## 3 Results and Analysis
### Analysis of Blade Performance and Model Establishment
To analyze the deviation's effect on the surface boundary layer in more detail, Figure 6 shows the momentum thickness and relative momentum thickness of the suction surface boundary layer from the 0 position to the 0.6 position. The relative momentum thickness was obtained by dividing the momentum thickness of the blade on the separated condition by the momentum thickness of the nominal blade. The region where the relative momentum thickness changes drastically is defined as the direct influence domain of the single deviation. In Figure 6a, the direct influence domains of deviations in the \(-0.1\) position and \(-0.3\) position are not overlapped a lot. Therefore, it can be considered that the deviation in the \(-0.1\) position has no other influence on the development of the boundary layer in the \(-0.3\) position except changing its upstream boundary layer thickness. Figure 6b shows that due to the thin boundary layer thickness and the close transition position, the direct influence domain of the deviation in the \(-0.1\) position will cover a long blade surface length. Furthermore, the wide direct influence domain means the coupled effect of \(-0.1\) position deviation and \(-0.3\) position deviation is very complex. Through the above analysis of the blade aerodynamic performance and the development of the boundary layer, it can be found that when the boundary layer of the incoming flow is thick enough, the influence of the downstream deviation is weakened. It is also clearly that as the height of the upstream deviation increases, the thickness of the downstream boundary layer after this deviation increases significantly. The degree of the weakening effect should be affected by the relative heights of the two deviations and the boundary layer. In addition, obviously, when the two deviations are very close, their coupled effect will be much larger than the effect when they are far away. So the distance between the two deviations will also affect this weakening effect. Therefore, considering the meaning of the exponential function, the coupled effect model on the positive incidence range, shown in Equation (2), can be constructed. \[\Delta_{X1\mathbf{6}X2 range}=\Delta_{X1 range}+[e^{-k\frac{\Delta S\cdot(k_{X1}/ \theta_{X2})}{(k_{X2}/\theta_{X2})}}]\cdot\Delta_{X2 range} \tag{2}\]  
where \(X1\) is the upstream deviation relative to the airflow, \(X2\) is the downstream deviation relative to the airflow, \(\Delta_{Xrange}\) is the change of the positive incidence range caused by the deviation in the \(X\) position, \(\Delta S\) is the normalized distance between the two deviations in the different positions, \(h_{X}/\theta_{X}\) is the ratio of the deviation height in the \(X\) position to the momentum thickness of the boundary layer on the nominal blade, and \(k\) is an undetermined coefficient (related to profile shape, flow state, etc.). The \(k\) value can be obtained by the least square method. This model assumes that the weakening effect of the downstream deviation is exponential. In addition, it considers the deviation height, the boundary layer thickness and the distance between the two deviations. Moreover, when the distance between  
Figure 6: Analysis of the boundary layer from the 0 position to the 0.6 position. (**a**) Detailed analysis of the boundary layer when the incidence is under the positive incidence limit. (**b**) Detailed analysis of the boundary layer when the incidence is under the negative incidence limit. the two deviations is 0, the model degenerates to a simple sum of the two deviations influences, which is consistent with the real situation.