Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-11T03:21:43.890Z Has data issue: false hasContentIssue false
  • English
  • Français

On the role of gravity and shear on inertial particle accelerations in near-wall turbulence

Published online by Cambridge University Press:  15 June 2010

V. LAVEZZO ,
A. SOLDATI ,
S. GERASHCHENKO ,
Z. WARHAFT  and
L. R. COLLINS
V. LAVEZZO
Affiliation:
Dipartimento di Energetica e Macchine, Università degli Studi di Udine, 33100 Udine, Italy
A. SOLDATI
Affiliation:
Dipartimento di Energetica e Macchine, Università degli Studi di Udine, 33100 Udine, Italy
S. GERASHCHENKO
Affiliation:
Sibley School for Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
Z. WARHAFT
Affiliation:
Sibley School for Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
L. R. COLLINS*
Affiliation:
Sibley School for Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: lc246@cornell.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Recent experiments in a turbulent boundary layer by Gerashchenko et al. (J. Fluid Mech., vol. 617, 2008, pp. 255–281) showed that the variance of inertial particle accelerations in the near-wall region increased with increasing particle inertia, contrary to the trend found in homogeneous and isotropic turbulence. This behaviour was attributed to the non-trivial interaction of the inertial particles with both the mean shear and gravity. To investigate this issue, we perform direct numerical simulations of channel flow with suspended inertial particles that are tracked in the Lagrangian frame of reference. Three simulations have been carried out considering (i) fluid particles, (ii) inertial particles with gravity and (iii) inertial particles without gravity. For each set of simulations, three particle response times were examined, corresponding to particle Stokes numbers (in wall units) of 0.9, 1.8 and 11.8. Mean and r.m.s. profiles of particle acceleration computed in the simulation are in qualitative (and in several cases quantitative) agreement with the experimental results, supporting the assumptions made in the simulations. Furthermore, by comparing results from simulations with and without gravity, we are able to isolate and quantify the significant effect of gravitational settling on the phenomenon.

