Sudden Valve Closure Research Articles

관수로 합성 부정류 차분화 마찰모형의 개발

이 논문에서는 관망시스템의 수격압 현상을 모의하기 위해서 합성 부정류 마찰 모형을 개발하였다. 부정류 마찰항을 고려하기 위한 방법으로 빈도 의존 마찰항과 순간 가속도 기반 마찰 모형을 합성하였으며, 특성선 방법을 모형 개발의 기반으로하였다. 관망에서의 부정류 모형으로 가장 널리 쓰이는 Zielke의 마찰항 모형과 Ramos의 마찰항 모형들과 종합적인 비교를 수행하였다. 모의 결과를 검증하기 위해서 고빈도로 수압을 측정할 수 있는 자료 획득체제를 구비한 관망시스템을 구축하였다. 정상상태에서 밸브 급폐로 야기된 수격압의 수압 시계열을 2가지 Reynolds수에서 확보하였다. 모의결과는 pilot 관망체제에서 확보한 실험 자료와 비교하였다. 부정류 마찰항 모형의 매개변수 보정을 위해서 시행착오 방법이 도입되었으며, 부정류 마찰항들을 비교한 결과는 수격압에서 수압이 감쇄되는 과정에 대한 전반적인 이해를 돕고자 하였다. 이와 같은 결과는 관망의 천이류를 적절히 예측하는데 부정류 마찰항의 적절한 고려가 필수적인 부분임을 알려 주고 있다. In this study, a combined unsteady friction model has been developed to simulate the waterhammer phenomenon for the pipeline system. The method of characteristics has been employed as the modeling platform for the integration of the acceleration based model and the frequency dependant model for unsteady friction. Both Zielke's model and Ramos model were also compared with pressure measurements of a pilot plant pipeline system. In order to validate the modeling approach, a pipeline system equipped with the high frequency pressure data acquisition system was fabricated. The time series of pressure, introduced by a sudden valve closure, were obtained for two Reynolds numbers. A trial and error method was used to calibrate parameters for unsteady friction model. The comparison between different unsteady friction contributions in pressure variation provided the comprehensive understanding in the pressure damping mechanism of waterhammer. The proper evaluation of unsteady friction impact is a critical factor for accurate simulation of hydraulic transient.

Water hammer reduces fouling during natural water ultrafiltration

Today’s ultrafiltration processes use permeate flow reversal to remove fouling deposits on the feed side of ultrafiltration membranes. We report an as effective method: the opening and rapid closing of a valve on the permeate side of an ultrafiltration module. The sudden valve closure generates pressure fluctuations due to fluid inertia and is commonly known as “water hammer”. Surface water was filtrated in hollow fiber ultrafiltration membranes with a small (5%) crossflow. Filtration experiments above sustainable flux levels (>125 l (m 2h) −1) show that a periodic closure of a valve on the permeate side improves filtration performance as a consequence of reduced fouling. It was shown that this effect depends on flux and actuation frequency of the valve. The time period that the valve was closed proved to have no effect on filtration performance. The pressure fluctuations generated by the sudden stop in fluid motion due to the valve closure are responsible for the effect of fouling reduction. High frequency recording of the dynamic pressure evolution shows water hammer related pressure fluctuations to occur in the order of 0.1 bar. The pressure fluctuations were higher at higher fluxes (higher velocities) which is in agreement with the theory. They were also more effective at higher fluxes with respect to fouling mitigation.

Estimation of Decay Coefficients for Unsteady Friction for Instantaneous, Acceleration-Based Models

This paper presents equations developed by using genetic algorithms (GA) to estimate decay coefficients for instantaneous acceleration–based (IAB) unsteady friction models in order to predict energy dissipation following sudden valve closures in simple elastic pipe systems. The GA searched for the optimum combination of IAB coefficients to reproduce pressure history at the valve location using the normalized root mean-squared error (NRMSE) as the minimization criteria. The measured results comprise nine downstream and five upstream sudden-valve-closure experiments performed in five laboratories around the globe. Three IAB unsteady models are compared: a one-coefficient model, a two-coefficient model discretizing the unsteady friction term using finite-difference approximations, and a new two-coefficient model that includes the unsteady friction term in the method of characteristics. The two-coefficient models produced a better match with the experimental data than the one-coefficient models. A new equation for the estimation of the decay coefficient of one-equation models, as well as average values for the decay coefficients for the two-coefficient models, is presented.

