# Instability Study of Magnetic Journal Bearing under S-CO\({}_{2}\) Condition
## 1 Introduction  
There are many reasons why the supercritical CO\({}_{2}\) (S-CO\({}_{2}\)) power cycle technology has been attracting attention from many researchers over the years. First, the S-CO\({}_{2}\) Brayton cycle can attain competitive efficiency (-50 %) with moderate temperature heat sources (450-750 \({}^{\circ}\)C) [1]. Its components are compact, and arrangement is simple. This leads to small footprints of the power system. These benefits mainly come from the specific properties of S-CO\({}_{2}\). These characteristics of an S-CO\({}_{2}\) power system make it possible to apply distributed generation [2]. However, in order to stay competitive with the S-CO\({}_{2}\) power cycle in the distributed power generation market, developing a bearing technology appropriate for the power cycle has been proven to be a major technical challenge [3]. To levitate the rotating shaft in the turbomachinery, a bearing system is necessary. Thus, design of a high-speed S-CO\({}_{2}\) turbomachine with a stable bearing system has always been accentuated for successful development of the S-CO\({}_{2}\) power cycle. A bearing system should be properly selected because of the power of an S-CO\({}_{2}\) power cycle, as shown in Figure 1[4]. The gas foil bearing technology is very challenging to levitate a shaft for power systems above 3 MWe. For wide applications of S-CO\({}_{2}\) power systems, enhancing bearing performance is necessary. Hydrodynamic oil bearing and hydrostatic bearing can handle higher load than other bearing technologies. However, because most oils dissolve in S-CO\({}_{2}\), maintaining the purity of S-CO\({}_{2}\) without complex systems can be a failure for long-term reliable cycle operation [5, 6]. Thus, magnetic bearing technology can be a favorable option for an S-CO\({}_{2}\) cycle with distributed generation with a long maintenance span. An active-control magnetic bearing (AMB) levitates the rotating shaft without direct contact by generating magnetic force using electromagnets. Recent AMBs are deal with many rotordynamic issues such as vibration suppression, stability control, and condition monitoring for flexible rotor-bearing systems [7]. Using a hybrid magnetic bearing is one solution for dealing with rotordynamic and power loss issues [8; 9]. There has also been research on magnetic bearing fault detection and diagnosis for reducing the rotor instability [10]. Until now, the magnetic bearing research has mostly been dealing with the air gap condition. With the air gap condition, the fluid force is assumed to be negligible compared to the magnetic force and magnetic loss. However, under the S-CO\({}_{2}\) condition, this hypothesis has not been tested and validated before, to the best of the authors' knowledge. If magnetic bearings were to be used under S-CO\({}_{2}\) conditions, this hypothesis has to be also tested and verified. If this hypothesis is tested, the fluid force has to be considered, although a new control technology could overcome this issue; magnetic bearings can offer better S-CO\({}_{2}\) power system architecture. This is because higher bearing capacity can be achieved without an oil recovery system, which greatly simplifies the current S-CO\({}_{2}\) power system. There have been several experiments of the radial AMB under S-CO\({}_{2}\) condition [11]. However, from these experiments, shaft control under an S-CO\({}_{2}\) environment was not reported as successful. This study repeatedly addresses the instability problem of high-speed operation tests under high pressure S-CO\({}_{2}\) conditions. Test data obtained from the Korea Atomic Energy Research Institute (KAERI) and Korea Advanced Institute of Science and Technology (KAIST) are shown in Figure 2[12]. Figure 1: Bearing options for supercritical carbon dioxide (S-CO\({}_{2}\)) Brayton cycles for various power scales [4].