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Particle tracking velocimetry and accelerometry (PTVA) measurements applied to quasi-two-dimensional multi-scale flows

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Abstract

We have developed and validated a new adaptive method, particle tracking velocimetry and accelerometry (PTVA), to measure velocity and acceleration from the post-processing of particle tracking (PT) data. This method is shown to be more accurate than non-adaptive methods based on PT: errors are about six times smaller on velocity measurements and about four times smaller on acceleration ones. We apply this method to a turbulent-like flow generated and controlled in the laboratory. Taking advantage of the Eulerian repeatability of our multi-scale laminar flow, we are able to extract the acceleration field, a, and all terms of Navier–Stokes equation. To complete this we extract u·a and ∇·a fields. We finally compare the probability density function of the acceleration components of our turbulent-like flow with one of the highly turbulent flows and show that they are similar. The quality of these PTVA results and their robustness (in particular to local convection) are extremely encouraging. This method allows access to a deeper insight into the physic of turbulent-like flows and its high accuracy may apply to a broader range of flows.

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Notes

  1. The PTVA method is based on a post-processing algorithm using existing tracked particle positions. The tracking of the particles is performed separately.

  2. If ϕsmall is unknown, as a first iteration, the initial ϕsmall could be estimated via the resolution of the measurement (e.g. ±1 px) and the diameter of the particles so as to determine Δtarget (taking \(\Updelta_{min} = \frac{\phi_{\rm small}}{2}\) and Δmax = 2Δtarget). The measurements and post-processing can then be adjusted according to this first iteration.

  3. Starting from an initial value of N t (keeping the value of N t used in the previous time step for a same trajectory), if Δ s  < Δtarget then N t is increased (else N t is decreased), until |Δ s  − Δtarget| ≤ ε, with ε small compared to Δtarget.

  4. The best accuracy is obtained with 21 positions (orders 2 and 4) for the velocity whilst it is obtained with 233 positions (order 4) and 75 positions (order 2) for the acceleration. 9, 21, 47, 75, 127, 181, 233, 287 and 339 positions have been tested for the non-adaptive methods. The discrepancy between the best number of positions for the measures of velocity and acceleration could be noted. The average number of positions used by the PTVA algorithm is 123. The errors obtained for the non-adaptive methods using this number of positions are 19.6 (order 2) and 7.3 (order 4) for the velocity and 23.7 (order 2) and 32.3 (order 4) for the acceleration.

  5. The best accuracy is obtained with 153 positions for the velocity and 199 positions for acceleration using order 4, whilst it is obtained with 35 positions for velocity and with 153 positions for acceleration using order 2. 17, 35, 63, 93, 153, 199, 243, 289 and 335 positions have been tested for the non-adaptive methods. The average number of positions used by the PTVA algorithm is 115. The errors obtained for the non-adaptive methods using this number of positions are 61.3 (order 2) and 24.2 (order 4) for the velocity and 93.1 (order 2) and 53.2 (order 4) for the acceleration.

References

  • Biferale L, Boffeta G, Celani A, Lanotte A, Toschi F (2004) Lagrangian statistcs in fully developed turbulence. arXiv:nlin.CD/0402032, 1–4

  • Chen L, Goto S, Vassilicos JC (2006) Turbulent clustering of stagnation points and inertial particles. J Fluid Mech 55:143–154

    Article  MathSciNet  Google Scholar 

  • Christensen KT, Adrian RJ (2002) Measurement of instantaneous Eulerian acceleration fields by particle image accelerometry: method and accuracy. Exp Fluids 33:759–769

    Google Scholar 

  • Dalziel SB (1992) Decay of rotating turbulence: some particle tracking experiments. Appl Sci Res 49:217–244

    Article  Google Scholar 

  • Dong P, Hsu TY, Atsavapranee P, Wei T (2002) Digital particle image accelerometry. Exp Fluids 33:759–769

    MATH  Google Scholar 

  • Goto S, Osborne DR, Vassilicos JC, Haigh JD (2005) Acceleration statistic as measures of statistical persistence of streamlines in isotropic turbulence. Phys Rev E 71:015301(R)

