Water Column Separation Research Articles

Numerical modeling of cavity collapse water hammer in pipeline systems: Internal mechanisms and influential factors of transient flow and secondary pressure rise dynamics

This study explores the dynamics of pressure wave propagation and cavitation in pressurized pipelines during and after the rapid closure of the pipeline's end ball valve, utilizing a three-dimensional computational fluid dynamics approach with the method of characteristics, validated against Bergant and Simpson's experimental data of three degrees of cavitation. It innovatively examines transient pressure dynamics through both energy transformation and wave propagation perspectives, focusing on the phases of water column separation and coalescence, and the dynamics of flow interruption bubbles. The research delves into the detailed mechanisms of pressure wave propagation and further assesses the effects of physical factors. Key findings include: (1) As initial inlet velocities increase, cavitation starts earlier, extends further, and intensifies, with higher final volume fractions near the valve, indicating that higher velocities exacerbate cavitation. Higher inlet velocities also correlate with more intricate and expansive vortex formations. (2) Secondary pressure surges in water hammer result from the superposition of two-stage positive pressure waves. Initially, positive pressure waves within the conduit reflect twice from air pockets and the upstream boundary, remaining positive. Subsequently, they interact with secondary positive pressure waves reflected by the valve, causing a secondary pressure surge. (3) The fluid flow is laterally symmetry in the pipe cross section, except for minor local asymmetrical spikes in areas with vapor bubbles. Velocity discrepancies are notable near the pipe walls due to vapor accumulation, primarily on the upper wall due to buoyancy. This accumulation may narrow the flow area, possibly accelerating the water passing by. (4) Lower flow velocities, downward inclines, and slower valve closures diminish secondary pressure rise amplitudes in water hammer events, while reduced static heads intensify cavitation despite lessening pulse amplitudes. These findings offer valuable insights for the design and operational guidance of complex hydraulic systems during transient processes in urban water supplies.

Evolution of Runner Forces during Simultaneous Pump-Trip Transient Process of Two Pump-Turbines

Abstract To ensure no cavitation and water column separation in pump-turbines, the suction heights of pump-turbines in high-head pumped-storage hydropower stations have to be decreased to about –100 m, which leads to high pressure in the draft-tube. During the pump-trip transient process of pump-turbines, the positive water hammer wave in draft-tube superposing the initial high pressure may cause an imbalance of rotating parts and even a lifting-up accident. To quantify the runner forces, two typical transient processes, with and without guide-vane closure after the simultaneous power-off of the two pump-turbines in one hydraulic system, were simulated by using the one-dimensional and three-dimensional coupled (1D-3D) computational fluid dynamics (CFD) method. The results show that the maximum upward axial force on the runner during the process without guide-vane closure (runaway) is significantly higher than that during the process with guide-vane closure. Two significant maximum upward axial forces were observed during the runaway process, and they were around the zero and the valley speed moments. The main causes are the pressure decrease in the runner’s high-pressure zone owing to high-speed bypass flows, and the spiral-case negative water-hammer wave and draft-tube positive water-hammer wave caused by discharge rise. However, the draft-tube positive water hammer wave superposing the high pressure did not cause the maximum axial force. The above two moments of highest axial forces during the runaway process and the proper guide-vane closure rule deserve special attention in the design and operation phases.

Maximum pressure of water column separation phenomenon applying the crow search algorithm

ABSTRACT The water distribution network is one of the vital infrastructures for every city whose transient flow can disturb its performance. Among the transient flow regimes, water column separation can cause severe pressure fluctuations in the network. In previous studies, the water column separation phenomenon in loop networks and its affecting factors have not been studied. Therefore, in this study, the ANSYS Fluent software simulates and determines the water column separation effective factors, and the optimal relationship between these effective factors and the maximum pressure generated in the network with the crow search algorithm was investigated. By conducting simulations and checking their output, it was determined that the valve’s closing time, the distance from the upstream valve and the water height in the tank (inlet pressure) are effective factors in the phenomenon. After determining the effective parameters, using the crow search algorithm, the optimized equation between each parameter and the maximum pressure in the network is provided. Then, the simulation was done with the values obtained from the equations for the maximum tolerable pressure of the network. The simulation indicates that the maximum pressure created in the network is lower than the tolerable pressure. Therefore, applying the values gained from these optimal relationships in the network can prevent water column separation and its consequences.

