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.

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.

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.

scholarly journals Pressure Wave Transmission in a Fluid Contained in a Plastically Deforming Pipe

1974 ◽  
Vol 96 (4) ◽  
pp. 258-262 ◽  
Author(s):  
G. L. Fox ◽  
D. D. Stepnewski
Keyword(s):  
Plastic Deformation ◽  
Pressure Wave ◽  
Pipe Wall ◽  
Experimental Tests ◽  
Elastic Wave Velocity ◽  
Wave Transmission ◽  
Pressure Waves ◽  
Transient Pressure ◽  
Cooling Systems ◽  
Wall Deformation

The transmission of high pressure pulses through piping loops such as reactor cooling systems is usually studied with water hammer analysis techniques. Conventional wave analysis includes only elastic pipe wall deformation. However, plastic deformation of the pipe wall is effective in reducing the magnitude of transmitted pressure waves if the pressure is of sufficient magnitude to cause plastic yielding. This effect can be treated using a one-dimensional dynamic analysis by noting the similarity between the equations describing pressure wave induced plastic deformation in a solid bar and wave transmission causing plastic strain in a fluid filled pipe. The results of the analysis show that at fluid pressures less than the pipe yield pressure, waves are transmitted at elastic wave velocity; however, at pressures which exceed the pipe yield point, wave velocities are substantially reduced and the waves are dispersed. These results demonstrate that plastic deformation from transient pressure loading is limited to a relatively short length of piping near the source of the pressure pulse. The significance of this behavior with respect to reactor cooling systems is that pressures above those causing yield are not transmitted to primary loop components such as pumps and heat exchangers. The theoretical results are compared with experimental tests and show reasonable agreement.

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.

Lung-Air-Sac Anatomy and Respiratory Pressures in the Bird

1972 ◽  
Vol 57 (2) ◽  
pp. 543-550
Author(s):  
JOHN H. BRACKENBURY
Keyword(s):  
Steady State ◽  
Tidal Volume ◽  
Pressure Wave ◽  
Airway Resistance ◽  
Equilibrium Distribution ◽  
Wave Form ◽  
Pressure Waves ◽  
Air Sacs ◽  
Maximum Value ◽  
Respiratory Phase

1. Regardless of its tidal volume an individual air sac shows a respiratory pressure-wave which is similar to that of every other sac. These is a process of pressure equilibration within the lung-air-sac system involving very short-lived streams of air between air sacs, whose significance becomes larger as pressure accelerations become bigger; and when a steady state has been achieved in any respiratory phase the pressure wave becomes normalized in all parts of the system. 2. Small pressure differentials between sacs are part of the equilibrium distribution of pressure within the lung-air-sac system. They result from differences in the resistance path through the lung to each sac, and differences in their respective tidal volumes. Their wave-form closely resembles that of the parent pressure waves and has a maximum value of one-tenth their value. 3. In general, the bronchial pathways to the posterior sacs have greater resistances to air flow than those to the anterior sacs. 4. During vocalization pressures in the coelom and air sacs exceed normal respiratory pressures by about 40 times. Airway resistance vastly increases as the syringeal membranes begin to vibrate.

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: 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.

scholarly journals Short-term Variations in Strain and Surface Tilt on Storglaciären, Kebnekaise, Northern Sweden

1989 ◽  
Vol 35 (120) ◽  
pp. 201-208 ◽  
Author(s):  
Peter Jansson ◽  
Roger LeB. Hooke
Keyword(s):  
Water Pressure ◽  
High Water ◽  
Ice Thickness ◽  
Gradual Change ◽  
Short Term ◽  
Glacier Surface ◽  
Vertical Movements ◽  
Bed Topography ◽  
The Waves ◽  
Local Uplift

