BWR steam line and turbine model with multiple piping capability

Power equipment deterioration occurs during operation, it causes loss in reliability and efficiency, unscheduled shutdowns, and accidents. Now predictive analytics is one of the promising directions in the field of power engineering which allows to control and analyze the technical condition of power equipment. The problems of localization of deviation of technological parameters and detection of anomaly in the operation of power equipment are consistently solved in the framework of predictive analytics. The problems of deviations localization and anomalies detection are solved by the methods of statistical modeling and the classification algorithms respectively. However, for steam turbines the localization of deviation and the detection of anomalies having slow-flowing character are a difficult problem. Therefore, the issue of development of a method for continuous monitoring of technical condition and maintenance diagnostics based on a mathematical model of the steam turbine section flow characteristics is worth noticing. The method allows us to consider the effect of changes in the open flow area of the individual sections of a steam turbine on the pressure distribution over the steam flow path. The model of a steam turbine has been developed within the matrix formalization methodology. The solution of the system of linear and nonlinear equations is carried out by methods of computational mathematics. The solution of the optimization problems of the steam flow path diagnostics is carried out by methods of mathematical programming. A mathematical model of the cogeneration steam turbine Т-250/305-23.5-DB and a method for continuous condition monitoring and maintenance diagnostics of steam turbine have been developed. It allows us to localize deviation and detect anomaly by recovery of the open flow area of the individual sections of a steam turbine based on the pressure distribution over the steam flow path. The results of the statistical analysis prove that a mathematical model of the cogeneration steam turbine Т-250/305-23.5-DB has been recognized adequate. The method for continuous condition monitoring and maintenance diagnostics of steam turbine has demonstrated consistency of the obtained results and ability to solve diagnostic problems in practice. The developed model and method can be used as a module in the development of a software package for predictive analytics of power equipment.

A one-dimensional dual-pressure steam turbine (ST) model for the marine Rankine cycle is built in this paper. Based on constructal theory, the optimal design of the dual-pressure ST is performed with a fixed total volume of the high- and low-pressure STs. The total power output (PO) of the dual-pressure ST is maximized. Seventeen parameters, including the dimensionless average diameters (DADs) of the stages, steam inlet angles (SIAs) of the stages, average reaction degrees (ARDs) of the stages, and volume ratio of the high-pressure ST are taken as optimization variables. The optimal structure parameters of the stages are gained. It reveals that the total PO of the dual-pressure ST is increased by 2.59% by optimizing the average diameter of the Curtis stage, and the change in the total PO is not obvious by optimizing the average diameter of the third stage of the low-pressure ST. Both the total PO and the corresponding efficiency of the dual-pressure ST are increased by 10.8% after simultaneously optimizing 17 variables with the help of the Matlab optimization toolbox. The novelty of this paper is introducing constructal theory into turbine performance optimization by varying seventeen structure, thermal and flow parameters, and the result shows that the constructal optimization effect is remarkable. Optimal designs of practical STs can be guided by the optimization results gained in this paper.

Prior to the initial steam admission to 1,000MW steam turbine in a thermal power plant after its construction, the turbine control system was verified by using a process model developed based on the heat balance and actual process operating data of same type thermal power plant. The total system where the process model was integrated into the controller hardware with input and output modules is generally called verification system. Unlike a widely used simulator composed of only personal computer and software in the laboratory, this verification system have a great difference which can be connected with actual speed control system and field devices by use of actual signal lines. So, if it is used for verification of control system and field devices immediately before steam turbine start up, though there is no steam from boiler to turbine, the field adaption test cab have a very similar result because the steam control valve in the field can be actuated according to the controller's command and its position can be transferred back to the controller. The above mentioned method is very helpful to verify the control algorithm and such field devices as poisoners, servo valves, limit switches and pressure switches. This paper introduces the whole procedure and the result of simulation test using the above mentioned verification system with actual control hardware and the steam turbine model.

Finite element models (FEMs) are extensively used in the design optimization of utility scale steam turbines. As an example, by simulating multiple startup scenarios of steam power plants, engineers can obtain turbine designs that minimize material utilization, and at the same time, avoid the damaging effects of large thermal stresses or rubs between rotating and stationary parts. Unfortunately, FEMs are computationally expensive and only a limited amount of simulations can be afforded to get the final design. For this reason, numerous model reduction techniques have been developed to reduce the size of the original model without a significant loss of accuracy. When the models are nonlinear, as is the case for steam turbine FEMs, model reduction techniques are relatively scarce and their effectiveness becomes application dependent. Although there is an abundant literature on model reduction for nonlinear systems, many of these techniques become impractical when applied to a realistic industrial problem. This paper focuses on a class of nonlinear FEM characteristic of thermo-elastic problems with large temperature excursions. A brief overview of popular model reduction techniques is presented along with a detailed description of the computational challenges faced when applying them to a realistic problem. The main contribution of this work is a set of modifications to existing methods to increase their computational efficiency. The methodology is demonstrated on a steam turbine model, achieving a model size reduction by four orders of magnitude with only 4% loss of accuracy with respect to the full order FEMs.

