Steam Turbine Rotor Research Articles

Damage-driven framework for reliability assessment of steam turbine rotors operating under flexible conditions

The high-temperature rotating structures (HTRS), e.g., steam turbine rotors, often operate in extremely harsh environments with a flexible load condition during peak shaving of power system. In this work, a damage-driven framework for reliability assessment is developed in terms of the cumulative damage-damage threshold interference (CD-DT) principle, in which the cumulative damage and damage threshold are regarded as two random parameters to address uncertainties. The CD-DT principle is founded on the engineering damage theory and incorporates physics-of-failure into the probabilistic modeling of high-temperature structural reliability. Probabilistic damage analysis, correlation analysis of weak sites, system-level reliability analysis, and sensitivity analysis have been encompassed in this framework. Three numerical examples are used to verify the effectiveness and applicability of the proposed framework. Application to steam turbine rotor involving multiple weak sites with multi-damage modes illustrate the implementation procedures of the framework. Results show that the reliability-based design life of rotor decreases with the increases of start-stop frequency, the implementation of a two-shift operation would pose a threat to meeting the safety requirement of a 30-year design life. Furthermore, sensitivity analysis highlights the critical influences of initial rotor temperature and speed rising rate on rotor reliability, providing insights for operational maintenance and reliability optimization.

Effect of Blade Material of Steam Turbine Rotor on Aeroelastic Characteristics

Elements of powerful steam turbines are subjected to significant unsteady loads, in particular the rotor blades of the last stages. These loads, in some cases, can cause self-excited oscillations, which are extremely dangerous and have a negative impact on the efficiency and service life of the blade cascade. Therefore, when designing new or modernizing existing steam turbine stages, it is recommended to study the aeroelastic characteristics of the blades. The conditions for the occurrence of self-excited oscillations are influenced by both the geometric characteristics and the alloy from which the blade is made. To determine the effect of the blade material on the aeroelastic behaviour, a numerical analysis of the aeroelastic characteristics of the last stage blades made of steel and titanium alloy was performed. For the analysis, the method of simultaneous modeling of unsteady gas flow through the blade cascades and elastic vibrations of the blades (coupled problem) was used, which allows obtaining the amplitude-frequency spectrum of the interaction of unsteady loads and blade vibrations. The paper presents the results of numerical analysis for harmonic oscillations with a given amplitude and a given inter-blade phase angle, as well as for the regime of coupled vibration of blades under the action of unsteady aerodynamic forces. The dependences of the aerodamping coefficient on the inter-blade phase angle and the distribution of the coefficient along the blade are presented. The results of modeling the coupled vibration of the blades for the first six natural forms are presented in the form of a time-evolving displacement of the blade peripheral section, as well as forces and moments acting on the peripheral section. The corresponding amplitude-frequency spectra of displacements and loads in the peripheral section are also presented. The analysis of the results showed an insignificant difference in the characteristics of the proposed blade materials. For the first natural form of blade oscillations, the possibility of self-excited oscillations was found, and for the second form, there are conditions for the appearance of stable self-oscillations.

Influence of Seal Structure on the Motion Characteristics and Stability of a Steam Turbine Rotor

Sealing aerodynamic characteristics are affected by the seal structure, and thus the stability of the rotor system is affected too. A 1.5-stage, three-dimensional, full-cycle model of the high-pressure cylinder of a 1000 MW steam turbine was established. The high eccentricity whirl of the rotor was realized using mesh deformation technology and the multi-frequency whirl model. The nonlinear steam-flow-exciting force of different sealing structures was obtained using CFD/FLUENT, and the motion equations with a nonlinear steam-exciting force were solved using the Runge–Kutta method. The motion characteristics and stability of the rotor system with different sealing structures were obtained. The results show that there are “inverted bifurcation” and “double bifurcation” phenomena in the bifurcation diagrams of different tooth numbers, boss numbers, and tooth lengths, and a 1/2 power frequency of different sealing structures goes through the process of weakening, disappearing, reproducing, and evolving into a 1/3 power frequency and a 2/3 power frequency. With the increasing load, the steam-flow-exciting force becomes stronger, and the multi-frequency vibration and dense frequency phenomena are significant. Under some load conditions, the change curves of three kinds of teeth in 1/3 and 2/3 power frequency vibrations are highly similar, and the tooth number has little influence on the system stability. Under the high load condition, with the boss number increasing, the chaos phenomenon is weakened. Increasing the tooth length is beneficial to the stability of the rotor.

