Understanding Line Packing in Frictional Water Hammer

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Jim C. P. Liou
Keyword(s):  
Numerical Methods ◽  
Wave Front ◽  
Water Hammer ◽  
Maximum Pressure ◽  
Valve Closure ◽  
Governing Equations ◽  
Front Line ◽  
Wave Fronts ◽  
Friction Term

For valve closure transients in pipelines, friction attenuates the amplitude of water hammer wave fronts and causes line packing. The latter is a sustained head increase behind the wave front. Line packing can lead to overpressure. Because of the nonlinearity of the friction term in the governing equations of water hammer, a satisfactory analytical explanation of line packing is not available. Although numerical methods can be used to compute line packing, an analytical explanation is desirable to better understand the phenomenon. This paper explains line packing analytically and presents a formula to compute the line packing that leads to the maximum pressure at the closed valve.

Maximum Pressure Head Due to Linear Valve Closure

1991 ◽  
Vol 113 (4) ◽  
pp. 643-647 ◽  
Author(s):  
Chyr Pyng Liou
Keyword(s):  
Flow Characteristic ◽  
Pressure Head ◽  
Head Loss ◽  
Water Hammer ◽  
Point Of View ◽  
Global Perspective ◽  
Maximum Pressure ◽  
Valve Closure ◽  
Subtle Effect ◽  
Dimensionless Variables

The maximum pressure head resulting from one-speed closure of wide open valves is investigated. The dimensionless variables formulated in this study make the subtle effect of the initial valve head loss explicit and separate from that of the pipe frictional head loss. The maximum head is related to initial pipe frictional head loss, the initial valve head loss, the inherent flow characteristic of the valve, and the closure period by plots of dimensionless variables. The trends of the variation of the maximum pressure head are discussed. An example is used to illustrate the usage of the plots, and to show the advantage of having a global perspective of the phenomenon in the selection and sizing of valves from the water hammer point of view.

Charts for water hammer in pipelines resulting from valve closure

1980 ◽  
Vol 7 (2) ◽  
pp. 243-255 ◽  
Author(s):  
Eugen Ruus ◽  
Farouk A. El-Fitiany
Keyword(s):  
Pipe Wall ◽  
Pressure Head ◽  
Water Hammer ◽  
Wall Friction ◽  
Maximum Pressure ◽  
Valve Closure ◽  
Closure Time ◽  
Basic Parameters

Maximum pressure head rises, which result from valve closure according to (a) uniform, (b) equal-percentage, and (c) optimum valve closure arrangements, are calculated and plotted for the valve end and for the midpoint of a simple pipeline. Basic parameters such as the pipeline constant, relative closure time, and pipe wall friction are considered for closures both from partial as well as from full valve openings. The results of this paper can be used to draw the maximum hydraulic grade line along the pipe for these closure arrangements. It is found that the equal-percentage closure arrangement yields consistently less pressure head rise than does the uniform closure arrangement. Further, the optimum closure arrangement yields consistently less head rise than the equal-percentage one. Closures from partial valve openings increase the pressure head rise considerably and must always be considered.

Effect of multi-valve closure on superposed pressure in a tree-type long distance gravitational water supply system

2019 ◽  
Vol 68 (6) ◽  
pp. 420-430
Author(s):  
Xingtao Wang ◽  
Jian Zhang ◽  
Xiaodong Yu ◽  
Sheng Chen ◽  
Wenlong Zhao ◽  
...  
Keyword(s):  
Water Supply ◽  
Pressure Rise ◽  
Water Hammer ◽  
Supply System ◽  
Water Supply System ◽  
Maximum Pressure ◽  
Valve Closure ◽  
Long Distance ◽  
Maximum Water ◽  
Tree Type

Abstract Valves are installed at the end of each branch pipeline in a tree-type long distance gravitational water supply system to regulate flow. However, the sequential closing of all valves may cause a tremendous superposed pressure rise, even larger than the pressure rise under simultaneous valve closure. In this paper, the effects of sequential valve closure on the superposed maximum water hammer pressure rise in a pipeline were investigated. By using the wave superposition principle, a sequential valve closure formula leading to maximum water hammer was proposed and verified using numerical simulation based on a practical project. In addition, the superposed maximum pressure rises in the pipeline were compared under single, simultaneous and sequential valve closure, respectively. The results show that the sequential valve closure formula agrees well with the numerical results and the pressure rise in the pipeline under the sequential closing was the largest. Moreover, compared with the superposed maximum pressure rises at the main pipeline, the effect of sequential valve closure on superposed maximum pressure rise at the branch pipeline is more sensitive.

scholarly journals Wave Fronts in a Causality-Violating Gödel-Type Metric

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Thomas P. Kling ◽  
Faizuddin Ahmed ◽  
Megan Lalumiere
Keyword(s):  
Wave Front ◽  
Space Time ◽  
Wave Fronts ◽  
Light Rays ◽  
Synchronized Clocks

The light rays and wave fronts in a linear class of the Gödel-type metric are examined to reveal the causality-violating features of the space-time. Noncausal features demonstrated by the development of unusual wave front singularities are shown to be related to the nonmonotonic advance of time along the light rays, as measured by a system of observers at rest with respect to one another with synchronized clocks.

