Viscous Dispersion in Water Hammer

1960 ◽  
Vol 82 (4) ◽  
pp. 759-763 ◽  
Author(s):  
M. L. Walker ◽  
E. T. Kirkpatrick ◽  
W. T. Rouleau
Keyword(s):  
Exact Solution ◽  
Upper Bound ◽  
Pressure Wave ◽  
Practical Interest ◽  
Water Hammer ◽  
Inviscid Fluid ◽  
Uniform Velocity ◽  
Step Discontinuity

When a column of fluid moving with uniform velocity is instantaneously stopped at the downstream end a pressure wave is propagated upstream. In an inviscid fluid the wave is a step discontinuity, and the pressure so calculated serves as an easily obtained upper bound for all practical “water-hammer” problems, the exact solution of which may be either difficult or impossible to obtain. This paper describes an analysis of viscous dispersion in relation to the upper bound. The conclusion is reached that in problems of practical interest the bound is not significantly changed by the dispersive effects of viscosity.

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. .

Diffraction of impulsive elastic waves by a fluid cylinder

1974 ◽  
Vol 75 (3) ◽  
pp. 391-404 ◽  
Author(s):  
Ramanand Jha
Keyword(s):  
Exact Solution ◽  
Circular Cylinder ◽  
Elastic Medium ◽  
Elastic Waves ◽  
Line Source ◽  
Inviscid Fluid ◽  
Geometrical Theory ◽  
Shadow Zone ◽  
Integral Transformations ◽  
Geometrical Theory Of Diffraction

AbstractIn this paper, the problem of diffraction of an impulsive P wave by a fluid circular cylinder has been considered. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with inviscid fluid material. The line source, giving rise to the incident front, is situated outside the cylinder parallel to its axis.The exact solution of the problem is obtained by using the method of dual integral transformations. The solution is evaluated approximately to obtain the motion on the wave front in the shadow zone of the elastic medium. Further, we interpret the approxi mate solutions in terms of Keller's geometrical theory of diffraction. Our result also gives a correction to an earlier investigation of the similar problem by Knopoff and Gilbert(s).

scholarly journals Effects of a water hammer and cavitation on jet formation in a test tube

2015 ◽  
Vol 787 ◽  
pp. 224-236 ◽  
Author(s):  
Akihito Kiyama ◽  
Yoshiyuki Tagawa ◽  
Keita Ando ◽  
Masaharu Kameda
Keyword(s):  
Pressure Wave ◽  
Flow Analysis ◽  
Water Hammer ◽  
Test Tube ◽  
Liquid Interface ◽  
Phase Changes ◽  
Liquid Jet ◽  
Jet Formation ◽  
Wave Interactions ◽  
The One

We investigate the motion of a gas–liquid interface in a test tube induced by a large acceleration via impulsive force. We conduct simple experiments in which the tube partially filled with a liquid falls under gravity and hits a rigid floor. A curved gas–liquid interface inside the tube reverses and eventually forms a so-called focused jet. In our experiments, there arises either vibration of the interface or an increment in the velocity of the liquid jet, accompanied by the onset of cavitation in the liquid column. These phenomena cannot be explained by a considering pressure impulse in a classical potential flow analysis, which does not account for finite speeds of sound or phase changes. Here we model such water-hammer events as a result of the one-dimensional propagation of a pressure wave and its interaction with boundaries through acoustic impedance mismatching. The method of characteristics is applied to describe pressure-wave interactions and the subsequent cavitation. The model proposed is found to be able to capture the time-dependent characteristics of the liquid jet.

Numerical Simulation of Turbulent Pipe Flow for Water Hammer

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Hamid Shamloo ◽  
Maryam Mousavifard
Keyword(s):  
Shear Wave ◽  
Pressure Wave ◽  
Transient Flow ◽  
Water Hammer ◽  
Turbulent Pipe Flow ◽  
Turbulence Structure ◽  
Governing Equations ◽  
Structure Changes ◽  
Dominant Feature ◽  
Voigt Model

A numerical model of turbulent transient flow is used to study the dynamics of turbulence during different periods of water hammer in a polymeric pipe. The governing equations of the transient flow are solved by using the finite difference (FD) method, and the effects of viscoelasticity are modeled by means of a two-dimensional (2D) Kelvin–Voigt model. The experimental data with the Ghidaoui parameter P in the order of one are chosen in which the generated shear wave propagates toward the center of the pipe, while the pressure wave passes the length of the pipe. By studying the turbulence shear force during different times, it is shown that the turbulence structure changes considerably in the first cycle of water hammer. In the accelerated phases, the dominant feature is the creation of a shear wave near the wall, and in the decelerated phases the dominant feature is the propagation of the shear wave created in the accelerated phase.

scholarly journals Added Masses and Forces on Two Bodies Approaching Central Impact in an Inviscid Fluid

1992 ◽  
Vol 36 (02) ◽  
pp. 99-122
Author(s):  
L. Landweber ◽  
A. Shahshahan
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Infinite Series ◽  
Numerical Differentiation ◽  
The Other ◽  
Asymptotic Formulas ◽  
Inviscid Fluid ◽  
Interaction Forces ◽  
Added Masses ◽  
Two Bodies

An integral-equation procedure has been developed to determine interaction forces on two bodies approaching central impact in an inviscid fluid. The accuracy of the results from that procedure is evaluated by applying it to a pair of circles and a pair of spheres for which exact solutions are available. A second purpose was to refine the procedure so that accurate solutions could be obtained at closer distances between the bodies. In the first part of this work, the classical theory is extended by deriving truncation corrections for the infinite series representing the exact solution and asymptotic formulas for computing interaction forces at small gaps. In the second part, two problems were resolved: one on the treatment of the sharp peaks of the integrands when the gap between the bodies was small, the other on reducing the errors in the numerical differentiation required to evaluate the forces. Results for various combinations of circle pairs, for equal spheres, and for an elliptical cylinder approaching a circular one are presented. A new relation between the interaction forces on a wall and on a body moving normal to it is presented. Addendum published in 1994 Volume 38, Issue 2 (June), pages 172–173, is included.