Dynamics of large cavity induced by valve closure in an undulating pipeline

The dynamics of large cavity and the accompanied water column separation and rejoining induced by fast closing of a butterfly valve in an undulating pipeline system are investigated in this study. The three-dimensional computational fluid dynamics numerical simulations are performed using a newly developed interfacial surface tension-based model (ISTM) that accounts for the surface tension effect on large cavities. The applicability of the ISTM model is validated with the experimental data, showing better accuracy in predicting pressure fluctuations and cavity evolutions than three typical cavitation models. Differences in cavitation characteristics are observed between upstream and downstream of the valve. Upstream the valve, cavitation primarily appears at the pipe top, with the vapor volume fraction varying sharply due to the rarefaction pressure waves (maximum value of 0.0073). Downstream the valve, the complete water-column separation occurs, and vapor volume fraction changes slowly correspond with the growth and collapse of the large cavity (maximum value of 0.647). The maximum length of the large cavity can reach about six times the pipe diameter, with a minimum water vapor interface angle of 16°. The cavitation evolution displays a transition from a clustered inception to a sheet-like growth and collapse pattern. These findings contribute to the design and operation guidance for complex hydraulic systems during transient processes.

Experimental Investigation of Column Separation Using Rapid Closure of an Upstream Valve

In this study, the phenomenon of column separation that occurs in the downstream pipeline of a rapid closure valve is experimentally investigated. Special attention is paid to the dynamic behavior of the formation, growth, and collapse processes of cavities, which are observed using a high-speed camera. Synchronized images of cavity patterns and measured pressure histories are analyzed to elucidate the process of water column separation, the mechanism of column separation events, and the influence of parameters on the transient flow. Experimental results indicate that during the collapse process of vapor cavities, a superposition phenomenon involving a positive pressure wave and collapse wave occurs, resulting in a nearly three times rise of Joukowsky pressure. In all test cases, the maximum pressure of the pipeline exceeded 150 times the reservoir static pressure. A new classification for a water hammer combined with cavitation (four types of pressure oscillation patterns) is proposed based on whether the duration of column separation decreases sequentially and the maximum pipeline pressure follows the first collapse of cavities at the valve. As the initial flow velocity increases, there is generally an increase in maximum pressure; however, this trend may be scattered under certain operation conditions.

Revealing the pressure pulsations that can cause water column separation in pump-turbine

Water column separation (WCS) can lead to a lifting-up of the rotating parts of pump-turbine and even a catastrophe in pumped-storage hydropower stations. However, the fundamental question, which pressure pulsations can trigger WCS, has not been answered. To answer this problem, we quantitatively analyzed the responses of a cavitation bubble in compressible unbounded water and cavitation cavities in a prototype pump-turbine to different pulsating pressures, using the Keller-Miksis equation and three-dimensional computational fluid dynamics. The findings reveal that a single cavitation nucleus oscillates around its initial radius when the lowest pulsating pressure is higher than the saturated vapor pressure (pv); as numerous cavitation nuclei grow to the maximum radius, they will coalesce a cavitation cavity when the lowest pulsating pressure drops to the pv and maintains 0.5Tf; the cavitation cavity can develop into a WCS when the pulsating pressure continue to maintain at the pv for about 1.0TRmax. Specifically, the lowest pulsating pressure dropping to the pv is a crucial prerequisite for WCS, and the pressure pulsations with frequencies below 0.83 Hz can make the cavitation cavity becoming a WCS in the prototype pump-turbine. This finding provides the theoretical base for the revision of the WCS criterion for pump-turbines.