    Article  MathSciNet  Google Scholar 

  • La Porta A, Voth GA, Crawford AM, Alexander J, Bodenschatz E (2001) Fluid particle accelerations in fully developed turbulence. Nature 409:1017–1019

    Article  Google Scholar 

  • Lowe KT, Simpson RL (2005) Measurements of velocity acceleration statistics in turbulent boundary layers. TSFP 4:1043–1048

    Google Scholar 

  • Luthi B, Tsinober A, Kinselbach W (2005) Lagrangian measurement of vorticity dynamics in turbulent flows. J Fluid Mech 529:87–118

    Article  Google Scholar 

  • Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30:543–574

    Article  Google Scholar 

  • Mordant N, Crawford AM, Bodenschatz E (2004) Experimental Lagrangian acceleration probability density function measurement. Physica D 193:245–251

    Article  MATH  Google Scholar 

  • Ottino JM (1989) The kinematics of mixing: stretching, chaos, and transport. Cambridge University Press, London, pp. 1–364

    MATH  Google Scholar 

  • Querzoli G (1996) A Lagrangian study of particle dispersion in the unstable boundary layer. Atmos Environ 30(16):2821–2829

    Article  Google Scholar 

  • Rossi L, Hascoet E, Vassilicos JC, Hardalupas Y (2005) 2D fractal flow generated by electromagnetic forcing: laboratory experiments and numerical simulations. TSFP 4:485–490

    Google Scholar 

  • Rossi L, Vassilicos JC, Hardalupas Y (2006a) Electromagnetically controlled multiple scale flows. J Fluid Mech 558:207–242

    Article  MATH  Google Scholar 

  • Rossi L, Vassilicos JC, Hardalupas Y (2006b) Multi-scale laminar flows with turbulent-like properties. Phys Rev Lett 97:144501

    Article  Google Scholar 

  • Tsinober A (2001) An informal introduction to turbulence. Kluwer Academic Publishers, Dordrecht, pp. 1–324

    MATH  Google Scholar 

  • Tsinober A, Vedula P, Yeung PK (2001b) Random Taylor hypothesis and the behavior of local and convective accelerations in isotropic turbulence. Phys Fluids 13(7):1974–1984

    Article  Google Scholar 

  • Vassilicos JC (2002) Mixing in vortical, chaotic and turbulent flows. Phil Trans R Soc Lond A 360:2819–2837

    Article  MATH  Google Scholar 

  • Vedula P, Yeung PK (1999) Similarity scaling of acceleration and pressure statistic in numerical simulations of isotropic turbulence. Phys Fluids 11(5):1208–1220

    Article  Google Scholar 

  • Virant M, Dracos T (1997) 3D PTV and its application on Lagrangian motion. Meas Sci Technol 8:1539–1552

    Article  Google Scholar 

  • Voth GA, La Porta A, Crawford AM, Alexander J, Bodenschatz E (2002) Measurement of particle accelerations in fully developed turbulence. J Fluid Mech 469:121–160

    Article  MATH  Google Scholar 

Download references

Acknowledgments

We acknowledge the Marie Curie Multi-Partner European Training Site on Environmental Turbulence, the Royal Society, The Leverhulme Trust, the EPSRC, S. Dalziel and Digiflow’s group, G. Querzoli, and J.C. Vassilicos.

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  1. Dipartimento di Ingegneria del Territorio, Università degli Studi di Cagliari, Piazza d’Armi, 09123, Cagliari, Italy

    Simone Ferrari

  2. Department of Aeronautics, Imperial College London, Prince Consort Rd, London, SW7 2AZ, United Kingdom

    Lionel Rossi

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  1. Simone Ferrari
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  2. Lionel Rossi
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Correspondence to Lionel Rossi.

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Ferrari, S., Rossi, L. Particle tracking velocimetry and accelerometry (PTVA) measurements applied to quasi-two-dimensional multi-scale flows. Exp Fluids 44, 873–886 (2008). https://doi.org/10.1007/s00348-007-0443-7

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  • DOI: https://doi.org/10.1007/s00348-007-0443-7

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