Hydraulic Transients Research Articles

4C code analysis of thermal–hydraulic transients in the KSTAR PF1 superconducting coil

The KSTAR tokamak, in operation since 2008 at the National Fusion Research Institute in Korea, is equipped with a full superconducting magnet system including the central solenoid (CS), which is made of four symmetric pairs of coils PF1L/U–PF4L/U. Each of the CS coils is pancake wound using Nb3Sn cable-in-conduit conductors with a square Incoloy jacket. The coils are cooled with supercritical He in forced circulation at nominal 4.5K and 5.5bar inlet conditions. During different test campaigns the measured temperature increase due to AC losses turned out to be higher than expected, which motivates the present study.The 4C code, already validated against and applied to different types of thermal–hydraulic transients in different superconducting coils, is applied here to the thermal–hydraulic analysis of a full set of trapezoidal current pulses in the PF1 coils, with different ramp rates. We find the value of the coupling time constant nτ that best fits, at each current ramp rate, the temperature increase up to the end of the heating at the coil outlet. The agreement between computed results and the whole set of measured data, including temperatures, pressures and mass flow rates, is then shown to be very good both at the inlet and at the outlet of the coil. The nτ values needed to explain the experimental results decrease at increasing current ramp rates, consistently with the results found in the literature.

New Approaches to the Propagation of Nonlinear Transients in Porous Media

Many problems in regional groundwater flow require the characterization and forecasting of variables, such as hydraulic heads, hydraulic gradients, and pore velocities. These variables describe hydraulic transients propagating in an aquifer, such as a river flood wave induced through an adjacent aquifer. The characterization of aquifer variables is usually accomplished via the solution of a transient differential equation subject to time-dependent boundary conditions. Modeling nonlinear wave propagation in porous media is traditionally approached via numerical solutions of governing differential equations. Temporal or spatial numerical discretization schemes permit a simplification of the equations. However, they may generate instability, and require a numerical linearization of true nonlinear problems. Traditional analytical solutions are continuous in space and time, and render a more stable solution, but they are usually applicable to linear problems and require regular domain shapes. The method of decomposition of Adomian is an approximate analytical series to solve linear or nonlinear differential equations. It has the advantages of both analytical and numerical procedures. An important limitation is that a decomposition expansion in a given coordinate explicitly uses the boundary conditions in such axis only, but not necessarily those on the others. In this article we present improvements of the method consisting of a combination of a partial decomposition expansion in each coordinate in conjunction with successive approximation that permits the consideration of boundary conditions imposed on all of the axes of a transient multidimensional problem; transient modeling of irregularly-shaped aquifer domains; and nonlinear transient analysis of groundwater flow equations. The method yields simple solutions of dependent variables that are continuous in space and time, which easily permit the derivation of heads, gradients, seepage velocities and fluxes, thus minimizing instability. It could be valuable in preliminary analysis prior to more elaborate numerical analysis. Verification was done by comparing decomposition solutions with exact analytical solutions when available, and with controlled experiments, with reasonable agreement. The effect of linearization of mildly nonlinear saturated groundwater equations is to underestimate the magnitude of the hydraulic heads in some portions of the aquifer. In some problems, such as unsaturated infiltration, linearization yields incorrect results.

Investigation of Hydraulic Transients in a Pipeline with Column Separation

The authors previously described a new method [based on the new discrete vapor cavity model (new DVCM)] for numerical prediction of pressure changes during the water hammer with liquid column separation together with results of preliminary experimental verification of this method. This paper is a continuation of the research and includes results of additional laboratory tests and visualization of the cavitation zones generated during transient flow with liquid column separation. The results of these studies provide a better understanding of the phenomenon. It is shown that the phenomenon can have a distributed nature, which means that gas-vapor zones may be observed not only locally, in the vicinity of the shutoff valve, but may be spread along the pipeline length, and the intensity of this phenomenon decreases with distance from the valve. Laboratory test results were also used for further verification of the new DVCM. This verification shows that agreement between calculated and experimental results strongly depends on the friction model incorporated into the calculation. This agreement also depends on the intensity of liquid column separation: for cases of severe separation, the differences between numerical and measured pressure changes are small and accepted from the practical point of view.

