# Flow Control of Radial Inlet Chamber and Downstream Effects on a Centrifugal Compressor Stage
## 2 Methodology
### Verification and Validation
#### 2.3.2 Validation of the Numerical Method  
In order to validate the reliability of the numerical results in the present study, the calculated flow parameters on the main sections in the radial inlet chamber and the predicted performance of the compressor stage were extracted and compared against the experimental results of the previously published literature [36; 37].  
Figure 6 shows the detailed flow distributions for the inlet and internal sections of the radial inlet chamber in the form of dimensionless Mach numbers. Compared with  
Figure 4: Computational grids for different components of the computational fluid dynamics (CFD) models.  
Figure 5: \(y^{+}\) distributions of the computational grids.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item** & **Radial Inlet Chamber** & **Guide Vanes** & **Compressor Stage** & **Recommended Value**[40; 41] \\ \hline Minimum orthogonality & 34.3\({}^{\circ}\) & 33.2\({}^{\circ}\) & 21.3\({}^{\circ}\) & \textgreater{}10\({}^{\circ}\) \\ Maximum aspect ratio & 750 & 408.9 & 839 & \textless{}5000 \\ Maximum expansion ratio & 1.51 & 1.91 & 3.84 & \textless{}5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Grid quality of the computational models.  
the experimental data, the ranges of the mainstreams for the sections were larger in the numerical results with a higher velocity gradient close to the wall, which was mainly caused by the smooth wall assumption of the CFD model. Since the machining chamfers and fillets were simplified in the numerical models to facilitate the grid meshing, small deviations would also be introduced to the flow simulation. Except for these slight differences, the flow characteristics predicted by the numerical method agreed well with the experimental data. This revealed that the CFD results obtained in this paper performed well in capturing the major characteristics and key details of the flow conditions inside the radial inlet chambers, which ensured an acceptable accuracy for the numerical flow analysis.  
For the CFD results of the compressor stage, a performance comparison between the numerical simulation and the model test was made under different operating conditions at the design's rotational speed. The predicted and measured performance parameters of the compressor stage (from 0 to _out_) are shown in Figure 7. The mass flow was dimensionless by the design's flow rate, and the total pressure ratio \(\varepsilon\) and polytropic efficiency \(\eta\) are calculated as follows [42]:  
\[\varepsilon_{0-out}=p_{t,out}/p_{t,0} \tag{5}\]  
Figure 6: Comparison of the measured and simulated Mach numbers in the radial inlet chamber. (**a**) Results for the inlet section. (**b**) Results for the interface of the intake and spiral channels.  
\[\eta_{0-out}=\frac{\kappa}{\kappa-1}\cdot\frac{\ln(p_{t,out}/p_{t,0})}{\ln(T_{t, out}/T_{t,0})} \tag{6}\]  
It can be clearly seen that the trend of the compressor performance curves obtained by the numerical simulation agreed well with the experimental data. For the whole compressor stage, the differences between the numerical and experimental results were less than 3% under most of the operating conditions. This further validates the reliability of the numerical method and computational results in the present research.