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Lagrangian statistics of light particles in turbulence
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/content/aip/journal/pof2/24/5/10.1063/1.4719148
1.
1. G. Voth, A. La Porta, A. M. Crawford, J. Alexander, and E. Bodenschatz, “Measurement of particle accelerations in fully developed turbulence,” J. Fluid Mech. 469, 121 (2002).
http://dx.doi.org/10.1017/S0022112002001842
2.
2. T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, and A. Uno, “Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics,” J. Fluid Mech. 592, 335 (2007).
http://dx.doi.org/10.1017/S0022112007008531
3.
3. S. Ayyalasomayajula, Z. Warhaft, and L. R. Collins, “Modeling inertial particle acceleration statistics in isotropic turbulence,” Phys. Fluids. 20, 095104 (2008).
http://dx.doi.org/10.1063/1.2976174
4.
4. S. Ayyalasomayajula, A. Gylfason, L. R. Collins, E. Bodenschatz, and Z. Warhaft, “Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence,” Phys. Rev. Lett. 97, 144507 (2006).
http://dx.doi.org/10.1103/PhysRevLett.97.144507
5.
5. F. Toschi and E. Bodenschatz, “Lagrangian properties of particles in turbulence,” Annu. Rev. Fluid Mech. 41, 375 (2009).
http://dx.doi.org/10.1146/annurev.fluid.010908.165210
6.
6. N. Mordant, A. M. Crawford, and E. Bodenschatz, “Experimental Lagrangian acceleration probability density function measurement,” Physica D 193, 245 (2004).
http://dx.doi.org/10.1016/j.physd.2004.01.041
7.
7. N. Mordant, A. M. Crawford, and E. Bodenschatz, “Three-dimensional structure of the Lagrangian acceleration in turbulent flows,” Phys. Rev. Lett. 93, 214501 (2004).
http://dx.doi.org/10.1103/PhysRevLett.93.214501
8.
8. L. Biferale, G. Boffetta, A. Celani, B. J. Devenish, A. Lanotte, and F. Toschi, “Multifractal statistics of Lagrangian velocity and acceleration in turbulence,” Phys. Rev. Lett. 93, 064502 (2004).
http://dx.doi.org/10.1103/PhysRevLett.93.064502
9.
9. I. Mazzitelli and D. Lohse, “Lagrangian statistics for fluid particles and bubbles in turbulence,” New J. Phys. 6, 203 (2004).
http://dx.doi.org/10.1088/1367-2630/6/1/203
10.
10. F. Toschi, L. Biferale, G. Boffetta, A. Celani, B. J. Devenish, and A. Lanotte, “Acceleration and vortex filaments in turbulence,” J. Turbul. 6, N15 (2005).
http://dx.doi.org/10.1080/14685240500103150
11.
11. N. M. Qureshi, U. Arrieta, C. Baudet, A. Cartellier, Y. Gagne, and M. Bourgoin, “Acceleration statistics of inertial particles in turbulent flow,” Eur. Phys. J. B 66, 531 (2008).
http://dx.doi.org/10.1140/epjb/e2008-00460-x
12.
12. R. Volk, E. Calzavarini, G. Verhille, D. Lohse, N. Mordant, J.-F. Pinton, and F. Toschi, “Acceleration of heavy and light particles in turbulence: Comparison between experiments and direct numerical simulations,” Physica D 237, 2084 (2008).
http://dx.doi.org/10.1016/j.physd.2008.01.016
13.
13. R. Volk, N. Mordant, G. Verhille, and J.-F. Pinton, “Laser Doppler measurement of inertial particle and bubble accelerations in turbulence,” Europhys. Lett. 81, 34002 (2008).
http://dx.doi.org/10.1209/0295-5075/81/34002
14.
14. M. Gibert, H. Xu, and E. Bodenschatz, “Inertial effects on two-particle relative dispersion in turbulent flows,” Europhys. Lett. 90, 64005 (2010).
http://dx.doi.org/10.1209/0295-5075/90/64005
15.
15. J. Bec, L. Biferale, G. Boffetta, A. Celani, M. Cencini, A. Lanotte, S. Musacchio, and F. Toschi, “Acceleration statistics of heavy particles in turbulence,” J. Fluid Mech. 550, 349 (2006).
http://dx.doi.org/10.1017/S002211200500844X
16.
16. R. Volk, E. Calzavarini, E. Leveque, and J.-F. Pinton, “Dynamics of inertial particles in a turbulent von Kármán flow,” J. Fluid Mech. 668, 223 (2011).
http://dx.doi.org/10.1017/S0022112010005690
17.
17. E. Calzavarini, R. Volk, M. Bourgoin, E. Leveque, J.-F. Pinton, and F. Toschi, “Acceleration statistics of finite-sized particles in turbulent flow: the role of Faxèn forces,” J. Fluid Mech. 630, 179 (2009).
http://dx.doi.org/10.1017/S0022112009006880
18.
18. R. D. Brown, Z. Warhaft, and G. A. Voth, “Acceleration statistics of neutrally buoyant spherical particles in intense turbulence,” Phys. Rev. Lett. 103, 194501 (2009).
http://dx.doi.org/10.1103/PhysRevLett.103.194501
19.
19. J. Rensen, S. Luther, and D. Lohse, “The effects of bubbles on developed turbulence,” J. Fluid Mech. 538, 153 (2005).
http://dx.doi.org/10.1017/S0022112005005276
20.
20. J. Martínez Mercado, D. Chehata Gómez, D. van Gils, C. Sun, and D. Lohse, “On bubble clustering and energy spectra in pseudo-turbulence,” J. Fluid Mech. 650, 287 (2010).
http://dx.doi.org/10.1017/S0022112009993570
21.
21. K. R. Sreenivasan, “On the universality of the Kolmogorov constant,” Phys. Fluids 7, 2778 (1995).
http://dx.doi.org/10.1063/1.868656
22.
22. K. Hoyer, M. Holzner, B. Lüthi, M. Guala, A. Liberzon, and W. Kinzelbach, “3D scanning particle tracking velocimetry,” Exp. Fluids 39, 923 (2005).
http://dx.doi.org/10.1007/s00348-005-0031-7
23.
23. Y. Tagawa, J. Martínez Mercado, V. N. Prakash, E. Calzavarini, C. Sun, and D. Lohse, “Three-dimensional Lagrangian Voronoi analysis for clustering of particles and bubbles in turbulence,” J. Fluid Mech. 693, 201 (2012).
http://dx.doi.org/10.1017/jfm.2011.510
24.
24. B. Lüthi, A. Tsinober, and W. Kinzelbach, “Lagrangian measurement of vorticity dynamics in turbulent flow,” J. Fluid Mech. 528, 87 (2005).
http://dx.doi.org/10.1017/S0022112004003283
25.
25. R. E. G. Poorte and A. Biesheuvel, “Experiments on the motion of gas bubbles in turbulence generated by an active grid,” J. Fluid Mech. 461, 127 (2002).
http://dx.doi.org/10.1017/S0022112002008273
26.
26. E. Calzavarini, M. Kerscher, D. Lohse, and F. Toschi, “Dimensionality and morphology of particle and bubble clusters in turbulent flow,” J. Fluid Mech. 607, 13 (2008).
http://dx.doi.org/10.1017/S0022112008001936
27.
27. S. Grossmann and D. Lohse, “Intermittency exponents,” Europhys. Lett. 21, 201 (1993).
http://dx.doi.org/10.1209/0295-5075/21/2/014
28.
28. F. Belin, P. Tabeling, and H. Willaime, “Exponents of the structure function in a low temperature helium experiment,” Physica D 93, 52 (1996).
http://dx.doi.org/10.1016/0167-2789(95)00279-0
29.
29. P. K. Yeung and S. B. Pope, “Lagrangian statistics from direct numerical numerical simulations of isotropic turbulence,” J. Fluid Mech. 207, 531 (1989).
http://dx.doi.org/10.1017/S0022112089002697
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/5/10.1063/1.4719148
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Figures

