Vortex Induced Vibration (VIV) of circular cylinders at high Reynolds numbers

D. Pastrana∗

daniel.pastrana@bsc.es,J. C. Cajas∗, O. Lehmkuhl∗, I. Rodriguez∗∗ and G. Houzeaux∗

Abstract—In this contribution, preliminary results on the study of the VIV at high Reynolds numbers are presented. First, a validationof the code and the turbulent LES WALE formulation in conjunction with a low-dissipative discretization is presented by means of thestudy of the smooth static cylinder at sub-critical and critical regimes: Re = 1.1 × 104 and Re = 3 × 105. Finally, some results of theforced damped oscillating cylinder for the Re = 1.1× 104 case are shown. One of the main objectives of this project is to analyse howthe movement of the cylinder affects the sub-critical and critical regimes and the influence of this changes in the aerodynamics forcesat high Reynolds numbers present in industrial applications.

Index Terms—Fluid-Structure Interaction, Turbulent Flow, Vortex Induced Vibrations.

F

1 INTRODUCTION

THE so-called Vortex Induced Vibration phenomenon(VIV) has been of great interest not only in flow con-

trol, for reducing oscillations structures that may causefatigue and degradation on the components of engineeringstructures, but also for energy harvesting. The canonicalproblem system, a rigid circular cylinder both, elasticallymounted and forced to oscillate at low Reynolds numbers,has been extensively studied and a good understanding ofthe physics that drives the phenomenon has been achieved.However, some important debates and unresolved prob-lems are still open. The reader is referred to the work ofWillamson and Govardhan [1] for a well-explained andcomprehensive overview of the phenomenon. On the otherhand, there are still few works neither experimental nornumerical simulations at high Reynolds numbers due tomeasurement difficulties in the near-wall region for theformer and the massive computational resources and extramodeling efforts required for the later. Here, we succinctlydescribe the methodology implemented and some resultobtained in this last direction.

2 METODOLOGY

A state-of-the-art turbulence methodology was recently de-veloped and implemented in Alya (BSC simulation codefor multi-physics problems). This methodology combines alow dissipation finite element (FE) scheme with the wall-adpating local eddy-viscosity (WALE) sub-grid scale(SGS)model. The low dissipative discretisation is base on the sameprinciples proposed by Verstappen and Veldman [3], gener-alised for Jofre et al. [4] and Trias et al. [7] for unstructuredfinite volumes and extended to FE by Lehmkuhl et. al [5].The set of equations is time integrated using an energyconserving Runge-Kutta explicit method lately proposedby Cappuano et al. [6] combine with an eigenvalue base

• ∗ Barcelona Super Computing Center.• ∗∗Universitat Politecnica de Catalunya BarcelonaTech.

time step estimator [7]. Fanally, the pressure stabilisationis achieved by means of a non-incremental fractional step.

The cylinder is treated as a rigid body allows to translatein two degrees of freedom, the in-line (x-axis) and thecross-flow (y-axis) directions govern by the forced dampedoscillator equation in non-dimentional form:

∂2xi

∂t2+ 4πfnζ

∂xi

∂t+ (2πfn)

2xi =2Ci

πm(1)

with i = 1, 2, m the mass ratio, fn dimensionless naturalfrequency ζ the damping ratio and Ci the forces coefficients.

3 RESULTS

In table 1 and Fig. 1 common physical statistical quantitiesand the near wake structure are presented for the fixedcylinder atRe = 1.1×104 and compared with data availablein the literature [2]. A good agreement of the statisticalquantities and an accurate reproduction of the vortex for-mation physics of the present LES simulations with reporteddata can be seen.

TABLE 1Physical statistical quantities for the fixed cylinder flow at Re = 1.14;

drag coefficient CD , base pressure coefficient −Cpb, Strouhal numberSt, and root mean square of the lift coefficient CL.

CD −Cpb St CL

LES Re = 1.1× 104 1.228 1.318 0.215 0.581

Dong et. al 2006 Re = 104 [2] 1.208 1.201 0.200 0.547

In Fig. 2 (a) the instantaneous velocity filed at two span-wise locations are shown. Clearly, an asymmetry is observednot only in 2D, with a subcritical like separation in thebottom and more supercritical in the top, but also witha 3D structure which is in good agreement with recentexperimental visualisation. Figures 2 (b) and (c) show theaverage drag force coefficient and Strouhal number. Generalspeaking fairly good agreement is observed for these valuescompared with experimental and numerical data available.

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(a) (b)

(c) (d)

Fig. 1. Contours of mean stream-wise velocity and normalized meanspan-wise vorticity for experimental data at Re = 104 (upper rowimages), and LES at Re = 1.1 × 104 for the present study (bottomrow images). Top images were taken from [2].

