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Due to the high technical and hydraulic performance and negligible environmental adverse impact of a porous weir, this structure is a reasonable substitute for conventional impermeable solid weirs in water transmission and distribution systems. This research focused on the hydraulic performance of porous broad-crested weirs (PBCWs) with sloping crests. To this end, 30 PBCWs models in free and submerged flow conditions were designed and examined under different operation conditions. In particular, a comparative study was performed between PBCWs with and without sloping crests, the performance of which were then compared with a solid broad-crested weir (SBCW) model. Based on the results and analysis, the PBCWs with sloping crests have a more significant discharge coefficient than common PBCWs (without sloping crests), and the upstream slope has a more significant impact on the discharge coefficient than the downstream slope. In addition, the PBCWs with sloping crests are more sensitive to tailwater than common PBCWs, and thus the discharge reduction factor of the weir with the upstream crest slope is lower than that of the downstream. Finally, based on the extensive experimental results, both nonlinear multi-variable regression and gene-expression programming approaches were applied to extract empirical equations for expressing the free flow discharge coefficient and submerged flow discharge reduction factor.

The optimal operation of water distribution systems is complicated due to multiple objectives that are in conflict, such as water quality versus cost. This work proposes to combine Strength Pareto ...

In this study, by calibrating creep coefficients using two methods of creep function and transient pressure, the effect of Kelvin-Voigt elements on creep behavior and pressure fluctuations is inves...

The renewable energy protocol in the world pushed most countries to extensive use of renewable energy sources, in exchange for a reduction of energy from conventional sources. In this article, the possibilities of exchange the water hammer energy to a column of water pressure evaluated experimentally. For this purpose, a ram pump made by two-inch internal diameter. Results indicated that ram pump power such as relative useful power (Pd/PT) and relative waste power (Pw/PT) were depended to length to diameter ratio of drive pipe (L/D), the relative energy due to steady flow velocity and impulse valve features (Ea/Ei), and the ratio of required pumping energy to maximum energy of water hammer (Ep/Em). The results showed that the mountainous area has potential to generate energy from water hammer as renewable energy, for a water system in highland that continuously needs to pumping water. Keywords: Ram pump, Power, Renewable energy, Water hammer, Impulse valve

This paper proposes a novel strategy to localize anomalies in the arterial network based on its response to controlled transient waves. The idea is borrowed from system identification theories in which wave reflections can render significant information about a target system. Cardiovascular system studies often focus on the waves originating from the heart pulsations, which are of low bandwidth and, hence, can hardly carry information about the arteries with the desired resolution.Our strategy uses a relatively higher bandwidth transient signal to characterize healthy and unhealthy arterial networks through a frequency response function (FRF). We tested our novel approach on data simulated using a one-dimensional cardiovascular model that produced pulse waves in the larger arteries of the arterial network. Specifically, we excited the blood flow from the brachial artery with a relatively high bandwidth flow disturbance and collected the subsequent pressure waveform at peripheral positions. To better differentiate FRFs of healthy and unhealthy networks, we used a FRF that removes the effects of heart pulsations.Results demonstrate the ability of the proposed FRF to detect and follow-up on the development of a common carotid artery (CCA) stenosis. We tested distinct geometrical variations of the stenosis (size, length and position) and observed differences between the FRFs of healthy and unhealthy networks in all cases; such differences were mainly due to geometrical variations determined by the stenosis.We have provided a theoretical proof of concept that demonstrates the ability of our novel strategy to detect and track the development of CCA stenosis by using peripheral pressure waves that can be measured non-invasively in clinical practice.

This paper applies the matched-field processing (MFP) method to leakage localization in a viscoelastic pipe. The viscoelasticity of pipe wall is included in the governing equations of transient wave via the generalized Kelvin-Voigt model and its effect is finally translated into a frequency-dependent wave speed. Then, a leak is localized by MFP via a 1D search of leak location along the pipe, independent of the leak size. Transient experiments with viscoelastic pipe in the Water Engineering Laboratory at University of Perugia and in the Water Resources Research Laboratory at Hong Kong University of Science and Technology are studied. Experimental results demonstrate that the inclusion of pipe wall viscoelasticity and using more frequencies (instead of using only resonant frequencies) improve significantly the leak localization accuracy. It is shown that the MFP leak localization is accurate even for a small leak (the flow ratio of leak and main pipe is approximately 10%) in a noisy environment: among 50 transient experiments, the maximum error of MFP leak localization is only 1.14 m and in the other 49 experiments the error is always lower than 1 m.

