# Design and Numerical Analysis of Recuperator for a Liquid Carbon Dioxide Energy Storage System
## 6 Conclusions  
In this study, the thermal design of a printed circuit recuperator used in the LCES was completed. The numerical solution method adopted was verified, and the flow characteristics and thermal performance of the recuperator under design parameters were analyzed. The effect of different discharge loads on the flow characteristics and thermal performance of the fluid was investigated. The key findings are as follows:  
1. The thermal design of the PCHE was completed. The structural form and dimensions of the PCHE have been determined. 2. The flow characteristics and heat transfer capability analysis of the PCHE adopting different turbulence models were compared. The SST k-\(\omega\) model matched the experimental data best. 3. Under design conditions, the resistance coefficient of the CO\({}_{2}\) on the cold side increased gradually, from the inlet to the outlet of the PCHE, while decreasing gradually on the hot side. The variations in the flow velocity of CO\({}_{2}\) on both sides were consistent with the changes in the resistance coefficient. The average temperature of CO\({}_{2}\) on the cold side increased rapidly, while the decline rate of temperature on the hot side gradually slowed down. Furthermore, the \(Nu\) of CO\({}_{2}\) on the cold side has a sharp increase firstly followed by a slow increase, and finally exhibits a gradual decrease. Conversely, the \(Nu\) exhibits a gradual increase on the hot side. 4. The flow characteristics and heat transfer of CO\({}_{2}\) in the PCHE under different discharge loads were studied. As the discharge load of LCES increased, the pressure drop of CO\({}_{2}\) in both the cold and hot sides increased, while the resistance coefficient on both sides decreased gradually. The \(HTC\) of CO\({}_{2}\) on both sides gradually increased. The \(Nu\) of the CO\({}_{2}\) on the front half of the cold side increased sharply while changing a little on the rear half. The \(Nu\) of CO\({}_{2}\) increased gradually along the flow on the hot side. From the perspective of the temperature and heat transfer capacity of the CO\({}_{2}\) on both sides under different loads, the designed PCHE meets the requirements for variable operating conditions of the energy storage system. Methodology, M.X. ; Software, Y.S. and M.X. ; Formal analysis, M.X. ; Data curation, M.W. ; Writing--original draft, Z.L. ; Writing--review & editing, M.W. ; Supervision, M.X. ; Funding acquisition, Z.L. All authors have read and agreed to the published version of the manuscript. Figure 21: Distribution of thermal conductivity of CO\({}_{2}\) both on the cold and hot sides under different loads. **Funding:** The authors are grateful for this work being supported by the National Natural Science Foundation of China (Grant No. 52076168). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. **Conflicts of Interest:** The authors declare no conflict of interest.