(a)

(b) (c)

Fig. 2. (a) Instantaneous flow velocity field at different span-wiselocations. (b) Drag coefficient (c) Strouhal number as a function theReynolds numbers where the results for the present simulations atRe = 3× 105 have been included (blue rectangle).

Finally, a comparison between the damped and un-damped oscillating cylinder is presented. The time historyof force coefficients and cross-flow direction displacement,as well as the main components of their power spectra forthe oscillating cylinder at Re = 1.1 × 104 are presented.Besides of being clear the effect of the structural damping onthe amplitude of the oscillations, it is also evident that themotion of the body with structural damping is also drivenby a frequency close to the main frequency of the lift force,absent in the non-damped case.

50 100 150 200

tU/D

−1.0

−0.5

0.0

0.5

1.0

1.5

CD,C

L,y/D

dispY

CL

CD

(a)

0.0 0.1 0.2 0.3 0.4 0.5

fD/U

0.0

0.2

0.4

0.6

0.8

1.0

Pow

er

dispX

dispY

CD

CL

(b)

50 100 150 200

tU/D

−1.0

−0.5

0.0

0.5

1.0

1.5

CD,C

L,y/D

dispY

CL

CD

(c)

0.0 0.1 0.2 0.3 0.4 0.5

fD/U

0.0

0.2

0.4

0.6

0.8

1.0

Pow

er

dispX

dispY

CD

CL

(d)

Fig. 3. Time history of lift and drag coefficients, and cross-flow directiondisplacement in flow past a circular cylinder at Re = 1.1 × 104

and fN = 0.15 (left). Power spectra of the lift and drag coefficientsand body displacement in both directions (right). (Top) Non-damped.(bottom) Damping, structural damping ξ = 0.5× 10−2.

4 CONCLUSION

A highly optimal and efficient turbulence methodology,recently developed and implemented in the Alya simulationcode, has been tested and validated for the flow around afixed circular cylinder at sub-critical and critical regimes.The methodology has been proved of being capable toaccurately reproduce the physics present in both regimesand it has been applied to a more complex FSI scenario.From this experience first results for the flow around a rigidcircular cylinder elastically mounted were presented andbriefly discussed.

ACKNOWLEDGMENTS

The first author thanks to the Consejo Nacional de Cienciay Tecnologa (CONACyT) for the SENER-CONACyT Ph.D.scholarship.

REFERENCES

[1] C. H. K. Williamson and R. N. Govardhan, (2004) Vortex-inducedvibrations, Annu. Rev. Fluid Mech. 36, 413–455.

[2] S. Dong and G. E. Karniadaskis, (2005) DNS of flow past a stationaryand oscillating cylinder at Re = 10000, J Fluids Struct., 20, 519–531.

[3] R. Verstappen and A. E. P. Veldman, (2003) Symmetry-preservingdiscretization of turbulent flow, Journal of Computational Physics,187, 343–368.

[4] L. Jofre, O. Lehmkuhl, J. Ventosa, F. X. Trias and A. Oliva, (2014)Conservation properties of unstructured finite-volume mesh schemes forthe Navier-Stokes equations, Numerical Heat Transfer, Part B:Fundamentals, 65, 1, 53–79.

[5] O. Lehmkuhl, G. Houzeaux, M. Avila, H. Owen, M. Vasquez andD. Mira, (2017) A low dissipation finite element scheme for the large eddysimulation on complex geometries, 19h International Conference onFinite Elements in Flow Problems - FEF 2017.

[6] F. Cappuano, G. Coppola, L. Rndez and L. de Luca, (2017) ExplicitRunge-Kutta schemes for incompressible flow with improved energy-conservation properties, Journal of Computational Physics, 328,86–94.

[7] F. X. Trias and O. Lehmkuhl, (2011) A self-adaptive strategy for the timeintegration of Navier-Stokes equations, Numerical Heat Transfer, PartB: Fundamentals, 60, 2, 116–134.

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Daniel Pastrana was born in Mexico City. Heholds a bachelor’s degree in physics (2012) anda master’s degree in Ocean and Costal Engi-neering (2015) from the Universidad NacionalAutonoma de Mexico (UNAM). In early 2016, hewas awarded by the Mexican government withSENER- CONACyT scholarship to study abroad.Nowadays, he is a PhD student in the Computa-tional and Applied Physics program at the Uni-versitat Poltecnica de Catalunya - BarcelonaT-ech (UPC) and works at the Department of Com-

puter Applications in Science and Engineering of Barcelona Supercom-puter Center. Daniel Pastrana has been involved in projects relatedto the study of heat transfer problems, fluid-structure interaction sim-ulations and its applications to coastal engineering and the study ofthe energy and intensity decay of tropical cyclones when they makelandfall. From this projects some important results have been publishedin international journals. Currently, his main research interests are High-Performance Computing, Fluid-Structure Interactions and Turbulencemodels and its industrial applications.

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