The sCO₂ power cycles provide highly efficient, highly dense and less corrosive power generation compared with other cycle (Incumbent Steam Rankine or Air Brayton Cycles) over a wide range of applications such as waste heat recovery, concentrating solar power, nuclear, and fossil energy.^1,2 Efficiency and power density in power conversion systems are the key criteria according to increasing energy demands over the world. In addition, corrosiveness is also significant issues for turbines and compressors in most power cycles.

Since the sCO₂ turbomachinery are generally small and operate at high rotational speeds, bearings pose a significant challenge to the design of turbo-compressors/expanders for sCO₂ power cycles.² Although the basic sCO₂ cycle consists of a compressor, turbine, heater and cooler as well as a recuperator, efficient, reliable and compact turbine and compressor for high-pressure environment are most significant components to realize robust operation and high-efficiency.¹

Magnetic bearings present several advantages over pure mechanical bearings such as rolling element bearing, hydrostatic/dynamic bearing, and gas foil bearing although bearing selection is rather complex and depends on many factors such as cost, duty cycle, load, speed, size/weight, efficiency, and dynamic performance.^3-6 For examples, a wide range of operating conditions, controllable bearing dynamics, and measurement of bearing forces are the well-known strong point of magnetic bearings. In addition, magnetic bearing technology has been gaining more and more area in turbomachinery and rotating equipment for couple of decades together with remarkable development and progress of integrated power electronics and semiconductor industries.⁷

Although journal bearing may have instability known as oil whirl and whip, fluid induced instability like oil whirl may also happen even with magnetic bearing under both high pressure and speed conditions of sCO₂ turbomachinery.⁸ Dedicate analysis was required to evaluate instability of journal bearing with sCO₂ since the supercritical fluids are generally 100 to 1,000 times denser than gases and slightly lighter than liquids.⁹ In addition, experimental investigation of rotordynamic performance is very important for designing critical components of turbomachinery such as rotor, bearing, seal and so on.¹⁰ However, there are few studies and practical guidelines on sCO₂ turbomachinery supported by magnetic bearings.

With magnetic bearing, vibration or instability of journal bearing can be reduced as well as the working condition of the rotating machinery can be extended or optimized.^11-13 Adding damping, coupled stiffness or preload with magnetic bearing may improve the rotordynamic stability.^14,15 In addition, the proper control of magnetic bearing enhances the rotordynamic performance.¹⁶

This paper presents experimental investigation on instability of a sCO₂ compressor supported by magnetic bearing. First, we introduce the sCO₂ compressor supported by magnetic bearing. Procedure to guarantee rotordynamic performance of the sCO₂ compressor supported by magnetic bearing is provided. Then, effects of working condition such as pressure and rotating speed on the fluid induced instability are investigated experimentally. Finally, a strategy to resolve the fluid-induced instability with conventional PID control are proposed and experimentally verified.

This sub-harmonic vibration frequency, near 270 Hz, is caused by cross-couple stiffness of the pressurized sCO₂ whirling. The cross-couple stiffness of the pressurized sCO₂ whirling equivalently reduces the damping of the bearing and causes the subharmonic vibration of the system, which is the average whirling velocity of the fluid between the rotor and the bearing.¹⁸

The damping of the sCO₂ compressor can be increased by tuning the PID control gains. After the gain is re-tuned, the vibration amplitude at 270 Hz can be reduced successfully, as shown in Fig. 8. The proportional gain remains low for the system stability while the derivative gain increases for sub-harmonic vibration. The vibration amplitude at 140 Hz is reduced by about 56%, from 5.9 to 2.6 μm, and the vibration amplitude at 270 Hz is reduced by about 67%, from 6.2 to 2.0 μm. The amplitude of the synchronous vibration was reduced by 45% from 12.4 to 6.8 μm.

Fig. 8 
Frequency spectrum of vibration under high pressure (70 bar) after re-tuning the position control gains

This paper presents experimental investigation on instability of a sCO₂ compressor supported by magnetic bearings. First, we introduce the sCO₂ compressor supported by magnetic bearings. Then, effects of working condition such as pressure and rotating speed on the fluid-induced instability are investigated experimentally. Finally, a strategy to resolve the fluid-induced instability with conventional PID control are proposed and experimentally verifie.