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FIG. 1.

The Twente Water Tunnel: an experimental facility for studying two-phase turbulent flows. The picture shows the measurement section and on top the active grid, which allows homogeneous and isotropic turbulent flows upto Re = 300, and the 4-camera particle tracking velocimetry (PTV) system to detect the positions of particles in three-dimensions. For illumination we use a high energy, high-repetition rate laser. Micro-bubbles with a diameter ≈340 μm are generated above the active grid using a ceramic porous plate and are advected downwards into the measurement volume.

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FIG. 2.

Flow parameters characterization from hot-wire measurements. Compensated second-order longitudinal structure function () calculated in order to estimate dissipation.

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FIG. 3.

The rms of the vertical component of the micro-bubble (a) velocity and (b) acceleration, and (c) the acceleration flatness at Re = 195 as a function of for polynomial smoothing. The arrows in the figures indicate the chosen value ( = 50) for the smoothing of the trajectories.

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FIG. 4.

(a) PDFs of the three components of micro-bubble velocity at Re = 195. The three velocity component distributions are nearly Gaussian compared to the solid line that represents a Gaussian distribution. (b) PDFs of the three components of the normalized micro-bubble acceleration at Re = 195. The three components of the acceleration are strongly non-Gaussian, i.e., the tails of the distribution show high intermittency.

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FIG. 5.

