# Design and Numerical Analysis of Recuperator for a Liquid Carbon Dioxide Energy Storage System
## 1 Introduction
In comparison with the straight-through channel, the sinusoidal shape was more beneficial for the heat transfer performance of the exchanger. Moreover, the heat transfer performance increased with the growth of amplitude and the decrease in wavelength. The flow distribution of a PCHE was studied in the literature [13]. The impacts of flow uniformity were suited by numerical simulations. The inlet header designed in the shape of a taper was optimized. It was concluded that the appropriate cone angle can make the flow distribution more uniform, resulting in improving the heat transfer property of PCHE by 17.3-19.7%. When pressure and temperature differences between PCHE channels are too large, it is easy to cause channel dispatching. The stress deviation of the main PCHE channels in the power generation system was studied by [PERSON] et al. [14] when the pressure difference between the PCHE channels was 19.5 Mpa and the temperature difference was 25 \({}^{\circ}\)C. The result showed that the stress intensity grew with the increase in misalignment. It is less safe than the condition without misalignment. Furthermore, some experimental research has been performed. The pressure resistance, leakage, corrosion conditions, flow characteristics, and thermal performance of PCHE with CO\({}_{2}\) as a working fluid were tested. [PERSON] et al. [15] simulated the impacts of channel width, pressure of spray, corrosion temperature, and corrosion time, by combining numerical simulation and experiment. [PERSON] et al. [16] fabricated straight-channel PCHE heat exchangers in two ways, diffusion bonding technology and photochemical etching technology. Under the same experimental conditions, the heat transfer and hydraulic properties using CO\({}_{2}\) and water as working mediums, respectively, were compared. The results showed that sCO\({}_{2}\) had better performance. The PCHE using CO\({}_{2}\) as a working fluid under different pressures was also studied by experiments. The finding revealed that the PCHE had better comprehensive performance when the pressure of CO\({}_{2}\) was higher. The PCHE was adopted as a precooler in a 100 kW class CO\({}_{2}\) Brayton cycle by [PERSON] et al. [17]. Zigzag fins are adopted on both sides of the PCHE, arranged in a single row. Under various Reynolds numbers and temperatures, the heat transfer coefficient (_HTC_) and pressure drop of the PCHE were tested. [PERSON] et al. [18] studied the PCHE _HTC_ of a small channel PCHE through experiments. A two-layer-channel PCHE with a channel hydraulic diameter of 1.83 mm was machined as a testing sample. The _HTC_ of boiling heat transfer, single-phase heat transfer, and condensation heat transfer were studied and compared under different temperatures. Given the above, there has been extensive research on the influence of channel structure and processing technology on the effectiveness of PCHE. However, in the process of numerical simulation or experiment, a unilateral channel with a constant value of wall temperature or heat flow was generally considered. Normally there was water or other working fluid on one side, and CO\({}_{2}\) on the other side. Only a few researchers carried out research with carbon dioxide on both sides and the temperature of the CO\({}_{2}\) did not vary much according to their research. However, for the LCES [19] investigated in this study, the state of CO\({}_{2}\) flowing in the recuperator on the cold side varied from liquid to supercritical, and the physical properties of the CO\({}_{2}\) changed sharply. Therefore, it is very important to establish an accurate model and study the heat transfer and fluid performance of the PCHE used as a recuperator, which is helpful for the performance evaluation of the LCES. For this study, the thermodynamic model of a printed circuit recuperator used in the LCES was studied, and the thermal design of the recuperator was completed.