## 3 Numerical Simulation
### Grid Topology and Verification  
Blade geometry creation and grid generation for the 2.5-stage axial compressor were conducted by using commercial software NUMCA Autogrid 5. Since the grid topology of each blade row is almost similar, this paper describes the grid topology of the second rotor in detail. Multi-block structured grids with hexahedral elements were used in the simulation. Around blade surfaces, the O grids were generated to improve the orthogonality, whereas H grids were used at the inlet, the passage, and the outlet. The distance between the first grid cell and the solid wall was set as \(1\times 10^{-6}\) m to meet the need of the solid wall y + \(<\) 3 for all computations. Figure 3 shows a single passage for the highly loaded compressor. To conduct grid independence to eliminate the influence of the number of grid nodes on the flow solution, three different numbers of grid nodes were used to calculate the predicted adiabatic efficiency and total pressure ratio. As can be seen in Figure 4, the adiabatic efficiency and total pressure ratio change slightly from three million grid nodes to four million grid nodes. It means that the number of grid nodes per blade passage was set to three million, which satisfies the requirement of grid independence in the steady-state simulation. Figure 3: Grid topology for the highly loaded compressor. The 2.5-stage highly loaded axial compressor test rig was built at the Institute of Engineering Thermophysics, Chinese Academy of Sciences. The test rig was operated in an open cycle. After the bellmouth and honeycomb, the compressor was driven by an 800 kW AC motor to change the rotational speed. The transmission ratio of the gearbox is 1:12. The range of rotational speed after gearbox is from 0 rpm up to 36,000 rpm, which was measured by an electromagnetic transducer with a relative measurement error within \(\pm\)0.15%. The mass flow rate was measured by the flow tube mounted in the bellmouth inlet duct within a relative measurement error of \(\pm\)0.5%. To measure the compressor map, the total temperature and total pressure were captured by probes at the inlet and outlet of the compressor. The temperature was measured by thermocouples with a measurement error of \(\pm\)0.8 \({}^{\circ}\)C. The total pressure was measured by piezoelectric pressure sensors with a relative full-scale measurement error of \(\pm\)0.2%. At the compressor inlet, the total pressure was measured by three pressure probes with five span-wise locations, while the total temperature was measured by three rate pressure probes with three span-wise locations. At the compressor outlet, the total pressure was measured by six rake pressure probes with three span-wise locations, while the total temperature was measured by six rake pressure probes with three span-wise locations. To verify the effectiveness of the numerical method, Figure 5 compared the data measured from the experiments and the results from the numerical calculation. The abscissas represented the dimensionless mass flow, which was normalized by the design mass flow. It can be seen that at the 80%, 90% and 100% design speed, the performance maps show the same trend in the adiabatic efficiency and total pressure ratio. For 100% design speed, the total pressure ratios and the peak efficiency in the numerical calculations were almost the same as the experimental value, but when the flow rate was lower than the peak efficiency point the adiabatic efficiency values were higher than the experimental value. The discrepancy of the efficiency maybe since the selected RANS simulation fails to predict the total temperature distribution close to the stall conditions (as shown in the literature [23], which usually occurs in axial compressors) or experimental measurement errors. But the direct numerical simulation calculation is computationally expensive, which makes this approach not suitable for engineering calculations.