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Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD

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Abstract

The flow past a circular cylinder at high Reynolds number is studied by means of PIV, 3C-PIV and Time-Resolved PIV techniques. One of the goals of this study was to allow comparisons with numerical simulations on a domain identical to that of the experiment. For this reason, the cylinder was placed in a confined environment, with a high blockage and a low aspect ratio, thereby allowing computations on a mesh of reasonable size, and avoiding “infinite conditions”. This paper deals with the decomposition of the flow in a coherent and random parts. To this aim, phase averaged quantities were first obtained using the wall pressure signal on the cylinder as a trigger signal. This was achieved using both conditional sampling and LSE with similar results. This decomposition is then analysed using the Time Resolved PIV measurements, as well as by comparison of the contributions of the organised and turbulent fluctuations to the time-independent Reynolds stress tensor with those estimated from velocity spectra by interpolation and integration of the continuous part. In agreement with other studies, it is found that the contribution of the turbulent motion is overestimated as a result of the occurence of phase jitter between the trigger and velocity signal. A POD analysis was then performed to extract the coherent motion and to compare this decomposition with that obtained by phase averaging. Similarly to the phase averaging, the POD allows the decomposition of the time-independent stress tensor as the sum of two contributions corresponding to the first N modes, and the rest of the modes. This decomposition is then analysed by comparing these contributions to those obtained from the velocity spectra, according to the value N chosen. It is found that these contributions are strongly dependent on N, and the contribution of the first modes greatly overestimate the coherent motion if N is too large. In order to obtain a good decomposition of the flow in coherent and random parts, the difficulty in this case lies in the choice of the modes. Finally, the POD coefficients of the first two modes are used instead of the pressure signal to determine the phase of the vortex shedding, and the phase averaging is reconsidered. It is found that the phase averaged vortices are less smeared by the averaging process, the turbulent stresses better follow the evolution of the vortices, and the contributions of both coherent and turbulent fluctuations are found to agree well with those evaluated from the velocity spectra. This enhancement is obtained because the phase angle is determined directly from the velocity fields to be averaged, thereby reducing the phase-jitter effect. A comparison with a detached eddy simulation is also briefly shown and demonstrates the high level of agreement obtainable between simulation and experiment, as well as confirming the enhancement of the phase averaging using this procedure.

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References

  • Adrian RJ (1975) On the role of conditional averages in turbulence theory. In: 4th Biennal symp on turbulence in liquids

  • Ben Chiekh M, Michard M, Grosjean N, Bera JC (2004) Reconstruction temporelle d’un champ aérodynamique instationnaire à partir de mesures PIV non résolues dans le temps. In: 9e Congrès Francophone de Vélocimétrie Laser

  • Berkooz G, Holmes P, Lumley JL (1993) The Proper Orthogonal Decomposition in the analysis of turbulent flows. Ann Rev Fluid Mech 25:539–575

    Article  Google Scholar 

  • Bloor M (1964) Transition to turbulence in the wake of a circular cylinder. J Fluid Mech 19:290–304

    Article  MATH  Google Scholar 

  • Borée J (2003) Extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows. Exp Fluids 35:188–192

    Article  Google Scholar 

  • Braza M, Chassaing P, Minh HH (1990) Prediction of large-scale transition features in the wake of a circular cylinder. Phys Fluids A 2(8):1461–1471

    Article  Google Scholar 

  • Cantwell B, Coles D (1983) An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder. J Fluid Mech 136:321–374

    Article  Google Scholar 

  • Cid E, Cazin S, Drouin V (2002) Validation de PIV stéréoscopique et application à un écoulement aérodynamique de sillage 3D. In: 8e Congrès Francophone de Vélocimétrie Laser. Meudon, France

  • Deane AE, Kevrekidis IG, Karniadakis GE, Orzag SA (1991) Low-dimensional models for complex geometry flows: application to grooved channels and circular cylinders. Phys Fluids A 3:2337–2354

    Article  MATH  Google Scholar 

  • Djeridi H, Braza M, Perrin R, Harran G, Cid E, Cazin S (2003) Near-wake turbulence properties around a circular cylinder at high Reynolds number. Flow Turbul Combust 71:19–34

    Article  MATH  Google Scholar 

  • Ewing D, Citriniti J (1999) Examination of a LSE/POD complementary techniques using single and multi-time information in the axisymetric shear layer. In: Sorensen, Hopfinger, Aubry (eds) Proceedings of the IUTAM symposium on simulation and identification of organised structures in flows, 25–29 May 1997. Kuwer, Lyngby, Denmark, pp 375–384

  • Hussain AKMF, Hakayawa M (1987) Eduction of large-scale organized structures in a turbulent plane wake. J Fluid Mech 180:193–229

    Article  Google Scholar 

  • Jeong J, Hussain F (1995) On the identification of a vortex. J Fluid Mech 285:69–94

    Article  MATH  Google Scholar 

  • Kourta A, Boisson HC, Chassaing P, Minh HH (1987) Nonlinear interaction and the transition to turbulence in the wake of a circular cylinder. J Fluid Mech 181:141–161

    Article  Google Scholar 

  • Leder A (1991) Dynamics of fluid mixing in separated flows. Phys Fluids A 3(7):1741–1748

