## 4 Validation and Applications
### Low-Speed Centrifugal Compressor (LSCC)
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Computation** & **Experiment** & **Error (\%)** \\ \hline Total pressure ratio & 1.159 & 1.141 & 1.8 \\ Isentropic efficiency & 0.919 & 0.922 & \(-\)0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computed and experimental LSCC performance on design point. Figure 4: Performance characteristics of LSCC. (**a**) Total pressure ratio; (**b**) isentropic efficiency. The meridional flow field of the LSCC at its design mass flow rate is detailed in Figure 5. As can be seen from Figure 5a, the relative Mach number inside the blade passage remained lower than 0.3, except near the shroud at the impeller inlet, and achieved the lowest value at the impeller exit. This kind of low-speed flow shows a slightly incompressible characteristic. Figure 5b shows the static pressure distribution along the flow passage. Though an overall diffusion process was achieved, the static pressure did not exhibit a monotonous lift. Instead, the static pressure drop was observed at the vaneless diffuser outlet. This was mainly due to the convergent passage area resulting from the dramatic decrease in the diffuser width at the passage outlet, though the radius increased. Figure 5c presents the total temperature rise due to the work done by the impeller on the airflow. It is noticeable that a uniform distribution of the total temperature along the blade span was observed at the impeller exit. The predicted entropy distribution is shown in Figure 5d. It can be seen that along the streamwise direction, the entropy increased continuously. Meanwhile, in the spanwise direction, the entropy was predicted to be of low value at midspan and at a higher value near the endwall. Specifically, the entropy product at the shroud was higher than that at the hub, which can be accounted for by the significant tip leakage loss. Overall, the reasonable flow details presented in Figure 5 demonstrate the adequacy of the developed throughflow method on the meridional flow simulation in the low-speed centrifugal compressors. The spanwise distribution of the flow parameters at the impeller outlet is always the key point that the designers are concerned with. Therefore, a comparison of the spanwise distribution of total temperature ratio at the design point between the throughflow results and experimental data was implemented and is shown in Figure 6. It can be seen that, except for the nearby shroud region, the calculated total temperature ratio was slightly lower than the experiment below the 25% spanwise location. At the other positions, the calculated results remained higher than the experimental values. This accounts for the higher total pressure prediction at the design point discussed above, as the isentropic efficiency was accurately predicted. Moreover, it can also be observed that the experimental distribution of the total temperature ratio had a distinct change below 40% spanwise. As a comparison, the throughflow result had a nearly flat distribution curve. This was mainly due to a uniformly distributed slip factor along the whole blade span in the throughflow simulation in this study. A more realistic distributing method of the slip factor suiting the throughflow calculation is still expected. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Mass Flow Rate (kg/s)** & **Incidence Loss (\%)** & **Blade Loading Loss (\%)** & **Skin Friction Loss (\%)** & **Clearance Loss (\%)** & **Mixing Loss (\%)** & **Disc Friction Loss (\%)** & **Recirculation Loss (\%)** & **Vaneless Diffuser Loss (\%)** \\ \hline
22.0 & 7.965 & 12.389 & 13.843 & 2.212 & 6.005 & 3.603 & 49.621 & 4.362 \\ \hline
30.0 & 3.209 & 19.652 & 33.422 & 5.080 & 26.738 & 6.417 & 0.000 & 5.481 \\ \hline
40.0 & 0.765 & 7.957 & 27.085 & 3.060 & 34.124 & 3.366 & 21.653 & 1.989 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Contributions of different losses for the LSCC case.