AbstractTiltmeters that can detect changes in slope of a glacier surface as small as 0.1 μ rad have been used on Storglaciären. The records obtained to date have been from the upper part of the ablation area, where the bed of the glacier is overdeepened. A total of 82 d of records has been obtained for various time periods between early June and early September.There is generally a gradual change in inclination of the glacier surface over periods of several days, but these changes do not appear to be systematic. In particular, they are not consistent with vertical movements of stakes located 2–3 ice thicknesses away from the tiltmeters. This suggests that the tiltmeters are sensing disturbances over areas with diameters comparable to the local ice thickness.Superimposed on these trends are diurnal signals suggesting rises and falls of the surface just up-glacier from the riegel that bounds the overdeepening on its down-glacier end. These may be due to waves of high water pressure originating in a crevassed area near the equilibrium line. If this interpretation is correct, the waves apparently move down-glacier at speeds of 20–60 m h−1and become sufficiently focused, either by the bed topography or by conduit constrictions, to result in local uplift of the surface. Also observed are abrupt tilts towards the glacier center line shortly after the beginning of heavy rainstorms. These appear to be due to longitudinal stretching as the part of the glacier below the riegel accelerates faster than that above. Water entering the glacier by way of a series of crevasses over the riegel is believed to be responsible for this differential acceleration. In June 1987, a dramatic event was registered, probably reflecting the initial summer acceleration of the glacier.

An experimental investigation of the nature and origin of microseisms at St. Louis, Missouri

1940 ◽  
Vol 30 (2) ◽  
pp. 139-178
Author(s):  
J. Emilio Ramirez
Keyword(s):  
Wave Length ◽  
Vertical Axis ◽  
The Other ◽  
Wave Form ◽  
Stationary Waves ◽  
Retrograde Motion ◽  
Time Signals ◽  
Group Form ◽  
Triangular Network ◽  
The Waves

Summary Over a period of six months, from July to December, 1938, an investigation on microseismic waves has been carried out in the Department of Geophysics of St. Louis University. Four electromagnetic seismographs, specially designed for recording microseisms, were installed in the city of St. Louis in the form of a triangular network. Two of these were E-W components, one at the St. Louis University Gymnasium and the other 6.4 km. due west at Washington University. The other two were arranged as N-S components, one at the St. Louis University Gymnasium and one 6.3 km. due south at Maryville College. The speed of the photographic paper was 60 mm/min., and time signals were recorded automatically and simultaneously on each paper from the same clock every minute and at shorter intervals from a special pendulum and “tickler” combination by means of telephone wires. The results have demonstrated beyond doubt that microseismic waves are traveling and not stationary waves. The same waves have been identified at each one of the stations of the network, and also at Florissant, 21.8 km. away from St. Louis University. The speed of microseismic waves at St. Louis was determined from several storms of microseisms and it was found to be 2.67±0.03 km/sec. The direction of microseisms was also established for most of the storms and it was found that about 80 per cent of incoming microseisms at St. Louis were from the northeast quadrant during the interval from July to December, 1938. No microseisms were recorded from the south, west, or southwest. The period of the waves varied between 3.5 and 7.5 sec. The average period was about 5.4 sec. The microseismic wave length was therefore of the order of 14¼ km. A study of the nature of microseismic waves from the three Galitzin-Wilip components of the Florissant station reveals in the waves many of the characteristics of the Rayleigh waves; that is, the particles in the passage of microseismic waves move in elliptical orbits of somewhat larger vertical axis and with retrograde motion. A comparison carried over a period of more than a year between microseisms and microbarometric oscillations recorded by specially designed microbarographs showed no direct relationship between the two phenomena in wave form, group form, period, or duration of storms. The source of microseisms is to be found not over the land, but rather out over the surface of the ocean. The amplitudes of microseisms depend only on the intensity and widespread character of barometric lows traveling over the ocean. Several correlations between the two phenomena seem to make this conclusion rather evident. Special emphasis is laid on the fact that all the determined directions of incoming microseisms at St. Louis point to a deep barometric low over the ocean. The period of microseisms seems to be a function of the distance between the station and the source of microseisms. The exact mechanism by which barometric lows over the ocean water result in the production of microseisms needs further investigation. Large microseisms have been produced without any indication of surf near the coasts, or with winds blowing from the land toward the ocean.

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