STUDYING OF WATERHAMMER PHENOMENON CAUSED BY SUDDEN VARIATION OF WATER DEMAND AT WATER SUPPLY PIPES NETWORK

Water hammer in water-supply networks and irrigation networks may give rise to high pressures, due to the superposition of reflected pressure waves. The problem is relevant nowadays for the common use of automatic valves in networks regulation. When large variations in user demand happen often, as in distribution networks, water hammer occurs daily. In irrigation networks, its effect was found to concur to high rate of pipe failures, which these networks usually suffer. This paper investigates the effect of sudden variation of water demands in pipes network on transient pressures variations through the network. WHAMO software was used in the analysis which uses the implicit finite difference scheme for solving the momentum and continuity equations at unsteady state case. The study was applied on a two loops pipe network composed of eight pipes of different diameters and elevations. The flow is fed in the network by elevated storage tank. The results showed that rapidly changing the demand could significantly increase or decrease the pressure head in distribution system and cause flow reversal in a network system. In this simulation, shorter increasing/decreasing time of demand change causes the greater magnitude of transient fluctuation. Therefore, it is very obvious that the operations of distribution system should be done with very careful caution. The slower opening rates significantly reduce the impact of hydraulic transients. When the distribution system is designed, many different cases of simulation with different scenarios should be performed for the economical and safe design.

Simulation of Thermal–Hydraulic Transients in the KSTAR PF1 Coil Using the 4C Code

KSTAR is a fully superconducting tokamak in operation since 2008 at the National Fusion Research Institute in Korea. All coils are wound using cable-in-conduit conductors and cooled with forced-flow supercritical helium at 4.5 K and 5.5 bar. We consider here the central pair, PF1U/L, of the central solenoid coils; during operation, these coils are subjected to sharp current transients, which induce ac losses in the coil. The thermal hydraulic transient following a trapezoidal current pulse, with a ramp-up to 10 kA at a rate of 1 kA/s and a ramp-down to 0 kA at a rate of 10 kA/s, is simulated here using the 4C code, and the results are compared with the measurements.

Dynamic Capability of Hydro Power Plants for Primary Load-Frequency Control

Abstract This paper presents the methodology used by EDF to evaluate the active power response of hydro power plants due to a grid frequency deviation. With knowledge of turbine and hydro circuit characteristics, it is possible to classify the plants: in one hand, units which can participate to Load-Frequency Control without constraints; on the other hand, units that are limited due to hydraulic transients. For these plants, further simulations are needed. The two tools (classification criteria and simulator) share a model based on a hydro-electrical analogy.

Fluid–structure interaction with pipe-wall viscoelasticity during water hammer

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.

Investigation on complete characteristics and hydraulic transient of centrifugal pump

An improved method was developed to obtain the complete characteristic of centrifugal pump. The conversion formula of complete characteristics is established based on the normal performance curve. An example was presented to illuminate the new method, and the complete characteristic curves of 14SA-10 centrifugal pump were obtained by the new method. The hydraulic transient of the centrifugal pump failure and start-up was simulated by method of characteristics (MOC), which quote the complete characteristics data. The results show that the inversion method is available to obtain the complete pump characteristic curves provided the normal performance curve. For hydraulic transient simulation, more accurate numerical result can be obtained, if the new model is adopted to convert the experimental normal performance curve to complete characteristics curve of centrifugal pump.

