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Settling regimes of inertial particles in isotropic turbulence

Published online by Cambridge University Press:  28 October 2014

G. H. Good ,
P. J. Ireland ,
G. P. Bewley ,
E. Bodenschatz ,
L. R. Collins  and
Z. Warhaft
G. H. Good*
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany International Collaboration for Turbulence Research
P. J. Ireland
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA International Collaboration for Turbulence Research
G. P. Bewley
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany International Collaboration for Turbulence Research
E. Bodenschatz
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany International Collaboration for Turbulence Research
L. R. Collins
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA International Collaboration for Turbulence Research
Z. Warhaft
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA Atkinson Center for a Sustainable Future, Cornell University, Ithaca, NY 14853, USA International Collaboration for Turbulence Research
*
†Email address for correspondence: ghg36@cornell.edu
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Abstract

We investigate the settling speeds and root mean square (r.m.s.) velocities of inertial particles in isotropic turbulence with gravity using experiments with water droplets in air turbulence from 32 loudspeaker jets and direct numerical simulations (DNS). The dependence on particle inertia, gravity and the scales of both the smallest and largest turbulent eddies is investigated. We isolate the mechanisms of turbulence settling modification and find that the reduced settling speeds of large particles in experiments are due to nonlinear drag effects. We demonstrate using DNS that reduced settling speeds with linear drag (e.g. see Nielsen, J. Sedim. Petrol., vol. 63, 1993, pp. 835–838) only arise in artificial flows that, by design, eliminate preferential sweeping by the eddies. Gravity and inertia both reduce the particle r.m.s. velocities and falling particles are more responsive to vertical than to horizontal fluctuations. The model by Wang & Stock (J. Atmos. Sci., vol. 50, 1993, pp. 1897–1913) captures these trends.

JFM classification

Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows Turbulent Flows: Turbulent Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 759 , 25 November 2014 , R3
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Copyright
© 2014 Cambridge University Press 