Exploring the performances of the dual technique-based water hammer redesign strategy in water supply systems

2019 ◽  
Vol 69 (1) ◽  
pp. 6-17 ◽  
Author(s):  
Mounir Trabelsi ◽  
Ali Triki
Keyword(s):  
Pressure Wave ◽  
Oscillation Period ◽  
Conventional Technique ◽  
Water Hammer ◽  
Water Supply Systems ◽  
Piping System ◽  
Wave Oscillation ◽  
Pressure Surge ◽  
Short Section ◽  
Steel Piping

Abstract This paper explored and compared the effectiveness of the inline and branching redesign strategies-based dual technique, implemented to enhance the conventional technique skills in terms of attenuation of positive and negative pressure surge magnitudes and limitation of the spreading of pressure wave oscillation period. Basically, this technique is based on splitting the single inline or branched plastic short-section, used in the conventional technique, into a couple of two sub-short-sections made of two distinct plastic material types. Investigations addressed positive and negative surge initiated water hammer events. Additionally, high and low density polyethylene materials were utilized for sub-short-section material. Results illustrated the reliability of the dual technique in protecting hydraulic systems from excessive pressure rise and drop, and evidenced that the (HDPE/LDPE) sub-short-sections' combination (where the former sub-short-section is attached to the sensitive region of the steel piping system parts, while the latter is attached to the second extremity of the steel piping system) is the most prominent configuration providing the best trade-off between pressure surge attenuation, and pressure wave oscillation period spreading. Lastly, it was found that the pressure head peak (or crest) and the pressure wave oscillation period values were markedly sensitive to the (HDPE) sub-short-section length and diameter.

scholarly journals Analysis of Water Hammer with Different Closing Valve Laws on Transient Flow of Hydrogen-Natural Gas Mixture

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Norazlina Subani ◽  
Norsarahaida Amin
Keyword(s):  
Natural Gas ◽  
Pressure Wave ◽  
Transient Flow ◽  
Water Hammer ◽  
Wave Profile ◽  
Maximum Pressure ◽  
Gas Mixture ◽  
Pressure Waves ◽  
Closing Time ◽  
Closure Laws

Water hammer on transient flow of hydrogen-natural gas mixture in a horizontal pipeline is analysed to determine the relationship between pressure waves and different modes of closing and opening of valves. Four types of laws applicable to closing valve, namely, instantaneous, linear, concave, and convex laws, are considered. These closure laws describe the speed variation of the hydrogen-natural gas mixture as the valve is closing. The numerical solution is obtained using the reduced order modelling technique. The results show that changes in the pressure wave profile and amplitude depend on the type of closing laws, valve closure times, and the number of polygonal segments in the closing function. The pressure wave profile varies from square to triangular and trapezoidal shape depending on the type of closing laws, while the amplitude of pressure waves reduces as the closing time is reduced and the numbers of polygonal segments are increased. The instantaneous and convex closing laws give rise to minimum and maximum pressure, respectively.

A Review of Water Hammer Theory and Practice

2005 ◽  
Vol 58 (1) ◽  
pp. 49-76 ◽  
Author(s):  
Mohamed S. Ghidaoui ◽  
Ming Zhao ◽  
Duncan A. McInnis ◽  
David H. Axworthy
Keyword(s):  
Numerical Solutions ◽  
Practical Interest ◽  
Water Hammer ◽  
Theory And Practice ◽  
Full Description ◽  
Turbulence Structure ◽  
Two Dimensional ◽  
Hydraulic Transients ◽  
Research And Practice ◽  
One Dimensional

Hydraulic transients in closed conduits have been a subject of both theoretical study and intense practical interest for more than one hundred years. While straightforward in terms of the one-dimensional nature of pipe networks, the full description of transient fluid flows pose interesting problems in fluid dynamics. For example, the response of the turbulence structure and strength to transient waves in pipes and the loss of flow axisymmetry in pipes due to hydrodynamic instabilities are currently not understood. Yet, such understanding is important for modeling energy dissipation and water quality in transient pipe flows. This paper presents an overview of both historic developments and present day research and practice in the field of hydraulic transients. In particular, the paper discusses mass and momentum equations for one-dimensional Flows, wavespeed, numerical solutions for one-dimensional problems, wall shear stress models; two-dimensional mass and momentum equations, turbulence models, numerical solutions for two-dimensional problems, boundary conditions, transient analysis software, and future practical and research needs in water hammer. The presentation emphasizes the assumptions and restrictions involved in various governing equations so as to illuminate the range of applicability as well as the limitations of these equations. Understanding the limitations of current models is essential for (i) interpreting their results, (ii) judging the reliability of the data obtained from them, (iii) minimizing misuse of water-hammer models in both research and practice, and (iv) delineating the contribution of physical processes from the contribution of numerical artifacts to the results of waterhammer models. There are 134 refrences cited in this review article.

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