Strain-life estimation of the last stage blade in steam turbine during low volume flow conditions

doi:10.1016/j.engfailanal.2021.105399

Engineering Failure Analysis

Volume 125, July 2021, 105399

https://doi.org/10.1016/j.engfailanal.2021.105399 Get rights and content

Highlights

•
The strain-life of the last stage under low volume flow conditions is predicted.
•
Two-way FSI method is adopted to calculate the strain range.
•
The strain-life is affected by the excitation of the rotor-stator clearance vortex.
•
The strain-life of 90% span of blade suction surface is the shortest.
•
The strain-life of blade decrease with the decrease of volume flow.

Abstract

Based on the elastic-plastic analysis, the local strain-life of the last stage of steam turbine under the low volume flow conditions is predicted. Considering the unsteady flow steam force and local high temperature of blade, the three-dimensional transient flow field, strain distribution and stress distribution of the last stage blade are calculated by the two-way fluid structure interaction method. Under low volume flow conditions, the temperature of blade tip increases with the decrease of volume flow. In addition, the self-excited unsteady frequency of rotor -stator clearance vortex is obtained at 90% span. According to the distribution of maximum equivalent stress on the rotor blade surface, three dangerous points are identified, which are located at the blade tip of the pressure surface (DP1), 90% span of the suction surface (DP2) and the trailing edge at the blade root of the pressure surface (DP3). With the decrease of volume flow, the equivalent stress and strain range of dangerous points increase, so the strain- life of dangerous points decreases. Among them, the strain-life of DP2 is the shortest at case3 condition. The strain response frequency of DP2 is consistent with the self-excited unsteady frequency of rotor -stator clearance vortex, which proves that it is necessary to consider the unsteady steam flow force in strain-life calculation. This study provides theoretical guidance for the safe operation time of the steam turbine under low volume flow conditions.

Introduction

As renewable energy power generation is advocated to reduce the environmental problems caused by thermal power units, thermal power plants may operate under low volume flow conditions for a considerable length of time. Therefore, the operation safety of the last stage blades in steam turbine has become a research hotspot. The last stage blade to be more susceptible to fatigue damage has been proved [1]. Under low volume flow conditions, the blade temperature is increased due to the steam absorbs energy from rotor blade. At the same time, because of the unsteady flow field, the last stage blade is subjected to cyclic steam flow force. Fatigue damage is cumulative when the structure is subjected to cyclic loading. The repeating maximum values of stresses during a cyclic loading induces microcracks, which could lead to the failure [2]. The prediction of fatigue life can provide a theoretical reference for the safe operation time of the last stage under low volume flow conditions [3].Various methods for predicting the fatigue life of turbine blades have been established [4], [5], [6], [7], [8], [9], [3]. Gao et al. [10] distributed collaborative response surface method to the reliability analysis of aeroengine turbine blade. Han et al. [11] proposed a prediction model which is combined high cycle fatigue (HCF) life and low cycle fatigue (LCF) life based on damage mechanics theory, which considered the nonlinear interaction between LCF and HCF. In general, the local cyclic plasticity deformation of structures under cyclic loading leads to fatigue damage and fracture in high stress regions, which can be evaluated by local strain approach (LSA) [12]. The well-known empirical relations of Manson-Coffin [6], [7], Morrow [8] and Smith Watson Topper (SWT) [13] are intensely applied to perform LSA. Manson-Coffin formula is an empirical formula of low cycle fatigue life derived by Manson and Coffin through a large number of experiments. Morrow proposed a modified Manson-Coffin formula considering mean stress. S. Cano [14] obtained the conclusion through calculation and comparison that SWT model can better predict the strain fatigue life at low stress level.

Under low volume flow conditions, the last stage blade undergoing cyclic loads results into the local cyclic plasticity deformation at the high-stress regions, so the relationship between the stress and strain at the dangerous point are nonlinear. Local cyclic plastic deformation is the main factor to reduce fatigue life of blade. The precise assessment of the local strain-stress for complex geometries or loadings is not easily performed when using the LSA. Therefore, Neuber [15] and Glinka [16] proposed empirical formulas. With the wide use of computers and the improvement of elastic-plastic finite element analysis, it is easy to perform the elastic-plastic finite element analysis. Zhu et al. [17] used elastic-plastic finite element analysis method to calculate the thermo-elasto-plastic stress and strain fields of turbine blade, and the fatigue life of blades is estimated. S. Cano et al. [14] proposed that steam load produced low level stresses in magnitude. However, it is still dangerous for blade structure. Therefore, it is necessary to consider the load spectrum under the unsteady flow steam force.

