## 4 Validation and Applications
### High-Performance Centrifugal Compressor (HPCC)  
The HPCC is an Allison Engine Company design with a design mass flow rate of 4.39 kg/s, a design pressure ratio of 4, and a design revolution speed of 21,789 RPM. This centrifugal compressor originates from a geometric scaling up to the DDA's 404-III  
Figure 5: Meridional flow field of the LSCC at design mass flow rate: (**a**) Relative Mach number; (**b**) Static pressure; (**c**) Total temperature; (**d**) Entropy. Figure 6: Comparison of total temperature ratio for LSCC. compressor, making use of the backward impeller and the truncated-impeller splitter. Detailed experimental measurements on its flow field and off-design performances have been determined by [PERSON] and [PERSON] et al. [55]. Compared with the LSCC case, the HPCC case apparently has a much higher design aerodynamic loading and can operate at the choke conditions if the boundary conditions are satisfied. This is feasible for the validation of the choking-prediction capability for the developed throughflow model in the centrifugal flow compressor simulation. Another challenge in the throughflow simulation of the HPCC is how to simulate the effects of the splitter blades, which do not exist in the LSCC case. In a throughflow model, the impeller blade is usually represented by its camber surface adding the corresponding blockage distribution. In this study, within the meridional region of the splitter, the new camber surface was generated by a weight average between the cambers of the impeller and splitter. For simplicity, an arithmetic average was adopted in this case. Meanwhile, the blockage factor corresponding to the thickness of the splitter was added to the original blockage factor caused by the impeller. Additionally, the losses caused by the splitter were considered by adopting the concept of \"equivalent blade number\", i.e., the number of splitters was converted to the equivalent number of the impeller blades according to their chord lengths. This equivalent number was then added to the impeller blade number as the input of the empirical loss models. The generated mesh for the HPCC case had 161 \(\times\) 20 points and is presented with corresponding blockage distribution in Figure 7.  
A typical computation for one operating condition can be converged within 1 min for this case. Convergence histories of the throughflow simulation of the HPCC at a typical operating point are shown in Figure 8 to present a comparative study of the different methods of CBC enforcement. It can be observed that with the same initialization and computational set, the developed CBCs based on [PERSON]'s method achieved convergence after approximately 3500 iterations, whereas the Riemann-invariant-based CBCs blew up at the beginning of the computation after about 40 iterations. The reason why the Riemann-invariant-based CBCs presented in [51] experience such difficulty in convergence is that this CBC method explicitly utilizes the velocity of the internal domain. When the initial value of the internal domain is not close to the real inlet boundary value, convergence difficulty occurs. In contrast, the CBCs based on [PERSON]'s method developed in this paper implicitly utilize the velocity at the inlet boundary, which preserves the computational accuracy at the inlet boundary. This result proves the superiority of the developed CBCs based on [PERSON]'s method in terms of computational robustness, at least for the throughflow simulation of centrifugal compressors with a high pressure ratio. Figure 7: Computational grid and blockage distribution of HPCC test case. (**a**) Computational mesh; (**b**) blockage distribution. The predicted characteristics of the total pressure ratio and the isentropic efficiency by the developed throughflow model were compared with the experimental data and 3D-CFD results at different speed lines as shown in Figure 9a,b, respectively.