Hyper-reduced-order model for estimating convection heat transfer coefficients of turbine rotors

Forced convection heat transfer occurs inside the steam turbine, and it is crucial for thermal and strength analysis to accurately estimate the convection heat transfer coefficients of the turbine rotor. This paper presents a hyper-reduced-order model for efficiently estimating the forced convection heat transfer coefficients of a steam turbine rotor. Unlike the full-order finite element method, the hyper-reduced-order model uses the discrete empirical interpolation method to approximate the domain integration of transient heat conduction simulations. This approach greatly reduces the degrees of freedom of numerical integration, thus substantially improving the computational efficiency of forward heat conduction problems. The hyper-reduced-order model and Levenberg–Marquardt algorithm are combined to minimize temperature errors between the numerical simulation results and remote sensor measurements and iteratively estimate the heat transfer coefficients of forced convection in the rotor. The accuracy and efficiency of the proposed model are verified through a transient heat conduction simulation. Moreover, the effects of the initial guess values and measurement errors are investigated to demonstrate the universality and robustness of the proposed approach in determining the convection heat transfer coefficient. Compared with the full-order finite element model, the proposed hyper-reduced-order model can increase the efficiency of forward heat conduction simulations of the turbine rotor by more than 10 times, and it only takes 0.87 s computer runtime in single transient step simulation, and then rapidly estimate the forced convection heat transfer coefficients. Furthermore, the performance of the proposed approach is insensitive to the initial guess values, and it exhibits great robustness under measurement error. The mean errors are 4.78 %, 2.67 % and 10.51 % when the initial values are 0.015 mW·mm−3·°C−1, 0.05 mW·mm−3·°C−1 and 0.15 mW·mm−3·°C−1 respectively. When there is no measurement error, the estimated error of the convection heat transfer coefficients is 2.67 %, and even if the measurement error reaches 5 %, and the accuracy loss is only 5.57 %. Consequently, this approach is highly suitable for estimating convection heat transfer coefficients during the dynamic operation of steam turbines, and this research provides reliable guidance for the optimization design and safe operation of steam turbines.

Tensile properties and deformation characteristics of nickel-iron-based superalloys for steam turbine rotors

Tensile properties and deformation characteristics of nickel-iron-based superalloys for steam turbine rotors

Comparative assessment of aerodynamic losses in turbine stages with supercritical carbon dioxide and steam

To investigate the aerodynamic loss mechanisms in supercritical carbon dioxide turbine (CT) and steam turbine (ST) stages, entropy generation and entropy generation rate are used to analyze various losses in stage passages. The results reveal that under sealing clearance at 2.5 % blade height, the leakage losses of CT and ST constitute over 7 % of total available energy. Rotor and stator losses of CT and ST decrease as the Mach number of stage outlet increases. The endwall losses of CT and ST rotor are both predominant, constituting over 1.78 % of total available energy, with lower endwall losses of CT rotor. Furthermore, the stator profile loss of CT represents the majority of stator loss and is notably higher than that of ST. The impact loss and separation loss are more pronounced in CT. The conclusions will provide direction, guidance, and data support for the design and optimization of CT and ST.

Damage Analysis and Startup Schedule Optimization of Steam Turbine Rotors With an Anisotropic Damage Coupled Viscoplastic Constitutive Model

Abstract The optimization of the operation scheme is of great significance for improving the flexibility of thermal power plants in energy systems dominated by renewable energy. However, thermal stress and corresponding thermomechanical fatigue damage are the main limitations. A unified viscoplastic constitutive model coupled with anisotropic damage is introduced and validated by comparing the experimental and simulated hysteresis loops and cyclic softening curves. The model is implemented into the ansys software by using the USERMAT subroutine to numerically investigate the high-temperature fatigue behavior of a 1000 MW steam turbine rotor on different startup schedules. The critical areas of the rotor are studied in terms of temperature, stress, accumulated inelastic strain, and damage. Based on the damage analysis, the hot start schedule is optimized and validated. The startup time can be significantly shortened within permitted fatigue damage. Moreover, the life expenditure under different loading-up rates is calculated and the extra startup costs can be evaluated accordingly for wider application.

