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Research Papers: Fundamental Issues and Canonical Flows

Unsteady Velocity Profiles in Laminar and Turbulent Water Hammer Flows

[+] Author and Article Information
Alireza Riasi1

Department of Mechanical Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iranariasi@ut.ac.ir

Ahmad Nourbakhsh, Mehrdad Raisee

Department of Mechanical Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran

1

Corresponding author.

J. Fluids Eng 131(12), 121202 (Nov 19, 2009) (8 pages) doi:10.1115/1.4000557 History: Received January 12, 2009; Revised October 07, 2009; Published November 19, 2009; Online November 19, 2009

The behavior of unsteady velocity profiles in laminar and turbulent water hammer flows is numerically investigated. In this way, the governing equations for the quasitwo-dimensional equations of transient flow in pipe are solved by using the modified implicit characteristics method. A k-ω turbulence model which is accurate for two-dimensional boundary layers under adverse and favorable pressure gradients is applied. The numerical results for both steady and unsteady turbulent pipe flows are in good agreement with the experimental data. The results indicate that both decelerating and accelerating flows are produced in a wave cycle of water hammer. During deceleration of the flow, a region of reverse flows and also strong gradients is formed near to the pipe wall. In case of the turbulent water hammer, this region is very close to the pipe wall compared with the laminar water hammer. Moreover, point of inflection and also point of zero velocity are formed in the unsteady velocity profile due to the water hammer problem. The results show that the point of zero velocity does not move very far from its initial location, while the point of inflection moves rapidly from the wall.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Positive and negative characteristics for water hammer problem

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Figure 2

Introduction of variables in a part of pipe for implicit characteristics method

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Figure 3

Velocity profile in steady turbulent pipe flow: (a) Re=40,000 and (b) Re=58,650

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Figure 4

Experimental apparatus with copper pipe line (17)

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Figure 5

Pressure-time history at the pipe-midpoint: (a) laminar water hammer, Re=82 and (b) turbulent water hammer, Re=6166

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Figure 6

Velocity profiles at the pipe-midpoint for the turbulent water hammer: (a) test no. 2, P=40 and (b) test no. 3, P=2

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Figure 7

Velocity contours along the pipe length for test no. 2 (the velocity values are normalized as a percentage of initial bulk velocity)

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Figure 8

Velocity profiles at the pipe-midpoint for the laminar water hammer, test no. 1

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Figure 9

Shear stress profiles at the pipe-midpoint for the turbulent water hammer, test no 2: (a) in the whole cross section of the pipe and (b) in the pipe near wall

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Figure 10

(a) Pressure gradient and (b) wall shear stress at the pipe-midpoint and for the turbulent water hammer, test no. 2

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Figure 11

(a) Calculated normalized maximum and minimum velocities, (b) local Reynolds number, and (c) point of zero velocity and point of inflection in the laminar water hammer, test no. 1

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Figure 12

(a) Calculated normalized maximum and minimum velocities, (b) local Reynolds number, and (c) point of zero velocity and point of inflection in the turbulent water hammer, test no. 3

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