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Research Papers: Multiphase Flows

Development of Accelerating Pipe Flow Starting From Rest

[+] Author and Article Information
Ivar Annus

e-mail: ivar.annus@ttu.ee

Tiit Koppel

Professor
e-mail: tiit.koppel@ttu.ee
Department of Mechanics,
Tallinn University of Technology,
Ehitajate tee 5,
Tallinn 19086, Estonia

Laur Sarv

Department of Information Technology,
Estonian Business School,
A. Lauteri 3,
Tallinn 10114, Estonia
e-mail: laur.sarv@gmail.com

Leo Ainola

Professor
Department of Mathematics,
Tallinn University of Technology,
Ehitajate tee 5,
Tallinn 19086, Estonia
e-mail: leo.ainola@ttu.ee

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 13, 2012; final manuscript received August 16, 2013; published online September 6, 2013. Assoc. Editor: Ye Zhou.

J. Fluids Eng 135(11), 111204 (Sep 06, 2013) (10 pages) Paper No: FE-12-1440; doi: 10.1115/1.4025256 History: Received September 13, 2012; Revised August 16, 2013

A uniformly accelerated laminar flow in a pipe, initially at rest, is analyzed. One-dimensional unsteady flow equations for start-up flow were derived from the Navier–Stokes and continuity equations. The dynamical boundary layer in a pipe is described theoretically with the Laplace transformation method for small values of time. A mathematical model describing the development of the velocity profile for accelerating flow starting from rest up to the point of transition to turbulence is given. The theoretical results are compared with experimental findings gained in a large-scale pipeline. Particle image velocimetry (PIV) technique is used to deduce the development of accelerating pipe flow starting from rest. The measured values of the axial velocity component are found to be in a good agreement with the analytical values.

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References

Figures

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Fig. 1

Test rig for accelerating flows

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Fig. 2

Variation of mean velocity, acceleration rate, and wall shear stress

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Fig. 3

Theoretical and measured ensemble-averaged dimensionless velocity profiles: (a) A = const; (b) A ≠ const

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Fig. 4

Variations of axial velocity components in three different radial positions and shear stress at the wall

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Fig. 5

Comparison between numerical and ensemble-averaged dimensionless pressures q1 and q2

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Fig. 6

The development of modeled dimensionless radial velocity over the radius in different time steps

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Fig. 7

Comparison between measured and modeled mean velocities

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