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Integration of non-time-resolved PIV and time-resolved velocity point sensors for dynamic estimation of velocity fields

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Abstract

We demonstrate a three-step method for estimating time-resolved velocity fields using time-resolved point measurements and non-time-resolved particle image velocimetry data. A variant of linear stochastic estimation is used to obtain an initial set of time-resolved estimates of the flow field. These estimates are then used to identify a linear model of the flow dynamics. The model is incorporated into a Kalman smoother, which provides an improved set of estimates. We verify this method with an experimental study of the wake behind an elliptical-leading-edge flat plate at a thickness Reynolds number of 3,600. We find that, for this particular flow, the Kalman smoother estimates are more accurate and more robust to noise than the initial, stochastic estimates. Consequently, dynamic mode decomposition more accurately identifies coherent structures in the flow when applied to the Kalman smoother estimates. Causal implementations of the estimators, which are necessary for flow control, are also investigated. Similar outcomes are observed, with model-based estimation outperforming stochastic estimation, though the advantages are less pronounced.

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References

  • Adrian RJ (1977) On the role of conditional averages in turbulence theory. In: Proceedings of the 5th Biennial Symposium on Turbulence in Liquids, AFOSR, pp 322–332

  • Adrian RJ (1994) Stochastic estimation of conditional structure—a review. Appl Sci Res 53(3–4):291–303

    Article  MATH  Google Scholar 

  • Adrian RJ, Moin P (1988) Stochastic estimation of organized turbulent structure: homogeneous shear-flow. J Fluid Mech 190:531–559

    Article  MATH  Google Scholar 

  • Akers JC, Bernstein DS (1997) Time-domain identification using ARMARKOV/Toeplitz models. In: Proceedings of the American Control Conference, pp 191–195

  • Arik EB, Carr J (1997) Digital particle image velocimetry system for real-time wind tunnel measurements. In: International Congress on Instrumentation in Aerospace Simulation Facilities, Pacific Grove, CA, pp 267–277

  • Bonnet JP, Cole DR, Delville J, Glauser MN, Ukeiley LS (1994) Stochastic estimation and proper orthogonal decomposition—complementary techniques for identifying structure. Exp Fluids 17(5):307–314

    Article  Google Scholar 

  • Cohen K, Siegel S, McLaughlin T (2006) A heuristic approach to effective sensor placement for modeling of a cylinder wake. Comput Fluids 35(1):103–120

    Article  MATH  Google Scholar 

  • Cole DR, Glauser MN, Guezennec YG (1992) An application of the stochastic estimation to the jet mixing layer. Phys Fluids A-Fluid 4(1):192–194

    Article  Google Scholar 

  • Deane AE, Kevrekidis IG, Karniadakis GE, Orszag SA (1991) Low-dimensional models for complex-geometry flows—application to grooved channels and circular-cylinders. Phys Fluids A-Fluid 3(10):2337–2354

    Article  MATH  Google Scholar 

  • Durgesh V, Naughton JW (2010) Multi-time-delay LSE-POD complementary approach applied to unsteady high-Reynolds-number near wake flow. Exp Fluids 49(3):571–583

    Article  Google Scholar 

  • Everson R, Sirovich L (1995) Karhunen-Loève procedure for gappy data. J Opt Soc Am A 12(8):1657–1664

    Article  Google Scholar 

  • Ewing D, Citriniti JH (1999) Examination of a LSE/POD complementary technique using single and multi-time information in the axisymmetric shear layer. In: Sorensen A Hopfinger (ed) Proceedings of the IUTAM Symposium on Simulation and Identification of Organized Structures in Flows. Kluwer, Lyngby, Denmark, pp 375–384

  • Gerhard J, Pastoor M, King R, Noack BR, Dillmann A, Morzyński M, Tadmor G (2003) Model-based control of vortex shedding using low-dimensional Galerkin models. AIAA Paper 2003-4262, 33rd AIAA Fluid Dynamics Conference and Exhibit

  • Glauser MN, Higuchi H, Ausseur J, Pinier J, Carlson H (2004) Feedback control of separated flows. AIAA Paper 2004-2521, 2nd Flow Control Conference

  • Griffin J, Schultz T, Holman R, Ukeiley LS, Cattafesta III LN (2010) Application of multivariate outlier detection to fluid velocity measurements. Exp Fluids 49(1, Si):305–317

