Fluid Mechanics, Water Hammer, Dynamic Stresses, and Piping Design

Water hammer imposes a steep rise in pipe pressure due to the rapid closure of a valve or a pump shutdown. Transversal strain waves propagate along the pipe wall at sonic velocities, and dynamic stresses are developed in the material, which can interact with discontinuities and contribute to an unexpected failure. Pressure increase has been modeled as a simple step front in a finite element model of a short section of a steel pipe. Boundary conditions have been considered to closely resemble the conditions of longer pipe behavior. The shock traveling along the length of the fluid-filled pipe causes a vibration response in the pipe wall. Dynamic strains and stresses follow the water hammer event with a certain delay, as is shown from the results of the FEA. Response of the material is strain rate dependent and dynamic peak stresses are substantially larger than the expected from the static pressure loads. Damping of the waves, neither by the material of the pipe nor by the interaction fluid-pipe, has not been considered in this simple model. Hoop, axial, radial, and Von Mises equivalent stresses have been evaluated both for the overshooting and the following phase of decompression of a pipe without discontinuities. However, dynamic stresses can be enhanced in the presence of discontinuities such as laminations, thickness losses in the pipe wall due to corrosion, changes in the wall thickness in neighboring pipe sections, dents, etc. These dynamic effects are able to explain how certain discontinuities that were reported as passing an Engineering Critical Assessment can eventually cause failure to the integrity of the structure. Deflections in the pipe wall can be altered by the welded transition from a pipe with a certain thickness to another with a smaller thickness, and wavelength changes of one order of magnitude can be expected. This can result in different approaches towards the risk assessment for discontinuities in the proximity of changes in wall thickness.

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Dynamic Pipe Stresses During Water Hammer: III — Complex Stress Relationships

Design and Analysis of Piping, Vessels, and Components ◽

10.1115/pvp2002-1273 ◽

2002 ◽

Cited By ~ 1

Author(s):

Robert A. Leishear

Keyword(s):

Pressure Wave ◽

Dynamic Stress ◽

Pipe Wall ◽

Three Dimensional ◽

Complex Stress ◽

Water Hammer ◽

Dynamic Stresses ◽

Vibration Theory ◽

Pressure Spike ◽

Fluid Transients

Complex three-dimensional dynamic stresses occur in a pipe following a water hammer event. Equations from vibration theory were adapted for use to describe the dynamic stresses at any point along the pipe wall. Hoop, radial, and axial dynamic stress equations are presented to approximate the stresses at a point on the pipe wall. Dynamic stress equations for beams and other simple shapes are also considered. The dynamic pipe stresses are affected principally by the types of water hammer waves or fluid transients, by the wave impacts at elbows or tees, and by the reflections of the waves from these elbows or tees. The three fluid transients considered are a moving step pressure wave, a ramp pressure, and a moving pressure spike. Approximate techniques are presented for evaluating the effects on piping due to the impingement of these transients on an elbow. For an equivalent pressure in a long pipe, application of the step pressure created the largest stress increases of the three transients considered. The vibration equations also prompt a solution to reduce water hammer effects. To this end, slow closing valves are frequently employed. Vibration theory may be applied to quantify the stress reductions afforded by these valves. Pipe stress equations may be manipulated to reduce pipe stresses for a linearly increasing, or ramp, pressure wave traveling along the pipe.

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Dynamic Pipe Stresses During Water Hammer: V — Applications

Recent Advances in Mechanics of Solids and Structures ◽

10.1115/imece2003-43875 ◽

2003 ◽

Cited By ~ 1

Author(s):

Robert A. Leishear ◽

Jeffrey H. Morehouse

Keyword(s):

Nuclear Waste ◽

Dynamic Stress ◽

Failure Mechanisms ◽

Water Hammer ◽

Dynamic Stresses ◽

Closed Form Solutions ◽

Fluid Transient ◽

Fluid Transients ◽

Waste Facility ◽

Insight Into

Theoretical equations to describe dynamic stresses during water hammer were developed in the first four parts of this series of papers, and this fifth paper applies those equations to analyze piping failures in a nuclear waste facility. The pipe failures were shown to be coincident to valve closures and pump shut downs, which caused fluid transients in the system. Magnitudes of the pressure increases during the transients were calculated and implemented in dynamic stress analyses for the piping. The maximum pipe stresses were then compared to the fatigue stresses of the pipes, and the failure mechanisms were thus established. By slowly closing valves, the effects of the fluid transient can be nearly eliminated. Using the closed from equations, the minimum time of valve closure may be calculated to prevent recurrent pipe failures. This application of the original closed form solutions provides further insight into the use and validity of the new dynamic stress equations.

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Dynamic Pipe Stresses During Water Hammer: A Finite Element Approach

Journal of Pressure Vessel Technology ◽

10.1115/1.2716420 ◽

2007 ◽

Vol 129 (2) ◽

pp. 226-233 ◽

Cited By ~ 4

Author(s):

Robert A. Leishear

Keyword(s):

Finite Element ◽

Pressure Wave ◽

Maximum Stress ◽

Pipe Wall ◽

Applied Pressure ◽

Three Dimensional ◽

Water Hammer ◽

Sudden Increase ◽

Element Analysis ◽

Dynamic Stresses

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.

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Dynamic Pipe Stresses During Water Hammer: I — A Finite Element Approach

Design and Analysis of Piping, Vessels, and Components ◽

10.1115/pvp2002-1265 ◽

2002 ◽

Cited By ~ 1

Author(s):

Robert A. Leishear ◽

Edward F. Young ◽

Curtis A. Rhodes ◽

Elisabeth M. Alford

Keyword(s):

Finite Element ◽

Pressure Wave ◽

Maximum Stress ◽

Pipe Wall ◽

Axial Stress ◽

Applied Pressure ◽

Water Hammer ◽

Sudden Increase ◽

Element Analysis ◽

Dynamic Stresses

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 which 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. At the same time, the radial stress was limited to the magnitude of the applied pressure, and the axial stress was equal to zero.

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