# Investigation on Unsteady Flow Characteristics of a SCO\({}_{2}\) Centrifugal Compressor
## 1 Introduction  
Supercritical carbon dioxide (SCO\({}_{2}\)) is a kind of supercritical fluid which has a critical point at around room temperature. Concretely, its critical temperature and pressure are respectively 304.2 K and 7.4 MPa [1]. As a working fluid in a centrifugal compressor, SCO\({}_{2}\) possesses lots of merits. For example, its critical condition is easy to reach and it is an environmentally friendly working fluid, which makes SCO\({}_{2}\) safe and cheap for industrial use [2]. The most useful advantages of SCO\({}_{2}\) are its high density, low viscosity, and large pressure increase with small enthalpy increase, which result in high efficiency, compact mechanical structure, and a larger pressure ratio with smaller input power in the centrifugal compressor [3; 4; 5]. The research on SCO\({}_{2}\) has gradually been increasing lately. In recent years, the investigations on SCO\({}_{2}\) Brayton cycle or SCO\({}_{2}\)-based solar Rankine cycle system have been covered [6; 7; 8]. SCO\({}_{2}\) cycle has been considered as the most promising and attractive candidate in concentrated solar power, coal power system, or bottoming cycle of fuel cells due to its abovementioned advantages [9; 10; 11]. As per turbomachinery, SCO\({}_{2}\) is also a promising working fluid. In miniature power units, compact radial turbines and centrifugal compressors with complex geometries are designed and used [12]. In large power units, axial turbines and compressors with SCO\({}_{2}\) as a working fluid can be obtained [13]. Centrifugal compressors of various power inputs with SCO\({}_{2}\) as a working fluid have drawn more and more attention lately. Both experimental and computational methods are applied. [PERSON] et al. [10; 14] conducted thorough research on SCO\({}_{2}\) systems and compared the aerodynamic performance of air and SCO\({}_{2}\) in conical diffusers. [PERSON] and [PERSON]. [15] studied the computer-based design and analysis of control systems for centrifugal compressors when the operating fluid is supercritical CO\({}_{2}\). [PERSON] et al. [16] from Tokyo Institute of Technology tested the aerodynamic characteristics of a centrifugal compressor working in supercritical carbon dioxide by an experimental method. Computational fluid dynamics (CFD) has been widely used as a tool for designing, evaluating, and improving turbomachinery devices, including compressors [17; 18], turbines [19; 20], and pumps [21; 22]. [PERSON] et al. [23] carried out the numerical investigation of two-phase flow characteristics on the blade tip of a supercritical CO\({}_{2}\) centrifugal compressor. [PERSON] and [PERSON]. [24] presented a novel modeling approach and the corresponding computer simulation of the SCO\({}_{2}\) flow inside a high-speed compact centrifugal compressor. [PERSON] et al. [25] conducted a 3D numerical study for the full SCO\({}_{2}\) compressor geometry including diffuser and volute. The predictions were compared with measurements obtained from the constructed SCO\({}_{2}\) compressor test facility. It demonstrated the accuracy and the feasibility of numerical investigation. Compared to normal CO\({}_{2}\), the centrifugal compressor with SCO\({}_{2}\) has higher efficiency, a more compact mechanical structure, and a larger pressure ratio [26]. Hence, the work in this paper is of great importance for future power systems. Nevertheless, one potential disadvantage of SCO\({}_{2}\) lies in the phase change near the critical point, which can lead to the instability of actual operation. In this paper, the state parameters of inlet are above the critical point of CO\({}_{2}\) and the geometry of impeller and diffuser is well designed to avoid the subcritical state of the working fluid as much as possible [27]. In this paper, based on the real gas property of SCO\({}_{2}\), a centrifugal compressor of large power and high pressure ratio, which has a large mass flow rate, has been designed. The corresponding geometrical parameters of the impeller and diffuser are obtained.