Cavitation evolution and flow field characteristics of transient flows with multi-point water-column separations in undulating pipeline

Transient flows with water-flow-induced multi-point cavitation inside an undulating pipeline are investigated experimentally under conditions of fast valve closure for three typical test cases by using high-precision pressure transducers, high-speed photography and particle image velocimetry (PIV) techniques. For low initial velocity condition, the transient pressure at the monitoring point (PT1) downstream the valve quickly decreases to the cavitation pressure and fluctuates near it. The leading-edge velocity of the dispersed bubble-like cavitation group first increases with its occurrence and then accelerates and reaches an extreme value before decreasing to zero due to the viscous force and the decrease of water flow inertia, and finally the water flows upstream in reverse, i.e. the leading-edge accelerates and collapses behind the valve. At the same time, the transient pressure rises sharply to maximum 81.86 m due to the return of the compression wave and then decreases sharply to cavitation again because of the switch of the pressure waves. Then, the second cavitation intensity is weak and the corresponding pattern is fog-like, and finally decreases gradually with a cyclic period of about 0.38 s. The transient pressure at the monitoring point (PT2) at the peak of the undulating pipeline also maintains at the cavitation pressure corresponding to the big bubble occurrence moment in addition to its fluctuation near the cavitation pressure including first and second cavitation. Its maximum pressure is 72.16 m and the corresponding cavitation pattern is small and bigger bubbles at different cavitation stages. For middle initial velocity, the typical pattern of the corresponding cavitation is the large cavity with free surface at PT2, the corresponding higher maximum pressures are 102.36 m at PT1 and 84.81 m at PT2. The evolution process of the cavity including bubble mergence, morphological deformation, motion and collapse is analysed based on the broken wave and hydraulic dynamic theories. For high initial velocity, larger cavities occur both downstream the valve and at the peak point of undulating pipeline, and thus the corresponding higher maximum pressures due to larger cavity collapse are 140.56 m at PT1 and 127.98 m at PT2. In particular, complete water column separation with transparent large cavity occur downstream the valve.

Water column separation under one-after-another load rejection in pumped storage station

A pumped storage power station operates on the principal of multiple pump-turbines sharing one tunnel. However, safety is a concern, particularly under one-after-another load rejection of multiple pump-turbines. In this study, we have implemented a model experiment based on water column separation experiment under the condition of one-after-another load rejection of a pumped storage model experimental platform with two pump-turbines sharing one tunnel. The results show that the unit with water column separation, which is Unit # 2, has the worst moment when it rejects full load 0.8 s after Unit #1. At this condition, the wall pressure of the draft tube of unit # 2 attains the vapor pressure and reverse water hammer pressure attains the maximum value of 6.8 m during water column bridging. However, the reverse water hammer pressure was 290 m in prototype unit. Under one-after-another load rejection, water column separation occurs when the draft tube attains the second extreme value, and the unit located in the turbine braking condition area. It was observed that the pressure pulsation frequency of the draft tube after one-after-another load rejection is composed of two parts. First, pressure pulsation frequency caused by swirling flow with a value of 0.4 f/fn and second, a broadband of 40–200 Hz generated by the reverse water hammer due to water column bridging and structural response of the unit.

Evolution mechanism of water column separation in pump turbine: Model experiment and occurrence criterion

Whether the superposition of pressure pulsation and water hammer pressure caused by the fast closing of guide vanes causes water column separation in draft tube inlets is a hot topic in engineering and academic fields. It is also not known whether the bridging of water column separation endangers the operation of the units. This study uses a model pumped storage power station platform with two units to perform water column separation. Data on the pressure pulsation at different measurement points, discharges, and speeds are collected by an acquisition system, whereas the development process of water column separation is characterized by a high-speed camera. The measured pressure is decomposed into the water hammer pressure, which migrates with the unit operation point and pressure pulsation. The test results reveal that the pressure in the inlet section of the draft tube below the vaporization pressure that lasts for several seconds is a sufficient and necessary condition for water column separation to occur. The water hammer pressure has a significant influence on the water column separation, while low-frequency pressure pulsation has less influence. Water column separation is divided into four stages: starting, improvement, separation, and bridging. The main frequency of the pressure pulsation in the water column separation process is the frequency of the water hammer caused by load rejection and has a value of 0.47f/fn. Cavity bridging generates a frequency of 0.30f/fn. The flow-speed curve remains in the braking condition of turbine for 1.25 s. The separation and part of the bridging stage occur under the braking condition of turbine.

