Damping Of Pressure Waves Research Articles

On Sources of Damping in Water-Hammer

Various potential causes of damping of pressure waves in water-hammer-like flows are discussed, with special attention being paid to their qualitative influences on measured pressure histories. A particular purpose is to highlight complications encountered when attempting to interpret causes of unexpected behaviour in pipe systems. For clarity, each potential cause of damping is considered in isolation even though two or more could exist simultaneously in real systems and could even interact. The main phenomena considered herein are skin friction, visco-elasticity, bubbly flows and porous pipe linings. All of these cause dispersive behaviour that can lead to continual reductions in pressure amplitudes. However, not all are dissipative and, in such cases, the possibility of pressure amplification also exists. A similar issue is discussed in the context of fluid–structure interactions. Consideration is also given to wavefront superpositions that can have a strong influence on pressure histories, especially in relatively short pipes that are commonly necessary in laboratory experiments. For completeness, attention is drawn towards numerical damping in simulations and to a physical phenomenon that has previously been wrongly cited as a cause of significant damping.

Modeling Transient Pipe Flow in Plastic Pipes with Modified Discrete Bubble Cavitation Model

Most of today’s water supply systems are based on plastic pipes. They are characterized by the retarded strain (RS) that takes place in the walls of these pipes. The occurrence of RS increases energy losses and leads to a different form of the basic equations describing the transient pipe flow. In this paper, the RS is calculated with the use of convolution integral of the local derivative of pressure and creep function that describes the viscoelastic behavior of the pipe-wall material. The main equations of a discrete bubble cavity model (DBCM) are based on a momentum equation of two-phase vaporous cavitating flow and continuity equations written initially separately for the gas and liquid phase. In transient flows, another important source of pressure damping is skin friction. Accordingly, the wall shear stress model also required necessary modifications. The final partial derivative set of equations was solved with the use of the method of characteristics (MOC), which transforms the original set of partial differential equations (PDE) into a set of ordinary differential equations (ODE). The developed numerical solutions along with the appropriate boundary conditions formed a basis to write a computer program that was used in comparison analysis. The comparisons between computed and measured results showed that the novel modified DBCM predicts pressure and velocity waveforms including cavitation and retarded strain effects with an acceptable accuracy. It was noticed that the influence of unsteady friction on damping of pressure waves was much smaller than the influence of retarded strain.

Effect of an entrapped air pocket on hydraulic transients in pressurized pipes

The current research focuses on the analysis of different dynamic effects of an air pocket located at mid-pipe length on transient pressures based on experimental data. Different flow rates and air pocket volumes are analysed. Several features are identified in the pressure-head signal associated with the air pocket: initial pressure drop, higher maximum overpressure peaks, increased pressure wave damping and delay. These features result from the superposition of pressure waves associated with the entrapped air contraction and expansion. Smaller air pockets generate minor reflections, whereas larger air-pockets tend to disperse and artificially attenuate maximum pressures. Video recording images of the air pocket during the transient event allow observation of two types of behaviour: one associated with lower transients, characterized by an air pocket volume variation with a clear air–water interface; and another one associated with more severe transients in which air mixes with water. Finally, there is a critical air pocket volume, independent of the initial flow rate, that leads to the highest overpressures.

Effect of integrating polymeric pipes on the pressure evolution and failure assessment in cast iron branched networks

Pressure response and structural integrity assessment of cast iron and HDPE pipes were investigated in this study. The failure analysis of pipes in a branched network was considered taking into consideration the maximum stress generated by hydraulic transient events and the presence of an initial external semi-elliptical defect. The numerical study was conducted based on a developed non-conventional transient solver that incorporates the viscoelasticity of polymeric pipes. Considering the replacement of pipes located in sensitive zones with high-density polyethylene (HDPE) pipes, the pressure evolution of the network was evaluated for different network states at different locations. The integration of polymeric pipes in the originally cast-iron network provided remarkable pressure wave damping and dispersing in some locations. Since the failure of pipes with a corrosion crater is likely to occur when the admissible stress is reached, a structural integrity analysis was conducted. Failure Assessment Diagram (FAD) using the SINTAP code was considered to calculate the safety factors for cast iron pipes with different metallic-plastic combinations, whereas a semi-empirical model that calculates the J-integral is used for HDPE pipes. The results of this study conclude that high attention should be paid when a longitudinal crack is located in the pipelines. It may be possible for integrated polymeric pipes to alleviate the risk of failure in the network. However, under large crack geometries, additional measures should be taken.

