Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-01T03:46:02.409Z Has data issue: false hasContentIssue false
  • English
  • Français

Modulation of isotropic turbulence by particles of Taylor length-scale size

Published online by Cambridge University Press:  19 March 2010

FRANCESCO LUCCI ,
ANTONINO FERRANTE  and
SAID ELGHOBASHI
FRANCESCO LUCCI
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
ANTONINO FERRANTE
Affiliation:
Department of Aeronautics and Astronautics, University of Washington, Seattle, WA 98195, USA
SAID ELGHOBASHI*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This study investigates the two-way coupling effects of finite-size solid spherical particles on decaying isotropic turbulence using direct numerical simulation with an immersed boundary method. We fully resolve all the relevant scales of turbulence around freely moving particles of the Taylor length-scale size, 1.2≤d/λ≤2.6. The particle diameter and Stokes number in terms of Kolmogorov length- and time scales are 16≤d/η≤35 and 38≤τp/τk≤178, respectively, at the time the particles are released in the flow. The particles mass fraction range is 0.026≤φm≤1.0, corresponding to a volume fraction of 0.01≤φv≤0.1 and density ratio of 2.56≤ρp/ρf≤10. The maximum number of dispersed particles is 6400 for φv=0.1. The typical particle Reynolds number is of O(10). The effects of the particles on the temporal development of turbulence kinetic energy E(t), its dissipation rate (t), its two-way coupling rate of change Ψp(t) and frequency spectra E(ω) are discussed.

In contrast to particles with d < η, the effect of the particles in this study, with d > η, is that E(t) is always smaller than that of the single-phase flow. In addition, Ψp(t) is always positive for particles with d > η, whereas it can be positive or negative for particles with d < η.

JFM classification

Turbulent Flows: Isotropic turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 650 , 10 May 2010 , pp. 5 - 55
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

Aris, R. 1962 Vectors, Tensors and the Basic Equations of Fluid Dynamics. Dover.Google Scholar
Brown, D., Cortez, R. & Minion, M. 2001 Accurate projection methods for the incompressible Navier–Stokes equations. J. Comput. Physics 168 (2), 464–499.CrossRefGoogle Scholar
Eggels, J. G. M. & Somers, J. A. 1995 Numerical simulation of free convective flow using the lattice-Boltzmann scheme. Intl J. Heat Fluid Flow 16, 357–364.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G. C. 1992 Direct simulation of particle dispersion in a decaying isotropic turbulence. J. Fluid Mech. 242, 655–700.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G. C. 1993 On the two way interaction between homogeneous turbulence and dispersed solid particles. I. Turbulence modifications. Phys. Fluids A 5 (7), 1790–1800.CrossRefGoogle Scholar
Ferrante, A. 2004 Reduction of skin-friction in a microbubble-laden spatially developing turbulent boundary layer over a flat plate. PhD thesis, University of California, Irvine.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanism of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15 (2), 315–329.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2007 On the effects of finite-size particles on decaying isotropic turbulence. International Conference on Multiphase Flow. Leipzig.Google Scholar
Glowinski, R., Pan, T., Hesla, T., Joseph, D. & Périaux, J. 2001 A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow. J. Comput. Phys. 169, 363–426.Google Scholar
Lu, J., Fernandez, A. & Tryggvason, G. 2005 The effect of bubbles on the wall drag in a turbulent channel flow. Phys. Fluids 17, 095102-1-12.Google Scholar
Lumley, J. L. 1978 Two-phase and non-newtonian flows. Topics Phys. 12, 290–324.Google Scholar
Maxey, M. R. & Riley, J. 1983 Equation of motion for a small rigid sphere in a turbulent fluid flow. Phys. Fluids 26 (4), 883–889.CrossRefGoogle Scholar
Mordant, N. & Pinton, J. 2000 Velocity measurement of a settling sphere. Eur. Phys. J. B. Condensed Matter Complex Systems 18 (2), 343–352.CrossRefGoogle Scholar
Peskin, C. 1972 Flow patterns around heart valves: a digital computer method for solving the equations of motion. PhD thesis, Albert Einstein College of Medicine.Google Scholar
Peskin, C. 2002 The immersed boundary method. Acta Numer. 11, 1–39.Google Scholar
Roma, A., Peskin, C. & Berger, M. 1999 An adaptive version of the immersed boundary method. J. Comput. Phys. 153, 509–534.CrossRefGoogle Scholar
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17, 095106-1-8.CrossRefGoogle Scholar
Saff, E. B. & Kuijlaars, A. B. J. 1997 Distributing many points on a sphere. Math. Intell. 19 (1), 5–11.CrossRefGoogle Scholar
Schumann, U. 1977 Realizability of Reynolds-stress turbulence models. Phys. Fluids 20, 721.CrossRefGoogle Scholar
Snyder, W. H. & Lumley, J. L. 1971 Some measurements of particle velocity autocorrelation functions in a turbulent flow. J. Fluid Mech. 48, 41.CrossRefGoogle Scholar
Ten Cate, A., Derksen, J. J., Portela, L. M. & Van den Akker, H. E. A. 2004 Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence. J. Fluid Mech. 519, 233–271.CrossRefGoogle Scholar
Uhlmann, M. 2003 First experiments with the simulation of particulate flows. Tech. Rep. 1020. CIEMAT, Madrid, Spain.Google Scholar
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209, 448–476.CrossRefGoogle Scholar
Uhlmann, M. 2008 Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20, 053305.Google Scholar
Zhang, Z. & Prosperetti, A. 2005 A second-order method for three-dimensional particle simulation. J. Comput. Phys. 210, 292–324.CrossRefGoogle Scholar

Lucci et al. supplementary movie

Movie 1. Instantaneous contours of sijsij in xz-plane (1.5 < t < 3) for single-phase flow (case A, left) and particle-laden flow (case F, right). In case F, the spherical uniform-size particles appear to be of different sizes because the xz-plane intersects with them while they are moving in the third direction (perpendicular to the plane). Red regions of high sijsij are formed downstream of the particles, thus increasing the dissipation rate of TKE. The speed of these animations is 1000 times slower than the actual speed for the case of liquid water carrier fluid.

Download Lucci et al. supplementary movie(Video)
Video 1.4 MB

Lucci et al. supplementary movie

Movie 2. TKE in xz-plane (1.5 < t < 3) for single-phase flow (case A, left) and particle-laden flow (case F, right). The high TKE regions (red) in case A are reduced by the particles in case F.

Download Lucci et al. supplementary movie(Video)
Video 1.4 MB

Lucci et al. supplementary movie

Movie 3. Instantaneous contours of ωy in xz-plane (1.5 < t < 3) for single-phase flow (case A, left) and particle-laden flow (case F, right). Counter-rotating (blue and red) vortices are created adjacent to the particle surface, thus increasing the ensemble-average enstrophy <ω2> (see Table 5).

Download Lucci et al. supplementary movie(Video)
Video 1.4 MB