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

2002 ◽  
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.

Dynamic Pipe Stresses During Water Hammer: A Finite Element Approach

2007 ◽  
Vol 129 (2) ◽  
pp. 226-233 ◽  
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.

Dynamic Pipe Stresses During Water Hammer: V — Applications

2003 ◽  
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.

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

2002 ◽  
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.

Finite Element Modeling of the Dynamic Response of a Steel Pipe During Water Hammer

2012 ◽  
Author(s):  
Juan C. Suárez ◽  
Paz Pinilla ◽  
Javier Alonso
Keyword(s):  
Finite Element ◽  
Wall Thickness ◽  
Pipe Wall ◽  
Element Model ◽  
Water Hammer ◽  
Steel Pipe ◽  
Dynamic Stresses ◽  
Rate Dependent ◽  
Simple Step ◽  
Von Mises

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.

Effects of Weakly Compressibility on Propagating Properties of Water Hammer in a Long Pipe

2013 ◽  
Vol 444-445 ◽  
pp. 490-497
Author(s):  
Kun Xiong Zhou ◽  
Li Xiang Zhang
Keyword(s):  
Pressure Wave ◽  
Pipe Wall ◽  
High Water ◽  
Water Hammer ◽  
Wave Form ◽  
Pressure Waves ◽  
Water Head ◽  
The Waves ◽  
Theoretical Analyses

This paper is concerned with propagating features of pressure waves induced by water hammer in a long liquid-conveyed pipe subjected to hyper high water head. Effects of dynamically weak compressibility of the water in pipe and pipe wall elasticity on the propagating physics were investigated by comparing in-site measurements and theoretical analyses. The pressure wave form and propagating speed were significantly effected due to weak compressibility of the water and the interactions of the waves. The wave performs a strong unsteadiness while it propagates along the pipe. This study tries to explain an event with consideration of both the dynamically weak compressibility of the water in pipe and the closing features of the valves controlled actively.

Effect of Wall Roughness and Flow Velocity on Water Hammer

2014 ◽  
Vol 1014 ◽  
pp. 185-191
Author(s):  
Qing Zheng Meng ◽  
Cheng Yang ◽  
Li Sheng Liu ◽  
Zhen Wang
Keyword(s):  
Flow Velocity ◽  
Pressure Wave ◽  
Pipe Wall ◽  
Influence Factors ◽  
Normal Pressure ◽  
Water Hammer ◽  
Simulation Software ◽  
Wall Roughness ◽  
Great Loss ◽  
Waveform Amplitude

Water hammer can occur in any fluid pipeline systems. The pressure caused by water hammer are far exceeding the pressure range of the pipe limit, and it can lead to the failure or fracture of the pipeline. Since a great loss has been caused by that, two influence factors (flow velocity and roughness of the pipe-wall) associated with water hammer have been performed by using the numerical simulation software CFX. Analysis of the results show that each factor effects differently in waveform, amplitude, period, attenuation of the water hammer wave. The different velocities only influences the peak of pressure wave but not the waveform and period. The pressure reduction as the increase of roughness can be neglected compared to the normal pressure.

Integrity Assessment of Damaged Flexible Pipe Cross-Sections

2014 ◽  
Author(s):  
Guomin Ji ◽  
Bernt J. Leira ◽  
Svein Sævik ◽  
Frank Klæbo ◽  
Gunnar Axelsson ◽  
...  
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Computer Code ◽  
Flexible Pipe ◽  
Dynamic Stresses ◽  
Integrity Assessment ◽  
Residual Capacity ◽  
Nonlinear Finite Element Model

This paper presents results from a case study performed to evaluate the residual capacity of a 6″ flexible pipe when exposed to corrosion damages in the tensile armour. A three-dimensional nonlinear finite element model was developed using the computer code MARC to evaluate the increase in mean and dynamic stresses for a given number of damaged inner tensile armor wires. The study also includes the effect of these damages with respect to the associated stresses in the pressure spiral. Furthermore, the implications of a sequence of wire failures with respect to the accumulated time until cross-section failure in a probabilistic sense are addressed.