The aim of the present research is to quantify the maximum feasible accuracy (location and size) for the transient-based blockage detection in a water supply pipeline. Owing to the randomness of transient measurements, a performance bound for the extended blockage detection exists which estimated parameters cannot exceed. The Cramér–Rao lower bound (CRLB) theorem is utilized to compute the lower bound variance of noise-induced estimation errors. It gives the minimum mean square error of any estimator according to information obtained from measurements and quantified by Fisher information. The Fisher information matrix is computed using direct differentiation of the compatibility equations obtained by the method of characteristics. The influence of relevant physical parameters including valve closure time, measurement time length and noise level on the best possible localization of blockage is investigated. The connection between the signal bandwidth, noise level and the performance limit is quantified for a typical case study. The results demonstrate trade-off between the size and the location/length of blockage estimates subject to different maneuver times, roughly offering half the wave speed times maneuver duration as the resolution limit.

The leak-induced reflection information forms the basis of developing and applying transient-based leak detection methods in water-filled pipelines. The transient reflection method (TRM) has been widely incorporated in various leakage problems, and affecting parameters in the process are closely investigated in specific cases. However, the TRM literature lacks a global assessment of the relative importance of each parameter for a general inference on the contribution of each independent variable to the desired reflection criterion, which assists in leakage management. Besides, in the majority of previous studies, the leak-induced reflection wave at the measurement point is approximated by that at the leaky point, i.e., the propagation behavior and process of the reflected wave from the potential leak location to measurement point is ignored, leading to inaccuracy in sizing potential leaks by the TRM. To resolve these issues, this study firstly derives the leak-induced reflection coefficient at the measurement point by incorporating the additional damping effect of the reflection wave propagation process along the pipeline, which is then fully validated by MOC-based numerical and experimental laboratory applications. To further understand the contribution of different factors in the derived reflection coefficient, a systematic analysis is conducted based on dimensional analysis and extensive numerical simulations. The obtained results are characterized by the dominance analysis so as to explore the importance ranking of different dimensionless factors to the leak-induced reflection coefficient in the pipeline system. The analysis results indicate that, amongst all the dimensionless parameters, the leak factor provides the largest influence and contribution to the wave reflection coefficient (with about 40% contribution), followed by the transient intensity (23%) and initial system and flow conditions (20%), and lastly the measurement distance from leak location (17%). The finding of this study is helpful in leakage management as it aims to understand and explain the applicability and effectiveness of the TRM under different conditions.

Despite preceding studies of transients in non-Newtonian fluids that use two-dimensional (2D) models to predict the velocity gradient required to estimate unsteady losses, this study propos...

This paper investigates the effect of fluid-structure interaction (FSI) on the efficiency of transient-based reflections analysis (TBRA) applied to the detection of extended deteriorations in a reservoir-pipe-valve system. A waterhammer-with-FSI solver, based on the method of characteristics (MOC) and the finite-element method (FEM), is used and validated against available numerical and experimental results. Analytical expressions for the magnitudes of pressure reflections caused by FSI are derived. They tell how the system parameters affect FSI. The results obtained for the considered situation reveal that both pipe wall vibration (FSI) and pipe wall deteriorations may affect transient pressure in a similar, and possibly indistinguishable, way. Neglecting FSI in TBRA would skew the estimated locations, lengths, and numbers of the deteriorations in systems with considerable pipe wall axial vibration, thus making TBRA a more complicated method in flexible pipe systems.

Fluid–Structure Interaction (FSI) in pipes can significantly affect pressure fluctuations during water hammer event. In transmission pipelines, anchors with axial stops have an important role in the waterhammer-induced FSI as they can suppress or allow the propagation of additional stress waves in the pipe wall. More specifically, a reduction in the number of axial stops and/or their stiffness causes significant oscillations in the observed pressure signal due to the enhancement of Poisson’s coupling. To confirm these physical arguments, this research conducts experimental investigations and then processes the collected pressure signals. The laboratory tests were run on an anchored pipeline with multiple axial supports which some of them removed at some sections to emerge Poisson’s coupling. The collected pressure signals are analyzed in the time and frequency domain in order to decipher fluctuations that stem from Poisson coupling and other anchors effects. The analysis of the laboratory data reveals that the pattern of the time signals of pressure is primarily affected by the stiffness and location of the supports. Likewise, the properties of structural boundaries characterize the frequency spectrum of the transient pressures, which is manifested by altering the amplitudes corresponding to dominant frequencies of the system. The study is of particular importance in practice of transient based defect detections and pipe system design.