Selection of parameters of optoelectronic systems for monitoring the wear for steam turbine rotor blading based on the value of the total error

Selection of parameters of optoelectronic systems for monitoring the wear for steam turbine rotor blading based on the value of the total error

Numerical investigations of transient thermal loading of steam turbines for SMR plants

One of the well-known technologies that fit well into the goal of reduction of greenhouse gas emissions is nuclear energy. In particular, the change in approach to the design and construction of nuclear power plants led to the development of small modular reactors (SMRs), which are characterized by a broader range of possible applications than large nuclear reactors and the ability to flexibly operate as per load demand. This paper presents an analysis of the thermal loads of a steam turbine rotor operating in a power plant with SMR. Steam-water cycle and turbine train of a 300 MW unit are presented. High-pressure steam turbine rotor and its thermal loading due to varying steam conditions are investigated for a cold startup designed with consideration of the thermal characteristics of nuclear reactors. It was shown by numerical simulations that steam condensation on rotor surfaces plays a crucial role in determining its thermal behaviour. Comparison with conventional rotors has shown that the thermal loading of nuclear turbine rotors is lower and more stable than that of conventional turbines.

Effect of cyclic overload on deformation, crack growth behavior and crack initiation/growth lives of a C(T) specimen for 12Cr steel under creep-fatigue condition

ABSTRACT In this study, using a C(T) specimen for 12Cr steel used for a steam turbine rotor, crack growth tests under creep-fatigue conditions with and without overloading were conducted and the fundamental behaviours of deformation and crack growth were investigated experimentally. As a result, load line displacement was found to be suppressed under overload condition regardless of temperature and stress holding time. Crack initiation life under high temperature and low stress condition with overloading was delayed as compared with no overload condition. However, under low temperature and high stress condition with short stress holding time, crack initiation was accelerated remarkably. Furthermore, although crack growth life under creep-fatigue conditions with overloading was found to be shortened as compared with no overloading, the effect of overloading on crack growth life was decreased with an increase in stress holding time.

Mitigating the risk for creep-fatigue cracking in steam turbine rotors: an end user's perspective

Over the last few years, cracks appeared at an early stage of operation on several steam turbine rotors due to low cycle fatigue damage induced by transient thermal events. These cracks led to expensive repair and associated unavailability of the units. A proper risk assessment is therefore key, especially given the expected increase in transient operation required from the conventional power plants in the future.To manage the risk for the ENGIE fleet, with a wide variety of different steam turbine rotors, ENGIE Laborelec has developed a fleet risk management program. At the heart of this are numerical and finite element (FE) models, along with damage assessment methodologies that can offer estimates on the past and future lifetime consumption. Experience with cracked rotors provided the unique opportunity to calibrate the approach, enabling a more accurate prediction for the rest of the ENGIE fleet.Based on the outcome of the lifetime study, different mitigation actions are proposed. Besides the reduction of operational gradients, a very interesting approach is to pro-actively machine the rotor surface before the onset of cracking.

Data-physics-model based fatigue reliability assessment methodology for high-temperature components and its application in steam turbine rotor

Data-physics-model based fatigue reliability assessment methodology for high-temperature components and its application in steam turbine rotor

Малоцикловая усталость 10 % Cr стали с высоким содержанием бора при комнатной температуре

High-chromium martensitic steels are a promising material for the production of elements of boilers and steam pipelines, as well as blades and rotors of steam turbines for new coal-burning thermal generating units. The use of such materials will give an opportunity for the transition to ultra-supercritical steam parameters (temperature of 600–620 °C and pressure of 25–30 MPa), which will allow increasing the efficiency of generating units to 45 %. Modifications of the chemical composition of high-chromium steels have led to significant improvements of high-temperature properties such as 100,000 h creep strength and 1 % creep limit, while resistance to softening due to low-cycle fatigue remains understudied in this field. This work covers the study of low-cycle fatigue at room temperature with different amplitudes of deformation of martensitic high-chromium 10%Cr–3%Co–2%W–0.5%Mo–0.2%Cu–0.2%Re–0.003%N–0.01%B steel. The steel was pre-subjected to normalizing at 1050 °С followed by tempering at 770 °С. After heat treatment, the steel structure was a tempered martensitic lath structure stabilised by the particles of secondary phases of M23C6 carbides, NbX carbonitrides, and M6C carbides. The average width of martensite laths was 380 nm, and the dislocation density was 1.4×1014 m−2. At low-cycle fatigue, with an increase in the strain amplitude from 0.2 to 1 %, the number of cycles before failure significantly decreases, and the value of plastic deformation in the middle of the number of loading cycles significantly increases. Maximum softening (18 %) is observed at a strain amplitude of 1 % in the middle of the number of loading cycles. In general, the steel structure after low-cycle fatigue tests does not undergo significant changes: the width of the laths increases by 18 % at a strain amplitude of more than 0.3 %, while the dislocation density remains at a rather high level (about 1014 m−2) at all strain amplitudes.

