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Appl. Sci. 2020, 10, 4999 2 of 21 Turbine is the “heart” of the whole power cycle. The power and efficiency of the system are directly affected by its performance. Therefore, the research on S-CO2 turbine has become a hot spot. Sandia National Laboratory [8] developed a 100 kW centripetal turbine and a 50 kW centrifugal compressor, and conducted a large number of S-CO2 closed cycle tests from 2007 to 2009. A labyrinth seal turbine wheel was developed by Korea Institute of Energy Research [9]. It was applied to a 10 kW S-CO2 Brayton experimental loop. Zhou et al. [10] proposed a design method of S-CO2 radial turbine. The one-dimensional (1-D) model and three-dimensional (3-D) numerical simulation methods were adopted to predict the off-design performance. Han et al. [11] completed the design of high-pressure and low-pressure axial-flow turbines applied to 5 MW S-CO2 reheated Brayton cycle by using the self-designed program. The isentropic efficiencies of the turbines were 82.88% and 82.26%, respectively. A 10 MW S-CO2 single stage centrifugal turbine was designed and numerically analyzed by Luo et al. [12]. The total-static efficiency after blade shape optimization was 89.02%. At present, computational fluid dynamics (CFD) is still the main method of turbine aerodynamic design and analysis. However, a lot of iterative calculations are needed to solve the Navier–Stokes (NS) equation. This is time-consuming and expensive to calculate. It also delays the entire design and analysis cycle. Therefore, it is necessary to develop a more efficient and accurate method than CFD. With the development of computers, CFD method is widely used. Hence, a large number of CFD data are generated in the process of design and optimization. Therefore, the data-based proxy model becomes more and more practical and important. Previous studies have shown that when the machine learning algorithm is properly selected and fully utilized, surrogate models based on that can well predict the performance of components in power cycle. Based on Levenberg–Marquardt algorithm, Yu et al. [13] proposed a back-propagation neural network to predict the off-design or overall dynamic performance of the gas turbine. Rossi and Renzi [14] developed a computational methodology based on artificial neural networks (ANNs). It could accurately predict the performance-curve and best-efficiency-point of turbo pump working in reverse mode. This proved that ANNs are a universal and effective evaluation tool. Based on neural network surrogate models, Palagi et al. [15] proposed an optimization model for main design parameters of the radial turbine. The designed neural networks had high accuracy and could accurately learn highly nonlinear physical model objects. Sarafraz et al. [16–18] developed the response surface methodology (RSM) for the optimization of a catalytic reforming micro-reactor and a thermosyphon heat pipe. The above examples have shown that machine learning can be used for component performance prediction, but such surrogate models belong to the black-box model, ignoring the physical relationship between parameters, and have little effect on grasping the operation rules of components and guiding component control. In recent years, some scholars have reconstructed similar heat transfer or mass transfer problems based on the rapidly developing deep learning algorithm, aiming to obtain a surrogate model that can consider the physical mechanism. Guo et al. [19] adopted a convolutional neural network (CNN) to the prediction of the velocity field with different geometric shapes, while convolution and deconvolution operations were used to perform image-to-image regression. Although the accuracy rate reached 98%, there were prediction errors near the boundary. Based on the deep convolutional neural network, the Cp-u model was proposed by Jin et al. [20] for the prediction of the unsteady velocity around a circular cylinder. Compared with the measured data, it had good accuracy. Ti et al. [21] proposed an innovative framework based on the machine learning and CFD simulation to improve the prediction accuracy of turbine wake. The results of the turbine wake model based on ANN were in good agreement with the numerical and experimental data, which showed that the ANN can establish the complex spatial relationship of the problem. In summary, deep learning has been used in the reconstruction of problems such as velocity field, pressure field, and temperature field, and has shown high accuracy and performance. Based on the above introduction, it can be found that there are two main methods to predict the performance of components in power cycles, especially S-CO2 turbines: the mechanism-based physical model and the data-based proxy model. The mechanism-based physical model is a conventionalPDF Image | Performance Prediction of a S-CO2 Turbine
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