JFM classification

Boundary Layers: Boundary Layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 229 - 246
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Ayyalasomayajula, S., Gylfason, A., Collins, L. R., Bodenschatz, E. & Warhaft, Z. 2006 Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence. Phys. Rev. Lett. 97, 144507.Google Scholar
Ayyalasomayajula, S., Warhaft, Z. & Collins, L. R. 2008 Modeling inertial particle acceleration statistics in isotropic turbulence. Phys. Fluids 20, 094104.CrossRefGoogle Scholar
Bec, J., Biferale, L., Boffetta, G., Celani, A., Cencini, M., Lanotte, A. S., Musacchio, S. & Toschi, F. 2006 Acceleration statistics of heavy particles in turbulence. J. Fluid Mech. 550, 349–358.CrossRefGoogle Scholar
Beck, C. 2001 a Dynamical foundations of nonextensive statistical mechanics. Phys. Rev. Lett. 87, 180601.CrossRefGoogle Scholar
Beck, C. 2001 b On the small-scale statistics of Lagrangian turbulence. Phys. Lett. A 27, 240.CrossRefGoogle Scholar
Berg, J. 2006 Lagrangian one-particle velocity statistics in a turbulent flow. J. Fluid Mech. 630, 179–189.Google Scholar
Biferale, L. & Toschi, F. 2006 Joint statistics of acceleration and vorticity in fully developed turbulence. J. Turbul. 6 (40), 1–8.Google Scholar
Bourgoin, M., Ouelette, N. T., Xu, H., Berg, J. & Bodenschatz, E. 2006 The role of pair dispersion in turbulent flow. Science 311, 835–838.CrossRefGoogle ScholarPubMed
Brown, R. D., Warhaft, Z. & Voth, G. A. 2009 Measurement of accelerations of large neutrally-buoyant particles in intense turbulence. Phys. Rev. Lett. 103, 194501.CrossRefGoogle ScholarPubMed
Chen, L., Gogo, S. & Vassilicos, J. C. 2006 Turbulent clustering of stagnation points and inertial particles. J. Fluid Mech. 553, 143–155.CrossRefGoogle Scholar
Chevillard, L., Roux, S. G., Leveque, E., Mordant, N., Pinton, J.-F. & Arneodo, A. 2005 Intermittency of velocity time increments in turbulence. Phys. Rev. Lett. 95, 064501.CrossRefGoogle ScholarPubMed
Choi, J., Yeo, K. & Lee, C. 2004 Lagrangian statistics in turbulent channel flow. Phys. Fluids 16, 779–793.CrossRefGoogle Scholar
Crawford, A. M., Mordant, N., Xu, H. & Bodenschatz, E. 2008 Fluid acceleration in the bulk of turbulent dilute polymer solutions. New J. Phys. 10, 123015.CrossRefGoogle Scholar
Eaton, J. K. & Fessler, J. R. 1994 Preferential concentration of particles by turbulence. Intl J. Multiphase Flow 20, 169–209.CrossRefGoogle Scholar
Elghobashi, S. E. & Truesdell, G. C. 1992 Direct simulation of a particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655.Google Scholar
Elghobashi, S. E. & Truesdell, G. C. 1993 On the two-way interaction between homogeneous turbulence and dispersed particles. Part I. Turbulence modification. Phys. Fluids A 5, 1790–1801.Google Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Gerashchenko, S., Sharp, N. S., Neuscamman, S. & Warhaft, Z. 2008 Lagrangian measurements of inertial particle accelerations in a turbulent boundary layer. J. Fluid Mech. 617, 255–281.CrossRefGoogle Scholar
Guala, M., Liberzon, A., Tsinober, A. & Kinzelbach, W. 2007 An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number. J. Fluid Mech. 574, 405–427.CrossRefGoogle Scholar
Guala, M., Lüthi, B., Liberzon, A., Tsinober, A. & Kinzelbach, W. 2005 On the evolution of material lines and vorticity in homogeneous turbulence. J. Fluid Mech. 533, 339–359.CrossRefGoogle Scholar
Gylfason, A. 2006 Particles, passive scalars, and the small-scale structure of turbulence. PhD thesis, Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY.Google Scholar
Hoyer, K., Holzner, M., Lüthi, B., Guala, M., Liberzon, A. & Kinzelbach, W. 2005 3D scanning particle velocimentry. Exp. Fluids 39, 923–934.Google Scholar
La Porta, A., Voth, G. A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2001 Fluid particle accelerations in fully developed turbulence. Nature 409, 1017–1019.CrossRefGoogle ScholarPubMed
Liberzon, A., Guala, M., Luthi, B., Kinzelbach, W. & Tsinober, A. 2005 Turbulence in dilute polymer solutions. Phys. Fluids 17, 031707.Google Scholar
Marchioli, C., Picciotto, M. & Soldati, A. 2007 Influence of gravity and lift on particle velocity statistics and transfer rates in turbulent vertical channel flow. Intl J. Multiphase Flow 33, 227–251.CrossRefGoogle Scholar
Marchioli, C. & Soldati, A. 2002 Mechanisms for particle transfer and segregation in a turbulent boundary layer. J. Fluid Mech. 468, 283–315.CrossRefGoogle Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889.Google Scholar