Computer simulation of a rotor creep

The issue of determining the stress-strain state during creep in models of rotors of steam and gas turbines is considered. The formulation of the problem is based on the general approach of Solid Mechanics using incremental theory to describe creep strains. The Finite Element Method was used as a solution method in the implementation of professional engineering software. The influence of the centrifugal forces on the stress-strain state, which varies during 10,000 hours of creep of the rotor material, is analyzed. Two models of the rotor are considered: a simplified cylindrical and a drum-type rotor, which is described by the geometry of the body of revolution and which consists of several cylindrical parts. Due to the symmetry of the models, the calculation schemes are built on the basis of the use of a two-dimensional finite element of the body of revolution. Algorithms are applied for the preparation of input data can be recommended for use in the design practice of energy industry enterprises. The Norton law was used for creep calculations. The creep of the models in different temperature conditions with the use of various steels used in turbo-building as their material was analyzed. According to the results of the performed computer simulation of the creep of rotor models, the levels of deformation and the nature of the redistribution of stresses that occur under the same load by centrifugal forces in different temperature conditions caused by the operational processes in the turbine have been established. The stress and strain levels in the drum-type rotor were analyzed and the most loaded and deformed areas of it were determined. It is noted that according to the simulation data for the considered model of the drum-type rotor, the level of accumulated strains, is moderate and does not exceed 0.4%, which is suitable from the point of view of the analysis of operational properties.

Continuum damage mechanics of cyclic viscoplasticity using asymptotic numerical method

Conscious efforts on reduction of greenhouse gas emissions have led to an energy transition to renewable energy, however uncertainties of renewable energy production have resulted in higher thermal cycling demands from conventional power plants. Thermal load cycling at high temperature regions of steam turbine components leads to enhanced creep-fatigue damage accumulation. It is well established that such damage mechanism is numerically best predicted by unified constitutive modeling including damage as a variable as per the formalism of continuum damage mechanics at an expense of considerable computational efforts using finite element analysis. In this paper, the non-iterative Asymptotic Numerical Method (ANM), currently limited to partial cycle analysis with linear hardening plasticity model, is proposed for the first time to address cyclic viscoplasticity problems including damage capable of handling multiple cycles and most generalized loading conditions. Regularization techniques additionally necessary to implement loading-unloading-reloading criteria and advanced constitutive models etc. are presented. The constitutive model chosen for the formulation includes the non-linear multiple back stress variable modified Chaboche model to include damage combined with modified Chaboche-Rousselier isotropic hardening model to include damage, power law for viscoplasticity, Lemaitre’s damage potential and Kachanov-Rabotnov’s creep damage law. The method is verified with defined error measures and then applied to two high pressure steam turbine rotors, one with and another without thermal stress relief groove (TSRG) at the inlet under service type loading conditions to study the beneficial effect of the TSRG on creep-fatigue damage evolution. The accumulated errors of the proposed ANM and computational time are compared to a conventional Newton-Raphson solution.

Constitutive Model-Based Efficient Creep-Fatigue Damage Computation Technique for Steam Turbine Rotors to Enhance Flexible Operational Capabilities

Abstract In the new era of renewable energy, flexible operation of conventional power plants is inevitable, causing high creep-fatigue life consumption. Conventional life assessment methods are deemed to be conservative to address the current requirements. The use of unified constitutive models for the analysis of damage evolution in steam turbine rotors in the past decade has shown promising results and is closely related to experimental data. However, identification of large number of material constants and high computational time hinder the widespread use of such models. In this paper, the latter is addressed using a novel representative input cycle (RIC) concept together with the noniterative asymptotic numerical method (ANM). Various startup shutdown sequences of a typical steam turbine rotor are studied using a unified constitutive model based on Chaboche's kinematic hardening including the damage parameter, Chaboche–Rousselier's isotropic hardening model including the damage parameter, Norton's viscoplastic flow model, Lemaitre's damage potential function and Kachanov–Rabotnov's creep damage law. First, a conventional finite element method (FEM) technique is used and then the proposed RIC method is used to study the evolution of inelastic variables. The reduction in computational time and the compromise in accuracy using the proposed method are studied.

