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Research Papers: Multiphase Flows

# Application of a Volume Averaged $k-ε$ Model to Particle-Laden Turbulent Channel Flow

[+] Author and Article Information
J. D. Schwarzkopf, C. T. Crowe

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920

P. Dutta

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920dutta@mme.wsu.edu

J. Fluids Eng 131(10), 101301 (Aug 26, 2009) (8 pages) doi:10.1115/1.3203204 History: Received December 08, 2008; Revised April 20, 2009; Published August 26, 2009

## Abstract

A closed set of volume averaged equations for modeling turbulence in the carrier phase of particle-laden flows is presented. The equations incorporate a recently developed dissipation transport equation that contains an additional production of dissipation term due to particle surfaces. In the development, it was assumed that each coefficient was the sum of the coefficient for single phase flow and a coefficient quantifying the contribution of the particulate phase. To assess the effects of this additional production term, a numerical model was developed and applied to particles falling in a channel of downward turbulent air flow. Boundary conditions were developed to ensure that the production of turbulent kinetic energy due to mean velocity gradients and particle surfaces balanced with the turbulent dissipation near the wall. The coefficients associated with the production of dissipation due to mean velocity gradients and particle surfaces were varied to assess the effects of the dispersed phase on the carrier phase turbulent kinetic energy across the channel. The results show that the model predicts a decrease in turbulent kinetic energy near the wall with increased particle loading, and that the dissipation coefficients play a critical role in predicting the turbulent kinetic energy in particle-laden turbulent flows.

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## Figures

Figure 1

Illustration of (a) a “point” in the flow relative to a particle and (b) many particles within the control volume of the continuous phase

Figure 2

A control volume containing N number of particles such that a statistical average can be discerned. This volume must be larger than the limiting volume of the fluid yet small enough to use differential operators.

Figure 3

A vector representation of the volume deviation velocity at a point within the control volume

Figure 4

Comparison of the unladen velocity profiles predicted by the model to the experimental data of Kulick (6) and Paris and Eaton (8)

Figure 5

Comparison of the unladen turbulent kinetic energy profiles predicted by the model to the experimental data of Kulick (6) and Paris and Eaton (8)

Figure 6

Comparison of the velocity profiles predicted by the model to the experimental data of Kulick (6)—copper particles, 70 μm dia., and mass loading indicated in the legend

Figure 7

Comparison of the particle-laden turbulent kinetic energy profiles predicted by the model to the experimental data of Kulick (6)—copper particles, 70 μm dia., and 10% mass loading

Figure 8

Comparison of the particle-laden turbulent kinetic energy profiles predicted by the model to the experimental data of Kulick (6)—copper particles, 70 μm dia., and 20% mass loading

Figure 9

Comparison of the particle-laden turbulent kinetic energy profiles predicted by the model to the experimental data of Kulick (6)—copper particles, 70 μm dia., and mass loading indicated in the legend

Figure 10

Comparison of the velocity profile predicted by the model to the experimental data of Paris and Eaton (8)—glass particles, 150 μm dia., and 20% loading

Figure 11

Comparison of the turbulent kinetic energy profile predicted by the model to the experimental data of Paris and Eaton (8)—glass particles, 150 μm dia., and 20% loading

Figure 12

Evaluation of the production of dissipation coefficient due to the particles—Kulick (6), 20% loading, and Cεp indicated in the legend

Figure 13

Effect of the production of dissipation on the velocity profile—Kulick (6), 20% loading, and Cεp indicated in the legend

Figure 14

Evaluation of the production of dissipation coefficient due to the mean velocity gradient on TKE—Kulick (6), 20% loading, and Cε1′ indicated in the legend

Figure 15

Effect of the production of dissipation coefficient due to the mean velocity gradient on the normalized velocity profile—Kulick (6), 20% loading, and Cε1′ indicated in the legend

## Errata

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