SUMMARYThe extended finite element method (X-FEM) has proven to be capable of simulating cracking and crack propagation in quasi-brittle materials, such as cement paste or concrete, without the need for re-meshing. In the framework of the X-FEM cracks are represented as surfaces of discontinuous displacements continuously propagating through finite elements. Since crack path continuity is required in X-FEM-based analyses, the reliability of numerical analyses of cracked structures crucially depends on the correct prediction of the crack path and, consequently, on the criterion used for the determination of the crack propagation direction. In this paper four different crack propagation criteria proposed in the literature are investigated including two local and two global criteria. The two local criteria include an averaged stress criterion and the maximum circumferential stress criterion based on the linear elastic fracture mechanics.
The demand for energy is increasingly covered through renewable energy sources. As a consequence, conventional power plants need to respond to power fluctuations in the grid much more frequently than in the past. Additionally, steam turbine components are expected to deal with high loads due to this new kind of energy management. Changes in steam temperature caused by rapid load changes or fast starts lead to high levels of thermal stress in the turbine components. Therefore, todays energy market requires highly efficient power plants which can be operated under flexible conditions. In order to meet the current and future market requirements, turbine components are optimized with respect to multi-dimensional target functions. The development of steam turbine components is a complex process involving different engineering disciplines and time-consuming calculations. Currently, optimization is used most frequently for subtasks within the individual discipline. For a holistic approach, highly efficient calculation methods, which are able to deal with high dimensional and multidisciplinary systems, are needed. One approach to solve this problem is the usage of surrogate models using mathematical methods e.g. polynomial regression or the more sophisticated Kriging. With proper training, these methods can deliver results which are nearly as accurate as the full model calculations themselves in a fraction of time. Surrogate models have to face different requirements: the underlying outputs can be, for example, highly non-linear, noisy or discontinuous. In addition, the surrogate models need to be constructed out of a large number of variables, where often only a few parameters are important. In order to achieve good prognosis quality only the most important parameters should be used to create the surrogate models. Unimportant parameters do not improve the prognosis quality but generate additional noise to the approximation result. Another challenge is to achieve good results with as little design information as possible. This is important because in practice the necessary information is usually only obtained by very time-consuming simulations. This paper presents an efficient optimization procedure using a self-developed hybrid surrogate model consisting of moving least squares and anisotropic Kriging. With its maximized prognosis quality, it is capable of handling the challenges mentioned above. This enables time-efficient optimization. Additionally, a preceding sensitivity analysis identifies the most important parameters regarding the objectives. This leads to a fast convergence of the optimization and a more accurate surrogate model. An example of this method is shown for the optimization of a labyrinth shaft seal used in steam turbines. Within the optimization the opposed objectives of minimizing leakage mass flow and decreasing total enthalpy increase due to friction are considered.
Flexibility and availability together with fast startup times become more and more important for steam turbine operation. Exact knowledge about the turbine components stresses and lifetime consumption during transient operation is a prerequisite in order to meet these requirements.A transient FE model of an intermediate pressure steam turbine rotor was generated, allowing the prediction of temperature and elastic stress field during turbine startup, load changes and shutdown. Operating data of the steam parameters and of a thermocouple inside the wall of the turbine inner casing were used to indirectly validate the thermal FE model in order to reproduce the measured metal temperatures in a proper accuracy.Subsequently a probabilistic sensitivity study was performed in order to identify the influence of scattering or not well known boundary conditions on the calculated lifetime consumption of the steam turbine rotor during a cold start. This in fact provides information about the accuracy of the prediction. The results of the sensitivity study also help to improve the model accuracy by identifying the boundary conditions with the largest impact on lifetime prediction uncertainty, i.e. the boundary conditions that need further investigation.
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