Pressure fluctuation characteristics of a pump turbine in a draft tube: New insight into water column separation

The pumped-storage hydropower station is the most reliable, economic, long-term, large capacity, and mature energy storage technology in the power system, and it is an important component of renewable energy. Cavitation and water column separation of a pumped storage unit are important and widely researched factors in the safe and stable operation of a unit. This study focused on the evolution of water column separation of a pump turbine and its relationship with the pressure distribution of the cross section of a draft tube as well as the pressure pulsation characteristics of different measuring points in the cross section of the draft tube. A pumped storage experimental platform that can realize water column separation is established, and experiments with different opening angles are carried out. The results show that there are three factors that impact water column separation and cavitation: gas nucleus, vaporization pressure, and duration of vaporization pressure. Water column separation is the development and continuation of cavitation. The difference between the center pressure of the vortex rope and the wall pressure is large, reaching 2.23 m at a large opening. The pressure fluctuation amplitude of the wall measuring point is greater than that of the other measuring points in the same cross section, but the frequency characteristics are the same. In the transition process, the pressure pulsation amplitude of the liquid column bridging is the largest, and the largest pressure pulsation amplitude can reach 4.18 m at a small opening.

Experimental study of cavitating vortex rope and water column separation in a pump turbine

During the transient processes in load rejection in a pumped-storage system, water column separation (WCS) can occur in the draft tube when the local pressure is less than the vapor pressure. The reverse water hammer due to water column bridging affects the safety of the unit and the tailrace tunnel. However, what are the conditions that trigger WCS? What is the physical mechanism? These questions have not been elucidated experimentally. Therefore, it is necessary to investigate the conditions that lead to WCS and the impact of the reverse water hammer generated by WCS bridging on the stability of the unit. In this study, a semi-open test rig was modified by installing a variable-frequency pump to reduce the static pressure, resulting in a cavitation vortex in the draft tube. The static pressure and the water hammer pressure derived from load rejection cause the pressure at the draft tube wall to fall below the vapor pressure for some time, interrupting the flow in the draft tube. This is a typical case of WCS in a pump turbine. If the pressure in the draft tube does not remain at the minimum pressure for long enough, imperfect water column separation may occur with bubble groups. The amplitude of the pressure pulsations during the initial and development stages was (−0.2 m, 0.2 m). It was 4.96% of the initial static pressure. Thus, the pressure fluctuations have a negligible effect on WCS.

Evolution and influence of pump-turbine cavitation during load rejection transients of a pumped-storage plant

Load rejection is one of the most dangerous transients in pumped-storage plants, during which cavitation in pump-turbines is normally inevitable. In this study, we applied the one-dimensional and three-dimensional coupled computational fluid dynamics method to simulate the 100% load rejection transient process of a middle-head plant, analysed the evolution and influence of cavitation cavities, and evaluated the safety. During the guide-vane closing process, a spiral-shaped cavitation cavity under the runner cone and nine wedge-shaped cavitation cavities inside the blade channel outlets occur successively. Although no water column separation happens in the draft tube inlet, the collapses of the wedge-shaped cavities induce obvious impacts on the runner, causing axial force fluctuations, to which attention should be paid in the plant design phase. This study further validated the feasibility of the coupled method and revealed the mechanism of the dynamic cavitation phenomenon, which provides references for research and engineering design.

Numerical modeling of water hammer in long water transmission pipeline

In the present study, a water transmission pipeline under steady conditions is modeled followed by examining the transient flow created by the failure of pumps in the pipeline. This pipeline is 31 km from the water transmission pipeline of Kerman, Iran. The software analysis results were compared with those of a numerical model for a laboratory test to validate transient flow modeling. While transient flows are created by pump failure, various areas of the water transmission pipelines will be affected by the transient waves produced. Long water transmission pipelines, usually large in diameter and flow rate, will pose problems in the negative pressure phase. The negative pressure causes threatening problems like water column separation and cavitation. The results indicated that using equipment like air valves when the pumps fail alone does not have the appropriate efficiency in eliminating the hazards in the water transmission pipelines. More examination showed that installing equipment like water flow feed and hydropneumatic tanks along the pipeline length in the right places prevents the negative pressure created and the pipeline risk significantly reduces.