This study offers a vast improvement to the established Matched Field Processing (MFP) method for leak identification in terms of its versatility to pinpoint leaks with a single spatial measurement. All the previous schemes require at least two measurement signals of pressure head as well as transient signal of the upstream flow rate so as to render a solution to the leak identification problem. This study reformulates the one-dimensional identification procedure so that localization can be accomplished using a single spatial measurement. The numerical results convincingly demonstrate that the new method outweighs the conventional one as it provides a smoother objective function and hence robust to identify leaks using observations of greater noise levels. Checked against two recent laboratory experiments, the proposed method gave satisfactory localization to both of which. The new scheme can provide an improved (both in terms of efficiency and accuracy) initial estimate to the multidimensional optimizations required to localize multiple leaks.

This paper addresses leak detection in the presence of measurement noise using the inverse transient method (ITM). The unknown leak parameters are determined by optimizing a merit function,...

Due to random noise in real measurements, leak detection (estimation of leak size and location) is subject to a degree of uncertainty. This paper provides a framework to investigate the low...

Waterhammer induced fluid–structure interaction (FSI) of a leaky viscoelastic (VE) pipe is simulated in the frequency-domain. The developed model is then applied to assess the accuracy of leak detection when both FSI and VE phenomena are represented. FSI arises due to the coupling of wall stress and pressure waves, which can significantly distort the response spectra. The frequency response of the transient waves is derived using the transfer matrix method, which is then exploited for localization using a maximum likelihood estimate. Several numerical cases including one or two leaks are studied while Poisson and junction coupling both with and without VE wall behaviour. The results demonstrate that including FSI effects can allow leaks to be more accurately located. Not surprisingly, the importance of FSI mechanisms in leak detection is shown to be more crucial in VE pipes than in elastic pipes because of their larger Poisson effects.

A sudden change in the flow rate brings about significant pressure oscillations in the piping system, known as water hammer (fluid hammer). Unsteady flow of a non-Newtonian fluid due to instantaneous valve closure is studied. Power law and Cross models are used to simulate non- Newtonian effects. Firstly, the appropriate governing equations are derived and then, they are solved by a numerical approach. A fourth-order Runge-Kutta scheme is used for the time integration, and the central difference scheme is employed for the spatial derivatives discretization. To verify the proposed mathematical model and numerical solution, a comparison with corresponding experimental results from the literature are made. The results reveal a remarkable deviation in pressure history and velocity profile with respect to the water hammer in Newtonian fluids. The significance of the non-Newtonian fluid behaviour is manifested in terms of the drag reduction and line packing effect observed in the pressure history results. A detailed discussion regarding the fluid viscosity and its shear-stress diagrams are also included. Nenadna sprememba pretoka v cevovodu povzroči velika tlačna nihanja, ki so znana pod imenom vodni (hidravlični) udar. V predstavljeni študiji je bil preučen laminarni prehodni tok nenewtonske tekočine, ki se pojavi zaradi hipnega zapiranja ventila. Za simulacijo nenewtonskih vplivov so bili uporabljeni Crossovi modeli in potenčni zakon. Delo podaja razširitev klasičnega modela vodnega udara, ki se uporablja za preučevanje prehodnih pojavov v newtonski tekočini v ravni elastični cevi, podprti pri ventilu in z zadostnim številom podpor vzdolž cevovoda za preprečitev interakcij med tekočino in konstrukcijo. V ta namen so bile izpeljane kvazidvodimenzionalne enačbe vodnega udara za nenewtonske tekočine in razrešene s primernim numeričnim postopkom na podlagi metode končnih razlik. Za integracijo sistema enačb v času je bila uporabljena shema Runge-Kutta četrtega reda. Prostorski odvodi so bili diskretizirani s centralno diferenčno shemo. Za odpravo numeričnih nihanj so bili dodani disipativni členi drugega reda. Ti členi učinkujejo samo v območju velikih gradientov, v gladkih območjih pa so praktično izključeni.

