Flow-structure interaction of the oscillating circular cylinder in the lock ...

Computational

Flow-structure interaction of the oscillating cylinder in the lock-in region: computational experimental approach comparison

The Fourth International Wind Engineering(CWE200G),

Symposium on Yokohama, 2006

circular versus

Giorgio Dianaa, Alberto Zassoa, Luigi Vigevanob, Franco Auterib, Luca Formaggiac, Fabio Nobilec aDipartimentodi Meccanica, Politecnicodi Milano,via La Masa 34, Milano,Italy bDipartimentodi IngegneriaAerospaziale, Politecnicodi Milano, via La Masa 34, Milano,Italy cDipartimentodr Matematica, Politecnicodi Milano,Piazza Leonardoda Vinci32, Milano,Italy ABSTRACT:The flow-structureinteraction of a circular cylinder oscillatingin the synchronization field at Rea 5.10-4has been addressed both experimentally(unsteadypressures and oscillationsmeasures)as well as by CFD simulations(2D DNS and k-coRANS). DNS allowed simulationof the expected2P vortex structures.The k-o approach,althoughsimulatingthe lockin phenomenon,showed2S vortex structuresand quite lowerunsteadylift CLvalues. KEYWORDS:Vortex shedding,circular cylinder,lock-in,unsteadypressures,CFD SGS. 1 INTRODUCTIONANDEXPERIMENTALREFERENCES The flow-structureinteractionof an oscillatingcircularcylinderin the synchronizationfield is still a research open point. The complexityof the phenomenon,is enhancedby possible coexistenceof differentfluidodynamicstates switchingas an effect of minor changes in the key governing parameters: non-dimensionaloscillation amplitude z* and critical velocity ratioUn [5]. A joint researchbetweenMechanical,Aerospace,Mathematicsand StructuralDept. has been set up at Politecnicodi Milano, aimed at a multi-disciplinaryexperimentaland computational approach to the analysis of flow-structureinteraction.The experimentalapproach has been designedto provide valuable data for CFD validation:a circular cylinder rigid model (aspect ratio AR©10)has been elasticallysuspended(cross-flowoscillationplane) and instrumentedwith 2 rings of 32 circumferentialpressuretaps allowinghigh resolutionmeasuresof both fluctuating and mean pressures.The cylinder motion has been monitoredthrough accelerometers.Large oscillationamplitudes were reached (o TM Z*TM1.25) thanks to the very low structural damping 3.10-4TM4s TM1.7.10-3 . A samplingfrequencyof 125 Hz alloweddefinitionof pressureshigherorder harmonicsup to the 18thof the fundamentalvortex shedding frequency.Several free motion build-upevents for 0.85TMUn TM1.3 have been recordedin the lock-inregion,allowing to measure unsteadysurfacepressuredistributions.The "Initial","Upper"and "Lower"states characterizing the vortex sheddinghave been identified,correspondingto the differenttopologiesof the wake vortex streetreportedin [3]. Examplesof instantaneouspressuredistributionsat largeamplitudes and oscillationbuild-up with transition between two different regimes are given in Figure 1, while extendedresultsof the experimentalapproachcan be found in [5] and [6]. 2 NUMERICALSIMULATIONS Four assignedmotiontest cases have beenanalyzed,with differentUn,Reynoldsnumber and oscillationamplitude.Results for Re=58200,Uri I.17, z =0.5 are reported.Two softwaresbased on differentnumericalapproacheshave been employed:a researchcode based on stabilizedP2P1 finite elementsand no turbulencemodel, a commercialsolverbased on finite volumes and a SSTturbulencemodel.

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Cross-flow displacement z' (c)z/D of the free oscillating cylinder at Un©l.28 being cyl.

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Strouhal ampl.,

, U,, (c)f frequency,

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of oscillation

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Figure 1. Experimental data: Lower and Upper Branch cylinder response at Un (c)1.28 -Von shedding during build-up -2P vortex shedding after transition from Lower to Upper Branch.

