Steam Turbine Rotor Transient Thermo-Structural Analysis and Lifetime Prediction

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Courtesy of SoftInWay Inc.

Market requirements for faster and more frequent power unit start-up events result in a much faster deterioration of equipment, and a shorter equipment lifespan. Significant heat exchange occurs between steam and turbine rotors during the start-up process and even more intensive heat exchange takes place during the condensation phase in cold start-up mode, which leads to further thermal stresses and lifetime reduction. Therefore, the accuracy of lifetime prediction is strongly affected and dependent on the accuracy of transient thermal state prediction.

In this study, transient thermal and structural analyses of a 30 MW steam turbine for a combined High and Intermediate pressures (HPIP) rotor during a full cold start cycle is performed and special attention is paid to initial start-up phase with ‘condensation’ thermal BC. All steps for rotor design and the thermal model preparation were done using the AxSTREAM™* software platform. It included the development of a two dimensional model of the rotor, thermal zones and corresponding thermal boundary conditions (heat transfer coefficients and steam temperatures) calculation during turbine start-up and shut down operation. Rotor thermal and structural simulations were done using commercial FE analysis software to evaluate the thermo-stress-strain state of the turbine rotor. Calculation and validation of thermal and structural state of the rotor was done using actual start-up cycle and measured data from a power plant, and it showed good agreement of the calculated and the measured data. Based on the results of thermo-structural analysis, the evaluation of rotor lifetime by means of a low cycle fatigue approach was performed and presented in this paper.

Nomenclature
BC – boundary conditions
FE – finite element
FEA – finite element analysis
HP – high pressure
HTC – heat transfer coefficient
IP – intermediate pressure
LCF – low cycle fatigue
���� – Reynold’s number
���� – Prandtl number

Introduction
During load transients, biaxial thermal strains are created as a result of the radial temperature gradient through the thickness of the rotor. During start-ups, the outer surface heats up faster than the bore or centerline. Compressive stresses appear in the outer surface of the shaft while tensile stresses are created at the bore/centerline. During shut downs, the opposite takes place; the outer surface is subject to tensile thermal stress (as it cools more rapidly than the bulk of the rotor mass) and the bore/centerline is subject to compressive thermal stress. Generally speaking, thermal stress/strain is proportional to the rate of temperature change and the square of the shaft diameter.

Turbine operators want quick starts to maximize output. Operators also expect long service life. These two requirements are conflicting because starting the turbine too quickly can result in premature component failure due to LCF cracking. Prior to the mid-1960s, the relationship between quick starts and LCF was not well understood in the industry. LCF cracking of high temperature rotors primarily at the shaft/wheel fillet as a result of rapid, uncontrolled starts and stops was common. During the mid-1960s, major OEMs began to provide customers with thermal loading (i.e ramp rate) guidelines and general starting and loading recommendations in the form of basic station starting and loading procedures. Later, electronic controllers for large fossil fired steam turbines included load change logic that would “select” a ramp rate based on an internal LCF calculation algorithm.

Today’s steam turbine rotor designer must be well informed about the overall controlling method, boiler characteristics, and any special pre-determined start up time or cycle requirements imposed by the customer or product specifications. From these, a “mission mix” representing the expected cyclic life of the steam turbine can be generated and evaluated based on the deterministic methods.

Turbine cyclic life could be limited by either component – rotor or stator- but in this article, considering limited size of the publication, we will present the results for a turbine rotor only. Cyclic life evaluation is based on thermo-stresses analysis and requires a high level of FE model detailing in order to capture stresses concentration in the rotor elements, like fillets, grooves, etc.

For differential expansion and clearances design, thermal expansion analysis for both components (casing and rotor) is required. In this study the level of FE model detailing does not need to be as high as at a stresses study.

Steam turbine transient operation is usually very complex with regards to thermo-mechanical state prediction, which usually consists of the following major steps for start-up:

  • flow path parameters and heat exchange conditions calculation (HTC’s and steam temperatures);
  • thermal analysis;
  • thermo-structural analysis;
  • lifetime evaluation.

Intensity of heat exchange and consequently thermal stresses significantly increase in case of phase change effect, when rotor surface temperature is lower than steam saturation temperature. The condensation process typically takes place at the initial phase of the start-up cycle and continues until the rotor surface temperature becomes higher than that of the steam saturation temperature. This situation is characterized by condensation heat exchange conditions with increased level of HTC’s on the rotor surface. Fundamentals of heat and mass transfer processes and basic principles of HTC simulation are considered in the monographs [1, 2]. Unfortunately, there are not many recommendations available on condensation HTC methodology for steam turbines and this effect imposes most of the uncertainty that exists for rotor thermo-structural analysis.A theoretical approach to account for the effect of condensation on HTC and validation against test data is presented and discussed in [3]. Some recommendations based on a summary of calculated and experimental data are presented in [4], and based on these results the condensation HTC are significantly higher than that of dry conditions and could reach up to 12000 [W/(m2K)].

High HTC’s during the condensation phase of the start-up lead to high thermal gradients, resulting in thermal stresses (thermal shock) and finally resulting in rotor lifetime reduction and early damage.

Numerous studies for thermo-mechanical analyses methodology with FEA approach have been developed and published recently in [5-12]. These and many other publications represent different aspects of thermo-structural analysis and turbine components behavior – FE model development, zones for heat transfer condition definition and HTC assignment, critical regions in turbine components, thermo-stresses during turbine transient operation, plasticity effect, life-time estimation methods, etc. At the same time, in the openly published works, not enough attention is paid to the effect of condensation and its impact on thermo-structural stresses and cyclic life. This is one of the methodological aspects which we would like to focus on and discuss in this article.

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