# Design and Numerical Analysis of Recuperator for a Liquid Carbon Dioxide Energy Storage System
## 5 Results
### Flow Characteristics and Thermal Performance of the PCHE under Different Loads  
The thermal parameters and boundary conditions vary with the changes in system operating loads. For the purpose of verifying the characteristics of the PCHE under variable running loads, the flow characteristics and thermal performance of the PCHE were numerically simulated when the load varied in the range of \(\pm\)20% during the discharge time. The mesh, turbulence model, and methods used in the calculations were consistent with the previous section. However, the boundary conditions were adjusted based on the loads of the energy storage system. The specific inlet and outlet parameters are presented in Table 6. Furthermore, in the following analysis, the direction of the arrows represents the flow direction of CO\({}_{2}\), where \"C\" denotes the cold side and \"H\" denotes the hot side. Figure 13: Temperature distributions of the CO\({}_{2}\) and solid material along the PCHE at different cross-sections. Figure 14 presents the distribution of average static pressures along the PCHE under different discharge loads. The pressure on both sides slightly decreases from the inlet to the outlet sides. The magnitude of pressure drop varies with discharge loads. In the cold channel, the pressure of CO\({}_{2}\) increases as the discharge load increases. Additionally, due to the increased flow rate with higher load, the pressure drops of CO\({}_{2}\) experience an increase on both sides. Figure 15 shows the distribution of resistance coefficients along the PCHE both on cold and hot sides under different discharge loads. It can be observed that the resistance coefficients exhibit similar trends under different loads. As the discharge load increases, the resistance coefficients on both sides decrease. It is because the pressure drops increase with the growth of discharge power, mainly due to the increased flow velocity of CO\({}_{2}\) caused by the larger mass flow rate. Since the velocity term appears in the denominator of the resistance coefficient equation, despite the pressure drops increasing with the growth of the discharge load, the resistance coefficient decreases. Figure 16 displays the flux profiles along the PCHE on both the cold and hot sides under different discharge loads. It can be observed that under the same load, the heat flux of the PCHE gradually rises from the inlet to the outlet on the cold side. The heat flux is consistent at the same position, indicating the accuracy of the calculations. Furthermore, with an increase in the discharge load, the heat flux of the PCHE increases. It is derived from the system flow rate growth as the discharge load increases, resulting in a higher heat capacity recovery requirement for the PCHE. Figure 17 presents the distribution of average temperatures of CO\({}_{2}\) on both sides under different discharge loads. Figure 18 shows the distribution of average temperatures of the solid material under different discharge loads. From both figures, it observed that along the direction of CO\({}_{2}\) flow on the cold side, the temperatures of CO\({}_{2}\), as well as the solid \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Unit** & **Loads/MW** & **Cold-Side Outlet** & **Hot-Side Outlet** & **Total Mass Flow kg/s** & **Cold-Side Inlet** \\  & **Pressure/MPa** & **Pressure/MPa** & **Pressure/MPa** & **Temperature/K** \\ \hline
12 & 27.88 & 6.5 & 69.84 & 298.2 \\
11 & 26.4 & 6.5 & 66.02 & 298.2 \\
10 & 25 & 6.5 & 62.19 & 298.2 \\
9 & 23.55 & 6.5 & 58.32 & 298.2 \\
8 & 22.10 & 6.5 & 54.43 & 298.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters of the PCHE under different discharge loads. Figure 14: Distribution of average pressures along the PCHE under different discharge loads. material of the recuperator, gradually increase on both sides. Furthermore, the growth in temperature increases gradually too.