Investigation of water column separation induced by pressure pulsation based on critical cavitation rate model

Significant pressure fluctuation may exists at the inlet of the draft pipe during load shedding of water pump and turbine sets. When the tail-water level is low, the minimum water hammer pressure at the inlet of the draft pipe set is higher than evaporation pressure; however, the overall pressure after superposition with pulsating pressure may reach the evaporation pressure in an instant. In these cases, it is unknown if a cavity is formed or water column separation is induced. It is also unknown how frequency and amplitude of the pulsating pressure affect the formation of cavity or water column separation. However, in terms of the physical formation of water column separation, liquid pressure reaching evaporation pressure is only the necessary condition of water column separation rather than a sufficient condition because the growth and aggregation of cavitations take time. In addition, water column separation could be induced only when the cavitation rate in the water reaches a specific value and gas-liquid relative motion occurs. In this study, based on the uniform cavitation distribution model, the critical of flow velocity gradients are calculated both in front and at the back of the section and are the sufficient condition of water column separation. This study uses the criterion of when the ratio of the vaporous cavitation volume to the volume of the pipe segment with a length of Δx exceeds a critical cavitation rate for classifying water column separation segments and non-water column separation segments. In water column separation segments, a concentrated vaporous cavitation model is used for calculation; however, dynamic meshes should be applied for tracking the change of vaporous cavitations. In the non-water column separation segments, the vaporous cavitation volume can be calculated according to the continuity equation but is converted into a cavitation rate in the pipe segment and substituted into gas-liquid two-phase equation to calculate wave velocity. Next, a case study was performed on a pipe-valve system. By taking into account the pulsating pressures with different frequencies and amplitudes on the downstream side in the valve closing process, water column separation and merging processes were analyzed and the change in flows, cavitation volumes and pressures on various sections and their laws during the transient process were concluded.

An Experimental Study on the Water Hammer with Cavity Collapse under Multiple Interruptions

Pressurized pipeline system damage is primarily caused by the highly destructive water hammer force. Currently, research on water hammer-caused collapse is mostly based on single-point collapse cases, but water hammer research, which involves multipoint collapse, is insufficient. Here, we establish an experimental platform to realize water hammers with multipoint collapse. With different schemes, i.e., various initial flow rates and valve closing speeds, we observed the hydraulic transient process with a high-speed camera, analyzed its characteristics and explained experimental phenomena with theoretical knowledge. Using experimental data analysis, we summarized the influencing factors and laws of the cavity length and water hammer pressure. Flow and pressure data for the different schemes were recorded to provide basic simulation data. Water column separation experimental phenomena were observed: completely atomized, completely cavitated and partially cavitated, and both cavitated and atomized. At the pump outlet, three hydraulic transition states occurred simultaneously in the horizontal pipe section: completely atomized, completely cavitated, and both cavitated and atomized. Two hydraulic transition states occurred in the knee region: completely and partially cavitated, and without atomization. The experimental results reveal that the initial flow rate and valve closing speed greatly affect the water hammer pressure rise and cavity length. The higher the initial flow rate and valve closing speed are, the larger the water hammer pressure rise and cavity length are.

Water column separation in pump-turbine after load rejection: 1D-3D coupled simulation of a model pumped-storage system

Water column separation (WCS), the breaking of continuous water flow by a vapor cavity, is extremely dangerous because the rejoining of the separated water columns would lead to tremendous pressure rises. Therefore, the turbine draft-tube pressure after the load rejection in hydropower stations should be controlled to prevent such an unbearable load of turbine units. To understand the forming, growing and collapsing processes of WCS in pump-turbines during the load rejection transients with guide-vane closing, a model pumped-storage system was simulated by the one-dimensional and three-dimensional coupled computational fluid dynamics model, in which the water conveyance system and pump-turbine were treated as one-dimensional and three-dimensional domains, respectively. The entire processes of the breaking and rejoining of water flow in the pump-turbine, as well as the variations in the pressure field and hydraulic forces on the runner, were analyzed. The main finding is that the collision of the separated water liquids and the collapses of the cavities occur separately with a time difference, which induces two high-amplitude mono-pulses in both the axial and radial forces on the runner. These two successive hydraulic impacts are extremely destructive and should be considered with greater emphasis when evaluates the risk of WCS.

