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Fundamental Issues and Canonical Flows

Turbulent Flow in D-Type Corrugated Pipes: Flow Pattern and Friction Factor

[+] Author and Article Information
R. H. Erthal

Thermal Sciences Laboratory (LACIT),
Federal University of Technology—Paraná (UTFPR),
CEP. 80230-901, Curitiba, PR, Brazil

M. A. L. Gonçalves

TE/CENPES/PETROBRAS,
21941-598 Rio de Janeiro, Brazil

R. E. M. Morales

Thermal Sciences Laboratory (LACIT),
Federal University of Technology—Paraná (UTFPR),
CEP. 80230-901, Curitiba, PR, Brazil
e-mail: rmorales@utfpr.edu.br

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 11, 2012; final manuscript received August 3, 2012; published online November 20, 2012. Assoc. Editor: Frank C. Visser.

J. Fluids Eng 134(12), 121202 (Nov 20, 2012) (9 pages) doi:10.1115/1.4007899 History: Received March 11, 2012; Revised August 03, 2012

Turbulent flow in d-type corrugated pipes of various aspect ratios has been numerically investigated in terms of flow pattern and friction factor, for Reynolds numbers ranging from 5000 to 100,000. The present numerical model was verified by comparing the friction factor with experimental and numerical results from the literature. The numerical analysis suggested that d-type behavior exists for groove aspect ratios up to w/k = (groove width/rib height) = 2 independent of the pitch. However, for a ratio of w/k = 3 an important change in the flow pattern occurs so that the pressure drag exerted by the groove walls becomes important. It is shown that the friction factor is independent of the groove height as long as the flow is similar to a flow in a d-type corrugated pipe. Moreover, the friction factor curve for d-type pipes shows a logarithmic behavior as function of the Reynolds number, so that a simple method can be used to derive an expression for the friction factor as a function of the Reynolds number and the relative groove width only. The results may be useful to engineering projects that require a better prediction of the friction factor in d-type corrugated pipes.

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References

Figures

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Fig. 1

Generic schematic drawing of the corrugated pipes studied. The dimensions for each of the geometric configurations are shown in Table 1.

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Fig. 2

Boundary conditions for the numerical domain with a single groove

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Fig. 3

Example of the numerical mesh

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Fig. 4

Comparison of the velocity profile in and above the groove for numerical domains with one, two, and three grooves

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Fig. 5

Validation of the numerical model (a) comparison of numerical friction factors and experimental data from Stel et al. [8], for the geometries listed in Table 2 (b) comparison of the velocity profile in and above a d-type groove with LES data of Vijiapurapu and Cui [10], for ReDo = 100,000

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Fig. 6

Numerical friction factors as a function of Reynolds number and groove width for fixed groove heights

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Fig. 7

Numerical friction factors as a function of Reynolds number and groove height for fixed groove widths

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Fig. 8

Streamlines from the numerical simulations for four Reynolds numbers and several representative geometric configurations

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Fig. 9

Difference of pressure between the vertical walls of the groove as a function of groove width and height for ReD = 50,000

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Fig. 10

Comparison of the numerical friction factors with the values obtained using Eq. (15) (a) values for both approaches as a function of Reynolds number and (b) direct comparison of the two approaches

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