## 4 Application of the Improved Inviscid Blade Force Model in a Highly Loaded Low-Speed Fan
### Numerical Analysis and Discussion  
Figure 27,b shows the overall characteristic lines acquired from the experiment, NUMECA and these two CAM methods. Figure 27 is shown for the characteristic of mass flow versus total pressure ratio. Figure 27 is for mass flow versus adiabatic efficiency. From these two figures, it is observed that the performance of efficiency is improved, and the characteristic of mass flow and pressure ratio remains unchanged.  
The performance parameters on the design point acquired from different calculation methods are shown in Table 3. When the original inviscid blade force model is applied, mass flow and pressure ratio from CAM, experiment and 3D method is nearly the same. However, the error of adiabatic efficiency between them is more than 4.0%. This is related to the simulation accuracy of the flow field. The original model is based on the assumption that the inviscid blade force is perpendicular to the average stream surface, which leads to the wrong prediction of the field. While in fact, the inviscid blade force is not. After the improved inviscid blade force model is applied, the error of adiabatic efficiency between throughflow and experiment or 3D simulation is about 1%.  
Figure 28,c shows the distribution of rotor pressure ratio and adiabatic efficiency, stator total pressure recovery coefficient, respectively. It reveals that the trend of adiabatic  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Mass Flow** & **Pressure** & **Adiabatic** & **Power (\&W)** & **Power Error (\%)** \\  & **(kg/s)** & **Ratio** & **Efficiency** & & & \\ \hline Experiment & 7.516 & 1.022 & 0.8583 & 15.81 & \\ NUMECA & 7.480 & 1.022 & 0.8531 & 15.83 & 0.128 \\ CAM & 7.485 & 1.022 & 0.8113 & 16.66 & 5.357 \\ Revised CAM & 7.421 & 1.022 & 0.8457 & 15.84 & 0.207 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance parameters of the TA36 near the design point.  
Figure 27: Performance characteristic of TA36: (a) total pressure ratio; (b) adiabatic efficiency.  
Figures 32 and 33 show the isolines of the axial velocity and the pressure obtained through two methods. From these pictures, it can be seen that these two isolines are nearly the same. The only difference exists at the hub of the rotor, where the flow accelerates. The phenomenon also can be seen at the isolines of pressure. These differences may arise from the reason that the inviscid blade force model still needs to be further modified to adapt to the variable incidences.  
To make the comparison between the results from 2D and 3D much clearer, the distributions of these parameters along a grid line in the streamwise direction are displayed. The axial component of the inviscid blade force and the axial velocity along the gridline are analyzed as two examples. Moreover, the gridline we choose is shown in Figure 34, which is red. The aerodynamic parameters along this line are shown in Figure 35. It is observed that the axial component of the inviscid blade force is almost the same from these two methods. Moreover, for the axial velocity, the trend of these two results is the same, and the biggest error is nearly 4%.  
Figure 31: Isolines of the tangential component of the inviscid blade force for the TA36: (**a**) revised CAM; (**b**) NUMECA.  
Figure 32: Isolines of the axial velocity for the TA36: (**a**) revised CAM; (**b**) NUMECA.