Karman

vortex

b

a

C

Figure 2. Lift coefficientCLand non-dimensional oscillationamplitudesz at Re=58000,Uri 1.17, z =0.5Experimental (c),2D DNS(a) andFluent2D(b) typicalresults. 2.1 Subgrid stabilized finite element method The incompressible Navier-Stokes equations were written in a noninertial frame of reference and discretized by a second order BDF projection method and a subgrid stabilization technique [1]. No turbulence model has been employed but, since only 2D motions are taken into account, the computations cannot be interpreted as true DNS or LES. A computational mesh with about 35K cells and a time discretization step of 10-4s were used in all the simulations. In Figure 2a the

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Figure3. Instantaneous Cpand corresponding instantaneous totalforceon thesectionat Re=58000 , U=1.17,Z=0.5 -E xperimental (c), 2DDNS(a) andFluent2D(b) typicalresults. 2.2 Commercial software simulations As a second numerical approach, the commercial code Fluent 6.2 has been used, solving the Reynolds Averaged Navier-Stokes (RANS) equations, with a k-co turbulence model for an incompressible 2D flow. The equations have been solved in the non-inertial frame of reference accounting for the cylinder motion. The numerical approximation is based on a finite volume scheme with second order treatment of the viscous term , and a second order discretization in time. A computational mesh with about 20K cells and a time discretization step of 10-3seconds were used in all the simulations. These discretization parameters are sufficient to reproduce an accurate vortex shedding frequency and lift coefficient for the flow past a fixed cylinder . Numerical computations for an inflow velocity Uc0=4.22 m/s gave a Strouhal number St=0.203 , a little higher than the measured one. As shown in Figure 2b, the lock-in phenomenon has been obtained by keeping the cylinder fixed until the Von-Karman wake was fully developed and starting the cylinder oscillations with a slowly increasing amplitude until the desired value of A/D was reached.

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2D DNS: the vorticity field clearly shows 2P vortex shedding structures (pairs of positive and negative vortices sequentially shed) (a); early separation causing high pressure in a wide region in the inner side (b). Fluent: 2D k-co simulations showing 2S structures (c).

a

Results obtained for the conditions: Re=5 8000, Un=1.17, z*=0.5.

b

ri

Figure4. Vorticityfieldsinneighbourhood of the cylinderat Re=58000, U1.17, z#=0.5. Even though the lift force is not perfectly sinusoidal, it is clear from the picture that it has a principal component synchronous with the cylinder oscillation. As shown in Figure 3c and 4c, the simulated fluid dynamics has a clear "2S" wake structure and a very low lift coefficient , in contrast with experiments. 3 CONCLUSIONS In conclusion: (1) 2D DNS simulations despite not being able to reproduce lock-in, succeeded in reproducing the fundamental properties of the interaction, such as 2P vortex shedding mode and high CL, shown by experiments at the same z and Un; (2) Fluent simulations were able to reproduce a clear lock-in regime. Conversely, they were not able to reproduce the very high lift coefficients observed experimentally and maintained a 2S wake structure although for high z* and Ut,values. An excess of numerical dissipation seems to prevent the Fluent simulations from correctly predicting the 2P vortex shedding mode. An effort is under way in order to understand the lock-in mechanism triggering the 2P vortex shedding with the cylinder oscillation, still not achieved by 2D DNS. 4 REFERENCES 1 Guermond, J.-L.,Marra,A., Quartapelle, L., Subgridstabilizedprojectionmethodfor 2D unsteadyflowsat high Reynoldsnumber,ComputerMethodsinAppliedMechanics and Engineering, in press(2006). 2 Carberry,J., Sheridan,J., Rockwell,D. 2005Controlledoscillationsof a cylinder:forcesand wakemodes, J. FluidMech.,(2005),vol.538,pp. 31-69. 3 Carberry,J., Govardhan,R., Sheridan,J., Rockwell,D., Williamson,C.H.K.2004 Wakestatesand response branchesof forcedand freelyoscillatingcylinders, EuropeanJournalof MechanicsB/Fluids,(2004),23, 89-97. 5 Zasso,A., Belloli,M., Giappino,S., Muggiasca, S. 2005Pressurefieldanalysison oscillatingcircularcylinder, Proc.6thAsiaPacificConference on WindEngineering APCWEVI, Seoul(Korea)12-14Sept.2005. 6 Zasso,A.,Belloli,M.,Giappino,S., Muggiasca,S. 2006Onthe pressureand forcefield on a circularcylinder oscillatingin the lock- in region at sub-criticalReynoldsnumber,Proc. PVP2006-ICPVT-11 , 2006 ASME PressureVesselsandPipingDivisionConference, July23-27,2006,Vancouver , BC,Canada.

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