# Design and Numerical Analysis of Recuperator for a Liquid Carbon Dioxide Energy Storage System
## 1 Introduction  
A compressed carbon dioxide energy storage system (CCES) is one of compressed gas energy storage that relies on the sCO\({}_{2}\) Brayton cycle. Compared with the compressed air energy storage system (CAES) [1] and LAES [2], the CCES is easier to liquefy and denser. Since Professor [PERSON] et al. [3] raised a system combining the trans-critical CO\({}_{2}\) cycle with the thermo-electrical energy storage system (TEES), many scholars dedicated themselves to the study of CCES. In 2015, [PERSON] et al. [4] proposed a transcritical CCES with heat storage. During the charging time, the gaseous carbon dioxide was pressurized by a set of compressors, and the compression heat was retained in a heat accumulator, then cooled by a throttle valve, and finally condensed into liquid through a condenser. During the discharging time, the pump was utilized to pressurize the liquid CO\({}_{2}\). After the high-pressure CO\({}_{2}\) absorbed heat in the recuperator, it became gas and then expanded in the turbine to do work. Finally, the exhaust gas was further condensed into liquid, and stored in a tank. Subsequently, [PERSON] et al. [5] proposed a CCES derived from the trans-critical CO\({}_{2}\) Brayton cycle. The thermodynamic model was developed and the thermodynamic performance was studied. The RTE of the system was lower compared to the adiabatic CAES (ACAES), but the storage density was 2.8 times that of ACAES. [PERSON] et al. [6] contrastivelyanalyzed the performance of ACAES, CAES, and CCES with a similar system arrangement. It was concluded that the RTE was lower than the RTE of the corresponding CAES when CO\({}_{2}\) was stored in gas, while it was higher than LAES after the carbon dioxide was stored as liquid, and the storage temperature was more easily reached. [PERSON] et al. [7] conducted a charge and discharge experiment of CCES with three 7 L cylinders. The maximum storage pressure was 0.3 MPa. The overall efficiency of the system was 46.2%. It was concluded that CCES had obvious advantages regarding efficiency and footprint compared with similar CAES systems. Some scholars have combined CCES with other cycling systems for better thermal performance. A transcortical CCES combined with a cooling heating and power (CCHP) system that utilized waste heat was proposed by [PERSON] et al. [8]. It was noted that system power efficiency and system energy efficiency were 0.48 and 1.19, respectively. The energy density was 11.51 kWh/m\({}^{3}\). Despite the fact that the CCES is generally acknowledged as a promising energy storage system, most works focus on the thermodynamic analysis of system integration, and further design of components for the system is not enough. The key components of CCES include heat storage devices, turbomachinery, and efficient heat exchangers. Among them, PCHE, a high-effectiveness heat exchanger, was first proposed in the 1980s and manufactured by Haynes in 1985 [9]. Subsequently, PCHE has been widely studied in the sCO\({}_{2}\) power cycle for its compact structure and efficiency, since [PERSON] et al. [10] published the study of the sCO\({}_{2}\) cycle, and the PCHE was adopted to transfer heat. It was found that the channel structures greatly impact the performance of the PCHE, then a lot of work on geometric structure optimization has been carried out. The common channel shapes include straight, U, Z, and S shapes. [PERSON]. et al. [11] compared the influence of a straight shape and a zigzag-shaped channel, and it can be observed that the channel diameter and Reynolds number had a significant impact on the pressure loss of working fluid. For the zigzag channel, increasing the bending angle and decreasing the linear pitch could benefit the performance of PCHE. The thermal performance of the \(Z\)-shaped channel was obviously superior to that of the straight channel while obtaining a larger drop loss. A sinusoidal shape channel PCHE was studied by [PERSON] et al. [12].