## 5 1-D Design and CFD Calculation for the Axial Compressor  
In order to verify the accuracy of the model and estimate the efficiency of the axial-flow compressor, an axial-flow compressor with the following parameters, shown in Table 3, has been constructed. Smith chart for optimum different reaction stages, which is based upon model tests of a range of axial compressor, is helpful for engineer to make a preliminary design [23]. But the chart may \begin{table}
\begin{tabular}{c c} \hline \hline
**Mass Flow Rate (Kg/s)** & **2000** \\ \hline Pressure ratio & 2.564 \\ Inlet pressure (MPa) & 7.8 \\ Inlet temperature (K) & 307.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Design parameters for the axial compressor. overestimate efficiency and overly pessimistically estimates stall range [20]. According to the Smith chart, once the flow coefficient has been determined, sensible range of work coefficient lies between the following two curves [23]. \[ \begin{array}{l}\psi_{\text{opt}}=0.185\sqrt{4\varphi^{2}}\\ \psi_{\text{max}}=0.32+0.2\varphi\end{array}  \tag{17}\]  
The axial flow compressor in this paper adopted free vortex flow with axial outflow and hub-shroud ratio was 0.7, hence the sensible range of flow and work coefficient as Figure 4:  
To avoid a large area of condensation, the work coefficient is slightly larger than the optimum value. Thus, the corresponding flow coefficient and work coefficient are selected as 0.33 and 0.3, respectively. In order to ensure the stable operation requirements, the calculation result shows that at least 9 stages are needed to avoid stalling. In addition, the tip clearance of the rotor is 2% of the blade height. The one-dimensional design result is displayed in Figure 5.  
As there are so many stages, only the first stage was calculated with CFD to evaluate the reliability of the axial compressor's loss models. At the same time, because the deviation angle model is not  
Figure 4: Sensible range of flow coefficient and work coefficient. Figure 5: Meridional plane of the axial compressor for 100 MWe. reliable at off-design conditions, which would bring about a large amount of error in prediction, only the design condition was calculated by the mean streamline method. The preliminary geometric parameters of the compressor were computed by an internal MATLAB code coupled with the NIST database and geometric modeling was completed in Numeca Autoblade. In order to reduce the amount of calculation, a single passage grid was employed and the interface between the rotor and stator was dealt with in the mixing plane. The H-block was located upstream and downstream of the blade and the O-block was applied in the rotor and stator passage. The total number of grid cells is 629,680. The geometry and grid are displayed in Figure 6.  
In order to take the real gas properties of SCO\({}_{2}\) into account, look-up tables were used during the calculation. These property tables were generated by the SW equation of state, in addition, they had been encrypted with logarithmic distribution near the critical point. But, if the property tables are too dense, the time of calculation will increase sharply, and it is easier to diverge. According to [PERSON]'s study [24], the range of the property table is 3-28 MPa and 270-500 K for pressure and temperature, respectively, and the resolution of the tables is 300 \(\times\) 300. This range is sufficient for the three compressors in this article. Figure 7 shows the density table employed in the CFD calculation. To ensure the reliability of the CFD, grid independence and y+ (\(<\)200) were taken into account and turbulence model was chosen as \(SST\) (Extended Wall Function) model. Compared with the \(k-\varepsilon\) model, it is more accurate near the wall layers and is more suitable for adverse pressure gradient flows, which reduces the problem of grid-induced separation for industrial flow simulations [25]. Another advantage of the \(SST\) model is its robustness near the wall treatment.