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Research Papers: Multiphase Flows

Effect of Domain Size on Fluid–Particle Statistics in Homogeneous, Gravity-Driven, Cluster-Induced Turbulence

[+] Author and Article Information
Jesse Capecelatro

Coordinated Science Laboratory,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: jcaps@illinois.edu

Olivier Desjardins

Sibley School of Mechanical
and Aerospace Engineering,
Cornell University,
Ithaca, NY 14853-7501
e-mail: olivier.desjardins@cornell.edu

Rodney O. Fox

Department of Chemical
and Biological Engineering,
Iowa State University,
Ames, IA 50011-2230
e-mail: rofox@iastate.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 15, 2014; final manuscript received September 28, 2015; published online December 8, 2015. Assoc. Editor: E. E. Michaelides.

J. Fluids Eng 138(4), 041301 (Dec 08, 2015) (8 pages) Paper No: FE-14-1752; doi: 10.1115/1.4031703 History: Received December 15, 2014; Revised September 28, 2015

Scaling of volume fraction and velocity fluctuations with domain size is investigated for high-mass-loading suspensions of finite-size inertial particles subject to gravity. Results from highly resolved Euler–Lagrange simulations are evaluated via an adaptive spatial filter with an averaging volume that varies with the local particle concentration. This filter enables the instantaneous particle velocity to be decomposed into a spatially correlated contribution used in defining the particle-phase turbulent kinetic energy (TKE), and a spatially uncorrelated contribution used in defining the granular temperature. The total granular energy is found to grow nearly linearly with the domain size, while the balance between the separate contributions remains approximately constant.

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Figures

Grahic Jump Location
Fig. 1

Decomposition of the instantaneous particle velocities vp(t) (a) into their spatially correlated up(x,t) (b) and spatially uncorrelated δv(t) (c) components from a hypothetical flow field

Grahic Jump Location
Fig. 2

Two-dimensional planes showing instantaneous fields of particle-phase volume fraction 0≤αp≤0.05 corresponding to the cases given in Table 1: (a) case 1, (b) case 2, (c) case 3, (d) case 4, (e) case 5, and (f) case 6

Grahic Jump Location
Fig. 3

Deviation of volume fraction fluctuations from a corresponding random distribution of particles as a function of domain size. The dashed curve is the logarithmic law y = 0.31 log x.

Grahic Jump Location
Fig. 4

Mean particle settling velocity normalized by the terminal velocity of an isolated particle in a corresponding flow as a function of domain size. The dashed curve is the power law y=−x0.18.

Grahic Jump Location
Fig. 5

Two-point velocity correlations computed in the vertical (i = 1) direction (circles and solid-line) and spanwise (i = 2) direction (triangles and dashed-line). Symbols represent Lagrangian (exact) two-point correlations, and lines represent the corresponding filtered two-point correlations using the adaptive filter given by Eq. (16): (a) case 1, Np = 0.1, (b) case 2, Np = 0.1, (c) case 3, Np = 0.5, (d) case 4, Np = 1.0, (e) case 5, Np = 2.0, and (f) case 6, Np = 4.0.

Grahic Jump Location
Fig. 6

Fluctuating energy as a function of domain size. κp (circles), kf (diamonds), kp (squares), and Θ (triangles). (a) Total fluctuating energy of each phase normalized by V2 and (b) separate contributions to the total particle-phase fluctuating energy normalized by κp.

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