    Article  Google Scholar 

  • Guezennec YG (1989) Stochastic estimation of coherent structures in turbulent boundary layers. Phys Fluids A-Fluid 1(6):1054–1060

    Article  MathSciNet  Google Scholar 

  • Holmes P, Lumley JL, Berkooz G (1996) Turbulence, coherent structures, dynamical systems and symmetry. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Hubert M, Vandervieren E (2008) An adjusted boxplot for skewed distributions. Comput Stat Data Anal 52(12):5186–5201

    Article  MathSciNet  MATH  Google Scholar 

  • Hyland DC (1991) Neural network architecture for online system identification and adaptively optimized control. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, England

  • Ilak M, Rowley CW (2008) Modeling of transitional channel flow using balanced proper orthogonal decomposition. Phys Fluids 20(3). Art no 034103

  • Juang JN, Pappa RS (1985) An eigensystem realization-algorithm for modal parameter-identification and model-reduction. J Guid Control Dyn 8(5):620–627

    Article  MATH  Google Scholar 

  • Juang JN, Phan M, Horta LG, Longman RW (1991) Identification of observer/Kalman filter Markov parameters: theory and experiments. Technical memorandum 104069, NASA

  • King R, Aleksić K, Gelbert G, Losse N, Muminovic R, Brunn A, Nitsche W, Bothien MR, Moeck JP, Paschereit CO, Noack BR, Rist U, Zengl M (2008) Model predictive flow control. AIAA Paper 2008-3975, 38th Fluid Dynamics Conference and Exhibit

  • Legrand M, Nogueira J, Lecuona A (2011a) Flow temporal reconstruction from non-time-resolved data part I: mathematic fundamentals. Exp Fluids 51(4):1047–1055

    Article  Google Scholar 

  • Legrand M, Nogueira J, Tachibana S, Lecuona A, Nauri S (2011b) Flow temporal reconstruction from non time-resolved data part II: practical implementation, methodology validation, and applications. Exp Fluids 51(4):861–870

    Article  Google Scholar 

  • Li F, Aubry N (2003) Feedback control of a flow past a cylinder via transverse motion. Phys Fluids 15(8):2163–2176

    Article  MathSciNet  Google Scholar 

  • Lumley JL (1967) The structure of inhomogeneous turbulence. In: Yaglom A, Tatarski V (eds) Atmospheric turbulence and wave propagation. Nauka, Moscow, pp 166–178

    Google Scholar 

  • Ma Z, Ahuja S, Rowley CW (2011) Reduced-order models for control of fluids using the eigensystem realization algorithm. Theor Comput Fluid Dyn 25(1–4, Si):233–247

    Article  Google Scholar 

  • Murray NE, Ukeiley LS (2003) Estimation of the flowfield from surface pressure measurements in an open cavity. AIAA J 41(5):969–972

    Article  Google Scholar 

  • Murray NE, Ukeiley LS (2007a) An application of gappy POD—for subsonic cavity flow PIV data. Exp Fluids 42(1):79–91

    Article  Google Scholar 

  • Murray NE, Ukeiley LS (2007b) Modified quadratic stochastic estimation of resonating subsonic cavity flow. J Turbul 8(53):1–23

    Google Scholar 

  • 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 BR, Afanasiev K, Morzyński 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  MathSciNet  MATH  Google Scholar 

  • Papoulis A (1984) Probability, random variables and stochastic theory. McGraw-Hill, New York

    Google Scholar 

  • Pastoor M, Noack BR, King R, Tadmor G (2006) Spatiotemporal waveform observers and feedback in shear layer control. AIAA Paper 2006-1402, 44th AIAA Aerospace Sciences Meeting and Exhibit

  • Pastoor M, Henning L, Noack BR, King R, Tadmor G (2008) Feedback shear layer control for bluff body drag reduction. J Fluid Mech 608:161–196

    Article  MATH  Google Scholar 

  • Phan M, Horta LG, Juang JN, Longman RW (1993) Linear-system identification via an asymptotically stable observer. J Optimiz Theory Appl 79(1):59–86

    Article  MathSciNet  MATH  Google Scholar 

  • Protas B (2004) Linear feedback stabilization of laminar vortex shedding based on a point vortex model. Phys Fluids 16(12):4473–4488

    Article  MathSciNet  Google Scholar 

  • Rowley CW (2005) Model reduction for fluids, using balanced proper orthogonal decomposition. Int J Bifurcat Chaos 15(3):997–1013