Relevance of Unsteady Friction to Pipe Size and Length in Pipe Fluid Transients

This paper investigates the importance of pipe system scale—specifically pipe length and diameter—on unsteady friction in pipe transients. A dimensionless analysis is conducted for the one-dimensional (1D) water-hammer model in this study and the analytical ex- pression for the relative importance of unsteady friction damping to the total friction damping is obtained in the frequency domain. In addition, a two-dimensional (2D) waterhammer model coupled with a 2D κ-e turbulence model is applied to a reservoir-pipe-valve system. A parametric study covering a number of pipe diameters, pipe lengths, and initial Reynolds numbers is conducted. The investigation spans a range of water-hammer travel time and turbulent radial diffusion timescales. In each case, the transient is generated by a sudden and complete valve closure. The analytical solution for the importance of unsteady friction is verified by the numerical simulations and the results show that unsteady friction damping has less effect on the damping rate of the transient envelope as (1) the ratio of the wave travel timescale to the radial diffusion timescale increases and (2) the product of the initial friction factor and Reynolds number increases. Furthermore, the findings of this study arevalidated by both laboratory and field experiments from literature. The implication of the findings is that the role of unsteady friction on the damping rate of the transient envelope diminishes with the scale ratio of pipe length and pipe diameter and that laboratory experiments, which are usually limited to relatively small scale ratios of pipe lengths and diameters, have lead researchers to overestimate the importance of unsteady friction on the damping of the transient envelope in real large pipe-scale systems. DOI: 10.1061/(ASCE)HY.1943-7900.0000497. © 2012 American Society of Civil Engineers. CE Database subject headings: Pipe sizes; Damping; Hydraulic transients; Friction; Reynolds number. Author keywords: Pipe length; Pipe diameter; System scale; Transients; Unsteady friction; Pressure head damping; Dimensionless ana- lysis; 1D analytical analysis; 2D κ-e model; Initial Reynolds number.

Influence of Entrapped Air Pockets on Hydraulic Transients in Water Pipelines

The pressure variations associated with a filling undulating pipeline containing an entrapped air pocket are investigated both experimentally and numerically. The influence of entrapped air on abnormal transient pressures is often ambiguous because the compressibility of the air pocket permits the liquid flow to accelerate but also partly cushions the system, with the balance of these tendencies being associated with the initial void fraction of the air pocket. Earlier experimental research involved systems with an initial void fraction greater than 5.8%; this paper focuses on initial void fractions ranging from 0 to 10% to more completely characterize the transient response. Experimental results show that the maximum pressure increases and then decreases as the initial void fraction decreases. A simplified model is developed by neglecting the liquid inertia and energy loss of a short water column near the air-water interface. Comparisons of the calculated and observed results show that the model is able ...

The Fehleranalyse Error Analysis of Fully Characteristic Curve of Pump to Be Nominalization and Study for the Influence on Result of Hydraulic Transients Calculation

In this paper，by transforming the fully characteristic curve of pump with eighty specific speed to be numeralization he obtained fehleranalyse error of discrete data were analyzed based on the pump similarity theory and the difference between certain assumed condition and real situation in numeralization process. Then the influence of the fehleranalyse error of numeralization method on the pressure boost caused by Pump-off water hammer was computed by a Pump-off water hammer calculation within an real engineering project. The reliability of numeric calculation method of fully characteristic curve of Pump is proved.

Head- and Flow-Based Formulations for Frequency Domain Analysis of Fluid Transients in Arbitrary Pipe Networks

Applications of frequency-domain analysis in pipelines and pipe networks include resonance analysis, time-domain simulation, and fault detection. Current frequency-domain analysis methods are restricted to series pipelines, single-branching pipelines, and single-loop networks and are not suited to complex networks. This paper presents a number of formulations for the frequency-domain solution in pipe networks of arbitrary topology and size. The formulations focus on the topology of arbitrary networks and do not consider any complex network devices or boundary conditions other than head and flow boundaries. The frequency-domain equations are presented for node elements and pipe elements, which correspond to the continuity of flow at a node and the unsteady flow in a pipe, respectively. Additionally, a pipe-node-pipe and reservoir-pipe pair set of equations are derived. A matrix-based approach is used to display the solution to entire networks in a systematic and powerful way. Three different formulations are derived based on the unknown variables of interest that are to be solved: head-formulation, flow-formulation, and head-flow-formulation. These hold significant analogies to different steady-state network solutions. The frequency-domain models are tested against the method of characteristics (a commonly used time-domain model) with good result. The computational efficiency of each formulation is discussed with the most efficient formulation being the head- formulation. DOI: 10.1061/(ASCE)HY.1943-7900.0000338. © 2011 American Society of Civil Engineers. CE Database subject headings: Hydraulic transients; Unsteady flow; Pipe networks; Numerical analysis; Fourier analysis. Author keywords: Transients; Unsteady flow; Pipes; Networks; Numerical analysis; Fourier analysis.