Under low volume flow conditions, regional blade works as a compressor [18]. At this time, the backflow vortex, the separation vortex and the rotor - stator clearance vortex are existence in the rotor blade passage [19]. Troyanovskii [20] described the change of flow structure with the decrease of volume flow. Because of the minimum reaction at the root of the rotor blade, the backflow vortex is formed at the root of the rotor blade outlet when the steam cannot fill the passage. Dilip et al. [21] found that the separation vortex was caused by the negative angle of incidence on the pressure surface of the rotor blade. The separation vortex has a high radial velocity with no stall unit occurs, so that the rotor blade can operate stably in the presence of separation vortex [22]. When the volume flow continues to decrease, the rotor - stator clearance vortex is formed at the tip clearance between the rotor and the stator blade, which moves in the circumference direction at a speed which closes to the rotating speed of rotor blade [23].

In the study of unsteady phenomena of the last stage under low volume flow conditions, the rotating instability similar to that of compressor was found. Pigott et al. [24] tried to study the rotating instability of LP turbine blades for the first time. Under low load conditions, large negative angle of incidence in the blade tip leads to the rotating stall. Gerschütz et al. [25] got the rotating instability of the last rotor blade in steam turbine under low load conditions. Megerle et al. [26] measured the unsteady flow of the model turbine in detail and simulated it by three-dimensional computational fluid dynamics method to reproduce the rotating excitation mechanism in the experiment. Therefore, the rotating stall captured by the unsteady CFD method was verified. Numerical simulation can accurately reproduce the phenomenon of rotating instability, and it is helpful to analyze the physical mechanism of rotating instability. Rzadkowski et al. [27] simulated the aeroelastic problem of the last rotor blade by CFD, and obtained the low frequency component of the axial force. The unsteady pressure disturbance causes the blade vibration in the bending-torsion mode. Rzadkowski et al [28] obtained that the low frequency unsteady harmonics of the rotor blade have a great influence on the blade tip.

In this paper, the transient flow field, the elastic-plastic stress and the transient strain response of the last stage blade in steam turbine are calculated by ANSYS Workbench. The blade temperature and unsteady characteristics of flow field are analyzed. The stress and strain distribution of the blade are obtained based on the elastic-plastic finite element analysis in the structural domain, and the dangerous points are identified. The strain range of the dangerous points can be obtained by the transient strain response of the last stage blade, and the effect of unsteady characteristic in flow field on the transient strain response of blade can be analyzed. Finally, the SWT strain-life analysis method is used to estimate the fatigue life of the last stage blade under different volume flow conditions.

Section snippets

The structural model

The research object of this paper was the last stage of a 600 MW steam turbine. A full model of the last stage comprising 52 stator blades and 80 rotor blades The parameters of the geometry model are shown in Table.1. According to the section profile coordinates of stator blades and rotor blades, a full-scale geometric model is established.

Five rotor blades were connected into a blade group by snubber. In order to reduce the computing resources and time, a blade group was selected for numerical

Unsteady characteristics of flow field

Under low load conditions, several vortices are formed in the fluid domain because the steam is not fully filled in the passage, which is called low volume flow conditions. The flow field of three cases are analyzed in this section. Fig. 8 (a) shows the pressure at the stator blade inlet (p₀), the pressure at the rotor blade inlet (p₁) and the pressure at the rotor blade outlet (p₂) along the blade height. It can be seen from the figure that the p₂ at the rotor blade root is greater than p₁,

Identification of danger points

The rotor blade is subjected to steam flow force, thermal stress and centrifugal force. Fig. 15 shows the distribution of equivalent stress on the pressure surface (ps) and suction surface (ss) of the rotor blade. Three regions of most large equivalent stress on the rotor blade surface are obtained, which are the tip of pressure surface, the 90% span of suction surface and the root of pressure surface. The maximum equivalent stress points of the three regions are identified as the research

Strain - fatigue life analysis

Fig. 17 shows the strain dynamic response of three dangerous points. The strain cycle of DP1 is short, and it is easy to see that the strain range of DP1 is small. Although the strain level of DP3 is lower than that of DP2, its strain range is larger than that of DP2. Combined with the maximum equivalent stress of the dangerous points, it is still unable to determine which dangerous points appears the crack first.

