Skip to main content Accessibility help
×
Home

Interactions of a stationary finite-sized particle with wall turbulence

  • LANYING ZENG (a1), S. BALACHANDAR (a1), PAUL FISCHER (a2) and FADY NAJJAR (a3)

Abstract

Reliable information on forces on a finite-sized particle in a turbulent boundary layer is lacking, so workers continue to use standard drag and lift correlations developed for a laminar flow to predict drag and lift forces. Here we consider direct numerical simulations of a turbulent channel flow over an isolated particle of finite size. The size of the particle and its location within the turbulent channel are systematically varied. All relevant length and time scales of turbulence, attached boundary layers on the particle, and particle wake are faithfully resolved, and thus we consider fully resolved direct numerical simulations. The results from the direct numerical simulation are compared with corresponding predictions based on the standard drag relation with and without the inclusion of added-mass and shear-induced lift forces. The influence of turbulent structures, such as streaks, quasi-streamwise vortices and hairpin packets, on particle force is explored. The effect of vortex shedding is also observed to be important for larger particles, whose Re exceeds a threshold.

Copyright

Corresponding author

Present address: Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA.

References

Hide All
Auton, T. R. 1987 The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183, 199218.
Bagchi, P. & Balachandar, S. 2002 a Effects of free rotation on the motion of a solid sphere in linear shear flow at moderate Re. Phys. Fluids 14, 27192737.
Bagchi, P. & Balachandar, S. 2002 b Shear versus vortex-induced lift force on a rigid sphere at moderate Re. J. Fluid Mech. 473, 379388.
Bagchi, P. & Balachandar, S. 2003 Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15, 34963513.
Bagchi, P. & Balachandar, S. 2004 Response of the wake of an isolated particle to an isotropic turbulent flow. J. Fluid Mech. 518, 95123.
Bagchi, P., Ha, M. Y. & Balachandar, S. 2001 Direct numerical simulation of flow and heat transfer from a sphere in a uniform cross-flow. Trans. ASME I: J. Fluids Engng 123, 347358.
Brooke, J. W. & Hanratty, T. J. 1993 Origin of turbulence-producing eddies in a channel flow. Phys. Fluids A5, 10111022.
Brooke, J. W., Hanratty, T. J. & McLaughlin, J. B. 1994 Free flight mixing and deposition of aerosols. Phys. Fluids 6, 34043415.
Brucato, A., Grisafi, F., & Montante, G. 1998 Particle drag coefficients in turbulent fluids. Chem. Engng Sci. 53, 32953314.
Caraman, N., Boree, J. & Simonin, O. 2003 Effect of collisions on the dispersed phase fluctuation in a tube 1flow: experimental and theoretical analysis. Phys. Fluids 1 15, 36023612.
Chakraborty, P., Balachandar, S. & Adrian, R. J. (2005) On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189214.
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433443.
Crowe, C. T., Sommerfeld, M., & Tsuji, Y. 1998 Multiphase flows with droplets and particles. CRC Press. New York.
Dandy, D. S. & Dwyer, H. A. 1990 A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag and heat transfer. J. Fluid Mech. 216, 381410.
Deville, M. O., Fischer, P. F. & Mund, E. H. 2002 High-order methods for incompressible fluid flow. Cambridge University Press.
Fessler, J. R., Kulick, J. D. & Eaton, J. K. 1994 Preferential concentration of heavy particles in a turbulent channel flow. Phys. Fluids 6, 37423749.
Gore, R. A. & Crowe, C. T. 1990 Discussion of particle drag in a dilute turbulent two-phase suspension flow. Intl J. Multiphase Flow 16, 359361.
Hall, D. 1988 Measurements of the mean force on a particle near a boundary in turbulent flow. J. Fluid Mech. 187, 451466.
Illiopoulos, I. & Hanratty, T. J. 1999 Turbulent dispersion in a non-homogeneous field. J. Fluid Mech. 392, 4571.
Johnson, T. A. & Patel, V. C. 1999 Flow past a sphere up to Reynolds number of 300. J. Fluid Mech. 378, 1970.
Kaftori, D., Hetsroni, G. & Banerjee, S. 1995 a Particle behavior in the turbulent boundary layer: I. Motion, deposition and entrainment. Phys. Fluids 7, 10951106.
Kaftori, D., Hetsroni, G. & Banerjee, S. 1995 b Particle behavior in the turbulent boundary layer: II. Velocity and distribution profiles, deposition and entrainment. Phys. Fluids 7, 11071121.
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Kurose, R. & Komori, S. 1999 Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384, 183206.
McLaughlin, J. B. 1991 Inertial migration of a small sphere in linear shear flows. J. Fluid Mech. 224, 261274.
Margavey, R. H. & Bishop, R. L. 1961 Transition ranges for three dimensional wakes. Can. J. Phys. 39, 14181422.
