# Experimental and Numerical Research on End-Wall Flow Mechanism of High-Loading Tandem Stators
## 2 Research Object and Method
### Verification of Numerical Simulation Methods  
Figure 7 shows the comparison of loading coefficient (\(\psi\)) and efficiency (\(\eta\)) between experimental measurement and numerical simulation. Typical working conditions of a compressor include near-blockage condition (NC, flow coefficient \(\phi\) = 0.63), design condition (DE, \(\phi\) = 0.55), maximum efficiency condition (ME, \(\phi\) = 0.51) and near-stall condition (NS, \(\phi\) = 0.43). The experimental loading coefficient at DE was 0.463, the efficiency was 92%, and the efficiency at ME was 92.8%. The calculated loading coefficient at DE was 0.453, and the efficiency was 90.2%. The highest efficiency was 91.2% at ME. Compared with the experimental results, the calculated load and efficiency demonstrated a marginal underestimation. \begin{table}
\begin{tabular}{c c c c} \hline  & **Rotor** & **Stator** & **Total** \\ \hline Mesh1 & 3,500,708 & 1,405,170 & 4,905,878 \\ Mesh2 & 6,298,500 & 2,483,946 & 8,782,446 \\ Mesh3 & 8,426,532 & 3,221,010 & 11,647,542 \\ \hline \end{tabular}
\end{table} 
Table 2: Mesh settings for the grid independence. Figure 6: Comparison of stage efficiency for the grid independence verification. Despite this, the simulation results exhibited an overall trend that was fundamentally consistent with the experimental data in terms of variation with mass flow rate. The difference was larger in the higher mass flow rates and smaller in the smaller mass flow rates. This was consistent with the focus of the paper, which was the flow characteristics of high-loading compressor stages from DE to NS. In addition, the mass flow of near stall calculated by several compressor cases was all close to those measured by experiment, which proved that the numerical method could accurately predict the stall points. Figure 8 shows that the spanwise distribution of the stator inlet and outlet flow coefficients at DE (In the figure, \"In\" and \"Out\" represented the inlet and outlet of the stator, respectively, and \"exp\" and \"cal\" represented the experimental and calculated data, respectively.) were consistent with the experiment, which meant that the calculated results accurately simulated the blockage at the root of the tandem stator, the mass flow distribution, and the blockage at the tip caused by the rotor leakage flow. Figure 9 shows the comparison of the outlet flow field of the tandem stator at NS, in which \(V_{z}/U_{m}\) denoted the ratio of axial velocity to mid-span rotating speed. The experiment identified two distinct low-energy fluid clusters, labeled \"A\" and \"B\", evident in the stator's exit region. Cluster \"A\" corresponded to the separation at the FB root corner, while cluster \"B\" represented the separation at the RB root corner (which will be analyzed in detail later). The calculated results successfully captured both corner regions, with the influence areas of the low-energy fluid clusters being relatively consistent. This indicated that the interaction between the FB and RB corner regions was well simulated. Figure 10 shows the calculated and experimental limit streamlines on the suction surface and hub at NS. The experimental results indicated the typical corner region of the stator and the flow direction of the hub limit streamline. Both experimental measurements and numerical simulations demonstrated that corner separation (CS) occurred at the FB root, with both methods showing almost identical extents of corner separation. A similar phenomenon was observed at the RB root. Although the calculated spanwise range of the corner separation was marginally smaller, it aligned with the experimental trend, indicating a decrease in the size of the corner separation region as the flow coefficient decreases. The migration of secondary flow from the FB outlet to the RB suction surface at the hub was also clearly captured by the calculations. Figure 7: Calculated and experimental characteristics of tandem-blade compressor. Figure 8: Calculated and experimental comparison of inlet and outlet flow coefficients at DE of the tandem stator.