The diversification of power generation methods within existing power networks has increased the requirement for operational flexibility of plants employing steam turbines. This has led to the situation where steam turbines may operate at very low volume flow conditions for extended periods of time. Under operating conditions where the volume flow through the last stage moving blades (LSMBs) of a low-pressure (LP) steam turbine falls below a certain limit, energy is returned to the working fluid rather than being extracted. This so-called “ventilation” phenomenon produces non-synchronous aerodynamic excitation, which has the potential to lead to high dynamic blade loading. The aerodynamic excitation is often the result of a rotating phenomenon, with similarities to rotating stall, which is well known in compressors. Detailed unsteady pressure measurements have been performed in a single stage model steam turbine operated with air under ventilation conditions. Detailed analysis revealed that the rotating excitation mechanism observed in operating steam turbines, is reproduced in the model turbine. 3D CFD has been applied to simulate the unsteady flow in the air model turbine. The numerical model consists of the single stage modeled as a full annulus, as well as the axial-radial diffuser. An unsteady CFD analysis has been performed for sufficient rotor revolutions such that the flow is globally periodic. It has been shown that the simulation reproduces well the characteristics of the phenomenon observed in the tests. The detailed insight into the flow field allows the drawing of conclusions as to the nature of the excitation mechanism. One result is that the LSMB tip clearance flow is found to have very little or no effect on the characteristics of mechanism for the case studied.

The use of polymeric pipes such as polyethylene (PE) and polyvinyl chloride (PVC) has recently increased in water distribution networks. This necessitates the understanding of the viscoelastic behaviour of these pipes in practice and in particular for transient flow analysis. The purpose of this study is to calibrate a developed numerical model based on the experimental results of transient flow in PE pipe networks. The linear viscoelastic model parameters were calibrated using the inverse transient analysis. Comparison of numerical results with experimental data indicated that the developed viscoelastic model was able to predict both pressure wave damping and dispersion in these pipe systems. Results confirmed a negligible viscoelastic effect of single pipe and pipe network on the linear viscoelastic model. Hence, the calibrated results of a single PE pipe were used to simulate the transient flow in the pipe network. The experimental and simulation results of pipe network transient flow in this study are new and advance previous studies.

The Terry turbine is a small, single-stage, compound-velocity impulse turbine originally designed and manufactured by the Terry Steam Turbine Company purchased by Ingersoll-Rand in 1974. Terry turbines are currently manufactured and marketed by Dresser-Rand. Terry turbines were principally designed for waste-steam applications. Terry turbopumps are ubiquitous to the US nuclear fleet as a steam driven turbopump in either the reactor core isolation cooling system (RCIC) and high pressure coolant injection systems for boiling water reactors (BWRs) or in the auxiliary feedwater system (AFW) system for pressurized water reactors (PWRs). Prior to the accidents at Fukushima Daiichi, assumptions and modeling of the performance of Terry turbopumps were based mostly on generic vendor use of NEMA SM23 Steam Turbine for Mechanical Drive Service guidance [1]. However, the RCIC/AFW system performance (i.e., the Terry turbopump) under beyond design basis event (BDBE) conditions is poorly known and largely based on conservative assumptions used in probabilistic risk assessment (PRA) applications. For example, common PRA practice holds that battery power (DC) is required for RCIC operation to control the vessel water level, and that loss of DC power results in RCIC flooding of the steam lines and an assumed subsequent failure of the RCIC turbopump system. This assumption for PRA implies that RCIC operation should terminate on battery depletion which can range from 4 to 12 hours. In contrast, real-world observation from Fukushima Daiichi Unit 2 shows that RCIC function was not terminated by uncontrolled steam line flooding or loss of control power, and in fact provided coolant injection for nearly three days [2]. There is a current effort being undertaken by the US industry, the US Department of Energy (DOE), and the Government of Japan to investigate the true operating band of the Terry turbopump for BDBE conditions. This paper provides a summary of the experimental and modeling efforts to date. Paper published with permission.

Geometric Modularity in the Thermal Modeling of Solar Steam Turbines

Subsynchronous vibration of high-pressure steam turbine is one of the difficult problems to improve the reliability of power plant. Extensive work has been done to prevent the low frequency vibration of high-capacity steam turbine and most of the problems were practically solved[1][2]. In the future, we must build up theoretical approach to design a new turbine operating under the steam condition of high-temperature and high-pressure. To design such an advanced steam turbine, it is necessary to solve the effect of partial admission on control stage of the steam turbine. This paper describes the experimental results from the scale model of the steam turbine and theoretical analysis of Alford force considered partial admission condition to solve the problem. (1) Subsynchronous vibration was reproduced in the scale model test. (2) Partial admission gave larger destabilizing force compared with full admission condition for same total flow rate. (3) Initial position of shaft center to the phase of admission arc on the partial admission had some effect on the stability of the rotor system. (4) Theoretical analysis of destabilizing force considered partial admission condition gave qualitative description of the experimental results from the scale model.