Simulation of transient flow in viscoelastic pipe networks

The use of polymeric pipes such as polyethylene (PE) and polyvinyl chloride (PVC) has recently increased in water distribution networks. This necessitates the understanding of the viscoelastic behaviour of these pipes in practice and in particular for transient flow analysis. The purpose of this study is to calibrate a developed numerical model based on the experimental results of transient flow in PE pipe networks. The linear viscoelastic model parameters were calibrated using the inverse transient analysis. Comparison of numerical results with experimental data indicated that the developed viscoelastic model was able to predict both pressure wave damping and dispersion in these pipe systems. Results confirmed a negligible viscoelastic effect of single pipe and pipe network on the linear viscoelastic model. Hence, the calibrated results of a single PE pipe were used to simulate the transient flow in the pipe network. The experimental and simulation results of pipe network transient flow in this study are new and advance previous studies.

Compound technique -based inline design strategy for water-hammer control in steel pressurized-piping systems

The inline design strategy was recognized as being an effective tool for water-hammer control in pressurized-pipe flow. Principally, this strategy is based on replacing a short-section of the existing steel-piping system by another made of polymeric material. However, this strategy leads to an excessive radial-strain amplification and a large spread-out of wave oscillation period. Alternatively, an innovative compound technique -based inline design strategy was reported in this paper to enhance the foregoing limitations. The proposed technique is based on splitting the single short-section used in the conventional technique into a couple of two sub short-sections made up of two distinct material types. The materials demonstrated in this study include high- and low-density polyethylene (HDPE) and (LDPE). The transient solver was based on the 1-D unconventional water-hammer model embedding the Vitkovsky et al. and Kelvin-Voigt formulation, while the numerical discretization was performed using the Fixed Gird Method of Characteristics (FG-MOC). The proposed method is validated through a comparison with experimental results. Further, detailed numerical results obtained from several scenarios are presented and discussed. Results illustrated the reliability of the proposed technique in mitigating excessive high- or low-pressures, and evidenced that the (HDPE–LDPE) sub short-sections combination (where the former is attached to hydraulic parts and the latter to the steel pipe) is the most prominent configuration providing an acceptable trade-off between piezometric-head and circumferential-stress attenuation (from one side), and limitation of the excessive spreading of oscillation period and amplification of radial-strain (from the other side). The findings of a parametric study of the sensitivity of pressure wave damping and spreading to the employed short-section length and diameter resulted in estimation of the near-optimal design values of the short-section size.

Pressure wave damping in transonic airfoil flow by means of micro vortex generators

In transonic airfoil flow, pressure waves are generated mainly at the trailing edge and in the case of a shock in the region of the shock/boundary layer interaction. Depending on the Mach number, these waves lead to oscillating shock waves and an unsteady pressure distribution. For a free steam Mach number of M=0.76 and a chord length based Reynolds number of Re=106, micro vortex generators (μVG) are applied to dampen pressure waves. This is studied experimentally in a shock tube and numerically by using a high-order finite difference scheme (under-resolved Direct Numerical Simulation). The agreement of the pressure distribution and Schlieren pictures between simulation and experiment is good. By means of numerical visualizations, instability waves are identified within the separated boundary layer above a marginal boundary layer separation bubble. The applicability of μVG for dampening the pressure waves and stabilizing the flow field is possible and is studied in this paper. By numerical Schlieren pictures and further visualizations, the flow around the VG is characterized. The spanwise oriented instability waves are partly disintegrated which is also confirmed by the analysis of the vorticity. Finally, the nonlinear wave propagation is investigated and an explanation for the typical 1 to 2 kHz pressure oscillation is given.

Experimental study of transient processes in oil pipeline caused by startups of pumping units

The patterns of pressure changes during transients caused by running the pumping unit were determined with the help of processed industrial data after experiments carried out on the main oil pipeline “Druzhba”. It was found out, that the actual value of abruptly changing pressure both on the inlet and outlet of the oil pumping station is 15–23 % less than the theoretically expected value, in particular, half the pressure which is created by the pump started. The actual pressure overload of the linear part of the oil pipeline, caused by running the pumping unit, was analyzed. The exponential dependencies of an abrupt oil pressure change on the distance to the origin of the disturbance were developed. The intensity of damping of high and low pressure waves of the transported oil in the pipeline was assessed. For the oil pipeline, on which the experiments were carried out, the analytical relation was proposed to calculate a coefficient of pressure wave damping as a function of oil flow rate and the Reynolds number in the oil pipeline before the beginning of the transient caused by running the pumping unit. It was determined that the damping coefficients of increased and decreased pressure waves are almost the same for a specific transitional mode of operation of the pipeline.

