Flux vector splitting solutions for coupling hydraulic transient of gas-liquid-solid three-phase flow in pipelines

The gas-liquid-solid three-phase mixed flow is the most general in multiphase mixed transportation. It is significant to exactly solve the coupling hydraulic transient problems of this type of multiphase mixed flow in pipelines. Presently, the method of characteristics is widely used to solve classical hydraulic transient problems. However, when it is used to solve coupling hydraulic transient problems, excessive interpolation errors may be introduced into the results due to unavoidable multiwave interpolated calculations. To deal with the problem, a finite difference scheme based on the Steger- Warming flux vector splitting is proposed. A flux vector splitting scheme is established for the coupling hydraulic transient model of gas-liquid-solid three-phase mixed flow in the pipelines. The flux subvectors are then discretized by the Lax-Wendroff central difference scheme and the Warming-Beam upwind difference scheme with second-order precision in both time and space. Under the Rankine-Hugoniot conditions and the corresponding boundary conditions, an effective solution to those points located at the boundaries is developed, which can avoid the problem beyond the calculation region directly induced by the second-order discrete technique. Numerical and experimental verifications indicate that the proposed scheme has several desirable advantages including high calculation precision, excellent shock wave capture capability without false numerical oscillation, low sensitivity to the Courant number, and good stability.

THEORETICAL ANALYSIS ON HYDRAULIC TRANSIENT RESULTED BY SUDDEN INCREASE OF INLET PRESSURE FOR LAMINAR PIPELINE FLOW

Hydraulic transient, which is resulted from sudden increase of inlet pressure for laminar pipeline flow, is studied. The partial differential equation, initial and boundary conditions for transient pressure were constructed, and the theoretical solution was obtained by variable-separation method. The partial differential equation, initial and boundary conditions for flow rate were obtained in accordance with the constraint correlation between flow rate and pressure while the transient flow rate distribution was also solved by variable-separation method. The theoretical solution conforms to numerical solution obtained by method of characteristics (MOC) very well.

SIMULATION OF HYDRAULIC TRANSIENTS IN HYDROPOWER SYSTEMS USING THE 1-D-3-D COUPLING APPROACH

Although the hydraulic transients in pipe systems are usually simulated by using a one-dimensional （l-D） approach, local three-dimensional （3-D） simulations are necessary because of obvious 3-D flow features in some local regions of the hydropower systems. This paper combines the 1-D method with a 3-D fluid flow model to simulate the Multi-Dimensional （MD） hydraulic transients in hydropower systems and proposes two methods for modeling the compressible water with the correct wave speed, and two strategies for efficiently coupling the 1-D and 3-D computational domains. The methods are validated by simulating the water hammer waves and the oscillations of the water level in a surge tank, and comparing the results ~with the 1-D solution data. An MD study is conducted for the transient flows in a realistic water conveying system that consists of a draft tube, a tailrace surge tank and a tailrace tunnel. It is shown that the 1-D-3-D coupling approach is an efficient and promising way to simulate the hydraulic transients in the hydropower systems in which the interactions between 1-D hydraulic fluctuations of the pipeline systems and the local 3-D flow patterns should be considered.

DOUBLE METHOD OF CHARACTERISTICS TO ANALYZE HYDRAULIC-THERMAL TRANSIENTS OF PIPELINE FLOW

The hydraulic and thermal transients in pipeline flow were studied. The method of characteristics for hydraulic transient analysis of batch transport of pipeline flow had been improved. The thermal transient equation, in which the term with v 3 was involved, had been inferred, while the corresponding method of characteristics was constructed. The double method of characteristics, which can be used to study the coherent hydraulic-thermal transients of batch transport of pipeline flow, was developed.

Equivalent pipe algorithm for metal spiral casing and its application in hydraulic transient computation based on equiangular spiral model

For the metal spiral casing of water turbines, a new equivalent pipe algorithm is developed based on the idea of equiangu-lar spiral. Prototype tests and computations are carried out to investigate the hydraulic transient characteristics. The computation re-sults by using the new model are in a good agreement with the prototype test data with respect to the maximum speed of the tur-bine-generator unit, the maximum water hammer pressure in the spiral casing and the maximum vacuum in the draft tube. The propo-sed method is a significant improvement over the conventional algorithm with the accuracy increased and the error reduced by about 3%.

Simulation of the load rejection transient process of a francis turbine by using a 1-D-3-D coupling approach

This paper presents the simulation and the analysis of the transient process of a Francis turbine during the load rejection by employing a one-dimensional and three-dimensional （1-D-3-D） coupling approach. The coupling is realized by partly overlapping the I-D and 3-D parts, the water hammer wave is modeled by defining the pressure dependent density, and the guide vane closure is treated by a dynamic mesh method. To verify the results of the coupling approach, the transient parameters for both typical models and a real power station are compared with the data obtained by the 1-D approach, and good agreements are found. To investigate the differences between the transient and steady states at the corresponding operating parameters, the flow characteristics inside a turbine of the real power station are simulated by both transient and steady methods, and the results are analyzed in details. Our analysis suggests that there are just a little differences in the turbine outer characteristics, thus the traditional 1-D method is in general acceptable. However, the flow patterns in the spiral casing, the draft tube, and the runner passages are quite different： the transient situation has obvious water hammer waves, the water inertia, and some other effects. These may be crucial for the draft tube pul- sation and need further studies.