Charts for water hammer in pipelines resulting from valve closure from full opening only

1985 ◽  
Vol 12 (2) ◽  
pp. 241-264 ◽  
Author(s):  
Bryan W. Karney ◽  
Eugen Ruus
Keyword(s):  
Good Accuracy ◽  
Pipe Wall ◽  
Pressure Head ◽  
Wall Friction ◽  
Maximum Pressure ◽  
Valve Closure ◽  
Closure Time ◽  
Basic Parameters ◽  
Valve Opening ◽  
Open Position

Maximum pressure head rises, which result from total closure of the valve from an initially fully open position, are calculated and plotted for the valve end and for the midpoint of a simple pipeline. Uniform, equal-percentage, optimum, and parabolic closure arrangements are analysed. Basic parameters such as pipeline constant, relative closure time, and pipe wall friction are considered with closures from full valve opening only. The results of this paper can be used to draw the maximum hydraulic grade line along the pipe with good accuracy for the closure arrangements considered. It is found that the equal-percentage closure arrangement yields consistently less pressure head rise than does the parabolic closure arrangement. Further, the optimum closure arrangement yields consistently less head rise than the equal-percentage one. Uniform closure produces pressure head rise that usually lies between those produced by the parabolic and the equal-percentage closure arrangements, except for the range of low pressure head rise combined with low or zero friction, where the rise due to uniform closure approaches that produced by optimum closure.

scholarly journals Analysis of a self-centring detonation wave generator

2021 ◽  
pp. 34-47
Author(s):  
Waldemar Trzciński ◽  
Józef Paszula ◽  
Leszek Szymańczyk
Keyword(s):  
Theoretical Analysis ◽  
Detonation Wave ◽  
Wave Front ◽  
Point Location ◽  
Wave Fronts ◽  
Initiation Point ◽  
X Ray ◽  
Detonation Wave Front ◽  
Main Charge ◽  
Wave Generator

The aim of the study was to determine the parameters of a detonator generating a self-centring detonation wave, based on experimental and theoretical analysis. The methods for manufacturing selfcentring detonation wave generators available in literature were reviewed and a detonator comprised of two explosives was proposed. The detonator geometry was analysed for its ability to centre the detonation wave. A physical detonator model was created and the detonation wave front downstream of the detonator, analysed and the detonator’s capability to compensate an off-centre detonation initiation, evaluated. The wave fronts were recorded using pulsed x-ray radiography. The study showed that the proposed detonator provides a symmetrical initiation of the main charge for the initiation point (location) offset, lower than the assumed maximum offset.

scholarly journals Characterization of Wave Fronts of Ultradistributions Using Directional Short-Time Fourier Transform

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 240
Author(s):  
Sanja Atanasova ◽  
Snježana Maksimović ◽  
Stevan Pilipović
Keyword(s):  
Fourier Transform ◽  
Wave Front ◽  
Short Time Fourier Transform ◽  
Wave Fronts ◽  
Directional Wave ◽  
Tempered Ultradistributions ◽  
Short Time

In this paper we give a characterization of Sobolev k-directional wave front of order p∈[1,∞) of tempered ultradistributions via the directional short-time Fourier transform.

scholarly journals Null Wave Front and Ryu–Takayanagi Surface

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1297
Author(s):  
Jun Tsujimura ◽  
Yasusada Nambu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Cosmological Constant ◽  
Minimal Surface ◽  
Wave Front ◽  
Entanglement Entropy ◽  
Necessary Condition ◽  
Quantum Field ◽  
Wave Fronts ◽  
Sufficient And Necessary Condition

The Ryu–Takayanagi formula provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu–Takayanagi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we consider null rays emitted from the AdS boundary and construct a flow representing the causal holographic information. We present a sufficient and necessary condition that the causal information surface coincides with Ryu–Takayanagi surface. In particular, we show that, in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu–Takayanagi surfaces. In addition, from the viewpoint of flow, we propose a wave optical formula to calculate the causal holographic information.

scholarly journals Pressure generated at the instant of impact between a liquid droplet and solid surface

2018 ◽  
Vol 5 (12) ◽  
pp. 181101 ◽  
Author(s):  
Y. Tatekura ◽  
M. Watanabe ◽  
K. Kobayashi ◽  
T. Sanada
Keyword(s):  
Solid Surface ◽  
Shape Factor ◽  
Liquid Droplet ◽  
Pressure Rise ◽  
Propagation Speed ◽  
Spherical Shape ◽  
Water Hammer ◽  
Droplet Impact ◽  
Maximum Pressure ◽  
The Impact

The prime objective of this study is to answer the question: How large is the pressure developed at the instant of a spherical liquid droplet impact on a solid surface? Engel first proposed that the maximum pressure rise generated by a spherical liquid droplet impact on a solid surface is different from the one-dimensional water-hammer pressure by a spherical shape factor (Engel 1955 J. Res. Natl Bur. Stand. 55 (5), 281–298). Many researchers have since proposed various factors to accurately predict the maximum pressure rise. We numerically found that the maximum pressure rise can be predicted by the combination of water-hammer theory and the shock relation; then, we analytically extended Engel’s elastic impact model, by realizing that the progression speed of the contact between the gas–liquid interface and the solid surface is much faster than the compression wavefront propagation speed at the instant of the impact. We successfully correct Engel’s theory so that it can accurately provide the maximum pressure rise at the instant of impact between a spherical liquid droplet and solid surface, that is, no shape factor appears in the theory.

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