## 2 Computation Methods  
The exit-stage rotor blade profile of a high-pressure compressor is taken as the research object. The blade profile is a typical multiple circular arc airfoil shape (chord length \(=21.94\) mm, \(Ma_{in}=0.5\), \(Re=1.0\times 10^{6}\), \(Tu=4\%\)). In this paper, the local geometric deviation( the blade profile deviation from the nominal blade profile in the local profile area) is investigated. In order to express the location of deviations simply and explicitly, the blade surface is normalized according to the suction surface arc length and the pressure surface arc length. The value of the normalized position is \(0\) at the leading edge, \(-1\) at the trailing edge of the suction surface and \(1\) at the trailing edge of the pressure surface (coincident with \(-1\)). This definition of the normalized position on the blade surface is shown in Figure 1.  
The Hicks-Henne function [16] was used to describe the form of different deviations. By controlling the interval length and the amplitude of the Hicks-Henne function, the deviation width and height can be easily simulated. In order to analyze the complex fluid m  
Figure 1: Definition of the representative position points on blade surface.  
width was fixed and only the deviation height changed during the sampling process. Table 1 shows the parameterized sample space of the different blade profile deviations. The sample selection refers to the reverse measurement data of actual high-pressure compressor blades.  
To directly study the aerodynamic performance influence of the coexisting multi-position deviations, the one-factor-at-a-time method of DOE was used for sampling. Figure 2 shows a set of sample points and the corresponding blade profiles with local geometric deviations in \(-0.1\) and \(-0.3\) positions. The MISES (Multiple blade Interacting Streamtube Euler Solver) program developed by MIT was used to solve the aerodynamic performance numerically. Because of good calculation reliability and fast solving speed, it has been widely used to acquire aerodynamic performance of blade with geometric deviations [8; 15]. The MISES calculation results and experimental data have been compared in the subsonic and transonic compressor flow condition to ensure the calculation accuracy. Table 2 shows the grid settings in MISES program. In this study, the profile loss \(\omega\) was defined in Equation (1), and the incidence range was defined as the condition at which the loss was 1.5 times the minimum value [8].  
\[\omega=\frac{p_{1}^{*}-p_{2}^{*}}{p_{1}^{*}-p_{1}} \tag{1}\]  
where \(p_{1}^{*}\) is the inlet total pressure, \(p_{2}^{*}\) is the outlet total pressure and \(p_{1}\) is the inlet static pressure.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Deviation Position** & **Parameter** & **Min/(mm)** & **Max/(mm)** & **Sample Interval/(mm)** \\ \hline \multirow{2}{*}{Leading edge} & Height & 0.01 & 0.1 & 0.01 \\  & Width & & 10\% Chord length & \\ \multirow{2}{*}{Profile body} & Height & 0.01 & 0.1 & 0.01 \\  & Width & & 20\% Chord length & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameterized sample space of the profile deviations.  
Figure 2: Sampling results when the local geometric deviations are in the \(-0.1\) and \(-0.3\) positions. (**a**) Sample points obtained by the DOE method. (**b**) Balde profile with deviations corresponding to the sample point.