ANALYSIS OF FIRST TRANSIENT PRESSURE OSCILLATION FOR LEAKDETECTION IN A SINGLE PIPELINE

The leak detection is of great importance in the reliable operation and management of a pipeline system. Recently, attention is shifted to the use of the time domain or frequency domain methods based on the transient analysis. These methods sometimes require accurate pressure signals obtained during the transient period or by creating ideal conditions in testing. This paper proposes a method that does not require transient simulations over the whole or an extended period of time, but uses the first transient pressure oscillation to detect leaks. The method considers the propagation of the pressure oscillation wave created from a fast valve closure and the reflected damp wave from the leak. A leak in the pipe gives rise to reflected waves which in turn create discontinuities in the observed signal at the measurement section. The timing of the reflected damp wave and the magnitude represent the location and the size of the leak, respectively. An analytical expression is derived based on the Method Of Characteristic （MOC） for the relationship between the leakage and the reflected magnitude. The leak detection procedure based on the method is also given. Then the reliability of the method is tested on numerically simulated pressure signals and experimental pressure signals with calibrated leak parameters, and the results indicate a successful application and the promising features of the method.

Transient simulation and analysis of the simultaneous load rejection process in pumped storage power stations using a 1-D-3-D coupling method

The load rejection imposes a danger in the pumped storage hydropower plants(PSPs),especially when two or more pump turbines reject their loads simultaneously.In this paper,the simultaneous load rejection scenarios in the PSPs are simulated and analyzed by using a 1-D,3-D coupling method.The PSP pipe system is modeled by using the 1-D method of characteristics(MOC)and one pump turbine is modeled by using the 3-D computational fluid dynamics(CFD).The simulated flow and head are transmitted between the 1-D,3-D regions through the interfaces between these two regions.By assuming that the installed pump turbines are of the same type and the corresponding branch pipes have the same properties,the variations of the transient pressures and the flowrates in different pump turbines will be identical.Therefore,only one pump turbine is modeled by the CFD in this study.A new branching junction boundary is proposed to assign the simulated dynamic pressures and flowrates obtained by the 3-D model to other pump turbines.The 1-D-3-D coupling method is validated by experiments with only one pump turbine rejecting its load.The simultaneous load rejection of two pump turbines is then simulated and validated by comparing the results with those of the 1-D simulation.By building only one pump turbine 3-D model,a large amount of computational resources can be saved.The simultaneous load rejection scenario is then analyzed and compared with the single load rejection scenario.Higher water hammer pressures and a larger rotational speed occur in the simultaneous load rejection scenario,which leads to larger pressure pulsations in the pump turbine.The larger pressure pulsations can be further explained by the flow patterns in the runner channels,in which heavier flow separations and vortexes can be observed in the simultaneous load rejection scenario.

3-D simulation of transient flow patterns in a corridor-shaped air-cushion surge chamber based on computational fluid dynamics

The 3-D characteristics of the water-air flow patterns in a corridor-shaped air-cushion surge chamber during hydraulic transients need to be considered in the shape optimization. To verify the reliability of the water-air two-phase model, namely, the volume of fluid model, the process of charging water into a closed air chamber is successfully simulated. Using the model, the 3-D flow characteristics under the load rejection and acceptance conditions within the air-cushion surge chamber of a specific hydro- power station are studied. The free surface waves, the flow patterns, and the pressure changes during the surge wave process are analyzed in detail. The longitudinal flow of water in the long corridor-shaped surge chamber is similar to the open channel flow with respect to the wave propagation, reflection and superposition characteristics. The lumped parameters of the 3-D numerical simulation agree with the results of a 1-D calculation of hydraulic transients in the whole water conveying system, which validates the 3-D method. The 3-D flow structures obtained can be applied to the shape optimization of the chamber.

Optimization of closing law of turbine guide vanes based on improved artificial ecosystem algorithm

Optimization of the closing law of the guide vane is the most economical and efficient way to reduce the risk incurred by pressure and speed excursions,thus guaranteeing the security of the hydro-turbine and the whole hydraulic network.In order to optimize the closing law of the guide vane of hydraulic turbine,an improved artificial ecosystem optimization algorithm was proposed(IAEO).The reverse learning was used to initialize the population,multi-strategy bound handing schemes was used to improve the algorithm convergence speed.Twenty-three mathematical benchmark functions were used to test the IAEO.Results showed an improvement in the IAEO algorithm convergence speed and a stronger exploration than other algorithms.IAEO algorithm was used to optimize the closing law of the guide vane of hydraulic turbine based on the hydraulic transient calculation.The results showed that the maximum pressure in the spiral casing inlet,the minimum pressure in the draft tube inlet and the maximum speed all meet the design requirements by use of the closing law of the guide vane optimized by IAEO.Compared with other algorithms such as particle swarm optimization(PSO),artificial ecosystem-based optimization(AEO)and grey wolf optimizer(GWO),the closing law of the guide vane optimized by IAEO algorithm was proved to be of great advantages in distribution of safety margin of each optimization goal.

变顶高尾水系统尾水管进口真空度的近似公式

本文研究了甩负荷工况下变顶高尾水管进口真空度的近似计算公式。在水击波相数较大情况下,可忽略水体和尾水洞壁弹性。本文从非恒定渐变流动的Bernoulli方程出发,推导出变顶高尾水系统在甩负荷情况下尾水管进口处真空度计算的基本方程。讨论了基本方程中的静力真空项、动力真空项和惯性真空项,得出并简化了最大真空度计算公式。该近似公式计算结果与物理模型试验结果接近。在水轮机导叶缓慢关闭和尾水洞较短的情况下,近似公式可应用于工程初步设计。