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RESEARCH PAPERS

Dynamic Pipe Stresses During Water Hammer: A Finite Element Approach

[+] Author and Article Information
Robert A. Leishear

 Washington Savannah River Company, 205 Longleaf Court, Aiken, South Carolina, 29803Leishear@aol.com

J. Pressure Vessel Technol 129(2), 226-233 (Jan 21, 2007) (8 pages) doi:10.1115/1.2716420 History: Received January 26, 2006; Revised January 21, 2007

Water hammer is defined as a sudden increase in pipe pressure, which results in pressure waves that travel along the pipe at sonic velocities. In the wake of the pressure wave, dynamic stresses are created in the pipe wall, which contribute to pipe failures. A finite element analysis computer program was used to determine the three-dimensional dynamic stresses that result from pipe wall vibration at a distance from the end of a pipe, during a water-hammer event. The analysis was used to model a moving shock wave in a pipe, using a step pressure wave. Both aluminum and steel were modeled for an 8 NPS pipe, using ABAQUS®. For either material, the maximum stress was seen to be equal when damping was neglected. At the time the maximum stress occurred, the hoop stress was equivalent to twice the stress that would be expected if an equivalent static stress was applied to the inner wall of the pipe. Also, the radial stress doubled the magnitude of the applied pressure.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Cross section of the pipe model

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Figure 2

Three-dimensional FEA model

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Figure 3

FEA model geometry and pressure loading

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Figure 4

Maximum stresses

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Figure 5

Vibration stresses occurring at point A on the inner wall of the pipe

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Figure 6

Initial pipe wall deflections as the water hammer wave reaches point A

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Figure 7

Pipe wall deflections

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Figure 8

Radial stresses at point A

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Figure 9

Radial pipe stresses as the water hammer wave reaches point A

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Figure 10

Radial stresses due to stress waves

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Figure 11

Comparison of stress distributions in steel and aluminum pipes at the time when the maximum stress occurred

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Figure 12

Comparison of median dynamic stresses to static equilibrium stresses

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Figure 13

Pipe wall deflections resulting from pressurizing the entire inner pipe wall

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Figure 14

Deflection of a short steel pipe with one end free

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Figure 15

Pipe stresses in a free end pipe due to a shock wave

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Figure 16

Contact stresses (shear stresses) in a fixed end static model

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Figure 17

Radial stresses in a fixed end static model

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Figure 18

Axial stresses in a free end static model

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