Runge–Kutta time‐stepping schemes with TVD central differencing for the water hammer equations

AbstractIn the present study, Runge–Kutta schemes are used to simulate unsteady flow in elastic pipes due to sudden valve closure. The spatial derivatives are discretized using a central difference scheme. Second‐order dissipative terms are added in regions of high gradients while they are switched off in smooth flow regions using a total variation diminishing (TVD) switch. The method is applied to both one‐ and two‐dimensional water hammer formulations. Both laminar and turbulent flow cases are simulated. Different turbulence models are tested including the Baldwin–Lomax and Cebeci–Smith models. The results of the present method are in good agreement with analytical results and with experimental data available in the literature. The two‐dimensional model is shown to predict more accurately the frictional damping of the pressure transient. Moreover, through order of magnitude and dimensional analysis, a non‐dimensional parameter is identified that controls the damping of pressure transients in elastic pipes. Copyright © 2006 John Wiley & Sons, Ltd.

WATER HAMMER EFFECT ON AN ACCELERATED TESTING MECHANICAL HEART VALVE

Background: The US FDA Replacement Heart Valve Guidance requires artificial heart valve accelerated fatigue tests to have a mean transvalvular pressure of 100 mmHg. Loading forces increase non-linearly with the test rate due to the water hammer effect during the backflow of sudden valve closure. Methods: A 27 mm Medtronic Hall mitral valve placed in a circulatory mock loop was evaluated under physiological conditions for loading force via piezoelectric force measurement ring, compressive wave via SPC 340 Millar catheter, and backflow rate via electromagnetic flowmeter. The results served as references for the same measurements later performed in a single chamber accelerated test system. Results: Peaks in backflow rate, compressive wave, and loading forces occurred at the instant of valve closure within both test systems. The maximum values rose from 9.7 to 21.3 L/min, 279 to 848 mmHg, and 38 to 102 N, respectively, when the accelerated test rate increased from 70 to 840 bpm. The increase in loading forces far exceeds physiologic range, meaning that accelerated conditions cause additional valve damage. The correlation coefficient between loading force and backflow rate was 0.99, while the loading force is approximately valve orifice area multiplied by twice the peak pressure value. Loading forces can be adjusted by controlling the backflow, making it a suitable parameter during accelerated fatigue testing.

722 分岐管における空気混入及びオリフィスによる水撃現象への影響に関する研究

The water hammer phenomenon occurs in water supply piping in common residence and building due to the sudden valve closure of one-touch lever. What was more excellent in both cost and the construction is desired as the device. In this study, the erection branch pipe of the different diameters is installed in a horizontal pipeline as a model of a water hammer absorber, and the effects of the air mixing and the orifice on the water hammer phenomenon are investigated.

Transient Behavior of a Cavitating Centrifugal Pump at Rapid Change in Operating Conditions—Part 3: Classifications of Transient Phenomena

Analytical studies were developed on the transient behavior of a cavitating centrifugal pump during the transient operations, including the sudden opening/closure of the discharge valve and the pump startup/shutdown. In order to investigate the mechanism of the low cycle oscillations of both the pressure and the flowrate at a rapid change of the pump system conditions, an unsteady flow analysis was made for the cavitating pump-system by assuming the transient pump performance to be quasi-steady. The calculated unsteady pressure and flowrate during the transient period agree with the corresponding measured time histories. It is shown that the fluctuations of delivery pressure and discharge flowrate at pump rapid startup or sudden valve opening are caused by peculiar oscillating cavitation dynamics inside the pump at rapid increase in flowrate, while the fluctuations at pump rapid shutdown or sudden valve closure are related to the collapse of cavitation bubbles or water column separation in the suction pipe at rapid decrease in flowrate. Moreover, the occurrence of transient fluctuations in pressure and flowrate was predicted by examining the critical condition which creates the occurrence of two different flow mechanisms i.e., (A) oscillating cavitation and (B) water column separation including also the collapse of the cavitation bubbles. These flow mechanisms were represented with two flow models i.e., (A) unsteady cavitating flow incorporating effects of cavitation compliance and mass flow gain factor and expressed by a set of ordinary differential equations solved with the Cardano Method and (B) water-hammer type model including Discrete Free Gas Model and solved with method of characteristics. The calculated critical conditions for the occurrence of the oscillating cavitation and water column separation agree qualitatively with measured ones.

Spline Interpolations for Water Hammer Analysis

The method of characteristics (MOC) with spline polynomials for interpolations was investigated for numerical water hammer analysis for a frictionless horizontal pipe. A new analysis quantifies numerical errors in a systematic and dimensionless way and is used to evaluate the performance of three spline polynomials and to compare them with other numerical schemes for water hammer analysis, as well as to assess the effect of required additional interpolation boundary conditions on the overall accuracy of spline and two-point fourth-order Hermite schemes. For the sudden valve closure test case investigated, the overall accuracy with splines is significantly improved compared to the MOC with linear interpolations or to second-order explicit finite difference techniques. Compared to the Hermite method, the spline scheme has about the same overall accuracy and has the advantage of offering a choice between several spline polynomials with different interpolating characteristics and of being unconditionally stable.