CFD investigation of flow inversion in typical MTR research reactor undergoing thermal–hydraulic transients

Three dimensional CFD full simulations of the fast loss of flow accident (FLOFA) of the IAEA 10 MW generic MTR research reactor are conducted. In this system the flow is initially downward. The transient scenario starts when the pump coasts down exponentially with a time constant of 1 s. As a result the temperatures of the heating element, the clad, and the coolant rise. When the flow reaches 85% of its nominal value the control rod system scrams and the power drops sharply resulting in the temperatures of the different components to drop. As the coolant flow continues to drop, the decay heat causes the temperatures to increase at a slower rate in the beginning. When the flow becomes laminar, the rate of temperature increase becomes larger and when the pumps completely stop a flow inversion occurs because of natural convection. The temperature will continue to rise at even higher rates until natural convection is established, that is when the temperatures settle off. The interesting 3D patterns of the flow during the inversion process are shown and investigated. The temperature history is also reported and is compared with those estimated by one-dimensional codes. Generally, very good agreement is achieved which provides confidence in the modeling approach.

MATLAB Calculation of Hydraulic Transients in Hydropower Simulation Application

In hydropower station in the operation of total with hydraulic transient process of the power station on the transition process analysis and calculation is quite important. This paper introduces the today's advanced scientific computing software MATLAB, and using the software of the Zipingpu hydropower station hydraulic transients from the mathematical model and calculation simulation etc is analyzed and calculated with research, in order to seek appropriate power operation mode, unit close regularities. For power station and water system design optimization, safe operation, provides the basis.

Critical superposition instant of surge waves in surge tank with long headrace tunnel

Superposed mass oscillation that often occurs in a throttled surge tank with a long headrace tunnel is studied. The instant of the worst superposition of mass oscillation in a surge tank is analysed. The analytical formula predicting the worst superposition instant is derived exactly and verified (1) with a numerical solution to the fundamental equations for the surge tank and (2) with a numerical simulation of hydraulic transients in an actual hydropower station. It is shown that the superposed oscillation provides the highest upsurge at the instant that the initial flow rate in the headrace tunnel and initial water level in the surge tank satisfy the judgement formula. The conclusion provides a theoretical and computational basis for the numerical simulation of maximum upsurge in a surge tank.

Finite Element Method For Capturing Hydraulic Jump In Open Channel

An efficient and accurate solution algorithm is developed for 1D unsteady flow problems in open channels. The method was the finite element solution of the Saint-Venant equations using the bi-tridiagonal matrix algorithm. For numerical stability, the time step was a function of depth and flow velocity, to avoid restriction due to the wave celerity variation in the computational analysis when using the method of characteristics. Validity of numerical models is obvious compared with the experimental data. Two examples were solved with the finite element method (FEM). The first involves routing a discharge hydrograph down a rectangular channel. The second example consists of routing a sudden shut off of all flow at the downstream end of the channel. These examples are taken from the text book of Streeter and Wylie [Hydraulic transients (Ann Arbor: F.E.B. Press, 1983)]. Numerical results agree well with those obtained by these authors and show that the proposed method is consistent, accurate and highly stable in capturing discontinuities propagation in free surface flows.

