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Research Papers: Fundamental Issues and Canonical Flows

Entry Lengths of Laminar Pipe and Channel Flows

[+] Author and Article Information
Yash Joshi

Department of Aerospace Engineering,
Indian Institute of Space
Science and Technology,
Thiruvananthapuram 695547, India

B. R. Vinoth

Department of Aerospace Engineering,
Indian Institute of Space
Science and Technology,
Thiruvananthapuram 695547, India
e-mail: vinothbr@iist.ac.in

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 27, 2017; final manuscript received November 12, 2017; published online February 14, 2018. Assoc. Editor: Riccardo Mereu.

J. Fluids Eng 140(6), 061203 (Feb 14, 2018) (8 pages) Paper No: FE-17-1457; doi: 10.1115/1.4038668 History: Received July 27, 2017; Revised November 12, 2017

Numerical simulations of laminar pipe and channel flows were carried out: (i) to understand the effect of inlet conditions, viz., flat inlet and streamtube inlet, on entry lengths, and (ii) to investigate the flow development in radial/transverse locations. Results show that hydrodynamic entry lengths from the streamtube inlet simulations are significantly lower compared to the entry lengths from the flat inlet simulations for low Reynolds numbers. Moreover, results from the current study (Newtonian flow with no-slip) as well as the results from the literature (non-Newtonian flow with no-slip) showed that for many flow situations, the slowest development of axial velocity in the transverse location happens to be very near to the wall. For the above cases, the existing entry length criteria (centerline as well as global entry length) are not appropriate to define the entry length. We have proposed a new entry length criterion based on the displacement thickness which is an integral measure of the velocity profile. A new entry length correlation using the displacement thickness criterion is proposed for Newtonian flows in pipe and channel based on simulations with the streamtube inlet condition.

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References

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Figures

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Fig. 1

Schematic diagram of conduit showing the details of inlet and boundary conditions for (a) flat inlet and (b) streamtube inlet

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Fig. 2

Transverse velocity field (Uy/Um) of channel flow at Re = 0.01 along with streamlines for (a) flat inlet and (b) streamtube inlet

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Fig. 3

Effect of Reynolds number on velocity profiles of channel flow from (a) flat inlet and (b) streamtube inlet at x/(H Re)=0.001

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Fig. 4

Variation of nondimensional entry length (Lc/D or Lc/H) based on centerline velocity criterion with Reynolds number (Re) for (a) pipe and (b) channel flows. Data from current simulation with different inlet conditions (flat inlet and streamtube inlet) as well as from boundary layer equations are plotted. Data of Durst et al. [2] which are obtained from the flat inlet condition also plotted for comparison.

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Fig. 5

Variation of nondimensional upstream influence distance (Lu/D or Lu/H) at centerline with Reynolds number (Re) for pipe and channel flows

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Fig. 6

Variation of nondimensional entry length (L/D and L/(DRe)) with radial locations (y/D) for pipe flow based on the streamtube inlet condition for Re = 0.001 and Re = 2000. Entry lengths from boundary layer solution are plotted for comparison.

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Fig. 7

Variation of nondimensional entry length (L/H and L/(HRe)) with transverse location (y/H) for channel flow based on the streamtube inlet condition for Re = 0.001 and Re = 2000. Entry lengths from boundary layer solution are plotted for comparison.

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Fig. 8

Nondimensional entry length (L/H) with Reynolds number (Re) based on different entry length criteria for channel flow

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Fig. 9

Nondimensional entry length (L/D) with Reynolds number (Re) based on different entry length criteria for pipe flow

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