Steam turbines are increasingly being used in industries for duties other than base load operations, where fast start-ups, rapid load changes, and frequent shutdowns are involved. Generally, industrial steam turbines operate with constant inlet steam parameters and are partial admission turbines having the first turbine stage as an impulse stage and the subsequent turbine stages as reaction stages on drum-type rotors. During start-up, as control valves open, steam is admitted and passes through impulse blading, wheel chamber, and through the subsequent reaction stages. The turbine outer casing is horizontally split and the parting plane flanges have relatively thick sections. To limit thermal stresses which arise due to temperature differences in outer casings and rotors, the steam flow has to be increased gradually. The rate at which the steam flow is to be increased depends on the efficiency of heat transfer, i.e., the heat transfer coefficient, and hence knowledge of inside heat transfer coefficient is essential. The high heat transfer coefficients, h, at the beginning of cold start are attributable to condensation of steam at initial stages. The value of h decreased with lapse of time, and also its variation reduced considerably over time. Further, the h value varies more with more » location rather than with lapse of time. The variations observed in h show the complexity of heat transfer process and also bring out the fact that semi-empirical formulas, such as Gazley`s (1958), are not accurate for application in steam turbines. More studies need to be conducted on models of steam turbines to generate adequate data based on which a new correlation for the heat transfer coefficient h for start-up phase of operation could be proposed. « less

The fault diagnosis model of steam turbine based on Bayesian network is direct impacts on the complexity of the diagnostic process, so the construction of Bayesian network model is the primary problem. According actual fault diagnosis system of steam turbine containing redundancy and uncertain information, proposed attribute reduction method to fault feature, obtained the minimal diagnosis rules. Based on two-node union reverse inference, proposed an improved program in the construction of Bayesian network. The Bayesian network model based on the minimum fault decision table can effectively reduce the complexity of the network structure, while the using of improved Bayesian network can further reduce complexity of structure and improve the diagnosis speed. Finally, the effectiveness and fastness of this method are validated by the result of practical fault diagnosis example in Bently-RK4 rotor vibration bench.

The article proposes an object-oriented method for modeling steam turbine plants. The novelty of the method is in the application of a steam turbine model that takes into account variations in internal efficiency under variable operating modes.The article presents the results of theoretical substantiation of nonlinear dependence of the power of the turbine compartments on the steam flow passing through them, based on the change in the internal efficiency of the stages under variable modes described by the Stodola-Flugel equation. An empirical dependence of the efficiency of the stage operation on the relative steam consumption is proposed. Recommendations on the use of empirical form in the development of models of steam turbine compartments are given. The empirical dependences of the relative internal efficiency of turbine compartments obtained from the results of thermal tests of an operating turbine unit are presented.As a factor of practical significance of the research, a model of PT-60-130/13 type steam turbine plant has been developed involving the use of an object-oriented programming language. Recommendations on the description of classes of objects within the steam turbine plant. The developed STP model enables to simulate any operating modes depending on electrical and thermal loads, as well as to take into account the influence of deviations of external factors from nominal values when developing a system of corrections or estimating an increase in fuel consumption associated with these deviations.

Reactive transport in unsaturated soil: Comprehensive modelling of the dynamic spatial and temporal mass balance of water and chemical components

Publication Rights Reserved This paper was prepared for the Society of Petroleum Engineers Gas Technology Symposium to be held in Omaha, Nebr. Sept. 15–16, 1966. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon requested to the Editor of the appropriate journal, provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers Office. Such discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper attacks the problem of computing transient flow in gas pipeline networks by means of finite differences and digital computation. Pressure (P) and flow (Q) are assumed to he dependent upon a single space variable (x) along the pipe and on the time (t). A greatly simplified but generally accepted mathematical model consistent, of a system of nonlinear partial differential equations is the point of departure: Following simple changes of variable (w = p2, v = Q2), the problem is reduced to the solution of: A stable predictor-corrector method of finite difference approximation due to Jim Douglas, Jr. and B.R. Jones, Jr. is employed to reduce the computation to the solution of a system of linear algebraic equations (matrix inversion). The incorporation of initial conditions, boundary conditions, and internal flow conservation equations, all of which in finite difference form become linear algebraic equations, results in a single matrix equation for the calculation of pressures and flows in the pipeline network. DERIVATION OF FINITE DIFFERENCE EQUATIONS The computation of transient flow in gas pipeline networks is complicated mathematically by the nonlinearity of the governing partial differential equations. This is in marked contrast, of course, to the situation in steady state flow, where the corresponding equations, at least in their simplest form, have exact mathematical solutions. The mathematical model we assume has resulted from a number of simplifications, including the neglect of altitude and temperature variation. Although it is beyond the scope of this note to discuss the validity and significance of these simplifications, it is generally believed that the equations we will discuss are an accurate first order description of the actual physical system.

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.