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Research Papers: Fundamental Issues and Canonical Flows

A General Macroscopic Turbulence Model for Flows in Packed Beds, Channels, Pipes, and Rod Bundles

[+] Author and Article Information
A. Nakayama, F. Kuwahara

Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu 432-8561, Japan

J. Fluids Eng 130(10), 101205 (Sep 04, 2008) (7 pages) doi:10.1115/1.2969461 History: Received October 24, 2007; Revised June 15, 2008; Published September 04, 2008

This study focuses on Nakayama and Kuwahara’s two-equation turbulence model and its modifications, previously proposed for flows in porous media, on the basis of the volume averaging theory. Nakayama and Kuwahara’s model is generalized so that it can be applied to most complex turbulent flows such as cross flows in banks of cylinders and packed beds, and longitudinal flows in channels, pipes, and rod bundles. For generalization, we shall reexamine the extra production terms due to the presence of the porous media, appearing in the transport equations of turbulence kinetic energy and its dissipation rate. In particular, we shall consider the mean flow kinetic energy balance within a pore, so as to seek general expressions for these additional production terms, which are valid for most kinds of porous media morphology. Thus, we establish the macroscopic turbulence model, which does not require any prior microscopic numerical experiments for the structure. Hence, for the given permeability and Forchheimer coefficient, the model can be used for analyzing most complex turbulent flow situations in homogeneous porous media without a detailed morphological information. Preliminary examination of the model made for the cases of packed bed flows and longitudinal flows through pipes and channels reveals its high versatility and performance.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Effect of Reynolds number on macroscopic pressure gradient

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Figure 2

Comparison of the model coefficients associated with Sk

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Figure 3

Comparison of the model coefficients associated with Sε

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Figure 4

Turbulence kinetic energy in a packed bed

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Figure 5

Effective viscosity in a packed bed

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Figure 6

Decay of turbulence in flow through an array of rods: (a) turbulence kinetic energy and (b) dissipation rate of turbulence kinetic energy

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Figure 7

Effect of Reynolds number on turbulence kinetic energy in channel and pipe flows

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Figure 8

Effect of Reynolds number on ck=(⟨ε⟩fdh)∕(4⟨k⟩f⟨u¯⟩f) in channel and pipe flows

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Figure 9

Decay of turbulence in flow through a stratified medium made by channels; (a) turbulence kinetic energy and (b) dissipation rate of turbulence kinetic energy

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