Mordant, N., Crawford, A. M. & Bodenschatz, E. 2004 a Experimental Lagrangian acceleration probability density function measurement. Physica D 193, 245–251.CrossRefGoogle Scholar
Mordant, N., Crawford, A. M. & Bodenschatz, E. 2004 b Three-dimensional structure of the Lagrangian acceleration in turbulent flows. Phys. Rev. Lett. 93, 214501.CrossRefGoogle ScholarPubMed
Mordant, N., Delour, J., Leveque, E., Michel, O., Arneodo, A. & Pinton, J.-F. 2003 Lagrangian velocity fluctuations in fully developed turbulence: scaling, intermittency, and dynamics. J. Stat. Phys. 113, 701–717.CrossRefGoogle Scholar
Mordant, N., Metz, P., Michel, O. & Pinton, J.-F. 2001 Measurement of Lagrangian velocity in fully developed turbulence. Phys. Rev. Lett. 87, 214501.CrossRefGoogle ScholarPubMed
Mordant, N., Metz, P., Pinton, J.-F. & Michel, O. 2005 Acoustical technique for Lagrangian velocity measurement. Rev. Sci. Instrum. 76, 025105.Google Scholar
Mydlarski, L. & Warhaft, Z. 1996 On the onset of high-Reynolds-number grid-generated wind tunnel turbulence. J. Fluid Mech. 320, 331–368.CrossRefGoogle Scholar
Ott, S. & Mann, J. 2000 An experimental investigation of the relative diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid Mech. 422, 207–223.CrossRefGoogle Scholar
Ouellette, N. T., Xu, H. & Bodenschatz, E. 2006 A quantitative study of three-dimensional particle tracking algorithms. Exp. Fluids 40, 301–313.CrossRefGoogle Scholar
Ouellette, N. T., Xu, H. & Bodenschatz, E. 2009 Bulk turbulence in dilute polymer solutions. J. Fluid Mech. 629, 375–385.CrossRefGoogle Scholar
Picciotto, M., Marchioli, C. & Soldati, A. 2005 Characterization of near-wall accumulation regions for inertial particles in turbulent boundary layers. Phys. Fluids 17, 098101.Google Scholar
Qureshi, N. M., Bourgoin, M., Aaudet, C., Cartellier, A. & Gagne, Y. 2007 Turbulent transport of material particles: an experimental study of finite size effects. Phys. Rev. Lett. 99, 184502.CrossRefGoogle ScholarPubMed
Reynolds, A. M. 2003 On the application of nonextensive statistics to Lagrangian turbulence. Phys. Fluids 15, L1–L4.CrossRefGoogle Scholar
Reynolds, A. M., Mordant, N., Crawford, A. M. & Bodenschatz, E. 2005 On the distribution of Lagrangian accelerations in turbulent flows. New J. Phys. 7, 58.CrossRefGoogle Scholar
Rouson, D. W. I. & Eaton, J. K. 2001 On the preferential concentration of solid particles in turbulent channel flow. J. Fluid Mech. 428, 149–169.Google Scholar
Salazar, J. P. L. C. & Collins, L. R. 2009 Two-particle dispersion in isotropic turbulent flows. Annu. Rev. Fluid Mech. 41, 405–432.Google Scholar
Schiller, L. & Neumann, A. 1933 Uber die grundlegenden berechungen bei der schwer kraftaufbereitung. Ver. Dtsch. Ing. 77, 318.Google Scholar
Soldati, A. & Banerjee, S. 1998 Turbulence modification by large-scale organized electrohydrodynamic flows. Phys. Fluids 10, 1742–1756.Google Scholar
Sundaram, S. & Collins, L. R. 1997 Collision statistics in an isotropic, particle-laden turbulent suspension. Part I. Direct numerical simulations. J. Fluid Mech. 335, 75–109.CrossRefGoogle Scholar
Sundaram, S. & Collins, L. R. 1999 A numerical study of the modulation of isotropic turbulence by suspended particles. J. Fluid Mech. 379, 105–143.CrossRefGoogle Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.CrossRefGoogle Scholar
Volk, R., Calzavarini, E., Verhille, G., Lohse, D., Mordant, N., Pinton, J.-F. & Toschi, F. 2008 a Acceleration of heavy and light particles in turbulence: comparison between experiments and direct numerical simulations. Physica D: Nonlinear Phenom. 237, 2084–2089.Google Scholar
Volk, R., Mordant, N., Verhille, G. & Pinton, J.-F. 2008 b Laser Doppler measurement of inertial particle and bubble accelerations in turbulence. Eur. Phys. Lett. 81, 34002.CrossRefGoogle Scholar
Voth, G. A., La Porta, A., Crawford, A. M., Alexander, J. & Bodenschatz, E. 2002 Measurement of particle accelerations in fully developed turbulence. J. Fluid Mech. 469, 121–160.Google Scholar
Voth, G. A., La Porta, A., Crawford, A. M., Bodenschatz, E. & Alexander, J. 2001 A silicon strip detector system for high resolution particle tracking in turbulence. Rev. Sci. Instrum. 72, 4348–4353.CrossRefGoogle Scholar
Wang, L. P. & Maxey, M. R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 27–68.CrossRefGoogle Scholar
Xu, H., Bourgoin, M., Ouellette, N. T. & Bodenschatz, E. 2006 High order Lagrangian velocity statistics in turbulence. Phys. Rev. Lett. 96, 024503.Google Scholar