    Article  Google Scholar 

  • Lumley JL (1967) The structure of inhomogeneous turbulent flows. In: Yaglom AM, Tatarski VI (eds) atmospheric turbulence and radio wave propagation. Nakua, Moscow, pp 166–178

    Google Scholar 

  • Ma X, Karamanos GS, Karniadakis GE (2000) Dynamics and low-dimensionality of a turbulent near wake. J Fluid Mech 410:29–65

    Article  MATH  Google Scholar 

  • Murray N, Ukeiley LS (2003) Estimation of the flow field from surface pressure measurements in an open cavity. AIAA J 41(5)

  • Naguib AM, Wark CE, Juckenhöfel O (2001) Stochastic estimation and flow sources associated with surface pressure events in a turbulent boundary layer. Phys Fluids 13(9):2611–2626

    Article  Google Scholar 

  • Noack B, Afanasiev K, Morzynski M, Tadmor G, Thiele F (2003) A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J Fluid Mech 497:335–363

    Article  MATH  Google Scholar 

  • Perrin R (2005) Analyse physique et modélidation d’écoulements incompressibles instationnaires turbulents autour d’un cylindre circulaire à grand nombre de Reynolds. Thèse de doctorat, Institut National Polytechnique de Toulouse

  • Perrin R, Braza M, Cid E, Cazin S, Moradei F, Barthet A, Sevrain A, Hoarau Y (2005) Near-wake turbulence properties in the high Reynolds incompressible flow around a circular cylinder by 2C and 3C PIV. In: 6th ERCOFTAC international symposium on engineering turbulence modelling and measurements, ETMM6. Sardinia, Italy

  • Perrin R, Cid E, Cazin S, Sevrain A, Braza M, Moradei F, Harran G (2007a) Phase averaged measurements of the turbulence properties in the near wake of a circular cylinder at high Reynolds number by 2C-PIV and 3C-PIV. Exp Fluids 42(1):93–109

    Article  Google Scholar 

  • Perrin R, Mockett C, Braza M, Cid E, Cazin S, Sevrain A, Chassaing P, Thiele F (2007b) Joint numerical and experimental investigation of the flow around a circular cylinder at high reynolds number. Topics App Phys PIVNET 2 (to be published)

  • Persillon H, Braza M (1998) Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation. J Fluid Mech 365:23–88

    Article  MATH  Google Scholar 

  • Podvin B, Fraigneau Y, Lusseyran F, Gougat P (2006) A reconstruction method for the flow past an open cavity. J Fluids Eng 128:531–540

    Article  Google Scholar 

  • Reynolds WC, Hussain AKMF (1972) The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J Fluid Mech 54:263–288

    Article  Google Scholar 

  • Sirovich L (1987) Turbulence and the dynamics of coherent structures. Parts I, II and III. Q Appl Math XLV(3):561–582

    Google Scholar 

  • Tinney CE, Coiffet F, Delville J, Hall AM, Jordan P, Glauser MN (2006) On spectral linear stochastic estimation. Exp Fluids 41(5):763–775

    Article  Google Scholar 

  • Van Oudheusden BW, Scarano F, Van Hinsberg NP, Watt DW (2005) Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence. Exp Fluids 39:86–98

    Article  Google Scholar 

  • Williamson CHK (1992) The natural and forced formation of spot-like vortex dislocations in the transition of a wake. J Fluid Mech 243:393–441

    Article  Google Scholar 

Download references

Acknowledgments

The authors acknowledge the partial funding of the work presented here by the European Community during the DESider project, and by the German Research Foundation (DFG) within the scope of the Collaborative Research Center SFB 557. The DESider project (Detached Eddy Simulation for Industrial Aerodynamics) is a collaboration between Alenia, ANSYS-CFX, Chalmers University, CNRS-Lille, Dassault, DLR, EADS-M, EUROCOPTER Germany, EDF, FOI-FFA, IMFT, Imperial College London, NLR, NTS, NUMECA, ONERA, TU Berlin, and UMIST. The project is funded by the European Community represented by the CEC, Research Directorate-General, in the 6th Framework Program, under Contract No. AST3-CT-2003-502842. The DES computations were conducted on the IBM pSeries 690 at the Zuse-Institut Berlin (ZIB) and the Norddeutschen Verbund fr Hoch- und Hchstleistungsrechnen (HLRN).

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Authors and Affiliations

  1. Institut de Mécanique de Fluides de Toulouse, allée Pr. Camile Soula, 31400, Toulouse, France

    R. Perrin, M. Braza, E. Cid, S. Cazin, A. Barthet & A. Sevrain

  2. ISTA, TU-Berlin Sekr. HF1, Müller-Breslau Str. 8, 10623, Berlin, Germany

    R. Perrin, C. Mockett & F. Thiele

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  1. R. Perrin
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  2. M. Braza
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  3. E. Cid
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  4. S. Cazin
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  5. A. Barthet
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  6. A. Sevrain
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  7. C. Mockett
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  8. F. Thiele
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Correspondence to R. Perrin.

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Perrin, R., Braza, M., Cid, E. et al. Obtaining phase averaged turbulence properties in the near wake of a circular cylinder at high Reynolds number using POD. Exp Fluids 43, 341–355 (2007). https://doi.org/10.1007/s00348-007-0347-6

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  • DOI: https://doi.org/10.1007/s00348-007-0347-6

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