Efficient Multi-Objective Optimization of Labyrinth Seal Leakage in Steam Turbines Based on Hybrid Surrogate Models

Abstract

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.

Combined optimisation of the last stage and diffuser in a steam turbine using meta-models

“…The meta model used here is a hybrid model combining a Kriging and a moving least square model. Details of the meta model are discussed in Cremanns et al (2016). Usually the first set of samples will not result in a meta model having a good enough prognosis quality to carry out an optimisation.…”

Prediction of the windage heating effect in steam turbine labyrinth seals

“…CFD simulations are carried out to gain necessary information about C(Geom) and α(Geom) to compute Equation 13 and Equation 14. Further information can be found in (Cremanns et al, 2016) and in the following:…”

“…A hybrid meta model is used to parametrize the contraction and the windage coefficients depending on s 1 , s 2 , T 2 and h. So the influence of different labyrinth geometries on flow behaviour is approximated by analytical relationships. This method replaces further CFD simulations and gives the opportunity for optimization (Cremanns et al, 2016). The meta model is able to compute the importance of single influence parameter on the objective criterion.…”

“…The meta model is able to compute the importance of single influence parameter on the objective criterion. Since T 1 is less important in the observed range of variation for the desired criteria (Cremanns et al, 2016), the equation calculated by the meta model does not include this parameters, but the most important ones.…”

“…CFD model of the labyrinth section. Reproduced fromCremanns et al (2016), with permission from Siemens AG.…”