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

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

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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Ferrante, M., and Brunone, B., 2003, “Pipe System Diagnosis and Leak Detection by Unsteady-state Tests. 1. Harmonic Analysis,” Adv. Water Resour., 26, pp. 95–105. [CrossRef]
Kapelan, Z., Savic, D. A., and Walters, G. A., 2004, “Incorporation of Prior Information in Inverse Analysis for Leak Determination and Roughness Calibration,” Urban Water, 1(2), pp. 129–141. [CrossRef]
Brown, F. T., 1962, “The Transient Response of Fluid Lines,” ASME J. Basic Eng., 84(3), pp. 547–553. [CrossRef]
D'Souza, A. F., and Oldenburger, R., 1964, “Dynamic Response of Fluid Lines,” ASME J. Basic Eng., 86(3), pp. 586–589.
Holmboe, E. I., and Rouleau, W. T., 1967, “The Effect of Viscous Shear on Transients in Liquid Lines,” ASME J. Basic Eng., 89(1), pp. 174–180. [CrossRef]
Zielke, W., 1968, “Frequency Dependent Friction in Transient Pipe Flow,” ASME J. Basic Eng., 90(1), pp. 109–115. [CrossRef]
Letelier, S. M., and Leutheusser, H. J., 1976, “Skin Friction in Unsteady Laminar Pipe Flow,” J. Hydr. Div., 102(1), pp. 41–56.
Achard, J. L., and Lespirand, G. H., 1981, “Structure of the Transient Wall-Friction Law in One-Dimensional Models of Laminar Pipe Flow,” J. Fluid Mech., 113, pp. 263–293. [CrossRef]
Vardy, A. E., and Hwang, K. L., 1991, “A Characteristic Model of Transient Friction in Pipes,” J. Hydr. Res., 29(5), pp. 669–685. [CrossRef]
Shuy, E. B., 1995, “Approximate Wall Shear Equation for Unsteady Laminar Pipe Flows,” J. Hydr. Res, 33(4), pp. 457–469. [CrossRef]
Vardy, A. E., and Brown, J. M. B., 1995, “Transient, Turbulent, Smooth Pipe Friction,” J. Hydr. Res., 33(4), pp. 435–456. [CrossRef]
Brereton, G. J., 2000, “The Interdependence of Friction, Pressure Gradient, and Flow Rate in Unsteady Laminar Parallel Flows,” Phys. Fluids, 12(3), pp. 518–530. [CrossRef]
Brereton, G. J., and Jiang.Y., 2005, “Exact Solutions for Some Fully Developed Laminar Pipe Flows Undergoing Arbitrary Unsteadiness,” Phys. Fluids, 17, p. 118104. [CrossRef]
Adamkowski, A., and Lewandowski, M., 2006, “Experimental Examination of Unsteady Friction Models for Transient Pipe Flow Simulation,” ASME J. Fluids Eng., 128, pp. 1351–1363. [CrossRef]
Ghidaoui, M. S., 2004, “On the Fundamental Equations of Water Hammer,” Urban Water, 1(4), pp. 71–83. [CrossRef]
Ghidaoui, M. S., Zhao, M., McInnis, D. A., and Axworthy, D. H., 2005, “A Review of Water Hammer Theory and Practice,” Appl. Mech. Rev., 58(1), pp. 49–76. [CrossRef]
Ainola, L., Koppel, T., Lamp, J., and Liiv, U., 1981, “On the Criteria of the Transition From Laminar to Turbulent in Starting Pipe Flow,” Trans. Tallinn Polyt. Inst., 505, pp. 17–29 (in Russian).
Ainola, L.Liiv, U., 1985, “Mathematical Models for Unsteady Flows in Pipes,” Trans. Tallinn Polyt. Inst, 593, pp. 85–94 (in Russian).
Koppel, T., and Ainola, L., 2006, “Identification of Transition to Turbulence in a Highly Accelerated Start-up Pipe Flow,” ASME J. Fluids Eng., 128(4), pp. 680–686. [CrossRef]
Ainola, L., Koppel, T., Lamp, J., and Liiv, U., 1979, “An Investigation of Local Velocities in the Pipe at Starting From Rest Unsteady Liquid Flow,” Trans. Tallinn Polyt. Inst., 472, pp. 35–45 (in Russian).
Ainola, L., Lamp, J., Sarv, L., and Liiv, U., 1981, “Study of Transition Process of Compressible Fluid in Pipes Using a Numerical Method,” Hydrotech. Build, 1, pp. 22–25 (in Russian).
Ghidaoui, M. S., and Kolyshkin, A. A., 2001, “Stability Analysis of Velocity Profiles in Water-Hammer Flows,” J. Hydr. Eng., 127(6), pp. 499–512. [CrossRef]
Brunone, B., Karney, B. W., Micarelli, M., and Ferrante, M., 2000, “Velocity Profiles and Unsteady Pipe Friction in Transient Flow,” J. Water Resour. Plann. Manage., 126(4), pp. 236–244. [CrossRef]
Das.D., and Arakeri.J. H., 1998, “Transition of Unsteady Velocity Profiles With Reverse Flow,” J. Fluid Mech., 374, pp. 251–283. [CrossRef]
Vardy, A. E., Bergant, A., He, S., Ariyaratne, C., Koppel, T., Annus, I., Tijsseling, A., and Hou, Q., 2009, “Unsteady Skin Friction Experimentation in a Large Diameter Pipe,” 3rd IAHR Int. Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, P.Rudolf, ed., Brno, Czech Republic, Vol. II, pp. 593–602.
Annus, I., and Koppel, T., 2011, “Transition to Turbulence in Accelerating Pipe Flow,” ASME J. Fluids Eng., 133(7), p. 071202. [CrossRef]
He, S., Ariyaratne, C., and Vardy, A. E., 2011, “Wall Shear Stress in Accelerating Turbulent Pipe Flow,” J. Fluid Mech., 685, pp. 440–460. [CrossRef]
Moisy, F., “PIVMat,” http://www.fast.u-psud.fr/pivmat/
He, S., and Ariyaratne, C., 2011, “Wall Shear Stress in the Early Stage of Unsteady Turbulent Pipe Flow,” J. Hydraul. Eng., 137(5). pp. 606–610. [CrossRef]
Ainola, L., Lamp, J., Liiv, U., and Sarv, L., 1979, “A Theoretical Investigation of the Unsteady Liquid Flow in Round Pipes Using a Dissipation Model,” Trans. Tallinn Polyt. Inst, 472, pp. 25–34 (in Russian).
Kurokawa, J., and Morikawa, M., 1986, “Accelerated and Decelerated Flows in Circular pipe (1st Report, Velocity Profiles and Friction Coefficient),” Bull. JSME, 29, pp. 758–765. [CrossRef]
Viola, J. P., and Leutheusser, H. J., 2004, “Experiments on Unsteady Turbulent Pipe Flow,” J. Eng. Mech., 130(2), pp. 240–244. [CrossRef]
British Association for the Advancement of Science, 1937, Mathematical Tables Volume VI. Bessel Functions Part I, Cambridge University, Cambridge, UK.
Abramowitz, M., and Stegun, I. A., 1979, Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, Nauka, Moscow.


Grahic Jump Location
Fig. 1

Test rig for accelerating flows

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

Comparison between measured and modeled mean velocities



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In