Unsteady friction and visco-elasticity in pipe fluid transients

The current waterhammer models coupled with friction models cannot adequately represent the pressure wave attenuation observed in real-world pipe systems, because the pressure wave damping is affected by additional effects not accounted for. One such effect is pipe visco-elasticity from the material behaviour of pipe-wall to be investigated herein. The numerical results indicate that the pressure head attenuation attributable to unsteady friction is comparable to the visco-elastic effect during the initial transient stage, while the visco-elastic effect becomes dominant both in terms of damping and phase shift at later stages. An analytical analysis shows that the visco-elastic effect is more critical if the visco-elastic retardation time is less than the wave travel time along the entire pipeline length. In addition, it is demonstrated that the visco-elastic term in waterhammer models is wrongly referred to in the literature as energy dissipation instead of energy transfer between fluid and pipe-wall by the work done by the pressure force.

Damping of pressure waves in visco-elastic, saturated bubbly magma

Abstract The attenuation of pressure waves in a saturated bubbly magma is examined in a model, coupling seismic wave-propagation with bubble growth dynamics. This model is solved analytically and numerically, including effects of diffusion of volatiles, visco-elasticity and bubble number density. We show that wave attenuation is controlled mainly by the Peclet and Deborah numbers. The Peclet number is a measure of the relative importance of advection to diffusion. The Deborah number is a visco-elastic measure, describing the importance of elasticity in comparison to viscous melt deformation. We solve numerically for wave attenuation for various magma properties corresponding to a wide range of Peclet and Deborah numbers. We show that the numerical solution can be approximated quite well for frequencies above 1 Hz, by an analytical end-member solution, obtained for high Peclet and low Deborah numbers. For lower frequencies, volatile transport should be accounted for, leading to higher attenuation with respect to the analytical solution. However, if the Deborah number is increased, either by longer relaxation time or by higher frequencies, then attenuation decreases with respect to the analytical solution. Therefore, visco-elasticity leads to a significant improvement of the resonating qualities of a magma-filled conduit and widens the depth and frequency ranges where pressure waves will propagate efficiently through the conduit.

Friction relaxation model for fast transient flows application to water hammer in two-phase flow – The WAHA code

The paper deals with the problem of the wall shear stress during rapid transient 1D flows in a piping system caused by water hammers in two-phase flow induced by a fast valve closure. The evolution of the transient wall shear stress is interpreted in terms of two steps. The first step is a sudden and dramatic change of the wall shear stress due to the passage of the pressure wave. The second step is a relaxation process of the shear stress which is modeled from the Extended Irreversible Thermodynamics theory. The friction relaxation model (FRM) presented in the first part of this paper describes both steps of the evolution of the wall shear stress during water hammers. The second part of the paper deals with the application of the FRM model as a closure law in the WAHA code. The main purpose of the WAHA code is to predict various situations relative to single- and two-phase water hammer transients in piping systems. The last part of the paper deals with the simulation of several cases from the UMSICHT databank using the adapted WAHA computer code with the FRM model. The results of these simulations are systematically compared with the experimental data. It is concluded that the new FRM model has a clear effect on water hammer pressure wave damping and on the pressure wave propagation velocity.

Pressure-wave damping in a liquid with bubbles produced by two kinds of gases

Pressure-wave damping in a liquid with bubbles produced by two kinds of gases

Efficient computation of a mathematical model for the damping of pressure waves in tubes of circular form

AbstractA computational method for a system of partial integrodifferential equations of Volterra type is developed. These equations describe the damping of pressure waves in tubes of circular form, taking into account the nonstationary increase of friction. The analytical solution of the model equations is given. A rapidly convergent expansion as well as sharp error estimates for the approximate solutions are obtained. Finally an efficient algorithm using recursion formulas is presented and the algorithm is compared numerically with the method of characteristics. © 1995 John Wiley & Sons, Inc.

