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Research Papers: Multiphase Flows

Study of Local Turbulence Profiles Relative to the Particle Surface in Particle-Laden Turbulent Flows

[+] Author and Article Information
Lian-Ping Wang

Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19716-3140
e-mail: lwang@udel.edu

Oscar G. C. Ardila

School of Mechanical Engineering,
Universidad del Valle,
Cali 12345, Colombia
e-mail: oscar.gerardo.castro@correounivalle.edu.co

Orlando Ayala

Department of Engineering Technology,
Old Dominion University,
Norfolk, VA 23529
e-mail: oayala@odu.edu

Hui Gao

United Technologies Research Center,
East Hartford, CT 06118
e-mail: gaoh@utrc.utc.com

Cheng Peng

Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19716-3140
e-mail: cpengxpp@udel.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 1, 2015; final manuscript received August 22, 2015; published online December 8, 2015. Assoc. Editor: E. E. Michaelides.

J. Fluids Eng 138(4), 041307 (Dec 08, 2015) (14 pages) Paper No: FE-15-1081; doi: 10.1115/1.4031692 History: Received February 01, 2015; Revised August 22, 2015

As particle-resolved simulations (PRSs) of turbulent flows laden with finite-size solid particles become feasible, methods are needed to analyze the simulated flows in order to convert the simulation data to a form useful for model development. In this paper, the focus is on turbulence statistics at the moving fluid–solid interfaces. An averaged governing equation is developed to quantify the radial transport of turbulent kinetic energy when viewed in a frame moving with a solid particle. Using an interface-resolved flow field solved by the lattice Boltzmann method (LBM), we computed each term in the transport equation for a forced, particle-laden, homogeneous isotropic turbulence. The results illustrate the distributions and relative importance of volumetric source and sink terms, as well as pressure work, viscous stress work, and turbulence transport. In a decaying particle-laden flow, the dissipation rate and kinetic energy profiles are found to be self-similar.

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Figures

Grahic Jump Location
Fig. 1

Time evolution of high-order statistics of turbulence for both particle-laden and unladen flow: (a) skewness and (b) flatness

Grahic Jump Location
Fig. 2

Zoom-in view of vorticity contour and particle location on a plane-cut of z = 255.5 in the 5123 simulation: (c) 0.47Te,0 and (d) 0.79Te,0. Note that the presence of particles is associated with high vorticity values (represented by the colors toward the red end in the online version (or the dark end in black and white)), indicating relatively large dissipation near particle surfaces. The corresponding vorticity contours for single-phase flow at the two times are shown in (a) and (b), respectively.

Grahic Jump Location
Fig. 3

Time evolution of (a) Taylor microscale Reynolds number and (b) normalized dissipation rate for both particle-laden and unladen flow

Grahic Jump Location
Fig. 4

Normalized (a) dissipation rate and (b) turbulent kinetic energy as a function of distance from the center of the solid particle. The horizontal line marks the level of 1.0.

Grahic Jump Location
Fig. 5

(a) Contour of the normalized local strain rate defined as ε/〈ε〉fluid and particle positions in an x–y plane at z = 128.5, from a PRS of three-dimensional, particle-laden, forced homogeneous isotropic turbulence. This figure is taken from Ref.[25]. Only a quarter of the plane is shown. (b) Profiles conditioned on the particle surface. Each is normalized by its respective field mean.

Grahic Jump Location
Fig. 6

Profiles of volumetric source and sink terms conditioned on the particle surface. All quantities are normalized by the fluid-phase average dissipation rate.

Grahic Jump Location
Fig. 7

Profiles of turbulent transport terms conditioned on the particle surface. All quantities are normalized by the fluid-phase average dissipation rate.

Grahic Jump Location
Fig. 8

Profile of viscous stress work conditioned on the particle surface. It is normalized by the fluid-phase average dissipation rate.

Grahic Jump Location
Fig. 9

Profiles of the pressure work and other terms in the balance equation (Eq. (22)). All quantities are normalized by the fluid-phase average dissipation rate.

Grahic Jump Location
Fig. 10

(a) The PDF of the bin node numbers and (b) a replot of Fig. 9 when weighted by the PDF in (a)

Grahic Jump Location
Fig. 11

Profile of bin-averaged 〈eijeij〉 as a function of distance from the particle center, obtained from two grid resolutions

Grahic Jump Location
Fig. 12

The normalized (a) dissipation rate and (b) turbulent kinetic energy as a function of the distance from the center of the nearest solid particle. The horizontal line marks the level of 1.0.

Grahic Jump Location
Fig. 13

Profiles of bin-averaged (a) dissipation rate and (b) turbulent kinetic energy as a function of distance from the center of a particle. Each is normalized by the field mean of the particle-laden flow at the same time instant.

Grahic Jump Location
Fig. 14

Profiles conditioned on the particle surface for the Stokes disturbance flow

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