The wide use of fir-tree root and groove in turbine structures prompts the expectation to find optimum configurations, which ensure that stresses are in the safe limits to avoid mechanical failure. To perform the optimization, the reasonable characterization of root configuration is required. The existing researches characterized the fir-tree root with straight line, arc or even elliptic fillet, then the parameters of these features were defined as design variables to perform root profile optimization. However, this feature-based optimization technique yields configuration which is only optimal under the feature assumption, the question why choose these feature and whether there is a better feature modeling technique is difficult to answer. In this work, instead of the feature-based method, spline curves technique is involved to characterize the root and groove configuration, and the horizontal coordinates of the control points are selected as design variables, which are modified in the vicinity of their initial values during optimization process. The objective function is to minimize the peak stress in the root and groove regions. With the Multi-island genetic algorithm, the optimal fir-tree root configuration can be obtained with better stress distributions and low stress concentrations. The proposed spline-based optimization approach may shed lights on the conceptual design of blade root and can be easily extended to other industrial equipment design.
In order to meet the high economic requirement of the 3rd generation Pressurized Water Reactor (PWR) or Boiling Water Reactor (BWR) applied in currently developing nuclear power plants, a series of half-speed extra-long last stage rotating blades with 26 ∼ 30 m2 nominal exhaust annular area is proposed, which covers a blade-height range from 1600 mm to 1900 mm. It is well known that developing an extra long blade is a tough job involving some special coordinated sub-process. This paper is dedicated to describe the progress of creating a long rotating blade for a large scaled steam turbine involved in the 3rd generation nuclear power project. At first the strategy of how to determine the appropriate height for the last-stage-rotating-blade for the steam turbine is provided. Then the quasi-3D flow field quick design method for the last three stages in LP casing is discussed as well as the airfoil optimization method. Furthermore a sophisticated blade structure design and analyzing system for a long blade is introduced to obtain the detail dimension of the blade focusing on the good reliability during the service period. Thus, except for CAD and experiment process, the whole pre-design phase of the extra-long turbine blade is presented which is regarded as an assurance of the operation efficiency and reliability.
Cyclic loads applied to a structure can develop local cyclic plasticity deformation, lead to fatigue damage and fracture at the high-stress regions, which can be assessed through a local strain approach. Each cycle of start-operation-stop steam turbine, making the low cycle fatigue (LCF) load of long blade, results in damage to the long blade, and the fatigue fracture occurs when the damage accumulated to its critical value. To evaluate the fatigue life, the experimental data illustrating the cyclic behavior of a material under simple loading condition must be gathered, and also a suitable local stress-strain range calculation approach needs to be chosen to represent the accurate material behavior under loadings. With the consideration of the difference between the specimen and actual blade, the influential factors, such as mean stress, geometry effect, blade surface quality, and water erosion, on the fatigue life should be investigated when using the cyclic fatigue data of specimen to predict fatigue life of actual blade. In this study, a new local stress-strain range approach is introduced based on elastoplastic finite element analysis and Neuber rule. And also a modified strain-life fatigue model is used by considering leading causes of fatigue and also the cumulative damage rule is set up to predict the LCF life of the steam turbine long blade. It is found that the assessment method proposed in this study is capable of predicting the LCF life of steam turbine long blade.
Due to its finite size and the large centrifugal load, the fir-tree root is highly stressed, which leads to the possible early failure of the gas turbine and steam turbine. To find an optimized fir-tree root is an important issue for the design of the turbine structures. In this paper, a superellipse-based design optimization approach is proposed for the fir-tree root. Rather than the straight line and arc used in literature, the combination of the superellipse curve and line are employed to characterize the fir-tree root since the superellipse curve represents a large family of curves with limited parameters, which makes the design optimization easy and economic. For the design optimization, the objective function is to minimize the peak stress, which is a typical min-max problem with possible severe iterative oscillation and subsequent convergence difficulty. To avoid this problem, a P-norm aggregation function is proposed. The superellipse parameters are defined as design variables, while the stress concentration factor and the stress at root neck are specified as optimization constraints. With the P-series fir-tree root design as example, it is proved that our approach is effective to find the optimized configuration with better stress distribution and lower stress concentration.
In the fast evolving and increasingly competitive wind energy market, to minimize initial capex and maximize production profits are essential when designing a wind farm. The electrical cable accounts for around 10% of the total capex, reasonable layout of cable connections might induce significant reduction of electrical and construction cost. In this paper, the Fuzzy C-means (FCM) clustering algorithm is adopted to determine the location of the substation(s) and the ISODATA (Iterative Self-Organizing Data Analysis Technique Algorithm) is employed to divide the wind farm into finite sub-domains, effectively reducing the complexity of the NP-hard (Non-deterministic polynomial-time hard) problem of cable layout optimization. The optimal cable layout in each sub-domain is obtained through the swap sequence based particle swarm optimization (SSPSO) and practical electrical constraints, while the objective function is to minimize the total cable costs, including material cost and cable laying cost. Current study highlights both applicability of clustering algorithm and particle swarm optimization to the cable layout problem in wind farm.
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