Mei, R. 1992 An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. Intl J. Multiphase Flow 18, 145147.
Mei, R. 1994 Effect of turbulence on the particle settling velocity in the nonlinear drag range. Intl J. Multiphase Flow 20, 273284.
Mei, R. & Adrian, R. 1992 Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number. J. Fluid Mech. 237, 323341.
Merle, A., Legendre, D. & Magnaudet, J. 2005 Forces on a high–Reynolds–number spherical bubble in a turbulent flow. J. Fluid Mech. 532, 5362.
Mito, Y. & Hanratty, T. J. 2002 Use of a modified Langevin equation to describe turbulent dispersion of fluid particles in a channel flow. Turbulence Combust. 68, 126.
Mittal, R. 2000 Response of the sphere wake to free–stream fluctuations. Theoret. Comput. Fluid Dyn. 13, 397419.
Mollinger, A. M. & Nieuwstadt, F. T. M. 1996 Measurement of the lift force on a particle fixed to the wall in the viscous sublayer of a fully developed turbulent boundary layer. J. Fluid Mech. 316, 285306.
Moore, D. W. 1963 The boundary layer on a spherical gas bubble. J. Fluid Mech. 16, 161176.
Moore, D. W. & Saffman, P. G. 1968 The rise of a body through a rotating fluid in a container of finite length. J. Fluid Mech. 31, 635642.
Natarajan, R. & Acrivos, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323344.
Pan, Y. & Banerjee, S. 1996 Numerical simulation of particle interactions with wall turbulence. Phys. Fluids 8, 27332755.
Pan, Y. & Banerjee, S. 1997 Numerical investigations of the effects of large particles in wall turbulence. Phys. Fluids 9, 37863807.
Ranz, W. E. & Marshall, W. R. 1952 Evaporation from drops. Chem. Engng Prog. 48, 141146.
Rashidi, M., Hetsroni, G. & Banerjee, S. 1990 Particle turbulence interaction in a boundary layer. Intl J. Multiphase Flow 16, 935949.
Reynolds, A. M. 1997 On the application of Thompson's random flight model to prediction of particle dispersion within a ventilated airspace. J. Wind Engng Indust. Aerodyn. 67–68, 627638.
Rudolff, R. R. & Bachalo, W. D. 1988 Measurement of droplet drag coefficients in polydispersed turbulent flow field. AIAA Paper 88-0235.
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385400.
Sakamoto, H. & Haniu, H. 1990 A study of vortex shedding from spheres in a uniform flow. Trans. ASME I: J. Fluids Engng 112, 386392.
Sato, Y. & Hishida, K. 1996 Transport process of turbulence energy in particle–laden turbulent flow. Intl J. Heat Fluid Flow 17, 202210.
Schiller, L. & Neumann, A. 1933 Uber die grundlegenden berechungen bei der schwer- kraftaufberereitung. Z. Vereines Deutsch. Ingen. 77, 318320.
Sirignano, W. A. 1999 Fluid dynamics and transport of droplets and sprays. Cambridge University Press.
Suzuki, Y., Ikenoya, M. & Kasagi, N. 2000 Simultaneous measurement of fluid and dispersed phases in a particle–laden turbulent channel flow with the aid of 3-D PTV. Exps. Fluids 29, s185s193.
Thompson, D.J. 1987 Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech. 180, 529556.
Tomboulides, A. G. & Orszag, S. A. 2000 Numerical investigation on transitional and weak turbulent flow past a sphere. J. Fluid Mech. 416, 4573.
Torobin, L. B. & Gauvin, W. H. 1959 Fundamental aspects of solid–gas flow. Can. J. Chem. Engng 38, 129.
Tsuji, Y. & Morikawa, Y. 1982 LDV measurements of an air–solid two-phase flow in a horizontal pipe. J. Fluid Mech. 120, 385409.
Tsuji, Y., Morikawa, Y. & Shiomi, H. 1984 LDV measurements of an air–solid two-phase flow in a vertical pipe. J. Fluid Mech. 139, 417434.
Uhlherr, P. H. T. & Sinclair, C. G. 1970 The effect of freestream turbulence on the drag coefficients of spheres. Proc. Chem. 1, 1.
Vasseur, P. & Cox, R. G. 1977 The lateral migration of spherical particles sedimenting in a stagnant bounded fluid. J. Fluid Mech. 80, 561591.
Wakaba, L. & Balachandar, S. 2005 History force on a sphere in a weak linear shear flow. Intl J Multiphase Flow 31, 9961014.
Wu, J. S. & Faeth, G. M. 1994 Sphere wakes at moderate Reynolds numbers in a turbulent environment. AIAA J. 32, 535541.
Young, J. B. & Hanratty, T. J. 1991 Optical studies on the turbulent motionsx of solid particles in a pipe flow. J. Fluid Mech. 231, 665688.
Zarin, N. A. & Nicholls, J. 1971 Sphere drag in solid rockets – non–continuum and turbulence effects. Combust. Sci. Technol. 3, 273.
Zeng, L. 2007 Interaction of a finite-size particle with wall turbulene. PhD thesis, University of Illinois, Urbana, IL.
Zeng, L. Balachandar, S. & Fischer, 2005 Wall-induced forces on a rigid sphere at finite Re. J. Fluid Mech. 536, 125.
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Related content

Powered by UNSILO

Interactions of a stationary finite-sized particle with wall turbulence

  • LANYING ZENG (a1), S. BALACHANDAR (a1), PAUL FISCHER (a2) and FADY NAJJAR (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.