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References

Aliseda, A., Cartellier, A., Hainaux, F. & Lasheras, J. C. 2002 Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 468, 77–105.CrossRefGoogle Scholar
Bec, J., Homann, H. & Ray, S. S. 2014 Gravity-driven enhancement of heavy particle clustering in turbulent flow. Phys. Rev. Lett. 112, 184501.CrossRefGoogle ScholarPubMed
Bewley, G. P., Chang, K. & Bodenschatz, E. 2012 On integral length scales in anisotropic turbulence. Phys. Fluids 24, 061702.Google Scholar
Bewley, G. P., Saw, E. W. & Bodenschatz, E. 2013 Observation of the sling effect. New J. Phys. 15, 083051.Google Scholar
Bosse, T. & Kleiser, L. 2006 Small particles in homogeneous turbulence: settling velocity enhancement by two-way coupling. Phys. Fluids 18, 027102.Google Scholar
Chang, K., Bewley, G. P. & Bodenschatz, E. 2012 Experimental study of the influence of anisotropy on the inertial scales of turbulence. J. Fluid Mech. 692, 464–481.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops, and Particles. Academic Press.Google Scholar
Csanady, G. T. 1963 Turbulent diffusion of heavy particles in the atmosphere. J. Atmos. Sci. 20, 201–208.Google Scholar
Dávila, J. & Hunt, J. C. R. 2001 Settling of small particles near vortices and in turbulence. J. Fluid Mech. 440, 117–145.CrossRefGoogle Scholar
Elghobashi, S. & Truesdell, G. C. 1993 On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: turbulence modification. Phys. Fluids A 5, 1790–1801.Google Scholar
Garcia-Villalba, M., Kidanemariam, A. G. & Uhlmann, M. 2012 DNS of vertical plane channel flow with finite-size particles: Voronoi analysis, acceleration statistics and particle-conditioned averaging. Intl J. Multiphase Flow 46, 54–74.Google Scholar
Ghosh, S., Dávila, J., Hunt, J. C. R., Srdic, A., Fernando, H. H. S. & Jonas, P. R. 2005 How turbulence enhances coalescence of settling particles with applications to rain in clouds. Proc. R. Soc. Lond. A 461, 3059–3088.Google Scholar
Good, G. H., Gerashchenko, S. & Warhaft, Z. 2012 Intermittency and inertial particle entrainment at a turbulent interface: the effect of the large-scale eddies. J. Fluid Mech. 694, 371–398.CrossRefGoogle Scholar
Gustavsson, K., Vajedi, S. & Mehlig, B. 2014 Clustering of particles falling in a turbulent flow. Phys. Rev. Lett. 112, 214501.Google Scholar
Hill, R. J. 2005 Geometric collision rates and trajectories of cloud droplets falling into a Burgers vortex. Phys. Fluids 17, 037103.Google Scholar
Ireland, P. J. & Collins, L. R. 2012 Direct numerical simulation of inertial particle entrainment in a shearless mixing layer. J. Fluid Mech. 704, 301–332.Google Scholar
Ireland, P. J., Vaithianathan, T., Sukheswalla, P. S., Ray, B. & Collins, L. R. 2013 Highly parallel particle-laden flow solver for turbulence research. Comput. Fluids 76, 170–177.CrossRefGoogle Scholar
Kawanisi, K. & Shiozaki, R. 2008 Turbulent effects on the settling velocity of suspended sediment. J. Hydraul. Engng 134 (2), 261–266.CrossRefGoogle Scholar
Kelley, D. H. & Ouellette, N. T. 2011 Using particle tracking to measure flow instabilities in an undergraduate laboratory experiment. Am. J. Phys. 79, 267–273.CrossRefGoogle Scholar
Lucci, F., Ferrante, A. & Elghobashi, S. 2010 Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650, 5–55.CrossRefGoogle Scholar
Maxey, M. R. 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.Google Scholar
Murray, S. P. 1970 Settling velocities and vertical diffusion of particles in turbulent water. J. Geophys. Res. 75, 1647–1654.Google Scholar
Nielsen, P. 1993 Turbulence effects on the settling of suspended particles. J. Sedim. Petrol. 63 (5), 835–838.Google Scholar
Salazar, J. P. L. C. & Collins, L. R. 2012 Inertial particle relative velocity statistics in homogeneous isotropic turbulence. J. Fluid Mech. 696, 45–66.Google Scholar
Sawford, B. L., Yeung, P. K., Borgas, M. S., Vedula, P., Porta, A. La, Crawford, A. M. & Bodenschatz, E. 2003 Conditional and unconditional acceleration statistics in turbulence. Phys. Fluids 15 (11), 3478–3489.Google Scholar
Srdic, A.1998 PhD thesis, Arizona State University.Google 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
Tchen, C. M.1947 PhD thesis, Technische Hogeschool Delft.Google Scholar
Tooby, P. F., Gerald, L. W. & John, D. I. 1977 The motion of a small sphere in a rotating velocity field: a possible mechanism for suspending particles in turbulence. J. Geophys. Res. 82 (15), 2096–2100.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
Wang, L. P. & Maxey, M. R. 1993 Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 256, 26–68.CrossRefGoogle Scholar
Wang, L.-P. & Stock, D. E. 1993 Dispersion of heavy particles by turbulent motion. J. Atmos. Sci. 50, 1897–1913.Google Scholar
Witkowska, A., Brasseur, J. G. & Juvé, D. 1997 Numerical study of noise from isotropic turbulence. J. Comput. Acoust. 5, 317–336.Google Scholar
Woittiez, E. J. P., Jonker, H. J. J. & Portela, L. M. 2009 On the combined effects of turbulence and gravity on droplet collisions in clouds: a numerical study. J. Atmos. Sci. 66, 1926–1943.CrossRefGoogle Scholar
Yang, C. Y. & Lei, U. 1998 The role of turbulent scales in the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech. 371, 179–205.Google Scholar
Yang, T. S. & Shy, S. S. 2003 The settling velocity of heavy particles in an aqueous near-isotropic turbulence. Phys. Fluids 15, 868–880.Google Scholar
Yang, T. S. & Shy, S. S. 2005 Two-way interaction between solid particles and homogeneous air turbulence: particle settling rate and turbulence modification measurements. J. Fluid Mech. 526, 171–216.Google Scholar
Yudine, M. I. 1959 Physical considerations of heavy-particle diffusion. Adv. Geophys. 6, 185–191.Google Scholar