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Research Papers: Forced Convection

Undershoots in the Heat Transfer Coefficient and Friction-Factor Distributions in the Entrance Region of Turbulent Pipe Flows

[+] Author and Article Information
Eph M. Sparrow

Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: esparrow@umn.edu

John M. Gorman

Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455
e-mail: gorma157@umn.edu

Daniel B. Bryant

Department of Mechanical Engineering,
University of Minnesota,
111 Church Street SE,
Minneapolis, MN 55455

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 19, 2017; final manuscript received November 24, 2017; published online March 9, 2018. Assoc. Editor: Jim A. Liburdy.

J. Heat Transfer 140(6), 061702 (Mar 09, 2018) (9 pages) Paper No: HT-17-1090; doi: 10.1115/1.4038843 History: Received February 19, 2017; Revised November 24, 2017

Heat transfer coefficients for turbulent pipe flow are typically envisioned as axially varying from very high values at the pipe inlet to a subsequent monotonic decrease to a constant fully developed value. This distribution, although well enshrined in the literature, may not be universally true. Here, by the use of high accuracy numerical simulation, it was shown that the initially decreasing values of the coefficient may attain a local minimum before subsequently increasing to a fully developed value. This local minimum may be characterized as an undershoot. It was found that whenever a turbulent flow laminarizes when it enters a round pipe, the undershoot phenomenon occurs. The occurrence of laminarization depends on the geometry of the pipe inlet, on fluid-flow conditions in the upstream space from which fluid is drawn into the pipe inlet, on the magnitude of the turbulence intensity, and on the Reynolds number. However, the presence of the undershoot does not affect the fully developed values of the heat transfer coefficient. It was also found that the Fanning friction factor may also experience an undershoot in its axial variation. The magnitude of the heat transfer undershoot is generally greater than that of the Fanning friction factor undershoot.

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References

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Figures

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Fig. 1

Schematic diagrams of the investigated physical situations

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Fig. 2

Comparison of fully developed Nusselt numbers from the present CFD results to data reported in Refs. [1] and [13] in addition to the experimentally based correlation of Ref. [20]

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Fig. 3

Comparison of developing Nusselt numbers from the present CFD results for a 8:1 bellmouth design, as illustrated in Fig. 1, to experimental data reported in Ref. [1]

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Fig. 4

(a) Heat transfer and Fanning friction factor undershoots for a flat inlet velocity profile and turbulence intensities Tu = 1%, 5%, and 10% for a round pipe with a Reynolds number of 25,000. (b) Heat transfer and Fanning friction factor undershoots for a flat inlet velocity profile and turbulence intensities Tu = 1%, 5%, and 10% for a round pipe with a Reynolds number of 100,000. (c) Heat transfer and Fanning friction factor undershoots for a flat inlet velocity profile and turbulence intensities Tu = 1%, 5%, and 10% for a round pipe with a Reynolds number of 400,000.

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Fig. 5

(a) Heat transfer and Fanning friction factor undershoots for a flat inlet pressure profile and turbulence intensities Tu = 1%, 5%, and 10% for a round pipe with a Reynolds number of 24,000. (b) Heat transfer and Fanning friction factor undershoots for a flat inlet pressure profile and turbulence intensities Tu = 1%, 5%, and 10% for a round pipe with a Reynolds number of 103,000.

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Fig. 6

(a) Axial variation of the Nusselt number and Fanning friction factor for the geometrical configurations of Fig. 1(b) (open inlet) and Fig. 1(c) (baffled inlet). Re = 18,000. (b) Axial variation of the Nusselt number and Fanning friction factor for the geometrical configurations of Fig. 1(b) (open inlet) and Fig. 1(c) (baffled inlet). Re = 75,000.

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Fig. 7

Axial variation of the local Nusselt number and Fanning friction factor for flow drawn into the pipe inlet from an upstream space through a bellmouth or a cone. (a) Re = 19,000, uniform wall temperature, and uniform pipe-inlet temperature; (b) Re = 105,000, uniform wall temperature, and uniform pipe-inlet temperature.

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Fig. 8

Radial variation of the local streamwise velocity u divided by the mean velocity umean for multiple x/D locations. (a) 4–1 bellmouth inlet for Re = 105,000 and (b) open area inlet for Re = 75,000.

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Fig. 9

Radial variation of the local dimensionless temperature for multiple x/D locations. (a) 4–1 bellmouth inlet for Re = 105,000 and (b) open area inlet for Re = 75,000.

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