Transient Friction in Pressurized Pipes. II: Two-Coefficient Instantaneous Acceleration–Based Model

The goal in the field of modeling of hydraulic transients is a comprehensive model for pipe networks that is computationally fast and accurate. The fastest models are the one-dimensional (1D) models that use instantaneous acceleration–based (IAB) properties, but unfortunately these models are not as accurate as the more demanding 1D convolution-based (CB) models or quasi two-dimensional models. Focusing on a single pipe, this paper investigates the fundamental behavior of the much more accurate 1D CB model to find two coefficients for use with the two-coefficient formulation of the much-used modified IAB (MIAB) model for complete closing of a downstream valve. Two coefficients are found based on the weighting function used in the CB model, and these coefficients vary along the pipe length. Simulations are compared with two experimental results from tests performed at University of Adelaide in Australia in 1995. The experimental results are for different initial Reynolds numbers of approximately 2,000 and ...

CATHARE 2 V2.5_2: A single version for various applications

This paper presents the new capabilities of CATHARE 2 as a multi-purpose multi-reactor concept system code. The CATHARE 2 code was originally devoted to best estimate calculations of thermal–hydraulic transients in Water-Cooled Reactors such as PWR, VVER or BWR. Recently, in the framework of the Generation IV International Forum, CEA launched several feasibility studies of future advanced reactor concepts including Gas-Cooled Reactors, Sodium-Cooled Fast-Breeder Reactors, Supercritical Water-Cooled Reactors. The 2-fluid model with non-condensable gases transport equations was first easily extended to Gas-Cooled Reactor applications with very few modifications. At the same time CEA seized opportunity to use CATHARE 2 to perform studies for non-nuclear industrial applications such as cryogenic rocket engines. New capabilities were implemented allowing passage from supercritical pressure to subcritical conditions and these features were then easily applied to Supercritical Water-Cooled Reactors. New developments were also necessary to extend the code to Sodium-Cooled Reactors. CATHARE 2 can now describe several circuits with various fluids either in single-phase gas or liquid, or in two-fluid conditions possibly with noncondensable gases, which allows simulating any kind of reactor concept and any kind of accidental transient. The development method for the extension to new fluids is presented with an overview of the most striking functional and modelling features that have been implemented in the new CATHARE 2 V2.5_2 version to be released mid-2009 for industrial applications.

Attenuation analysis of hydraulic transients with laminar-turbulent flow alternations

An improved compound mathematical model is established to simulate the attenuation of hydraulic transients with laminar-turbulent alternations, which usually occur when the pipeline flow velocity fluctuates near the critical velocity. The laminar friction resistance and the turbulent friction resistance are considered respectively in this model by applying different resistance schemes to the characteristics method of fluid transient analysis. The hydraulic transients of the valve closing process are simulated using the model. A more reasonable attenuation of hydraulic transients is obtained. The accurate attenuation is more distinct than that obtained from the traditional mathematical model. The research shows that the hydraulic transient is a type of energy waves, and its attenuation is caused by the friction resistance. The laminar friction resistance is more important than the turbulent friction resistance if the flow velocity is smaller than the critical velocity. Otherwise the turbulent friction resistance is more important. The laminar friction resistance is important in the attenuation of hydraulic transients for the closing process. Thus, it is significant to consider the different resistances separately to obtain more accurate attenuation of hydraulic transients.

Effects of water–air mixtures on hydraulic transients

The purpose of this study is to investigate pressurized pipelines and the potential effects on pressure transients of air entrained at the downstream end of large entrapped air pockets followed by a hydraulic jump in pressurized pipelines. The homogeneous two-phase flow model is used to simulate the transient response of the bubbly mixture after a pump shutdown. The results show that pressure transients are significantly reduced with increasing air-pocket volumes and bubbly flow air content. Experimental investigations were carried out to analyze the impact of different air-pocket volumes located at high points of pressurized pipelines. A case study of an existing pumping system was considered to exemplify the impact of the bubbly flow air content on hydraulic transients.