Steam Turbine Exhaust Optimization Based on Gaussian Covariance Networks Using Transient CFD Simulations

Abstract

Renewable energies are increasingly contributing to the overall volume of the electricity grid and demand besides high efficiency, greater flexibility of the conventional fossil power plants. To optimize these objectives, extensive CFD calculations are required in most cases. For example, transient CFD calculations are only rarely combined with an optimizer because of their high demand on computational resources and time. Surrogate models, which are mathematical methods to learn and approximate the relationship between input and output parameters, are a common way to solve these problems. Once they are trained, they can perform the evaluations within seconds and replace the expensive simulation. Of course, real calculations are still needed to generate the training data. Therefore, it is useful to apply efficient and sequentially extensible design plans. This paper presents a new surrogate model method, based on a deep neural network learning the non-stationary hyperparameters of combined Gaussian process covariance matrices. It is used to approximate the complex and time consuming transient CFD simulation of a combined high-intermediate pressure steam turbine double shell outer casing. To minimize the exergy loss, the exhaust geometry is optimized in a single and multi-objective optimization on the surrogate models. The multi-objective optimization also includes the uniform velocity distribution of the steam in different areas of the casing, to predict the thermal loading of the steam turbine inner casing and to avoid an imbalanced thermal loading. A sequential sampling approach combined with a sensitivity analysis is used to find the minimum number of samples needed to train the surrogate models in order to gain sufficient prediction quality. Additionally, the paper describes the initial geometry, its numerical setup and the required control mechanisms to avoid noisy designs, which might complicate the surrogate model training. There is also a comparison of the initial and chosen optimal designs.

Calibrated simplex-mapping classification

“…Several recent publications propose to couple a deep neural network with Gaussian processes (GPs) for an improved uncertainty estimate of model predictions [6][7][8][9][10]. Alternative approaches explore the use of deep neural networks not as feature extraction methods but, for instance, to suitably estimate the mean functions of GPs [11] or to predict their covariance functions and hyperparameters [12]. Yet, due to the high complexity of the deep neural network components in these models, the algorithms mentioned above are well-suited for large data sets with abundant training data available [13].…”

Advances in coupled axial turbine and nonaxisymmetric exhaust volute aerodynamics for turbomachinery

“…The optimized results showed that the exhaust volute total pressure loss is decreased by 9.82% on the design condition without increasing the inlet static pressure. Furthermore, coupled with the exhaust diffuser parameterization method, volute aerodynamic performance evaluation method and combinatorial optimization strategy, the aerodynamic optimization design system of exhaust volutes for the maximum static pressure recovery coefficient was established based on the mentioned optimization method and software by Yang et al 33 Recently, a new surrogate model method, based on a deep neural network learning the non-stationary hyperparameters of combined Gaussian process covariance matrices was built by Cremanns et al 48 The presented results showed an efficient way to optimize and analyze a very time expensive and complex simulation model.…”