Fluid-structure interaction (FSI) during water hammer in a viscoelastic (VE) pipe is studied in the frequency domain. The main aim is to investigate pressure and stress waves using Transfer Matrix Method (TMM) in a typical reservoir-VE pipe-valve (RPV) system. Both major coupling mechanisms namely Poisson and junction are taken into account. The generalized Kelvin-Voigt model simulates VE behavior during water hammer, which is generated by a quick closing/opening of downstream valve. The effect of viscoelasticity is modeled by Volterra integrals (in time) which are written as the products of transforms of the creep function and pressure (or stress) in the Laplace domain. The developed formulation is adopted to solve two well-known FSI problems from literature, and both demonstrate favorable agreement with available analytical and experimental data. To investigate the sole/simultaneous effect of Poisson and/or junction coupling and viscoelasticity, a hypothetical case study is considered and the corresponding results are closely investigated. The robust performance of the Transfer Matrix Method (TMM) allows for deducing the drop of pressure amplitudes due to viscoelasticity, frequency shift of Poisson coupling, and remarkable discrepancy of odd frequencies (relative to classical model) induced by junction coupling. This research is of crucial importance when frequency-response-based methods are utilized for defect detection of unrestrained pipes.

Waterhammer modeling with fluid–structure interaction (FSI) in a pipeline with axial viscoelastic supports is the aim of this research. The viscoelastic materials of supports (or the pipe wall) were described using the generalized Kelvin–Voigt model. Hydraulic governing equations were solved by the method of characteristic (MOC) and axial vibration equation of the pipe wall was solved using the finite element method (FEM) in the time domain. For a typical case study, four different types for supporting the pipeline in the axial direction: fully free to move; fixed (rigid support); elastic and viscoelastic supports, subject to a waterhammer are analyzed and the results are scrutinized. The results quantitatively confirm that the use of supports with viscoelastic behavior in the axial direction of the pipeline can significantly reduce axial-pipe vibrations (displacements and stresses). The consequences of this structural damping on the attenuation of the internal fluid pressure are further demonstrated.

Two new finite element based methods for time-domain dynamic analysis of viscoelastic solids are proposed in this research. The viscoelastic property is given by either the relaxation or creep functions and is simulated by the conventional generalized Kelvin-Voigt model. The viscoelastic behavior during the dynamic response is taken into account by the Volterra integral. This avoids the difficulties associated with the need for high order time-derivatives used in differential models of viscoelasticity. An accurate numerical approximation for the Volterra integrals is provided. It is used for implementation of the finite-element procedure in the time domain by the introduction of additional terms to the mass matrix (or the stiffness matrix) and the force vector. The additional terms are functions of calculations at the previous time step. In the two provided finite element formulations, one uses the relaxation and the other employs the creep compliance function. This makes it unnecessary to calculate the creep function from the given relaxation modulus or vice versa which are cumbersome operations. As a case study, the wave propagation in a one- and three-dimensional viscoelastic rod subject to a step and sinusoidal load is formulated and solved by the proposed two finite element methods. The computations were validated by direct solutions based on the Laplace transform method. A mathematical description of viscoelastic solids based on the generalized Kelvin-Voigt model is presented and it is applied to modeling vibrations in a solid.Two finite element methods for either creep or relaxation functions as the input data are proposed for the analysis of viscoelastic materials.The longitudinal wave propagation subject to a step and a sinusoidal excitation is studied and compared in an elastic and viscoelastic media.Analytical solutions based on the Laplace transform method are provided for the case studies.The accuracy of the proposed computational methods were estimated in terms of their error variation and mesh size.

Poisson's ratio in viscoelastic materials is a function of time. However, recently developed waterhammer models of viscoelastic pipes consider it constant. This simplifying assumption avoids cumbersome calculations of double convolution integrals which appear if Poisson's ratio is time-dependent. The present research develops a mathematical model taking the time dependency of Poisson's ratio into account for linear viscoelastic pipes. Poisson's ratio is written in terms of relaxation function and bulk modulus which is assumed to be constant. The relaxation function is obtained from creep function given as the viscoelastic property data of pipe material. The results obtained from the present waterhammer model are compared with the experimental data for two different flow rates. The comparison reveals that with the application of the time-dependent Poisson's ratio and unsteady friction, the viscoelastic data of mechanical tests can directly be used for waterhammer analysis with less need for the calibration of the flow configuration. It was also shown that the creep curve calibrated based on the present model is closer to the actual creep curve than that calibrated based on previous models.