The frequency spectrum of the strain response of DP2 is obtained by Fast Fourier

Conclusion

In this paper, the two-way FSI method is used to apply unsteady steam flow load on the last stage blade of steam turbine under low volume flow conditions. Based on the elastic-plastic finite element analysis, the dynamic response of the blade is numerically simulated, and the strain-life is evaluated by SWT method. The conclusions are as follows:

(1)
Under low volume flow conditions, the unsteady characteristics of the backflow vortex and the separation vortex are derived from the blade rotation

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The authors would like to thank for the financial support of the National Key R&D Plan (2017YFB0902100)

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Cited by (5)

Vibration characteristics and life prediction of last stage blade in steam turbine Based on wet steam model
2024, Engineering Failure Analysis
This paper takes the last stage blade of a 600 MW steam turbine as the research object. By considering the distribution information of wet steam in the last stage flow field and the process of the droplets hitting the blade wall, the stress distribution of the blade surface under two steam models with THA and 30 % THA conditions is obtained via fluid–structure coupling calculation method. Then, the vibration characteristics of single blade and disk-blades in the last stage under wet steam model are analyzed. Finally, according to calculated displacement and stress curves, the fatigue life of the last stage blade is predicted by Smith-Watson-Topper fatigue life calculation method. The results show that the equivalent stress decreases first, and then increases along the blade height direction, and reaches maximum at 90 % of the blade height, with the maximum value 712 MPa, which is lower than the yield limit of the material. The vibration mode shapes of the last stage blade are dominated by bending and torsional vibrations. The natural frequency of the blade is much smaller than the frequency corresponding to the high-frequency excitation force. In terms of fatigue life prediction for dangerous points, under different steam models and corresponding operating conditions, the number of cycles corresponding to the trailing edge tip of the blade suction surface (DISP 2) is the smallest, followed by the leading edge tip of the blade pressure surface (DISP 3), and the number of cycles corresponding to the 90 % blade height position of the blade suction surface (DISP 4) is the highest. In addition, the number of cycles obtained by wet steam model is lower than that by ideal gas model, and this trend is more obvious under 30 % THA working condition.
Failure study of steam turbine Last-Stage rotor blades under a High-Speed wet steam environment
2023, Engineering Failure Analysis
The failure mechanism of the last-stage rotor blade of the low-pressure cylinder of a steam turbine when exposed to high-speed wet steam was elucidated. The results indicated that the combined effects of water erosion, stress corrosion, and corrosion fatigue resulted in the failure of the shroud-lacing wire section (which was made of martensitic stainless steel through the high-frequency induction hardening method) on the steam inlet side. Furthermore, the combined action of the water hammer pressure of the secondary water droplets and the pressure of the cavitation jet caused water erosion and the formation of pits. Additionally, the combined action of the stress concentration at the ends of the pits, the stress concentration at the inlet side structure, and the alternating stress-induced crack initiation at the inlet-side shroud-lacing wire section. Finally, the crack propagation was accelerated by the combined action of stress corrosion and corrosion fatigue. This study provides theoretical guidance for inhibiting the growth of pits and prolonging the fatigue life of blades.
Dynamic response of turbine blade considering a droplet-wall interaction in wet steam region
2023, Energy
Citation Excerpt :
Results showed that the wet steam model has little effect on the pressure disturbance; however, it significantly affects the propagation of the disturbance, resulting in the difference of aerodynamic damping. By considering both the steam flow excitation force from the unsteady flow and local high temperature of the blade, Cao et al. [29] adopted the wet steam material Steam3vl under IF97 module to calculate the 3D transient flow field and stress and strain distributions of the last stage blade, and finally determined the dangerous position on the blade surface. Briefly, most researchers studied the motion characteristics of droplet particles in the LP cylinder of steam turbine; however, the influence of force generated by droplet particles hitting blade surface on blade vibration has not been studied till date.
The high-speed impact of liquid droplets on blades in wet steam region seriously affects the safe operation of steam turbine. For blade stability and response characteristics, most studies utilized ideal gas as working medium and few studies focused on the role of droplets in the flow field. In this study, both the distribution information of droplet particles in the flow field and the impact of droplet particles on blades were comprehensively considered. First, the droplet distribution at the last stage inlet was calculated, and then the droplet-wall interaction model was determined and loaded into calculation process. The pressure distribution on blade surface, blade force variation, mechanical properties, and further dynamic response characteristics of blade were analyzed with ideal gas and wet steam models, respectively, by using one-/two-way fluid-structure interaction. Results show that the blade displacement of leading and trailing edges under wet steam model reaches the maximum at near 80% blade height, and there is a low frequency amplitude corresponding to 460 Hz–470 Hz with the peak value in the range of 22Pa–26Pa. The variations of the maximum displacement and maximum equivalent stress of the blade with time are more intense under wet steam model compared with those under ideal gas model.
Structure and modal analysis of the last stage blade in steam turbine under low volume flow conditions
2022, Engineering Failure Analysis
Citation Excerpt :
This model may be used for materials that obey Von Mises yield criteria (includes most metals). The tangent modulus cannot be less than zero or greater than the elastic modulus [24]. This option uses the von Mises yield criterion with the associated flow rule and kinematic hardening [26]:
To explore the prestressed modal characteristics of the last stage blade in steam turbine under low volume flow conditions, the fluid–structure interaction (FSI) method of ANSYS mechanical + CFX is adopted to consider the effect of flow field on the strength performance of the rotor blade. The cyclic symmetry analysis is adopted to calculate the strength performance and modal characteristics of the rotor blade. The results show that the flow field of the last stage is composed of backflow vortex, separation vortex and tip clearance vortex under low volume flow conditions. The tip clearance vortex has high circumferential velocity and temperature. The maximum deformation of the rotor blade is on the leading edge of the blade at 80% span, and the maximum equivalent stress is on the suction surface at 90% span. With the decrease of the steam flow, the temperature at the blade tip increases significantly, which increases the maximum deformation and the equivalent stress of the rotor blade. The plastic deformation occurs when the steam flow is reduced to 15% turbine heat acceptance (THA). In addition, the elastic modulus of blade material decreases with the increase of temperature, which leads to the decrease of natural frequencies. From 35 %THA to 5% THA condition, the natural frequencies of the blade decrease by 34-136 Hz. This study provides a theoretical reference for the identification, diagnosis and prediction of the vibration of the last stage blade under low volume flow conditions.
OFF-DESIGN FLOW ANALYSIS OF COGENERATION STEAM TURBINE WITH REAL PROCESS DATA
2022, Thermal Science

