Regular Article

Multi-objective optimization of a small scale SCO₂ turbine rotor system with a shaft cooler

¹ School of Mechatronics Engineering, Henan University of Science and Technology, Henan 471003, China
² Henan Key Laboratory for Machinery Design and Transmission System, Henan University of Science and Technology, Luoyang, Henan 471003, China
³ School of Mechanical and Mining Engineering, University of Queensland, Brisbane, Australia

^* e-mail: li_jishun@163.com

Received: 24 November 2021
Accepted: 9 June 2022

Abstract

The SCO₂ turbine machines exchange energy through supercritical carbon dioxide. Their impeller has the features of high-temperature and −speed to enhance energy conversion efficiency, but the rotor needs to be cooled to be compatible with bearings and seals. The paper introduces a pivotal parameter optimization of a concentrating solar SCO₂ turbine rotor and seeks to control the harmonic response amplitude while preserving the distance between the critical speed and the working speed. The optimization considers several parameters including bearing span, stiffness, effective mass and damping of the bearing hub, and gas film stiffness coefficients of the cooler. The optimization is accomplished using a multi-objective and −scale quantum harmonic oscillator algorithm (mMQHOA) that couples an information interaction algorithm and transfer matrix model. The application of information interaction accelerates the convergence speed of the objective functions. The verification results from the three-dimensional finite element (3D-FE) indicate that the non-dominant design reduces resonance amplitude of the disc by approximately 71.91%, while the critical frequency increases by about 34.33% in the direction away from the operating frequency, and imply a trade-off relationship between harmonic response amplitude and critical speed. It is further reveal that the increased gas film stiffness of cooler in the primary level interval (<1E6 N/m) has no significant effect on the harmonic response of the system. The optimization is based not only on the analysis of design parameters, but also focuses on the sensitivity of objective functions that can significantly affect dynamic performance. The models with a single variable of bearing span and film stiffness are investigated respectively, and then the sensitivity of the system response is analyzed. In addition, three different objective functions are proposed, with the purpose of constructing a universally applicable model that can be further used to optimize the analogous bearing rotor system.