The use of pumps linked in parallel or series in large scale pipe systems is usually inevitable, to meet the required head and discharge. Transient flow occurs following a pump failure in a pump group as a result of variations in the flow rate. This research is an investigation about waterhammer caused by one or more pump-switch off in a pump group when they are connected in parallel. The operation of each pump in the group during steady and unsteady state is analyzed. For this purpose, the fluid flow equations as well as the pumps relations including rotational speed change and head loss are combined and simultaneously solved in the time domain by the method of characteristic. From the results one can quantitatively conceive that the intermittent shut-down compared to suddenly switching off the whole pump group produces much less waterhammer pressures. Furthermore in the intermittent shut-down with different pump characteristics, it is suggested to firstly switch off the most powerful pump, and then the rest which are weaker. Appropriate interpretation about the transition results have been included.

Uncertain parameters in the transient analysis of pipe networks lead to uncertain responses. Typical uncertainties are nodal demand, pipe friction coefficient and wave speed, which not only are imprecise in nature but also change significantly over time. Exploiting the fuzzy set theory and a simple scheme of the simulated annealing method, a conceptual model is developed. It can take into account the uncertainties of conventional transient analysis. This model helps designers of pipe systems in finding out the extent to which uncertainties in the inputs can spread to the transient highest and lowest pressures. A real piping system is analyzed herein as the case study. The results show that the transient extreme pressures can be highly affected by the uncertainties.

Fluid–structure interaction (FSI) due to water hammer in a pipeline which has viscoelastic wall behaviour is studied. Appropriate governing equations are derived and numerically solved. In the numerical implementation of the hydraulic and structural equations, viscoelasticity is incorporated using the Kelvin–Voigt mechanical model. The equations are solved by two different approaches, namely the Method of Characteristics–Finite Element Method (MOC-FEM) and full MOC. In both approaches two important effects of FSI in fluid-filled pipes, namely Poisson and junction coupling, are taken into account. The study proposes a more comprehensive model for studying fluid transients in pipelines as compared to previous works, which take into account either FSI or viscoelasticity. To verify the proposed mathematical model and its numerical solutions, the following problems are investigated: axial vibration of a viscoelastic bar subjected to a step uniaxial loading, FSI in an elastic pipe, and hydraulic transients in a pressurised polyethylene pipe without FSI. The results of each case are checked with available exact and experimental results. Then, to study the simultaneous effects of FSI and viscoelasticity, which is the new element of the present research, one problem is solved by the two different numerical approaches. Both numerical methods give the same results, thus confirming the correctness of the solutions.

In this study of water hammer with fluid–structure interaction (FSI) the main aim was the investigation of junction coupling effects. Junction coupling effects were studied in various types of discrete points, such as pumps, valves and branches. The emphasis was placed on an unrestrained pump and branch in the system, and the associated relations were derived for modelling them. Proposed relations were considered as boundary conditions for the numerical modelling which was implemented using the finite element method for the structural equations and the method of characteristics for the hydraulic equations. The results can be used by engineers in finding where junction coupling is significant.

This work introduces a simple and straightforward approach for the creep function determination in viscoelastic pipes on the basis of transient flow analysis. The governing equations are expanded and analytically solved for the first half period of the transient. This solution results in a direct formula for the viscoelastic Joukowsky pressure head as a function of the creep function coefficients which are a priori unknown. Utilizing the measured data, only in the first half water hammer period and the proposed viscoelastic Joukowsky formula, the problem unknowns are determined. To investigate the method’s merits and limitations, two experimental polyethylene pipes are taken into account from the literature. The results show that the proposed approach works very well for long enough pipelines which are completely crept in the half period of the transient flow. The method is found to be computationally efficient and easy to implement in comparison with traditional inverse transient analysis techniques.

There are four popular items which may affect classical waterhammer results: unsteady friction (UF), column separation (CS), fluid-structure interaction (FSI) and viscoelasticity (VE), each of which has been investigated separately in numerous researches. In this study, waterhammer in a reservoir-pipe-valve system is simulated including – for the first time – all four items CS, FSI, UF and VE. The relative importance of each of the four items is assessed. Conclusions are drawn by looking at the numerical simulations corresponding to all possible combinations of the mentioned items.

The corrective smoothed particle method (CSPM) is used to simulate water hammer. The spatial derivatives in the water-hammer equations are approximated by a corrective kernel estimate. For the temporal derivatives, the Euler-forward time integration algorithm is employed. The CSPM results are in good agreement with solutions obtained by the method of characteristics (MOC). A parametric study gives insight in the e¿ects of particle distribution, smoothing length and kernel function. Three typical water-hammer problems are solved. CSPM will not beat MOC in classical water-hammer, but it has potential for water-hammer problems with free surfaces as seen in column separation and slug impact.