# Mechanisms of Sweep on the Performance of Transonic Centrifugal Compressor Impellers
## Numerical Method and Validation
### Validation  
The rig tests of the datum compressor stage have been carried out to validate the performance prediction of CFD. Schematic of the compressor test sections is illustrated in Figure 6, where section A and B represents compressor inlet and exit test section, respectively. The CFD calculation domain for validations is also set between section A and B.  
The characteristics of the datum compressor obtained from experiments and CFD are showed in Figure 7. To represent the maximum discrepancy among different tests on the same compressor, error bars are plotted in the experiment performance lines. The satisfactory agreement is obtained with respect to the choking flow prediction and the tendency of pressure curves, although there is inconsistency for surge point prediction. In this steady case, the surge point is defined as the converged point with the highest backpressure. However, it is misleading to deduce the time-dependent system  
Figure 5: Grid independence: (**a**) performance at design speed and (**b**) spanwise distribution of static pressure at impeller exit, peak efficiency condition at design speed.  
oscillations from numerical steady-state instabilities. Moreover, the application of a rotor-stator interface model will influence surge point prediction as well. At the design speed of the datum compressor stage, instability is initiated from the vaned diffuser part. Since the mixing plane model is applied to the radial gap between the impeller and the vaned diffuser, the incoming flow condition of the vaned diffuser will be different from reality, which then introduces errors in surge prediction. At 95% design speed, because the origin of instability will be shifted from the vaned diffuser to the impeller when decreasing the operating speed [35], the impact of the mixing plane model will be reduced, and thus the discrepancy on surge point prediction will also be decreased. To avoid the impeller-diffuser matching issue as well as the application of a rotor-stator interface model, only the datum impeller attached with an extended vaneless diffuser is considered in the following research.  
To further validate the numerical method for predicting performances and detailed flow fields of impellers with vaneless diffusers, the open transonic centrifugal compressor SRV2-O has been investigated applying the same numerical method. Its geometry specification has been given by  
Figure 6: Schematic of compressor test sections.  
Figure 7: Comparison of pressure ratio of the datum impeller with vaned diffuser. CFD: computational fluid dynamics.  
[PERSON] et al. [36] and its measurement results have been provided by [PERSON] et al. [37]. The compared pressure curves are at 60%, 70% and 80% of design speeds, where the operating pressure ratios are similar to the investigated case. The compared flow field is taking from the m/m\({}_{\text{c}}\) = 0.89 operating point at design speed, where a strong shock wave occurs at the leading edge of the main blade. Figure 8 compares pressure curves of the SRV2-O compressor between experiments and CFD, where the CFD results agree well with the experiments. The comparison of relative Mach number near the inlet and the exit respectively is presented in Figure 8. It is illustrated that both the shock position and the shock strength have been well captured at the tip section. The numerical method is therefore considered capable of predicting the compressor performance and the flow details near the peak efficiency condition, which is sufficient for the following discussions.