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applied sciences Article Off-Design Performance Prediction of a S-CO2 Turbine Based on Field Reconstruction Using Deep-Learning Approach Dongbo Shi, Lei Sun and Yonghui Xie * State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China; sdb_xjtu@126.com (D.S.); sltc123@stu.xjtu.edu.cn (L.S.) * Correspondence: yhxie@mail.xjtu.edu.cn; Tel.: +86-029-82664443 Received: 18 June 2020; Accepted: 16 July 2020; Published: 21 July 2020 Featured Application: In this research, a two-stage deep convolutional neural network is proposed to predict the off-design performance of a S-CO2 turbine based on field reconstruction. Once the deep model is well-trained, the calculation with graphics processing unit (GPU)-acceleration can quickly predict the physical fields on the blade surface and turbine performance. In practical engineering applications, the proposed method can not only reduce the design cycle of components but also help to grasp the actual operating conditions in real time. Abstract: The reliable design of the supercritical carbon dioxide (S-CO2) turbine is the core of the advanced S-CO2 power generation technology. However, the traditional computational fluid dynamics (CFD) method is usually applied in the S-CO2 turbine design-optimization, which is a high computational cost, high memory requirement, and long time-consuming solver. In this research, a flexible end-to-end deep learning approach is presented for the off-design performance prediction of the S-CO2 turbine based on physical fields reconstruction. Our approach consists of three steps: firstly, an optimal design of a 60,000 rpm S-CO2 turbine is established. Secondly, five design variables for off-design analysis are selected to reconstruct the temperature and pressure fields on the blade surface through a deconvolutional neural network. Finally, the power and efficiency of the turbine is predicted by a convolutional neural network according to reconstruction fields. The results show that the prediction approach not only outperforms five classical machine learning models but also focused on the physical mechanism of turbine design. In addition, once the deep model is well-trained, the calculation with graphics processing unit (GPU)-accelerated can quickly predict the physical fields and performance. This prediction approach requires less human intervention and has the advantages of being universal, flexible, and easy to implement. Keywords: deep learning; S-CO2 turbine; field reconstruction; off-design performance 1. Introduction Supercritical carbon dioxide (S-CO2) refers to the carbon dioxide fluid above the critical point (30.98 ◦C, 7.38 MPa) [1]. It has the advantages of being stable chemical properties, weak high-temperature corrosion, non-toxic, and non-combustible. At the same time, it has the characteristics of high specific heat capacity and density, high thermal conductivity, and low viscosity. S-CO2 is an ideal low-cost working medium [2,3]. Therefore, a Brayton power generation system with S-CO2 has the advantages of high-efficiency, small-volume, and low-noise (mainly high-frequency noise). It has become one of the main research directions in the field of power generation technology (nuclear energy, solar energy, geothermal energy, waste heat, etc.) [4–7]. Appl. Sci. 2020, 10, 4999; doi:10.3390/app10144999 www.mdpi.com/journal/applsciPDF Image | Performance Prediction of a S-CO2 Turbine
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