Spectral distortions of the microwave background radiation resulting from the damping of pressure waves

view Abstract Citations (108) References (28) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Spectral Distortions of the Microwave Background Radiation Resulting from the Damping of Pressure Waves Daly, R. A. Abstract Initial inhomogeneities of the energy density of the primeval radiation field which enter the horizon prior to recombination lead to the formation of pressure waves as they enter the horizon. On scales less than about 5 × 1016 M_s these waves will be damped prior to recombination by the processes of nonlinear dissipation and photon diffusion. The damping of these waves leaves its signature in spectral distortions of the microwave background radiation. The type of distortion depends upon the epoch of the damping. The magnitude of the distortion may be related to the amplitude of the waves which have been damped during a particular epoch. The amplitude of the perturbations of the energy density of the radiation field on a given scale may be related to those of the mass distribution on the same scale, in a manner which depends on whether the perturbations are of the isocurvature or adiabatic type. The limit on the amplitude of the initial perturbations of the mass distribution on the damping scale is used in conjunction with that on a much larger scale: the amplitude of the initial perturbations of the mass distribution needed to account for the observed variance of the number counts of galaxies at the current epoch, which depends on cosmological parameters. Combining these, an upper bound to the index of the initial power spectrum of the mass distribution is obtained. This bound depends on cosmological parameters, and on whether the initial perturbations are of the isocurvature or adiabatic type. The current and projected limits of the magnitude of the Compton y-parameter and of a chemical potential are used to constrain the index of the initial power spectrum of the mass distribution for several cosmological parameter sets for isocurvature and adiabatic perturbations. Publication: The Astrophysical Journal Pub Date: April 1991 DOI: 10.1086/169866 Bibcode: 1991ApJ...371...14D Keywords: Astronomical Spectroscopy; Damping; Elastic Waves; Microwaves; Relic Radiation; Universe; Computational Astrophysics; Mass Distribution; Perturbation Theory; Photons; Power Spectra; Radiation Distribution; Astrophysics; Damping; Relic Radiation; Power Spectra; Cosmic Background Radiation; Cosmology; Early Universe; Wave Motions full text sources ADS |

Pressure wave damping in branched pipes with arbitrary angles

Strong pressure waves may occur frequently as undesired phenomena leading to high loading on piping systems of nuclear power plants and chemical industries. This is occasionally observed when piping systems of different pressures are suddenly and unforeseenly connected together producing pressure or even shock waves. For an unsymmetrical branched channel, as a simple geometrical model of a complete piping system, the attenuation of shock waves is calculated. This calculation is based on the fluid-in-cell method for an unsteady, two-dimensional flow. The results agree with experiments and serve as a check for the applicability of earlier models.

Arterial stenosis: an experiment to determine how best to quantify the hydraulic effects of a stenosis

The hydraulic effects of arteriosclerosis in major arteries are difficult to evaluate, and conclusions based on measurements of mean flow are often contradictory. In a model, which represents ideal circumstances, the hydraulic effects of stenoses have been quantified in terms of several indices. Indices based on measurements of input impedance and pressure wave damping were the most sensitive to changes in the degree of stenosis whilst mean flow was insensitive to all but the most severe constrictions.

Gas Release During Transient Cavitation in Pipes

Some applications are presented of a mathematical model concerning water hammer and release of dissolved gas in pipelines in the case where the pressure drops to the vapor pressure of the liquid transported. Column separation and cavitation in extensive parts of the pipeline, referred to as cavitating flow, are dealt with. A smoothing procedure is adopted in order to suppress nonlinear instability. Gas release is found to cause some damping of pressure waves in cases where only cavitating flow occurs. Gas release at a column separation cavity tends to increase the duration of column separation, whereas gas release in a possible cavitating flow region adjacent to the separation diminishes this duration, thus causing considerable damping of pressure peaks following subsequent column separations. Good agreement is obtained with experimental results available in the literature. Further experimentation is required as regards the parameters on which gas release depends.

Oscillatory Burning of Solid Propellants including Gas Phase Time Lag

An analysis has been performed for oscillatory burning of solid propellants including gas phase time lag. The gaseous flame is assumed to be premixed and laminar with a one-step overall chemical reaction. The propellant is assumed to decompose according to the Arrenhius Law, with no condensed phase reaction. With this model, strong gas phase resonance has been found in certain cases at the characteristic gas-phase frequencies, but the peaking of the acoustic admittance is in the direction favoring the damping of pressure waves. At still higher frequencies, moderate wave-amplifying ability was found. The limit of low frequency response obtained previously by Denison and Baum was recovered, and the limitations of the quasi-steady theory were investigated.