Theory to Help the Use of Electromagnetic Flow Meters

2002 ◽  
Author(s):  
Xiao-Zhang Zhang
Keyword(s):  
Pipe Wall ◽  
Three Dimensional ◽  
Electromagnetic Properties ◽  
Reasonable Accuracy ◽  
Flow Meter ◽  
Flow Meters ◽  
Electromagnetic Flow ◽  
Gas Liquid Flow ◽  
Electromagnetic Flow Meter ◽  
Theory Research

Compared with other flow meters, the theory of electromagnetic flow meter is well developed. Until now, we are able to predict the three dimensional characteristics of this kind of flow meters with reasonable accuracy. This has given much help to the designers to improve the flow meters. On the other hand, the theory can offer a tool for the users of this kind of flow meters to judge the application situations, estimate the possible measurement error, etc. This paper introduces the recent work of the author on the theory of the electromagnetic flow meter. The basic physical conceptions and equations are given with a brief history review of the theory research. Several examples are given of using the theory to analyze the meters’ behavior in different application situations. They are: effect of the conducting pipe connections; errors caused by a pipe wall of different electromagnetic properties; gas-liquid flow and errors caused by a relative motion of the probe.

scholarly journals A Story on the Wave Spectral Properties of Water Hammer

2021 ◽  
Author(s):  
Shiblu Sarker
Keyword(s):  
Spectral Density ◽  
Pressure Wave ◽  
Spectral Properties ◽  
Unsteady Flows ◽  
Water Hammer ◽  
Excessive Pressure ◽  
Pipe System ◽  
Power Spectral ◽  
Physical Information ◽  
Frequency Domain Approach

The prevention of excessive pressure build-up in pipelines requires a thorough understanding of water hammer. Seminal scholars have looked into this phenomena and come up with useful solutions using theoretical techniques. In this study, We propose a power spectral density approach on the pressure wave generated by water hammer in order to improve our understanding of the frequency-domain approach. This approach has the potential to explain some useful properties of the unsteady flow at a given section, attempting to make investigations of the dynamic characteristics of pipelines more effectively. We employ a basic pipe system to mimic the proposed approach based on the data acquired, which yields a lot of relevant physical information for pipeline construction. The proposed method is expected to be useful and efficient in gaining a better understanding of the intricate properties of unsteady flows as well as sound acoustics in a pipe system and their design.

scholarly journals Assessment of water hammer effects on boiling water nuclear reactor core dynamics

2007 ◽  
Vol 22 (1) ◽  
pp. 18-33 ◽  
Author(s):  
Anis Bousbia-Salah
Keyword(s):  
Pressure Wave ◽  
Nuclear Power ◽  
Power Plants ◽  
Nuclear Reactor ◽  
Reactor Core ◽  
Water Hammer ◽  
Pressure Wave Amplitude ◽  
Sensitivity Studies ◽  
Rapid Transients ◽  
Complex Phenomena

Complex phenomena, as water hammer transients, occurring in nuclear power plants are still not very well investigated by the current best estimate computational tools. Within this frame work, a rapid positive reactivity addition into the core generated by a water hammer transient is considered. The numerical simulation of such phenomena was carried out using the coupled RELAP5/PARCS code. An over all data comparison shows good agreement between the calculated and measured core pressure wave trends. However, the predicted power response during the excursion phase did not correctly match the experimental tendency. Because of this, sensitivity studies have been carried out in order to identify the most influential parameters that govern the dynamics of the power excursion. After investigating the pressure wave amplitude and the void feed back responses, it was found that the disagreement between the calculated and measured data occurs mainly due to the RELAP5 low void condensation rate which seems to be questionable during rapid transients. .

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