthlyWeather Review vol 140 no10 pp 3220ndash3234 2012

[29] L Bruno N Coste and D Fransos ldquoSimulated flow arounda rectangular 51 cylinder spanwise discretisation effects andemerging flow featuresrdquo Journal of Wind Engineering andIndustrial Aerodynamics vol 104ndash106 pp 203ndash215 2012

[30] L Bruno D Fransos N Coste andA Bosco ldquo3D flow around arectangular cylinder A Computational Studyrdquo Journal of WindEngineering and Industrial Aerodynamics vol 98 no 6-7 pp263ndash276 2010

[31] J Jeong and F Hussain ldquoOn the identification of a vortexrdquoJournal of Fluid Mechanics vol 285 pp 69ndash94 1995

[32] L Bruno N Coste and D Fransos ldquoEffect of the spanwisefeature of the computational domain on the simulated flowaround a 51 cylinderrdquo in Proceedings of the 13th InternationalConference onWind Engineering AmsterdamTheNetherlandsJuly 2011

[33] A N Grozescu L Bruno D Franzos and M V SalvettildquoThree-dimensional numerical simulation of flow around a 15rectangular cylinderrdquo in Proceedings of the 20th Italian Con-ference on Theoretical and Applied Mechanics Bologna ItalySeptember 2011

[34] C Mannini A Soda and G Schewe ldquoNumerical investigationon the three-dimensional unsteady flow past a 51 rectangularcylinderrdquo Journal of Wind Engineering and Industrial Aerody-namics vol 99 no 4 pp 469ndash482 2011

[35] G Schewe ldquoReynolds-number-effects in flow around a rectan-gular cylinder with aspect ratio 1 5rdquo Journal of Fluids and Struc-tures vol 39 pp 15ndash26 2013

[36] K Sasaki and M Kiya ldquoThree-dimensional vortex structure ina leading-edge separation bubble at moderate Reynolds num-bersrdquo Journal of Fluids Engineering Transactions of the ASMEvol 113 no 3 pp 405ndash410 1991

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of