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Research Papers: Flows in Complex Systems

# Three-Dimensional Numerical Analysis of Turbulent Flow in Porous Media Formed by Periodic Arrays of Cubic, Spherical, or Ellipsoidal Particles

[+] Author and Article Information
Q. W. Wang

e-mail: wangqw@mail.xjtu.edu.cn
Key Laboratory of Thermo-Fluid Science
and Engineering,
Ministry of Education,
School of Energy and Power Engineering,
Xi'an Jiaotong University, Xi'an,
Shaanxi 710049, PRC

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 21, 2013; final manuscript received September 4, 2013; published online October 7, 2013. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 136(1), 011102 (Oct 07, 2013) (10 pages) Paper No: FE-13-1180; doi: 10.1115/1.4025365 History: Received March 21, 2013; Revised September 04, 2013

## Abstract

In the present paper, three-dimensional (3D) turbulent flow in the porous media formed by periodic arrays of particles is numerically investigated. 3D Navier–Stokes equations and a standard k-ε turbulence model with enhanced wall function are adopted to model the turbulent flow inside the pores. Both local and macroscopic turbulence characteristics for different particle types (cubic, spherical, and ellipsoidal particles) and array forms [simple cubic (SC) and body center cubic arrays (BCC)] with different pore Reynolds numbers and porosities are carefully examined. It is revealed that, in the structural arrays of particles, the effects of particle shape and array form would be remarkable. With the same Reynolds number and porosity, the magnitudes of turbulence kinetic energy and its dissipation rate for the simple cubic array of spheres (SC-S) would be higher than those for the other arrays. Furthermore, with a nonlinear fitting method, the macroscopic correlations for extra turbulence quantities $k∞$ and $ɛ∞$ in the structural arrays for different particle types and array forms are extracted. The forms of present correlations can fit well with those of Nakayama and Kuwahara's correlations [Nakayama and Kuwahara, 1999, “A Macroscopic Turbulence Model for Flow in Porous Media,” ASME J. Fluids Eng., 121(2), pp. 427–433], but some model constants would be lower.

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## References

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## Figures

Fig. 3

Part of computational grid for SC-C (cube) and SC-S (sphere) arrays: (a) SC-C (cube) and (b) SC-S (sphere)

Fig. 4

2D physical model in Refs. [9,23]

Fig. 7

Validation of pressure drop with Ref. [20]

Fig. 9

Local turbulence kinetic energy and its dissipation rate distributions in SC array cells of different particles (φ = 0.7, Rep = 105): (a) k for SC-C (cube), (b) ε for SC-C (cube), (c) k for SC-S (sphere), (d) ε for SC-S (sphere), (e) k for SC-E (ellipsoid), and (f) ε for SC-E (ellipsoid)

Fig. 10

Variations of intrinsic volume averaged turbulence kinetic energy and its dissipation rate with porosity for SC arrays of different particles (Rep = 105 and 106): (a) Turbulence kinetic energy and (b) dissipation rate of turbulence kinetic energy

Fig. 2

3D array cells (φ = 0.7): (a) SC-C (cube), (b) SC-S (sphere), (c) SC-E (ellipsoid), and (d) BCC-S (sphere)

Fig. 1

Physical model: (a) 3D periodic array and (b) representative computational domain

Fig. 5

Validation of pressure drop with Ref. [23] (φ = 0.84)

Fig. 6

Validations of intrinsic volume averaged turbulence kinetic energy and its dissipation rate with Ref. [9] (ReH = 105): (a) Turbulence kinetic energy and (b) dissipation rate of turbulence kinetic energy

Fig. 8

Local streamline distributions in SC array cells of different particles (φ = 0.7, Rep = 105): (a) SC-C (cube), (b) SC-S (sphere), and (c) SC-E (ellipsoid)

Fig. 11

Local turbulence kinetic energy and its dissipation rate distributions in different array cells of spherical particles (φ = 0.7, Rep = 105): (a) k for SC-S (sphere), (b) ε for SC-S (sphere), (c) k for BCC-S (sphere), and (d) ε for BCC-S (sphere)

Fig. 12

Variations of intrinsic volume averaged turbulence kinetic energy and its dissipation rate with porosity for different arrays of spherical particles (Rep = 105 and 106): (a) Turbulence kinetic energy and (b) dissipation rate of turbulence kinetic energy

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