# Design and Numerical Analysis of Recuperator for a Liquid Carbon Dioxide Energy Storage System
## 3 Numerical Calculation Method and Validation of Numerical Method
### Verification of Turbulence Model for Geometric Structure  
Turbulence models are established on a series of assumptions; thus, different turbulence models are required for different physical models. The turbulence model has a great impact on the calculation results. Therefore, the numerical simulation for the recuperator discussed in this paper is needed to verify the results obtained using various turbulence models with experimental results. This verification of turbulence mode is essential to ensure the dependability of subsequent simulation results.  
The turbulence model was verified by using experimental results of heat transfer characters for PCHE conducted by [PERSON] et al. [22] and [PERSON] et al. [23] from the Tokyo Institute of Technology, Japan. Figure 2a presents the experimental setup, the geometric  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Hot-Side Inlet** & **Cold-Side Inlet** \\ \hline Temperature/K & 674.3 & 298.2 \\ Pressure/MPa & 6.5 & 25 \\ Mass Flow Rate/kg\(\cdot\)s\({}^{-1}\) & 62.19 & 62.19 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Inlet and outlet thermodynamic parameters of the PCHE.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Channel Diameter/mm & 2.11 & Number of Cold Channels & 7.6 \(\times\) 10\({}^{4}\) \\ Horizontal Spacing/mm & 2.4 & Length/m & 1.72 \\ Metal Plate Thickness/mm & 1.5 & Cold-Side Pressure Drop/kPa & 42.8 \\ Number of Hot Channels & 7.6 \(\times\) 10\({}^{4}\) & Hot-Side Pressure Drop/kPa & 58.2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Values and calculated results of channel geometric structure.  
structure, and the arrangement of the heat exchanger test section. The PCHE test section consisted of 12 layers with a total of 144 channels for CO\({}_{2}\) on the hot side and 6 layers with a total of 66 channels on the cold side. The core dimensions were 71 \(\times\) 76 \(\times\) 896 mm\({}^{3}\). The channel arrangement is exhibited in Figure 2b, and the specific structure and dimensions of the channels on both sides are shown in Figure 2c. A Z-shaped flow path was utilized in the experiments, and the specific parameters of the structure are illustrated in Table 3. During the experiments, the pressure and temperature ranges for CO\({}_{2}\) on the hot side were 2.2-3.2 MPa and 280-300 \({}^{\circ}\)C, respectively, and on the cold side, the ranges were 6.5-10.5 MPa and 90-108 \({}^{\circ}\)C, respectively. The mass flow rates on both sides were the same, varying from 40 to 80 kg\(\cdot\)h\({}^{-1}\). Finally, [PERSON] et al. [22] provided experimental data in the open literature under the conditions of 108 \({}^{\circ}\)C on the cold side and 280 \({}^{\circ}\)C on the hot side.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Channels** & **Diameter/mm** & **Angle/\({}^{\circ}\)** & **Segment Length/mm** & **Effective Length/mm** & **Core Length/mm** \\ \hline Hot side & 144 & 1.9 & 32.5 & 4.5 & 1000 & 896 \\ Cold side & 66 & 1.8 & 40 & 3.62 & 1100 & 896 \\ \hline \end{tabular}
\end{table}
Table 3: PCHE geometric data in the experiments conducted by [PERSON] et al. [22].  
Figure 2: Experimental test facility of PCHE [22; 23].  
It would require a large amount of computation if the same structure was adopted in numerical simulation as tested by [PERSON] et al. Referring to the research experience provided by [PERSON] et al. [24; 25], the experimental model can be simplified to one cold and one hot model with angles of 32.5\({}^{\circ}\) or 40.0\({}^{\circ}\), respectively. The schematic diagram illustrating the corresponding structures compared with the experiments is shown in Figure 3. Therefore, to further reduce the number of grids and consequently decrease the computational demand, the length of the flow path in the heat exchanger for this paper was also shortened from the original 896 mm to 54 mm. The geometric parameters of the models used for the final validation of the turbulence model are presented in Table 4.