Computational Fluid Dynamics (CFD) simulation of liquid column separation in pipe transients

The present study deals with the computational simulation of transient events of water hammer and column separation in a water pipeline system. Three-dimensional CFD simulations based on the Finite-Volume (FV) approach are performed to predict pressure fluctuations and to visualize liquid column separation/rejoining caused by the sudden closure of a valve located at the upstream end of the pipe. Explanation of vaporous cavitation phenomena is also presented. The Volume of Fluid (VOF) model and Schnerr-Sauer cavitation model are used to describe the multiphase flow and the transient vaporous cavitation, respectively. Moreover, the shear-stress transport (SST) turbulence model is applied to model the Reynolds stresses using the Boussinesq hypothesis. Present results are compared with available experimental and numerical results from the literature. The comparisons show that the present method gives adequate results. Also, the 3D model adopted is deemed physically superior to the existing 1D models as it removes the restriction of the 1D models that vapor cavities, when formed, fill the whole cross-section of the pipe without radial variation. In addition, 1D models are not able to predict the stratification effect due to density variation of the two phases. Consequently, the 3D model can better visualize the phenomenon of liquid column separation/rejoining in pipes than 1D models.

A Simulation Calculation Method of a Water Hammer with Multpoint Collapsing

The traditional discrete vapor cavity model (DVCM) is widely used in water hammer simulation. Water column separation in pipelines is usually predicted with this model. Nevertheless, the main weaknesses of this model consist of numerical instability and nonconvergence. Regarding the weaknesses of the traditional model, this paper discusses an improved method. The new method uses a new water hammer velocity formula, a new cavity model, and a floating grid method. Through simulations to test the effects of the new model, an experimental platform can be established to realize a water hammer with multipoint collapsing. The numerical simulation was programmed in C++ and the test was carried out with an actual pipeline model built in the laboratory. After certain modelling and calibration, the parameters in the simulation calculation were consistent with the measured parameters in the test. The numerical simulation results were compared with the experimental results. For the hydraulic transient system with multipoint collapsing, the superposition effect of the wave crest of the pseudo-water hammer in the traditional calculation model was obvious. The pressure of the water hammer in the simulation calculation was significantly higher than the actual value and the convergence effect of the water hammer wave was not good. Compared with the results of the traditional model, the simulation results of the new model were closer to the measured values. Therefore, the new model has better numerical solution accuracy, stability, and convergence, which is worth further study and promotion.

Dynamic Closing Modelling of the Penstock Protection Valve for Pipe Burst Simulations

The penstock protection valve equipped with downstream air valve is a safety component aiming to cut off the discharge in case of pipe burst. The hydraulic transient simulation of pipe burst scenario is challenging since the closing time results from the system dynamics, air is admitted through the downstream air valve and cavitation may occur in the penstock. To perform such simulation, a dynamic model of the penstock protection valve is developed and presented in this paper. Closing time, maximum flow rate reached during the pipe burst or maximum oil pressure in the cylinder of servomotor during the non-linear closing law are results derived with this model. Moreover, influence of cavitation in the valve and in the penstock are considered in the model. It is showed that simulation of pipe burst should consider i) cavitation model in the penstock protection valve, ii) water column separation in the penstock and iii) air admission by the air valves located downstream to the valve to obtain realistic results.

Experimental Assessment of Water Hammer-Induced Column Separation in Oil-Hydraulic Pipe Flow

Cavitation erosion through water hammer and column separation is a major concern in hydraulic applications such as percussive rock drilling. Cavitation aspects must be considered both in early and late design stages, which require deep knowledge and tools for prediction. In this study, an oil-hydraulic test equipment for water hammer assessment was designed using state-of-the-art simulation tools. Several tests were performed, with and without column separation, showing good repeatability on measured pressures. At higher flow rates, column separation was the dominating feature and several high-pressure peaks with subsequent time delay reduction could be observed. These patterns were affected by the oil temperature, with most substantial changes at lower temperature ranges (<32 °C). Standard transmission line simulations managed to predict the water hammer, but as expected not the column separation, which is the theme of future work using this setup.