Dissipative and nondissipative fluid wave propagation in pipes

This presentation focuses on the pressure response at various locations along a finite fluid‐filled pipe to changes in the conditions at one end of the pipe. Initiated changes in the conditions represent valve operations that may be sudden valve closure or opening, or a gradual valve operation. The properties of the fluid are calculated via an equation of state, and the model presented is capable of simulating nondissipative and dissipative fluid dynamics. In addition, varying pipe diameters are considered along with pipe elasticity. For the nondissipative (no friction losses in the pipe) configuration, the numerical model is compared with a newly derived analytical solution, which describes the water hammer phenomena along the pipeline in response to a sudden valve closure. The pressure response propagates at the speed of sound through the fluid and oscillates in a combination of step changes. For the dissipative (with friction losses along the pipe) configuration, the kinetic energy is transformed into elastic energy of fluid and pipe by the valve operation. Also, the pressure response declines due to the friction energy losses. This model may apply to any pipeline setting such as transportation pipelines, oil, gas and water wells, water distribution systems, and plant circulating systems.

Shock phenomena in a one-component two-phase bubbly flow. 2nd Report. Pressure rise and propagation velocity of pressure waves.

The characteristics of shock phenomena in a one-component two-phase bubbly flow induced by a sudden valve closure are investigated. The pressure rise and the propagation velocity of the pressure waves and their decay in the axial direction are obtained experimentally and are discussed quantitatively. Their characteristics are different from those of a two-component two-phase flow because of the mass transfer between the vapor and the liquid. The potential surge can be expressed by ΔPpso=CTPρTPjTP by extrapolating the value ΔPpso at time t=0 before the occurrence of the mass transfer. The values of pressure rise and propagation velocity are also compared with the analytical results by the linearization method described in a previous report. It is shown that they can be expressed well in generalized forms which depend on the relaxation time τM of the mass transfer, obtained by the linearization method.

Shock phenomena in a one-component two-phase bubbly flow. 1st report Experimental results on transient pressure profiles.

The characteristics of shockphenomena in a one-component two-phase bubbly flow induced by a sudden valve closure at the downstream end of a test section are investigated. An experiment was conducted for a two-phase flow in a horizontal stainless tube of 21.4 mm ID and 16.17 m length with a surge tank having a gas chamber at the upstream end, using Freon-113 as the working fluid. The pressure transients are presented and discussed qualitativity. They are different from those of two-component two-phase flow due to the mass transfer between the vapor and the liquid. The effects of each facter such as the initial void fraction, the liquid velocity, the initial pressure, and the valve closing time, on the profiles of the transient pressure are shown. Also, the behaviors of the vapor bubbles after valve closure are sketched and explained, and are compared with the profiles of transient pressure.

An Analysis of Water Hammering in Bubbly Flows : 2nd Report, Transient Pressure Profiles in One-component Flows

Water hammer phenomena caused by a sudden valve closure are investigated in one-component two-phase flows. The phenomena in one-component two-phase flows are more complicated than those in two-component two-phase flows because of the presence of mass transfer between liquid and vapor. Basic partial differential epuations based on a one-dimensional homogeneous flow model are solved analytically by linearization and iterated Laplace transformation. The profile of the pressure transients at the closing valve are given. It is shown that the mass transfer between the two phases has a great influence on the profile of the pressure transients, and that the magnitude of the influence depends on the relaxation time τM of the interphase mass transfer.

Analysis of Water Hammering in Bubbly Flows : 1st Report, Two-component Two-phase Flows

Water hammer phenomena caused by a sudden valve closure are considered in two-component bubbly flows where the phenomena are more complicated than in single-phase flows because of the presence of a compressible component. Basic partial differential equations based on a one-dimensional homogeneous flow model are solved analytically by linearization and iterated Laplace transformation. As a result, the profiles of the pressure transients, the propagation velocity of a pressure wave with a small amplitude, and the effects of valve closure on transient pressures are found. Further, the effect of friction factor on pressure profiles is shown and approximated by a simple equation. It is also shown that reflection and transmission occur at the interphase where the void fraction changes.