    Article  MathSciNet  MATH  Google Scholar 

  • Rowley CW, Mezić I, Bagheri S, Schlatter P, Henningson DS (2009) Spectral analysis of nonlinear flows. J Fluid Mech 641:115–127

    Article  MathSciNet  MATH  Google Scholar 

  • Schlegel M, Noack BR, Jordan P, Dillmann A, Gröeschel E, Schröeder W, Wei M, Freund JB, Lehmann O, Tadmor G (2012) On least-order flow representations for aerodynamics and aeroacoustics. J Fluid Mech 697:367–398

    Article  MATH  Google Scholar 

  • Schmid PJ (2010) Dynamic mode decomposition of numerical and experimental data. J Fluid Mech 656:5–28

    Article  MathSciNet  MATH  Google Scholar 

  • Simon D (2006) Optimal state estimation. Wiley, New York

    Book  Google Scholar 

  • Sirovich L (1987a) Turbulence and the dynamics of coherent structures. 1. Coherent structures. Q Appl Math 45(3):561–571

    MathSciNet  MATH  Google Scholar 

  • Sirovich L (1987b) Turbulence and the dynamics of coherent structures. 2. Symmetries and transformations. Q Appl Math 45(3):573–582

    MathSciNet  Google Scholar 

  • Taylor JA, Glauser MN (2004) Towards practical flow sensing and control via POD and LSE based low-dimensional tools. J Fluids Eng 126(3):337–345

    Article  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 

  • Tinney CE, Ukeiley LS, Glauser MN (2008) Low-dimensional characteristics of a transonic jet. Part 2. Estimate and far-field prediction. J Fluid Mech 615:53–92

    Article  MATH  Google Scholar 

  • Tu JH, Rowley CW, Aram E, Mittal R (2011) Koopman spectral analysis of separated flow over a finite-thickness flat plate with elliptical leading edge. AIAA Paper 2011-38, 49th AIAA Aerospace Sciences Meeting and Exhibit

  • Tung TC, Adrian RJ (1980) Higher-order estimates of conditional eddies in isotropic turbulence. Phys Fluids 23(7):1469–1470

    Article  Google Scholar 

  • Ukeiley LS, Murray NE, Song Q, Cattafesta III LN (2008) Dynamic surface pressure based estimation for flow control. In: IUTAM Symposium on Flow Control and MEMS, Springer, pp 183–189

  • Westerweel J (1994) Efficient detection of spurious vectors in particle image velocimetry data. Exp Fluids 16(3–4):236–247

    Google Scholar 

  • Westerweel J, Scarano F (2005) Universal outlier detection for PIV data. Exp Fluids 39(6):1096–1100

    Article  Google Scholar 

  • Yu H, Leeser M, Tadmor G, Siegel S (2006) Real-time particle image velocimetry for feedback loops using FPGA implementation. J Aerosp Comput Inf Commun 3(2):52–62

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by the Air Force Office of Scientific Research (Grant FA9550-09-1-0257), under Dr. Doug Smith, whom we would like to thank for his support, the Office of Naval Research (Grant N00014-11-1-0554), monitored by Dr. Ron Joslin, the National Science Foundation Graduate Research Fellowship Program, and the Florida Center for Advanced Aero-Propulsion.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ, 08544, USA

    Jonathan H. Tu & Clarence W. Rowley

  2. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 32611, USA

    John Griffin & Lawrence S. Ukeiley

  3. Department of Mechanical and Aerospace Engineering, University of Florida, REEF, Shalimar, FL, 32579, USA

    Adam Hart

  4. Department of Mechanical Engineering, Florida State University, Tallahassee, FL, 32301, USA

    Louis N. Cattafesta III

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  1. Jonathan H. Tu
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  6. Lawrence S. Ukeiley
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Correspondence to Jonathan H. Tu.

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This article is part of the collection Topics in Flow Control. Guest Editors J. P. Bonnet and L. Cattafesta.

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Tu, J.H., Griffin, J., Hart, A. et al. Integration of non-time-resolved PIV and time-resolved velocity point sensors for dynamic estimation of velocity fields. Exp Fluids 54, 1429 (2013). https://doi.org/10.1007/s00348-012-1429-7

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  • DOI: https://doi.org/10.1007/s00348-012-1429-7

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