Asymptotic numerical method for cyclic elasto-plasticity and its application to a steam turbine rotor

Flexible operation of the conventional power plants is necessary for the integration of renewables in the energy mix. Steam turbine rotors are one of the most affected components due to the daily thermal load cycling requirements. In order to accurately study the effect of cycling on fatigue, it is necessary to solve cyclic 3D elasto-plasticity problems for a large number of cycles. The established methods are iterative in nature to arrive at the current yield surface for each elasto-plastic step and are computationally extensive. In this paper, we propose the non-iterative Asymptotic Numerical Method (ANM) based solution technique for 3D cyclic elasto-plasticity problems for the first time by a novel regularized Kuhn-Tucker condition. Regularization techniques used in previous works take care of the partial cycle only, i.e., elastic loading, elastic-plastic transition, elasto-plastic flow and elastic unloading for simple linear work hardening models of plasticity. In the present work, the proposed method extends the applicability of ANM by incorporating elastic-plastic transition and elasto-plasticity in reverse loading, second unloading and repeated loading for any number of cycles so that the computationally efficient fatigue analysis can be carried out. In addition, the extension also includes the application of ANM to non-linear kinematic hardening through the Chaboche plasticity model combined with isotropic hardening. For these advancements, additional regularizations are proposed and implemented in a Finite Element Code. The obtained results are then compared to the solutions obtained from the conventional Newton Raphson (NR) solution technique. The proposed ANM is applied to a steam turbine rotor undergoing a typical thermal load cycling and the cyclic elasto-plastic response is compared with that obtained using the conventional Newton Raphson solution technique.

Milling Force Modeling Methods for Slot Milling Cutters

The slot milling cutter is primarily used for machining the tongue and groove of the steam turbine rotor, which is a critical operation in the manufacturing process of the steam turbine rotor. It is challenging to predict the milling force of a groove milling cutter due to variations in rake, rake angles and cutting speeds of the main cutting edge. Firstly, based on a limited amount of experimental data on turning, we have developed an equivalent turning force model that takes into account the impact of the rounded cutting edge radius, the tool’s tip radius and the feed rate on tool’s geometric angle. It provides a more accurate frontal angle for the identification method of the Johnson–Cook material constitutive equation. Secondly, the physical parameters, such as shear stress, shear strain and strain rate on the main shear plane, are calculated through the analysis of experimental data and application of the orthogonal cutting theory. Thirdly, the range of initial constitutive parameters of the material was determined through the split Hopkinson pressure bar (SHPB) test. The objective function was defined as the minimum error between the theoretical and experimental values. The optimal values of the Johnson–Cook constitutive equation parameters A, B, C, n and m are obtained through a global search using a genetic algorithm. Finally, the shear stress is determined by the governing equations of deformation, temperature and material. The axial force, torque and bending moment of each micro-segment are calculated and summed using the unit cutting force vector of each micro-segment. As a result, a milling force prediction model for slot milling cutters is established, and its validity is verified through experiments.

The cyclic response behavior, failure mechanism, and life prediction model of 9% Cr‐based steel under different strain ratios in the low cyclic fatigue regime at 430°C

AbstractDuring steam turbine rotor operation, the startup and showdown processes can cause asymmetric loading stress, leading to fatigue damage. To research the cyclic deformation behavior and fatigue failure mechanisms of 9% Cr‐based steel under asymmetric loading conditions, the strain ratios including −1, 0, and 0.1 are introduced into the low cyclic fatigue tests at 430°C. The results show the cyclic softening behavior is observed under three strain ratios at 430°C. As the strain ratio increases, the crack initiation sources, plastic strain, and consumed energy present an increasing trend. Comparing the microstructure morphology at different strain ratios, the coarsening lath and carbides affect fatigue crack initiation. Besides, the grain rotation and dynamic recrystallization can be observed, resulting in the cyclic softening behavior during the fatigue test. Finally, a new fatigue life prediction model is proposed at 430°C.

Calibration of Multi Hole Pressure Probes for Three Dimensional Flow Measurements in Subsonic Flow*

The calibration of two multi hole pressure probes with four and five pressure holes are presented at three Mach numbers, viz. M=0.3, 0.4 and 0.5. The calibration was carried out in a subsonic calibration tunnel in yaw angle and pitch angle range of ± 30° at 5° interval. Calibration curves are presented and compared at the three Mach numbers. Calibration data at one Mach number are used as calibration data and calibration data at other Mach numbers are used as measured data to find the flow parameters namely, total pressure and static pressure and flow yaw angle and pitch angle using a lookup table method at these Mach numbers. The interpolation errors are small when the yaw angle and pitch angle range is from -20° to 20° for the four hole probe and from -15° to 15° for the five hole probe. Mach number effects on the flow measurements can be incorporated using the iterative method presented. This method is used to obtain flow parameters in the wake of a steam turbine rotor tip cascade blade. The differences in the obtained values using calibration coefficients at three Mach numbers are found to be negligible.