Shock Phenomena in a One-component Two-phase Bubbly Flow : 1st Report, Experimental Results on Transient Pressure Profiles

Characteristics of shock phenomena in a one-component two-phase bubbly flow induced by a sudden valve closure at the downstream end of a test section are investigated. An experiment was conducted for a two-phase flow in a horizontal stainless tube of 21.4mm Id and 16.17m length with a surge tank having a gas chamber at the upstream end, using Freon-113 as the working fluid. The pressure transients are presented and discussed qualitatively. They are different from those of a two-component two-phase flow due to the mass transfer between the vapor and the liquid. The effect of factors such as the initial void fraction, the liquid velocity, the initial pressure, and the valve closing time on the profiles of the transient pressure are shown. Also, the behaviors of the vapor bubbles after the valve closure are sketched and explained, comparing with the profiles of transient pressure.

An analysis of water hammering in bubbly flows. 2nd report Transient pressure profiles in one-component flows.

Water hammer phenomena caused by a sudden valve closure investigated in one-component two-phase flows. The phenomena in one-component two-phase flows are more complicated than those in two-component two-phase flows because of the presence of mass transfer between liquid and vapor. Basic partial differential equations based on a one-dimensional homogeneous flow model are solved analytically by linearization and iterated Laplace transformation. The profiles of the pressure transients at the closing valve are given. It is shown that the mass transfer between the two phases has a great influence on the profile of the pressure transients, and that the magnitude of the influence depends on the relaxation time τM of the interphase mass transfer.

Analysis of water hammering in bubbly flows. 1st report. Two-component two-phase flows.

Water hammer phenomena caused by a sudden valve closure are considered in two-component bubbly flows where the phenomena are more complicated than in single-phase flows because of the presence of a compressible component. Basic partial differential equations based on a one-dimensional homogeneous flow model are solved analytically by linearization and iterated Laplace transformation. As a result, the profiles of the pressure transients, the propagation velocity of a pressure wave with a small amplitude, and the effects of valve closure on transient pressures are found. Further, the effect of friction factor on pressure profiles is shown and approximated by a simple equation. It is also shown that reflection and transmission occur at the interphase where the void fraction changes.

The Transient Characteristics of Fluid Pipes including Mechanical Load : 2nd Report, Theoretical Analysis on Effects of Valve Closure

This paper deals with transient characteristics of a valve-controled hydraulic driving system consisting of actuator, fluid pipe and operation valve, especially with pressure surge generation in a pipe due to sudden valve closure. Pressure variation was measured under various system and operating parameters, such as valve closure time, valve closure process, valve orifice shape, etc., and compared with theoretical results of the preceding paper. Consequently, the following matters became evident. (1) The theoretical results which were obtained by employing a wave equation of two-dimensional viscous flow for an unsteady pipe flow agree well with experimental results in any system parameters and valve closure process. (2) An approximate solution which was obtained by considering only the compressibility of fluid in pipe is accurate enough for practical usage in case of very slow valve closure. (3) Variation of discharge coefficient of valve depending on Reynolds number, saturation of valve flow at large opening and leakage flow through valve orifice after closure can not be disregarded in case of gradual valve closure.

The steamhammer problem: dynamic shock loading of critical reactor piping systems

In the course of both pre-operational testing and power operation of commercial nuclear power plants, relatively large amplitude transient vibrations of steam piping systems have been experienced with damage to the piping supports in at least one recent case. These transient vibrations result from ‘steamhammer’ or dynamic shock loading induced by pressure and momentum transient conditions generated in the piping by sudden changes to the flow conditions, such as are produced by sudden valve opening or closure. In particular, vibrations have been experienced in by-pass and discharge lines as a result of relief valve discharge, and in main steam lines as a result of sudden main stop valve closure. Piping in both BWR and PWR reactor systems has been found to be susceptible to these conditions. This paper is concerned with the evaluation of the pressure and momentum transients resulting from sudden valve operation, and the determination of the dynamic response of the piping to the induced transient loading. The characteristics of the transient conditions existing immediately following both sudden valve opening and closure as encountered in BWR and PWR plants are discussed. The procedures used to calculate the transient time history functions are outlined. The derivation of the loading induced in the piping by the pressure and momentum transients is discussed and the determination of the dynamic response of the piping is presented. The procedures described in the paper are illustrated by actual examples from BWR and PWR plants, and the significance of steamhammer effects relative to other loading conditions is discussed.

Some aspects of wave propagation in viscous liquids in conduits

The two-dimensional dispersion of water hammer type waves, specifically the waves initiated by sudden valve closure in fully developed laminar flow, in viscous liquids contained in a closed conduit is investigated by an approximate method. The problems of flow between two infinite parallel plates and in a circular cylinder are considered.