(a) The rms values of the three components of the micro-bubble velocity for all Re, compared with the hot-film probe measurements. (b) The rms values of the three components of the micro-bubble acceleration for all Re.

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FIG. 6.

PDFs of the vertical component of the normalized micro-bubble acceleration. (a) Comparison with experiments under similar flow conditions (grid-generated turbulence in a wind-tunnel) at Re = 250. Our results are shown with open symbols; stars are heavy particles 4 and black crosses represent tracer particles. 3 (b) Comparison with von Kármán flow results: fit for tracers at Re = 140–690 (Refs. 1 and 6 ) is the black line; bubbles at Re = 850 (Refs. 12 and 13 ) are shown with a blue line. (c) Comparison with DNS simulations for point particles at Re = 180 (from iCFDdatabase http://cfd.cineca.it): the red line indicates tracers and the black line bubbles.

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FIG. 7.

(a) PDF of the vertical component of the micro-bubble acceleration at Re = 195. Open squares are the experimental data, solid line is the fitted stretched exponential function. The inset shows the plot of the fourth-order moment 4PDF() for experimental data and fit. (b) The flatness value of the fitted PDFs of micro-bubble acceleration as a function of Re. (c) The flatness values versus the Reynolds number. Comparison with Voth 1 and Ishihara 2 reveals that the present micro-bubble trend agrees well with the data in the literature, at least till = 225.

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FIG. 8.

Autocorrelation function of the three components of the micro-bubble acceleration at Re = 195. The acceleration autocorrelation of the micro-bubbles is nearly isotropic. The time lag is normalized with the Kolmogorov time scale τ.

Image of FIG. 9.

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FIG. 9.

(a) Autocorrelation function of the vertical component of the micro-bubble acceleration for the different Re measured. The correlation of the micro-bubble acceleration persists longer with increasing Reynolds number. (b) The decorrelation time of the autocorrelation function for the three components of the micro-bubble acceleration as a function of Re. The decorrelation time increases with the turbulent intensity. In the inset, we show also the result of Volk 12 at a very high Re = 850 (⧫), their experimental point agrees with the trend of increasing decorrelation time with turbulent intensity. The linear fit obtained with our experimental data extrapolates a value of = 0.27 at Re = 850, which is slightly higher than their experimental value of = 0.25.

Tables

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Table I.

Summary of the flow parameters. : water mean flow speed, : Taylor-Reynolds number, : mean velocity fluctuation, η = (ν3/ε)1/4 and τ = (ν/ε)1/2: are the Kolmogorov's length scale and time scale, respectively, : integral length scale of the flow, ε: mean energy dissipation rate, = τ: Stokes number, and : number of data points used to calculate the Lagrangian statistics.

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Table II.

Flatness values of the distribution of micro-bubble velocities.

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/content/aip/journal/pof2/24/5/10.1063/1.4719148
2012-05-18
2014-04-19

Abstract

We study the Lagrangian velocity and acceleration statistics of light particles (micro-bubbles in water) in homogeneous isotropic turbulence. Micro-bubbles with a diameter = 340 μm and Stokes number from 0.02 to 0.09 are dispersed in a turbulent water tunnel operated at Taylor-Reynolds numbers (Re) ranging from 160 to 265. We reconstruct the bubble trajectories by employing three-dimensional particle tracking velocimetry. It is found that the probability density functions (PDFs) of the micro-bubble acceleration show a highly non-Gaussian behavior with flatness values in the range 23 to 30. The acceleration flatness values show an increasing trend with Re, consistent with previous experiments [G. Voth, A. La Porta, A. M. Crawford, J. Alexander, and E. Bodenschatz, “Measurement of particle accelerations in fully developed turbulence,” J. Fluid Mech.469, 121 (2002)] and numerics [T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, and A. Uno, “Small-scale statistics in highresolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics,” J. Fluid Mech.592, 335 (2007)]. These acceleration PDFs show a higher intermittency compared to tracers [S. Ayyalasomayajula, Z. Warhaft, and L. R. Collins, “Modeling inertial particle acceleration statistics in isotropic turbulence,” Phys. Fluids.20, 095104 (2008)] and heavy particles [S. Ayyalasomayajula, A. Gylfason, L. R. Collins, E. Bodenschatz, and Z. Warhaft, “Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence,” Phys. Rev. Lett.97, 144507 (2006)] in wind tunnel experiments. In addition, the micro-bubble acceleration autocorrelation function decorrelates slower with increasing Re. We also compare our results with experiments in von Kármán flows and point-particle direct numerical simulations with periodic boundary conditions.

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Scitation: Lagrangian statistics of light particles in turbulence
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/5/10.1063/1.4719148
10.1063/1.4719148
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