View full text

Strain-life estimation of the last stage blade in steam turbine during low volume flow conditions

Highlights

Abstract

Introduction

Section snippets

The structural model

Unsteady characteristics of flow field

Identification of danger points

Strain - fatigue life analysis

Conclusion

Declaration of Competing Interest

Acknowledgement

Int. J. Fatigue

Thermal Turb.

Int. J. Fatigue

Aerosp. Sci. Technol.

Eng. Fract. Mech.

Int. J. Heat Mass Transfer

The diagnosis and correction of steam turbine blade problems

Fatigue life estimation procedure for a turbine blade under transient loads

J. Eng. Gas Turb. Power

A study of the effects of cyclic thermal stress on a ductile metal

Trans. Am. Soc. Mech. Eng.

Cyclic plastic strain energy and the fatigue of metals. Internal friction, damping and cyclic plasticity

ASTM Spec. Tech. Publ.

A method of fatigue damage analysis

Combined high and low cycle fatigue life prediction model based on damage mechanics and its application in determining the aluminized location of turbine blade

Int. J. Fatigue

A LCF life assessment method for steam turbine long blade based on elastoplastic analysis and local strain approach

Volume 8: Microturbines Turbochargers Small Turbomach. Steam Turb.

Mean stress effects on low cycle fatigue for a high strength steel

Fatigue Fract. Eng. Mater. Struct.