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Research Papers: Multiphase Flows

Modeling Dilute Gas–Solid Flows Using a Polykinetic Moment Method Approach

[+] Author and Article Information
Dennis M. Dunn

School for Engineering of Matter,
Transport and Energy,
Arizona State University
Tempe, AZ 85287-6106
e-mail: dennis.dunn@asu.edu

Kyle D. Squires

School for Engineering of Matter,
Transport and Energy,
Arizona State University
Tempe, AZ 85287-6106
e-mail: squires@asu.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 16, 2014; final manuscript received August 20, 2015; published online December 8, 2015. Assoc. Editor: E.E. Michaelides.

J. Fluids Eng 138(4), 041303 (Dec 08, 2015) (12 pages) Paper No: FE-14-1755; doi: 10.1115/1.4031687 History: Received December 16, 2014; Revised August 20, 2015

Modeling a dilute suspension of particles in a polykinetic Eulerian framework is described using the conditional quadrature method of moments (CQMOM). The particular regimes of interest are multiphase flows comprised of particles with diameters small compared to the smallest length scale of the turbulent carrier flow and particle material densities much larger than that of the fluid. These regimes correspond to moderate granular Knudsen number and large particle Stokes numbers in which interparticle collisions and/or particle trajectory crossing (PTC) can be significant. The probability density function (PDF) of the particle velocity space is discretized with a two-point quadrature, the minimum resolution required to capture PTC which is common to these flows. Both two-dimensional (2D) test cases (designed to assess numerical procedures) and a three-dimensional (3D) fully developed particle-laden turbulent channel flow were implemented for collisionless particles. The driving gas-phase carrier flow is computed using direct numerical simulation of the incompressible Navier–Stokes (N–S) equations and one-way coupled to the particle phase via the drag force. Visualizations and statistical descriptors demonstrate that CQMOM predicts physical features such as PTC, particle accumulation near the channel walls, and more uniform particle velocity profiles relative to the carrier flow. The improvements in modeling compared to monokinetic representations are highlighted.

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Figures

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Fig. 1

Knudsen number regimes and terminology [6,22]

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Fig. 2

Two-point, 1D quadrature representation (abscissas Uα and weights φα) of a sample 1D PDF for x-velocity, v1

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Fig. 3

Limited one-point quadrature (monokinetic) test which fails to realize PTC: (a) M(0), (b) M100(1), and (c) {U,V}

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Fig. 4

Planar contours of mass and x-momentum for two slope limiters on uniform grid: (a) minmod M(0), (b) minmod M100(1), (c) minmod {U,V}, (d) superbee M(0), (e) superbee M100(1), and (f) superbee {U,V}

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Fig. 5

Planar contours of mass and x-momentum for two slope-limiters on nonuniform grid: (a) minmod M(0), (b) minmod M100(1), (c) {U,V}, (d) superbee M(0), (e) superbee M100(1), and (f) {U,V}

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Fig. 6

Centerline of free-jet crossing with minmod limiter: (a) x-moment subset, (b) x abscissas, Uα, and (c) y abscissas, Vα

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Fig. 7

Centerline of free-jet crossing with superbee limiter: (a) x-moment subset, (b) x abscissas, Uα, and (c) y abscissas, Vα

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Fig. 8

Wall-normal profile of one-point quadrature channel flow: (a) volume fraction, M(0) and (b) mean streamwise velocity, 〈v1〉

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Fig. 9

Wall-normal profile of two-point quadrature channel flow: (a) volume fraction and (b) mean streamwise velocity, 〈v1〉

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Fig. 10

Wall-parallel plane at y+≈0 of volume fraction, M(0), in channel flow for St=2.5

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Fig. 11

Six simple moment fields in x and y, and volume fraction for St=2.5 : (a) M100(1), (b) M010(1), (c) M200(2), (d) M020(2), (e) M300(3), (f) M030(3), and (g) M(0)

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Fig. 12

Correlation between fluid velocity and particle volume fraction at y+≈0 for St=2.5 : (a) carrier fluid streamwise velocity, v1 and (b) CQMOM particle volume fraction, M(0)

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